[    {        "title": "1503.08088v1.Study_of_helium_irradiation_induced_hardening_in_MNHS_steel.pdf",        "content": "submitted to 'Chinese Physics C'\nStudy of helium irradiation induced hardening in MNHS steel*\nJi WANG1;2;3;1)Zhi-Guang WANG1Er-Qing Xie1Ning GAO1Ming-Huan CUI1Kong-Fang WEI1\nCun-Feng YAO1Tie-Long SHEN1Jian-Rong SUN1Ya-Bin ZHU1Li-Long PANG1\nDong WANG1;2Hui-Ping ZHU1;2Yang-Yang DU1;2\n1Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, China\n2University of Chinese Academy of Sciences, Beijing, 100049, China\n3School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000, China\nAbstract: A recently developed reduced activation ferritic/martensitic steel MNHS was irradiated with 200keV\nHe ions to a \ruence of 1 \u00021020ions=m2at 300\u000eCand 1\u00021021ions=m2at 300\u000eCand 450\u000eC, respectively. The\nirradiation hardening of the steel was investigated by nanoindentation measurements combined with transmission\nelectron microscopy (TEM) analysis. Dispersed barrier-hardening (DBH) model was applied to predict the hardness\nincrements based on TEM analysis. The predicted hardness increments are consistent with the values obtained by\nnanoindentation tests. It is found that dislocation loops and He bubbles are hard barriers against dislocation motion\nand they are the main contributions to He irradiation-induced hardening of MNHS steel. The obstacle strength of\nHe bubbles is stronger than the obstacle strength of dislocation loops.\nKey words: helium irradiation, irradiation induced hardening, F/M steel\nPACS: 28.50.Ft, 28.52.Fa\n1 Introduction\nReduced activation ferritic/martensitic steels are\nconsidered as one of the promising candidate structural\nmaterials for future fusion reactors because of their ex-\ncellent mechanical properties, good thermal properties,\nlow residual radioactivity and high swelling resistance\n[1]. Under the intense radiation \felds in reactors, dis-\nplacement damage and impurities (He and H) produced\nby transmutation reactions (i.e. (n, \u000b) and (n, p) reac-\ntions) are inevitable. Defects formed by accumulation of\ndisplaced atoms and the impurities such as dislocation\nloops, bubbles and clusters are thought to be obstacles\nto dislocation movement. As a result, structural mate-\nrials served in reactors exhibit a hardness increase [2-7].\nHowever, due to the nature of defect, the in\ruences of\ndi\u000berent types of defects on the materials hardness are\ndi\u000berent. The role of dislocation loops and He bubbles\namong other types of irradiation-induced defects in ma-\nterials hardness is still unclear. In order to investigate\nthe e\u000bects of them on structural materials hardening,\ntheoretic analysis based on dispersed barrier-hardening\n(DBH) model combined with TEM analysis and nanoin-\ndentation measurements were carried out to investigate\nthe hardness changes of He implanted steels.2 Experimental\nThe material used in this study is a recently devel-\noped reduced-activation ferritic/martensitic steel modi-\n\fed novel high silicon steel (MNHS). Chemical composi-\ntion of the steel is listed in Table 1.\nTable 1. Chemical composition (wt.%) of the steel\ninvestigated in this study.\nFe C Cr W Mn Si V Nb\nBal. 0.25 10.78 1.19 0.54 1.42 0.19 0.01\nThe steel was normalized at 1050\u000eCfor 30 minutes and\ntempered at 760\u000eCfor 90 minutes. Slices of 15 \u000215\u00021mm3\nwere cut from the ingots after heat treatment. All spec-\nimens were prepared by mechanically polishing with SiC\npaper (up to 4000 grit) before polishing with diamond\nsuspension (particle size \u00181\u0016m). After mechanical pol-\nishing, all the specimens were electropolished to remove\nthe work hardened surface. Irradiation experiments were\ncarried out in a terminal chamber of the 320kV multi-\ndiscipline research platform for highly charged ion at In-\nstitute of Modern Physics (IMP) in Lanzhou, China. The\nspecimens were irradiated with 200keV He ions to a \ru-\nence of 1 \u00021020ions=m2at 300\u00065\u000eCand 1\u00021021ions=m2\nat 300\u00065\u000eCand 450 \u00065\u000eC, respectively. Vacuum within\n\u0003Supported by the National Basic Research Program of China (2010CB832902, 91026002) and National Natural Science Foundation\nof China (U1232121)\n1) E-mail: wangji10@impcas.ac.cn\nc\r2013 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of\nModern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd\n010201-1arXiv:1503.08088v1  [cond-mat.mtrl-sci]  25 Mar 2015submitted to 'Chinese Physics C'\nthe terminal chamber was maintained below 5 \u000210\u00005Pa.\nDisplacement damage and He concentration as a func-\ntion of depth were calculated with SRIM code as shown\nin Fig.1.\nFig. 1. Depth pro\fle of displacement damage and\nHe concentration.\nThe displacement energy (Ed) was set to 40eV in\nSRIM calculation as recommended in ASTM E521-89\n[8]. Nano-indentation tests were carried out using a Ag-\nilent Nano Indenter G200 with a Berkovich tip in a con-\ntinuous sti\u000bness mode (CSM). The indenter was normal\nto the samples surface. Each indentation was set ap-\nproximately 30 \u0016m apart in order to avoid any overlap\nof the deformation region caused by other indentations.\nCare was taken to avoid uneven areas and areas where\nscratch, pitting and purities could be seen when label-\ning coordinates for indentations. Cross-sectional TEM\nsamples were prepared by ion milling in a Gatan preci-\nsion ion polishing system after the indentation tests on\nthe specimens \fnished. TEM analysis was performed in\na FEI-TF20 transmission electron microscope operating\nat 200kV.\n3 Results and discussion\n3.1 Characterization of He bubbles and disloca-\ntion loops in MNHS steel\nMicrostructure of MNHS without He implantation is\nshown in Fig. 2.\nFig. 2. TEM image of MNHS steel without He\nirradiation\nIt can be seen that martensitic lath structures are the\nmain features of this type of steel. Precipitations are\nfound along lath boundaries. The average width of the\nmartensitic lath is \u0018300nm. No dislocation loops could\nbe detected. After He ions irradiation, large numbers\nof bubbles and dislocation loops are found. Most of\nthem distribute in a band region between the depth of\n\u0018400nm and \u0018600nm from surface. This is consistent\nwith SRIM prediction as shown in Fig.1. Fig. 3 shows\nHe bubbles in samples under di\u000berent irradiation condi-\ntions.\nFig. 3. TEM images of He bubbles in MNHS\nsteels after He irradiation to (a)1 \u00021020ions=m2\nat 300\u000eC, (b)1\u00021021ions=m2at 300\u000eC, (c) 1 \u0002\n1021ions=m2at 450\u000eC.\nAll the images were taken in the regions of the highest He\nconcentration. Statistics on He bubbles size and number\ndensity were made and presented in Table 2.\nTable 2. Number density( \u001abfor bubbles, \u001alfor dislocation loops), mean diameter( Rbfor bubbles, Rlfor dislocation\nloops ) of dislocation loops and He bubbles in He irradiated MNHS steel.\nTemperature(\u000eC) Dose (ions =m2) Rl(nm) Rb(nm) \u001al(=m3) \u001ab(=m3)\n300 1 \u00021020ions=m25.22 1.74 2 :4\u000210222:17\u00021023\n300 1 \u00021021ions=m27.06 2.34 9 :85\u000210224:73\u00021023\n450 1 \u00021021ions=m211.45 3.56 8 :76\u000210215:91\u00021022\n010201-2submitted to 'Chinese Physics C'\nIt can be seen that the number density of bubbles in-\ncreases as the increase of irradiation dose and decreases\nas the irradiation temperature increases while the size\nof bubbles increases when irradiation dose and irradia-\ntion temperature increase, respectively. Large amount\nof dislocation loops are also found in high helium con-\ncentration region as shown in Fig. 4. Statistics made on\nthe size and number density of dislocation loops are also\nshown in Table 2, which indicates that the size of dis-\nlocation loops increases as the increasing of irradiation\ntemperature and dose, respectively.\nFig. 4. TEM images of dislocation loops in MNHS\nsteels after He irradiation to (a)1 \u00021020ions=m2\nat 300\u000eC, (b)1\u00021021ions=m2at 300\u000eC, (c) 1 \u0002\n1021ions=m2at 450\u000eC.\n3.2 Nano-indentation tests\nThe values of hardness in this study were obtained by\naveraging six individual indentation results on each sam-\nple. Occasionally, a hardness versus depth curve would\nbe far away from the average values, which may be due\nto a simple failure during the indentation test or the sub-\nsurface precipitates near the indenter tip. Such outliers\nwere removed in this work. Due to the uncertainty of in-\ndenter geometry and testing artifacts, hardness data at\nthe depth<50nm from surface were not reliable. Thus,\nwe took the values at the depth over 50 nm for analysis.\nFig. 5 shows the average hardness as a function of inden-\ntation depth for irradiated samples and an unirradiated\nsample.\nFig. 5. Indentation depth pro\fle of hardness of\nirradiated and unirradiated MNHS steels.\nFor the irradiated samples, a hardness peak is observed\nat depth of \u0018100 nm, di\u000berent from the irradiation dam-\nage peak of \u0018500 nm. This is consistent with previous\nwork [5,9,10] that the depth of damage peak is 5-7 times\nof the depth of the hardness peak. The reason for above\ndi\u000berence is probably due to the fact that the depth of a\nplastic zone with an approximately hemispherical shape\nunder the indentation reaches about 5-7 times of the\ndepth at which indenter tip can reach[7,10]. At the depth\nof hardness peak, the indenter was mostly sampling the\nHe implanted region and the surface e\u000bects were reduced.\nTherefore, the hardness peak in fact indicates the e\u000bects\nof helium implantation region. We therefore take the\nhardness values at the depth of 100nm for comparing the\nrelative hardening among samples. The relative hardness\nincrements of He implanted samples obtained by nanoin-\ndentation tests (\u0001 He) were summarized in table 3.\nTable 3. Comparison of predicted hardness\nincrement(\u0001 Hp) and experimentally obtained\nhardness increment(\u0001 He).\nTemperature(oC)Dose (ions=m2) \u0001Hp(GPa) \u0001 He(GPa)\n300 1 \u000210201.50 1.68\n300 1 \u000210212.71 2.61\n450 1 \u000210211.15 1.18\n3.3 Analysis of irradiation induced hardening\nStructural materials for fusion reactors exhibit\nradiation-induced hardening when irradiated with neu-\ntron or energetic ions [2-7, 11]. This hardening is thought\nto be caused by defects formed during irradiation such as\nclusters of interstitial atoms, small bubbles, precipitates\nand dislocation loops [11-14]. Previous studies showed\nthat dislocation loops and bubbles are strong obstacles\nthat act as barriers to dislocation motion, resulting in the\nincrease of hardness of irradiated materials [3,4,6,14,15].\nIn order to have a better understanding of the hardness\nchanges caused by dislocation loops and He bubbles. An\n010201-3submitted to 'Chinese Physics C'\nattempt is made below to analyses the hardness increase\nbased on dispersed barrier-hardening (DBH) model. As\nthe interstitial dislocation loops and He bubbles are clas-\nsi\fed as short-range obstacles [2]. The increase of yield\nstrength due to one type of short-range obstacle could\nbe expressed as\n\u0001\u001by=M\u000b\u0016b (Nd)1/2: (1)\nWhere\u0001\u001byis the yield strength increment, M is the\nTaylor factor, \u000bis the barrier strength factor, \u0016is the\nshear modulus, b is the Burgers vector, N and d are num-\nber density and mean size of obstacles, respectively. For\ntwo types of short-range strong obstacles, the superposi-\ntion rule could be expressed as following\n\u0001\u001b2= \u0001\u001b2\n1+\u0001\u001b2\n2: (2)\n\u0001\u001b2\n1=M\u000b 1\u0016b(N1d1)1/2: (3)\n\u0001\u001b2\n2=M\u000b 2\u0016b(N2d2)1/2: (4)\nM is 3.06 for bcc metals, the shear modulus for MNHS\nsteel is 80GPa and b=2 :48\u000210\u000010m. The number den-\nsity and mean size of dislocation loops and bubbles in\nthree sets of samples under di\u000berent He ions irradiation\nconditions are summarized in Table 2. According to pre-\nvious work, dislocation loops and bubbles are thought as\nstrong obstacles with the \u000bof 0.25 - 0.5 and 0.3 - 0.5\n[3,6,15], respectively (some work show higher values of\n\u000b). We apply above values (with \u000bvalues of 0.25 for dis-\nlocation loops and 0.4 for He bubbles) in equations (2)\nto (4), then the predicted increments of yield strength\n(\u0001\u001by) were got for steels irradiated under 200keV He\nions.\nIt is reported that the correlation between change in\nhardness and change in yield stress was determined to\nbe [16].\n\u0001H = 3\u0001\u001by: (5)\nUsing this relationship, the predicted hardness incre-\nment (\u0001H p) could be calculated based on DBH model.It is thus possible to compare the predicted hardness\nchanges with hardness changes obtained by nanoinden-\ntation tests. The comparison between predicted hard-\nness changes (\u0001H p) and experimentally obtained hard-\nness changes (\u0001H e) is summarized in Table 3. It can\nbe seen that the predicted changes of hardness based\non DBH model are consistent with hardness changes ob-\ntained by nanoindentation tests. This suggests that both\ndislocation loops and He bubbles are the main contri-\nbutions to irradiation-induced materials hardening and\ndislocation loops and He bubbles are strong pinning cen-\nters with the pinning strength of He bubbles ( \u000b=0.4)\nstronger than the pinning strength of dislocation loops\n(\u000b=0.25). However, a note should be mentioned about\nthe rates of introduction of displacement damage and\nhelium. It is known that radiation-induced defects ac-\ncumulate di\u000berently under di\u000berent damage and helium\nproduction rates [17]. As a result, mechanical properties\nof irradiated structural materials vary accordingly [13].\nIn this experiment, the damage rate and introduction\nrate of helium are 6 :39\u000210\u00004dpa/s and 6.67appm/s,\nrespectively.\n4 Conclusions\nThe e\u000bects of helium under conditions of simulta-\nneous displacement damage production on the hard-\nness of ferritic/martensitic steel MNHS were studied by\nHe implantation into MNHS steel combined with nano-\nindentation technique and TEM analysis. The DBH\nmodel was adopted to predict the hardness changes\ncaused by dislocation loops and He bubbles. it is found\nthat the predicted hardness changes based on DBH\nmodel are consistent with the experimentally obtained\nhardness changes. Dislocation loops and He bubbles are\nhard obstacles against dislocation motion and they are\nthe main contributions to He irradiation-induced hard-\nening of MNHS steel. The barrier strength of He bubbles\n(\u000b=0.4) is stronger than the barrier strength of disloca-\ntion loops ( \u000b=0.25).\nThis work was supported by the National Ba-\nsic Research Program of China (2010CB832902,\n91026002), National Natural Science Foundation of\nChina (U1232121). The authors greatly appreciate all\nthe help from sta\u000b of 320kV multi-discipline research\nplatform for highly charged ions during the implantation\nexperiments.\n010201-4submitted to 'Chinese Physics C'\nReferences\n1 Klueh R L, Kai Ji-Jung, Alexander D J. J. Nucl. Mater., 1995,\n225: 175|186\n2 Was G S. Fundamentals of Radiation Materials Science,\nSpringer, 2007\n3 Lucas G E. J. Nucl. Mater., 1993, 206: 287|305\n4 Hashimoto N, Wakai E, Robertson J P. J. Nucl. Mater., 1999,\n273: 95|101\n5 Hunn J D,Lee E H, Byun T S, Mansur L K. J. Nucl. Mater.,\n2000, 282: 131|136\n6 Ando M, Katoh Y, Tanigawa H, Kohyama A, Iwai T, J. Nucl.\nMater., 2000, 283|287 : 423|427\n7 Hiroyasu et al. J. Nucl. Mater., 2000, 283|287 : 470|473\n8 ASTM Designation E521-89, Standard Practice for NeutronRadiation Damage Simulation by Charged particle Irradiation,\nAmerican Society for Testing and Materials, vol. 12.02, 1989.\n9 Jin Hyung-Ha et al. Nucl. Instr. and Meth. B. 2008, 266:\n4845|4848\n10 Katoh Y et al. J. Nucl. Mater., 2003, 323: 251|262\n11 Gaganidze E, Schneider H C, Da\u000berner B, Aktaa J. J. Nucl.\nMater., 2006, 355: 83|88\n12 Iwase A et al. Nucl. Instr. and Meth. B, 2002, 195: 309|314\n13 Takuya et al. J. Nucl. Mater., 2006, 356: 27|49\n14 Rodney D. et al. Mater. Sci. Eng. A, 2001, 309|310 : 198|\n202\n15 Olander D R, Fundamental Aspects of Nuclear Reactor Fuel\nElements, Technical Information Center, ERDA , 1976\n16 Lucas G E, Odette G R, Maiti R, Sheckherd J W, ASTM 956,\n1987, 379\n17 Mansur L K, J. Nucl. Mater., 1994, 216: 97\n010201-5"    },    {        "title": "0708.2678v1.Eigen_electric_moments_of_magnetic_dipolar_modes_in_quasi_2D_ferrite_disk_particles.pdf",        "content": "Eigen electric moments of magnetic-di polar modes in quasi-2D ferrite disk \nparticles \n \nM. Sigalov, E.O. Kamenetskii, and R. Shavit \n \nBen-Gurion University of the Negev, Beer Sheva 84105, Israel \n \nAugust 20, 2007 \n \n \nAbstract \nA property associated with a vortex structure beco mes evident from an analysis of confinement \nphenomena of magnetic oscillations  in a quasi-2D ferrite disk with a dominating role of \nmagnetic-dipolar (non-exchange-int eraction) spectra. The vortices are guaranteed by the chiral \nedge states of magnetic-dipolar modes which re sult in appearance of eigen electric moments \noriented normally to the disk plane. Due to the eigen-electric-moment properties, a ferrite disk \nplaced in a microwave cavity is strongly affected  by the cavity RF electric field with a clear \nevidence for multi-resonance oscillations. For diffe rent cavity parameters, one may observe the \n\"resonance absorption\" and \"resona nce repulsion\" behaviors.  \n PACS numbers: 76.50.+g, 68.65.-k, 73.22.Gk, 84.40.-x  \n \n  In a dot of a ferromagnetic material of micr ometer or submicrometer size, a curling spin \nconfiguration – that is, a magne tization vortex – has been propose d. The vortex consists of an \nin-plane, flux-closure magnetizat ion distribution and a central core whose magnetization is \nperpendicular to the dot plane. It has been show n that under certain condit ions a vortex structure \nwill be stable because of competition between the exchange and dipole interactions [1]. In spite \nof the fact that vortices can app ear in different kinds of physical  phenomena, yet such \"swirling\" \nentities seem to elude an all-inclusive defini tion. It appears that th e character of magnetic \nvortices in magnetically soft \"small\" (with the dipolar and exchange energy competition) and \nmagnetically saturated \"big\" (when the exchange is  neglected) ferrite disk s is very different. A \nmagnetization vortex in a magnetica lly soft sample cannot be char acterized by some invariant, \nsuch as the flux of vorticity. So  a vorticity thread may not be  defined for the magnetization \nvortex [2]. At the same time, in magnetically saturated samples with magnetic-dipolar vortices \none can observe the flux of the pseudo-electric (gauge) fields [3, 4]. The vortices of magnetic-\ndipolar-mode (MDM) oscillations  in a ferrite disk become apparent due to the symmetry \nbreaking effects which result in appearance of eigen electric moments oriented normally to the \ndisk plane [3 – 5].     A property associated with a vortex structur e in a ferrite disk with a dominating role of \nmagnetic-dipolar (non-exchange-i nteraction) spectra becomes evident from an analysis of \nconfinement phenomena of magnetic-dipolar oscillat ions. It has been shown [3, 4, 6] that for \nMDMs in a ferrite disk one has evident quantum- like attributes. The spectrum is characterized \nby energy eigenstate oscillations . It appears, however, that be cause of the boundary condition on \na lateral surface of a ferrite disk, MS-potential eigen functions cannot be considered as single- 2valued functions. This fact raises a question ab out validity of the energy orthogonality relation \nfor the MDMs. The most basic implication of the existence of a phase fact or in eigen functions \nis operative in the case on the bo rder ring region. It fo llows that in order to cancel the \"edge \nanomaly\", the boundary excitation must be  described by chiral  states [3, 4]. \n    The topological effects in the MDM ferrite  disk are manifested through the generation of \nrelative phases which accumulat e on the boundary wave functions ±δ [3, 4]:  \n \n                                                                       θδ±−\n±±≡iqef .                                                        (1) \n \nThe quantities ±q are equal to 21l± , ... ,5 ,3 ,1=l  For amplitudes  f we have − +−=f f  with \nnormalization ±f = 1. To preserve the single-valued na ture of the membrane functions of the \nMDM oscillations, functions ±δ must change its sign when a disk angle coordinate θ is rotated \nby π2 so that 12−=−πmiqe . A sign of a full chiral rotation, πθ=+q  or πθ−=−q , should be \ncorrelated with a sign of the parameter aiµ – the off-diagonal component of the permeability \ntensor µt. This becomes evident from the fact that a sign of aiµ is related to a precession \ndirection of a magnetic moment mr. In a ferromagnetic resonance, the bias field sets up a \npreferential precession direction. It means that  for a normally magnetized ferrite disk with a \ngiven direction of a DC bias magnetic field, ther e are two types of resona nt oscillations, which \nwe conventionally designate as the (+) resonance and the (–) resonance. For the (+) resonance, a \ndirection of an edge chiral ro tation coincides with the precessi on magnetization direction, while \nfor the (–) resonance, a direct ion of an edge chir al rotation is opposite to the precession \nmagnetization direction. Fig. 1 gives an exam ple of the edge-functi on chiral rotation in \ncorrelation with the RF magnetization evolution for the (+) resonance. \n    For a ferrite disk with r and θ in-plane coordinates and normal-axis z coordinate, the total \nMS-potential function ψ is represented as a pr oduct of three functions: \n \n                                                             ± = δξθηψ  )( ),(~z r ,                                                        (2) \n \nwhere ),(~θηr is a single-valued membrane function, )(zξ  is the function characterizing z-\ndistribution of the MS potenti al in a ferrite disk, and ±δ is a double-valued edge (spin-\ncoordinate-like) function. We may introduce a \"spin variable\" σ, representing the orientation of \nthe \"spin moment\" and two doubl ed-valued wave functions, )(σδ+  and )(σδ− , the former \ncorresponding to the eigen value 21+=+q  and the latter to the eigen value 21−=−q . The two \nwave functions are normalized and mutually orthogonal, so that  they satisfy the equations                \n1  )(2=∫+σσδ d ,1  )(2=∫−σσδ d , and 0  )( )( =− +∫σσδσδ d . A wave function ψ is then a \nfunction of four coordinates, three positional coordinates such as ,,θr and z, and the \"spin \ncoordinate\" σ. We write )( )( ),(~σδξθηψ+ = z r  and )( )( ),(~σδξθηψ− = z r  as two wave \nfunctions corresponding to the positional wave function  )( ),(~z rξθη , which is a solution of the \nWalker equation for a ferrite disk with the so-called essential boundary conditions [6].  \n    It is evident that for a ferrite disk of radius ℜ, circulation of gradient  \n \n                                              θθ\nθ θθδδ e efqi eiq\nrr r r\n±−±±\nℜ=±\n±ℜ−=∂∂\nℜ=∇1                                       (3) \n  3along a disk border contour ℜ=π2C  gives a nonzero quantity when ±q is a number divisible by \n21. We consider the quantity ±∇δθ as the velocity of an irrotational \"border\" flow:  \n \n                                                                 ()± ±∇≡δθ θrrv .                                                             (4)                 \n \nIn such a sense, functions ±δ are the velocity potentials. Circulation of ()±θvr along a contour C  \nis equal to ()± ± ±−=∇ℜ=⋅∫∫f d Cd\nC2   v2\n0π\nθ θ θδrr. \n    In a case of a cylindrical ferrite disk, a single-valued membrane fu nction is represented as \n()( ) ( ) θφθη rR r=,~, where ) (rR  is described by the Bessel functions and θνθφ ~)(ie−, \n....3,2,1±±±=ν  Taking into account the \"orbital\" function ) (θφ , we may consider the quantity \n()[]ℜ=±∇r  δφθr\n as the total (\"orbital\" and \"spin\") velo city of an irrotational \"border\" flow:  \n \n                                                         ()()[]ℜ=± ±∇≡r V   δφθ θrr\n.                                                        (5)        \nIt is evident that  \n \n                                                     ()()()\nθθ\nθ e efqvi Vqvir r\n±+−±±\n±ℜ+−= .                                             (6) \n \nFor a given membrane function η~and given z-distribution of the MS potential, ) (zξ , we can \ndefine now the strength of a vortex of a whole disk as  \n \n      () () ∫ ∫∫∫∫ℜ=± ± ℜ= ± ℜ=± −=⋅ ℜ=⋅ ≡d\nrd\nr\nCd\nredzz Rf de Vdzz R Cd Vdzz R s\n02\n0 0 0)( 2  )(  )( ξ θ ξ ξπ\nθθ θrr rr\n,           (7) \n \nwhere d is a disk thickness. \n    The quantity ()±θVr\n has a clear physical meaning. In th e spectral problem  for MDM ferrite \ndisks, non-singlevaluedness of the MS-potential wave function appears due to the border term \nwhich is defined as ()ℜ=−r aHiθµ . This border term arises from the demand of conservation of \nthe magnetic flux density [3, 4]. It  is evident that an annual magnetic field on the border circle, \n()ℜ=rHθ , is expressed as  \n \n                                                      ()()±ℜ=±−=θ θ ξ Vz zH\nrr r\n)( )() ( .                                                  (8) \n \n    We define now an angular moment ea±r: \n \n                                           ()[]e\na\nCr ad\nesi dzCde Hi a± ℜ= ± =⋅ −≡∫∫    \n0µ µθ θrr.                                  (9)       \n \nThis angular moment can be formally represented as a result of a circulation of a quantity, which \nwe call a density of an eff ective boundary magnetic current mir\n: \n  4                                                              dzCdi ad\nCm e  4\n0∫∫⋅ =± ±rr\nπ ,                                                (10) \n \nwhere ()± ±≡θρV im mr r\n  and ℜ= ≡ra mR i  4ξπµρ .                                                                                    \n    In our continuous-medium model, a characte r of the magnetization motion becomes apparent \nvia the gyration parameter aµ in the boundary term for the spectral problem. There is \nmagnetization motion through a non-simply-connected  region. On the edge region, the chiral \nsymmetry of the magnetization prec ession is broken to form a flux-closure structure. The edge \nmagnetic currents can be observable only via its circ ulation integrals, not pointwise. This results \nin the moment oriented along a disk normal. It  was shown experimentally [5] that such a \nmoment has a response in an exte rnal RF electric field. This clarifies a physical meaning of a \nsuperscript \"e\" in designations of es± and ea±. In a ferrite disk particle, the vector ear is an \nelectric moment characterizing by special symm etry properties. There are the anapole-moment \nproperties [3, 4].     The purpose of this letter is to analyze th e spectral distribution of eigen electric (anapole) \nmoments of a MDM ferrite disk. Ou r experimental studies of absorp tion spectra for a ferrite disk \nplaced in a microwave cavity are aimed to investig ate possible mechanisms of interaction of the \ndisk eigen electric moments with an external  RF electric field and to verify the proposed \ntheoretical model for the an apole moment oscillations. \n    Experimental results showed in [5] leav ed unclear the physics of a possible mechanism of \ninteraction between a MDM ferrite  disk and external RF elec tric fields. One can suppose a \nclassical mechanism of interact ion between the disk eigen electric moment and the cavity E-\nfield. But the question is why this interaction gives the multiresonance spectral pictures similar to the pictures shown in well known experiments w ith a ferrite disk placed in an external RF \nmagnetic field [7]. The main aspects concern the question how one may obtain effective \nresonance interactions between the edge doubl e valued functions (determining the anapole-\nmoment properties) and the me mbrane single valued functions  (determining the energy eigen \nstates). To understand this mechanism we suggest here the following qualitative model. Fig. 2 \n(a) shows the double-valued functions \n)(θδ′+  and ) (θδθ′∇+′  for 21+=q . Here we use \ndesignation θ′ to distinguish a \"spin\" angular coordinate from a regular angle coordinate. \nBecause of the edge-function chiral  rotation [3, 4], one has to select only positive derivatives: \n0>′∂∂+\nθδ. The corresponding parts of the graphs are distinguished in Fig.  2 (a) by bold lines. \nFigs. 2 (b) and 2 (c) give two cases of the membrane single valued functions ) (~θη  which may \nlead to resonance \"spin-orbital\" in teractions. It is evident that in  a case of Fig. 2 (b), a positive \nhalf of function )(θδ′+  is phased for a resonance interaction with the positive halves of function \n)(~θη , while in a case of Fig. 2 (c ) a positive half of function )(θδ′+  is phased for a resonance \ninteraction with the negative halves of function ) (~θη . This results in a non-zero integral in Eq. \n(7) and explains how the double-valued-functi on spins precessing on the edge region may \ninteract with the single-valued- function spins precessing in the core region. For a case of Fig. 2 \n(b) one has the \"resonance absorption\" and for a case of Fig. 2 (c) one has the \"resonance \nrepulsion\". Both types of interac tions are equiprobable. One may expect that for different cavity \nparameters, two the above cases, the \"resonance absorption\" and \"reson ance repulsion\", can be \nexhibited separately. One may also expect that in a certain situation transitions between these \ntwo resonance behaviors can be demonstrated. Ou r experiments clearly verify this model of \nresonance interactions.      5    In experiments, we used a disk sample of a diameter mm 3 2=ℜ made of the YIG film on the \nGGG substrate (the YIG film thickness mkm 50=d , saturation magnetization G  1880  40=Mπ , \nlinewidth Oe 8.0=∆H ) and a short-wall rectangular-wavegui de cavity with an entering iris. A \nnormally magnetized ferrite disk was placed in a cavity in a maximal RF electric field of the \nTE102 mode and was oriented normally to the E-field (Fig. 3). In Fig. 4, showing the frequency \ndependence of the cavity reflection coefficien t (CRC), we point out three characteristic \nfrequencies used in experiments.     An analysis made in [5] allows clearly specif y the main spectral features of an interaction of a \nMDM ferrite disk with a cavity RF electric field. Fig 5 (a) shows a typical multiresonance spectrum of such an interaction. This is a depe ndence of the absolute value of the CRC on a bias \nmagnetic field obtained for a critically c oupled cavity at the resonance frequency f\n1 =7.085 GHz. \nThe digits are the MDM numbers. For the cavities with reduced Q-factors and resonant at the \nsame frequency (to preserve the resonance fr equency we used small tuning elements), the \ncharacter of the ferrite-disk spectrum remains the same [see Figs. 5 (b), (c)]. Following the above analysis one can conclude that the spectra in Figs. 5 (a),  (b) and (c) co rrespond to the \n\"resonance repulsion\". When we put a small piece of a metallic wire (made of copper) above a \nferrite disk and parallel to the cavity E-field, we obtained a very st rong interaction between the \ndisk and cavity [Fig. 5 (d)]. In this case we can di scern two fundamental aspects. First of all, the \nfact that an additional small cap acitive coupling strongly affect s on magnetic oscillation proves, \nonce again, the presence of the electric-dipole moments of the MDMs in a quasi-2D ferrite disk. \nSecondly, we see very unique features in the spectral picture. There are sharp jumps of the \nCRCs in the regions of the disk resonance peaks. It can be definitely supposed that these jumps \nare caused by sharp phase transitions between two \nπ2-behaviors shown in Figs. 2 (b) and (c).  \n    To investigate more in details transitions between behaviors of the \"resonance repulsion\" and \n\"resonance absorption\" we analyzed the ferrite di sk spectra measured at different frequencies. \nThese frequencies, 3 ,2 1  and , f ff , correspond to different positions on the resonance curve of the \ncavity (see Fig. 4). The multiresonance spectral pi ctures for these frequencies are shown in Fig \n6. Since the permeability tensor parameters are dependent both on frequency and a bias \nmagnetic field, we were able to match the peak position by small variations of a bias field. The \nfields corresponding to the first pe aks are adduced in the figure.  \n    The spectrum in Fig. 6 (a), corresponding to 1f [and being the same as the spectrum in Fig. 5 \n(b)], represents the \"resonance re pulsion\" behavior. At the same ti me, the spectrum in Fig. 6 (c), \ncorresponding to3f, clearly demonstrates the \"resonan ce absorption\" behavior. It becomes \nevident that the spectrum in Fig. 6 (b), corresponding to2f, shows the transitions between the \n\"resonance repulsion\" and \"resona nce absorption\". A qualitative explanation of the observed \nthree cases could be the fo llowing. Since at frequency 1f the cavity is \"viewed\" by the incoming \nsignal as an active load, one can cl early observe the \"resona nce repulsion\" due to a ferrite disk.   \nContrary, at frequency 3f the cavity is characterized mainly as a reactive load. In this case one \nobserves the \"resonanc e absorption\" behavior.  At frequency 2f both cases are mixed and a \ntransitional behavior takes place. It is worth noti ng that for transitional behaviors shown in Figs. \n5 (d) and 6 (b), the \"between-peak derivatives\" of  CRCs with respect to the bias field are of \ndifferent signs.      For the above disk parameters used in expe riments we calculated amp litudes of eigen electric \nmoments of MDMs based on Eq. (10) . The calculations of functions \n)(zξ  and ()rR were made \nfor \"orbital\" azimuth number 1=ν  and for the essential boundary conditions based on the \nmethods used in [6]. The calculation results of  the eigen-electric-moment amplitudes are shown \nin Fig. 7. To compare the calculation results w ith the experimental one s we took the measured \nrelative peak amplitudes. We \"tied\" together th e calculated and measured amplitudes of the first-\nmode peaks and normalized them to unit. Evidently that since the mode peak amplitudes were measured with respect to a bias magnetic field at the constant frequenc y, we had negligibly  6small \"from-mode-to-mode\" variations of the cavity E-field amplitudes. So the measured \nrelative peak amplitudes should correspond to e xperimental MDM distributions of the eigen \nelectric moments. Fig. 7 shows relatively good agreement between the experimental and \ncalculation results. Some disagreement can be  explained by certain inaccuracy in precise \nexperimental characterization of amplitudes of very sharp resonant peaks.        In conclusion, we have to note that the eigen electric moments of a ferrite disk arises not from \nthe classical curl electric fields  of magnetostatic oscillations. At the same time, any induced \nelectric polarization effects in YIG or GGG materials are be yond the frames of the observed \nmultiresonance spectra. We sum up that in this le tter we calculated the spectral distribution of \nthe eigen electric (anapole) moments of a MDM ferrite disk. We discussed a model which gives \na possible picture of interaction of the MDM osci llations with external RF electric fields. Our \nexperimental results, shown in  this letter, convin cingly confirmed th e proposed model of \nanapole moment oscillations caused by edge ch iral rotations in a MDM ferrite disk. We \ndemonstrated good correlation between the calculat ed and experimental results.        \n ====================== [1] T. Shinjo et al., Science \n289, 930 (2000); K.Yu. Guslienko et al, Phys. Rev. B 65, 024414 \n(2001). \n[2] J. Miltat and A. Thiaville, Science 298, 555 (2002).  \n[3] E.O. Kamenetskii, Phys. Rev. E 73, 016602 (2006). \n[4] E.O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007). \n[5] E.O. Kamenetskii, A.K. Saha, and I. Awai, Phys. Lett. A 332, 303 (2004). \n[6] E.O. Kamenetskii, M. Sigalov, a nd R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005). \n[7] J.F. Dillon Jr., J. Appl. Phys. 31, 1605 (1960). \n \nFigure captions \nFig. 1. Edge-function chiral rota tion in correlation with the RF  magnetization evolution for the \n(+) resonance. Fig. 2. The model explaining res onance interactions of  the MDM ferrite disk with the cavity \nelectric field.              Fig. 3. A waveguide cavity with  an enclosed ferrite disk.  \nFig. 4.  Frequency dependence of the cavity reflection coefficient. \nFig. 5. Spectral pictures of re flection coefficients for different cavity structures: (a) Critically \ncoupled cavity; (b) Non criti cally coupled cavity; (c) Cavity w ith an inserted loss material; (d) \nCritically coupled cavity with inserted sm all metallic wire above a ferrite disk. \nFig. 6. Spectral pictures of reflection coe fficients obtained at di fferent frequencies. \nFig. 7. Calculated and measured electri c moment amplitudes versus MDM numbers.  \n  7 \nFig. 1. Edge-function chiral rota tion in correlation with the RF  magnetization evolution for the \n(+) resonance.    \n \n Fig. 2. The model explaining res onance interactions of  the MDM ferrite disk with the cavity \nelectric field.                    mr\nmrmr\n \nmr0=θ\n43πθ=πθ=4πθ=\n2πθ=θℜ\nℜ 8 \n     \n         \n  \n \n(b) \n  \n \nFig. 3. A waveguide cavity with  an enclosed ferrite disk.  \n   \n \n \n \n \n \n \nFig. 4.  Frequency dependence of the cavity reflection coefficient. \n \n \n  \n  9 \n \n \n  \n \n  \n \n \nFig. 5. Spectral pictures of reflection coefficien ts for different cavity structures: (a) Critically \ncoupled cavity; (b) Non criti cally coupled cavity; (c) Cavity w ith an inserted loss material; (d) \nCritically coupled cavity with inserted sm all metallic wire above a ferrite disk. \n  10\n \n \nFig. 6. Spectral pictures of reflection coeffi cients obtained at diffe rent frequencies.  \n \n  \n \n \n \n  \n \n  \n  11\n \n \nFig. 7. Calculated and measured electri c moment amplitudes versus MDM numbers.  \n \n \n \n  \n \n  \n \n  \n \n  \n \n  \n \n  \n "    },    {        "title": "0809.0395v1.Parametrically_stimulated_recovery_of_a_microwave_signal_using_standing_spin_wave_modes_of_a_magnetic_film.pdf",        "content": "arXiv:0809.0395v1  [cond-mat.other]  2 Sep 2008Parametrically-stimulated recovery of a microwave signal using standing spin-wave\nmodes of a magnetic film\nA.V. Chumak,∗A.A. Serga, and B. Hillebrands\nFachbereich Physik and Forschungszentrum OPTIMAS,\nTechnische Universitat Kaiserslautern, 67663 Kaiserslau tern, Germany\nG.A. Melkov\nDepartment of Radiophysics, Taras Shevchenko National Uni versity of Kiev, Kiev, Ukraine\nV. Tiberkevich and A.N. Slavin\nDepartment of Physics, Oakland University, Rochester, Mic higan 48309, USA\n(Dated: August 20, 2021)\nThe phenomenon of storage and parametrically-stimulated r ecovery of a microwave signal in a\nferrite film has been studied both experimentally and theore tically. The microwave signal is stored\nin the form of standing spin-wave modes existing in the film du e to its finite thickness. Signal\nrecovery is performed by means of frequency-selective ampl ification of one of these standing modes\nby double-frequency parametric pumping process. The time o f recovery, as well as the duration\nand magnitude of the recovered signal, depend on the timing a nd amplitudes of both the input and\npumping pulses. A mean-field theory of the recovery process b ased on the competitive interaction\nof the signal-induced standing spin-wave mode and thermal m agnons with the parametric pumping\nfield is developed and compared to the experimental data.\nPACS numbers: 75.30.Ds, 76.50.+g, 85.70.Ge\nINTRODUCTION\nThe problem of microwave information storage and\nprocessing using elementary excitations of matter has\nbeen intensively studied both theoretically and experi-\nmentally. For a long time the search concentrated on\ndifferent types of echo-based phenomena involving phase\nconjugation techniques [1, 2].\nSeveral years ago, a new method of signal restoration\nwas proposed and tested in the experiments with dipolar\nspin waves scattered on random impurities and defects\nof a ferrimagnetic medium [3]. In the framework of this\nmethod, to achieve the signal restoration, a frequency-\nselective parametric amplification of a narrow band of\nscattered spin waves (having frequencies close to the fre-\nquency of the input signal) was used. As a result of this\nselective amplification, a uniform distribution of the sec-\nondary (scattered) spin waves in the phase space of the\nsystem was distorted, and a macroscopic noise-like signal\nwas registered at the output [4]. The noise-like character\nof the restored signal is caused by the fact that this sig-\nnal is formed by many individual scattered spin waves,\nhaving close, but arbitrarily shifted phases.\nRecently [5], we have reported experimental results\non storage and recovery of a microwave signal using a\nsinglestanding spin-wave mode belonging to the dis-\ncrete spin-wave spectrum, which is caused by the spa-\ntial confinement of the magnon gas in a thin yttrium-\niron-garnet (YIG) ferrite film. The storage effect was\nrealized through the conversion of the input microwave\nsignal into a propagating magnetostatic wave (or dipo-Microwave\nSource\nMicrowave\nSwitchMicrowave\nSource\nMicrowave\nSwitch\nInput□PulseDelayed□and\nRestored\nPulses\nPumping\nH0Detector\n048x(mm)Oscilloscope Pulse□Generator\niiiiii iv\nInput\nAntennaOutput\nAntenna\nSpinwaveResonator hYIG\nFIG. 1: (color online) Experimental setup and typical wave-\nforms: “i” – input pulse; “ii” – pumping pulse; “iii” – delaye d\nrunning spin-wave pulse; “iv” – restored signal.\nlar spin wave), and, then, into an exchange-dominated\nstanding spin-wave modes (or thickness modes) of the\nfilm. The recovery of the signal was performed by means\nof frequency-selective parametric amplification, but, in\ncontrast with [3], the restored signal was formed by a\nsingle standing spin-wave mode of the film, and had a\npractically noiseless character. The mechanism of such a2\nrestoration is highly non-trivial. Therefore, in our first\nreport [5] we used an approximate empirical theoretical\nmodel to explain this rather complicated restoration pro-\ncess.\nIn our present paper we give a detailed theoretical ex-\nplanation of the restoration effect. This explanation is\nbased on the general theory of parametric interaction of\nspin waves (so-called “S-theory”) [6] and takes into ac-\ncount interactions between different groups of spin waves\nexisting in a ferrite film. Using the developed theory we\ncalculate parameters of the restored pulse (power, dura-\ntion, and delay in respect to the input pulse) as func-\ntions of the power of the input and pumping pulses, and\ncompared these calculated parameterswith experimental\ndata.\nEXPERIMENT\nForthereasonofcompletenesswereporthereagainthe\nexperimental findings presented in [5], amended by ad-\nditional experimental investigations. The experimental\nsetup is shown in Fig. 1. The input electromagnetic mi-\ncrowave pulse is converted by the input microstrip trans-\nducer into dipolar spin waves, that propagate in a long\nand narrow (30 ×1mm2), 5µm thick yttrium iron garnet\n(YIG) film waveguide(saturationmagnetization 4 πMs=\n1750G, exchange constant D= 5.4·10−9Oe·cm2). The\nother transducer, used to receive the output microwave\nsignals, is placed at a distance of l= 8mm from the\ninput one. A bias magnetic field of H0= 1706Oe is ap-\nplied in the plane of the YIG film waveguide, along its\nwidth andperpendicular to the direction ofthe spin wave\npropagation.\nThe input rectangular electromagnetic pulses having a\nduration of 100ns, carrier frequency of fin= 7.040GHz,\nand varying power of 0.1 µW< Pin<6mW were sup-\nplied to the input transducer. These input pulses excite\nwavepacketsofmagnetostaticsurfacewaves(MSSW) (or\nDamon-Eshbach magnetostatic waves [7]), having a car-\nrier wave number kin≃100cm−1. The group velocity\nvgof the excited wave packet is about 2.3cm /µs. This\ngroup velocity determines the time delay of the propa-\ngating wave packet between the input and output trans-\nducers of about 350ns. The spin-wavepacket received by\nthe output transducer is, again, converted into an elec-\ntromagneticpulse. After amplificationanddetection, the\noutput signal is observed with an oscilloscope.\nAs it was pointed out in [5], the propagating MSSW\nexcited in the ferrite film standing (thickness) spin-wave\nmodes that continued to exist in the film long after the\npropagating MSSW signal reach the output transducer.\nTo recover the microwave signal stored in these stand-\ning spin-wave modes it is necessary to apply to the film\nan external pumping microwave field with the frequency\nthat is approximately two times larger than the carrierfrequency of the stored microwave signal. To supply this\ndouble-frequency pumping pulse an open dielectric res-\nonatorisplacedin the middleofthe YIG waveguide. The\nresonator is excited by an external microwavesource and\nproduces a pumping magnetic field /vectorhpthat is parallel\nto the static bias magnetic field /vectorH0, see Fig. 1. The\nresonance frequency of the pumping dielectric resonator\nfr= 14.078GHz was chosen to be close to twice the car-\nrier frequency of the input microwave pulse. Thus, the\nconditions for the processofparallel parametricpumping\n[8] are fulfilled in our experiment. Under these condi-\ntions the energy of the pumping field is most effectively\ntransferred to the magnetic oscillations and waves that\nhave the frequency that is exactly half of frequency of\nthe pumping signal.\nThe experiment starts at the initial moment of time\nt= 0 when an external microwave pulse is supplied to\nthe input transducer (see waveform “i” in Fig. 1). The\nMSSW packet, excited at the input transducer by this\nsignal, propagates to the output transducer and creates\nthere a delayed output microwave signal of similar dura-\ntion(seewaveform“iii”inFig.1). Thedelaytime tpropof\nthis output pulse is determined by the MSSW group ve-\nlocity and the distance between the transducers. Then,\nat the time t > tprop, a relatively long (see waveform\n“ii” in Fig. 1) and powerful pumping pulse with a car-\nrier frequency approximately twice as large as the carrier\nfrequency of the input pulse is supplied to the pumping\nresonator. Then, during the action of the pumping pulse\nthe restored signal appears after a certain delay at the\noutput transducer (see waveform “iv” in Fig. 1).\nIt is necessary to stress here, that the parametrically\nrecoveredsignal(waveform“iv”in Fig.1) originatesfrom\nthe input microwave signal (waveform “i” in Fig. 1, and\nnever appears without the previous application of the\ninput signal. At the same time, the main characteristics\nof this restored pulse (such as peak power, duration, and\ndelay time) are not directly related to similar parameters\nof the input pulse, and are mainly determined by the\nprocess of parametric interaction of the trailof the input\nsignal (in the form of standing spin-wave modes) with\nthe pulsed parametric pumping.\nTypical experimental oscillograms demonstrating the\nnormalized waveforms of the restored output pulse mea-\nsured for different values of the pumping power are pre-\nsented in Fig. 2(a). It is evident from Fig. 2(a) that the\nincrease of the pumping power Ppleads to a significant\nvariation of the restored pulse parameters: decrease of\nthe recovery time trand decrease of the restored pulse\nduration ∆ tr. The experiment shows (although it is not\nseen in the normalized graphs of Fig. 2(a)) that the peak\npowerProf the restored pulse increases with the increase\nof the pumping power Pp.\nFigure 2(b) shows the profiles of the output restored\npulse calculated using the theoretical model presented\nbelow. It is clear from the comparison of the experimen-3\n0 1 2 3 4 5 60101Pp4 Pp3 Pp2\nTime□( s) /c109(a)\n(b)Pp4 Pp3 Pp2Intensity□(a.u.)\nIntensity□(a.u.)Pp1\nPp1\nFIG. 2: (color online) Experimental (a) and calculated (b)\nwaveforms of the delayed and recovered pulses for different\nvalues of the pumping power Pp:Pp1= 3.67W,Pp2=\n1.28W,Pp3= 0.52W,Pp4= 0.34W. Waveforms are nor-\nmalized by the maximum intensity of each of the recovered\npulses.\ntal and theoretical waveforms presented in Fig. 2(a),(b)\nthat this model gives a good quantitative description\nof the experimental data. In the following section we\npresent a detailed description of this theoretical model.\nLookingat Fig. 2 one can notice that the recoverytime\nof the restored pulse is much larger than the time of\nthe spin wave propagation between the input and output\ntransducers. This means that very slow spin-wave modes\nparticipate in the process of signal storage and restora-\ntion. In order to better understand the signal storage\nmechanism an additional experiment was performed. In\nthis experiment an additional (second) receiving trans-\nducer was placed at a distance of 1.5 mm from the first\n(main) one. The time profiles of the spin-wave signal\nreceived at the main and additional transducers are pre-\nsented in Fig. 3. These profiles consist of two peaks:\nthe first narrow peak, corresponding to the propagat-\ning MSSW packet excited by the input microwave pulse,\nandthe secondbroaderpeak, correspondingto thestored\nand, then, parametrically recovered spin-wave packet.\nOne can see that the time interval between the ap-\npearance of the fronts of these two peaks at a particu-\nlar transducer is the same. This result means that the\ngroup velocities of the two delayed spin-wave packets,\nwhich are detected by the two output transducers are\nthe same within the error margins. Thus, the excitation\nof the second (restored) peak at the output transducer\nis performed by the fast propagating MSSW mode, the\nsame spin-wavemode that wasexcited initially by the in-0.5 1 1.5 2\nTime□( s) /c109Power□(a.u.)65□ns\nii65□ns\niiii\nFIG. 3: (color online) Waveforms of the delayed and restored\npulses received on the output antennae placed 6.5 mm (wave-\nform “i”) and 8 mm (waveform “ii”) apart from the input\nantenna.\nput microwave pulse and which created the first narrow\ndelayed peak at the output transducer.\nTheexperimentalresultshowninFig.3, indicatesthat,\napart from the propagating MSSW, a different spin-wave\nmode having a negligible group velocity (or, in other\nwords, a standing spin-wave mode) must take part in\nthe signal storage and recovery process. This standing\nspin-wave mode stores the information about the input\nmicrowave signal for a couple of microseconds and, then,\nis amplified by a parametric pumping pulse supplied to\nthe open dielectric resonator. It is then converted into\na propagating MSSW packet. Obviously, the parameter\nthat is the most important one for this recovery pro-\ncess is the amplitude of the standing spin-wave mode in\nthe immediate vicinity of the pumping resonator, as the\npumping field of the resonator can only effectively inter-\nact with spin waves located near the resonator.\nQUALITATIVE MODEL\nDipole-exchange spin-wave spectrum of a ferrite film\nTo understand the mechanism governing the observed\nstorage-and-recovery effect of a microwave signal in a\nferrite film of a finite thickness Llet us consider the\ndipole-exchange spectrum of such a film in the case of\nthe MSSW geometry, when the spin-wave carrier wave\nnumberkxis in the film plane and perpendicular to\nthe bias magnetic field H. A calculated spin-wave spec-\ntrum for this case is shown in Fig. 4(b). It consists of\na dipole-dominated (Damon-Eshbach-like [7]) spin-wave\nmode, having the largest group velocity, and a series of\nexchange-dominated thickness spin-wave modes of the\nfilm having very low group velocities (see [9] for details).\nThese exchange-dominated modes are close to the stand-4\n7.007.057.10\nn=13\nWave□vector (rad/cm) kx0 100 200 300(b)\nFrequency□(GHz)\nIntensity\n(a.u.)(a)\nn=11\nn=9\nn=7\nn=5\nn=3\nFIG. 4: (color online) (a) Frequencyspectraof theinputpul se\n(blue, dotted line) and pumping pulse (transferred to the ha lf\nof the carrier pumping frequency) (red, solid line); (b) Cal -\nculated dipole-exchange spectrum of traveling spin waves i n\nthe experimental YIG film ( nis a number of a corresponding\nthickness mode).\ning thickness modes of a spin-wave resonance of the film,\nand in the simple case of unpinned surface spins these\nmodes have discrete values of the perpendicular (to the\nfilm plane) wave vector defined as k⊥=πn/L, where\nn= 1,2,3.... Near the crossing points of the lowest\n(n= 0) and higher-order spin-wave modes the dipolar\nhybridization of the spin-wave spectrum takes place, and\nthe so-called “dipolar gaps” in the spin-wave spectrum\nof the film are formed [9].\nThe qualitative picture of the storage and recovery of\nthe microwave signal in ferrite film looks as follows. A\nrelatively short (duration 100ns) input microwave pulse\nsupplied to the input transducer excites a packet ofprop-\nagating MSSW in the ferrite film waveguide. Under the\nconditions of our experiment the frequency separation\nbetween the discrete quasi-standing spin-wave modes of\nthe film spectrum is around 10-20MHz, depending on\nthe mode number n. At the same time, the width of\nthe frequency spectrum of a relatively short (duration\n100ns) input microwave pulse, which excites a propa-\ngating MSSW packet in the film, is several times larger.\nTherefore, this packet can simultaneously excite several\nquasi-standing spin-wave modes in the film. Due to their\nextremely low group velocity these quasi-standing spin-\nwave modes do not propagate awayfrom the point where\nthey are excited. Instead, they form a “trail” along the\npath of the propagating MSSW packet, and this “trail”\nexists for over a microsecond after the MSSW packet it-\nself is gone from the film.\nIt is worth noting, that the “trail” of quasi-standing\nspin-wave modes is excited mainly in the spectral regions\noffrequency hybridization (“dipolargaps”)in the dipole-\nexchange spectrum of the film (see Fig. 4) [9]. The am-\nplitude of this ”trail” decays exponentially with time due\nto the natural magnetic dissipation in the film.Toobservetherestorationofthemicrowavesignalfrom\nthe “trail” it is necessary to supply the pumping pulse at\nthe time, when the “trai” has not yet decreased to the\nthermal level. When the pumping is applied, the ampli-\ntudes of the quasi-standing spin-wave modes forming a\n“trail” start to increase due to the parametric amplifi-\ncation. If the pumping pulse is long enough, so that the\npumping has a relatively narrow frequency spectrum and\nis, therefore, frequency-selective,only onequasi-standing\nspin-wave mode is amplified parametrically.\nThe increase of the amplitude of this quasi-standing\nmode is, eventually, limited by nonlinear spin-wave in-\nteraction processes that will be discussed in detail below.\nOne of the most important nonlinear processes of this\nkind is the interaction of the parametrically amplified\nquasi-standing dipole-exchange spin-wave mode with the\npacket of exchange-dominated spin waves, that are ex-\ncited by the parallel pumping from the thermal level [10].\nAt the same time, the back-conversion of the paramet-\nrically amplified quasi-standing spin-wave mode into a\npropagating MSSW packet takes place in the frequency\ninterval near the ”dipole gap” that is resonant with the\npumping carrier frequency. This process results in the\nformation of the restored microwave signal at the output\ntransducer (see the waveform “iv” in Fig. 1).\nWe would like to emphasize one more time, that the\nrestored delayed pulse (waveform “iv” in Fig. 1) is nota\nproduct of a direct parametric amplification of the prop-\nagating MSSW packet, since it can be observed even if\nthe pumping pulse is supplied afterthe input MSSW has\npassed the pumping resonator. Moreover, at a given car-\nrier frequency of the input microwave pulse, the recov-\nered pulse is observed only if the half-frequency of the\nmicrowave pumping lies inside a narrow frequency inter-\nval close to the position of one of the the dipole gaps\nin the frequency spectrum of the magnetic film (see e.g.\nChapter 7 in [8] and [9]). The observation of the restored\nspin-wave packets only in these narrow frequency inter-\nvals suggests that the process of storage and restoration\nof the initial microwavesignal is caused by the excitation\nofthediscretethickness-relatedquasi-standingspin-wave\nmodes of the magnetic film.\nStorage and restoration of a signal as a multi-step\nprocess involving several groups of spin waves\nIn order to explain the above described signal restora-\ntion effect a model of interaction of two magnon groups\nwith parametrical pumping was proposed in [5]. In this\nmodel we analyze the interaction between the electro-\nmagnetic parametric pumping with effective amplitude\nVhpand frequency ωp(wherehpis a variable pump-\ning magnetic field, Vis the parametrical coupling coeffi-\ncient), standing spin-wave mode with effective amplitude\ncharacterized by the magnon number Nsand frequency5\nωp/2, and, the so-called, “dominating” spin-wave group\nwith effective amplitude characterized by the magnon\nnumberNκand frequency ωp/2. In this model the condi-\ntion for the energy conservation [6] is always fulfilled au-\ntomatically, becausethe frequency ofall the wavestaking\npart in the effective parametricinteractionwith pumping\nis twice smaller than the frequency of pumping. We call\nthe group of spin waves that is excited by parametric\npumping from the thermal level “dominating” because\nthis group of waves has the smallest relaxation param-\neter. Therefore, if the pumping acts for a sufficiently\nlong time, so that the system reaches a saturated sta-\ntionary regime, this dominating group suppresses all the\nother spin waves taking part in the process of paramet-\nric interaction. The initial amplitude of the dominat-\ning group, characterized by the magnon number Nκ0, is\ndetermined by the thermal noise level, while the initial\namplitude of the standing spin-wave mode, characterized\nby the magnon number Ns0, is determined by the ampli-\ntude of the applied input signal, relaxation parameter of\nthis mode, and the time delay between the signal and\npumping pulses.\nThe process of signal restoration involves competition\nof two wave groups: the signal-induced standing wave\ngroup and the noise-induced dominating wave group,\nwhile both these groups are parametrically amplified by\npumping. The relative efficiency of this parametric am-\nplification is determined by the relaxation parameters of\nthe wave groups, and, as it was mentioned above, the\ndominating spin-wave group has the smallest relaxation\nparameter Γ κ. Thus, the amplification of this group is\nhigher in comparison to the amplification of all the other\nspin-waves groups, including the standing wave group.\nThe rapid increase of the amplitude of the dominating\ngroup of spin waves will lead to its interference with\nthe standing spin-wave group, and, eventually, to the\ndecrease of parametric amplification and saturation of\ndominating group amplitude in the stationary regime.\nSimultaneously, the amplitude of the standing spin-wave\nmode, which is competing with the dominating group for\nthe energy from the pumping, will decrease, because in\nthis nonlinear competition process the mode with larger\namplitude (i.e. the dominating mode) will get a propor-\ntionally larger share of the pumping energy [6].\nA qualitative sketch of the temporal evolution of\nthe amplitudes of standing (solid line) and dominat-\ning (dashed line) wave groups interacting with constant-\namplitude parametric pumping is presented in Fig. 5.\nAt the initial time point, when the pumping is switched\non, (point “ a” in the figure) the signal-induced stand-\ning spin-wave mode (solid line) has the amplitude that\nis larger than the amplitude of the noise-induced domi-\nnating spin-wave group (dashed line). In the region be-\ntween the points “ a” and “c” the amplitudes of both\nwave groups exponentially increase due to the paramet-\nric amplification: the amplitude of the dominating groupad c\nb\n0 1 2 3 4 5 6 710121014101610181020\ndominating□group\nstanding□wave□group\nTime□( s) /c109Spin□wave□amplitude□(a.u.)\nFIG. 5: (color online) Qualitative picture of the temporal\nevolution of the amplitudes of standing (solid line) and dom -\ninating (dashed line) spin-wave groups interacting with th e\nconstant-amplitude parametric pumping that was switched\non att= 0. Point “ a” – start of parametrical amplification;\n“b” – point where the amplitude of the dominating spin-wave\ngroupbecomes larger thantheamplitude ofthestandingwave\ngroup; “c” – saturation point where the parametrical ampli-\nfication stops; “ d” – stationary regime where the amplitude\nof the dominating group is constant and the amplitude of the\nstanding wave group vanishes.\nincreaseswithtime tasexp[(hpV−Γκ)t], whiletheampli-\ntude of the signal-induced standing wave group increases\nas exp[(hpV−Γs)t] (where Γ κ<Γsare the relaxation\nparameters of the dominating and standing wave groups\ncorrespondingly and Vis the coefficient of parametric\ncoupling between the wave group and the pumping field\nhp).\nIt is clear that the amplification of the dominating\ngroup is larger, because of the smaller relaxation param-\neter for this wave group, and beyond the point “ b” in\nFig. 5 the amplitude of the dominating group overtakes\nthe amplitude of the standing mode. Then, at the point\ncthe amplitude of the dominating wave group reaches a\ncertain critical value after which it starts to renormalize\nthe effective pumping, which leads to saturationand stop\nof parametric amplification. The effective pumping am-\nplitudeheff\npVat the saturation point “ c” becomes equal\ntothe relaxationparameterofthedominatingwaveswith\nthe smallest relaxation [6].\nFor the conditions of our experiment this means that\nheff\npV= Γκin the stationary regime (region between “ c”\nand “d”). Sinceheff\npV <Γsthe amplitude of the signal-\ninduced standing wave group start to decrease beyond\nthe point cwith the factor exp[( heff\npV−Γs)t] = exp[(Γ κ−\nΓs)t], as it is shown in the figure. Thus, the restored\nsignal reaches its maximum amplitude at the time point\n“c”.\nThe mechanism of saturation of parametric amplifica-\ntion leading to the decrease of the restored signal ampli-\ntude can be explained in the framework of the general\nnonlinear theory of parametric wave interaction [6, 8].\nAccording to this theory there are three main processes\nwhich can limit the parametric amplification: nonlinear6\nfrequency shift, nonlinear dissipation, and the so-called\nphase mechanism of amplification limitation. It was,\nhowever, established in [6] that it is the phase mecha-\nnism that, for the most part, limits the parametric am-\nplification in the process of parallel pumping used in our\ncurrent experiment. This phase mechanism is based on\nthe idea that the nonlinear interaction between pairs of\nspin waves parametrically excited by pumping creates a\nnonlinear shift of their phase, which leads to the decrease\nofthe efficiency ofthe pairsinteractionwith pumping [6].\nIt is well-known, that in order to fulfill the conditions\nof parametric amplification of a spin wave (having wave\nvectorkand frequency ωk) by an external electromag-\nnetic pumping it is necessary to fulfil the conservation\nlaws for both energy and wave vector [11]. If the pump-\ning is quasi-uniform, i.e. the pumping wave vector is\nsmallkp≈0, the interaction of the signal wave ckwith\npumping leads to the appearance of the “idle” wave c−k\nwhich has the wave vector −kand forms a pair ( k,−k)\nwith the signal wave. The sum of phases in the pair is\nfully determined by the phase of the pumping according\nto the equation [6]:\nϕk+ϕ−k=ϕp+π/2, (1)\nwhereϕkis the signal wave phase, ϕ−kis the idle wave\nphase andϕpis the pumping phase (including the phase\nof the coupling coefficient between pumping and spin\nwaves).\nWhen the spin-wave amplitudes are small Eq. (1) can\nbe easily satisfied as the “idle” wave with the proper\nphase can be chosen from the multitude of thermally\nexcites spin waves. With the increase of the spin-wave\namplitudes the pairs of the parametrically excited spin\nwaves start to interact with each other through the four-\nwave process of pair interaction. As a result of this inter-\naction process the sum of phases ψk=ϕk+ϕ−kstarts to\nchange, the condition (1) breaks, and the efficiency ofthe\npumping-induced parametric amplification of the signal\nwaves is drastically reduced [6].\nIn our first paper [5] describing the signal restoration\nprocess we obtained analytic expressions for the time of\nappearance and the amplitude of the parametrically re-\nstored pulse, but did not analyze the nonlinear processes\nleading to the limitation of parametricamplification and,\ntherefore, to the finite duration of the restoredpulse. Be-\nlow, we present a detailed theoretical model of the signal\nrestoration where all the relevant nonlinear processes of\nwave interaction are taken into account.\nTHEORETICAL MODEL\nIn order to explain the above described effect of mi-\ncrowave signal restoration we use the general theory\nof parametric interaction of spin waves (so-called “S-\ntheory”) [6]. The equation for the amplitude of a spinwave interacting with the parametric pumping can be\nwritten in the form (see also [8]):\n/bracketleftbiggd\ndt+Γ−i(˜ωk−ωp/2)/bracketrightbigg\nck−iPkc∗\n−k= 0,(2)\nwhereckandc∗\n−kare the amplitudes of signal and idle\nwaves of frequency ωkand wave number k, Γ is the spin-\nwave relaxation parameter, and ωp= 2πfpis the pump-\ning frequency.\n˜ωk=ωk+2/summationdisplay\nk1Tkk1|ck1|2(3)\nis a spin-wave frequency with account of nonlinear fre-\nquency shift, Tkk1is the corresponding nonlinear param-\neter,\nPk=hpV+/summationdisplay\nk1Skk1ck1c−k1 (4)\nistheeffectiveinternalamplitudeofparametricpumping,\nandSkk1is the nonlinear coefficient describing four-wave\ninteraction of spin-wave pairs. The analogous equation\nfor the amplitude of the idle wave c∗\n−kis omitted for\nbrevity.\nThe spin-wave formalism is substantially simplified if,\ninsteadoftheindividualcomplexamplitudesofthesignal\nand idle waves, we introduce new variables characteriz-\ning combined amplitudes (or magnon densities per unit\nvolume for a given wave number k) and phases of the\nspin-wave pairs, following [6]:\nnk=M0/2(γ¯h/)ckc−ke−iψk(5)\nψk=ϕk+ϕ−k, (6)\nwhereγ= 2.8MHz/Oeisthegyromagneticratio, ¯ histhe\nPlanckconstant, and M0isthesaturationmagnetization.\nIn these “pair” variables the equations for the ampli-\ntudes of parametrically interacting spin waves can be\nwritten in a simple form [6]: equation (2) can be pre-\nsented in a form:\n1\n2dnk\ndt=nk[−Γk+Im(P∗\nkeiψk)]\n1\n2dψk\ndt= ˜ωk−ωp/2+Re(P∗\nkeiψk).(7)\nIn our model we analyze the existence of two magnon\ngroups (or two effective magnon pairs): the dominating\ngroupwith magnondensity nκ(note, that index κisused\ntomarkthisdominatingspin-wavegroup)andthesignal-\ninduced quasi-standing group of spin waves with magnon\ndensityns[5].\nBelow, we shall assume for simplicity that the coeffi-\ncient of four-wavepair interaction for all the wave groups\nhas approximately the same value Skk1=S00, and that7\nthe effective pair phase is approximately equal for both\nspin-wave groups (dominating and standing) involved in\nthe parametric interaction with pumping. Under these\nassumptions we can substantially simplify the expression\n(4) for the amplitude of the effective pumping:\nPk=hpV+S(/summationdisplay\nκnκ+/summationdisplay\nsns)eiψ=hpV+S(Nκ+Ns)eiψ.\n(8)\nHereNκ=/summationtext\nκnκandNs=/summationtext\nsnsare the total\nnumber of magnons per unit of volume for the domi-\nnating and standing spin-wave groups, correspondingly,\nS= 2(γ¯h/M0)S00is the renormalized coefficient of pair\ninteraction, and ψ=ψkis the effective phase of the col-\nlective magnon pairs.\nAt a first glance our assumption that the effective\nphase of all spin-wave groups involved in the paramet-\nric interaction with pumping is approximately the same\nseems to be rather arbitrary. However, the theory of\nparametric interaction of waves [6] states, that all the\nexcited wave groups are involved in the renormalization\nof the effective pumping according to Eqs. (4), (8), and\nthat the combined effect of all these groups determines\nthe acting amplitude of the effective pumping. Thus,\nas a first approximation, we can assume that the effec-\ntive phases of different spin-wavegroups do not differ too\nmuch.\nAnother significant simplification of our model is the\nassumption that all the wave groups participating in the\nparametric interaction with pumping are always in exact\nparametric resonance with it ( i.e. ˜ ωk=ωp/2) inde-\npendently of the effective amplitude of a particular wave\ngroup. In other words, in our model we assume that\nthe nonlinear frequency shift described by the four-wave\nnonlinear coefficients Tkk1in Eq. 3 does not play a sig-\nnificant role in the parametric interaction since the wave\nvectors of the waves participating in this interaction are\nautomatically adjusted to fulfil the condition of the exact\nparametric resonance ˜ ωk=ωp/2 when the effective am-\nplitude of the wave group changes. We believe that this\nsimplifying assumption is reasonable for the conditions\nof our experiment, because the frequency of pumping (or\nthe bias magnetic field) in our experiment was always\ntuned in order to obtain the maximum amplitude of the\nrestored pulse i.e. the pumping frequency or bias field\nwere always adjusted to achieve the optimum conditions\nof parametric interaction.\nUsing all the above described simplifying assumptions,\nwe can write the equations for the magnon densities Ni\nof the two wave groups (where i=κfor the dominating\nspin-wave group and i= s for the standing spin-wavegroup) and their common phase ψin the form\n1\n2dNκ\ndt=Nκ[−Γκ+Vhpsinψ]\n1\n2dNs\ndt=Ns[−Γs+Vhpsinψ] (9)\n1\n2dψ\ndt=Vhpcosψ+S(Nκ+Ns),\nwhere Γκ/(2π) = 0.6 MHz, Γ s/(2π) = 0.69 MHz are the\nrelaxation parameters for dominating and standing spin-\nwave groups, correspondingly. The physical meaning of\nthe magnon densities NκandNsis simple – they charac-\nterize the effective amplitude of all the spin waves that\nbelong to a corresponding wave group.\nAt first, the parametric interaction of both spin-wave\ngroupswithpumpingleadsonlytotheincreaseofthecor-\nrespondingmagnondensities NκandNs. Later,whenthe\nthe increasing magnon densities become significant they\nstart to renormalize pumping through the phase mecha-\nnism described in [6], which leads to the limitation of the\nparametric amplification for the both spin-wave groups.\nLet us now analyze some of the particular solutions of\nEq. (9). The simplest solution one can get is the solution\nfor the initial quasi-linear regime, when the system is far\nfromsaturationandtheinfluenceoftheexcitedspinwave\non the pumping is negligible. It is known [6] that the\nphaseψin this case is equal π/2. The magnon densities\nin this quasi-linear regime can be found as:\nNκ=N0\nκexp[2(hpV−Γκ)t]\nNs=N0\nsexp[2(hpV−Γs)t], (10)\nwhereN0\nκ,N0\nsare the initial magnon densities of the\ndominatingandstandingspin-wavegroups. Wenotethat\nthequasi-linearresult(10)agreeswellwiththepreviously\ndescribed qualitative picture of the development of para-\nmetric interaction in our experimental system (see region\nbetween points “ a” and “c” in Fig. 5).\nAnother particular solution of the system (9) can be\nobtained in the stationary regime, when the pumping is\nrenormalized by the excited spin waves and the system\nis saturated. It is clear, that in this stationary regime\nthe magnon densities of both spin-wave groups and their\ncommon phase ψare constant: dNκ/dt=dNs/dt=\ndψ/dt= 0. If we assume that in this saturation regime\nΓs>Γκand that the common spin-wave phase ψvaries\nin the interval π/2< ψ < π we obtain the following\nstationary solution of the system (9)\nsinψ= Γκ/(hpV)\nNs= 0 (11)\nNκ=1\nS/radicalBig\n(hpV)2−Γ2κ.\nThe analytic result (11) also agrees well with the above\npresented qualitative picture of parametric interaction8\nwith pumping and it describes the state reached by the\nsystem beyond point “ d” in Fig. 5).\nTo get more detailed information about the temporal\nbehavior of the magnon densities of two magnon groups\nwesolvedthesystemsofequation(9)numerically,assum-\ning that at the initial moment the phase ψis the same\nas in the quasi-linear case ψ=ψ0=π/2.\nThe initial value of the magnon density of the dom-\ninating spin-wave group is determined by the level of\nthermal noise existing at a given temperature in a ferrite\nfilm, and can be estimated using standard methods [6].\nOur estimation performed assuming that the dominating\nspin-wave group consists of short-wavelength exchange-\ndominated spin waves propagating perpendicular to the\ndirection of the bias magnetic field gave the following\nvalue for the total number of magnons per unit volume\nof ferrite film\nNκT|T=300K≈10121/cm3.\nThis estimation does not take into account the fact\nthat the initial microwave signal could heat-up the dom-\ninating spin-wave group even before the pumping is\nswitched on. However, to account for this effect we need\nfirst to evaluate the number of magnons in the group of\nstanding spin waves created by the input signal.\nThe estimation of the initial magnon density for the\nstanding spin-wave group N0\nsturns out to be a rather\ncomplicated task, because it involves the calculation of\nthe transformation coefficient of the microwave signal\ninto a propagating MSSW and, also, the coefficient of\npartial transformation of the MSSW into the standing\n(thickness) spin-wave modes of the film. It is clear, how-\never, that the initial magnon density N0\nsin the standing\nspin-wavegroupmustbe proportionaltothe powerofthe\ninput microwave signal N0\ns=KsPs0. It is also clear that\nas soon as the input signal pulse is gone from the film the\nmagnondensityofthe standingwavegroupwill decayex-\nponentially with time with the exponent Γ sequal to the\nrelaxation parameter of the standing spin waves. Thus,\nif the delay time between the input signal pulse and the\npumping pulse is tpwe can evaluate the magnon density\nin the standing spin-wave group at the initial moment of\nparametric amplification (i.e. at the moment when the\npumping pule is switched on) as\nN0\ns=KsPs0·exp(−2Γstp),\nwherePs0is the power of input signal, Γ s/(2π) =\n0.69 MHz is a relaxation parameter of the standing spin-\nwave group, tp= 280 ns is the delay time between the\ninput sinalpulse and the pumping pulse, and Ksis a phe-\nnomenologicalcoefficient describing the multi-step trans-\nformationofthe input microwavesignalintothe standing\nspin-wavemode. Forthe conditionsofourexperiment we\nevaluated the coefficient KsasKs= 4·1016W−1cm−3,\nwhich means that for the input signal power Ps0=10µWtheinitialtotalmagnondensityinthestandingspin-wave\ngroup is equal to\nN0\ns= 3.6·10131/cm3.\nThus, at the initial moment of parametric interaction\nwith pumping the standing spin-wave group in our case\nis approximately 40 times stronger than the dominating\nspin-wave group, caused mostly by thermal magnons.\nIn order to make our model more realistic we need to\ntake into account another effect that plays an important\nrole in the process of microwave signal restoration by\nparametric pumping. This important effect is the effect\nof elastic two-magnon scattering which is always present\nin real magnetic systems. It leads to a partial transfer of\nenergy from one spin-wave groups to another, while the\nspin-wave frequency is conserved.\nUnder the conditions of our experiment the effect of\ntwo-magnon scattering leads to partial transfer of energy\nfrom the standing spin-wave group (excited by the input\nsignal) to the dominating spin-wave group. Thus, this\neffect amounts to an effective heating-up of the initial\nthermalspinwavelevel. Thisheating-upeffectwasinves-\ntigated in a previous article [12], where the nonresonant\nsignal restoration (i.e. the process where the signal fre-\nquency was not equal to half of the pumping frequency)\nwas investigated. Below, we shall use an approach sim-\nilar to [12], and we will introduce a phenomenological\ncoefficientβwhich accounts for this heating-up. In the\nframework of this phenomenological approach the initial\namplitude of the dominating spin-wave group, after the\napplication of the input signal pulse, could be evaluated\nas\nN0\nκ=NκT+βN0\ns,\nwhereβ= 4·10−2cm3is a phenomenological parameter\ndescribing the efficiency of two-magnon scattering. Tak-\ning into account this two-magnon heating-up effect we\nwere able to get a more realistic evaluation for the initial\nmagnondensityofthe dominatingspin-wavegroupin the\ncasewhentheinput pulsepowerwasequalto Ps0=10µW\nN0\nκ= 2.4·10121/cm3,\nwhich means that the difference between the initial am-\nplitudes of the standing and the dominating wave groups\nin our experiment was about 15 times.\nAnother important feature of our model is the ac-\ncount of nonlinear dissipation in the standing (signal-\ngenerated) spin-wave group. In contrast with the dom-\ninating spin-wave group, excited mostly by the ther-\nmal noise and having arbitrary phases of individual spin\nwaves, the standing spin-wave group is coherent, and all\nthe spin-wave phases in this wave group are determined\nby the phase of the input signal. Thus, the spin waves in\nthe standing spin-wave group can effectively participate9\nin four-wave (second-order) parametric interactions both\nwithin the group and with the spin waves belonging to\nother groups. This interaction leads to an effective trans-\nfer ofenergyfromthe standingspin-wavegroup, that can\nbe phenomenologicallydescribed as nonlinear dissipation\nby the following form:\nΓs= Γs0(1+η(Nκ+Ns)).\nThe coefficient of nonlinear damping ηfor the conditions\nof our experiment was evaluated as η= 1.7·10−20cm3.\nAs it was mentioned in the previous section, the non-\nlinear damping of spin waves is one of the possible mech-\nanisms leading to the limitation of parametric ampli-\nfication. However, we would like to stress one more\ntime, that in our experiments the nonlinear damping\nof the standing wave group, described by the coefficient\nη, played a relatively minor role, and the limitation of\nparametric amplification was mainly caused by the phase\nmechanism [6] described in our model (9) by the nonlin-\near coefficient S.\nThecoefficient Softhe nonlinearfour-waveinteraction\nbetween the pairs of excited spin waves was calculated\nusing the expressions presented in [8] to give S≈5·\n10−13cm3/s.\nThe pumping magnetic field was calculated from the\nexperimental power of the pumping pulse as hpV=/radicalbig\nPp/Kp, whereKp= 1.07·10−7s·W is the coeffi-\ncient which describes the efficiency of the open dielectric\nresonatorthrough which the pumping pulse was supplied\nto the ferrite film in our experiment.\nThe model (9) with the initial conditions and param-\neters described above was solved numerically to describe\nthe temporal evolution of the amplitudes of two wave\ngroups participating in the parametric interaction with\npumping.\nRESULTS AND DISCUSSION\nThe results of the numerical solution of the system\nof equations (9) for the above specified parameters are\npresented in Fig. 2, Fig. 6, Fig. 7 and Fig. 8. We shall\ndiscuss below each of these figures.\nTemporal dynamics of the parametric interaction\nprocess\nThe temporal dynamics of parametric interaction\nof the two excited spin-wave groups with constant-\namplitude pumping that was switched on abruptly at\ntimet= 0 is illustrated by Fig. 6. The upper frame\ndemonstrates the evolution of the collective spin-wave\nphaseψand the amplitude Pkof the renormalized effec-\ntive parametric pumping, while the lower frame of Fig. 6\nillustrates the evolution of the magnon densities Nκand0 1 2 3 4 5 60.00.51.00.40.60.81.01.2\nsignal□group Nsdominant□group N/c1070.50.60.70.8\nTime□( s) /c109Magnon□density(□10 cm )N\n19 -3Magnon□pairsphase ( )/c121 /c112\nEffective□parametricpumping (MHz)Pk\n/c71/c107Vkhp\nFIG. 6: (color online) Temporal evolution of the spin-wave\neffective phase ψand amplitude of the renormalized effective\npumping(upperframe)andtemporal evolutionofthemagnon\ndensitiesNκandNsofthedominatingandstandingspin-wave\ngroups (lower frame).\nNsof the dominating and standing spin-wave groups, re-\nspectively.\nThe numerical results presented in Fig. 6 clearly con-\nfirm the qualitative picture of the parametric interaction\nshown in Fig. 5.\nIn the initial time interval ( 0 < t<∼2.2µs) a quasi-\nlinear parametric amplification of the both spin-wave\ngroups takes place. In this quasi-linear regime the ef-\nfective spin-wave phase ψ=π/2, the effective pumping\nis not significantly renormalized and is practically equal\ntoVhp, while the magnon densities NκandNsare very\nwell described by the analytical result (10).\nAt the final stage of parametric interaction ( t>∼\n3.5µs), when the system reaches stationary (or satura-\ntion) regime, we also recover the above derived analytic\nresult (11). In this stationary regime the effective pump-\ningPkis stronglyrenormalizedbythe excited spinwaves,\nand is stabilized at the value Pk= Γκ<Vhp, at which it\njust compensates the losses of the dominating spin-wave\ngroup. Under these conditions the magnon density Nκof\nthe dominating spin-wavegroup becomes constant, while\nthe magnon density Nsof the standing spin-wave group\nvanishes.\nIn the transitional region ( 2 .2µs<∼t<∼3.5µs) the am-\nplitudeNsofthestandingspin-wavegroupfirstincreases,\nand then begins to decrease, which results in the appear-\nance of a finite-duration restored pulse at the output of\nthe system. The theoretically calculated profiles of the\nrestoredoutput microwavepulse shown in Fig. 2(b) prac-\ntically repeat the temporal profile of the magnon density\nNs(t) of the standing spin-wavegroup shown in the lower\nframe of Fig. 6.10\nPumping□power (W) PpPulse□duration ( s)/c68 /c109TrRecovery□time ( s)tr/c109\nPulse□power (a.u.)Pr\n0.5 1.0 1.5 2.0 2.5 3.0 3.50.00.51.01.5010203040\n12345\nFIG. 7: Delay time (squares), peak power (open circles), and\nduration (triangles) of the restored pulse as functions of t he\npumping power. Solid lines: results of calculation. Input\nsignal power Ps0= 10µW.\nRestored signal parameters vs pumping power\nAs it was mentioned above, the characteristics of the\nrestored microwave pulse, such as the peak power, du-\nration, and delay time, are mainly determined by the\nprocess of parametric interaction with pumping. This\nfact is illustrated by Fig. 2(a), where the experimental\nnormalized profiles of the restored pulses are presented\nfor different values of the pumping power. In Fig. 2(b)\ncalculated normalized profiles of the restored pulse are\npresented for the same pumping powers. It is clear from\nthis figure, that with increasing pumping power both the\ndelay time and duration of the restored pulse decrease.\nThis effect can be easily explained by the fact that in\ncase of higher pumping power the system saturates (i.e.\nreaches a stationary regime) faster, and, as a result, the\nrestored microwave pulse appears earlier.\nThe experimental (symbols) and theoretical (solid\nlines) dependencies of the peak power Pr, recovery time\ntr, and duration ∆ trof the restored pulse on the pump-\ning powerPpare shown in Fig. 7. It is evident that the\nincrease of the pumping power Ppleads to decrease of\ntrand ∆tr, and, at the same time, to the increase of\nthe peak power Prof the restored signal. The above\nshown behavior of the restored pulse peak power can\nbe explained by that fact that with increasing pump-\ning power the amplification rates exp[( hpV−Γκ)t] and\nexp[(hpV−Γs)t] become closer and the difference in the\npeak amplitudes of the standing and dominating spin-\nwave groups becomes smaller. Thus, as a result, the am-\nplitude of the restored pulse becomes larger.\nIt is clear from Fig. 7 that the theoretical results for-30 -20 -10 02.02.53.0\n0510\nInput□signal□power (dBm) Ps0Recovery□time ( s)tr/c109\nPulse□power (a.u.)Pr\nFIG. 8: Delay time (squares) and peak power (open circles) of\ntherestoredpulseas functions oftheinputsignal power. So lid\nlines: results of calculation. Pumping power Pp= 0.52W.\nthe restoration time and power of the restored pulse are\nin good agreement with experiment. At the same time,\nthe calculated dependence of the restored pulse duration\non the pumping power agrees with the experiment only\nqualitatively. We believe that a significantly better de-\nscription of the experimental results could be achieved\nif the theoretical model is modified to take into account\nsuch experimental parameters as the finite duration of\nthe input signal, realistic widths of the dipole-exchange\ngaps in the ferrite film spectrum, and the frequency se-\nlective character of the parametric amplification process.\nRestored signal parameters vs input signal power\nUsing our theoretical model we also calculated the in-\nfluence of the input signal power Ps0on the parameters\nof the restored microwave pulse.\nAccording to the simple analytical model presented in\n[5] wherethe increaseof the input signalpowerthe power\nofthe restoredpulse increaseslinearly, while the recovery\ntime should remain constant.\nAt the same time, our experiments (see Fig. 8) clearly\ndemonstrate that the increase of the input signal power\nPs0leads to decrease of the recovery time trand to in-\ncrease of the restored pulse power Pr, with the experi-\nmentally observed increase being not linear.\nIt is evidentfrom Fig. 8that ournew theoreticalmodel\n(9) describes the experiment rather well and, therefore,\nsignificantly improves the simple analytical model pre-\nsented in [5]. There are two reasons why our new model\n(9) improves the accuracy of the theoretical description.\nFirst of all, in the analytical model [5] only the dominat-\ning spin-wave group participates in the process of sat-\nuration of the parametric amplification, while in reality\nboth spin-wave groups significantly influence the satura-\ntion process. Another reason, which also plays an im-\nportant role in the parametric interaction process, is the\nheating of the thermal magnons by the input signal (see\n[12] for details). This effect was taken into account in\nthe model by the introduction of the phenomenological11\ncoefficientβ.\nSUMMARY AND CONCLUSION\nIn conclusion, we investigated the effect of storage and\nrecovery of a microwave signal in a ferrite film having\ndiscrete dipole-exchange spin-wave spectrum. The signal\nis stored in the form of standing spin waves (thickness\nmodes) excited by the input microwave pulse in the fre-\nquency intervals near the dipole-exchange gaps in the\nspin-wave spectrum of a ferrite film. The signal is re-\ncovered in the process of parametric interaction of these\nstanding spin-wave modes forming a trail of the input\npulse with a long and powerful pumping pulse having the\ncarrier frequency that is close to the double frequency of\none of the dipole-exchange gaps in the ferrite film spec-\ntrum. An approximate (mean field) theoretical model,\ntaking into account the competition of two spin-wave\ngroups interacting with parametric pumping, and involv-\ning a nonlinear phase mechanism of limitation of para-\nmetrical amplification was used to describe the experi-\nmental results. The developed model provides a good\nquantitative description of the experimentally observed\neffect of storage and recovery of microwave pulses in fer-\nrite films.\nThis work was supported by the Deutsche Forschungs-\ngemeinschaft (SFB/TRR 49), by the Ukrainian Fund for\nFundamental Research (25.2/009), by the MURI grant\nW911NF-04-1-0247from the U.S. Army Research Office,\nand by the Oakland University Foundation.\n∗Electronic address: chumak@physik.uni-kl.de;\nAlso at Department of Radiophysics, Taras ShevchenkoNational University of Kiev, Kiev, Ukraine.\n[1] A. Korpel and M. Chatterjee, Proc. IEEE 69, 1539\n(1981).\n[2] G.A. Melkov, A.A. Serga, V.S. Tiberkevich,\nA.N. Oliynyk, and A.N. Slavin, Phys. Rev. Lett.\n84, 3438 (2000).\n[3] G.A. Melkov, Yu.V. Kobljanskyj, A.A. Serga,\nV.S. Tiberkevich, and A.N. Slavin, Phys. Rev. Lett. 86,\n4918 (2001).\n[4] Yu.V. Kobljanskyj, V.S. Tiberkevich, A.V. Chumak,\nV.I. Vasyuchka, G.A. Melkov, and A.N. Slavin, J. Magn.\nMagn. Mater. 272, 991 (2004).\n[5] A.A. Serga, A.V. Chumak, A. Andre, G.A. Melkov,\nA.N. Slavin, S.O. Demokritov and B. Hillebrands Phys.\nRev. Lett. 99, 227202 (2007).\n[6] V.S. L’vov, Wave Turbulence under Parametric Excita-\ntions. Applications to Magnetics. (Springer-Verlag, 1994)\n[7] R.W. Damon and J.R. Eshbach, J. Phys. Chem. Solids\n19, 308 (1961).\n[8] A.G. Gurevich and G.A. Melkov, Magnetization oscilla-\ntions and waves (CRC Press, New York, 1996).\n[9] B.A. Kalinikos and A.N. Slavin, J. Phys. C 19, 7013\n(1986).\n[10] G.A. Melkov, A.A. Serga, V.S. Tiberkevich,\nA.N. Oliynyk, A.V. Bagada, and A.N. Slavin, J.\nExp. Theor. Phys. (JETP) 89, 1189 (1999).\n[11] A.A. Serga, B. Hillebrands, S.O. Demokritov, A.N.\nSlavin, P. Wierzbicki, V. Vasyuchka, O. Dzyapko, and\nA. Chumak, Phys. Rev. Lett. 94, 167202 (2005).\n[12] S. Sch¨ afer, A.V. Chumak, A.A. Serga, G.A. Melkov, and\nB. Hillebrands, Appl. Phys. Lett. 92, 162514 (2008)."    },    {        "title": "1611.09595v2.Superdirectional_Beam_of_Surface_Spin_Wave.pdf",        "content": "1 \n \nSuperdirectional  Beam  of Surface Spin Wave  \nA. Yu. Annenkov, S . V. Gerus and E . H. Lock *  \nKotel’nikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Fryazino branch  \nThe v isualized diffraction patterns of surface spin wave excited by arbitrarily oriented linear transducer are \ninvestigated experimentally in the plane of tangentially magnetized ferrite film for the case where the transducer \nlength D is much larger than the wavelength λ0. It is shown experimentally and theoretically that the  angular width \nof diffracted surface spin wave beam in anisotropic ferrite film can take values greater or less than λ0/D and can also \nbe zero. For the last case superdirectional  (nonexpanding) beam of the surface spin wave is observed \nexperimentally : the smearing of the beam energy along the film plane is absent and the length of the beam \ntrajectory is maximal (~50 mm).  It is found, that well known Rayleigh criterion used in isotropic media can’ t be \nused to estimate the angular width of spin wave beams.  The experimental results are in good agreement with \ntheoretical investigations, predict ions, calculations and formulas obtained recently.  \n \n \nRecently it was investigated theoretically a two-\ndimensional diffraction patterns arising in the far -field \nregion of a ferrite film surface  for the common geometry, \nwhen a plane surface spin wave with noncollinear group \nand phase velocities is incident on the wide slit in opaque \nscreen with arbitrary orientation [1, 2]. In contrast to the \nsimilar problem for isotropic media it was found in \nmagnetostatic approximation [3], that the angular width \nψ of the diffracted spin wave beam is defined not only \nby the ratio λ/D (here λ is the incident wavelength, and D \nis the slit length) but also by the mathematical properties \nof isofre quency dependence  (ID) for the diffracted wave  \n(in other works ID can be termed as “section of \nwavevector surface”, “section of the isoenergy surface” , \n“equifrequency line” , ets. [2]). The general formula for \nthe angular width ψ of a diffracted beam was derived  as \na result of this investigation . It was shown that this \nformula is valid not only for various types of spin waves, \nbut also for other waves, propagating in various \nanisotropic media and structures (including \nmetamaterials , which are characterize d by ID too ). As \nfollows from the obtained formula, in contrast with \nRayleigh criterion  the angular width of the beam in \nanisotropic media can not only take values greater or less \nthan λ/ D, but also can be equal to zero under certain \nconditions [2]. Analysing the mathematical properties of \nthe wave ID in various anisotropic media and structures , \none can find out specific geometries giving possibility to \nexcit e experimentally these superdirectional  beams (i.e. \nbeams with zero angular width) . Using the same analysis \nit is found in the work s [4, 5] that superdirectional  beams \nof the backward spin waves can be observed in the free \nferrite slab too. Mention must be made, that the similar \nresults for the backward spin wave beams was predic ted \nalso recently  in the  paper [ 6], where for superdirect ional \npropagation of the beam it was used the term s “focusing “ \nand “ caustic propaga tion”.  \nIn this Paper , we demonstrate the  validity and \navailability of the general  formula described above  and discuss below experimental  diffraction patterns of the \nsurface spin wave beams propagated in a tangentially \nmagnetized ferrite film for certain geometries, including \nthe case where the angular width of the beam can be \nequal to zero.  \nThe general scheme of experimental setup  is \nshown in Fig. 1. Propagation of spin wave beams is \nstudied in y ttrium iron garnet (YIG) film grown on a 0.5-\nmm thick substrate of gadolinium gallium garnet (GGG) . \nYIG film (5 in Fig. 1 ) having diameter 76 mm , thickness \ns = 14.7 m and magnetization 4M0 = 1855.8 Gs is \nmagnetized to saturation by the tangential uniform \nmagnetic field H0 with a value H0 = 471.5 Oe . \nMicrowave signal, propagating as a spin wave in the YIG \nfilm from input transducer 6 to output transducer  4, is \ngenerated and received by device 1, that can measur e also \na complex coefficient of transmission signal . Analog \nsignal received by device 1 is transformed then by \nanalo g-to-digital converter and is analy sed by computer \n2. Input transducer 6, exciting spin wave beam, and \noutput receiving transducer 4 are made of gold-plated \ntungsten wire of 12 m thick. E xciting transducer 6 has \nthe length  D = 5 mm and receiving transducer 4 has the \naperture L ~ 0.5 mm. Two identical systems provide in -\nplane displacement of the receiving transducer in two \northogonally directions of YIG film plane  (along  y and z \naxes) . Thus, receiving transducer equipped also by the \nspecial position  sensors 3 is turned into  movable scanning \nprobe, directed by computer 2.  \nThe distribution of spin wave beam in the plane of \nthe yttrium iron garnet film is studied experimentally by \nmeans of the probe  scanning method, that was used \nearlier in [ 7, 8]. Recently this method was improved \ncardinally [ 9] and now it is possible to vis ualise \ndistribution of amplitude and phase of spin wave along \nthe film surface by means of computer signal processing \n(for more detail see [ 9]). Note that dipole spin wave \ndistribution may occupy a large area  compared with YIG \nfilm surface of 76 mm in diam eter. Therefore, the 2 \n \ndescribed measurement method  is appear much more \neffective for dipole spin waves than  the similar well \nknown method based on the Brillouin scattering of light \nby the spin wave [ 10] (it would take a lot of time to probe \nthe whole YIG film surface by the Brillouin method ).  \n \n \nFig. 1. Schematic view of the experimental setup: 1 – \ndevice measuring complex coefficient  of transmission signal , 2 \n– computer, 3 – sensors of the transducer position, 4 – receiving \ntransducer (probe), 5 – YIG film, 6 –linear transducer  exciting \nspin wave .  \n \nMention must be made that theory [2] is also valid \nfor the case, where spin wave beam is excited by \narbitrary oriented linear transducer. In this case, one can \nassume  that the spin wave vector k0 is approximately \nperpendicular to the linear exciting transducer  (this \nassumption is justified in section 9 of [2])  and, therefore , \ngeneral formula (30) in [2] , describing angular beam \nwidth Δψ, is simplified  to the next form  \n0\n0()d\nDd\n.   (1) \nHere angle φ0 is orientation of the wave vector k0 respect \nto the y axis (or angle φ0 may be considered \napproximately  as orientation of transducer line respect to \nthe vector H0); angles φ and ψ are orientation s for an \narbitrary wave vector k and a corresponding group \nvelocity vector V respectively ; dψ/dφ(φ0) – the derivative \nvalue , corresponding to  the point of ID in which the wave \nvector k0 is ended  (for more detail see section 8 in [2]) .  \nCharacterizing spin wave beam  parameter s it is \nconvenient to use both absolute  angular beam width Δψ and relative  angular beam width σ which is equal to the \nratio between the value Δψ (in radians) and the value \nΔψisotr = λ0/D representing the angular width of a similar \ndiffracted beam in isotropic medium  (in radians  too):  \n0\n0/isotrd\nDd      \n.  (2) \nFrom the physical standpoint, relative angular width σ \nshows how much value Δψ is smaller (or greater) than the \nabsolute angular width Δψisotr for the similar beam (i.e., \nfor the beam with the same ratio λ0/D) propagating in \nisotropic medi um.  \nFormula (1) shows , that the angular beam width \nΔψ is determined not only by the ratio λ0/D, but also by \nthe derivative value dψ/dφ (φ0) characteriz ing the \ncurvature of ID. So if one can find the structure (medium) \nand geometry (excitation topology) , at which dψ/dφ (φ0) \n= 0, then one can observe superdirectional  \n(nonexpanding) beam with angular width Δψ = 0, i.e. the \nbeam retain ing constant absolute width during its \npropagation!   \nAs it is found in [2], the value dψ/dφ (φ0) can be \nequal to zero for surface spin wave  with frequenc y lying \nnot far from the beginning frequency of the spectrum  (for \nmore detail see Fig. 7b, curve 2 in [2])  \n0 0 0( 4 ) / 2begf H H M  \n.   (3) \nSo to observe superdirectional  (nonexpanding) \nbeam corresponding to the case dψ/dφ (φ0) = 0 we ha ve \ncalculated ID for the surface spin wave s with various \nfrequencies (Fig. 2) and corresponding dependences \nψ (φ) (Fig. 3 a), dψ/dφ (φ) and σ(φ) (Fig. 3 b) for the \nparameters of YIG film mentioned above. Since it is \nshown in [2] that numerical calculations of value σ and \ncalculations based on formula (2) coincide with good \naccuracy  (see Fig. 8 – 11 in [2]) , so only values σ \ncalculat ed by the formula (2) are given in Fig. 3b.   \n \n \n \nFig. 2. Isofrequency dependences of the surface spin \nwave for the frequencies 2950, 2999 , 3100, 3242 and 3400 \nMHz (curves 1 – 5 respectively). An arbitrary vectors k and V \nwith their orientation angles φ and ψ are also shown.  \n 3 \n \n \n \n \nFig. 3. Orientation angle ψ of the group velocity vector \nV (a) and relative angular width σ (b) as a function of the  \norientation angle φ between the wavevector k of the surface \nspin wave and the y-axis for the frequencies 2950, 2999, 3100, \n3242 and 3400 MHz (curves 1 – 5 respectively).   \n \nThen to observe experimentally superdirectional  \nbeam propagation,  we fixed position of exciting \ntransducer at a n orientation φ0 = -45o for which the \nrelative angular width σ can be zero for frequenc y about 3 \nGHz (see Fig. 3b, curve 2).  Since calculations based on \nthe theory [2] do not take into account a number of \nparameters (such as anisotropy, applied field and \nmagnetization inhomogeneity, etc.) influencing on the \nspin waves characteristics, visualized p atterns in the 120 \nMHz frequency  band with a 1 MHz step are obtained for \nspin wave beams propagation at this orientation φ0. \nBelow in Fig. 4 we present the measured visualized pattern  havin g the m inimal angular beam  width for the \nspin wave frequency f0 = 2999 MHz.  For the selected \nvalues f0 and φ0 the spin wave vector k0 had magnitude k0 \n= 56.5 cm-1 (wave length λ0 = 1110 m) and the ratio \nλ0/D was 0.222 .  \n \n \nFig. 4. Amplitude d istribution of superdirectional  spin \nwave beam  in the plane of ferrite film for the next beam \nparameters: f0 = 2999  MHz, k0 = 56.5 cm-1, λ0 = 1110 μm, \nλ0/D = 0.222, φ0 = -45o, Δψexp = 0.4о, σexp = 0.03.  Colour or \ngreyscale  change corresponds to the 3 dB change of spin wave \namplitude  relative to  the maximal amplitude .  \n \nThe pattern in Fig. 4 describ es the distribution of \nspin wave amplitude in the YIG film plane . As it is seen \nfrom Fig.  4 surface spin wave has noncollinear \norientation of the wave vector k0 and group velocity \nvector V0. It should be noted, that in isotropic media such \nbeam ( having  ratio λ0/D = 0.222) would have angular \nwidth about 12o whereas in Fig.  4 spin wave beam has \nabsolute angular width Δ ψexp = 0.4o and relative angular \nwidth σexp = 0.03! These experimentally measured values \nΔψexp and σexp are slightly differ from calculated zero \nvalue . This fact is explained as follows: since the aperture \nof the receiving probe is 0.5 mm and the maximal length \nof the spin wave trajectory is ~ 50 mm  (because of the \npresence of dissipation  in real YIG films ), the minim al \nangle that can be measured is ~ 0.5 /50/2 = 0.005 rad  \n0.3o. Unfortunately, we have to state that since spin \nwaves, in contrast to light  waves , propagate only at a \ndistance ~ 50 mm, so it is possible to measure only the 4 \n \nangular beam width exceeding  0.3° by means of a probe \nwith aperture 0.5 mm . Mention must be made that the usе  \nof the probe with a smaller aperture does not increase the \naccuracy of measurement at the large distances because \nthe probe sensitivity is decreased proportionally to the \naperture size. We also note that, since the \nsuperdirectional  beam does not expand pr actically, the \norientation ψ0 of the group velocity vector for this beam  \ncan be measured with the highest accuracy.   \nIn order to demonstrate how strongly the relative \nangular beam width σ can change in anisotropic media, \nwe study also visualized picture of the surface spin wave \nbeam  propagation  for the geometry , where relative \nangular beam width σ has high value ~ 2.  As it may seem \nfrom Fig. 3b,  geometries characterized by the value σ ~ 2 \ncan be realized at angles  φ0 lying near angle s of cut off \nφcut, but these geometries can ’t be realized because it is \nimpossible to excite spin waves with very large value of \nthe wave number  k0. However, value σ ~ 2 appears also \nin the geometr ies, where surface spin wave is excited by \nlinear transducer oriented closely to the vector  H0, i.e. at \nφ0 ~ 0 (Fig. 3b) . Below we describe the beam propagation \nfor the most widely used  geometry where transducer is \norientated along vector  H0. Superposition of both \namplitude and phase d istribution s for th is geometry is \nshown in Fig. 5 for spin wave frequency f0 = 3242  MHz , \nk0 = 110.8  cm-1 (λ0 = 567 μm ) and  λ0/D = 0.113 .  \nAs one can see from Fig. 5 , maximal part of the \nspin wave energy is transferred along the group velocity \nvector V0 in the form of the gradual widening main beam, \nhaving angular width Δψexp = 12.9о (in the Fig. 5 brigh test \narea located along y axis corresponds to the main beam ). \nThe experimental value Δψexp is measured for the part of \nthe beam lying at interval y < 22 mm. At y > 22 mm \namplitude of the beam is small and it is hardly to analyze \namplitude distribution in the plane of ferrite film with \ngood accuracy . Note, that little part of the spin wave \nenergy spreads on the whole rest of area located between \ntwo straight lines corresponding to the cut -off angles ψ1cut \nand ψ2cut of the group velocity  (Fig.  5). Large deep areas \nlocated below these straight lines correspond  to the ferrite \nfilm regions in which spin wave can’t exist . Most dark \nnarrow angle s ectors  in the Fig.  5 located along  the \nangles, at which magnetic potential of the spin wave \nbeam is equal to zero (amplitude d istribution for \nmagnetic potential of studied spin wave beam in the far-\nfield region is similar to the d istribution shown in the Fig. \n5 (curve 1) in [2]). On the contrary , brightest area near \nthe y axis in the Fig.  5 correspond s to the greatest \nmaximum of the magnetic potential d istribution.  \nIt is usually assumed that if the exciting linear \ntransducer  is oriented parallel to the vector H0, a surface \nspin wave with collinear orientation of the vectors k and \nV is excited in a ferrite film  and both k and V vectors are \ndirected exactly along the optical axis y (named also axis \nof collinear propagation).  However, as it is seen from Fig. 5, the spin wave fronts are slightly inclined respect to \nthe transducer  line and the beam path ( location of the \ngreatest beam maximum ) is only approximately  directed \nalong y axis – in fact inclin ation of the beam path to the y \naxis is about 5°. This inclination arises because of at \n~3 GHz  (wavelength ~10 cm) there is a small phase \ndifference between the initial and final points of exciting \nlinear transducer  (distance between these points is 5 mm)  \nand this phase difference leads to the certain inclinat ions \nfor both wave vector k and group velocity vector V from \nthe normal to the exciting transducer  line. Thus, exactly \nspeaking, linear transducer  is not cophased exciter at \nmicrowaves .  \n \n \nFig. 5. Superposition of a mplitude and phase \ndistribution s in the plane of ferrite film for the beam  of spin \nwave with collinear vectors k and V. Beam has the next \nparameters: f0 = 3242 MHz, k0 = 110.8  cm-1, λ0 = 567 μm, \nλ0/D = 0.113, φ0 = 0o, Δψ exp = 12.9о, σexp = 2. . Colour or \ngreyscale  change corresponds to the 3 dB change of spin wave \namplitude  relative to  the maximal amplitude . Spin wave front s \nwith the same phase are shown al so.  \n \nComparison of parameters for spin wave beam in \nFig. 4 and 5 shows that the beam in Fig. 4 almost does \nnot change its width along the whole its trajectory  (Δψexp \n= 0.4o and σexp = 0.03 ). Quite the contrary, spin wave 5 \n \nbeam in Fig. 5 is significantly expanded (Δψexp = 12.9o \nand σexp = 2), despite the fact that  for this beam the ratio \nλ0/D = 0.113 is 2 times smaller than the ratio λ0/D = 0.222 \nfor th e beam in Fig. 4. The experimental results are in \ngood agree ment  with theoretical investigations, \ncalculations and formulas in the work [1, 2].   \nIn summary , we investigate experimentally the \ndiffraction  pattern s of the surface spin wave excited by \narbitrarily oriented linear transducer in tangentially \nmagnetized ferrite film for the case wh ere the transducer \nlength D is much larger than the wavelength λ0. In the \nstudy there is used the scanning probe  method , that give \npossibility to visualise the amplitude and phase \ndistribution s of the spin wave along the film surface. The \nangular be am width of spin waves is measured \nexperimentally and is calculated theoretically by means \nof the general formula derived in [2] for the angular beam \nwidth in anisotropic media . It is proved experimentally \nthat as a distinct from the beams in isotropic media the \nangular beam width ψ of the surface spin wave is not \nconstant  value: it depends on transducer orientation φ0 \nand can take values greater  or smaller  than the ratio λ0/D \n(where λ0 is exited wavelength and D is the exciter \nlength) . Moreover, it is found such experimental \nparameters and transducer orientation, at which angular \nbeam width ψ is about zero  (it means physically, that \nthe beam retains its absolute width during propagation) . \nThus it is shown that such phenomenon as \n“superdirectional  propagation of the waves” exist s in the \nnature . This phenomenon  takes place when the wave \nvector orientation φ0 (or the transducer orientation) \ncorresponds to the inflexion point of i sofrequency \ndependence for the excited spin wave.  It is also evidently \nthat well known Rayleigh criterion used in isotropic \nmedia can ’t be used to estimate the angular width of spin \nwave beams . An example of the surface spin wave \ndiffraction gives us hope that the same diffractive \nphenomena can take place in the other anisotropic media \nand structures.  \nIn addition it was found that linear transducer \noriented parallel to external constant magnetic field H0 \nexcites surface spin wave with wave vectors k and group \nvelocity vector V which are only approximately directed \nalong the perpendicular to the vector H0, since there is a \nsmall phase difference between the initial and final points \nof linear transducer .  \nThe experimental results  are in good agreement \nwith theoretical investigations, predictions, calculations \nand formulas on the basis of works [1, 2].  Moreover , on \nthe basis of theory [1, 2] it was predicted another \ngeometry in which superdirectional  spin wave beam \n(with zero angular width) can be excited  [4, 5].  \nThe work is supported by Russian Foundation for \nBasic Rese arch (project No. 17 -07-00016 ).  \n \n * edwin@ms.ire.rssi.ru  \n \n[1] Edwin H. Lock. Cornell University  Library : \nhttp://arxiv.org/abs/1112.3929  \n[2] E. H. Lock. Physics -Uspekhi. 55, 1239 (2012).  \n[3] R.W. Damon, J.R. Eshbach. J. Phys. Chem. Solids 19, \n308 (1961) .  \n[4] E. G. Lokk. J. Commun. Technol. Electron . 60, 97 (2015).  \n[5] A. Yu. Annenkov, S. V. Gerus and E. H. Lock  in Book of \nAbstracts of Moscow International Symposium on \nMagnetism, Moscow, 1 – 5 July, 2017, p. 1089.  \n[6] V. Veerakumar and R. E. Camley. Phys. Rev. B 74, \n214401 (2006).  \n[7]  A.V. Vashkovsky, V.I Zubkov, E.H. Lock  and V.I. \nShcheglov. IEEE Trans. on Magn. 26, 1480 (1990).  \n[8] A.Yu. Anne nkov, I.V. Vasil’ev, S.V. Gerus and  S.I. \nKovalev. Tech. Phys. 40, 330 (1995).  \n[9] A.Yu. Annenkov  and S.V. Gerus. J. Commun. Technol. \nElectron . 57, 519 (2012).   \n[10] S.O. Demokritov and V.E. Demidov. IEEE  Trans . on \nMagn . 44, 6 (2008).  "    },    {        "title": "1202.4135v1.Nanoscale_austenite_reversion_through_partitioning__segregation__and_kinetic_freezing__Example_of_a_ductile_2_GPa_Fe_Cr_C_steel.pdf",        "content": "1 \n Nanoscale austenite reversion through partitioning , segregation, \nand kinetic freezing: Example of a ductile 2 GPa Fe-Cr-C steel \n \n \n \nL. Yuan1, D. Ponge1, J. Wittig1,2, P. Choi1, J. A. Jiménez3, D. Raabe1 \n \n1  Max-Planck -Institut für Eisenforschung, Max -Planck -Str. 1, 40237 Dü sseldorf, Germany  \n2  Vanderbil t University, Nashville, TN 37235 -1683, USA  \n3  CENIM -CSIC, Avda. Gregorio del Amo 8, 28040 -Madrid, Spain  \n \n \n \nAbstract   \nAustenite reversion during tempering of a Fe -13.6Cr -0.44C (wt.%) martensit e results in an ultra -\nhigh strength ferritic stainless steel with excellent ductility. The austenite reversion mechanism is \ncoupled to the kinetic freezing of carbon during low-temperature partitioning at the interfaces \nbetween martensite and retained austenite and to carbon segregation at martensite -martensite grain \nboundaries. An advantage of austenite reversion is its scalability, i.e., changing tempering time and \ntemperature tailors the desired strength -ductility profiles (e.g. tempering at 400°C for 1 min. \nproduces a 2 GPa ultimate tensile strength (UTS) and 14% elongation while 30 min. a t 400°C \nresults in a UTS of ~ 1.75 GPa with an elongation of 23%).  The austenite reversion process, \ncarbide precipitation, and carbon segregation have been characterized by XRD, EBSD, TEM, and \natom probe tomography (APT) in order to develop the structure -property relationships that control \nthe material’s strength and ductility.  \n \n \nKey words : austenite reversion, partitioning, diffusion, strength, ductility, ultra high strength, \ncarbon  partition ing, martensi te, stainless steel, atom probe tomograph y, electro n backscatter \ndiffraction  *Text only\nClick here to view linked References2 \n   \n1. Introduction  \nA high demand exists for lean, ductile, and high strength Fe-Cr stainless steels in the fields of \nenergy conversion, mobility, and industrial infrastructure . As c onventional  martensitic stainless \nsteels (MSS) typically exhibit brittle  behavior , supermartensitic Fe-Cr stainless steel s (SMSS ) with \nenhanced ductility  have been designed in the past years by reducing carbon (<0.03  wt.%) and \nadding nickel (4% -6.5 wt.%) and molybdenum (2.5  wt.%) [1-4]. The heat-treate d microstructure s of \nthese materials  are characterized by tempered martensite and retained austenite[1-4].  \nIn this work  we present an alternative approach of designing MSS steels  with both, high strength \nand ductility . Our method is based on nanoscale austenite reversion and martensite relaxation  via a \nmodest heat treatment  at 300-500°C for several minutes . We make the surprising observation that \nthis method  leads to very high strength (up to 2 GPa) of a Fe -13.6Cr -0.44C  (wt.%) steel without \nloss in duct ility (X44Cr13, 1.4034, AISI 420 ). \nQuenching followed by tempering is known to improve the strength and toughness of martensitic \nsteels[5-7]. Specifically , quench  and partition ing (Q&P) treatments are efficient for produc ing steels  \nwith retained austenite  and improved ductility[8]. The heat treatment sequence for Q&P steel \ninvolves quenching to a temperature between the martensite -start (Ms) and martensite -finish (M f) \ntemperatures, followed by a  partitioning treatment either at, or above, the initial quenc h temperature . \nPartitioning is typically designed in a way to enrich and stabilize the retained austenite with carbon  \nfrom the supersaturated  martensite  [9]. In conventional Q&P pr ocess es, the quench temperature i s \nhence chosen in a way that some retained austenite  prevails and subsequent tempering  leads to \ncarbon partition ing between martensite and austenite. Typically,  no new austenite is formed during \npartitioning .  \nIn our study  we modify this approach with the aim to increase the amount of austenite during low-\ntemperature partitioning. We start with austenitization and water quenching to room temperature. \nThis provides a martensitic -austenitic starting microstructure. During a subse quent heat treatment  in \nthe range 300°C -500°C , austenite reversion[10-15] takes place on the basis of partial partitioning  \naccording to local equilibrium , segregation , and kinetic freezing of carbon inside the newly formed \naustenite .  \nIt is important to po int out that the phenomena occurring during austenite reversion are in the \npresent case different from conventional Q&P approaches : In Q&P processing, the carbon diffuses 3 \n from martensite into the already present austenite during tempering  where equilibrati on of the \ncarbon  distribution inside the austenite is generally assumed . In the current case  of low -temperature \npartitioning , however, the carbon is enriched in front of the austenite boundary and accumulates \nthere since it has a much higher  diffusion rate in bcc than in fcc. The accumulated carbon at the \nmartensite -austenite interface than provide s a high local driving force for austenite reversion.  Once \ncaptured by the growing austenite, the carbon is kinetically frozen owing to its small m obility in fcc.  \nThe phenomena occurring during austenite reversion in Fe-Cr-C stainless steels are compl ex due to \nthe high content of carbon and substitutional alloy ing elements . In contrast to typical Q&P steels \nwhere carbide precipitation  (M3C) is suppressed by alloying with Si and/or Al[16], in the present  \nalloy M3C-type carbide precipitation occurs at 400°C.  This means that a kinetic and thermodynamic \ncompetition  exists for carbon between austenite reversion , enrichment of retained austenite,  and \ncarbide formation during tempering.  \nTherefore, the partitioning temperature  must be chosen on a theoretically well founded basis for \ntwo reasons : First, low temperature annealing  requires more local carbon enrichment to provide a \ndriving force high en ough for austenite reversion . We emphasize in this context that the local \nequilibrium matters for this process, i.e. a high carbon content is required at the martensite -\naustenite interface  (not everywhere within the austenite) . Equilibration of the carbon inside of the \naustenite is not necessarily required.  Second, high temperature annealing may cause  more carbide  \nform ation , consuming too much carbon , so that austenite reversion is suppressed  due to an \ninsufficient carbon  chemical potential to promote it .  \nIn order to elucidate the  competing phenomena  occurring during such low -temperature partitioning , \nnamely , carbide formation vs. austenite reversion  as well as the carbon redistribution  inside the \nretained and reversed austenite fractions , atom probe tomogr aphy (APT) was used . This method \nallows us to measure the carbon content inside the austenite, which determines its stability , as well \nas inside the martensite and the carbides [17-28]. The APT  method allows for three -dimensional  \nelemental map ping with nearly atomic resolution  and provides information about internal interfaces \nand local chemical gradients[28-32].  \n \n2. Experiment al \nThe material used in this study was a martensitic stainless steel with the chemical composition Fe-\n13.6Cr -0.44C (wt.% ; 1.4034, X44Cr13, AISI 420 ) which  was provided by Thy ssenKrupp Nirosta 4 \n as a cold rolled sheet , table 1 . The Ae3 temperature , calculated by Thermo -Calc[33] using the TCFE 5 \ndata base[34], indicates that the incipient holding temperature for full austenitization should be above \n800°C. The calculation further reveals that full dissolution  of chromium carbides in austenite is \nachieved at about 1100°C. Hence, the annealing conditions were set to 1150°C for 5 minutes.  \nDilatometer tests were performed using a Bähr Dil 805 A/D quenching and deformation device  to \nidentify the M s temperature during quench ing. After water quench ing, tempering at  300°C,  400°C , \nand 500°C , respectively,  with different holding times was performed to study carbon redistribution , \naustenite  reversion , and carbide formation (Fig. 1).   \nMechanical properties were determined by tensile and Vickers hardness measurements (980N load, \nHV10). Tensile tests were carried out along the rolling direction of the samples at room temperature. \nFlat tensile sp ecimens were machined with a cross section of 2.5mm x 8mm and a gauge length of \n40mm. The tests were conducted on a Zwick/Roell Z100 tensile testing machine at a constant cross \nhead speed of 1mm/min, corresponding to an initial strain rate of 4.2 10-4s-1. \nThe volu me fraction of the austenite phase after heat treatments (carbide dissolution annealing and \ntempering at 400ºC for 1, 2, 10 and 30 minutes) was measured by x -ray diffractometry (XRD), \nelectron back scattering diffraction (EBSD),  and magnetic charac terization (Feritscope MP30E -S).  \nEBSD samples were prepared by standard mechanical grinding and polishing procedures  normal to \nthe rolling direction . Subsequently, these samples were electropolished using Struers electrolyte A3 \nat room temperature using a  voltage of 40V, a flow rate of 20/s and a polishing time of 20 s. EBSD \nwas performed on a JEOL -6500F high-resolution field-emission scanning electron microscope \noperated at 15  kV [35].  \nX ray diffraction (XRD) measurements were carried out using Co Kα radiation. XRD data were \ncollected over a 2  range of 30 -138º with a step width of 0.05º and a counting time of 10 s/step. \nThe Rietveld method was used for the calculation of the structural parameters from the diffraction \ndata of the polycrystalline bulk materials. We used version 4.0 of the Rietveld analysis program \nTOPAS (Bruker AXS). The analysis protocol included consideration of background, zero \ndisplacement, scale factors, peak breath, unit cell parameter , and texture parameters. The room \ntemperature  structures used in the refinement were martensite/ferrite and austenite.  \nThin foils were prepared using standar d twin-jet electropolishing from the as -quenched material \nand the tempered samples  before and after deformation[36]. These samples  were examine d in a \nPhilips  CM 20 transmission electron microscope (TEM) at an acceleration voltage of 200 kV  to 5 \n characterize the carbide evolution and the formation of reverted austenite . Carbide characterization \nwas also carried out by using a carbon extraction replica technique[37] and investigated by electron \ndiffraction and energy dispersive spectroscopy (EDS)  in the TEM . \nNeedle -shaped APT samples were prepared  applying a combination of standard electropolishing \nand subsequent ion-milling  with a focused -ion-beam (FIB) device. APT analyses were performed \nwith a local electrode atom probe ( LEAPTM 3000X HR ) in voltage mode at a specimen temperature \nof about 60 K. The pulse to base voltage ratio and the pulse rate were 15% and 200 kHz , \nrespectivel y. Data analysis was performed using the IVAS software (Cameca  Instruments ).  \n \n3. Results  \n3.1 Mechanical properties  \nThe as-received cold rolled and recrystallized material has an ult imate  tensile strength (UTS) of 640 \nMPa and a uniform elongation of 19% , Fig. 2a . After austenitization at 1150°C and water \nquench ing, the material is brittle and fail s before the yield stress is reached at a stress of 400 MPa  \n(Fig. 2a). Thus, the true UTS for the as quenched state could be only estimated from the indentation \nhardness . The relationship between Vickers hardness (HV) and tensile strength was calculated \nconsidering a linear relationship of the form HV = K × UTS.  A constant K of 3.5 was \ndetermined by linear regression through data obtained from the hardness and UTS valu es obtained \nfrom samples after tempering at 400ºC for different times. Fig 2e  suggests that  the hardness for the \nas-quenched state corresponds to a tensile strength of more than 2300 MPa.  \nFig. 2a also shows the stress -strain curves obtained from the tensil e tests performed on samples \ntempered at 400ºC for different times.  The most remarkable feature of these curves is the transition \nfrom a brittle behavior in the as quenched material to a ductile one after tempering. When the \ntempering time is increased, w e observe an increase in uniform elongation and a decrease in UTS.  \nAfter 30 minutes, the uniform elongation of the sample reaches a value of about 22% and a UTS \nabove 1760 MPa.  This value for the UTS can be also reached upon tempering at 500°C, but in th is \ncase, a gradual increase in total elongation upon increase in tempering time is not observed, Fig 2b.  \nIt can be observed that in this case the stress does not go through a maximum; that is, /e (the \npartial derivative of the stress with respect to st rain) does not go through zero. This would indicate \nthat the sample fractures before the strain reaches the necking value. At 300°C, after 1 minute, the \nductility improves slightly, i.e. longer tempering is required for obtaining better ductility at this 6 \n temperature, as shown in Fig. 2c. When comparing the mechanical properties of samples tempered \nat different temperatures (Fig. 2d), the 400 °C treatment yields the optimum improvement in both \nUTS and total elongation (TE).  \n \n3.2  Phase fraction s and kinetics: predictions and experiments  \nThermo -Calc was used to calculate the phase equilibrium  at the different partition ing temperatures . \nFor evaluating kinetics during heating and cooling, we conducted dilatometer tests (Fig. 3 ). The \nheating and cooling rates were  set to 10  K/s and -30 K/s, respectively . Above 876°C, the \nmicrostructure is fully austeni tic. The M s temperatures were derived from the dilatometer tests \n(118°C after 1150°C annealing and 360°C after 950°C annealing).  The Thermo -Calc calculation s \nwere used  to predict the equilibrium carbon content of the austenite after annealing at different \ntemperature s (Fig. 3c).  \nFig. 4 shows the phase fraction of austenite versus tempering time for 400°C  measured by \nferitscope (magnetic signal), EBSD, and XRD. For the as-quenched state the EBSD result provides \na higher volume fraction (20%) than the magnetic (14.5%) and the XRD data (8%) which is \nattributed to the limited statistics of the EBSD method. During the first 2 minutes  of tempering  the \namount of austenite incr eases rapidly , indicating austenite  reversion . After 30 minutes, nearly 40  \nvol.% austenite is observed  consistent ly for all three methods .  \nFig. 5 shows in situ EBSD observations of the austenite during tempering . Fig. 5(a) maps the \nmaterial in the as -quenched state containing only retained austenite.  Fig. 5(b) shows the same area \nduring the in-situ experiment containing both, retained plus reverted austenite after 5 minutes \ntempering at 400°C  subsequent to the quenching treatmen t. The EBSD map reveals the fine \ndispersion of the n ewly formed reverted austenite after 5 minutes . We observe two kinds of \naustenite, namely, one with a coarse topology and another one with a fine and disperse d topology . \nThe microstructures of the samples  tempered for 0, 1 and 2 minutes , respectively,  are shown in Fig. \n6. The as-quenched material (0 minute  tempering) is brittle and failed already in the elastic regime \nduring tensile test ing. From the microstructure it can be seen (Fig. 6 b, left: before tensile test; right: \nafter tensile test , for each state ) that only a small amount of austenite was transformed to martensite \nwhen the material failed , i.e. austenite bands can still be observed near the f racture  interface . For \nsamples after 400°C tempering , no premature failure takes place and the total elongation (TE) \nreaches 14%  (engineering strain) . The microstructure at the fracture zone show s nearly no 7 \n remaining austenite. This observation indicat es that deformation -driven austenite -to-martensite \ntrans formation t akes place. Secondary cracks along the tensile direction are visible in the EBSD \nmaps . It seems that these cracks follow the band -like former retained austenite regions, which \ntransformed during straining into martensite.  \n \n \n3.3 TEM characterization  \nAfter solid solution and subsequent water quenching, we found no retained austenite in the TEM \nfoils (Figs. 7a,b). This is in contrast to the results obtained from the EBSD maps which show \nretained austenite in the as -quenched state (Figs. 5,6). We attribu te this discrepancy between TEM \nand EBSD results to the fact that the as -quenched metastable retained austenite - when thinned for \nTEM analysis - is no longer constrained by the surrounding martensite and hence transforms into \nmartensite.  \nAfter 1 minute t empering at 400°C we observe a high tensile strength of 2 GPa, Fig. 2a. The \ncorresponding microstructure was monitored by TEM, Fig. 7. Figs. 7c,d give an overview of the \nnanoscaled elongated carbides formed during tempering.  \nThe carbides have an average l ength of 70nm and an average width of 5nm. After 30 minutes \ntempering the average particle spacing is about 80nm and the length 110 nm. The carbides after 1 \nminute tempering at 400°C were examined via carbon extraction replica. The diffraction patterns \nreveal that they have M 3C structure. This means that the formation of M 23C6 carbides is suppressed \nat such a low tempering temperature. Energy Dispersive Spectroscopy (EDS) analys es show ed that \nthe metal content in the carbide (M in M 3C) amounts to 74 at.%  Fe and 26 at.% Cr, i.e. the Cr/Fe \natomic ratio is 0.35. Th e measured chromium content in  the M 3C carbides significantly  deviates \nfrom the nominal chromium concentration of 14.2 at.% Cr / 82.5 at.% Fe = 0.17.  \nFig. 7e shows the formation of a thin austenite  layer that is located at a former martensite -\nmartensite grain boundary. Fig. 7f is a close -up view of a thin austenite zone that is surrounded by \nmartensite. Electron diffraction analysis reveals that a Kurdjumov -Sachs orientation relationship \nexists betw een the martensite matrix and the thin austenite layer, Fig. 7g [38]. In line with the in -situ \nEBSD results in Fig. 5 , where we observed reverted austenite formed between martensitic grains, \nthe austenite film observed here in TEM might be either retained or reversed austenite. In order to \ndetermine more reliably which of the two kinds is observed local atomic scale chemical analysis is 8 \n conducted by using APT as outlined below. The two types of austenite can then be distinguished in \nterms of their carbon co ntent : Retained austenite has at first the nominal quenched -in C content \n(about 2 at.% in the present case) of the alloy while reverted austenite has a higher C content (up to \n9 at.%) owing to local partitioning and kinetic freezing.   However, we also have  to account for the \npossibility that the retained austenite can have a higher C content as the lath martensite mechanism \nis slow enough to allow for som e C diffusion out of th e martensite into the retained austenite during \nquenching.  \n \n3.4 Atom probe tomography  \nThe local chemical compositions and their changes during 400°C tempering of the martensite, \naustenite, carbides, and interface regions were studied by atom probe tomography. Phase \nidentification is in all cases achieved via the characteristic carbon content s of the present phases . \nFig. 8 shows the 3D atom  maps  after water quenching (Fig. 8a) , water quenching plus tempering at \n400°C for 1 min (Fig. 8b) , and water quenching plus tempering at 400°C for 30 minutes (Fig. 8c). \nCarbon atoms are visualized as  pink dots and carbon iso -concentration surfaces in green for a value \nof 2 at.% . This value corresponds to the nominal carbon concentration of the alloy of 0.44 wt.%. \nThe different phases (martensite, austenite, carbide) are marked. They were identified in terms of \ntheir characteristic carbon content and the TEM and EBSD data presented above. For more \nquantitative analys es, one-dimensional compositional  profiles of carbon across the martensite -\nmartensite and martensite -austenite inter faces were plotted ( along cylinders marked in yellow in the \n3D atom maps ). \n \n3.4.1 As-quenched condition  \nFig. 8a reveals that in the probed volume carbon is enrich ed along the martensite -austenite interface. \nThe interface region , shown as composition  profile in Fig. 8a , reveals an average  carbon \nconcen tration of about 1.90 at.% in  the austenite with strong local variations and of about 0.98 at.% \nin the abutting supersaturated martensite. The carbon concentration in the austenite nearly matches \nthe nomi nal carbon concentration of the alloy. Some carbon clusters occur in both phases . The \ncarbon concentration in these clusters is abo ut 3 at.%, i.e. they are not carbides. In a thin interface \nlayer of only about 5 nm , the carbon content is very high and reaches a level  of 4-6 at.%.  In contrast 9 \n to the variation in the carbon distribution, the chromium content is the same in the martensite, the \ninterface, and the austenite, Fig. 8a.  \n \n3.4.2   400°C t empered condition  after quenching  \nAfter 1 minute tempering  at 400°C , a carbon enriched austenite layer (15 -20 nm width) is observed \nbetween two abutting martensite regions  (Fig. 8b). The thin austenite zone contains in average \nabout 6.86 at.% carbon  while the martensite  matrix contains only about 0.82 at.% carbon. The \nidentification of the phases in these diagrams follows their characteristic carbon  content .  \nAfter 30 minutes tempering  (Fig. 8c) , different carbon enriched areas appear. They correspond to \nindividual phases. The analyzed volume can be divided into 2 zones . The top region with low \ncarbon content corresponds to martensite . The bottom zone with higher carbon content corresponds \nto austenite. Inside the martensitic region there are areas with very high carbon content  (see arrow \nin Fig. 8c). The carbon content is 25.1 at.% in this particle indicating M 3C cementite  stoichiometry . \nIn the martensitic matrix surrounding the precipitate the carbon content amounts to only 0.48 at.%. \nCarbon partitioning to  the different phases  can be quantified in terms of an enrichment factor ε =(at.% \nC tempered)/(at .% C as quenched)  to compare the composition s in the phase s before and after \ntempering . The observed value s of ε for each state are listed in Table 2.  The carbon content in the \nmartensite decreases continuously duri ng tempering , which can be ascribed to carbon partitioning \nfrom the super -saturated martensite to the austenite and to carbide formation  [39-50].  \n \n4. Discussion  \n4.1 Mechanism s of partitioning and austenite reversion  \nThe microstructure observed by EBSD and TE M allows us to monitor the austenite development  at \nthe mesoscopic scale : during the initial high temperature solution annealing  in the austenitic regime  \n(1150°C for 5 minutes) , all carbides were  dissolved (Fig. 3c). The high content of solute carbon that \nis present in the austenite after carbide dissolution decreases the M s and the Mf temperature s of the \naustenite below room temperature . Hence, 8-20 vol.% retained austenite exists  after quenching the \nsolution annealed material to room temperature , Fig. 4. The differences in retained austenite are due \nto the individual precision of the different characterization methods. EBSD provides a direct \nmethod and hence is assumed to give a realistic value within its statistical limits.  10 \n After tempering at 400°C for 30 minutes t he area fraction of austenite increases to about 40%. This \nchange documents that strong austenite reversion take s place even at this low temperature. The \nlocal variation s in the austenite dispersion after short tempering were larger compare d to longer \ntempering time s. We attribute this heterogeneity in the re -austenitization kinetics and topology to \nthe mean diffusion range of the carbon  and to the distribution of the carbon sources. Using the data \nof Speer et al. [40] for the diffusion coefficients in ferrite D α= 2×10-12 m2/s and in austenite Dγ= \n5×10-17 m2/s we obtain a mean free path for carbon of 1.5×10-4 m in ferrite and 7.4×10-7 m in \naustenite at 400°C and 30 minutes.   \nThis means that austenite reversion starts at decorated defects (e.g. internal interfaces) where the \nlocal carbon concentration is high enough and the nucleation energy low enough to promote the \nformation of this phase. Fig. 7e confirms this assumption. The TEM analysis also suggests that \naustenite re version proceeds via a Kurdjumov -Sachs orientation relationship. Shtansky et al .[38] \nfound the same crystallographic relationship during reverse transformation in an Fe –17Cr –0.5C \ntempered martensite  (wt.%) . \nAn important aspect of the pronounced austenite reversion in the current case is that the competing \nformation of M 23C6 carbide s is suppressed at 400°C.  This means that more carbon is available to \nstabilize and promote austenite formation  [38,45-47]. \nWe used Thermo -Calc predictions[33,34] to estimate  the driving force for austenite revers ion for the \ncurrent alloy and the employed tempering conditions , Fig. 9b . The results reveal that if the carbon \nconcentration in the bulk martensite (α’) exceeds 1.21 wt.% (5.45 at.%), austenite (γ) will form at \n400°C , provided that the nucleation barrier is overcome . This result confirms our suggestion made \nabove, namely, that no bulk austenit ization  can occur at this temperature since the average carbon \ncontent of the matrix is too low. Instead we a ssume that only certain lattice defects (interfaces) that \nexperience very high elastic distortions and carbon segregation can provide the nucleation \nconditions and a sufficiently high carbon concentration for local austenite formation , Fig. 7 e,f,g, \nFig. 8 . This leads to an increase in the overall austenite fraction. Fig. 6a shows that a 2 minutes heat \ntreatment at 400°C leads to an increase in the austenite content from 18.9 vol.% to 29.7 vol.%.  \nThermo -Calc predictions show that in the current alloy carbon  provid es the required driving force \nfor this low-temperature austenite reversion . Substitutional atoms , particularly  Cr, do not participate \nin reversion in the current alloy owing to their limited mobility at 400°C , i.e. the driving force for 11 \n transformati on is here provided exclusively by the high carbon enrichment rather than by \nsubstitutional depletion of the austenite , Fig. 8a [39].  \nBased on these thermodynamic boundary conditions t he APT results  allow us now to monitor and \nevaluate the kinetics of carbon at different stages of tempering in more detail (Fig. 8). Fig 8a shows \nthe as quenched state: During solution annealing where the material is completely austenitic the \nelements distribute homogeneously  within that phase .  \nAt the onset of water qu enching, the majority of  the austenite starts to transform into martensite \nwithout at first changing its chemical composition. However, as the solubility of carbon in the \nquench ed-in martensite is very small, carbon starts to leave the martensite during an d after the γ→α’ \ntransformation and enriche s at the γ -α’ interfaces , Fig. 8 a [45.-50]. This process can happen extremely \nfast: Speer  et al. [40,41 ] show ed that carbon partitioning between martensite and austenite in a 0.19C -\n1.59Mn -1.63Si (wt.%) steel required at 400°C less than 0.1s owing to the relatively high diffusion \nrate of carbon in martensite. In contrast, the further distribution of the newly acquired carbon within \nthe austenite is nearly three orders of magnitude more slowly  [40-50]. This mean s that in this case the \nescape rate of carbon from the newly forming lath martensite is much higher than the carbon \nequilibration within the austenite  [48-50]. \nIn the present quenching process, carbon segregation takes place even faster  than in the study \nquoted above[40,41]. In the current case the c arbon has already started to partition and segregate at \nthe martensite -austenite interfaces during the early stages of water quench ing immediately after the \nfirst martensite has formed[45-50]. Th e fast kinetics is due to the high mobility of carbon  in \nmartensite , table 3. Such pronounced c arbon segregation at the martensite -austenite interfaces is \nclearly observed in the as quenched state  (Fig. 8a) . In the interface area the carbon content reach es \nup to 4-6 at.%  within a narrow layer of about 5 nm . This value is clearly above the nominal \ncomposition that purely retained austenite would have[45-50]. Owing to the high escape rate of \ncarbon from the martensite this zone is interpreted as a port ion of initially retained austenite which \nhas been enriched in carbon during quenching  [45-50]. \nAs explained above this high level of carbon segregation in the present case is a consequence of \ntwo effects, namely, first, the rapid carbon escape from the ne wly formed martensite and second, \nthe low mobility of carbon within the retained austenite . According to table 3  at 400°C in 1 minute \ncarbon can diffuse 27.000 nm in the martensite and only 130 nm in the austenite[40]. Other sources \nsuggest a 10-20% smaller mean free path  of carbon in the martensite [43,44]. 12 \n Hence, t he carbon segregation observed after quenching (Fig. 8a) is due to a partitioning step and a \nkineti c freezing step (limited mobility of carbon once it arrives in the austenite) . From compa ring \nthis experimentally observed frozen -in value of 4-6 at.%  carbon at the martensite -austenite \ninterface (Fig. 8a) with the value that is predicted by Thermo -Calc as a driving force required for \naustenite reversion at 400°C (5.45 at.%) we conclude that a ustenite reversion will occur under the \ncurrent conditions  at this interface  upon heat treatment .  \nAfter 1 minute tempering  at 400°C , a carbon enriched austenite layer is observed between two \nmartensite regions (Fig. 8 b). In principle this thin austenite layer could originate either from a very \nthin layer of retained austenite that was enriched with carbon due to partition ing from the abutting \nlath martensite  or from austenite reversion without any preceding retained austenite.  If the carbon -\nrich zone wou ld be retained austenite the carbon profile in the austenite region would assume a ‘V’ \ntype distribution . This type of concentration profile  would be characterized by a high content at the \ntwo martensite -austenite interfaces and a low conte nt in the center  of the austenite layer (hence ‘V’) . \nAlso, retained austenite would have the nominal composition, i.e. in the center of the retained \naustenite zone the carbon content should be 2 at.%  or slightly above as in Fig. 8a .  This type of \ncarbon distribution is no t observed though.  Instead, Fig. 8b shows that the carbon profile assumes a \n‘/\\’ shape  within the austenite layer  with a maximum carbon concentration above 8 at.% . It is hence \nplausible to assume that this profile is due to carbon segregation on a former martensite -martensite \ngrain boundary  according to the Gibbs adsorption isotherm . This means that during water \nquench ing the carbon that is segregated at the martensite grain boundary has come  from both sides . \nTherefore, the maximum carbon concentration  revealed in Fig. 8b , which highly exceeds the \nequilibrium concentration that it would have had in the austenite, is in the center of the enrichment \nlayer rather than at its rims . This means that during tempering austenite reversion starts in the \ncenter of thi s carbon enriched area, i.e. at the former martensite -martensite grain boundary. The \nresulting average carbon concentration in this reverted austenite grain is very high , namely, 6.86 at.%  \n(with a maximum above 8 at.%) . The fact that the pronounced ‘/ \\’ shape of the carbon is preserved \n(frozen in) inside the austenite is due to the low mobility of carbon in austenite , table 3 . These \nobservations suggest that th e carbon -rich zone in Fig. 8b is a newly formed austenite layer . If the \ncarbon enriched area had been located between a martensite and an austenite grain,  such as at the \nposition s observed in Figs. 8a and c , the carbon atoms would have arrived only from one side, \nnamely, from the martensite side  (Fig. 9 ). The thickness of the newly formed reverted austenite 13 \n layer in Fig. 8 b is about 15 nm. With increasing tempering time, more reverted austenite is formed  \n(Fig. 4,9).  \nIn summary, t he behavior of carbon in the current alloy can be described as follows: during \nquenching, carbon segregate s to martensite -martensite grain boundaries (equilibrium segregation) \nor to martensit e-retained austenite interfaces  (partitioning plus kinetic freezing) . In the first case \n(equilibrium segregation between two lath martensite zones) d uring tempering, these carbon  \nenriched area s in the martensite revert to austenite  when the driving force is high enough  owing to \nthe favorable nucleation barrier at the interfaces . In the second case (partitioning at retained \naustenite) the carbon enrichment leads to austenite growth  according to local equilibrium. If the so \nreverted austenite is located at or in the vicinity of the austenite -martensite phase boundary, carbon \ncan diffuse from the reverted austenite further into the retained austenite  provided that the \ntempering time i s long enough . This carbon enrich ment  stabilizes the retained austenite . Also, this \neffect makes it generally difficult to distinguish reverted austenite from retained austenite  (Fig. 9). \nAfter 1 minute tempering, the reverted austenite has a high carbon c ontent  of 6.86 at.% ( enrichment \nfactor ε=3.61). With increasing tempering time, the diffusion of carbon from reverted austenite into \nretained austenite leads to an increase in the carbon concentration of the retained austenite. After 30 \nminutes tempering, the carbon concentration in the retained austenite  increases to an average value \nof 2.42 at.% (Fig. 8c ). If the diffusion distance to the nearest phase boundary is too far, e.g. inside \nthe bulk martensite, the high concentration of carbon leads to the form ation of carbides  inside the \nmartensite . \nAfter 30 minutes tempering time, the carbon content in the carbides is 25.1  at.% as measured by \nAPT . This value agree s with the stoichiometric content of carbon in M 3C (25  at.%). Due to the \ncarbon partitioning to au stenite , austenite  reversion , and the competing formation of carbides, the \ncarbon content  of the martensite continuously decrease s during tempering. The amount of carbon in \neach phase before and after tempering is listed in Table 2 for the different stages . The other \nelements, for example chromium , have nearly the same content in both , austenite and martensite. \nThis means that during 400°C tempering, medium range diffusion of carbon can be observed, but \nthe substitutional elements only experience short dist ance diffusion. For all tempering conditions \nanalyzed above we observe that not the nominal (global) but the local chemical potential of carbon \ndirectly at the martensite -austenite and martensite -martensite interfaces and the smaller nucleation 14 \n energy at t he interfaces determine the kinetics of austenite reversion. Similar trends were observed \nin maraging steels during aging [28,51,52]. \nIn a though t experiment , assuming infinite mobility of the carbon when entering from martensite \ninto austenite, the reversion would proceed more slowly  owing to the smaller chemical driving \nforce at the interface when carbon is distributed more homogeneously inside the austenite . In the \ncurrent situations, however, carbon becomes trapped and highly enriched at the martensite -austenite \ninterface owing to the partitioning and its low mobility within the austenite. This provides a much \nhigher local driving force for austenite reversi on. We refer to this mechanism as low temperature \npartitioning and kinetic freezing effect because the carbon is fast inside the martensite when leaving \nit but slow (and, hence, frozen) when entering the austenite. A similar effect was recently observed \nin Fe-Mn steels [28].  \n \n \n4.2 Transformation induced plasticity ( TRIP ) effect  \nDuring tensile  testing, the volume fraction  of austenite decreases not only in the quenched  samples \nbut also in the tempered sample s (Fig. 6). When t he brittle as -quenched sample f ailed  at an early \nstage of loading (Fig. 2a, green curve) , the amount of retained austenite had decrease d from 18.9 to \n10.8 vol.%. At failure most of the quenched -in martensite was still in the elastic regime . This means \nthat stress -induced  austenite -to-martensite transformation prevailed since the material took nearly \nno plastic strain until fracture. After 400°C austenite -reversion tempering, the ductility of the \nmaterial improve s drastically (F ig. 2 ). The EBSD results reveal that nearly all of the aust enite \ntransformed into martensite during tensile testing especially in the near-fracture zones (F ig. 6a,b). \nThis observation suggests that strain -induced austenite -to-martensite transformation (rather than \nstress -induced transformation) prevails in the tem pered samples containing reverted nano -sized \naustenite .  \nThe difference in the displacive deformation behavior between the as -quenched and tempered \nsamples is due to the fact that directly after water quenching, the retained austenite is unstable due \nto its relatively low carbon content . In the as -quenched state (i.e. without tempering) the carbon \ncontent of the retained austenite is equal to the nominal composition after solution treatment . A \nrelatively weak load is, hence, required  to transform this retained and rather unstable austenite into \nmartensite at the onset of the tensile test . Transforming a l arge amount of austenite at the same time , \nnamely, at the beginning of deformation , promotes crack formation and premature failure . In 15 \n contrast to this as -quenched and rather unstable austenite, subsequent tempering  enriches the \nretained austenite with carbon due to partitioning . The higher carbon content stabilizes the retained \nand the reverted austenite  so that austenite  portions with different carbon con tent undergo  the TRIP \neffect at different stage s of deformation . These differences in carbon content of different austenite \nportions in the same sample is due to the fact th at only the local  chemical potential of the carbon at \nthe hetero -interfaces determi nes the partitioning and reversing rates and, hence, also the exact \ncarbon content of the abutting austenite. This means that retained and reverted austenite zones that \nare carbon -enriched through partitioning have a kinetically determined composition whic h is \nsubject to local variations in the chemical potential (of carbon). This context explains the more \ncontinuous displacive transformation sequence in the tempered material and hence the observed \nductility improvement.   \nAnother aspect of the TRIP effect i n this material is that austenite reversion, obtained from \ntempering, does not only stabilize the austenite via a higher carbon content but also increases its \noverall volume fraction at least after sufficient tempering time. Fig. 6a reveals that the austen ite \nfraction increases from 18.9 vol.% after quenching to 29.7 vol.% after 2 minutes at 400°C. \nInterestingly, after 1 minute at 400°C the austenite fraction did not change much. This means that \nfor the short -annealing case (1 minute) the austenite stability and its more sequential transformation \nas outlined above are more important for the ductilization than its mere volume fraction.  \n \n \n4.3 Precipitation development  \nThe TEM and APT observations confirm that the carbides formed during tempering have are of \nM3C type (instead of M 23C6). The formation of M 3C is associated with a smaller loss of chromium \nfrom the matrix (into carbides) compared to M 23C6-type carbides which can have a high chromium \ncontent. Some authors found a sequence of carbide formatio n in Fe -Cr-C systems during tempering  \naccording to  MC → M 3C → M 7C3 + M 23C6 + M6C[53]. In our study  M3C carbide s prevailed up to 30 \nminutes  annealing time . Samples taken from the as -quenched state show the highest hardness due \nto carbon in solid solution. The hardness decrease observed during tempering is related to carbide \nformation because carbon has a higher strengthening effect in solid solution than in t he form of \ncarbides. However, the small carbides (Fig. 8c) also contribute to the strength as observed with \nTEM (see Fig. 7b). The strain hardening rate decreases with increasing tempering time. This might \nbe due to the coarsening of the carbides and due to the increas e in the average carbide spacing 16 \n (from ~ 40 nm after 1 minute to ~80 nm after 30 minutes tempering  at 400°C ).  Further we observe \nthat the yield stress increases during tempering. This might be due to the change in the internal \nstress state of the martensite  matrix . After  water quench ing, high elastic stress es prevail  in the \nmartensite. These lead to early microplastic yielding of the material  prior to percolative bulk plastic \nyielding . During tempering, the internal stress state of the martensi te is relaxed due to the escape of \ncarbon . This leads to a delay in the yielding of the tempered samples.  \n \n \n4.4 Relationship between nanostructure and stress -strain behavior  \nIn the preceding sections we presented experimental evidence of grain boundary seg regation, \nhetero -interface partitioning, kinetic freezing, carbide precipitation, retained austenite  formation \nand stabilization , austenite reversion, and the TRIP effect.  \nIn this part we discuss the joint influence of these phenomena on the  excellent strength -ductility \nprofile of this steel  (Fig. 2 a,d).  \nWe differentiate between mechanisms that provide higher strength and those promoting ductility : \nThe most relevant phase responsible for the high strength of the steel after heat treatment is  the \nrelaxed martensite. The quenched -in martensite with an extrapolated tensile strength of more than \n2300 MPa (approximated from hardness data) is very brittle. Already a very modest heat treatment \nof 1 minute at 400°C though (Fig. 2a) provides sufficien t carbon mobility. This leads to carbon re -\ndistribution (carbide formation, grain boundary segregation, dislocation decoration, martensite -\naustenite interface segregation , austenite solution ) and thus to a reduction in the internal stress es of \nthe martensi te. Th e reduc ed carbon content renders the martensite into a phase that can be \nplastically deformed without immediate fracture.  The second contributi on to the increase in \nstrength are the nanoscaled carbides  which provide Orowan strengthening , Fig. 7 (TEM), Fig. 8c \n(APT).  Their average spacing increases from about 50 nm (1 minute at 400°C) to about 80nm (30 \nminute at 400°C) , Fig. 8b.  These two effects , viz. , conventional martensite strength (via high \ndislocation density, high internal interface density , internal stresses, solid solution strengthening)  \nand Orowan strengthening explain the high strength of the material , but they do not explain its high \nductility.  \nIn this context the TRIP effect, i.e. the displacive transformation of retained and reverted austenite, \nbecomes relevant: Fig. 6a reveals a drop in the austenite content from 29.7 vol.% to about 2.7 vol.% \nduring deformation for the sample heat treated at 400°C for 2 minutes.  Fig. 10 shows the true 17 \n stress -true strain curves and their corresponding derivatives (strain hardening) after 400°C heat \ntreatment at different times. The data reveal that the tempering, which increase s the austenite \ncontent via reversion, leads indeed to higher strain hardening reserves at the later stages of \ndeformation due t o the TRIP effect, Fig. 6b. Since longer heat treatments lead to higher volume \nfractions of reverted austenite the TRIP -related strain hardening assumes a higher level for these \nsamples  (Fig. 10). \nAnother  important effect that might promote ductility in this context is the wide distribution of the \naustenite dispersion and stability (carbon content) which are both characteristic for this material. As \nrevealed in Fig. 8 we can differentiate 3 types of austenite , Fig. 9a : The first type is the as -quenched  \nretained austenite with the nominal carbon content and relatively low stability. The second one is \nretained austenite which assumes an increased carbon content due to partitioning during quenching \nand particularly during heat treatment and has thus higher  stability against displacive \ntransformation. The third type of austenite is the reverted one. These three types of austenite have \ndifferent carbon concentration, volume fraction , and size. Both, carbon content and size affect \naustenite stability. T his mea ns that the displacive transformation during tensile testing and the \nassociated accommodation plasticity occur more gradually upon loading compared to a TRIP effect \nthat affects a more homogeneous austenite . We refer to this mechanism as a heterogeneous TR IP \neffect.  \nAnother important aspect is the composite -like architecture of the reverted austenite, which is \nlocated at the martensite -martensite and at the martensite -austenite interfaces in the form of \nnanoscaled seams (see Fig s. 8 and 11). Such a topology  might act as a soft barrier against incoming \ncracks or stress -strain localizations from the martensite. We hence speculate that the austenite seam \nis a compliance or respectively repair layer that can immobilize defects through its high formability \nand pr event cracks from percolating from one martensite grain into another (Fig. 11).  In this \ncontext it is important to note that conventional martensite -martensite interfaces often have a small -\nangle grain boundary between them which facilitates crack penetrat ion from one lath to another. \nHere, a compliant austenite seam between the laths might hence be very efficient in stopping cracks.  \nWe emphasize this point since the increase in macroscopic ductility can generally be promoted by \nboth, an increase in strain hardening at the later stages of deformation and by mechanism s that \nprevent premature damage initiation.  \n  18 \n  \n5. Conclusions  \nWe studied carbon partitioning, retained austenite, austenite stabilization, nanoscale austenite \nreversion, carbide formation, and kinetic freezing of carbon during heat treatment of a martensitic \nstainless steel Fe-13.6Cr -0.44C (wt.% ).  The main results are: \n(1) Austenite formation in carbon  enriched martensite -austenite interface areas is confirmed by \nXRD, EBSD, TEM, and APT. Both, the formation of retained austenite and austenite reversion \nduring low -temperature partitioning is discussed. The enrichment of carbon  at martensite -\nmartensite grain boundaries and martensite -retained austenite phase boundaries  provides  the \ndriving force f or austenite reversion.  The reverted austenite zones have nano scopic  size (about \n15-20 nm) . The driving forces for austenite reversion are determined by local and not by global \nchemical equilibrium.  \n(2) Martensite -to-austenite reversion proceeds fast. This applies to both, the formation of rever sed \naustenite at retained austenite layers and austenite reversion among martensite laths. The \nvolume fraction of austenite has nearly doubled after 2 minutes at 400°C . \n(3) The carbides formed during tempering have M 3C structure. With increasing tempering time the \ndispersion of the carbides decreases  due to the Gibbs -Thomson effect . \n(4) During tempering between 300°C and 500°C c arbon redistributes in three different ways : \nDuring quenching, in the vicinity of martensite -austeni te interface s, carbon segregate s from the \nsupersaturated martensite to both, the hetero -interface s and to homophase grain boundaries. \nDuring tempering, carbon continuously partition s to martensite -austenite interfaces , driving t he \ncarbon enriched areas towards austenite  reversion  (irrespective of whether the nucleation zones \nwere initially retained or reversed austenite) . Carbon inside martensite , far away from any \ninterfaces, tends to form M 3C carbides.  This means that carbon segregates to martensite grain \nboundaries, to martensite -austenite interfaces , and forms carbides.   \n(5) We differentiate between 3 different types of austenite, namely, first, as -quenched retained \naustenite with nominal carbon content a nd low stability; second, retained austenite with \nincreased carbon content an d higher stability due to partitioning according to the local chemical \npotential of carbon; and third, reverted austenite.  \n(6) The nanoscale structural changes lead to drastic improve ments in the mechanical properties. A \nsample after 1 minute tempering at 400°C has 2 GPa tensile strength with  14% total elongation . \nThe strength increase is attributed to the high carbon content of the martensite and the \ninteraction between dislocations a nd nano -sized carbides . The TRIP effect of  the austenite \nduring deformation, including the reverted nano -scale austenite, contributes to a strain \nhardening capacity and, hence, promotes the ductility.  Also, the topology of the reverted \naustenite is importa nt: We suggest that the nanoscaled seam topology of the austenite \nsurrounding the martensite acts as a soft barrier which has compliance and repair function. This \nmight immobiliz e defects and prevent cracks from growth and inter -grain percolat ion. \n(7) We attri bute the fast nanoscale austenite reversion to an effect that we refer to as kinetic \nfreezing of carbon. This means that the carbon is fast inside the martensite when leaving it but \nslow (and, hence, frozen) when entering the austenite. This means that car bon becomes trapped \nand highly enriched at the martensite -austenite interfaces owing to its low mobility within the \naustenite  during low -temperature partitioning . This provides a much higher local driving force \nfor austenite reversion. This means that the formation of nanoscaled reverted austenite depends \nmainly on the local but not on the global chemical potential of carbon at internal interfaces.  \n 19 \n Acknowledgements  \nThe authors are grateful for discussions on carbon partitioning and martensite tempering with \nProfessor George D.W. Smith from Oxford University.  \n \nTables  \nTable 1:  Chemical composition  of material used for the investigation  (1.4034, X44Cr13, AISI 420).  \n \n C Cr Mn Ni Si N Fe \nwt.%  0.437  13.6 0.53 0.16 0.284  0.0205  Bal. \nat.% 1.97 14.19  0.52 0.15 0.55 0.079  Bal. \n \n \n \n \nTable 2. Change of the carbon content observed in each phase via atom probe tomography during \nannealing, quenching , and austenite reversion . The carbon partitioning to the different phases is \nquantified in terms of the enrichment factor ε=(at.% C tempered)/(at.% C as quenched) which \nallows us to compare the chemical composition in the phases before and after tempering.                        \n \nState of samples  Retained austenite  \n(at.%)  martensite  \n(at.%)  interface  \n(at.%)  reverted  \naustenite (at.%)  \nnominal composition  \n(annealing at 1150°C)  1.97%  -- -- -- \nas quenched  1.90%  0.98%  4.52%  -- \nquenched plus tempering  \n(400°C/1 min)  -- 0.82%  \n(ε=0.84)  -- 6.86%  \n(ε=3.61)  \nquenched plus tempering  \n(400°C/30 min)  2.42%  \n(ε=1.27)  0.48%  \n(ε=0.49)  -- -- \n \n \n \nTable 3. Diffusion data for carbon in ferrite and austenite taken from [40]. For the current heat \ntreatment case of 400°C (673K) the diffusion coefficient in ferrite is D α= 2×10-12 m2/s and in \naustenite  Dγ= 5×10-17 m2/s. The table gives the mean free path for the different tempering stages. \nThe diffusion of carbon on the ferrite can be regarded as a lower bound. The corresponding value \nfor martensite is likely to be higher owing to the high defect densit y of the martensite.   \n \nTime / min  Austenite / m  Ferrite / m  \n1 1.3×10-7 2.7×10-5 \n2 1.9×10-7 3.8×10-5 \n30 7.4×10-7 1.5×10-4 \n \n \n \n  20 \n Reference s \n \n  [1] Zou D, Han Y, Zhang W, Fang X. J Iron Steel Res Int 2010;17(8):50.  \n  [2] Rodrigues CAD, Lorenzo PLD, Sokolowski A, Barbosa CA, Rollo JMDA. Mater Sci Eng 2007;A \n460–461:149.  \n  [3] Karlsen M, Grong O, Soefferud M, Hjelen J, Roervik G, Chiron R. Metall Mater Trans \n2009;40A:310.  \n  [4] Pieta G, Leite R, Kwietniewski C, Clarke T, Strohaecker T. J. Mater. Eng. P erform \n2010;19(9):1318.  \n  [5] Kurdjumov GV. Twelfth Hatfield Memorial Lecture. 1959.  \n  [6] Clarke AJ, Speer JG, Miller MK, Hackenberg RE, Edmonds DV, Matlock DK, Rizzo FC, Clarke \nKD, Moor ED. Acta Mater 2008;56:16.  \n  [7] Malakondaiah G, Srinivas M, Rao PR . Prog Mater Sci 1997;42:209.  \n  [8] Speer JG, Matlock DK, Cooman BCD, Schroth JG. Acta Mater 2003;51:2611.  \n  [9] Edmonds DV, Hea K, Rizzo FC, Cooman BCD, Matlock DK, Speer JG. Mater Sci Eng \n2006;A438 –440:25.  \n[10] Tomimura K, Takaki S, Tanimoto S, Tokunaga Y. ISIJ Int 1991;31:721.  \n[11] Tomimura K, Takaki S, Tokunaga Y. ISIJ Int 1991;31:1431.  \n[12] Takaki S, Tomimura K, Ueda S. ISIJ Int 1994;34:522.  \n[13] Nakada N, Tsuchiyama T, Takaki S, Hashizume S. ISIJ Int 2007;47:1527.  \n[14] Furuhara T, Kikumoto K, Saito H,  Sekine T, Ogawa T, Morito S, Maki T. ISIJ Int 2008;48:1038.  \n[15] Nakada N, Tsuchiyama T, Takaki S, Miyano N. ISIJ Int 2011;51:299.  \n[16] Nayak SS, Anumolu R, Misra RDK, Kim KH, Lee DL. Mater Sci Eng 2008;A498:442.  \n[17] Cerezo A, Godfrey TJ, Smith GDW. Rev Sci Instrum 1988;59:862.  \n[18] Blavette D, Deconihout B, Bostel A, Sarrau JM, Bouet M, Menand A. Rev Sci Instrum \n1993;64:2911.  \n[19] Miller MK, Cerezo A, Hetherington MG, Smith GDW. Atom probe field ion microscopy. Oxford: \nOxford University Press; 1996.  \n[20] Thuvander M, Miller MK, Stiller K. Mater Sci Eng 1999;A270:38.  \n[21] Miller MK. Atom probe tomography analysis at the atomic scale. New York: Kluwer \nAcademic/Plenum; 2000.  \n[22] Kelly TF, Miller MK. Rev Sci Instrum 2007;78:031101.  \n[23] Seidman D. Annu Rev  Mater Sci 2007;37:127.  \n[24] Miller MK, Forbes RG. Mater Charact 2009;60:461.  \n[25] Marquis EA, Miller MK, Blavette D, Ringer SP, Sudbrack CK, Smith GDW. MRS Bull \n2009;34:725.  21 \n [26] Pereloma EV, Stohr RA, Miller MK, Ringer SP. Metall Mater Trans 2009;40A:306 9. \n[27] Sauvage X, Lefebvre W, Genevois C, Ohsaki S, Hono K. Scripta Mater 2009;60:1056.  \n[28] Dmitrieva O, Ponge D, Inden G, Millán J, Choi P, Sietsma J, Raabe D, Acta Mater 2011;59:364.  \n[29] Gerezo A, Godfrey TJ, Smith GDW: Rev Sci Instrum 1988; 59:862.  \n[30] Raabe D, Choi PP, Li YJ, Kostka A, Sauvage X, Lecouturier F, Hono K, Kirchheim R, Pippan R, \nEmbury D: MRS Bulletin 2010; 35: 982.  \n[31] Ohsaki S, Raabe D, Hono K: Acta Mater  2009 ; 57:5254 . \n[32] Choi P, da Silva M, Klement U, Al -Kassab T, Kirchheim R: Acta Mater 2005;53:4473.  \n[33] Thermo -Calc User’s Guide, Version R. Stockholm: Thermo -Calc software AB and Foundation of \nComputational Thermodynamics; 1995 -2006.  \n[34] Thermodynamic database TCFE5 -TCS Steels/Fe -Alloys Database, Version 5, Thermo -Calc \nSoftwar e, www. Thermocalc.com.  \n[35] Sato H, Zaefferer S: Acta Mater 2009;  57:1931.  \n[36] Jiménez J.A, Carsí M, Frommeyer G, Knippscher S, Wittig J, Ruano O.A. Intermetallics \n2005;13:1021.  \n[37] Rühle M. Vol. 9, Metallography and microstructures, in: Transmission el ectron microscopy, ASM \nhandbook, Materials Park, OH: ASM International; 1995.  \n[38] Shtansky D V, Nakai K, Ohmori Y: Acta Mater 2000; 48, 1679.  \n[39] Miyamoto G, Usuki H, Li ZD, Furuhara T: Acta Mater 2010; 58:4492.  \n[40] Speer JG, Edmonds DV, Rizzo FC, Matl ock DK. Curr. Opin. Solid State Mater. Sci 2004;8:219.  \n[41] Streicher AM, Speer JG, Matlock DK, De Cooman BC : Proceedings of the International \nConference on Advanced High Strength Sheet Steels for Automotive Applications 2004;51.  \n[42] Zhong N, Wang XD, Wan g L, Rong YH : Mater Sci Eng 2009;  A506:111.  \n[43] MCLellan R B, Wasz M L: J. Phys. Chem. Solids 1993; 54: 583.  \n[44] Haasen P, Physikalische Metallkunde, Springer -Verlag 1974 : 173 \n[45] Zhu C, Xiong X Y, Cerezo A, Hardwicke R, Krauss G, Smith G.D.W. Ultramicroscopy: IFES \n2006, Proc. 50th Intern. Field Emission Symposium/19th IVNC 107, 808 -812, 2007.  \n[46] Sarikaya  M, Thomas  G, Steeds J W, Barnard  S J, Smith  G D W. Proc. Solid -Solid Phase \nTransformations Conf., Pittsburgh, PA, August 1981,  Published by The Metallurgical Society of \nthe A.I.M.E., Warrendale, PA, USA  \n[47] Barnard  S J, Smith  G D W , Sarikaya  M, Thomas  G. Scripta Metall  1981 ; 15: 387. \n[48] Bhadeshia  H K D H . Metal Science 1983 ; 17: 151. \n[49] Bhadeshia  H K D H . Metal Science 1981 ; 15: 175. \n[50] Thomas  G, Sarikaya  M, Smith  G D W, Barnard  S J. Advances in the Physical Metallurgy and  \nApplications of Steels (London, The Metals Society, 1983) 259 -265.   22 \n [51] Höring S, Abou -Ras D, Wanderka N, Leitner H, Clemens H, Banhart J: Steel Res Intern 2009; 80: \n84. \n[52] Schnitzer R, Radis R, Nöhrer M, Schober M, Hochfellner R, Zinner S, Povoden -Karadeniz E, \nKozeschnik E, Leitner H: Mater Chem Phys 2010; 122: 138.  \n[53] Yan F, Shi H, Fan J, Xu Z : Mater Chara 2008;59:883.  \n    Figures , page  1  \nFig. 1  Schematic diagram of  the heat treatment  route  (WQ: water quench ing). \n \n \n \n \n \n \n \n \n(a)                                                             \n \n \nWQ T \ntime WQ 1min  2min  10min  30min  300°C, 400°C , 500°C  1150°C 5min  \nWQ WQ WQ Figure(s)   Figures , page  2 \n0 5 10 15 20 25025050075010001250150017502000\nTempered at 500°C30min10min2min1min\n  Engineering stress / MPa\nEngineering strain / % \n  (b) \n    Figures , page  3  \n(c)  \n                                                                         \n   Figures , page  4  \n (d) \n   Figures , page  5  \n(e) \nFig. 2  Mechanical properties  of the quenched and partitioned stainless steel Fe -13.6Cr -0.44C (wt.%, \n1.4034 , AISI 420 ) after different types of partitioning and austenit e reversion treatment s. The \noriginal state of a commercial alloy ( 1.4034 , cold band ) is shown as reference . The term 'cold band' \nrefers here to hot rolled, cold rolled, and finally recrystallized material.  \n(a-c) stress stra in curve  of samples tempered at 4 00°C, 500°C, 300°C , respectively . Note in (a) that \nthe as -quenched sample (green) fails already in the elastic regime ;  (d) Multiplied quantity UTS  \n×TE as a function of annealing time for the three different temperatures;  (e) UTS -HV relationship .  \n(UTS: ultimate tensile strength; HV: Vickers hardness ; TE: total elongation ) \n \n \n \n \n \n \n   Figures , page  6 \n0 200 400 600 800 1000 1200-50050100150 Change in length / m\nTemperature / °C360°C\n \n-30°C/s10°C/s855°C Austenizing\n950°C / 5 min       \n(a)                                                                                \n0 200 400 600 800 1000 1200-50050100150\n10°C/s\n-30°C/s\n118°C876°C838°C\n  Change in length / m\nTemperature / °C  Austenizing\n1150°C / 5min\n \n (b)        Figures , page  7  \n800 900 1000 1100 12000,00,10,20,30,40,5\n   wt.% carbon in austeniteAnnealing temperature / °C  \n               (c) \nFig. 3 Results of the dilatometer tests of the stainless steel Fe -13.6Cr -0.44C (wt.%, 1.4034).  \n (a) Austeni tization at 950°C for 5min     (b) Austeni tization  at 1150°C for 5min     (c) calculated \nequilibr ium carbon content in austenite at different annealing temperature (Thermo -Calc TCFE5)  \n     Figures , page  8  \nFig. 4 Austenite volume fraction as a function of tempering time  (at 400°C) measured by feritscope \n(magnetic signal), EBSD, and XRD.  \n \n \n \n \n \n \n   Figures , page  9  \n(a)                                            (b) \nFig. 5 EBSD inverse pole figure map of the same specimen region showing  retained and reverted \naustenite  (IPF||ND, only austenite shown) :  (a) shows the material as quenched containing only \nretained austenite.  (b) shows the material containing both, retained plus reverted austenite after \nquenching and 5 minutes tempering at 400°C  (EBSD: Electron back scattering diffraction ; IPF: \ninverse pole figure color code; ND: normal direction ). \n \n \n   Figures , page  1  \n \n \n(a) \n \n(b) \nFigure(s)   Figures , page  2 Fig. 6 (a) EBSD phase maps of samples tempered at 400°C for 0, 1, and 2 minutes at 400°C , and of the \nTRIP effect  obtained from EBSD phase analysis . The red columns show the austenite content before \nand the black ones after the tensile tests. (b) Microstructure of samples  before and after tensile test ing \nsubjected to different temper ing conditions (left: before tensile test; right: after tensile test);  BCC: \nmartensite phase; FCC: austenite phase.  \n \n \n \n \n \n \n(a) \n \n   Figures , page  3  \n(b) \n \n   Figures , page  4  \n(c) \n \n   Figures , page  5  \n(d) \n \n   Figures , page  6   \n(e) \n \n   Figures , page  7  \n(f) \n \n   Figures , page  8  \n(g) \n \n \nFig. 7 TEM images of as quenched sample (only lath martensite was found, a,b);  \nTEM images of samples tempered at 400°C for 1min : c) Overview image of the very dense array of \nnanoscaled carbides that is formed during tempering; d) In -grain view of the carbides; e) Overview \nimage of the formation of a reverted austenite grain that is located at a former martensite -martensite \ngrain boundary; f) Close -up view o f reverted austenite that is surrounded by martensite; g) Electron \ndiffraction analysis reveals that a Kurdjumov -Sachs  growth  orientation relationship  exists between \nthe martensite matrix and the reverted austenite.  \n \n \n   Figures , page  1  \n \n \n \n \n \n \nFigure(s)   Figures , page  2  \n \n   Figures , page  3  \n(a) \n \n \n   Figures , page  4  \n   Figures , page  5  \n \n(b) \n \n \n   Figures , page  6  \n \n \n \n   Figures , page  7  \n(c) \n \nFig. 8   (a) 3-D reconstructions  (frame scale in nm)  of sample after water quench ing;  The data \nclearly show that carbon redistribution already occurs during quenching. Cr redistribution does not \noccur. (b) tempered at 400°C for 1 minute;   (c) tempered at 400°C for 30 minutes. Carbon atoms \nare displayed pink. The different phases are marked in the picture s. Carbon  iso-concentration \nsurface (2 at.%, correspond ing to 0.44 wt.%, green)  and concentration profiles across the phase \nboundaries along the yellow cylinder ) are also shown.  \n \n \n \n \nFig. 9a Schematic illustration of austenite reversion . M: martensite; CRI : carbon -rich interface ; RA: \nretained austenite  as obtained after quenching with equilibrium austenite carbon content ;   rA: \nrevert ed austenite  formed during 300°C -500°C tempering at interfaces owing to the higher local \ncarbon conent ;   After sufficient long diffusion time the carbon content in both types of austenite \nbecomes similar . \n   Figures , page  8  \n \nFig. 9b Calculated driving force for austenite reversion at 400°C (Thermo -Calc TCFE5) . \n \n \n \n \n \n \n \n   Figures , page  9  \n \nFig. 10 True stress -true strain curves and corresponding strain hardening curves for the steel after \n400°C heat treatment at different times. The data reveal that the tempering, associated with the \nincrease in the austenite content via austenite reversion, yields higher strain hardening reserves at \nthe later stages of deformation due to the TRIP effect.  \n \n \n \n \n   Figures , page  10  \n \nFig. 1 1  High resolution EBSD map  (20 nm step size) of the sample tempered at 400°C for 30 \nminutes. The map shows that on some martensite grain boundaries a very thin reverted austenite \nlayer exists. This thin austenite seam can act as a compliance or respectively repair layer against \ndamage percolation ent ering from the martensite grain. A ustenite : red; martensite : green.  \n \n"    },    {        "title": "1911.06493v1.Exchange_bias_and_training_effect_in_an_amorphous_zinc_ferrite__nanocrystalline_gallium_ferrite_bilayer_thin_film.pdf",        "content": "1 \n Exchange bias and training effect in an amorphous zinc \nferrite/ nanocrystalline gallium ferrite  bilayer thin film \n \nHimadri Roy Dakua  \nDepartment of Physics, Indian Institute of Technology Bombay, Mumbai, India - 400076  \nEmail: hroy89d@gmail.com   \n \n \nAbstract  \nIn this paper I report, exchange bias effect in a bilayer thin film of  amorphous zinc ferrite  and \nnano crystalline  gallium ferrite . The amorphous  zinc ferrite layer was deposited at room \ntemperature  (TS = RT)  on top of a nano crystalline gallium ferrite thin film using a pulsed laser. \nThis bilayer film showed large exchange bias effect (HE ~ 418 Oe at 2 K). The  exchange bias \nshift decreased exponentially as the temperature increased  and disappeared for T > 30  K. Along \nwith the exchange bias shift the film also showed enhanced magnetization in Field Cooled (FC) \nmeasurements as compared to the Zero Field Cooled (ZFC) magnetization. The bilayer film \nalso showed training effect at 2 K , which followed  spin configurational relaxation model . The \nobserved exchange bias effect could be  attributed  to the pinning anisotropy of the spin glass  \namorphous zinc ferrite layer  pinned at the interface of ga llium ferrite . \n \n1. Introduction  \nThe coupling between two different magnetic materials  along their interface provides  many \nphenomena  of both scientif ic and technological importance [1-3] such as the exchange bias \neffect [4-6], proximity effect [7-9], exchange spring  permanent magnet [10-12] etc. The coupling \nbetween an  Antiferromagnetic (AFM) and a F erromagnetic  (FM)  materials  generally provides  \nthe exchange bias effect. [5,13] The exchange bias effect manifest s a shift in the magnetic \nhysteresis loop along the field ax is when  the system is  field cooled below the Néel temperature \nof the AFM phase .[5,6] The utility of the exchange bias systems in many magnetoelectronics \ndevices [14-16] helped to grow  the research interest in this topic and  it also led to the discovery \nof exchange bias effect in a lot of different systems such as AFM) - FM[17-19], AFM -\nFerrimagnetic (FIM) [20-22], FIM -FM[23], Spin Glass (SG) -FM[24] heterostructure o xides, 2 \n alloys and nanomaterials [25] and also in some single phase ( crystallographic) materials. [25,26] \nHowever, the complete understanding  and a univer sal microscopic model for  the exchange bi as \neffect are yet to be achieved.  \nThe earliest model  for the exchange bias effect was  provided by Meicklejohn and Bean  and \nthe exchange bias field was expressed as[27-29] \nHE= −JSFMSAFM\ntFMMFM.          (1) \nWhere J is the exchange coupling constant between the interfacial magnetization S AFM  and \nSFM of the AFM and FM layer s respectively . MFM and t FM are the saturation magnetization and \nthe thickness  of the FM layer  respectively .[30] The equation 1 indicates that the interfacial \nmagnetization of AFM layer plays an important role for the exchange bias effect, as the \nsaturation magnetizati on of the FM  layer  (MFM) and S FM are most likely to remain  \nunchanged .[30] The uncompensated AFM spin states at the interface  provide  a net AFM \ninterfacial moment, S AFM, along (or opposite to) the field direction . These uncompensated spin s \nare in thermodynamic non -equilibrium  states as compared to the  compensated AFM spins . The \ndecay of this interfacial moment towards an equilibrium state leads to a decrease in the \nexchange bias effect in the training measurements or as the temperature incre ased. [28,30] \nIn this paper, I show the exchange bias  and training  effect in a bilayer thin film of amorphous \nzinc ferrite and nanocrystalline gallium ferrite. Gallium ferrite is one the few materials that \nshow  near room temperature magnetoele ctric properties. [31,32] The coupling between the \nmagnetic and ferroelectric/ dielectric properties of a magnetoelectric material provides an \nopportunity to control the one by means of the other. [33,34] The exchange bias effect i n the se \nmagnetoelectric system s, might  help to control the exchange bias related phenomena  by an \nexternal electric field. [3] This unique property of the syste m might  be useful  in future magnetic \ndevices.  The observed exchange bias effect in this amorphous zinc ferrite and nanocrystalline \ngallium ferrite bilayer thin film is found to obey the Meicklejohn and Bean model (equation 1) \nas the interfacial magnetization of the AFM layer is replaced by that of the  spin glass \namorphous zinc ferrite layer.  \n \n2. Experimental Details  \nThe gallium f errite (GFO) thin film was deposited on an amorphous  quartz substrate using a \nNd:YAG pulsed laser. A single phase high density GFO PLD target was used for the 3 \n deposition. In this  process, t he laser energy density was kept at ~2 Joule/ cm2, pulse repetition s \nrate was 10 shots/sec and the deposition duration was 30 minutes . The film was deposited in \noxygen atmosphere (0.16 mbar pressure) and the substrate was kept  at room temperatur e \n(TS = RT) at  4.5 cm from the PLD target. The deposited single layer thin film was ex -situ \nannealed at T a = 750°C for 2 hours, in air atmo sphere. This annealed film showed  single phase \nnanostructured gallium ferrite  features . On top of this nano structured  gallium fer rite thin film  \nan amorphous zinc ferrite layer  was deposited . A stoichiometric, high density zinc f errite  (ZFO)  \nPLD target was used to deposit this layer. The deposition condition s for the top amorphous \nzinc ferrite layer was kept same as that of the single layer gallium ferrite.  The as deposited  \nbilayer film was used to study the EB effect.  \n \n3. Result s and discussion s \na. Structural and microstructural properties of the film  \nThe structural and the microstructural properties of the  bilayer  film were  studied using XRD \nand FEG -SEM. Fig. 1 shows the XRD of the bilayer thin film deposited on the amorphous \nquartz substrate. The XRD of the bilayer thin film is compare d with the XRD of single layer \ngallium ferrite thin film (red data) and the single layer  zinc ferrite thin film  (black data) . The \nsingle layer GFO  thin film was deposited and annealed in same conditions as that of gallium \nferrite layer of the b ilayer thin film. Similarly, ZFO  single layer thin film was also deposited \nin same condition s as that of the top layer of the bilayer thin film.  The XRD of the single layer \nZFO thin film deposited on amorphous quartz substrate at T S = RT did not show any Bragg’s \npeaks which indicates that the deposited film is amorphous (within the limit of the XRD). The \namorphous nature of ferrite film deposited (using Physical Vapour Deposition (PVD) process) \nat room temperature (RT) is a commonly observed phenomenon. [35-37] On the other hand, \nthe GFO single layer film deposited a t TS = RT and annealed at T a = 750 °C for 2 hours shows \nBragg’s peaks corresponding to the orthorhombic crystal structure of GaFeO 3 of space group \nPc2 1n. While the bilayer film shows fewer Bragg’s peaks which are observed at same positions \nas that of the s ingle layer GFO film. However, similar to the ZFO single layer amorphous thin \nfilm, the bilayer film also did not show any peak either corresponds to the Zn -ferrite cubic \nspinel phase or any other impurity phase. This indicates that the top layer of the bi layer film is \namorphous zinc ferrite.  \n 4 \n  \n \n30 40 50 60 70 80 \n  \nGFO - ZFO(121)(211)\n(130)\n(221)\n(002)\n(311)\n(040) (231)\n(122)\n(042) (341)\n(441)\n(223)\n(600)\nZFOIntensity (arb. unit)\n \n2(degree)GFO\n \nFig. 1. XRD of the samples. GFO -ZFO: XRD o f the amorphous zinc ferrite/ nanocrystalline \ngallium ferrite bilayer, GFO: XRD of the nanocrystalline gal lium ferrite single layer and \nZFO: XRD of the amorphous zinc ferrite single layer.  \n \nThe FEG -SEM of the single layer GFO  thin film deposited at T S = RT and annealed at T a = \n750 ° C for 2 hours are shown in  Fig. 2 (a  - b). This film showed almost isolated nanostructure s \nof average si ze ~100 nm. The thickness of the single  layer  nanostructured  GFO film is \n~160 nm. Fig. 2 (c ) shows the FEG -SEM image of the  bilayer thin film. Fig. 2 (d ) shows the \ncross sectional FEG -SEM image of the bilayer thin film. The thickness of the  bilayer  film is ~ \n275 nm.  Therefore , the average thickness  of the top amorphous ZFO layer  could be estimated \nas ~115  nm. However, a rough interface of these two layer s could be expected as the bottom \ngallium ferrite layer showed  isolated nanostructure like feature s.  5 \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig. 2.  FEG -SEM images of the single gallium ferrite and gallium ferrite/ amorphous zinc \nferrite bilayer. (a) Top surface of single layer GFO film, (b) cross -section of single layer GFO \nfilm, (c) top surface of bilayer film and (d) cross -section of the bilayer fi lm.  \n \nb. Magnetic properties of the film  \nFig. 3 shows the M -T data of the bilayer film measured in both Field Cooled (FC) and Zero \nField Cooled (ZFC) mode. The magnetic field was applied along the film’s plane.  The inset \nof the figure  shows derivative  of the FC  magnetization, dM/dT as a function of temperature. \nThe transition temperature  (TC) was  obtained  from the minimum  of this data (T C = 235 K ), \nwhich is comparable with the T C of the single layer nanostructured gallium ferrite thin film  and \nbulk gal lium ferrite polycrystalline sample .[31,32] A large difference in the FC and the ZFC \nmagnetization of the film could be due to the high anisotropy of gallium ferrite [38,39] and spin \nglass  properties of top amorphous layer.  \nGFO  (b) (c) \n(d) (b) \nZFO  \nGFO  6 \n \n0 100 200 300 40001020\n100 200 300-300n-200n-100n0\n  FC\n ZFC\n  M (emu/cc )\nT (K)1 kOeTC\n  dM/dT\nT (K)1 kOe FC \nFig. 3. Temperature dependence ZFC and FC magnetization of the  amorphous ZFO/ \nnanocrystalline GFO  bilayer film. The Z FO layer  was deposited on top of nanocrystalline GFO \nlayer, at T S = RT . \n \nFig. 4 shows a part of the 300  K M-H curve  and 5 K ZFC M -H loop of the bilayer thin film.  \nAs expected from the M -T data, the 300 K M-H data shows almost linear variation with the \nmagnetic field and  no coercivity. This clearly indicate that the film is  in paramagnetic  state at \nroom temperature. However , the 5 K ZFC M -H loop shows a large coercivity \n(HC = (HC2 - HC1)/2 = 5560 Oe ), which is equivalent to the coercivity of the single layer \nnanostructured gallium ferrite thin film.  The 5 K ZFC M-H loop also shows un saturated \nbehaviour. However, unlike the minor M -H loop s, this  data did not show any vertical shift of \nthe loop (|M +50 kOe| = |M 50 kOe |) and it also showed almost  reversible behaviour  in the high field  \nZFC M-H curves . The unsaturated behaviour of the M -H loop  could be attributed to the high \nanisotropy of gallium fer rite and the glassy behaviour of the to p amorphous zinc ferrite \nlayer. [39,40] 7 \n \n-40 -20 0 20 40-75-50-250255075\nHC1\nHC2ZFC5 K\n  M (emu/cc )\nH (kOe)300 K \nFig. 4 . ZFC M-H data o f the film measured at 5 K  and 300 K  \n \nc. Exchange bias effect in the film  \nThis amorphous ZFO/  nanocrystalline GFO bilayer thin film showed exchange bias effect. \nHere , I present the details of the observed exchange bias effect in this film.  Fig. 5 shows \nzoomed view of a ZFC and a FC M -H loops meas ured at 2 K. For the  FC measurement, t he \nsample was cooled down to 2 K from RT in presence of 50 kOe magnetic field applied along \nthe film ’s plane.  The FC M -H loop shows exchange bias shift (H E = (HC2 + HC1)/2) along the \nnegative field axis. The  magnitude of  exchange bias shift  at 2 K is HE = 418 Oe. The coercivity \nof the FC M -H loop is HC = 5938  Oe at 2 K which is higher than the ZFC HC (= 5840 Oe at 2 \nK). The increase in  coercivity (H C) due field cooling is a commonly observed  phenomena  in \ndifferent exchange bias systems. [6,41,42] The pinned spins of the AFM or glassy states at the \ninterface of the ferromagnetic layer contribute significantly in the coercivity enhancement of \nthe FC M -H loops.  These pinned spins switched  irreversibly while reversing the magnetization \nof the FM la yer. The work done due to this  irreversible switching resulted in broadening of the \nM-H loop. [41] \n One also need s to note that the remanence magnetization  (Mr1) of the film  is increased in \nthe FC M -H loop as compare d to the ZFC M -H loop. This increase in remanence magnetization \nis also associated with an increase in the high field magnetization (M50 kOe ) of the FC M -H loop 8 \n as compared to the ZFC M -H loop.  The enhance ment  of magnetization of the FC M -H loop \nas compare to the ZFC M -H loop was a lso reported in different EB systems. [43-45] This \nincreased high filed magnetization of the bilayer film could be due to the pinning of the \ninterface spins of the glassy amorphous ZFO layer along magnetization of the nanocrystalline \ngallium ferrite layer.  \n-10 -8 -6 -4 -2 0 2 4 6 810-40-2002040\n-40-2002040-75075\nMr2Mr1  ZFC\n  50 kOe FC\n  M (emu/cc )\nH (kOe)2 K\n \n  \n2 K\n \nFig. 5 . Low field part of 2 K ZFC and FC M -H loops . The film shows exchange bias effect.  \nInset: the M -H loops are shown for ±  50 kOe field range.  \n \nThe temperature dependence of the exchange bias effect is also studied in this film. Fig. 6 \n(a) shows the exchange bias field H E of 50 kOe FC M -H loops of the  bilayer  film measured at \ndifferent temperatures. Fig. 6 (b) shows the coercivity H C of the FC M -H loops as a function \nof temperature. The exchange bias shift (H E) decreased monotonically as the  temperature \nincreased and it almost disappeared at T > 30 K. The coercivity (H C) of the sample also \ndecreased as the temperature increased.  These decrease in the exchange bias shift (HE) and the \ncoercivity  (HC) of the film followed an exponential decay as  shown in equation 2 (a) and (b).  \nHE=HE0e−T/T0                        (2.a) \nHC=HC0e−T/Tc0                       (2.b) 9 \n Where HE0 and HC0 are the exchange bias field and coercivity at T = 0 K. \n0 5 10 15 20 25 300100200300400\n0 5 10 15 20 25 305.05.56.0\nHE0 = 577.5 Oe\nTE0 = 6.03 K HE = HE0e(-T/TE0) (a)\n  HE (Oe)\nT (K)  HE\n  Fit\n50 kOe FCHC0 = 5973 Oe\nTC0 = 143.5 K HC = HC0e(-T/TC0) (b)\n  HC (kOe)\nT (K)50 kOe FC\nFig. 6. The temperature dependence of the (a) exchange bias field H E and (b) coercivity H C of \nthe film. The solid lines are the fitted data  \n \nThe value of the fitted parameters are shown in the Fig.  6 (a-b). The exponential decrease of \nthe exchange bias field (H E) and the coercivity (H C) were  generally reported in the systems \nwith spin glass or magnetically frustrated interface s[46-48] such as SrMnO 3 and La 0.7-\nSr0.3MnO 3 bilayer, where the competing magnetic order led to  formation of a spin glass state \nat the interface. [49] The increase in temperature unfreeze the glassy spins of the amorphous \nzinc ferrite layer and turned them into paramagnetic spins above the blocking temperature. The \nspins in the paramagnetic region could  not provide unidirectional anisotropy  to the system and \nthe exchange bias effect  disappeared in higher temperature . \n \nd. Training effect  \nThe exchange bias system s generally show  a decrease in  the exchange bias shift due to \nconsecutive M -H loop iterations, which is know n as training effect. [28,30,50,51] The training \neffect is  also observed in this  amorphous ZFO/ nanocrystalline  GFO bilayer thin film . The \ntraining effect was measured after cooling down the film from room temperature to 2 K in \npresence of 50 kOe applied magnetic field. The field was cycled from +50 kOe to -50 kOe to \n+50 kOe for each consecutive M -H loop iteration s. Fig. 7 (a) shows the low field part of \ntraining M -H loops of the film for 1st and 8th iterations (n = 1 and 8)  along with  their 10 \n corresponding inverted  loops,  (-M)-(-H). Fig. 7 (b) shows the high field part of the n = 1 and 8 \nM-H loops.  \n \n-8 -7 -6 -5-10-50510\n20 25 30 35 40 45506070\n- HC2HC1(a)\n  M (emu/cc)\nH (kOe) n = 1\n inverted n = 1\n n = 8\n inverted n = 82 K (b)\n  M (emu/cc)\nH (kOe) n = 1\n n = 8\n \nFig. 7 . Training effect of the film measured at 2 K after cooling in 50 kOe magnetic field.  \n(a) Normal and inverted low field magnetization curve of first (n = 1) and n = 8th M-H loops \niterations . (b) High field magnetization of t he n = 1 and 8 M -H loops.  \n \nThe exchange bias shift (H E) as well as the high field magnetization (M50 kOe ) of the film \ndecreased as the loop iterations (loop index: ‘ n’) increased. Fig. 8 shows the variation of the \nexchange bias field (H E) obtained as a function of  ‘n’ in this  training measurements .  \n \n \n \n \n \n \n \n \n \n \n \nFig. 8 . Training loop index  (n) dependence of the exchange bias field H E. \n12345678150200250300350400450\n  HE (Oe)\nLoop index (n) HE\n  Fitted\n  Calculated2 K11 \n The decrease in the H E of the film showed  a very similar trend as compared to the training \neffect of different EB systems  reported previously .[6,25] I fitted the se exchange bias field s \nwith the  well-known  empirical power law for training effect  \nHE(n)−HE∞= k\n√n              (3) \nWhere, HE∞ is the exchange bias field for n = ∞ and  k is a sample dependent proportionality \nconstant. [52] The exchange bias field shows good fit  with equation 3  for n > 1. The solid curve  \nin the Fig. 8 represents the fitted data with this equation.  The fitted data is extrapolated upto  \nn = 1. The fitted parameters are k=217 .3 Oe and  HE∞= 124.5 Oe.  This empirical power law \nbehaviour of the exchange shift was observed  in many  exchange bias systems. [6,25] However, \nthe physical origin of such behaviour is still not very clear. Hochstrat et al.  had also observed \nsimilar power law decay of the training exchange bias fields  with n (for n > 1) in NiO/Fe \nheterostructure. [28] Later, Binek [30] proposed an analytical model for the exchange bias \ntraining effect in the same system. He considered thermodynamic non -equilibrium spin states \nat the interface of the AFM -FM heterostr ucture. The training measurements lead to spin \nconfigurational relaxation of the interface AFM spins  towards an equilibrium state. The process \nwas formulated as [30] \nHE(n+1)−HE(n)= −γ(HE(n)−HE∞)3                                 (4) \nHere, γ is a sa mple dependent parameter. The experimentally observed 𝐻𝐸(1) is considered \nas the initial value while calculating  HE(n) using  this recursive formula. [30] The circles in the \nFig. 8 r epresents data obtained from this  calculation. The parameters cor responding to these \ncalculated  data are HE∞= 81.5 Oe and γ = 3.494 ×10-5 Oe-2. We can see that a  much closer to \nthe experimental data w as obtained using the equation 4 .  \nThe other important features  of the exchange bias effect in this film are the enhancement of \nthe high field magnetizati on in the FC M -H loop  as compared to the ZFC M -H loop  and the \ndecrease in the high field magnetization with  the increasing  M-H loop iterations in the training \nmeasurements. Fig. 9 shows the exchange bias shift of the film as a function of average high \nfield magnetization M 50 kOe  (=M+50 kOe +|M−50 kOe |\n2) obtained in the training measurements. The \ninset of Fig. 9 shows the M 50 kOe  as a function of the training loop index  ‘n’.  12 \n \n70 71 72 73 74200250300350400450500\n0 2 4 6 815916216516817112345678707274\n7654\n32n = 1\n  HE (Oe)\nM50 kOe (emu/cc )2 K  M5o kOe (emu/cc )\nn Expt.\n Calculated \nFig. 9 . Almost linear decrease in H E with the magnetization is observed in the training \nmeasurements of this system. Inset: M 50 kOe  as a function of ‘n’.  \n \nSimilar to the exchange Bias field (H E), the high field magnetization (M50 kOe ) of the film also \ndecreased w ith the increasing ‘n’ . According  to Binek, [30] this decrease in the  high field  \nmagnetization could be  attributed to  the relaxation of the coupled thermodynamically \nnonequilibrium interfacial spins  of the amorphous Z FOlayer  towards an equilibrium state as a \nresult of consecutive M -H loop iteration s. Thus the decrease of the high field  moment could be  \nformulate d in a similar way as that of the exchange bias shift (H E) in equation 4.[30]  \nM50 kOe(n+1)−M50 kOe(n)= −γ′(M50 kOe(n)−M50 kOe∞)3             (5) \nThe inset  of Fig. 9  shows the calculated data  (open squares)  using the equation 5. Almost \nsimilar to the experimental data was obtained by using  M50 kOe∞= 67.37 emu/cc and \nγ' = 7.93× 10-3 (emu/cc)-2 in the recursive equation 5 . According to Meicklejohn and Bean  \nmodel  (equation 1) [27], the exchange bias shift should decre ase linearly with the decrease in \nthe couple d interface moment  (SAFM). Fig. 9 shows that  our sample also shows almost a linear \ndecrease in the exchange bias field with the decrease in the average high field moment of the \nsample.  \n 13 \n It is known that  the exchange bias effec t requires two magnetic phases , a reversible  magnetic \nphase couple d with another phase tha t fixes this  reversible phase in a certain direction (along \nor opposite the field direction  for negative and positive exchange bias effect respectively ).[43] \nIn this system , the amorphous ZFO layer act like the reversible phase.  This amorphous zinc \nferrite top layer of the bilyer film turned into a spin glass state at low temperature due to the \npresence of competing local exchange interactions. [40] The spin glass amorphous  ZFO have \nmultiple spin configuration al ground state s[43,53] and spins get  frozen  in these ground states \nin random direction s below the blocking temperature . However, as the system was  field cooled \n(from room  temperature , which is  much above the blocking temperature ), some  spins of the \nglassy  amorphous ZFO  layer get frozen  along the applied magnetic field  direction  (or along \nmagnetization of GFO layer) below the blocking temperature . The  aligned frozen interfacial \nspins of the glassy layer pinned at the interface of the ferrimagnetic  (GaFeO 3) layer and \nprovided a pinning unidirectional anisotropy  to it, which  resulted in an exchange bias shift in \nFC M-H loop of the bilayer film. The spins pinned along the magnetization of GFO layer also \nincreased the net magnetization of the bilayer film. However, it is likely that these aligned  \npinned spins of the interfacial glassy , amorphous  ZFO layer are in higher energy state s as \ncompared to their grou nd state energy. [28,30,53] The consecutive M -H loop  iterations  helped  \nto relaxed  some of the aligned spins into the permissible ground state s of the spin glass \nconfiguration s. This le d to a decrease in the magnetization as well as the exchange bias shift in \nthe training effect measurements. Similarly, the temperature variation could be attributed to the \ndecrease in the pinned spins of the glassy states as a result of increased thermal fluctuation with \nincreasing temperature.   \n \n4. Conclusion  \nIn this paper a detail study of exchange bias effe ct in an amorphous zinc ferrite/  \nnanocrystalline gallium ferrite bilayer thin film is presented. The exchange bias shift of the \nfilm was found to decrease exponentially as the temperature increased. The exchange bias \neffect was also associated with an increase of the net magnetization of  the Field Cooled film \nas compared to the Zero Field Cooled. This enhancement in the magnetization is attributed  to \nthe interfacial magnetization of the spin glass amorphous zinc ferrite layer. The exchange bias \nshift was also found to decrease linearly wi th the decrease in the net magnetization (interfacial) 14 \n of the film in the training effect measurements, which is a typical behaviour of the exchange \neffect one could expect from the Meicklejohn - Bean model .  \n \nAcknowledgements  \nThe author  thank s Prof. Shiva Prasad and Prof. N. Venkataramani for  the PLD facilities. The \nauthor thanks B. N. Sahu  for providing the zinc ferrite PLD target. The author  also thank s SAIF \nand IRCC of IIT Bombay, for the VSM, SVSM, XRD and FEG -SEM facilities . \n \nReferences  \n[1] F. Hellman  et al. , Reviews of modern physics 89, 025006 (2017).  \n[2] P. Manna and S. Yusuf, Physics Reports 535, 61 (2014).  \n[3] S. M. Wu, S. A. Cybart, P. Yu, M. D. Rossell, J. X. Zhang, R. Ramesh, and R. C. Dynes, Nat \nMater 9, 756 (20 10). \n[4] A. E. Berkowitz and K. Takano, Journal of Magnetism and Magnetic Materials 200, 552 \n(1999).  \n[5] M. Kiwi, Journal of Magnetism and Magnetic Materials 234, 584 (2001).  \n[6] J. Nogués and I. K. Schuller, Journal of Magnetism and Magnetic Materials 192, 203 (1999).  \n[7] I. Vobornik, U. Manju, J. Fujii, F. Borgatti, P. Torelli, D. Krizmancic, Y. S. Hor, R. J. Cava, and G. \nPanaccione, Nano letters 11, 4079 (2011).  \n[8] P. Manna, S. Yusuf, M. Basu, and T. Pal, Journal of Physics: Condensed Matter 23, 506004 \n(2011).  \n[9] I. Golosovsky, G. Salazar -Alvarez, A. López -Ortega, M. González, J. Sort, M. Estrader, S. \nSuriñach, M. Baró, and J. Nogués, Physical review letters 102, 247201 (2009).  \n[10] E. F. Kneller and R. Hawig, Magnetics, IEEE Transactions on 27, 3588 (1 991).  \n[11] E. E. Fullerton, J. S. Jiang, M. Grimsditch, C. H. Sowers, and S. D. Bader, Physical Review B 58, \n12193 (1998).  \n[12] H. Zeng, J. Li, J. P. Liu, Z. L. Wang, and S. Sun, Nature 420, 395 (2002).  \n[13] M. D. Stiles and R. D. McMichael, Physical Revie w B 59, 3722 (1999).  \n[14] V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Reviews of Modern \nPhysics 90, 015005 (2018).  \n[15] B. Park  et al. , Nature materials 10, 347 (2011).  \n[16] J. Allibe, S. Fusil, K. Bouzehouane, C. Daumont, D. Sando, E. Jacquet, C. Deranlot, M. Bibes, \nand A. Barthelemy, Nano letters 12, 1141 (2012).  \n[17] F. Radu and H. Zabel, in Magnetic Heterostructures , edited by H. Zabel, and S. Bader \n(Springer Berlin Heidel berg, 2008), pp. 97.  \n[18] F. Radu, M. Etzkorn, R. Siebrecht, T. Schmitte, K. Westerholt, and H. Zabel, Physical Review B \n67, 134409 (2003).  \n[19] S. Laureti, S. Y. Suck, H. Haas, E. Prestat, O. Bourgeois, and D. Givord, Physical review letters \n108, 077205 ( 2012).  \n[20] X. Sun, N. Frey Huls, A. Sigdel, and S. Sun, Nano letters 12, 246 (2011).  \n[21] D. Kavich, J. Dickerson, S. Mahajan, S. Hasan, and J. -H. Park, Physical Review B 78, 174414 \n(2008).  15 \n [22] A. Berkowitz, G. Rodriguez, J. Hong, K. An, T. Hyeon, N. Aga rwal, D. Smith, and E. Fullerton, \nPhysical Review B 77, 024403 (2008).  \n[23] Q. K. Ong, A. Wei, and X. -M. Lin, Physical Review B 80, 134418 (2009).  \n[24] M. Ali, P. Adie, C. H. Marrows, D. Greig, B. J. Hickey, and R. L. Stamps, Nature Materials 6, 70 \n(2007).  \n[25] S. Giri, M. Patra, and S. Majumdar, Journal of Physics: Condensed Matter 23, 073201 (2011).  \n[26] H. R. Dakua, arXiv preprint arXiv:1910.10948  (2019).  \n[27] W. H. Meiklejohn and C. P. Bean, Physical Review 105, 904 (1957).  \n[28] A. Hochstrat, C. Binek, and W. Kleemann, Physical Review B 66, 092409 (2002).  \n[29] S. Karmakar, S. Taran, E. Bose, B. Chaudhuri, C. Sun, C. Huang, and H. Yang, Physical Review B \n77, 144409 (2008).  \n[30] C. Binek, Physical Review B 70, 014421 (2004).  \n[31] S. Mukherjee, A. Roy, S. Auluck, R. Prasad, R. Gupta, and A. Garg, Physical review letters 111, \n087601 (2013).  \n[32] T. Arima  et al. , Physical Review B 70, 064426 (2004).  \n[33] R. Ramesh and N. A. Spaldin, Nat Mater 6, 21 (2007).  \n[34] S.-W. Cheong and M. Mosto voy, Nat Mater 6, 13 (2007).  \n[35] M. Bohra, S. Prasad, N. Kumar, D. Misra, S. Sahoo, N. Venkataramani, and R. Krishnan, \nApplied Physics Letters 88, 262506 (2006).  \n[36] N. Kumar, S. Prasad, D. S. Misra, N. Venkataramani, M. Bohra, and R. Krishnan, Journal o f \nMagnetism and Magnetic Materials 320, 2233 (2008).  \n[37] N. Wakiya, K. Muraoka, T. Kadowaki, T. Kiguchi, N. Mizutani, H. Suzuki, and K. Shinozaki, \nJournal of Magnetism and Magnetic Materials 310, 2546 (2007).  \n[38] M. J. Han, T. Ozaki, and J. Yu, Physical Review B 75, 060404 (2007).  \n[39] V. R. Reddy, K. Sharma, A. Gupta, and A. Banerjee, Journal of Magnetism and Magnetic \nMaterials 362, 97 (2014).  \n[40] V. Korenivski, R. Van Dover, Y. Suzuki, E. Gyorgy, J. Phillips, and R. Felder, Journal of applied \nphysics 79, 5926 (1996).  \n[41] M. D. Stiles and R. D. McMichael, Physical review B 63, 064405 (2001).  \n[42] C. Leighton, J. Nogués, B. Jönsson -Åkerman, and I. K. Schuller, Physical review letters 84, \n3466 (2000).  \n[43] R. Zheng, G. Wen, K. Fung, and X. Zhang, Physical  Review B 69, 214431 (2004).  \n[44] H. Khurshid, S. Chandra, W. Li, M. Phan, G. Hadjipanayis, P. Mukherjee, and H. Srikanth, \nJournal of Applied Physics 113, 17B508 (2013).  \n[45] Z. Tian, S. Yuan, L. Liu, S. Yin, L. Jia, P. Li, S. Huo, and J. Li, Journal of Ph ysics D: Applied \nPhysics 42, 035008 (2009).  \n[46] M. Vafaee, S. Finizio, H. Deniz, D. Hesse, H. Zabel, G. Jakob, and M. Kläui, Applied Physics \nLetters 108, 072401 (2016).  \n[47] N. Moutis, C. Christides, I. Panagiotopoulos, and D. Niarchos, Physical Review B 64, 094429 \n(2001).  \n[48] X. Zhang, J. Yuan, Y. Xie, Y. Yu, F. Kuang, H. Yu, X. Zhu, and H. Shen, Physical Review B 97, \n104405 (2018).  \n[49] J. Ding  et al. , Physical Review B 87, 054428 (2013).  \n[50] T. Hauet, J. Borchers, P. Mangin, Y. Henry, and S. Mangin, P hysical review letters 96, 067207 \n(2006).  \n[51] A. G. Biternas, U. Nowak, and R. W. Chantrell, Physical Review B 80, 134419 (2009).  \n[52] D. Paccard, C. Schlenker, O. Massenet, R. Montmory, and A. Yelon, physica status solidi (b) \n16, 301 (1966).  \n[53] K. Bind er and A. P. Young, Reviews of Modern physics 58, 801 (1986).  \n "    },    {        "title": "1006.3187v1.Sub_monolayers_of_carbon_on_alpha_iron_facets__an_ab_initio_study.pdf",        "content": "Sub-monolayers of carbon on \u000b\u0000iron facets: an ab initio study\nS. Riikonen,1;2A. V. Krasheninnikov,1;3and R. M. Nieminen1\u0003\n1COMP/Department of Applied Physics, Helsinki University of Technology, P.O. Box 1100, FI-02015, Finland\n2Laboratory of Physical Chemistry, Department of Chemistry,\nHelsinki University of Technology P.O. Box 55, FI-00014, Finland and\n3Department of Physics, University of Helsinki, P.O. Box 43, FI-00014, Finland\nMotivated by recent in situ studies of carbon nanotube growth from large transition-metal\nnanoparticles, we study various \u000b\u0000iron (ferrite) facets at di\u000berent carbon concentrations using\nab initio methods. The studied (110), (100) and (111) facets show qualitatively di\u000berent behaviour\nwhen carbon concentration changes. In particular, adsorbed carbon atoms repel each other on the\n(110) facet, resulting in carbon dimer and graphitic material formation. Carbon on the (100) facet\nforms stable structures at concentrations of about 0.5 monolayer and at 1.0 monolayer this facet\nbecomes unstable due to a frustration of the top layer iron atoms. The stability of the (111) facet\nis weakly a\u000bected by the amount of adsorbed carbon and its stability increases further with respect\nto the (100) facet with increasing carbon concentration. The exchange of carbon atoms between\nthe surface and sub-surface regions on the (111) facet is easier than on the other facets and the\nformation of carbon dimers is exothermic. These \fndings are in accordance with a recent in situ ex-\nperimental study where the existence of graphene decorated (111) facets is related to increased\ncarbon concentration.\nPACS numbers: 31.15.ae,34.50.Lf,36.40.Jn,75.50.Bb,75.70.Rf\nI. INTRODUCTION\nCarbon nanotubes (CNTs) are a versatile material\nwith a wide range of potential technological applications\nin \felds such as mechanical engineering, electronics and\nbiotechnology. The chemical vapor deposition (CVD)\nmethod has established itself as the most e\u000bective way to\nproduce CNTs in mass quantities. In this method, car-\nbon containing molecules (hydrocarbons, CO) are disso-\nciated on catalytic nanoparticles (consisting typically of\ntransition metals and their alloys) where carbon eventu-\nally forms graphitic structures and nanotubes. For wider\ntechnological exploitation of CNTs, better control over\nthe growth process is needed. Controlling nanotube chi-\nrality and preventing particle poisoning and CNT growth\ntermination are the most important aspects. In order to\ngain such a control, insight at microscopic level into the\nCNT growth process is needed. This kind of insight can\nbe obtained by performing in situ experiments where the\nCNT growth is directly observed.\nRecently, several in situ environmental transmission-\nelectron microscopy (TEM) studies of carbon \fber and\nnanotube growth have been carried out1{10. In these\nstudies, the catalyst particles were either crystalline\nand/or \\liquid-like\" (i.e. crystalline with high self-\ndi\u000busivity) during the growth process. Studied nanopar-\nticle materials ranged from nickel2,3,5,9, cobalt4,7,9and\niron6,7to alloys7of these metals. A common factor in\nmany of these investigations is the appearance of step\nedges and new facets as carbon is introduced to the\nnanoparticle and the growth of graphene layers from\nthese special regions2,5{7. In the case of nickel, this phe-\nnomenon was attributed to the stabilization of nanopar-\nticle step edges upon carbon adsorption and the trans-\nport of catalyst metal atoms away from the step edgeregion.2,5,11The energy barrier for carbon bulk di\u000busion\nin nickel was concluded to be very high when compared\nto any surface related di\u000busion phenomena.5\nIn several studies, the dominant role of surface and\nsub-surface has been emphasized3{5while other stud-\nies, considering mainly iron, suggest the importante of\nbulk di\u000busion7,9,12. Very recently, CNT growth from car-\nbidic phase (cementite) in iron nanoparticles has been\ndemonstrated8,10.\nIn a very recent study, solid-state \u000b\u0000iron nanopar-\nticle was encapsulated inside multi-walled carbon nan-\notubes (MWCNTs) while carbon was injected into the\nnanoparticle by electromigration6. The nanoparticle was\nobserved to stay solid and crystalline during the growth.\nSimilar to earlier in situ studies, new facets, showing\ngrowth of graphitic material, appeared on the nanoparti-\ncle surface. The orientation of the nanoparticle was ana-\nlyzed and the MWCNT walls encapsulating the nanopar-\nticle were parallel to the (110) facet. The existence of\nthe (111) facet was observed to depend strongly on car-\nbon concentration, and nanotube cap was formed on a\nrounded (100) facet. Ab-initio simulations were per-\nformed for \\graphenated\" and carbon saturated surfaces\nin order to reproduce the nanoparticle shape6.\nIn the case of \u000b\u0000iron, the morphology of (110), (100)\nand (111) facets is quite di\u000berent. This can result in\nvery di\u000berent di\u000busion barriers, carbon-carbon bond for-\nmation energetics and kinetics. For better understand-\ning of experiments it is important to perform ab ini-\ntiosimulations and correlate computational results to the\nphenomena observed in the in situ studies. In particu-\nlar, surface energies can be used to produce the physical\nshape of the nanoparticle which can be compared with\nthe experiments6,13. Activation energies of di\u000busion on\nand into the facets may provide information about rate-arXiv:1006.3187v1  [physics.chem-ph]  16 Jun 20102\nlimiting steps of graphitic material formation5,14.\nRecently, there have been several ab initio studies re-\nlated to these issues: pure \u000b\u0000iron facets have been stud-\nied extensively by B l\u0013 onski and Kiejna15,16, while carbon\nadsorption and di\u000busion on and into the (110) and (100)\nfacets were studied by Jiang and Carter17. The (100)\nfacet has drawn some attention very recently, as segre-\ngated carbon atoms form stable, periodic structures on\nthis facet18{20. Some carbide surfaces have been studied\nwith ab initio methods by Chiou and Carter21.\nIn this work we study the \u000b\u0000iron (110), (100) and\n(111) facets at di\u000berent carbon concentrations. We ad-\ndress such topics as the interaction of adsorbate atoms\nin coadsorption con\fgurations, carbon di\u000busion (for the\n(111) facet) and formation of stable carbon-rich struc-\ntures (mainly on the (100) facet) in the topmost iron\nlayer. Relative surface energies as function of carbon\nconcentration and energetics of the smallest units in-\nvolved in graphitic growth, the C 2molecules, are studied.\nThis work is organized as follows: in Sec.(II), simulation\nof iron-carbon systems, di\u000berent carbon chemical poten-\ntials, calculation of surface energies and computational\ndetails are discussed. In Sec.(III) the morphology of the\nstudied\u000b\u0000iron facets is discussed followed by the com-\nputational results. Discussions and conclusions are made\nin Sec.(IV).\nII. METHODS\nA. Iron-carbon systems\nIron with dissolved carbon exhibits a complex phase\ndiagram as a function of temperature and carbon con-\ncentration, where \u000b\u0000iron (\\ferrite\", bcc crystalline, fer-\nromagnetic), \r-iron (\\austenite\", fcc crystalline, antifer-\nromagnetic) and cementite (Fe 3C) are among the com-\npeting phases22. When considering nanoparticles instead\nof bulk, the phase diagram will be modi\fed; in particu-\nlar, it is known that small iron nanoparticles prefer the\n\r-iron phase instead of the bulk \u000b\u0000iron phase23,24.\nWhile collinear spin calculations within the Density\nFunctional Theory (DFT) and General Gradient Approx-\nimation (GGA)25seem to work very well for \u000b\u0000iron26,\nit is not obvious how to perform calculations for \r-iron,\nas the FCC iron, observed only at high temperatures,\nis paramagnetic. These and some other problems have\nbeen discussed in detail by Jiang and Carter in Ref.[26].\nConsidering systems involving nanoparticles, it has\nbeen shown that \\large\" iron nanoparticles (more than \u0019\n100 atoms) prefer the bcc structure23. This structure was\nalso observed in the large iron nanoparticle investigated\nin the recent in situ experimental study6.B. Technical Details\nIn order to visualize the di\u000berent \u000b\u0000iron facets, a\nsmall volume of bulk, cleaved into several directions\nis illustrated in Fig.1(g). The form of this bulk vol-\nume mimicks the elongated nanoparticles seen in the in\nsituexperiment6. A real nanoparticle has, of course, sev-\neral other facets which are not visualized in Fig.1(g) and\nnot considered in this work. Top and side views of the\nfacets are illustrated in panels (a-f) of Fig.1.\nWe employ the periodic supercell method to model the\niron facets. An in\fnite surface is modelled by a slab con-\nsisting of few layers of iron atoms, with su\u000ecient vacuum\nof 15\u0017A between the slabs. The slabs we have used are de-\npicted in Fig.1 and they consist of 3 \u00023\u00026 (the last num-\nber denoting the number of layers) and 2 \u00022\u000212 slabs for\n(110), (100) and (111) surfaces, respectively. Areas of\nthe unit cells depicted in Fig.1 are 51 \u0017A2, 72\u0017A2, and 56\n\u0017A2for (110), (100) and (111) slabs, respectively.\nNext, in order to calculate adsorption and reaction en-\nergies on the surface, we de\fne a convenient energy quan-\ntity E s(shifted energies) as follows:\nEs(X\u0003) =E(X\u0003)\u0000E0; (1)\nwhereE(X\u0003) is the energy of the adsorbed surface species\nX\u0003and E 0is the energy of a surface unit cell without\nadsorbates. Now the adsorption energy can be written\nas follows:\nEads=E(X\u0003)\u0000E(X)\u0000E0=Es(X\u0003)\u0000E(X);(2)\nwhereE(X) is the energy of an isolated atom in vacuum.\nWe also present adsorption energies, especially in the\ncase of high carbon coverage, by using some other chem-\nical potential:\nEc=E(X\u0003)\u0000(E0+n\u0016c) =Es(X\u0003)\u0000n\u0016c;(3)\nwherenis the number of carbon atoms and \u0016cis the\nchemical potential. We take the chemical potential as\nthe energy per atom in graphene. Energy E cthen re-\n\rects the energy cost to accommodate carbon atoms into\nthe metal adsorbant instead of graphene. In previous\nworks6,20,26various chemical potentials have been used,\nincluding the energy per isolated carbon atom and the\nenergy per carbon atom in graphite or in graphene.\nThe shifted energy values of Eq.(1) can be used to cal-\nculate reaction energetics on the adsorbate, i.e. to look\nat energetics of processes like C\u0003+C\u0003!C\u0003\n2. In the case\nof adsorbate-adsorbate repulsion on the lattice, this can\nprovide information about stress release upon dimer for-\nmation on the iron surface. The energy for a reaction\nX\u0003+Y\u0003!XY\u0003can be calculated as follows:\n\u0001E=\u0000\nE(XY\u0003) +E0\u0001\n\u0000\u0000\nE(X\u0003) +E(Y\u0003)\u0001\n; (4)\nThis equation can be written, using the energy values E s\nof Eq.(1) as follows:\n\u0001E=Es(XY\u0003)\u0000(Es(X\u0003) +Es(Y\u0003)): (5)3\ny\nzx\n011\n011011100\n011 111\n100011\n100011100010001011111211\n011 211011111\n100011(g) (a)\n(b)(e)\n(d)(c)\n(f)\nFigure 1: (color on-line) Computational unit cells for di\u000berent \u000b\u0000iron surfaces used in the simulations viewed from (a,c,e) top\nand from (b,d,f) side. (a-b): (110), (c-d): (100) and (e-f): (111) surfaces. Atoms in topmost (lowermost) layers are marked\nwith brighter (darker) shades. Atoms in the unit cells used in this work are marked with blue color. (g) A portion of bulk\n\u000b-iron cut at di\u000berent angles, demonstrating the positions of di\u000berent crystallographic surfaces. For (100) surface, the topmost\nlayer is marked with black colour. For (111) surface, the two topmost layers are marked with blue colour. For (110) and (100)\nthe unit cells correspond to 3 \u00023 periodicity, while for (111) to 2 \u00022 periodicity.\n= octahedral site\n(110) (100) (111)\nABA\nBAAB\nA=2.00 Å\nB=1.48 Å(b) (c) (d) (a)\nFigure 2: (color on-line) Local coordination at the bulk octahedral site in \u000b\u0000iron and how it is exposed on the (110), (100)\nand (111) facets. The octahedral site is marked in all insets with green color. (a) The coordination of octahedral site in the\nbulk. Coordination of octahedral sites on the (b) (110), (c) (100) and (d) (111) facets.\nIn the Results section, we tabulate values of E sand then\nuse these tabulated values to calculate reaction energetics\nX\u0003+Y\u0003!XY\u0003using Eq.(5).\nThe surface energy G of a speci\fc nanoparticle facet\nwith adsorbates has in some earlier works6,27been de-\n\fned as follows:\nG=E(X\u0003)\u0000NEbulk\u0000n\u0016c; (6)\nwhereNis the number of the surface atoms in the slab\nused for simulations and Ebulkis the energy per atom in\nthe bulk. As Eq.(6) re\rects the energy cost to create a\nsurface from the bulk and adsorbing atoms on the surface,\nit is more accurate to use an equation involving explicitly\nthe surface energy Esurf as follows:\nG=Esurf+Ec; (7)\nwhere E cis the adsorption energy of Eq.(3). In Eq.(7) the\nsurface energy Esurfis a well de\fned quantity, while thechemical potential of the carbon adsorbates is sensitive\nto the source of carbon atoms.\nIn this work we use the values calculated by\nB l\u0013 onski and Kjiena15,16for the (110), (100) and (111)\nfacets which have been evaluated as discussed by\nBoettger28. These are E surf=140 meV/ \u0017A for the Fe(110)\nand Fe(100) surfaces and E surf=160 meV/ \u0017A for the\nFe(111) surface16.\nOur calculations were performed in the framework of\nthe density functional theory (DFT), as implemented in\nthe VASP code29,30. All calculations were done using\nprojector-augmented waves (PAWs)31and the Perdew-\nBurke-Ernzerhof (PBE) generalized gradient approxima-\ntion (GGA)25. We used the Monkhorst-Pack (MP)\nsampling32of the Brillouin zone in calculations involving\nthe slab. The sampling used was 7 \u00027\u00021 in the case of all\nthe slabs which corresponds to A BZ\u00190.01 \u0017A\u00002(area in\nthe reciprocal space per sampled k-point). A systematic\nsearch to \fnd the optimal adsorption sites for C atoms4\nand C 2molecules was performed on the slabs of Fig.1\nalong the lines of Ref.[33].\nSpin polarization was included in all calculations. The\ncuto\u000b energy of the plane wave basis set was always 420\neV. The mixing scheme in the electronic relaxation was\nthe Methfessel-Paxton method34of order 1. Conjugate-\ngradient (CG) relaxation of the geometry was performed\nand if needed, the relaxation was continued with a semi-\nNewton scheme. This way we were able to reach a max-\nimum force residual of \u00190.01 eV/ \u0017A. In all calculations\nthe special Davidson block iteration scheme was used and\nsymmetries of the adsorption geometries were not uti-\nlized.\nAs carbon chemical potential, we used either the en-\nergy of an isolated atom in vacuum or the energy per\natom in graphene. For calculation of the chemical poten-\ntial, identical parameters to those described earlier in this\nsection were used. For an isolated, spin-polarized carbon\natom calculated in a cubic unit cell with 15 \u0017A sides, we\nobtained the total energy of E=-1.28 eV. For graphene,\nand using a k-point sampling of 25 \u000225\u00021 we obtained\na lattice constant a=2.468 \u0017A. This is slightly larger than\nvalues obtained by LDA,35but is identical to a previous\ncalculation using GGA36. The energy per carbon atom\nin graphene we obtained is E=-9.23 eV.\nNudged elastic band (NEB) calculations37were per-\nformed with VASP. Atoms in the topmost layer were al-\nlowed to move freely, and in some cases, the atoms below\nthe topmost layer were allowed to move into z-direction\n(normal to surface) only. Thus we were able to avoid the\n(arti\fcial) collective movement of the surface slab atoms\nthat sometimes occured during the minimization.\nIII. RESULTS\nA. Morphology of \u000b\u0000iron facets\nWe can expect from some earlier studies concerning\ncarbon solution into bulk iron and adsorption on iron\nsurfaces,17,26that carbon prefers sites of maximum co-\nordination: in bulk iron, it prefers the 6-fold octahe-\ndral site26and on the (110) and (100) facets, carbon\nmoves into sites that o\u000ber highest possible number of\niron neighbours17. Keeping this in mind, we will give in\nthis section a qualitative picture of carbon adsorption on\ndi\u000berent facets. This analysis is based on the octahedral\nsite of bulk \u000b\u0000iron.\nThe local coordination of the octahedral site is illus-\ntrated in Fig.2(a). When carbon is adsorbed into this\nsite, a tetragonal distortion in the bcc lattice takes place\nand distance B is expanded. As the bulk is cleaved along\na speci\fc direction in order to create a surface, the octa-\nhedra become cleaved in a speci\fc way, exposing octahe-\ndral sites. The way the octahedral sites are exposed in\ndi\u000berent facets, has been illustrated in Fig.2(b-d). On the\n(110) surface, the exposed octahedral sites have neigh-\nboring iron atoms at distances A and B. In the case ofthe (100) surface, there are several exposed octahedral\nsites where the neighboring iron atoms are simply at a\ndistance A.\nAssuming that carbon tries to maximize its coordina-\ntion with iron on the surface (as discussed above), it will\nalways prefer an exposed octahedral site, as this kind of\nsite o\u000bers maximum coordination within the bcc lattice.\nThe displacements of iron atoms surrounding a surface\nexposed octahedral should be very similar to the bulk\ntetragonal distortion (i.e. expansion of (B) and a slight\ncontraction of (A)). This distortion must be energetically\nvery di\u000berent on the distinct surfaces. Depending on how\nthe distortion of A and B \fts the facet morphology, quite\ndi\u000berent adsorbate-adsorbate repulsions can be formed;\nfor example, expanding B on the (110) facet (Fig.2(e))\nconsists of pushing neighboring iron atoms apart. On\nthe (100) facet there are many sites with no need to re-\narrange the iron atoms as only small contraction of A is\nneeded.\nB. Bulk \u000b\u0000iron facets\nFor the bulk iron lattice constant we obtained\na=2.83 \u0017A, which agrees well with an earlier computa-\ntional value26and the experimental value of 2.87 \u0017A[38].\nFor the bulk magnetic moment we obtained M=2.18\n\u0016B. In earlier works, interlayer relaxations for various\n\u000b\u0000iron facets have been studied15,16. The most impor-\ntant e\u000bect is the inward relaxation of the outermost layer.\nThe interlayer relaxations can be sensitive to the slab size\nand to the scheme used (symmetric/non-symmetric slab,\nnumber of \fxed layers)15,16. In Tab.I we compare our\nresults with previous ones. In our scheme, the slab is\nnon-symmetric as the atoms in the three bottom layers\nare \fxed. In Ref.[15] three topmost layers were allowed\nto relax, while in Ref.[16] freestanding slabs were consid-\nered. As evident from Tab.I we can see that the type\nof relaxation (either expansion or contraction) is quite\nconsistent. Magnitudes of expansion/contraction have a\nfew di\u000berences of the order of 10% in the case of the\n(111) facet, but on the other hand, in this facet the bulk\ninterlayer distances are very small ( \u00190.82\u0017A).\nValues of magnetic moment in di\u000berent layers are pre-\nsented in Tab.II. Consistent with earlier results16we ob-\nserve that (100) has the highest top layer magnetic mo-\nment and that in all slabs, the value of magnetic mo-\nment approach to that of bulk as we move inside the\nslab. Our values for the moments in the topmost layer,\n2.56\u0016B(110), 2.96\u0016B(100) and 2.84 \u0016B(111), compare\nwell with the values of Ref.[16], namely 2.59 \u0016B(110),\n2.95\u0016B(100) and 2.81 \u0016B(111).\nC. Atomic carbon, coadsorption, dimers\nIn this section we study atomic carbon adsorption\u0000\n1/9\nML coverage for (110) and (100) and 1/4 ML coverage5\nd12d23d34d45d56d67\n(110)\n-0.1 0.3 -0.5 -0.2 0.04 0.2 Ref.[16]\n-0.11 1.16 1.14 Ref.[15]\n-0.4 0.5 -0.7 This work\n(100)\n-3.6 2.3 0.4 -0.4 -0.01 -0.5 Ref.[16]\n-3.09 2.83 1.93 Ref.[15]\n-1.2 3.4 3.5 This work\n(111)\n-17.7 -8.4 11.0 -1.0 -0.5 0.1 Ref.[16]\n-6.74 - 16.89 12.4 Ref.[15]\n-3.8 -18.0 11.0 0.0 -0.7 1.6 This work\nTable I: Interlayer relaxations in the slabs of Fig.1 as percent-\nage of the bulk distances. dijis the distance between layers i\nand j.\n1 2 3 4 5 6\n1102.57 2.28 2.17 2.17 2.29 2.56\n1002.96 2.37 2.47 2.50 2.38 2.96\n1111 2 3 4 5 6\n2.89 2.39 2.49 2.30 2.28 2.15\n7 8 9 10 11 12\n2.20 2.24 2.29 2.46 2.29 2.84\nTable II: Magnetic moment of atoms in di\u000berent layers ( \u0016B)\nin the slabs of Fig.1. Number 1 denotes the bottom layer.\nfor (111)\u0001\nas well as dimer- and co-adsorption. We study\nin detail how the adsorbates either repel or attract neigh-\nboring iron atoms in the topmost iron layers and will use\nthe resulting displacements of iron atoms as our leading\nargument when describing the energetics at higher car-\nbon concentrations in the next section.\n1. Atomic carbon\nAdsorption geometries for carbon atoms (C-1, C-2,\netc.) on the di\u000berent facets are illustrated in Figs.3-\n5. Corresponding energetics are tabulated in Tab.III.\nTaking a closer look at Figs.3-5, we can see that carbon\nfavors the exposed octahedral sites of Fig.2 as discussed\nin Sec.(III A).\nThe most favorable (C-1) sites for (110) and (100) are\nconsistent with previous calculations6,17,20. From Tab.III\nthe adsorption energies are -7.98 eV and -8.45 eV for the\n(110) and (100) surfaces, respectively. These compare\nwell with earlier computed values of -7.92 eV[17] and -\n7.97 eV[6] for (110) and with -8.33 eV[17], -8.335 eV[20]\nfor the (100) surface.\nThe iron atom below the adsorbed carbon atom on\n100/C-1 shifts downwards, corresponding to expansion\nof (B) in Fig.2. The coordination of carbon on (100)\nis \fvefold17,20and it is bonded to the iron atom below\nat a distance of 1 :98\u0017A. In the following we analyze in\nmore detail the intralayer relaxations in the topmost sur-Adsorbate Eads(eV) Ec(eV) Es(eV) BL (\u0017A)\nFe(110)\nC-1 -7.98 -0.03 -9.26\nC-2 -6.91 1.04 -8.19\nC-3 -5.48 2.47 -6.76\nC2-1 -8.19 0.73 -17.72 1.35 (1.31)\nC2-2 -8.04 0.88 -17.57 1.38\nC2-3 -7.12 1.81 -16.64 1.32\nCA-1 0.2 -18.26\nCA-2 0.74 -17.71\nFe(100)\nC-1 -8.45 -0.5 -9.73\nC-2 -7.2 0.74 -8.48\nC-3 -7.18 0.77 -8.46\nC2-1 -8.26 0.67 -17.79 1.33\nC2-2 -7.91 1.01 -17.44 1.36\nC2-3 -7.51 1.42 -17.03 1.44\nCA-1 -1.02 -19.48\nCA-2 -0.92 -19.38\nFe(111)\nC-1 -7.74 0.2 -9.02\nC-2 -7.69 0.26 -8.96\nC-3 -7.43 0.52 -8.71\nC-4 -7.41 0.53 -8.69\nC2-1 -8.95 -0.02 -18.47 1.40\nC2-2 -8.87 0.05 -18.4 1.38\nCA-1 0.61 -17.84\nCA-2 0.82 -17.63\nTable III: Adsorption energies E ads(see Eq.(2)), energies E c\n(see Eq.(3)) and shifted energies E s(see Eq.(1)). Values of\nEscan be used directly to calculate reaction energies on the\nsurface by using Eq.(5). Values for C atoms and C 2molecules\nin di\u000berent adsorption geometries on the \u000b-iron (110), (100)\nand (111) surfaces have been tabulated. Bond lengths (BL)\nfor adsorbates and in vacuum (in parenthesis) are listed. Sites\nand geometries have the same labels as in Figs.3-4 and in\nTab.IV. Coadsorption geometries are tagged with the label\n\\CA\".\nface layer, using as a guide the qualitative discussion of\nthese relaxations made in Sec.(III A); this kind of analy-\nsis, based on the tetragonal distortion of bulk adsorption,\nwas made to some extent in Ref.[17], but only for the case\nof sub-surface adsorption.\nIn 110/C-1 of Fig.3 there are considerable intralayer\nrelaxations in the topmost layer. The distance between\niron atoms (b) and (d) contracts by 5 % (0.20 \u0017A, corre-\nsponding to contraction of A in Fig.2) while the distance\nbetween (a) and (c) expands 23% (0.65 \u0017A, corresponding\nto expansion of B). In 100/C-1 of Fig.4 the displacement\nof iron atoms is smaller: now both distances (bd) and\n(bc) contract only by 5 % (0.15 \u0017A), corresponding simply\nto the slight contraction of A; due to the speci\fc cleav-\ning of the octahedron in Fig.2, the Fe(100) surface o\u000bers\nexposed octahedral sites for carbon with very little need\nto move the surrounding iron atoms.\nFrom Tab.III we can see that adsorption into 100/C-1\nis 0.47 eV more favorable than adsorption into 110/C-\n1 (similar to the value of 0.41 eV obtained in Ref.[17]).6\nFe(110)\nC−1 C−2 C−3 C  −12\nC  −22C  −32\nCA−1CA−2ab\nc\nd\nab\nc\ndab\nc\ndab\nc\nd\nFigure 3: Some of the most stable geometries for C and C 2on the Fe(110) surface. Di\u000berent geometries are tagged with the\nsame labels as in Tab.III. Coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label\n\\CA\". Iron atom displacements upon carbon adsorption in (C-1) have been marked with arrows. These can be related to Fig.2.\nIn (CA-2) one adsorbed carbon atom is pushed towards vacuum.\nFe(100)\nC−1 C−3 C−2 C  −12\nC  −22 C  −32 CA−1 CA−2ab\nab c ab c\nddab c\nd dc\nFigure 4: Some of the most stable geometries for C and C 2on the Fe(100) surface. Di\u000berent geometries are tagged with the\nsame labels as in Tab.III. Coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label\n\\CA\". Iron atom displacements upon carbon adsorption in (C-1) have been marked with arrows. These can be related to Fig.2.\nWhen looking at energies E c, we observe that at a low\ncoverage of 1/9 ML (i.e. single adsorbed atom), it is\nmore favorable for the carbon atom to be adsorbed into\nthe iron surface than to be incorporated into graphene.\nWhile in the case of (110), this tendency is very weak\n(only\u001830 meV), for (100) it is more signi\fcant (0.5\neV). As will be discussed below, E cis very sensitive to\nthe amount of carbon adsorbed on the facets: at lower\nconcentrations than we are considering in this paper (less\nthan 1/9 ML), E cshould clearly become negative also for\n(110).\nThe remaining adsorption geometries for (110), i.e.110/C-2 and 110/C-3 are metastable down to \u00190.012\nmeV/ \u0017A and they lie more than 1 eV higher in energy than\n110/C-1. Their characteristics (local minimum, higher\norder saddle point, etc.) have been discussed in more\ndetail in Ref.[17]..\nComparing Fig.2(d) and the optimal adsorption sites\nof carbon atoms in Fig.5 we can see that carbon prefers\nexposed octahedral sites on the (111) facet. In 111/C-1,\nthere is a 0.74 \u0017A expansion in the distance of atoms (b-d)\nand a 0.2 \u0017A contraction in the distance of atoms (a-c), cor-\nresponding again to (B) and (A) in (Fig.2(a)). While ad-\nsorbate 111/C-2 exhibits very similar distortions, 111/C-7\nFe(111)\nC−1 C−3 C−2 C−4\nCA−1 C  −22 C  −12 CA−2abcda c\ndab\nc\ndb\nc ab\nFigure 5: Some of the most stable geometries for C and C 2on the Fe(111) surface. Di\u000berent geometries are tagged with the\nsame labels as in Tab.III. Coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label\n\\CA\". Iron atom displacements upon carbon adsorption in (C-1) have been marked with arrows. These can be related to Fig.2.\n3 breaks the trend a bit as it does not adsorb into an\nexposed octahedral site. It \fnds a high coordination by\nmoving atoms (a),(b) and (c) instead. Atoms (a),(b) and\n(c) all move symmetrically \u00180.3\u0017A and their distance to\nthe carbon atoms becomes 2.1 \u0017A. There is also one iron\natom directly below the carbon at a distance of 1.85 \u0017A.\nAdsorbate 111/C-4 is simply a carbon atom adsorbed at\na bulk-like octahedral site.\nWhen looking at the adsorption geometry C-1, we can\nobserve that it is by de\fnition a \\sub-surface\" site, i.e.\nthe carbon atom resides below the topmost iron layer.\nOn the other hand, it has not yet obtained a coordination\nwith surrounding iron atoms similar to that in bulk. On\nthe contrary, C-2 is clearly a \\surface\" adsorption site.\nThe energy di\u000berence between C-1 (a \\semi\" sub-surface\nsite) and C-2 (\\surface\" site) is minimal, only 50 meV.\nThe energetics for carbon adsorption on (111) in\nTab.III are not directly comparable to those reported in\nRef.[6], as in that work the motion of iron atoms was\nconstrained (some of the sites will have di\u000bent local ge-\nometries upon relaxation). Our values for the C-1 (-7.74\neV) and C-3 (-7.43 eV) sites are very close to the value\nreported in Ref.[6] (-7.60 eV) for a similar site.\n2. C 2dimer\nAssuming that carbon atoms in the dimer prefer sim-\nilar high-coordinated sites as the individual atoms while\nmaintaining a reasonable carbon-carbon bond length,\nthere are not good possibilities to achieve this on the\n(110) and (100) surfaces, as the optimal C-1 sites lie far\naway from each other. The case of (111) is very di\u000berent;\nlooking at Fig.2(d) we can see that there is an abundance\nof optimal adsorption sites within the bond length of acarbon dimer. We can then expect that C 2dimer is most\nstable on the (111) surface.\nThe optimal C 2adsorption geometries on the (110) and\n(100) of Figs.3-4 are in both facets quite similar: individ-\nual carbon atoms are 1-3 fold coordinated to iron: one\nFe-C distance in both cases is 1.85 \u0017A, while the remain-\ning two Fe-C distances are \u00192.0\u0017A. The C-C bond length\nfor 110/C 2-1 is slightly expanded while for 100/C 2-1 it is\ncloser to the isolated C 2bond length. In 110/C 2-1, both\niron atom distances ac and bd expand by \u00185% while\nin 100/C 2-1, the distance between a and c is expanded\nby\u001815%. Of the remaining C 2adsorption geometries\n110/C 2-2 exhibits similar trend as C 2-1: both C atoms\nreside in a site\u00183-fold to iron atoms. Other C 2adsorp-\ntion geometries are trying to adopt positions where the\nadsorbed carbon can reside in C-1, C-2 or C-3 sites\nThe optimal position, C 2-1 for the carbon dimer on\n(111) is depicted in Fig.5. Both carbon atoms reside in\na C-1 site while the Fe-C distances are \u00192\u0017A. The C-C\nlength in the dimer is expanded by \u00196%. The adsorbate\nC2-2 exhibits a similar trend. Comparing the adsorp-\ntion energies of C 2-1 in the case of the di\u000berent facets\n(Tab.III), the adsorption of the carbon dimer on 111 is\nat least\u00190.7 eV more favorable than on the other facets;\nas discussed above, this is because the (111) facet o\u000bers\nnearby optimal adsorption sites for the carbon atoms.\nThe reaction energetic of Tab.IV further demonstrate\nthat it is much more favorable to form carbon dimers on\nthe (111) facet than on the (110) and (100) facets. The\n(100) facet favors less dimer formation than the other\nones, as having carbon in atomic form is energetically\nmost favorable on this facet.8\n3. Coadsorption\nWe have studied coadsorption con\fgurations by plac-\ning two carbon atoms in a sublattice of the most optimal\nadsorption sites of the individual carbon atoms. The op-\ntimal coadsorption sites we found are marked with tags\n\\CA\" in Figs.3-5.\nIn the case of (110) (Fig.4) the two coadsorption con\fg-\nurations considered become very di\u000berent; in 110/CA-1,\nboth atoms reside in a 110/C-1 adsorption site. However,\nin 110/CA-2, one of the atoms is forced to move from the\nC-1 site towards vacuum. As discussed earlier, this re-\nsults from the expansion of distance (B) (Fig.2) on the\n(110) facet; in 110/C-1, atoms (a) and (c) are pushed\napart and in 110/CA-2 the carbon atoms are pushing\nthe same atom (c) into opposite directions. This creates\nstrong repulsion between the carbon atoms and only one\ncarbon atom can be accomodated into the C-1 site. This\nresults in a notable, 0.5 eV energy di\u000berence between the\n110/CA-1 and 110/CA-2 con\fgurations\nThe situation is very di\u000berent on the (100) surface. As\ndiscussed above, the adsorption of carbon to the 100/C-1\nsite does not involve considerable motion of the surface\niron atoms, as the only displacement needed is the very\nsmall contraction of (A) (Fig.2). In the optimal coadsorp-\ntion geometries 100/CA-1 and 100/CA-2 of Fig.4 there\nare indeed very minor displacements of iron atoms to-\nwards the adsorbed carbon. In CA-2 both carbon atoms\nattract iron atoms (c) and (d), while in CA-1 they pull\nonly one common iron atom (c). In Tab.III we can see\nthat this results in a small 0.1 eV energy di\u000berence be-\ntween CA-1 and CA-2.\nIn the case of the (111) surface, there are quite many\nneighboring optimal adsorption sites (C-1 and C-2) and\nso the number of coadsorption con\fgurations becomes\nlarge. The two most optimal con\fgurations we found\n(CA-1 and CA-2) are illustrated in Fig.4. As evident\nfrom Tab.III, their energy di\u000berence is only 0.2 eV.\nD. Higher carbon concentrations\nIn this section, we study the e\u000bect of high carbon con-\ncentrations\u0000\n>2/9 ML for (110) and (100), >3/4 ML for\n(111)\u0001\non energies E c(Eq.(3)). Carbon is adsorbed on\nthe sublattice formed by the most favorable C-1 adsorp-\ntion sites. Our study is most systematic for the (100)\nsurface as there is an obvious way how to place an in-\ncreasing number of carbon atoms on the surface: we do\nnot expect considerable displacement of iron atoms from\nthe bulk positions nor the displacement of carbon atoms\naway from the optimal C-1 adsorption sites. On the other\nhand, as we saw in previous sections, on (110) surface ad-\nsorbed carbon atoms start to repel each other, while on\n(111) we can expect dimer formation. Our objective for\n(110) and (111) is simply to further demonstrate these\npoints (adsorbate repulsion, dimer formation) at higher\ncarbon concentrations. We start with the case we studiedmost systematically, i.e. with the (100) surface.\n(100) surface. Carbon concentration of up to 1 ML\nhas been considered for the (100) facet in Fig.6. A mini-\nmum of energy E cas function of carbon concentration oc-\ncurs at the coverage of 6/9 = 0.667 ML at an adsorption\ncon\fguration \\3p\n(2)\u0002p\n(2)\" that has been reported ear-\nlier in an experimental19and theoretical20study; in this\nadsorption con\fguration, carbon atoms form an in\fnite,\ntwo atom wide ribbon on the C-1 sublattice. There exists\neven more favorable coadsorption con\fguration \\c(2 \u00022)\"\nwhich takes place at the coverage of 0.50 ML17,18,20. Both\nof these stable structures have been analyzed using STM\nand/or LEED18,19For the 6/9 ML coadsorption struc-\nture presented in Fig.6 we observe same phenomena as\nreported in an earlier study20, most notably the displace-\nments of iron atoms in the topmost layer as illustrated\nschematically in Fig.6.\nThe most interesting phenomena in the case of the\n(100) surface is the behaviour of E cin Fig.6 as func-\ntion of carbon concentration: the energy lowers as more\ncarbon is adsorbed, implying the existence of stable iron-\ncarbon phases, while at increased >0.5 ML carbon con-\ncentrations the situation becomes unstable and graphene\nformation is favored. This behaviour can be explained\nby considering the displacements of iron atoms in the\ntopmost surface layer.\nFrom the reconstruction patterns presented by arrows\nin Fig.6 we can see that iron atoms move always towards\nthe adsorbed carbon. These changes in iron atom po-\nsitions are typically in the range of \u00180.2-0.3 \u0017A and, this\nis in accordance what was discussed in earlier sections.\nAs carbon concentration increases, iron atoms become\nincreasingly \\frustrated\" as they are surrounded by car-\nbon; at 1.0 ML, an iron atom has so many neighboring\ncarbon atoms that it cannot obtain optimal bonding con-\nditions with any one of them.\nThis frustration mechanism results in sudden change in\nthe energetics on the (100) facet; even at such a high con-\ncentration as 8/9 ML, it is more favorable to adsorb car-\nbon atoms to the C-1 sublattice than incorporate them\ninto graphene, but when going from 8/9 ML to 1 ML,\nthis tendency is suddenly reversed. In the last row and\ncolumn of Fig.6, we present the energy gain when releas-\ning surface frustration by dimer formation. It is quite\nlarge, over 1 eV.\n(110) surface. Some con\fgurations of carbon for\nup to 1 ML have been considered for the (110) facet in\nFig.7. The initial con\fgurations consisted of adsorbing\ncarbon atoms on either the C-1, C-3 or C2-1 sublattice\n(see Fig.3) and the \fnal, relaxed geometries are presented\nin Fig.7. As we discussed in Sec.(III C 3), at 2/9 ML cov-\nerage there are coadsorption con\fgurations where carbon\nadsorbates start to repel each other. Such e\u000bects be-\ncome more important at higher carbon concentrations.\nIn Fig.7 and for a 3/9 ML concentration, there is still\none possibility to adsorb carbon without creating an ex-\ncess of surface stress, similar to CA-1 of Fig.3 and this\nis illustrated in the string-like con\fguration of C3-1. If9\nFe(110)\nReaction \u0001E\n2 (C-1)!C2-1 0.79\n2 (C-2)!C2-1 -1.35\n(C-1) + (C-2)!C2-1-0.28\nCA-1!C2-1 0.53\nCA-2!C2-1 -0.01\n2 (C-1)!CA-1 0.26\n2 (C-1)!CA-2 0.81Fe(100)\nReaction \u0001E\n2 (C-1)!C2-1 1.67\n2 (C-2)!C2-1 -0.82\n(C-1) + (C-2)!C2-10.43\nCA-1!C2-1 1.69\nCA-2!C2-1 1.59\n2 (C-1)!CA-1 -0.02\n2 (C-1)!CA-2 0.08Fe(111)\nReaction \u0001E\n2 (C-1)!C2-1 -0.42\n2 (C-2)!C2-1 -0.54\n(C-1) + (C-2)!C2-1-0.48\nCA-1!C2-1 -0.63\nCA-2!C2-1 -0.84\n2 (C-1)!CA-1 0.21\n2 (C-1)!CA-2 0.41\nTable IV: Reaction energies for forming C 2dimers and for bringing carbon atoms into coadsorption con\fgurations. Geometries\nare tagged with the same labels (C-1, C-2, etc.) as in Tab.III and Figs.3-4. Reaction energies are calculated by taking the\ncorresponding energies E sfrom Tab.III and applying Eq.(5).\nFigure 6: Adsorption geometries where carbon atoms are adsorbed in the sublattice formed by the C-1 sites (see Fig.4). N C\nis the number of carbon atoms and N conf the number of all possible coadsorption con\fgurations when N Catoms are adsorbed\non a (3\u00023) C-1 sublattice. For a particular coadsorption geometry illustrated in the table, energy E cand the mean Bader\nelectron occupations for carbon atoms ( \u0016Qb) have been tabulated. Displacements of some iron atoms upon carbon adsorption\nhave been highlighted by blue arrows. In the last row and column, the energy gain when forming a C 2molecule at the 1 ML\nconcentration is calculated.\nwe place atoms at the same 3/9 ML concentration to a\nC3-1 sublattice, only one carbon atom is adsorbed into\na C-1 site and the remaining atoms form spontaneously\na dimer. This is demonstrated in con\fguration C3-2 of\nFig.7.\nAt 4/9 ML coverage we have considered several di\u000ber-\nent con\fgurations: C4-1 is very similar to CA-2 of Fig.4\nand the surface stress is again released by expulsing two\natoms towards vacuum while maintaining at least twoother atoms on the C-1 site; in C4-4, a complex recon-\nstruction, where all carbon atoms are residing in 3-fold\nadsorption sites occurs; at 6/9 ML concentration, even\niron atoms are expelled from the surface in order to re-\nlease surface strain and to accommodate carbon atoms in\nthe C-1 site; in C6-2, a C-Fe-C molecule is spontaneously\nformed.\n(111) surface. In the case of the (111) we discussed\nhow there is an abundance of open octahedral sites (C-110\nFigure 7: Relaxed adsorption geometries on (110) after carbon atoms have been placed in a sublattice formed by the C-1\n(C3-1, C4-1,C6-2), C-3 (C3-2, C4-4, C6-1) and C 2-1 (C4-2, C4-3) con\fgurations of Fig.3. Number of carbon atoms per unit\ncell (N C) and energies E chave been tabulated.\nFigure 8: Relaxed adsorption geometries on (111) after carbon atoms have been placed in a sublattice formed by the C-1 and\nC-2 sites (see Fig.5). Number of carbon atoms per unit cell (N C) and energies E chave been tabulated.11\ncN  =C6−1\n111\n100C3−1C3−2C4−1C4−3\nC−1 CA−1C −12C−1C −12CA−1C3−1\n1 3 ..\n2110\nconcentration (1/Å )2(meV/Å  )2G\nFigure 9: Surface energy G (Eq.(7)) as function of carbon coverage (atoms per \u0017A2) on the (110), (100) and (111) facets.\nEnergies correspond to the fully relaxed adsorption geometries of Figs.3-8. Energy at zero concentration has been \fxed to the\nsurface energy of the facet\u0000\n140 meV/ \u0017A2for (110) and (100), 160 meV/ \u0017A2for (111)\u0001\n, as described by Eq.(7).\nand C-2 in Fig.5). We also noted that these sites are close\nto each other so that C 2dimers are naturally formed.\nSome of the most favorable coadsorption con\fgurations\nat higher concentrations on the (111) surface have been\nillustrated in Fig.8. From the energetics in Fig.8, we see\nthat there is an energy cost when adsorbing more carbon\non the surface, but not as high as in the case of (110);\nno strong repulsion of carbon atoms takes place as there\nare plenty of adsorption sites and the top layer atoms\nin (111) are \rexible to move. In (110), the C 2dimers\nwere formed above the topmost surface, resulting from\nexpulsion of carbon atoms from the C-1 sites, while in the\n(111), the carbon dimers are formed below the topmost\nlayer, in the very same sites where the atomic carbon is\nadsorbed.\nSurface energies. The energetics of Tab.III and\nFigs.6-8 are also shown in Fig.9 as surface energies (em-\nploying Eq.(7)). This \fgure is not to be taken as an\nexact representation of surface energies as function of\ncarbon concentration; situations with \\graphenated\" sur-\nfaces (see Ref.[6]) and many possible carbon adsorption\ncon\fgurations are missing. However, one can see some\nclear trends: the steep rise in the surface energy as func-\ntion of carbon concentration in the (110) facet implies\naggressive graphene formation on this facet; the (100)\nfacet forms stable carbidic phases near 0.5 ML = 0.08\n1/\u0017A2; at high carbon concentrations the (111) facet gains\nin relative stability with respect to (100) facet. This sta-\nbilization can be understood in terms of frustration of\nthe (100) facet, and from the bigger number of adsorp-tion sites available and the \rexibility of the topmost iron\natoms on the (111) facet, as discussed above.\nE. Di\u000busion\nDi\u000busion on and into the (110) and (100) facets has\nbeen described earlier by Jiang and Carter17. We re-\npeated their calculations for the activation barriers of\ncarbon di\u000busion on the topmost iron layer and obtained\nidentical results. Here we report resuls for carbon di\u000bu-\nsion on the (111) facet which, to our knowledge, have not\nbeen calculated earlier using ab initio methods.\nWhen studying sub-surface adsorption and di\u000busion,\none must keep in mind the deep interlayer relaxations\nof pure iron slabs and the elongation/contraction of dis-\ntances (A) and (B) (Fig.2) which might propagate far\nin the lattice. Then a thorough investigation of activa-\ntion energies and energy cost for carbon atom to enter\nthe bulk would require calculations with very thick slabs,\nconsidering increasing adsorption depths until bulk val-\nues are recovered.\nIn Ref.[17] barriers and energetics for (110) and (100)\nwere calculated down to the \frst sub-surface layer. As\ndiscussed in Sec.(III C 1) for (111) facet, the 111/C-1 site\nof Fig.5 can be classi\fed as \\semi\" sub-surface site. In\nour calculations, we have considered also the \frst \\true\"\nsub-surface site (i.e. a site that has bulk-like coordina-\ntion), but have not pursued the calculation of the di\u000bu-\nsion barrier when going very deep inside the slab as the12\n1.12 eV\n0.05 eV0.43 eV\nC−1C−2\nC−20.77 eV\n0.52 eV\nC−1(a) (b)\n0.25 eV\nFigure 10: (a) Di\u000busion on (111) into the C-1 and C-2 sites (Fig.4) and (b) into a deeper sub-surface site.\nlimits of our \fnite slab are quickly reached.\nCarbon di\u000busion between neighboring C-2 sites and\nbetween the C-1 and C-2 sites has been illustrated in\nFig.10(a). Di\u000busion from C-2 to deeper inside the slab\nand reaching a site where carbon has similar coordination\nas in the bulk octahedral site, is illustrated in Fig.10(b).\nThis site, not reported in Fig.5, should not be confused\nwith the C-4 adsorbate which lies even deeper inside the\nslab.\nThe activation energy E a=1.12 eV for surface di\u000busion\nreported here for the (111) surface is smaller than for the\n(100) surface (1.45 eV), but slightly bigger than for the\n(110) surface (0.96 eV)[17]. Going from C-2 site to the\n\\semi\" sub-surface site C-1 has a very low barrier of 0.43\neV. Going deeper inside the slab has a barrier of 0.77 eV.\nAs illustrated in the insets of Fig.10(b), in the transition\nstate of the minimum energy path, one atom in the top-\nmost iron layer is pushed away from the carbon atom.\nHowever, the barrier is low (0.77 eV) because the iron\natoms in the (111) topmost layer are low coordinated\nand \rexible to move. We identify the 0.77 eV barrier\ntentatively as the activation energy for carbon atom to\nenter the surface and it is smaller than those reported\nfor (110) (1.18 eV) and (100) (1.47 eV). Moreover, from\nTab.III the energy di\u000berence between the 111/C-1 and\n111/C-4 sites, is only 0.33 eV, which is smaller than the\nsame energy di\u000berence in (110) (0.62 eV) and (100) (1.19\neV)[17]. There are then clear indications that the ex-\nchange of carbon atoms between the topmost and deeper\nlayers is easier on the (111) facet than on (110) and (100)\nfacets.\nIV. DISCUSSIONS AND CONCLUSIONS\nThis work was motivated by the recent in situ studies\nof carbon nanotube growth from \\large\" iron nanopar-\nticles where di\u000berent nanoparticle facets seem to behavein a very di\u000berent manner. The facets studied in this\nwork correspond to those identi\fed in Ref.[6], namely the\n\u000b\u0000iron (110), (100) and (111) surfaces. We have studied\nthe e\u000bect of adsorbing increasing amounts of carbon on\nthese surfaces\nThe repulsion among adsorbed carbon atoms on the\n(110) facet is strong and because of this, carbon atoms\nare expulsed from the optimal adsorption sites when car-\nbon concentration is increased. This may happen already\nat the relatively low 0.22 ML concentration, resulting in\ndimer and graphene formation.\nThe (100) facet behaves in a very di\u000berent way, as\nstable, carbon rich structures are formed near 0.5 ML\nconcentration. When approaching 1 ML carbon concen-\ntration, (100) is destabilized due to frustration of the top\nlayer iron atoms, which can be released by dimer and\ngraphitic material formation.\nThe (111) surface behaves again in a distinct manner;\nthe surface energy is rather insensitive to the amount of\ncarbon adsorbed on it (at similar atoms/ \u0017A2concentra-\ntions where (100) becomes unstable). This results from\nthe abundance of adsorption sites and from the \rexibility\nof the topmost iron atom layer.\nCarbon nanotube and graphene formation are known\nto be highly kinetic processes, so one must be cautious\nwhen relating the present work - based mainly on to-\ntal energies of di\u000berent adsorbed carbon concentrations\n- to these processes. However, the arguments concerning\nthe nature of adsorbate repulsions and surface iron atom\nfrustration on the di\u000berent facets are valid also in a dy-\nnamical situation and at higher temperatures, as long as\nthe nanoparticles are crystalline.\nThe sudden carbon \\supersaturation\" at the (100)\nfacet near 1 ML carbon concentration might be related\nto the lift of graphitic caps from this facet as more car-\nbon is injected into the nanoparticle as seen in the in\nsituexperiment6. When carbon feedstock is exhausted\nin the experiment, the (111) facets start to shrink, even-13\ntually disappearing6. This is very likely related to our\ncomputational results: the relative stabilities of (100)\nand (111) were observed to be sensitive to the amount\nof adsorbed carbon. At low carbon concentration (100)\ngains in stability while at high concentrations, (111) be-\ncomes equally stable. The exchange of carbon between\nthe topmost iron layer and the subsurface layers was seen\nto be easier on (111) than on the other facets. Carbon\ndimer formation was observed to be most favorable on\n(111). This could be related to the typical TEM image of\na CVD grown multi-walled carbon nanotubes that show\nseveral graphitic layers emerging from the (111) facet6.\nThese last observations can be important when trying\nto understand the growth mechanisms of carbon nan-\notubes in general: in a pure \u000b\u0000iron nanoparticle, the\nportion of (111) facets is very small16. As carbon con-\ncentration on the nanoparticle surface gets higher, (111)\nfacets will be stabilized. Once these facets have been es-\ntablished, graphitic material growth from them can pro-\nceed as they favor C 2formation and as the movement of\ncarbon atoms between sub-surface and surface is easier.\nHowever, in order to make this idea more solid, more in-\nvestigation about the di\u000busion of carbon and kinetics of\ngraphene growth on the (111) facet must be performed.To summarize, carbon concentrations of up to one\nmonolayer were studied on \u000b\u0000iron facets. Such aspects\nas repulsion between carbon adsorbates on the (110) the\nfrustration of iron atoms on the (100) surface and the\ndimer formation on (111) facet together with their e\u000bect\non the surface energies were discussed. Di\u000busion on and\ninto the (111) facet was studied. Our \fndings were re-\nlated to a recent in situ study where the appearance\nof (111) facets correlates with increased carbon concen-\ntration. A general idea where increased carbon concen-\ntration stabilizes the (111) facets followed by growth of\ngraphitic material from these facets was proposed.\nV. ACKNOWLEDGEMENTS\nWe wish to thank the Center for Scienti\fc Comput-\ning, for use of its computational resources. This work\nhas been supported in part by the European Commission\nunder the Framework Programme (STREP project BNC\nTubes, contract number NMP4-CT-2006-03350) and the\nAcademy of Finland through its Centre of Excellence\nProgramme (2006-2011).\n\u0003Electronic address: sampsa.riikonen@iki.\f\n1R. Sharma and Z. Iqbal, Appl. Phys. Lett. 84, 990 (2004).\n2S. Helveg, C. Lopez-Cartes, J. Sehested, P. L. Hansen,\nB. S. Clausen, J. R. Rostrup-Nielsen, F. Abild-Pedersen,\nand J. K. N\u001crskov, Nature 427, 426 (2004).\n3S. Hofmann, R. Sharma, C. Ducati, G. Du, C. Mattevi,\nC. Cepek, M. Cantoro, S. Pisana, A. Parvez, F. Cervantes-\nSodi, et al., Nano Lett. 7, 602 (2007).\n4K. Jensen, W. Mickelson, W. Han, and A. Zettl, Appl.\nPhys. Lett. 86, 173107 (pages 3) (2005).\n5F. Abild-Pedersen, J. K. N\u001crskov, J. R. Rostrup-Nielsen,\nJ. Sehested, and S. Helveg, Phys. Rev. B 73, 115419\n(2006).\n6G. E. Begtrup, W. Gannett, J. C. Meyer, T. D. Yuzvinsky,\nE. Ertekin, J. C. Grossman, and A. Zettl, Phys. Rev. B 79,\n205409 (pages 6) (2009).\n7J. A. Rodriguez-Manzo, M. Terrones, H. Terrones, H. W.\nKroto, L. Sun, and F. Banhart, Nature Nanotechnology 2,\n307 (2007).\n8H. Yoshida, S. Takeda, T. Uchiyama, H. Kohno, and\nY. Homma, Nano Lett. 8, 2082 (2008).\n9J. A. Rodr\u0013 \u0010guez-Manzo, I. Janowska, C. Pham-Huu,\nA. Tolvanen, A. V. Krasheninnikov, K. Nordlund, and\nF. Banhart, Small 5, 2710 (2009).\n10R. Sharma, E. Moore, P. Rez, and M. M. J. Treacy, Nano\nLett. 9, 689 (2009).\n11H. S. Bengaard, J. K. N\u001crskov, J. Sehested, B. S. Clausen,\nL. P. Nielsen, A. M. Molenbroek, and J. R. Rostrup-\nNielsen, J. of Catalysis 209, 365 (2002).\n12A. R. Harutyunyan, N. Awasthi, A. Jiang, W. Setyawan,\nE. Mora, T. Tokune, K. Bolton, and S. Curtarolo, Phys.\nRev. Lett. 100, 195502 (pages 4) (2008).\n13A. S. Barnard and P. Zapol, The J. of Chem. Phys. 121,4276 (2004).\n14S. Hofmann, G. Csanyi, A. C. Ferrari, M. C. Payne, and\nJ. Robertson, Phys. Rev. Lett. 95, 036101 (pages 4) (2005).\n15P. B l\u0013 onski and A. Kiejna, Vacuum 74, 179 (2004).\n16P. B l\u0013 onski and A. Kiejna, Surface Science 601, 123 (2007).\n17D. E. Jiang and E. A. Carter, Phys. Rev. B 71, 045402\n(2005).\n18V. Blum, A. Schmidt, W. Meier, L. Hammer, and K. Heinz,\nJ. of Physics: Condensed Matter 15, 3517 (2003).\n19G. Panaccione, J. Fujii, I. Vobornik, G. Trimarchi,\nN. Binggeli, A. Goldoni, R. Larciprete, and G. Rossi, Phys.\nRev. B 73, 035431 (2006).\n20X. Tan, J. Zhou, F. Liu, Y. Peng, and B. Zhao, The Euro-\npean Physical Journal B 74, 555 (2010).\n21W. C. Chiou and E. A. Carter, Surface Science 530, 88\n(2003).\n22R. J. D. Tilley, Understanding Solids: The Science of Ma-\nterials (Wiley, 2004).\n23G. Rollmann, M. E. Gruner, A. Hucht, R. Meyer, P. Entel,\nM. L. Tiago, and J. R. Chelikowsky, Phys. Rev. Lett. 99,\n083402 (2007).\n24A. Postnikov, P. Entel, and J. Soler, European Physical\nJournal D 25, 261 (2003).\n25J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.\nLett. 77, 3865 (1996).\n26D. E. Jiang and E. A. Carter, Phys. Rev. B 67, 214103\n(2003).\n27A. S. Barnard and P. Zapol, Phys. Rev. B 70, 235403\n(2004).\n28J. C. Boettger, Phys. Rev. B 53, 13133 (1996).\n29G. Kresse and J. Furthm uller, Phys. Rev. B 54, 11169\n(1996).\n30G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).14\n31P. E. Bl ochl, Phys. Rev. B 50, 17953 (1994).\n32H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188\n(1976).\n33S. Riikonen, A. S. Foster, A. V. Krasheninnikov, and R. M.\nNieminen, Phys. Rev. B 80, 155429 (2009).\n34M. Methfessel and A. T. Paxton, Phys. Rev. B 40, 3616\n(1989).\n35L. Wirtz and A. Rubio, Solid State Communications 131,141 (2004).\n36G. Gui, J. Li, and J. Zhong, Phys. Rev. B 78, 075435\n(2008).\n37G. Henkelman, B. P. Uberuaga, and H. J\u0013 onsson, The J. of\nChem. Phys. 113, 9901 (2000).\n38C. Kittel, Introduction to Solid State Physics, 6.th edition.\n(Wiley, New York, 1986)."    },    {        "title": "2102.09597v1.Modelling_the_relationship_between_deformed_microstructures_and_static_recrystallization_textures__application_to_ferritic_stainless_steels.pdf",        "content": "Modelling the relationship between deformed\nmicrostructures and static recrystallization textures:\napplication to ferritic stainless steels\nA. Despr\u0013 esa,b,, J. D. Mithieuxc, C. W. Sinclaira\naDepartment of Materials Engineering, The University of British Columbia, 309-6350\nStores Road, Vancouver, Canada\nbUniv. Grenoble Alpes, CNRS, Grenoble INP, SIMaP, F-38000, Grenoble, France\ncAPERAM, F-62330, Isbergues, France\nAbstract\nWe present an original approach for predicting the static recrystallization\ntexture development during annealing of deformed crystalline materials. The\nmicrostructure is considered as a population of subgrains and grains whose\nsizes and boundary properties determine their growth rates. The model input\nparameters are measured directly on orientation maps maps of the deformed\nmicrostructure measured by electron backscattered di\u000braction. The anisotropy\nin subgrain properties then drives a competitive growth giving rise to the recrys-\ntallization texture development. The method is illustrated by a simulation of\nthe static recrystallization texture development in a hot rolled ferritic stainless\nsteel. The model predictions are found to be in good agreement with the exper-\nimental measurements, and allow for an in-depth investigation of the formation\nsequence of the recrystallization texture. A distinction is established between\nthe texture components which develop due to favorable growth conditions and\nthose developing due to their predominance in the prior deformed state. The\nhigh fraction of \u000b\fbre orientations in the recrystallized state is shown to be a\nconsequence of their predominance in the deformed microstructure rather than\na preferred growth mechanism. A close control of the fraction of these ori-\nentations before annealing is thus required to minimize their presence in the\nEmail address: arthur.despres@grenoble-inp.fr (A. Despr\u0013 es)\nPreprint submitted to Elsevier February 22, 2021arXiv:2102.09597v1  [cond-mat.mtrl-sci]  18 Feb 2021recrystallized state.\nKeywords: recrystallization, texture, modelling, ferritic stainless steels\n1. Introduction\nThe crystallographic texture development occuring during static recrystal-\nlization of polycrystalline materials is commonly thought to result from a com-\nplex combination of microstructural features in the deformed state. In \frst ap-\nproximation, orientations whose grains are associated with boundaries of high\nenergy and mobility are most likely to develop [1, 2, 3]. The anisotropy and\nspatial distribution of stored energy and subgrain size may also play a role in\nthe texture development. In materials deformed to moderate strains and at\nhigh temperatures, recrystallized grains tend to have orientations associated\nwith low stored energy, while in materials deformed to high strains and at cold\ntemperatures, high stored energy orientations are usually prefered [4, 5].\nThe two principal approaches to express the relationship between deformed\nmicrostructures and recrystallization textures regard the recrystallization tex-\nture development either from the perspective of `nucleation' or `growth', al-\nthough some models consider both aspects. In models focused on growth, the\norientation relationship between the deformed microstructure and the orienta-\ntions known to recrystallize is investigated. For example, the model of Bunge\nand K ohler investigates the orientations most likely to grow in the deformed\ntextures of fcc and bcc metals [6]. Engler implemented a similar approach to\ninvestigate orientation pinning, i.e. the selective slowing down of speci\fc recrys-\ntallized grains with the progress of recrystallization [7]. In the model of Sebald\nand Gottstein, the mobility of the recrystallized grains depends on the orien-\ntation relationship between the recrystallized and deformed grain orientations\n[8]. The general conclusion of these phenomenological models is that the texture\ncomponents known to develop in recrystallized grains must be, from a statistical\npoint of view, in favourable conditions for growing in a microstructure whose\norientations correspond to the deformed texture.\n2As the recrystallization texture is a product of the deformed microstruc-\nture, several attempts have also been made to link the preferential nucleation\nof orientations to their behaviour during plastic deformation. Di\u000berences in\nnucleation rates between the texture components, have been, for example, at-\ntributed to intergranular slip activity contrasts (estimated by Taylor factors)\n[9, 10], resolved shear stresses [11, 12], and intragranular disorientation levels\n[13] calculated from crystal plasticity simulations. In a recent work, Steiner et\nal.[14] related the preferential nucleation of orientations to measurements of\nkernel average disorientation made on electron backscattered di\u000braction maps\nof the deformed microstructure.\nAs pointed out by Raabe [15], the inhomogeneities that lead to the for-\nmation of recrystallized grains are often overlooked to maintain computational\ne\u000eciency of models. Thus, in most cases, the success in predicting the texture\nresults more from a careful choice of rules and simulation parameters than from\nan apropriate description of the mechanisms driving recrystallization. These\nmodels are, of course, helpful to identify the \frst-order parameters leading the\ntexture development, but their reliability and their sensitivity to the state of\nthe microstructure is limited in proportion to these assumptions.\nIn this article, we present a cellular growth model for predicting static re-\ncrystallization textures which takes as input the experimentally measured char-\nacteristics of deformed microstructures. The model is adapted from an earlier\ntheoretical work [16], where it was assumed that recrystallization occurs by the\ncompetitive growth of subgrains in the deformed microstructure. The initial\nsubgrain properties, which drive the recrystallization kinetics and the devel-\nopment of texture, are calculated directly from orientation maps measured by\nelectron backscattered di\u000braction.\nThe model is illustrated by simulating the recrystallization texture devel-\noped during annealing of a hot rolled ferritic stainless steel sheet. This is an\ninteresting test case for several reasons. Ferritic stainless steels have a high\nstacking-fault energy and readily form subgrains during deformation, in partic-\nular hot deformation. In addition, recrystallization of hot rolled ferritic stainless\n3steels is known to develop so called \u000b\fbre orientations which are deleterious for\nformability and ridging [17, 18, 19], and which demand signi\fcant e\u000borts to be\nremoved during the subsequent processing steps. Little information is currently\navailable in the literature about the origin of this texture, and, importantly, it\nis not reproduced by simulations.\nIn what follows, experimental measurements of the microstructure and tex-\nture evolution during recrystallization of the selected steel are presented \frst.\nNext, the model is described. This is followed by its application to the experi-\nmentally investigated case. A discussion is \fnally conducted on the origin of the\nrecrystallization texture of hot rolled ferritic stainless steels and on the aspects\nof processing which it may be sensitive to.\n2. The experimental data\n2.1. Materials and processing\nThe experiments were conducted using a AISI445 grade of ferritic stainless\nsteel grade produced by APERAM. The nominal composition of the alloy is\ngiven in Table 1. The bcc phase is stable at all temperatures up to the melt-\ning point. Titanium and niobium may precipitate into carbides and nitrides,\nbut at the temperatures investigated these particles are large and present in a\nsu\u000eciently small fraction that their e\u000bect on recrystallization can be neglected\n[20].\nTable 1: Nominal composition of the grade studied, in wt.%\nC N Si Mn Cr Ti+Nb Cu Fe\n0.015 0.028 0.25 0.25 20.20 0.65 0.45 bal.\nA 100mm long, 80mm wide and 15mm thick strip was machined from the\ncenter of an industrially produced transfer bar (i.e. the product between the\nroughing and \fnishing mills in hot rolling). This strip was reheated in a box\nfurnace at 1150\u000eC during 40mn, before being rolled using a laboratory rolling\nmill. The sample was air-cooled to 1100\u000eC, before being rolled to 75% thickness\n4reduction in one pass and then water quenched. The rolling temperature was\nmonitored with thermocouples inserted at the center of the thickness. The\naverage strain rate during rolling was estimated to 23s\u00001, while the Zener-\nHollomon parameter was \u00183\u00021013s\u00001(see ref. [21] for more details). The\nlab scale rolling operation was performed at the OCAS R&D center in Ghent,\nBelgium.\nNext, samples of 60mm \u000210mm\u00023.75mm were prepared from the middle of\nthe width of the hot rolled strip, with the length parallel to the rolling direction.\nThese were annealed in a DSI Gleeble thermomechanical apparatus to induce\nstatic recrystallization of the deformed microstructures. The samples were an-\nnealed at 1100\u000eC for respectively 2s, 5s and 12s, with a preliminary heating\nstep of 3s. Temperature was monitored and controlled by thermocouples placed\nat the center of the samples. At the end of the treatment, the samples were\nwater-quenched.\n2.2. Observation tools\nMicrostructures and textures of the deformed and recrystallized samples\nwere characterized from orientation maps obtained by electron back-scattered\ndi\u000braction (EBSD). Samples were prepared by standard mechanical polishing\ndown to 1\u0016m diamond surface \fnish, followed by electropolishing in a solu-\ntion of 5% perchloric acid + 95% acetic acid. Observations were conducted at\nthe location of the Gleeble thermocouples, in the central third of the sample\nthickness, where the deformation results from approximately plane strain com-\npression [22, 23]. All maps were acquired with a step size of 1 \u0016m to allow for\ndi\u000berentiation of subgrains and recrystallized grains at the same time. After ac-\nquisition, maps were pre-processed using a Kuwahara \flter to reveal subgrains\nseparated by boundaries with disorientation angle of 0.3\u000eor more (i.e. the stan-\ndard angular resolution obtained by this method [24, 25]). Details about the\nimplementation of the Kuwahara \flter are given in Appendix A. While small\nregions of interest will be shown in the illustrative \fgures below, it is impor-\ntant to have in mind that the results were obtained for each condition from\n5several large maps to ensure representativity of the measurements (as a rule of\nthumb, 5000 to 10000 individual orientations are required for proper texture\ncalculation [26]). Finally, orientation distribution functions (ODF) were calcu-\nlated with the Kernel method of MTEX, with a half-width of 5\u000eand assuming\northotropic sample symmetry. ODFs were plotted in the '2= 45\u000esection of\nEuler space as it contains most of the important texture information for ferritic\nstainless steels [22].\nOn the \fltered orientation maps, subgrains were de\fned as regions enclosed\nby boundaries of disorientation angle higher than 0.3\u000eand whose equivalent-\narea diameter is smaller than recrystallized grains. By contrast, recrystallized\ngrains were de\fned as regions enclosed by boundaries of disorientation angle\nhigher than 0.3\u000ewhose equivalent-area diameter is above 30 \u0016m. Note that, as\nfor any recrystallization study, the de\fnition of recrystallized grains is motivated\nby practical considerations and only aims to provide a threshold that describes\ncorrectly the observations. No requirement was imposed on the presence of\nhigh-angle boundaries surrounding recrystallized grains as these are often but\nnot systematically in contact with high-angle boundaries [27].\n2.3. Measurements of recrystallization\nFigure 1 shows inverse pole \fgure (IPF) maps of the microstructure after\ndeformation and annealing. The colours represent the crystallographic axis par-\nallel to the sheet's normal direction (ND). The microstructure after deformation\n(Figure 1a) is composed of deformed grains elongated in the rolling direction\n(RD). These appear as large agregates of subgrains, are surrounded mostly by\nboundaries of misorientation angle higher than 10\u000e, and exhibit rather homo-\ngeneous internal orientation spreads. Their interior is composed of numerous\nsubgrains of mean equivalent-area diameter equal to 6.85 \u0016m. Note that about\n1.8\u0002105subgrains were measured for this condition. The magnitude of the sub-\ngrain size, i.e. a few microns, is consistent with other work on hot deformed\nferritic stainless steels [21, 28]. As no subgrain exceeds the threshold recrystal-\nlized grain diameter (Figure 1d), the recrystallized fraction is 0% in this state.\n6(a)\n (b)\n (c)\n(d)\n (e)\n (f)\nFigure 1: ND-IPF maps of the microstructure a) after deformation, b) after 2s annealing\nat 1100\u000eC, c) after 12s annealing at 1100\u000eC. In d-e), the identi\fed recrystallized grains are\nhighlighted with enhanced brightness. The maps have been pre-processed with the Kuwahara\n\flter.\n7After 2s of annealing (Figure 1b), the microstructure has coarsened in a\nheterogeneous way, giving rise to a few subgrains much larger than others. The\nsubgrains above the threshold recrystallized grain diameter are identi\fed as\nrecrystallized grains (Figure 1e), and the calculated recrystallized fraction is\n44%. The recrystallized grain boundaries are preferentially of high-angle, but\ndo not exhibit particular orientation relationships. For example, the fraction of\nboundaries having a disorientation angle above 10\u000eis 75% between recrystallized\ngrains and non-recrystallized regions of the microstructure, while it is 94% if\ntaken between recrystallized grains themselves. Assuming a 5\u000edeviation around\nthe exact relationship, boundaries with the \u000619a relationship (i.e. 27\u000erotation\naround theh110iaxis), make up only 1.3% of boundaries between recrystallized\ngrains and deformed grains, and 1.4% of those between recrystallized grains\nthemselves. These boundaries have been suggested to be very important for\nrecrystallization textures in ferritic stainless steels [29].\nAfter 12s of annealing, the initial microstructure has been fully replaced\nby large grains surrounded mostly by high angle boundaries (Figure 1c). The\ncalculated recrystallized fraction is 96%. In essence, the microstructure at this\nstage is fully recrystallized. Indeed, with the chosen de\fnition of recrystallized\ngrains, the recrystallized fraction cannot reach exactly 100% since there will al-\nways be grains whose apparent diameter on an image in two dimension is below\nthe threshold recrystallized grain diameter (Figure 1f). The fraction of bound-\naries with disorientation angles above 10\u000eis 94% for the whole microstructure.\nIt is also noticeable that the recrystallized grain diameters have become much\nlarger than the initial deformed grain size in the normal direction. This indicates\nthat recrystallized grains grow mostly towards the deformed grains neighbouring\ntheir parent deformed grains. As, in addition, most high-angle boundaries in the\ndeformed microstructure are pre-existing deformed grain boundaries, one may\nconclude that recrystallization occurs by the bulging of deformed grain bound-\naries. This interpretation is consistent with the opinion that materials deformed\nat high temperature and low strain rate recrystallize by this mechanism [4, 30].\nFigure 2 shows the e\u000bect static recrystallization on texture. To help the\n8reader, the location in Euler space of several low-index components is shown in\nFigure 2a. The deformation texture shown in Figure 2b is composed of strong\n\u000b,\rand cube \fbre orientations, with a maximum intensity at the rotated\ncube orientation f001gh110i. This texture is common to hot rolled sheets of\nmany ferritic steels [17, 19, 20, 31]. Following the classic argument [32], the\nexceptional strength of the rotated cube orientation is likely caused by dynamic\nrecrystallization occuring during deformation as it cannot be reproduced by\ncrystal plasticity simulations [21].\nAfter 12s of annealing (full recrystallization), the texture has weakened sig-\nni\fcantly. The cube \fbre and upper portion of the \u000b\fbre remain the preferred\norientations, with the two strongest components located near the rotated cube\norientationf001gh110iand at the cube orientation f001gh100i. Again, the ODF\nis very similar to that of previous reports on recrystallization of hot rolled ferritic\nsteels [20, 33, 19].\n(a)\n (b)\n (c)\nFigure 2: a) position of the low-index components in the '2= 45\u000esection of the Euler space.\nNote the distinction between the cube orientation f001gh100iand the cube \fbre orientation\nf001ghuvwi. b) ODF of the deformed microstructure, c) ODF of the microstructure after 12s\nof annealing. The scalebar is in multiple of random (m.r.d).\nTo complement this analysis, Table 2 provides a measure of the texture\nevolution in terms of volume fraction of low-index components in the defor-\nmation and recrystallization texture. The values con\frm the weakening of the\nrotated cube orientation f001gh110iand the strengthening of the cube orien-\ntationf001gh100i. Interestingly, even if the Goss orientation f110gh001iis a\n9minor component in both textures, it strenghens proportionally more than any\nof the major components. This aspect will be discussed later in this article.\nTable 2: Volume fraction of orientations within \u000615\u000eof the low index components in the\ndeformed and 12s annealed (i.e. recrystallized) samples.\nf001gh110i f 112gh110i f 111gh110i f 111gh121i f 001gh100i f 110gh001i\nDef. 18.1% 6.2% 5.6% 8.4% 5.53% 0.1%\nRex. 8.1% 5.3% 2.9% 1.8% 10.2% 2.1%\n3. Model\nThe modelling approach presented in this article relies extensively on as-\nsumptions developed in an earlier work [16], where recrystallization was simu-\nlated by cellular growth laws applied to a population of subgrains pre-existing\nin the deformed microstructure. This assumption is common for high stacking-\nfault energy materials [20, 34, 35, 36], and seems apropriate for the case under\ninvestigation.\nA key di\u000berence must be noted between the work in ref. [16] and the present\nwork. In [16], the subgrain boundary properties were estimated statistically for\na synthetic microstructure exhibiting intragranular recrystallization, i.e. for a\ncase where recrystallized grains grow within their parent deformed grain. In the\npresent work, recrystallization is intergranular since the recrystallized grains\ngrow towards neighbouring deformed grains. In this con\fguration, recrystal-\nlization depends mostly on the subgrains in contact with the deformed grain\nboundaries. This feature cannot be accounted for by the statistical approach\ndeveloped previously. Therefore, in the following sections, a di\u000berent approach\nis implemented to extract the boundary properties directly from the experimen-\ntal measurements.\n3.1. Growth laws\nThe microstructure is considered as a set of individual spherical grains and\nsubgrains characterized by diameter D(i), mean boundary energy \u0000 (i)and mean\n10boundary mobility M(i), embedded in a homogeneous medium of properties \u0016D\nand\u0016\u0000. The model makes no distinction between grains and subgrains, the same\nlaws being applied to all objects. Assuming that these parameters are known,\nthe growth rate of a grain or subgrain in three dimension is given by [16]:\ndD(i)\ndt=2M(i)\u0000(i)\nD(i;t)\u0012\na(i)\u0012\n3 +16D(i;t)\n9\u0016D(t)\u0013\n\u00005\u0013\n(1)\nWhere the capillary term a(i)= 6sin\u00001(\u0000(i)=2\u0016\u0000)=\u0019\u00143 accounts for the\nvariations of boundary curvature as a function of the heterogeneity of boundary\nenergy between the individual grain or subgrain and the medium. This equation\nis derived from the MacPherson-Srolovitz equation extended to anisotropic mi-\ncrostructures [37, 38] with empirical assumptions about the relationship between\nthe grain or subgrain size and its number of faces [16, 39]. The translation of\nthe capillary term to experimental microstructures is not straightforward since\nthe mean boundary energy of the medium \u0016\u0000 can be de\fned at the local scale\nor for the whole microstructure. It was noticed, however, that the model pre-\ndictions are not sensitive to this term regardless of its de\fnition. Therefore, we\nmake the simplifying assumption that \u0000 (i)=\u0016\u0000, i.e thata(i)= 1. This is true\non average since most subgrains grow within their deformed grains, where the\norientation spread and thus the boundary network are homogeneous. In this\ncase, Equation 1 becomes:\ndD(i)\ndt= 4M(i)\u0000(i)\u00128\n9\u0016D\u00001\nD(i)\u0013\n(2)\nThis equation is almost identical to that derived by Hillert for the growth\nof grains in 3D [40]. In this formulation, the growth rate of a grain or sub-\ngrain depends solely on its intrinsic properties and on the mean subgrain size,\nwhile the properties of the surrounding boundary network a\u000bect all grains and\nsubgrains similarly (i.e. a(i)= 1). As discussed above, this assumption is rea-\nsonable for the present case, but its validity may need to be re-evalutated for\nmore heterogeneous microstructures.\nTo update the grain and subgrain diameters, Equation 2 is integrated using\n11Euler's method\u0002\nD(i)\u0003\nt+dt=\u0002\nD(i)\u0003\nt+hdD (i)\ndti\ntdt. The mean grain and subgrain\ndiameter \u0016Dis also updated by performing a simple arithmetic mean of the list\nof diameters over the entire map. The model predictions are insensitive to the\nchoice ofdtso long as the average increase in grain and subgrain volume per time\nincrement remains below 1%. After each time increment, the smallest subgrains\nand those of negative radius are removed in order to maintain a constant total\nsimulation volume [16]. This removal procedure a\u000bects all subgrains regardless\nof their parent deformed grains. Orientations whose grains and subgrains have\nfast growth rates will thus increase their fraction, while those associated with\nslower growth rates can subsist for some time but are ultimately removed from\nthe simulation.\nAs the microstructure evolves, recrystallized grains are identi\fed, as in ex-\nperiments, based on a threshold diameter D(i)\u001530\u0016m. At high recrystallized\nfractions, the model predictions are almost insensitive to the de\fnition of the\nthreshold recrystallized grain diameter as kinetics and the texture are dominated\nby grains whose size has become several times that of the threshold.\n3.2. Determination of the input parameters\nTo compute the growth rates given by Equation 2, the list of individual\ngrain and subgrain diameters D(i), the mean diameter \u0016Dand the mean bound-\nary energies \u0000 (i)and mobilities M(i)must be known. The individual grain and\nsubgrain diameters are obtained from the equivalent-area diameters measured\non the experimentally measured orientation maps. It can be remarked that the\ngrains and subgrains are assumed to grow in three dimensions and to possess\nvolumes, even though their initial size is measured on two dimmensional sec-\ntions. This considered, in \frst approximation, to have a negligible e\u000bect on\nthe predictions since the apparent diameter of spherical grains and subgrains\nmeasured from two dimensional sections does not vary much on average from\ntheir real diameter in three dimensions [41, 42]. In addition, the cellular growth\nequations in 2D and 3D are almost identical in terms of their sensitivity to\ndiameters and boundary properties [16].\n12Next, the mean boundary properties are estimated from the boundaries sep-\narating each subgrain and its environment in the orientation maps. First, the\nboundary energy and mobility are assumed to be functions of the boundary\ndisorientation angle \u0012. The boundary energy \r(\u0012) is taken to obey the Read-\nShockley equation [43]:\n\r(\u0012) =8\n><\n>:\rc\u0012\n\u0012c\u0010\n1\u0000ln\u0012\n\u0012c\u0011\nif\u0012\u0014\u0012c\n\rc if\u0012>\u0012c(3)\nWhere\rcis a constant and \u0012cis a cut-o\u000b angle set to 15\u000eto simulate a\nhigh angle boundary. The boundary mobility \u0016(\u0012) is set to follow the empirical\nrelation [44, 45]:\n\u0016(\u0012) =\u0016c\u0010\n1\u0000e\u0000B(\u0012\n\u0012c)\u0011\u0011\n(4)\nWhere\u0016cis a constant, B= 5 and\u0011= 4 [44, 45]. The constants \rcand\n\u0016chave no in\ruence on the prediction of the recrystallization texture, but the\nkinetics scale with their magnitude. The choice of these equations leads, in\nthe simulation, to the development of recrystallized grains with boundaries of\nhigh disorientation angles [2, 16]. This outcome is consistent with the fact that\nrecrystallized grains are mostly separated from the surrounding deformed grains\nand from other recrystallized grains by high-angle boundaries with no particular\norientation relationship.\nHaving set the boundary energy and mobility laws, one can then calculate the\nmean boundary properties of subgrains. The method is illustrated in Figure 3.\nThe mean boundary energy of a subgrain iis given by the aritmetic mean:\n\u0000(i)=n(i)X\nk=1\r\u0000\n\u0012(i;k)\u0001\n=n(i) (5)\nWheren(i)is the number of unit segments de\fning the subgrain boundary\nand\u0012(i;k)is the disorientation angle of the k-th segment.\n13Similarly, the mean boundary mobility assigned to the subgrain is given by:\nM(i)=n(i)X\nk=1\u0016\u0000\n\u0012(i;k)\u0001\n=n(i) (6)\nIn our previous work [16], the mean boundary energy and mobility were\ncalculated by second order Taylor series expansions of the boundary energy and\nmobility laws around the means and variances of the boundary disorientation\nangle distributions. Except small discrepancies linked to sampling, the Taylor\nseries leads to identical results as the arithmetic mean if the means and variances\nused for the Taylor series are calculated at the scale of each individual subgrain.\nThe arithmetic mean is prefered here as, from a theoretical point of view, Taylor\nseries expansions must converge towards the arithmetic mean when the order\ntends to +1.\nFigure 3: Illustration of the measurement of disorientation angles at the boundaries of a given\nsubgraini. The unit segment of disorientation angle \u0012(i;k)has the length of the EBSD step\nsize.\nFinally, it is convenient to also calculate the mean boundary disorientation\nof individual grains and subgrains even though this is not an input parameter of\nthe model. This parameter has some utility for discussing the model prediction\nas both boundary energy and mobility depend on disorientation angle. It is\n14given by:\n\u0002(i)=n(i)X\nk=1\u0012(i;k)=n(i) (7)\nNote that, for simplicity, the boundary properties are not updated with time.\nThis assumption is expected to have a negligible e\u000bect on the texture predic-\ntion since it was noticed in the orientation maps that even though the mean\nboundary properties of grains and subgrains evolve during recrystallization, ori-\nentations associated to grains and subgrains of high boundary energy and mo-\nbility maintain these high values throughout recrystallization. In addition, the\ndi\u000berences in boundary properties between grains and subgrains located within\ndeformed grains and those adjacent to deformed grain boundaries are expected\nto remain similar throughout recrystallization. On the one hand, those within\ndeformed grains will mainly retain boundaries of low disorientation angles since\nthey grow in regions with weak orientation gradients. On the other hand the\nhigh disorientation angles of grains and subgrains at deformed grain boundaries\nare geometrically necessary to rotate from orientations on the one side to those\non the other side of the boundaries.\n3.3. Algorithm\nThe input parameters to the model are obtained from the experimentally\nmeasured orientation maps of the deformed microstructure. The initial sim-\nulation volume is obtained by summing the volumes of all subgrains in the\ninput microstructure. The subgrains volumes are calculated from their diam-\neters assuming spherical particles. Then a time iteration loop is started, with\nthe following sequence executed between times tandt+dt:\n1. Identify the recrystallized grains, i.e. the subgrains with D(i)\u001530\u0016m.\n2. Calculate the growth rate of each grain and subgrain using Equation 2.\n3. Integrate the growth rates over a time increment to update the grain\nand subgrain diameters. The new diameters are representative of the\nmicrostructure at time t+dt.\n154. Remove the subgrains of negative diameter and the smallest subgrains\nof positive diameter so as to minimize the di\u000berence between the initial\nmicrostructure volume and the sum of grain and subgrain volumes at t+dt.\n5. Update the average diameter \u0016D.\nAt each time step, the recrystallized fraction and the orientation of the\nrecrystallized grains are known. Therefore, both the recrystallization kinetics\nand texture can be predicted.\n4. Results and discussion\n4.1. Kinetics and texture prediction\nFigure 4 compares the recrystallization kinetics predicted by the model to\nthe experimental datapoints. The predicted kinetics follows the sigmoidal shape\ncharacteristic of recrystallization kinetics, and \fts the datapoints when setting\n\rc= 0:8J:m\u00002and\u0016c= 1\u000210\u000010m4:J\u00001:K\u00001. The time required to reach\nthe annealing temperature has not been considered in the simulation. In pre-\nvious models for recrystallization of ferritic steels, \rcusually ranges from 0.65\nto 0.8J:m\u00002[20, 46]. For \u0016c, the Arrhenius law suggested by Jacquet [20] gives\n\u0016c= 0:96\u000210\u000010m4:J:s\u00001at 1100\u000eC1. The order of magnitude of the \ftting\nconstants is thus in good agreement with that found in the literature. The\nability of this model to predict the recrystallization kinetics had been suggested\npreviously on the basis of full-\feld and mean-\feld simulations [16]. The present\nresult can be considered as a \frst successful case using experimental measure-\nments as input.\nFigure 5 compares the experimental and predicted recrystallization textures\nat 96% recrystallized fraction. The measured deformation texture is shown\n1To simulate the recrystallisation kinetics in a hot rolled AISI445 ferritic stainless steel\nusing a Bailey-Hirsch type of model, Jacquet suggested \u0016c=\u0016c;0exp(\u0000Q=RT ), with\u0016c;0=\n5\u000210\u00006m4:J:s\u00001,Q= 124kJ:mol\u00001andRthe ideal gas constant [20]. These parameters\nwere obtained from grain growth experiments.\n16Figure 4: Experimental and simulated recrystallization kinetics. The energy and mobility\nfactors have been set to \rc= 0:8\u000210\u000012J:\u0016m\u00002and\u0016c= 1\u00021014\u0016m4:J\u00001:K\u00001.\nagain in Figure 5a to illustrate the di\u000berences with the measured and predicted\nrecrystallization textures in Figure 5b and c. The prediction captures the weak-\nening of the texture strength with recrystallization as well as the development\nof the cube orientation f001gh100ias the strongest texture component. With\nthis way of representing the texture, the most visible discrepancy between the\nexperimental and predicted texture is the absence of a local maximum near the\nrotated cube orientation f110gh100i. Overall, however, the evolution of this\ncomponent is well captured if one compares with its strength in the deformed\nstate.\n(a)\n (b)\n (c)\nFigure 5: ODFs sections in the '2= 45\u000esection of the Euler space for (a) the experimentally\nmeasured deformation texture, (b) the experimentally measured texture at 97% of recrystal-\nlized fraction (after 12s annealing), (c) the predicted texture at 97% of recrystallized fraction.\nThe scalebar is in multiple of random (m.r.d).\n17Recall that the recrystallization texture was simulated starting from a list\n1.8\u0002105subgrains measured in the deformed microstructure. Out of these,\nabout 750 reached the threshold recrystallized grain size at the end of recrys-\ntallization2. Including a larger number of initial subgrains did not lead to\nsigni\fcant di\u000berences in the predicted texture. It can be remarked that this\nnumber of measured subgrains in the deformed microstructure can be acquired\nrapidly with modern EBSD systems. Thus sampling of the inital deformed\nmicrostructure is not a major constraint for the simulation.\n4.2. Dynamics of the recrystallization texture development\nFigure 6 shows the volume fraction of several low-index texture components\nin the recrystallized grains as a function of the recrystallized fraction. The mea-\nsurements corresponding to the 2s, 5s and 12s annealing conditions are shown\nin dots while the model predictions are shown as lines. The volume fraction\nis taken here as another way of quantitatively comparing the textures. Plot-\nted in this way, the volume fraction of the cube orientation f001gh100iseems\noverpredicted. However, the discrepancy is not more than 50% for all condi-\ntions, which is satisfactory given the complexity of the mechanisms simulated\nand the number of simplifying assumptions. Besides, the general evolution of\nthis component is well captured by the model as its volume fraction increases\nsigni\fcantly between the deformed and the recrystallized state, as was found in\nthe experiment (see Table 2).\nBoth the experimental points and the model predictions show that the vol-\nume fractions of recrystallization texture components are set at low recrystal-\nlized fractions and do not evolve much with the progress of recrystallization. It\nwould be tempting to relate this behaviour to a phenomenon of `oriented nu-\ncleation', where the recrystallization texture is dominated by the di\u000berences in\n2If the simulations are performed assuming 2D growth (using equations developed in ref.\n[16]), the number of recrystallized grains reaches several thousands for an almost identical\ntexture prediction.\n18Figure 6: Volume fraction of recrystallized grains within 15\u000efrom some low-index texture\ncomponents as a function of the recrystallized fraction. The experimental measurements are\nshown in dots and the predictions in lines.\nnucleation rate of recrystallized grains as a function of their orientation [4, 5].\nHowever, we prefer not to use this term as the distinction between nucleation\nand growth is not well suited to the present case. Indeed, according to the\nmodel, the texture change results from the competitive growth of subgrains,\nand nucleation of recrystallized grains is controlled by a size threshold that has\nno fundamental meaning.\nThe stability of the recrystallization texture throughout recrystallization is\nnot necessarily surprising if one considers the topological aspects of recrystalliza-\ntion in this material and the theoretical conditions giving rise to recrystallized\ngrains. According to Equation 2 and in agreement with the classic point of\nview [1, 2], the subgrains with boundaries of highest energy and mobility have\nthe fastest growth rates and, as a consequence, are the most likely to reach the\nthreshold recrystallized grain size. As boundary energy and mobility are re-\nlated to the boundary disorientation angle, subgrains surrounded by high-angle\nboundaries have the highest chances of forming recrystallized grains. As recrys-\ntallized grains grow towards their neighbouring deformed grains (see Figure 1),\ntheir boundaries mainly retain high disorientation angles. For example, if one\nconsiders that the orientation of the recrystallized grains and of the deformed\nmicrostructure are spatially uncorrelated, a recrystallized grain of exact rotated\n19cube orientation has a 96% chance of sharing a boundary of disorientation an-\ngle above 10\u000ewith the deformed texture. This probability is even higher for\nthe other texture components since they are present in lower fraction in the\ndeformed texture. The stability of the recrystallized grain boundary properties\nthroughout recrystallization helps to explain why the relative amount of each\nrecrystallization texture component does not change after the appearance of the\n\frst recrystallized grains. As the early stages of the microstructure evolution\ndetermine most of the texture change, an examination of the initial distribution\nof subgrain properties should su\u000ece to explain the origin of the recrystallization\ntexture in this material.\n4.3. Origin of the recrystallization texture\nIn the model, the distribution of subgrain properties and the initial number\nof subgrains belonging to each texture component determine the recrystalliza-\ntion texture development. To simplify the analysis, we evaluate separately the\ne\u000bect of the di\u000berent subgrain parameters on the recrystallization texture devel-\nopment. For this, Figure 7 shows the distributions of subgrain diameters, mean\nboundary energy, mean boundary mobility and mean boundary disorientation\nangle for several low-index components measured from the orientation maps of\nthe deformed microstructure. On the same plots, the shaded areas represent the\nfraction of subgrains reaching the recrystallized grain size at 97% recrystallized\nfraction. Figure 7a to c con\frm that the probability for a subgrain to reach\nthe recrystallized grain size increases with the subgrain diameter, mean bound-\nary energy and mobility. As boundary energy and mobility are related to the\nboundary disorientation, Figure 7d shows that the probability of turning into a\nrecrystallized grain also increases as a function of the mean disorientation angle,\nin agreement with the common perception [1, 2]. Note that even if subgrains\nof extreme properties have the most chance of reaching the recrystallized grain\nsize, they do not necessarily represent the majority of the recrystallized grains\nsince they make up a very small fraction of the deformed microstructure.\nInterestingly, subgrains of the \u000b\fbre, i.e. thef001gh110i,f112gh110i,\n20(a)\nFigure 7: Distribution of subgrain properties in the deformed microstructure as a function\nof their orientation (in coloured lines). The grey areas represent the fraction of the initial\nsubgrains having reached the threshold recrystallized grain size at a recrystallized fraction of\n97%. a) subgrain diameter, b) mean boundary mobility, c) mean boundary energy, d) mean\nboundary disorientation angle.\n21f111gh110iorientations do not exhibit particularly extreme boundary proper-\nties (Figure 7b-d), even though they form the one of main components of the\nrecrystallization texture. Thus, their presence in the recrystallized state can be\nattributed to their high fraction in the deformed state. This interpretation is\nsupported by the fact that the volume fraction of these components decreases\nwith recrystallization (see Table 2). By contrast, subgrains of the cube orienta-\ntionf001gh100ipossess higher boundary energy and mobility (Figure 7b and c),\nwhich gives them a higher probability of turning into recrystallized grains and\nexplains why this component develops preferentially. The general weakening of\ntexture with recrystallization can be explained using the same reasoning since\ncomponents such as the Goss orientation f110gh001ipossess boundary proper-\nties that allow them to develop to a much higher extent than the components\nthat are much more present in the deformed texture.\n4.4. Origin of the anisotropy in subgrain properties\nThe present analysis suggests that the anisotropy in subgrain properties and\nthe deformation texture prior to recrystallization control the recrystallization\ntexture development. While the principal aim of this work is not to explain how\nto control the anisotropy in subgrain properties, it is interesting to point out\nthat this originates from the material's behaviour during prior deformation.\nTo begin with, Figure 7a shows a slight increase in subgrain size along the \u000b\n\fbre from thef111gh110ito thef001gh110iorientations. This evolution is well\ndocumented in the literature, and is attributed to di\u000berences in slip activity as\na function of orientation [31, 47, 48]. The anisotropy in subgrain size is however\nless signi\fcant than that observed in cold rolled materials [47], because the high\nstrain rate sensitivity of hot rolled materials homogenizes the plastic response of\ngrains as a function of orientations [31]. In Figure 7b-d, the boundary properties\nof the main deformation texture components (i.e. the f001gh110i,f112gh110i,\nf111gh110iandf111gh121iorientations) appear quasi self-similar, most likely\nfor the same reason\nBy contrast, the exceptionally high boundary properties of the cube ori-\n22entationf001gh100iand Goss orientation f110gh001ican be explained by the\nfact that these are metastable orientations under plane strain compression of\nbcc materials and develop in low fraction in the deformed microstructure [49].\nSuch structures have been called transition bands by Dillamore et al. [49], al-\nthough the term is rarely used for ferritic steels. From their point of view, the\npresence of locally strong orientation gradients and the low fraction of these\ncomponents should ensure that they possess with the rest of the microstructure\nmore high-angle boundaries than the other texture components. This assertion\nis supported by Figure 7d, where the cube f001gh100iand Gossf110gh001i\norientations are shown to possess a higher fraction of boundaries with angles\nabove approximately 10\u000ethan the other investigated components.\nAt constant rolling temperature, the anisotropy in subgrain properties is un-\nlikely to change radically since it is imposed by the strain rate sensitivity, which\nis temperature dependent [20]. This seems to be con\frmed by measurements\nof subgrain properties in the same material deformed at 1100\u000eC with a 50%\nreduction rate [21]. Thus, to radically change the recrystallization texture, one\nwould have to play on the rolling temperature. Warm and cold deformation\nare known to induce more strain heterogeneities and a larger fraction of high-\nangle boundaries in \r\fbre grains [50, 51]. This is expected to help lowering the\nfraction of\u000b\fbre orientations in the as-recrystallized state [17, 50].\n4.5. Merits and potential of the model\nThe principal merit of this model is its simple expression of the relationship\nbetween subgrain parameters in the deformed state and the texture development\nduring recrystallization. The parameters which drive recrystallization, namely\nthe distributions of subgrain size and boundary property, can be measured di-\nrectly on orientation maps obtained from experiments. Therefore, one can use\nthe model to investigate the characteristics of the subgrains in the deformed\nmicrostructure which give rise to recrystallized grains. This can be done in\na statistical way, as presented in Figure 7. But one may also use the model\nresults to identify the most favourable sites for the formation of recrystallized\n23grains on the orientation maps of the deformed microstructure. For example, in\nthe material investigated here, recrystallized grains are expected to form near\nthe pre-existing deformed grain boundaries since this is where most high-angle\nboundaries are located. In a material exhibiting a higher degree of intragranular\nheterogeneities, one may expect the model to locate more frequently the origin\nof recrystallized grains in the interior of the deformed grains. This analysis is\nnot possible with other models of the literature where the predicted texture\nis tuned by parametrically weighting the contribution of di\u000berent regions of\nthe microstructure (e.g. transition bands, deformed grain boundaries) to the\nformation of recrystallized grains [8, 10, 13].\nOne can also view this model as part of an e\u000bort to develop physically\nsound approaches for predicting the texture evolution of wrought materials\nduring thermomechanical processing. For example, its input parameters could\nbe measured from synthetic orientation maps obtained by full-\feld crystal-\nplasticity simulations instead of experimentally measured maps. Another possi-\nbility would be to use the outcomes of mean-\feld crystal plasticity simulations\nto estimate the subgrains properties. As discussed previously [16], this is made\npossible by the fact that the outputs of mean-\feld crystal-plasticity models are\nvery much similar to the input parameters of the recrystallization model. For\nexample, distributions of disorientation angles can be generated from the intra-\ngranular orientation spreads calculated by the model of Zecevic et al. [52, 13].\nSubgrain sizes are not usually an output of crystal plasticity models, but these\ncan be estimated, in \frst approximation, from the variations of Taylor factors\n[31]. Using mean-\feld models to feed recrystallization models seems a par-\nticularly interesting strategy to perform through-process modelling of texture\nevolution as it would retain a high computational e\u000eciency.\nAs a \fnal remark, it is worth pointing out that the model assumptions have\nbeen selected after a careful examination of the microstructures shown in Fig-\nure 1. As a result, the model is expected to be most suited to the recrystalliza-\ntion of high-stacking fault energy materials, where the deformed microstructure\ncan reasonably be considered as a subgrain network with low dislocation den-\n24sity. The proposed implementation is however \rexible since its formalism of\ncellular growth is comparable to the models existing in the literature [34, 35]\n. Mathematical expressions accounting for the e\u000bect of other microstructural\nfeatures such as orientation gradients [53, 54], stored energy due to tangled\ndislocations [35], and precipitate pinning [44] have been proposed elsewhere.\nIncluding these e\u000bects could be readily accomplished by altering some of the\nassumptions presented here.\n5. Conclusion\nA model was developed to predict the static recrystallization texture devel-\nopment during annealing of deformed polycrystals. The model assumes that\nrecrystallization arises from the competitive growth of subgrains, driven by the\nanisotropy of subgrain properties. One of its distinctive features compared to\nother models of the literature is its ability to use as input parameters exper-\nimental measurements of the subgrain properties. This approach allows one\nto establish a direct relation between the state of the deformed microstructure\nand the recrystallization texture. The recrystallization kinetics can also be pre-\ndicted.\nThe model predictions are in good agreement with the experimental mea-\nsurements of a hot rolled and recrystallized ferritic stainless steel sheets. The\nresults indicate that the strength of the texture and its main components de-\nvelop at the early stages of recrystallization and are mostly determined by the\ninitial distributions of subgrain properties. Due to their large initial fraction,\nthe main components of the deformation texture compose the dominant frac-\ntion of the recrystallization texture even though they are not particularly in\nfavourable growth conditions. The weakening of the texture with recrystalliza-\ntion is, on the other hand, explained by the rapid growth of the minor compo-\nnents. To minimize the fraction of deleterious \u000band cube \fbre orientations in\nthe recrystallized grains, one must minimize their presence in the states before\nrecrystallization. Another possibility is to decrease the rolling temperature to\n25induce more anisotropy in the subgrain properties.\nThe model assumptions have been chosen after a careful examination of\nthe microstructural features of the material in its deformed and recrystallized\nstates. As a result, the implementation proposed here is most suited to the\nsimulation of recrystallization in high-stacking fault energy materials, whose\ndeformation microstructure can be considered as a population of subgrains. It\nis also expected to perform well in cases where the recrystallization texture\nis determined by the early stages of the microstructure evolution, since the\nboundary properties are set constant with time. The model is however quite\n\rexible, and its assumptions could be relaxed or modi\fed to account for other\nmicrostructural features such as orientation gradients, stored energy due to\ntangled dislocation or precipitate pinning.\nSupplementary material\nThe model input \fle is provided in supplementary material.\nAckowledgements\nThis work was \fnancially supported by APERAM. The authors express their\nthanks to Francis Chassagne from APERAM for his contribution to this project\nbefore his retirement.\nReferences\n[1] A. Rollett, On the growth of abnormal grains, Scripta Materialia 36 (9)\n(1997) 975{980. doi:10.1016/S1359-6462(96)00501-5 .\nURL https://linkinghub.elsevier.com/retrieve/pii/\nS1359646296005015\n[2] F. J. Humphreys, A uni\fed theory of recovery, recrystallization and grain\ngrowth, based on the stability and growth of cellular microstructures|II.\nThe e\u000bect of second-phase particles, Acta Materialia 45 (12) (1997)\n265031{5039. doi:10.1016/S1359-6454(97)00173-0 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645497001730\n[3] Y. Br\u0013 echet, G. Martin, Nucleation problems in metallurgy of the solid\nstate: recent developments and open questions, Comptes Rendus de\nPhysique 7 (9{10) (2006) 959{976. doi:10.1016/j.crhy.2006.10.014 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1631070506002258\n[4] F. J. Humphreys, G. S. Rohrer, A. Rollett, Recrystallization and Related\nAnnealing Phenomena, 3rd Edition, Elsevier, 2017.\n[5] R. D. Doherty, D. A. Hughes, F. J. Humphreys, J. J. Jonas,\nD. Juul Jensen, M. E. Kassner, W. E. King, T. R. McNelley, H. J.\nMcQueen, A. D. Rollett, Current issues in recrystallization: a re-\nview, Materials Science and Engineering: A 238 (2) (1997) 219{274.\ndoi:10.1016/S0921-5093(97)00424-3 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0921509397004243\n[6] H. J. Bunge, U. K ohler, Model calculations of primary recrystallization\ntextures, Scripta Metallurgica et Materialia 27 (11) (1992) 1539{1543.\ndoi:10.1016/0956-716X(92)90141-Z .\nURL https://www.sciencedirect.com/science/article/pii/\n0956716X9290141Z?via%3Dihub\n[7] O. Engler, On the in\ruence of orientation pinning on growth selec-\ntion of recrystallisation, Acta Materialia 46 (5) (1998) 1555{1568.\ndoi:10.1016/S1359-6454(97)00354-6 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645497003546\n[8] R. Sebald, G. Gottstein, Modeling of recrystallization textures:: interac-\ntion of nucleation and growth, Acta Materialia 50 (6) (2002) 1587{1598.\n27doi:10.1016/S1359-6454(02)00020-4 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645402000204\n[9] L. Kestens, J. J. Jonas, Modeling texture change during the static recrystal-\nlization of interstitial free steels, Metallurgical and Materials Transactions\nA 27 (1) (1996) 155{164. doi:10.1007/BF02647756 .\nURL http://link.springer.com/10.1007/BF02647756\n[10] J. J. Sidor, R. H. Petrov, L. A. I. Kestens, Modeling the crystallographic\ntexture changes in aluminum alloys during recrystallization, Acta Materi-\nalia 59 (14) (2011) 5735{5748. doi:10.1016/j.actamat.2011.05.050 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645411003909\n[11] H. R. Wenk, G. Canova, Y. Br\u0013 echet, L. Flandin, A deformation-based\nmodel for recrystallization of anisotropic materials, Acta Materialia 45 (8)\n(1997) 3283{3296. doi:10.1016/S1359-6454(96)00409-0 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645496004090\n[12] R. A. Lebensohn, H. R. Wenk, C. N. Tom\u0013 e, Modelling deformation\nand recrystallization textures in calcite, Acta Materialia 46 (8) (1998)\n2683{2693. doi:10.1016/S1359-6454(97)00477-1 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645497004771\n[13] M. Zecevic, R. A. Lebensohn, R. J. McCabe, M. Knezevic, Modelling\nrecrystallization textures driven by intragranular \ructuations implemented\nin the viscoplastic self-consistent formulation, Acta Materialia 164 (2019)\n530{546. doi:10.1016/j.actamat.2018.11.002 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645418308772\n28[14] M. A. Steiner, R. J. McCabe, E. Garlea, S. R. Agnew, Monte Carlo mod-\neling of recrystallization processes in alpha-uranium, Journal of Nuclear\nMaterials 492 (2017) 74{87. doi:10.1016/j.jnucmat.2017.04.026 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0022311516310212\n[15] D. Raabe, 23 - Recovery and Recrystallization: Phenomena, Physics,\nModels, Simulation, in: D. E. Laughlin, K. Hono (Eds.), Physical\nMetallurgy (Fifth Edition), Elsevier, Oxford, 2014, pp. 2291{2397.\ndoi:10.1016/B978-0-444-53770-6.00023-X .\nURL http://www.sciencedirect.com/science/article/pii/\nB978044453770600023X\n[16] A. Despr\u0013 es, M. Greenwood, C. W. Sinclair, A mean-\feld\nmodel of static recrystallization considering orientation spreads\nand their time-evolution, Acta Materialia 199 (2020) 116{128.\ndoi:10.1016/j.actamat.2020.08.013 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645420306108\n[17] C. Zhang, Z. Liu, G. Wang, E\u000bects of hot rolled shear bands on formabil-\nity and surface ridging of an ultra puri\fed 21%Cr ferritic stainless steel,\nJournal of Materials Processing Technology 211 (6) (2011) 1051{1059.\ndoi:10.1016/j.jmatprotec.2011.01.005 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0924013611000082\n[18] D. Raabe, K. L uucke, Textures of ferritic stainless steels, Materials Science\nand Technology 9 (4) (1993) 302{312, publisher: Taylor & Francis eprint:\nhttps://doi.org/10.1179/mst.1993.9.4.302. doi:10.1179/mst.1993.9.4.\n302.\nURL https://doi.org/10.1179/mst.1993.9.4.302\n29[19] S. Mehtonen, E. Palmiere, D. Misra, P. Karjalainen, D. Porter, Microstruc-\ntural and Texture Development during Multi-Pass Hot Deformation of a\nStabilized High-Chromium Ferritic Stainless Steel, ISIJ International 54 (6)\n(2014) 1406{1415. doi:10.2355/isijinternational.54.1406 .\n[20] G. Jacquet, Etude de la cin\u0013 etique de recristallisation au cours du laminage\n\u0012 a chaud d'aciers inoxydables ferritiques stabilis\u0013 es, PhD thesis, Ecole Na-\ntionale Sup\u0013 erieure des Mines de Saint-Etienne (Oct. 2013).\nURL https://tel.archives-ouvertes.fr/tel-00975379\n[21] A. Despres, On the origin of hot rolling textures of ferritic stainless steels,\nPhD thesis, University of British Columbia (2019).\nURL http://hdl.handle.net/2429/71664\n[22] O. Engler, C. N. Tom\u0013 e, M. Y. Huh, A study of through-thickness texture\ngradients in rolled sheets, Metallurgical and Materials Transactions A 31 (9)\n(2000) 2299{2315. doi:10.1007/s11661-000-0146-7 .\nURL https://doi.org/10.1007/s11661-000-0146-7\n[23] R. Roumina, C. Sinclair, Deformation Geometry and Through-Thickness\nStrain Gradients in Asymmetric Rolling, Metallurgical and Materials\nTransactions A 39 (10) (2008) 2495. doi:10.1007/s11661-008-9582-6 .\nURL https://doi.org/10.1007/s11661-008-9582-6\n[24] I. Brough, P. S. Bate, F. J. Humphreys, Optimising the an-\ngular resolution of EBSD, Materials Science and Technol-\nogy 22 (11) (2006) 1279{1286, publisher: Taylor & Fran-\ncis eprint: https://doi.org/10.1179/174328406X130902. doi:\n10.1179/174328406X130902 .\nURL https://doi.org/10.1179/174328406X130902\n[25] F. J. Humphreys, P. S. Bate, P. J. Hurley, Orientation averaging of elec-\ntron backscattered di\u000braction data, Journal of Microscopy 201 (1) (2001)\n50{58, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365-\n2818.2001.00777.x. doi:https://doi.org/10.1046/j.1365-2818.2001.\n3000777.x .\nURL http://onlinelibrary.wiley.com/doi/abs/10.1046/j.\n1365-2818.2001.00777.x\n[26] S. I. Wright, M. M. Nowell, J. F. Bingert, A Comparison of Textures\nMeasured Using X-Ray and Electron Backscatter Di\u000braction, Metallurgi-\ncal and Materials Transactions A 38 (8) (2007) 1845{1855. doi:10.1007/\ns11661-007-9226-2 .\nURL http://link.springer.com/10.1007/s11661-007-9226-2\n[27] S. I. Wright, M. Nowell, D. Field, A Review of Strain Analysis Using Elec-\ntron Backscatter Di\u000braction, Microscopy and Microanalysis 17 (03) (2011)\n316{329. doi:10.1017/S1431927611000055 .\nURL http://journals.cambridge.org/article_S1431927611000055\n[28] S. V. Mehtonen, E. J. Palmiere, R. D. K. Misra, L. P. Karjalainen, D. A.\nPorter, Dynamic restoration mechanisms in a Ti{Nb stabilized ferritic\nstainless steel during hot deformation, Materials Science and Engineering:\nA 601 (2014) 7{19. doi:10.1016/j.msea.2014.02.039 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0921509314001828\n[29] D. Raabe, K. L ucke, Selective particle drag during primary recrystal-\nlization of Fe-Cr alloys, Scripta Metallurgica et Materialia 26 (1) (1992)\n19{24. doi:10.1016/0956-716X(92)90361-H .\nURL https://linkinghub.elsevier.com/retrieve/pii/\n0956716X9290361H\n[30] P. Bate, W. B. Hutchinson, A re-evaluation of the mecha-\nnism of SIBM, Scripta Materialia 36 (2) (1997) 195{198. doi:\n10.1016/S1359-6462(96)00361-2 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359646296003612\n31[31] B. Hutchinson, Deformation microstructures and textures in steels, Philo-\nsophical Transactions of the Royal Society of London. Series A: Mathe-\nmatical, Physical and Engineering Sciences 357 (1756) (1999) 1471{1485,\npublisher: Royal Society. doi:10.1098/rsta.1999.0385 .\nURL https://royalsocietypublishing.org/doi/abs/10.1098/rsta.\n1999.0385\n[32] F. Kocks, C. Tom\u0013 e, H.-R. Wenk, Texture and Anisotropy. Preferred Ori-\nentations in Polycrystals and Their E\u000bect on Material Properties, 2000.\n[33] J. J. Jonas, E\u000bects of shear band formation on texture development in\nwarm-rolled IF steels, Journal of Materials Processing Technology 117 (3)\n(2001) 293{299. doi:10.1016/S0924-0136(01)00786-5 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0924013601007865\n[34] P. J. Hurley, F. J. Humphreys, Modelling the recrystallization of\nsingle-phase aluminium, Acta Materialia 51 (13) (2003) 3779{3793.\ndoi:10.1016/S1359-6454(03)00192-7 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645403001927\n[35] H. S. Zurob, Y. Br\u0013 echet, J. Dunlop, Quantitative criterion for re-\ncrystallization nucleation in single-phase alloys: Prediction of critical\nstrains and incubation times, Acta Materialia 54 (15) (2006) 3983{3990.\ndoi:10.1016/j.actamat.2006.04.028 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645406003181\n[36] M. Ferry, F. J. Humphreys, Discontinuous subgrain growth in deformed\nand annealed $f110g<001>$aluminium single crystals, Acta Materialia\n44 (4) (1996) 1293{1308. doi:10.1016/1359-6454(95)00316-9 .\nURL http://www.sciencedirect.com/science/article/pii/\n1359645495003169\n32[37] R. D. MacPherson, D. J. Srolovitz, The von Neumann relation generalized\nto coarsening of three-dimensional microstructures, Nature 446 (7139)\n(2007) 1053{1055. doi:10.1038/nature05745 .\nURL https://www-nature-com.ezproxy.library.ubc.ca/articles/\nnature05745\n[38] M. E. Glicksman, P. R. Rios, D. J. Lewis, Mean width and caliper character-\nistics of network polyhedra, Philosophical Magazine 89 (4) (2009) 389{403.\ndoi:10.1080/14786430802651513 .\nURL https://doi.org/10.1080/14786430802651513\n[39] J. Zhang, Y. Zhang, W. Ludwig, D. Rowenhorst, P. W. Voorhees,\nH. F. Poulsen, Three-dimensional grain growth in pure iron. Part\nI. statistics on the grain level, Acta Materialia 156 (2018) 76{85.\ndoi:10.1016/j.actamat.2018.06.021 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645418304890\n[40] M. Hillert, On the theory of normal and abnormal grain growth, Acta Met-\nallurgica 13 (3) (1965) 227{238. doi:10.1016/0001-6160(65)90200-2 .\nURL http://www.sciencedirect.com/science/article/pii/\n0001616065902002\n[41] M. I. Mendelson, Average Grain Size in Polycrystalline Ceram-\nics, Journal of the American Ceramic Society 52 (8) (1969) 443{\n446, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1151-\n2916.1969.tb11975.x. doi:https://doi.org/10.1111/j.1151-2916.\n1969.tb11975.x .\nURL http://ceramics.onlinelibrary.wiley.com/doi/abs/10.1111/\nj.1151-2916.1969.tb11975.x\n[42] A. R. C. Gerlt, R. S. Picard, A. E. Saurber, A. K. Criner, S. L.\nSemiatin, E. J. Payton, A Transfer Function for Relating Mean 2D\nCross-Section Measurements to Mean 3D Particle Sizes, Metallurgical\n33and Materials Transactions A 49 (10) (2018) 4424{4428. doi:10.1007/\ns11661-018-4808-8 .\nURL http://link.springer.com/10.1007/s11661-018-4808-8\n[43] W. T. Read, W. Shockley, Dislocation Models of Crystal Grain Boundaries,\nPhys. Rev. 78 (3) (1950) 275{289. doi:10.1103/PhysRev.78.275 .\nURL http://link.aps.org/doi/10.1103/PhysRev.78.275\n[44] F. J. Humphreys, A uni\fed theory of recovery, recrystallization and\ngrain growth, based on the stability and growth of cellular microstruc-\ntures|I. The basic model, Acta Materialia 45 (10) (1997) 4231{4240.\ndoi:10.1016/S1359-6454(97)00070-0 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645497000700\n[45] Y. Huang, F. J. Humphreys, Subgrain growth and low angle boundary\nmobility in aluminium crystals of orientation f110g(001), Acta Materialia\n48 (8) (2000) 2017{2030. doi:10.1016/S1359-6454(99)00418-8 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645499004188\n[46] C. Sinclair, C. Hutchinson, Y. Br\u0013 echet, The E\u000bect of Nb on the Recrystal-\nlization and Grain Growth of Ultra-High-Purity alpha-Fe: A Combinatorial\nApproach, Metallurgical and Materials Transactions A 38 (4) (2007) 821{\n830. doi:10.1007/s11661-007-9106-9 .\nURL https://doi.org/10.1007/s11661-007-9106-9\n[47] I. L. Dillamore, C. J. E. Smith, T. W. Watson, Oriented Nucle-\nation in the Formation of Annealing Textures in Iron, Metal Sci-\nence Journal 1 (1) (1967) 49{54, publisher: Taylor & Francis eprint:\nhttps://doi.org/10.1179/msc.1967.1.1.49. doi:10.1179/msc.1967.1.1.\n49.\nURL https://doi.org/10.1179/msc.1967.1.1.49\n34[48] L. Kestens, J. J. Jonas, Modelling Texture Change during the Static Re-\ncrystallization of a Cold Rolled and Annealed Ultra Low Carbon Steel\nPreviously Warm Rolled in the Ferrite Region, ISIJ International 37 (8)\n(1997) 807{814. doi:10.2355/isijinternational.37.807 .\n[49] I. L. Dillamore, P. L. Morris, C. J. E. Smith, W. B. Hutchinson, G. V.\nRaynor, Transition bands and recrystallization in metals, Proceedings\nof the Royal Society of London. A. Mathematical and Physical Sciences\n329 (1579) (1972) 405{420, publisher: Royal Society. doi:10.1098/rspa.\n1972.0120 .\nURL https://royalsocietypublishing.org/doi/abs/10.1098/rspa.\n1972.0120\n[50] M. R. Barnett, Role of In-grain Shear Bands in the Nucleation of\n<111>//ND Recrystallization Textures in Warm Rolled Steel, ISIJ Inter-\nnational 38 (1) (1998) 78{85. doi:10.2355/isijinternational.38.78 .\n[51] A. Despr\u0013 es, M. Zecevic, R. A. Lebensohn, J. D. Mithieux, F. Chassagne,\nC. W. Sinclair, Contribution of intragranular misorientations to the cold\nrolling textures of ferritic stainless steels, Acta Materialia 182 (2020)\n184{196. doi:10.1016/j.actamat.2019.10.023 .\nURL http://www.sciencedirect.com/science/article/pii/\nS1359645419306858\n[52] M. Zecevic, R. A. Lebensohn, R. J. McCabe, M. Knezevic, Mod-\neling of intragranular misorientation and grain fragmentation in\npolycrystalline materials using the viscoplastic self-consistent for-\nmulation, International Journal of Plasticity 109 (2018) 193{211.\ndoi:10.1016/j.ijplas.2018.06.004 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0749641918301074\n[53] W. Pantleon, Retrieving orientation correlations in deformation structures\nfrom orientation maps, Materials Science and Technology 21 (12) (2005)\n351392{1396. doi:10.1179/174328405X71657 .\nURL http://www.tandfonline.com/doi/full/10.1179/\n174328405X71657\n[54] F. Lefevre-Schlick, Y. Brechet, H. S. Zurob, G. Purdy, D. Embury,\nOn the activation of recrystallization nucleation sites in Cu and\nFe, Materials Science and Engineering: A 502 (1) (2009) 70{78.\ndoi:10.1016/j.msea.2008.10.015 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0921509308011702\n[55] F. J. Humphreys, Review Grain and subgrain characterisation by electron\nbackscatter di\u000braction, Journal of Materials Science 36 (16) (2001) 3833{\n3854. doi:10.1023/A:1017973432592 .\nURL https://doi.org/10.1023/A:1017973432592\n[56] MTEX.\nURL https://mtex-toolbox.github.io/\nAppendices\nA. Implementation of the Kuwahara \flter\nThe Kuwhara \flter is an edge-preserving smoothing \flter, whose application\nto orientation maps has \frst been developed by Humphreys et al. [24, 25, 55].\nOn raw orientation maps, the array of pixels surrounding each individual pixel\nis divided in four sub-arrays (north-east, north-west, south-west, south-east),\nand the individual pixel is reassigned the mean orientation of the sub-array\nhaving the least variance in orientation. According to Brough et al. [24], using\nthis \flter allows the noise level to be reduced to below 0.3\u000ewhile conserving\nthe subgrain boundaries. As recommended [25], 3 passes were performed with\nan array of 5x5 and subarrays of 3x3 pixels. Filtering was performed with the\n36scripts implemented in MTEX [56].\nFigure A.8a and b illustrate the e\u000bect of \fltering on a portion of IPF map\nof the deformed microstructure. Figure A.8c shows that \fltering preserves the\norientation gradient (point-to-origin disorientations) as well as the boundary\ndisorientation angles which are already above a few degrees in the raw orienta-\ntion map (note that these boundaries can shift horizontally and vertically of a\nfew pixels). On the other hand, the minimum level of boundary disorientation\nangle falls to 0 in the \fltered map. Modifying the threshold disorientation an-\ngle for subgrains is not expected to change signi\fcantly the main results of this\nstudy. For example, if a 1\u000eangle instead of 0.3\u000eis choosen to de\fne subgrain\nboundaries, the average subgrain size increases of only 8.5%, and the anisotropy\nin subgrain properties remains similar.\n(a)\n (b)\n (c)\nFigure A.8: The e\u000bect of Kuwahara \fltering on subgrain characterization in the deformed\nmicrostructure. (a) raw ND-IPF map, (b) \fltered ND-IPF map, (c) disorientation pro\fle\nalong the green pro\fle.\n37"    },    {        "title": "0808.1198v1.Spectral_properties_of_interacting_magnetoelectric_particles.pdf",        "content": "Spectral properties of interact ing magnetoelectric particles \n \nE.O. Kamenetskii  \n \nBen-Gurion University of th e Negev, Beer Sheva 84105, Israel  \n \nAugust 7, 2008 \n \nAbstract \n \nThe linear magnetoelectric (ME) effect provides a special route for linki ng magnetic and electric \nproperties. In microwaves, a loca l ME effect appears due to the dynamical symmetry breakings of \nmagnetic-dipolar modes (MDMs) in a ferrite disk pa rticle. The fact that for MDMs in a ferrite disk \none has evident both classical and quantum-like a ttributes, puts special demands on the methods \nused for study of interacting ME particles. A pr oper model for coupled particles should be based \non the spectral characteristics of MDM oscillations and an analysis  of the overlap integrals for \ninteracting eigen oscillating ME elements. In this paper, we present theoreti cal studies of spectral \nproperties of literally coupled of  MDM ME disks. We show that  there exists the \"exchange\" \nmechanism of interaction between the particles,  which is distinctive from the magnetostatic \ninteraction between magnetic dipoles. The spectra l method proposed in this paper may further the \ndevelopment of a theory of ME \"molecules\"  and realization of local ME composites. \n PACS number(s): 75.10.- b, 75.10.Jm, 03.65.Vf, 85.80.Jm \n  \nI. INTRODUCTION  \n \nThe symmetry relationships between the elec tric polarization and the magnetization make \nquestionable an idea of simple combination of tw o (electric and magnetic) di poles to realize local \nmagnetoelectric (ME) particles. The electric polar ization is parity-odd and time-reversal-even. At \nthe same time, the magnetization is parity-even and time-reversal- odd [1]. If one supposes that he \nhas created an \"artificial atom\" with the local cross-polarization effect  one, certainly, should \ndemonstrate a special ME field in the near-field  region. It means that using a gedankenexperiment \nwith two quasistatic, electric a nd magnetic, point probes for the ME  near-field characterization, \none should observe not only an electrostatic-pot ential distribution (becau se of the electric \npolarization) and not only a ma gnetostatic-potential distribution (because of the magnetic \npolarization), one also should observe a special  cross-potential term (because of the cross-\npolarization effect). This fact contradicts to  classical electrodynamics. One cannot consider \n(classical electrodynamically) tw o coupled electric and magnetic di poles – the ME particles – as \nlocal (near-field) sources of the electromagnetic fiel d [1]. So in a presupposition that an \"artificial \natom\" with the near-field cross-po larization effect is really created, one has to show that in this \nparticle there are speci al internal dynamical motion processe s different from the classical motion \nprocesses [2]. Numerous classical models of so ca lled bianisotropic particles proposed in literature \n[3] do not provide the reader w ith real physics of ME coupling be tween the microscopic electric \nand magnetic currents.      Physically, there are different characteri zations of magnetoelectric ity, or ME effect. For \nexample, one can characterize the ME effect as the appearance of an el ectric field in certain \nsubstances, when they are subject ed to a static magnetic field. A nother characterization of the ME \neffect is related to linear coupling between magnetiz ation and polarization in solid-state structures. \nNatural magnetoelectric crystals are solid-stat e structures with li near coupling between  2magnetization and polarization. Physics of the ME e ffect in crystals becomes evident not from a \npure classical basis. In differe nt physical problems, ME coup ling is due to symmetry breaking \nphenomena. In crystals and molecular systems,  magnetoelectricity takes place when space \ninversion is locally broken [4]. If the ME eff ect exists, the interacti on between electrons and \nelementary magnetic cells appears in such a way that the resulting local polarization and \nmagnetization break the local relativistic crystallin e symmetry. In natural crystals, ME properties \nare evident or at very low frequencies, or in an  optical region. Recently, the microwave ME effect \nwas demonstrated in layered ferrite /piezoelectric structures [5].  \n    Natural magnetoelectric crystals and layered ferrite/piezoelectric structures are not materials composed by small structural elements – local ME  particles. In a proposition of particulate ME \ncomposites one may suppose that the unified ME fields originated fr om a point ME particle (when \nsuch a particle is created) will not be the classical fields, but the quantum (quantum-like) fields. It means that the motion equations inside a local ME  particle should be the quantum (quantum-like) \nmotion equations with special  symmetry properties.  \n    The fundamental discrete symmetries of par ity (P), time reversal (T) and charge conjugation \n(C), and their violations in certa in situations, are central in modern elementary particle physics, \nand in atomic and molecular physics.  As a basic principle,  the weak interaction is consider ed as the \nonly fundamental interaction, which does not respect  left-right symmetry. Th e mutual interaction \nof magnetic and electric charges in the dynamical construction of the elementary particles could \nlead in a natural way to the parity violation observe d in weak interactions [6 ]. Atoms are chiral due \nto the parity-violating weak neutral current inter action between the nucleus and the electrons [7]. \nFollowing ideas of some recent theories, one sees th at ME interactions in crystal structures with \nsymmetry breakdown arise from special toroidal di stributions of currents and are described by so-\ncalled anapole moments [8]. The an apole moment takes place in systems with the parity violation \nand with the annual magnetic field [9]. At present, the role of anapole moment s is considered as an \nimportant factor in understanding chirality (helicity) in different  atomic, molecular and condense-\nmatter phenomena. The anapole moment plays the e ssential role in nuclea r helimagnetism [10, 11]. \nIt was considered as an intrinsic proper ty of a diatomic polar molecule [12].  \n    One of the reasons why the anapole moment s appear is Stone's spinning-solenoid Hamiltonian \n[13] and ME properties of Stone's Hamiltonian b ecome apparent because of Berry's curvature of \nthe electronic wavefunctions. In r ecent theories of spin waves in  magnetic-order cr ystals, a Berry \ncurvature is stated as playing a key role [ 14, 15]. The Berry phase may also influence the \nproperties of magnons. If the magn etic medium in which the ma gnon is propagating is spatially \nnon uniform, a Berry phase may be accumulated along a closed circuit in space. It has been \nrecently indicated [16] that th e geometric Berry phase due to a non-coplanar texture of the \nmagnetization of a ferromagnetic ring would aff ect the dispersion of magnons, lifting the \ndegeneracy of clockwise and anticlockwise pr opagating magnons. It was found [16] that the \nmagnetization transport by magnons in a noncollinear spin structure is accompanied by an electric \npolarization. This electric polariz ation can be experimentally obser ved not only in th e vicinity of \nthe mesoscopic ring [16] but also in the vicini ty of the magnetic wire  [17]. Moving magnetic \ndipoles represent an electric dipol e moment [18] and are therefore a ffected by electric fields. Such \na ME effect in magnetic nanostructures is, in fact, the relativistic effect of a transformation of \nmagnetization to the electric field in the moving frame. At the same  time, because of the electronic \nstructure of the material, the magnitude of such  ME coupling can be much larger than a bare \nrelativistic effect [19].      This small survey is not a formal enumer ation of basic concepts. The above microscopic and \nmesoscopic aspects of chirality and magnetoelectric ity should, certainly, be related to the problems \nof local ME particles and the unifi ed ME fields originated from su ch point sources, and necessarily \nshould become the main subject for realization of local ME composites. One can formulate the \nconcept of particulate ME composites as possibl e unification of the processes of dipole motions  3and symmetry breaking phenomena. Following the re sults of recent studies, we may come to a \ncertain deduction that spectral properties of magnetostatic modes (MSMs), or magnetic-dipolar \nmodes (MDMs) in ferrite disks may put us in to a proper way. It was shown that MDMs in a \nnormally magnetized ferrite disk  are characterized by the dynami cal symmetry breaking effects \nresulting in ME properties [20 – 25]. Artificial ME materials s hould be realized as patterned \nstructures composed with special -symmetry ferromagnetic elements. \n    The purpose of this paper is to analyze interactions between MDM ferrite disks for possible \nrealization of ME \"molecules\" a nd local ME composites. We involve  a rigorous spectral treatment \nwhich uses the two-\"atom\" locali zed orbital picture as its basis and show a quantum-like behavior \nof the ME-particle interactions.   \nII. THEORIES OF INTERACTING OSCI LLATING ELEMENTS AND A MODEL FOR \nCOUPLED ME PARTICLES  \n \nThe microwave ME effect in a fe rrite disk particle appears due to the vortex states of eigen \nmagnetic-dipolar-mode (MDM) oscillations [23]. The fact that for MDMs in a ferrite disk one has \nevident both classical an d quantum-like attributes [20 – 26], puts special demands on the methods \nused for study of interacting fe rrite ME particles. To develop a proper model for coupled ferrite \nME particles we have to make a preliminary analys is of the main aspects related to the subject. \nThis concerns the known models of the magneti zation dynamics and the pr oblems of interacting \nferromagnetic dots; the methods of the coupled-mode  theory for classical and quantum guiding and \noscillating systems. As special questions, we have to dwell on the spectral properties of MDM \noscillations in a ferrite disk  particle and the dynamical symm etry breaking effects of MDM \noscillations.   \nA. Models for the magnetization dynamics  in interacting ferromagnetic elements \n \nAt present, studies of resonant modes of structures of interact ing ferromagnetic elements (slabs, \nwires and dots) are a subject of an interest fo r many researches. Different  classical approaches \nhave been developed for such systems. The interp article coupling, mainly of dipolar nature, affects \nboth the static and dynamic behaviors of the ma gnetization. For any distribution of magnetization, \nboth for continuum ferromagnetic media and for patte rned structures with ferromagnetic elements, \nthe magnetic dipole intera ction is described by the magnetost atic solution. If we consider the \nmotion of the magnetization in a particular ferroma gnetic element, then a dynamic magnetic dipole \nfield is generated in the spatia l region outside the element by the precession of the magnetization. \nWhen elements are arranged in the form of a peri odic structure, one may seek solutions of the \nBloch form.       The effective magnetic dipolar intera ction between single domain two-dimensional \nferromagnetic particles (magnetic dots) was analyzed  in paper [27]. Each particle behaves as a \nsingle spin \nsNSrr\n = , where N is the total number of local spins sr in the particle. The effective \ninteraction between particles of spins iSr\n and jSr\n in a lattice is described as the classical \nmagnetostatic interaction between two magnetic di poles. As it is discu ssed in [27], dipolar \ncoupling between particles may induce ferromagnetic  long range order. Based on a dynamical \nmatrix method, a theory for the de termination of the collective spin -wave modes of regular arrays \nof magnetic particles (taking in to account the dipolar interacti on between particles) has been \ndeveloped in [28]. A method of an analysis of magnetic-particl e arrays based on an assumption \nthat a body is represented by an  array of macrospins, each cons isting of many true spins, was \ndeveloped in [29]. This microma gnetic-simulation method (viewed by th e authors of Ref. [29] as a  4discrete version of the Landau-Lifshitz equati on) involves a solution of the coupled Larmor \nequations of the individual dipoles with all fields acting on them.   \n    Aiming to realization of microwave ME compos ites, the most interesting aspect for our studies \nconcerns an analysis of the known publicati ons of coupled disks with the vortex states. \nMagnetically soft ferromagnetic materials genera lly form domain structures to reduce their \nmagnetostatic (MS) energy. In this context, closur e domains are especially suitable. Such magnetic \nobjects are characterized by a closed flux circ uit having no magnetic flux leakage outside the \nmaterial. In very small systems, however, the formation of domain walls  is not energetically \nfavored. Specifically, in a dot of  a ferromagnetic material of micr ometer or submicrometer size, a \ncurling spin configuration – that  is, a magnetization vortex – has been proposed to occur in place \nof domains. The vortex consists of an in-pla ne, flux-closure magnetiza tion distribution and a \ncentral core whose magnetization is  perpendicular to the dot plane.  It has been shown that under \ncertain conditions a vortex structure will be stab le because of competition between the exchange \nand dipole interactions. For magnetic vortices, one obtains the clockwise (CW) and counter-\nclockwise (CCW) rotations of magnetization vector mr in the dot plane [30 – 32].  \n    Two closely spaced vortex-dynamics ferro magnetic disks can be coupled due to the MS \ninteractions. It was shown [33, 34] that the vort ex core exhibits circular motion around the disk \ncenter. When the vortex core is shifted from a disk center, magnetic charges emerge on the side \nsurface of the disk. Due to these charges one ma y have the MS interaction between the vortex-\ndynamics disks [35, 36]. Micromagnetic simulati on shows that the coupled vortices coherently \nrotate around the disk centers and the CW or CCW rotational directions  do not influence the \ndynamics of vortices [35]. Rotational directions of the magnetization play, however, an important \nrole in the vortex coupling in asymmetrical disks.  In an isolated perfect circular disk, CW and \nCCW states are energetically degenerate. By introducing asymmetry in the disk, vortex motion \nbecomes chirality-controlled. In a pair of asymmetr ical ferrite disks one has chirality-controlled \nmagnetostatic interactions  [37]. The knowledge of the vortex m ode structure in an isolated dot \nallows studies of collective waves for an array of  magnetic dots in the vorte x state [38]. In paper \n[38], solutions were obtained with an assumption that dots, having the same  states of vorticity and \npolarization, are couple d via the MS dipolar mechanism of interaction. \n \nB. Overlap integrals and the coupled mode theories \n \nIn all the papers, to the best of our knowledge, analyzing magnetization dynamics of interacting \nnanoscale magnetic elements, the problem of in terdot coupling is described by the Poisson \nequation for the magnetostatic potential. At th e same time, in numerous spectral problems of \ninteracting eigen oscillating elements, an interac tion is considered via ev anescent exponential tails \nof eigen wave functions locali zed inside a separate element and is described by the overlap \nintegral.       Generally, a form of the overlap integral is  determined by the orthogona lity conditions of eigen \nmodes in a separate element. This concerns both  classical electromagnetic structures and quantum \nsystems. In a case of electromagnetic waveguides,  the coupling between ad jacent guides induces \nthe transverse dynamics. Energy exchange is caused by the overlap of the ev anescent tails of the \nguided modes. In several couple d-mode formulations for coupled  waveguide systems, one has \ndifferent expressions for the overlap integrals and so different formulas for coupling coefficients  \n[39 – 45].      Methods of the coupled-mode theory are applicable also for an analysis of coupled \nelectromagnetic resonators [46]. Dielectric resonators with extr emely high values of the quality \nfactor Q use high-order azimuth oscillations, the so- called whispering-galle ry modes [47]. Such \nmodes are, in fact, the Mie-res onance modes of small particles [ 48]. There are, however, not the \nmodes which arise from the real-norm orthogonality relation of the spectral problem. The peak  5positions of these resonant modes are dependent on a character of excitation [49]. In spite of the \nevidently high Q factor of resonators with whisperi ng-gallery modes, al l these modes must \nnecessarily be leaky [50]. The an alyses of coupled Mie-resonan ce dielectric particles are made \nbased on phenomenologically introd uced overlap integrals, as th e analogy with overlap between \nthe modes of coupled quantum wells (atoms). Howe ver, as it was noted in [49], the complete \nanalogy between coupled Mie-resonance dielectric  particles and coupled quantum particles does \nnot hold because the Mie-resonance states are not enough bound within the dielec tric particle. This \nextended behavior does not guara ntee the convergence of the ove rlap integral between the \nresonance states of the neighbor ing particles [49]. Ne vertheless, in the theory of coupled \nwhispering-gallery resonators, the overlap is used  as a \"direct\" modal coupling term. The coherent \ncoupling results in the frequency splitting of th e corresponding whispering- gallery modes and is a \nmanifestation of the well known phenomena of th e normal mode splitting in coupled harmonic \noscillators [51].      In quantum systems, an overlap integral is  usually defined as the integral over space of the \nproduct of the wave function of a particle and the complex conjugate of the wave function of \nanother particle. An analysis of a spectrum of two horizontally coupled 2D quantum dots with two \nconfined electrons is based on the theory of a double-quantum- dot hydrogen molecule. Due to the \nCoulomb interaction and the Pauli exclusion princi ple one obtains a highly entangled spin state of \ntwo coupled electron wave functi ons. The exchange coupling between  two confined electron states \narises as a result of their spatial behavior and can be expressed as an effective spin-spin interaction \n[52 – 54]. Together with an analysis of the H ilbert space structure of horizontally coupled double-\nquantum-dot system, a vertically coupled double-quant um-dot system has also been studied [55].  \nRecently, the concepts of the classical coupled-mode theory were used for coupled electron-wave quantum waveguides [56]. The electron wave propa gating in a coupled-quantum-well system is \nexpressed as a linear combination of two guid ed electron-wave modes in separate quantum \nwaveguides. The overlap integral is determined by the orthogonality conditions of eigen modes in \nan individual quantum well. An analysis establ ishes the basic relations between the normal modes \nof the coupled well system and the isolated modes of  the individual wells. It allows calculating the \ncoupling and propagation constants from basi c physical quantities of  the uncoupled modes. \n \nC. Energy eigenstates of MDM oscillations and a model for coupled MDM ferrite disks \n \nIn an analysis of the MDM oscillating spectra, a fe rrite-disk particle is considered as a section of \nan axially magnetized ferri te rod. For a flat ferrite disk, having a diameter much bigger than a disk \nthickness, one can successfully use separation of variables for the MS-potential wave  function [26, \n57]. A similar way of separation variables is us ed in solving the electromagnetic-wave spectral \nproblem in dielectric disks [58].      For MDMs in a ferrite di sk one has evident qua ntum-like attributes. The spectrum is \ncharacterized by energy eigenstate oscillations wh ich are characterized by a two-dimensional (“in-\nplane”) differential operator  \n                                                                    \n2 16ˆ\n⊥ ⊥ ∇=µπqgF ,                                                           (1)                    \n \nwhere 2\n⊥∇ is the two-dimensional (with respect to cross-sectional coordinates) Laplace operator, \nµ is a diagonal component of the permeability tensor, and qg is a dimensional normalization \ncoefficient for mode q. Operator ⊥Fˆ is positive definite for negative quantities µ. The normalized \naverage (on the RF period) density of  accumulated magnetic energy of mode q is determined as \n  6                                                                    ()2\n16qzq\nqgE βπ= ,                                                         (2) \n \nwhere \nqzβ is the propagation constant of mode q along disk axis z. The energy eigenvalue problem \nis defined by the differential equation: \n \n                                                                    qq qE Fηη~ ~=⊥),                                                               (3) \n \nwhere qη~ is a dimensionless membrane MS-potentia l wave function [21, 23]. At a constant \nfrequency, the energy orthonormality for MD Ms in a ferrite disk is written as: \n  \n                                                              0~~) ( = −∫∗\n′ ′\nSqq q q dS E E ηη ,                                                    (4)                     \n \nwhere S is a cylindrical cross section of an open disk . One has different mode energies at different \nquantities of a bias magnetic field. From the prin ciple of superposition of states, it follows that \nwave functions qη~ ( ,...2,1=q ), describing our \"quantum\" system , are \"vectors\" in an abstract \nspace of an infinite number of dime nsions – the Hilbert space. In quantum mechanics, this is the \ncase of so-called energetic representation, when the system energy runs through a discrete sequence of values. In the energetic representati on, a square of a modulus of the wave function \ndefines probability to find a system with a cert ain energy value [59, 60]. In our case, scalar-wave \nmembrane function \nη~ can be represented as  \n \n                                                                     ∑=\nqqqaηη~ ~                                                               (5)                    \n \nand the probability to find a system in a certain state q is defined as \n \n                                                                 2\n*2~ ~∫=\nSq q dS aηη .                                                          (6)                   \n \n    It was shown [21, 23] that because of th e boundary condition on a late ral surface of  a ferrite \ndisk, the topological effects ar e manifested through the genera tion of relative phases which \naccumulate on the boundary wave function ±δ. There exist the vortex-state resonances which \nconventionally designated as the (+ ) and the (–) resonances. For the (+) resonance, a direction of \nan edge chiral rotation coincides with the precession magnetization direction, while for the (–) resonance, a direction of an edge chiral ro tation is opposite to the precession magnetization \ndirection. For a given cross-s ectional state (described by th e mode membrane function), one \ndefines the strength of a vortex of a whole disk, \nes± , and a moment  \n \n                                                                      e\naesi a± ±=  µ ,                                                                (7) \n \nwhere aµ is an off-diagonal component of th e permeability tensor. The superscript \" e\" means \n\"electric\" since moment ear has the symmetry of an el ectric dipole. [21, 23].   7    MDMs in a normally magne tized ferrite disk are characte rized by the dynamical symmetry \nbreakings resulting in the ME effects. A moment ea± has the anapole moment properties [9, 20 – \n24]. From an analysis of the spectral problem fo r MS-potential wave function it becomes evident \nthat in magnetically saturated cylindrical dots there is a property associated with the vortex structures. The vortices are guaranteed by the chiral  edge states of magnetic-dipolar modes in a \nquasi-2D ferrite disk. Physical nature of such vortices is different from the vortices found in \nmagnetically soft \"small\" (with the dipolar and exchange energy competition) cylindrical dots [30 \n– 32].      Spectral properties of MDM oscillations in a fe rrite disk determine the basis for elaboration and \nan analysis of a model for coupled MDM disks. Following Eq. (1), one can see that the energy \nsplitting in coupled MDM disks w ill be defined by the wavenumber  deviations at a constant \nfrequency. This certainly differs from the internal  energy splitting in coupled  dielectric resonators \nwhich is defined by the frequenc y deviations [51]. Because of eigen electric moments oriented \nnormally to the disk plane, coupling between two ferrite disk particles s hould be described by the \n\"exchange interaction\" overlapping integrals for eigen MS-wave functi ons. To a certain extent, this \ncan be considered as a dual case with respec t to coupled quantum dots with the exchange \ninteraction described by overlappi ng integrals for eigen electron wa ve functions [52 – 54]. At the \nsame time, symmetry breaking effects for MDM osci llations result in a ppearance of special ME \ninteractions for coupled ferrite disks.     Since, in an analysis of the MDM oscillatin g spectra a disk is repres ented as a section of an \naxially magnetized ferrite rod, c oupled quasi-2D ferrite disk par ticles should be analyzed as a \nsection of coupled MDM waveguides. The coupled-mode formulation for MDM ferrite \nwaveguides demands a special cons ideration. Development of the coupled-mode model for such \nwaveguide structures we should st art with consideration of the power flow density for MDMs.  \n \nIII. MDM FLOW DENSITY IN A FERRITE ROD  \n \nAny kind of a wave process is char acterized by a certain flow density jr\n. The physical meaning of \nflow jr\n is determined by a type of a differential eq uation describing a wave process. For Maxwell \nequations, there is the Poynting vector, for Schrödinger equation, there is the probability flow \ndensity. These flows have different physics: in the Maxwell theory, we can define a positive-\ndefinite energy density, while cannot define a positive-definite probability density.  \n    In a waveguide structure, there is a longitudinal flow density||jr\n, where subscript || means \npropagation along a waveguide axis. Integr ation over a waveguide cross section, ∫⋅≡\nSzdSej Jrr\n|| || , \ngives a total flow along a waveguide (zev is the unit vector along z axis). In a case of an \nelectromagnetic waveguide one ha s the longitudinal electromagne tic power flow density (the \nPoynting vector) [1]  \n                                                      \n()( )⊥⊥⊥⊥ ×+×= H E H EcjEMrrrr r* *\n||4π,                                             (8) \n \nwhere subscript ⊥ means transversal field component s. For a quantum waveguide, the \nlongitudinal probability flow density is expressed as [59, 60]                                                       \n                                                       \n()( )φφφφ     2||* *\n|| || ∇−∇=mijQMh r\n,                                              (9)  8 \nwhere m is the electron mass, φ is the electron wave function, and operator ||∇ denotes \ndifferentiation along a waveguide axis. For a MS-wave waveguide, the longitudinal power flow \ndensity is expressed as [23]                                                      \n                                                           \n() ()*\n|| ||*\n||  16B BijMSWrr r\nψψπω− = ,                                              (10) \n \nwhere ψ is the MS-potentia l wave function and Br\n is the magnetic flux density. Eq. (10) \nrepresents a classical flow density  but, at the same time, for a certa in configuration,  it looks like \nthe probability flow density in a quantum waveguide . Really, for an axially magnetized ferrite rod, \none has [23]  \n                                                       \n() ( )ψψψψπω\n||* *\n|| ||   16∇−∇=ijMSWr\n.                                         (11) \n \n    Let us consider a quantity || ||jr\n⋅∇ . For a lossless and sourcele ss linear waveguide one has  \n \n                                                                       0|| ||=⋅∇jr\n.                                                              (12)                     \n \nIt means conservation of the flow density ||j along a waveguide. For a MS-wave waveguide, \ndivergence || ||jr\n⋅∇  is expressed as \n \n                              () ( )ψψψψπωψψψψπω2\n||* * 2\n|| ||* *\n|| || || ||  16 16∇−∇=∇−∇⋅∇=⋅∇i ijr\n.                      (13) \n \nFor an open ferrite rod (with homogeneous materi al parameters), one ha s the following second-\norder equations for MS-potential wave function ψ. There is the Walker eq uation inside a ferrite  \n \n                                                                   0    2\n||2=∇+∇⊥ψψµ                                                      (14) \n \nand the Laplace equation outside a ferrite  \n                                                                    \n0   2\n||2=∇+∇⊥ψψ .                                                      (15) \n \nBased on Eqs. (14) and (15), one rewrites Eq. (13) as   \n                         \n() ( )ψψψψπµωψψψψπµω\n⊥ ⊥ ⊥ ⊥ ⊥ ∇−∇⋅∇−=∇−∇−=⋅∇* * 2 * * 2\n|| ||  16 16i i jr                      (16) \n \nfor an internal ferrite region and  \n                         \n() ( )ψψψψπωψψψψπω\n⊥ ⊥ ⊥ ⊥ ⊥ ∇−∇⋅∇−=∇−∇−=⋅∇* * 2 * * 2\n|| ||  16 16i i jr                     (17) \n \nfor an external dielectric region.  9    Let a ferrite core be a cylinder of radius ℜ. A necessary requirement of conservation of the \npower flow density in a lossle ss regular MS-wave waveguide  \n \n                                                             0  || || || || =⋅∇≡⋅∇∫dSj J\nSr r\n,                                                   (18) \noccuring for boundary conditions on a latera l surface of a ferrite rod [21, 23]:  \n \n                                                                       \n+ − ℜ= ℜ==r rψψ                                                          (19) \n \nand   \n                                                             \n0  =⎟\n⎠⎞⎜\n⎝⎛\n∂∂−⎟\n⎠⎞⎜\n⎝⎛\n∂∂\n+ − ℜ= ℜ= r r r rψ ψµ                                             (20)   \n \nis in an evident contradiction with another physical requireme nt, namely, conservation of the \nmagnetic flux density, 0=⋅∇Br\n. The continuity of a normal component of Br\n on a cylindrical \nsurface of a ferrite region takes place if          \n \n                                                     \nℜ= ℜ= ℜ=⎟\n⎠⎞⎜\n⎝⎛\n∂∂=⎟\n⎠⎞⎜\n⎝⎛\n∂∂−⎟\n⎠⎞⎜\n⎝⎛\n∂∂\n+ − ra\nr rir r θψµψ ψµ .                                 (21)                    \n \nSo one becomes faced with a paradox physical situ ation that a wave proce ss in a lossless MS-wave \nwaveguide should be accompanied with the \"edge anomaly\" on a cylindrical  surface of a ferrite \nrod caused by the non-zero term \nℜ=⎟\n⎠⎞⎜\n⎝⎛\n∂∂\nraiθψµ . In order to cancel this \"edge anomaly\", the \nboundary excitation must be described by chiral stat es [21, 23]. These chiral  states represent an \nadditional degree of freedom resulting in elimin ation of the \"edge anomaly\". Referring to the \nboundary conditions used in variational methods, Eq. (20) corresponds to so called essential \nboundary conditions, while Eq. (21) corresponds to so called natural boundary conditions [57, 61]. \nThe oscillating modes have the en ergy orthogonality properties and (due  to the edge chiral states) \npseudoelectric gauge fields. A flat ferrite disk is  considered as a thin section of a ferrite MSW \nwaveguide with an eigen electric  moment. This electri c moment is describe d with the spinning \n(double-valued) coordinates [21, 23].      Now let us consider two parallel  identical cylindrical MSW waveguides, a and b. The ferrite \nrods are axially magnetized along z axis. When we analyze this structure as an entire  guiding \nsystem, equation   \n                                                               \n0  || || || || =⋅∇≡⋅∇∫\nΣdSj J\nSr r\n                                                  (22) \n \n(where ΣS is a cross section of a whole two-rod open system) will be satisfied if together with \ncontinuity of MS-potential wavefunction on late ral of ferrite rods one has the following boundary \nconditions for derivatives:   10                                                             0  =⎟\n⎠⎞⎜\n⎝⎛\n∂∂−⎟\n⎠⎞⎜\n⎝⎛\n∂∂\n+ − ℜ= ℜ=a ar r r rψ ψµ                                             (23)   \n \nand  \n                                                              \n0  =⎟\n⎠⎞⎜\n⎝⎛\n∂∂−⎟\n⎠⎞⎜\n⎝⎛\n∂∂\n+ − ℜ= ℜ=b br r r rψ ψµ .                                          (24) \n \nAt the same time, the conditions of continuity of a normal compone nt of the magnetic flux density \non a cylindrical surface of every ferrite rod are satisfied by two equations similar to Eq. (21). To \ncancel the \"edge anomaly\", the boundary excitation must be desc ribed by chiral states on \ncylindrical surfaces of each ferrite rods, a and b. \n    An entire structure of two horizontally coupled ferrite disks is considered as a thin section of a \ntwo-rod open system of ferrite MSW waveguides w ith two eigen electric moments. It can be \nsupposed that there should be two separate states: (a) eigen electric moment s of interacting ferrite \ndisks are parallel and (b) eigen electric mome nts of ferrite disks are anti parallel.  \n \nIV. COUPLED-MODE ANALYSIS FO R MDM FERRITE WAVEGUIDES  \n \nIn a coupled-mode theory, two parallel waveguides are not co nsidered as an entire  guiding system. \nThis theory is based on an an alysis of the individual-wave guide mode interactions and \ntransformations which appear because of the pres ence of another waveguide. When we put another \nwaveguide parallel and in close vicinity to th e first one, the coupling between adjacent guides \ninduces the transverse dynamics. The overlap inte grals are the main ingr edients in the modal \ndescription of the waveguide coupling. These overl ap integrals \"tell\" about  the compatibility of \ninteracting modes in both waveguides.     Let us start, however, with a s ituation when waveguides are placed at infinite  distance one from \nanother. For every propagating mode in separate waveguide l ( bal,\n= ) we have [26] \n \n                                                                          0 ˆ=llVL ,                                                              (25) \n \nwhere ()\n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n⋅∇−∇≡−\n0ˆ1l\nlLµt\nis the differential-matrix operator, µt is the permeability tensor, and \n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛≡ll\nlBV\nψr\n is the vector function included in the domain of definition of operator lLˆ. Outside of \nferrite regions one has the same equations but with Itt=µ , where It\n is the unit matrix. Eq. (25) can \nbe rewritten as \n \n                                                                   0~ )ˆ ˆ( = −⊥l l lVRi Lβ ,                                                   (26) \n \nwhere ()\n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n⋅∇−∇≡\n⊥⊥−\n⊥0ˆ1l\nlLµt\n, subscript ⊥ means differentiation over a waveguide cross section, lβ \nis the MS-wave propagation constant along z axis, ⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n≡\nll\nlBV\nψ~~~r\n is the membrane vector  11function )~( zil lleV Vβ−≡ , ⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n−≡00ˆ\nzz\neeRrr\n, zer is a unit vector along the axis of the wave \npropagation. \n    For finite  distances between two parallel waveguides,  the wave process of  every mode in a \nseparate waveguide becomes perturbed by anothe r waveguide. The coupling can be exhibited via \nperturbation of the power flow lJ||r\n of a separate waveguide l. Formally, in this case we can write \n \n                                                                              l llQ VL=ˆ ,                                                        (27) \n \nwhere lQ are the \"source vectors\" which will be defined below. In presence of \"sources\", Eq. (26) \nshould be rewritten as  \n \n                                                                    l lQVRzL =∂∂+⊥  )ˆ ˆ( .                                                   (28) \n \nTo solve the excitation problem we can use either complete orthonormal basis  of modes of the \nguide a, or complete orthonormal basis  of modes of the guide b. If the functional basis of \nwaveguide a is used, we have   \n \n                                                                  ∑∞\n===\n1~ )(\npa\np paVza VV ,                                                (29) \n \nwhere a\npV~ is a membrane function of mode p in a waveguide a. When we use the basis of \nwaveguide b, we can write  \n \n                                                                  ∑∞\n===\n1~ )(\nqb\nq qbVzb VV ,                                                 (30) \n \nwhere b\nqV~ is a membrane function of mode q in a waveguide b. Based on representation (29) and \ntaking into account Eq. (26), we can write Eq. (28) for waveguide a as \n \n                                                      ∑∞\n==⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n+\n1ˆ)(\n)(1\npa a a\npp\npQ VR idzz da\nzaβ ,                                      (31)               \n \nwhile for waveguide b we have \n                                            \n                                                       ∑∞\n==⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛\n+\n1ˆ)(\n)(1\npb b b\nqq\nqQ VR idzzdb\nzbβ .                                      (32) \n \nHere a\npβ and b\nqβ are propagation constants for modes p and q in unperturbed waveguides a and b, \nrespectively. \n    The excitation equation for mode p in waveguide a is  \n  12                                                  () dC VQNzaidzz da\nbCa\npa\na\nppa\npp∫⋅ = +*~ 1)()(β                                     (33) \n \nand the excitation equation for mode q in waveguide b is written as \n \n                                                  () dCVQNzbidzzdb\naCb\nqb\nb\nqqb\nqq∫⋅ = +*~ 1)()(β .                                    (34) \n \nHere ()() dS VVR Na\np\nSa\npa\np\na∗∫≡~ ~ˆ  and ()()dS VVR Nb\nq\nSb\nqb\nq\nb∗∫≡~ ~ˆ  are the norms of modes p and q in \nwaveguides a and b, respectively. \n    What are the \"source vectors\" lQ? The overlap of the evanescen t tails of the guided modes \ndetermines the transverse dynamics of the energy  exchange in a coupled-waveguide system. When \none puts one waveguide in the vicinity of anot her waveguide, there should be induced sources \nwhich make 0  || || || || ≠⋅∇≡⋅∇∫dSj J\nSl lr r\n in every separate waveguide . Since no bulk magnetic charges \nexist, there cannot be any induced  \"bulk sources\" for MS-potential  wave functions and their space \nderivatives. At the same time, we can see that fo r a separate MS-wave wave guide continuity of the \npower flow takes place when the boundary condition (2 0) is satisfied. So it becomes evident that \nthere are induced \"surface magnetic sources\" caused  by fractures of derivatives of MS-potential \nwave functions of modes ν of a waveguide  a on a surface of waveguide b:   \n \n                                                         () ()\nbCbaam\nsnborder  on  1~\n1∑∞\n=⎥⎦⎤\n⎢⎣⎡\n∂∂−=\nννψµ ρ .                                      (35) \n \nSimilarly, the induced \"surface magnetic sources\"  caused by fractures of derivatives of MS-\npotential wave functions of modes χ of waveguide  b on a surface of waveguide a are expressed as \n \n                                                          () ()\naCab\nbm\nsn\nborder  on  1~\n1∑∞\n= ⎥⎥\n⎦⎤\n⎢⎢\n⎣⎡\n∂∂−=\nχχψµ ρ .                                     (36) \n \nIn Eqs. (35) and (36), an and bn are external normals to border contours aC and bC, respectively. \nWe suppose that ferrite rods a and b are characterized by the same  material parameters. It is \nnecessary to note also that in an axially magn etized ferrite rod, MDMs propagate at negative \nquantity µ [26, 57]. \n    For coupled MDM waveguides the \"source vector\" lQ is expressed as \n \n                                                                         ()⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛≡ lm\nsli Qρ0 ,                                                     (37) \n \nAs a result, we rewrite Eq s. (33) and (34) as  \n                                                  13                                () () dCr Nizaidzz da\nbbCa\np\nCa\na\nppa\npp∫∑⎪⎭⎪⎬⎫\n⎪⎩⎪⎨⎧\n⎥⎦⎤\n⎢⎣⎡\n∂∂− = +∞\n=*\nborder  on  1~ ~\n11)()(ψψµ β\nνν              (38) \n \nand  \n                                \n() () dCr Nizbidzzdb\na aCb\nq\nCb\nb\nqqb\nqq∫∑⎪⎭⎪⎬⎫\n⎪⎩⎪⎨⎧\n⎥⎥\n⎦⎤\n⎢⎢\n⎣⎡\n∂∂− = +∞\n=*\nborder  on  1~ ~\n11)()(ψψµ β\nχχ.              (39) \n \n    In the theory of coupled waveguide stru ctures, one usually restri cts an analysis with \nconsideration of two mode s in separate waveguides. Followi ng this idea of a coupled-mode model \nwe express the total field V as a linear combination of two guided modes in waveguides a and b:   \n                                    \n                                                           b\nq qa\np p VzB VzAV~ )(~ )(+ ≈ .                                                   (40)     \n \nBased on this approximate representation, we  write the excitation equations for modes p and q as  \n \n                                            )( )( )()(zBiKzAiKzaidzz da\nqab\npq paa\npp pa\npp+ = +β ,                                   (41) \n \n                                            )( )( )()(zAiKzBiKzbidzzdb\nqba\nqp qbb\nqq qb\nqq+ = +β ,                                     (42) \n \nwhere   \n                                               \n() () dCr NKa\np\nCa\np\na\npaa\npp\nb*~ ~\n11ψψµ∫⎥⎥\n⎦⎤\n⎢⎢\n⎣⎡\n∂∂− = ,                                               (43) \n                                                                 \n                                               () () dCr NKa\np\nCb\nq\na\npab\npq\nb*~ ~\n11ψψµ∫⎥⎥\n⎦⎤\n⎢⎢\n⎣⎡\n∂∂− = ,                                               (44) \n \n                                               () () dCr NKb\nq\nCb\nq\nb\nqbb\nqq\na*~ ~\n11ψψµ∫⎥⎥\n⎦⎤\n⎢⎢\n⎣⎡\n∂∂− = ,                                               (45) \n                                                                                                    \n                                               () () dCr NKb\nq\nCa\np\nb\nqba\nqp\na*~ ~\n11ψψµ∫⎥⎥\n⎦⎤\n⎢⎢\n⎣⎡\n∂∂− = .                                               (46) \n \nOn the basis of representations (29), (30) and using the mode orthogonali ty relations [26], we \nobtain  \n                                                       \n)( )( )( zBCzAzaqab\npq p p += ,                                                      (47) \n  14                                                       )( )( )( zACzBzbpba\nqp q q += ,                                                       (48) \n \nwhere coefficients ab\npqC and ba\nqpC describe the mode overlap  \n \n                                                        ()()dS VVRNC\nSa\npb\nq a\npab\npq∫=*~~ˆ1,                                                 (49) \n \n                                                           ()()dSVVRNC\nSb\nqa\np b\nqba\nqp∫=*~~ˆ1,                                                 (50) \n \nAfter some manupulations we ha ve the coupled-mode equations \n \n                                                   )( )()(zBikzAidzz dA\nqab\npa p+ −=δ ,                                               (51) \n \n                                                   )( )()(zAikzBidzz dB\nqba\nqb q+ −=δ ,                                                (52) \n \nwhere \n \n                                      ()\nba\nqpab\npqa\npb\nqba\nqpab\npqba\nqpab\npqaa\npp a\npa\nCCCC KC K\n−− +−+=1βββδ ,                                         (53) \n \n                                      ()\nba\nqpab\npqb\nqa\npba\nqpab\npqab\npqba\nqpbb\nqq b\nqb\nCCCC KC K\n−− +−+=1βββδ ,                                          (54) \n \n                                      ()\nba\nqpab\npqbb\nqqab\npqa\npb\nqab\npqab\npq ab\nCCKC C Kk−−−+=1ββ,                                                       (55) \n \n                                      ()\nba\nqpab\npqaa\nppba\nqpb\nqa\npba\nqpba\nqp ba\nCCKC C Kk−−−+=1ββ.                                                       (56) \n \n    Assuming that solutions of Eq s. (51), (52) are proportional to )  exp( ziϑ− , where ϑ is a \npropagation constant of an enti re two-rod guiding system, one obt ains from the characteristic \nequation:  \n                                                \nba abb a b a\nkk−⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛−±+=2\n2 2δδδδϑ .                                           (57) \n \nThere are propagation constants for eige n modes in an entire guiding system. \n    For further coupled-mode anal ysis we will consider only the case when two separate ferrite rods \nhave identical parameters and identical modes,  that is, in Eqs. (51) – (57) we use: b\nqa\npββ= . For a  15given type of a mode in a separate rod, we  have two solutions fo r propagation constant ϑ in a \ncoupled-rod system. These solu tions correspond to symmetrical and anti-symmetrical field \ndistributions for membrane f unctions in ferrite rods.  \n    Based on our approach for a single MDM ferrite  disk [26, 57], we can analyze literally coupled \nMDM ferrite disks as a section of coupled MDM wave guides. In such a model (which is applicable \nfor ferrite disks with big diameter-to-thickne ss ratios), one obtains eigen wavenumbers of \noscillating modes as a result of jo int solutions of two equations: (a ) Eq. (57) for a two-rod guiding \nsystem and (b) a transcendental equation for a normally magnetized ferrite film \n \n                                                            µµϑ+−−=12) ( tan h ,                                                         (58) \n \nwhere h is thickness of a disk; µ is a negative quantity . Based on solutions of Eqs. (57), (58) and \ntaking into account Eq. (1), one  has the energy for symmetrical (S) and anti-symmetrical (A) MDM \nmodes in coupled ferrite disks:  \n                                                             \n()2),(),(\n),(\n16ASAS\nAS gE ϑπ= .                                                    (59) \n \nV. IDENTITY AND \"EXCHANGE\" IN TERACTION OF MDM FERRITE DISKS \n \nTwo laterally interacting ferrite samples are considered as identical  particles when a separate \nMDM disk cannot be clearly distinc tive as the \"left\" or \"right\" one. We will s how that the fact of \nidentity of two MDM ferrite disk s depends on a combined effect of symmetry properties of the \nsingle-valued membrane wave function, double-valued  edge wave function, and a direction of the \nRF magnetization precession.     Following our previous notations (see e.g. [ 57]) we represent a membrane function for a certain \nmode p as  \n \n                                                                     \npp pCϕψ~ ~= ,                                                               (60) \n \nwhere pC is a dimensional normalization coefficient and pϕ~ is a dimensionless membrane \nfunction.  At the same time, for a ferrite disk with r and θ in-plane coordinate s, the MS-potential \nmembrane function ϕ~ is represented as a product of two functions [21, 23]: \n \n                                                                  ± =δθηϕ  ),(~~r ,                                                             (61)                    \n \nwhere ),(~θηr is a single-valued membrane function, and ±δ is a double-valued edge (spin-\ncoordinate-like) function. The function ),(~θηr[which satisfies, in fact, the boundary condition \n(20)] defines the energy eigen states in a ferrit e disk, while the topological effects in the MDM \nferrite disk are manifested through the genera tion of relative phases which accumulate on the \nboundary wave functions θδ±−\n±±≡iqef . For better understanding the topological properties of \nMDM oscillations, we may intr oduce also a \"spin variable\" θ′, defining the orientation of the \n\"spin moment\" and two double-valued wave functions, )(θδ′+  and )(θδ′− , the former \ncorresponding to the eigen value 21l q+=+  and the latter to the eigen value 21l q−=− , where  16... ,5 ,3 ,1=l  The two wave functions are normalized and mutually orthogonal, so  that they satisfy \nthe equations 1  )(2=′′∫+θθδ d ,1  )(2=′′∫−θθδ d , and 0  )( )( =′′′− +∫θθδθδ d . A membrane wave \nfunction ϕ~ is then a function of three coordinates, two positional coordinates such as , ,θr and the \n\"spin coordinate\" θ′. For the positional wave function ) ,(~θηr, there could be two equiprobable  \nsolutions for the membrane wave functions: )( ),(~ ~θδθηϕ ′ =+ + r  and )( ),(~ ~θδθηϕ ′ =− − r . \n    For a ferrite disk of radius ℜ, circulation of gradient  θθ\nθδ e efqiiqr r\n±−±±\n±ℜ−=∇   along a disk \nborder contour ℜ=π2C  gives a nonzero quantity when ±q is a number divisible by 21. The \nquantity ±∇δθ is defined as the velocity of  an irrotational \"border\" flow: ()± ±∇≡δθ θrrv . In such a \nsense, functions ±δ are the velocity poten tials. Circulation of ()±θvr along a contour C is equal to \n()± ±′ ± ±−=′∇ℜ=∇ℜ=⋅ ∫∫∫f d d Cd\nC2    v\n02\n0π\nθπ\nθ θ θδ θδrr. Taking into account that the total MS-potential \nfunction ψ is represented as a product: ) ( ~zξψψ=  [57], where ) (zξ  is the function characterizing \nz-distribution of the MS potential in a ferrite disk , we define the \"spin moment\" of a whole ferrite \ndisk as  \n                                                     \n()∫∫∫± ± ± −=⋅ ≡h\nCh\nedzz f Cd dzz\n0 0)( 2  v )( ξ ξσθrr.                             (62)     \n \nIn a case of a cylindrical ferr ite disk, a single-valued membra ne function is represented as \n()( ) ( ) θφθη rR r=,~, where )(rR  is described by the Bessel functions and θνθφ ~)(ie−, \n....3,2,1±±±=ν  Taking into account th e \"orbital\" function )(θφ , we may consider the quantity \n()[]ℜ=±∇r  ~δηθ  as the total (\"orbital\" and \"spin\") velocity of  an irrotational \"border\" flow:                                   \n \n                      ()()[] ()θθν\nθ θ θ θνηδδηδη e ef Rqi Vq i\nr r rr r) ( ) ( ~ ~  ~ ±+−\n±ℜ=±\nℜ= ±± ℜ=± ±ℜ+−=∇+∇= ∇≡ .        (63) \n \nWe define the strength of the total (\"orbita l\" and \"spin\") vortex of a whole disk as  \n \n      () () ∫ ∫∫∫∫ℜ=± ± ℜ= ± ℜ=± −=⋅ ℜ=⋅ ≡h\nrh\nr\nCh\nredzz Rf de Vdzz R Cd Vdzz R s\n02\n0 0 0)( 2  )(  )( ξ θ ξ ξπ\nθθ θrr rr\n.              (64) \n \nThis circulation around a lateral border of a fe rrite disk is a non-zero quantity because of the \npresence of double-valued edge (s pin-coordinate-like) functions ±δ (it is evident that the \ncirculation is non-zero due to the term ±∇δηθr~, while the circulation of the term ηδθ~∇±r\n is equal to \nzero). It is important to note that the circulation integral of function ()±θVr\n and therefore a quantity \nof es± do not depend on the azimuth phase relation between functions )(~θη  and )(θδ± . \n    The quantity ()±θVr\n has a clear physical meaning. In the sp ectral problem for MDM ferrite disks, \nthe border term ()ℜ=−r aHiθµ  arises from the demand of conservation of the magnetic flux density.  17Circulation of this border term defines a moment ea±r which is expressed by Eq. (7). This moment \ncan be formally represented as a result of a circul ation of a quantity, which we call a density of an \neffective boundary magnetic current mir\n:  \n \n                                                             )( 4\n0∫∫⋅ =± ±h\nCm eCdidzz arr\nξπ ,                                                (65)                     \n \nwhere ()± ±≡θρV im mr r\n  and ℜ= ≡ra mR i  4ξπµρ . In our continuous-medium m odel, a character of the \nmagnetization motion becomes apparent via the gyration parameter aµ in the boundary term for \nthe spectral problem. There is the magnetizatio n motion through a non-simply-connected region. \nOn the edge region, the chiral symmetry of the ma gnetization precession is broken to form a flux-\nclosure structure. The edge magnetic  currents can be observable only  via its circulation integrals, \nnot pointwise. This results in the moment oriented along a disk normal. As it was shown \nexperimentally, such a moment ha s a response in an external RF electric field [24, 62]. The eigen \nelectric moments of a ferrite disk arises not from the classical curl electric fields of magnetostatic \noscillations. At the same time, a ny induced electric polarization e ffects in a ferrite material are \nbeyond the frames of the experimentally observed multiresonance spectra. An electric moment ea± \nis characterized by the anapole-moment properties.  This is a certain-type toroidal moment. Some \nimportant notes should be given here to characterize properties of moment ear. From classical \nconsideration it follows that for a given electric current eir\n, a magnetic dipole moment is described \nas  ∫×= dvircMe 21rrr\n, while the toroidal dipole moment is described as  ()∫××= dvirrcte 31 rrrr \n(see e.g. [63]). When we introduce the notion of an elementary magnet: e\nelem ir Mrrr\n×≡ , we can \nrepresent the toroid al dipole moment as a linear  integral around a loop: ∫×= dl Mrctelem 31rrr. It is \nconsidered as a ring of elementary magnets. In this formulation, it is clear that a toroidal moment is \nparity odd and time reversal odd. In a case when mr is time varying (due to precession), one has a \nmagnetic current θetMielem m r r\n  ~∂∂, where θer is a unit vector along a tangent of a loop. A linear \nintegral of this current around a loop defines a mo ment which is parity odd and time reversal even. \nFor oscillating MDMs one has the azimuth varyi ng border-loop magnetic current (see Fig. 3 in \nRef. [23]). The magnetic current mi is described by the double valued functions. This results in \nappearance of an anapole moment ear, which has the symmetry of an electric dipole – the parity-\nodd and time-reversal even properties.  \n    Let us choose the azimuth phase relation between functions ) (~θη  and )(θδ′±  so that a \nmaximum (minimum) of function )(~θη corresponds to zero of function )(θδ′± . Following this \nchoice of the azimuth phase  relation betw een functions )(~θη  and )(θδ′± in a disk, let us consider \nnow two separate identical-parameter ferrite di sks with the same direction of a normal bias \nmagnetic field (i.e. with the same dir ection of the RF magnetization precession mr). Let membrane \nwave functions η~ of these disks are mutually shifted in phase by o180  and the disks are \ncharacterized by different double-valued wave functions, +δ and −δ. Since a difference between \neigen values +q and −q of double-valued wave functions δ is an integer quantity, it is evident that \nsuch disks are absolutely identica l. There are, however, two cases of the disk identity. Fig. 1 (a)  18illustrates the first case of the disk identi ty. The types of membrane wave functions η~ of these \ndisks are conventionally represented as combinati ons of two different colour-texture spots on a \ndisk surface. The double-valued wave functions, +δ and −δ, are conventionally shown by arrows. \nThere are also shown or ientations of vectors eσr, esr, and ear. Below the pictures of ferrite disks \none sees the graphs of functions )(θδ′± , )(θδθ′∇±′r\n and ) (~θη . The second case of the disk identity \nis shown in Fig. 1 (b). This case has another correlation between signs of functions η~ and δ. \nFollowing the pictures of the η~- and δ-function distributions, it is wo rth noting that for two cases \nshown in Figs. 1 (a) and 1 (b) one has for iden tical disks coinciding di rections of vectors esr and \near, and opposite directions of vectors eσr.   \n    Now let us consider two la terally coupled disks. The disks ha ve identical parameters and are \nbiased by the same DC magnetic field. Follow ing the above coupled-mode theory, one has \nsymmetrical )(~Sη and anti-symmetrical )(~Aη  solutions for the positi onal wave function in the \ncoupled-disk system. The energy splitting is defined by the wavenumber deviation \nbetween )~()( )( S Sηχχ≡  and )~()( )( A Aηχχ≡  at a constant frequency [see Eq. (59)]. It becomes \nevident that in a case of a symmetrical )(~Sη solution, two neighboring disks have the azimuth-\ncoordinate MS-potential-distr ibution pictures shifted to π. No such a shift one has in a case of an \nantisymmetrical )(~Aη  solution. For a coupled structure, tw o disks should be identical when one \nsimultaneously exchanges positional coordinates a nd \"spin coordinates\".  Because of symmetry \nproperties of edge-function chiral rota tions, it means that a symmetrical )(~Sη solution will be \nassociated with anti-symmetr ical edge-function chiral rota tions, and conversely, an anti-\nsymmetrical )(~Aη  solution will be associated with symm etrical edge-function chiral rotations. \nThese cases are illustrated in Figs. 2 and 3, resp ectively. Taking into account the spin coordinates \none sees that in a case of Fig. 2 there are opposite directed \"spins moments\" eσrof two disks, while \nin a case of Fig. 3 the \"spins moments\" have the same directions. The above situation clearly \nresembles the Pauli principle for two electrons in the hydrogen molecule: the total (taking into account the positional and spin coordinates) wave f unction must be antisymmetric with respect to \nthe simultaneous interchange of the coordinates and of the spin variables of the electrons. For two \ndifferent states of the \"spin mo ment\" orientations there are two different \"exchange\" energies of \nthe \"molecule\": \n↑↑E and ↑↓E, where arrows show directions of vectors eσr. For the \"molecule\" \nwith the \"exchange\" energy ↑↑E a total \"spin moment\" is equal to an odd integer quantity, while \nfor the \"molecule\" with the energy ↑↓E the total \"spin order\" is zero or an even integer quantity. \nWith increasing distance between disk centers, th e overlap between the disk membrane functions \nfalls off exponentially resulting in rapid de crease the \"exchange\" energy. The \"exchange\" \ninteraction between MDM ferrite disks is not the same as the magnetostatic interaction between \nmagnetic dipoles.  \nVI. ON THE ELECTRIC INTERACTION BETWEEN LATERALLY COUPLED MDM \nFERRITE DISKS  \n \nThe \"exchange\" interaction between identical disks is connected with necessary correlation \nappearing because of the \"spin\" symmetrization of  the MDM wave functions. Because of existing \npseudo-electric fluxes in MDM ferr ite disks, an electric interac tion has to be ta ken also into \nconsideration. The MDM electric  interaction implies the ability  of the edge function in one \nlocation to produce phase accumula tion in the edge func tion in another loca tion. The physics of \nsuch an interaction is base d on the Aharonov-Bohm effect.   19 \n    In accordance with the spectral analysis in  Ref. [23] it follows that the flux of the pseudo-\nelectric field in a MDM ferrite disk arises from necessity to preserve the single-valued nature of \nthe membrane functions. For a separate particle, to compensate for sign ambiguities and thus to make wave functions single valued we added a v ector-potential-type term to the MS-potential \nHamiltonian. A circulation of vector \nmAθr\n should enclose a certain flux. The corresponding flux of \npseudo-electric field ∈r (the gauge field) through a circle of radius ℜ is obtained as: \n \n                                              () ()()± ± ± ±=Ξ=⋅∈=⋅∫∫q Sd Cd Ae\nS Cmπθ 2rrrr\n,                                    (66) \n \nwhere ()±Ξe is the flux of pseudo-electric field. Ther e should be the positive and negative fluxes. \nThese different-sign fluxes should be inequivale nt to avoid the cancellation [23, 64]. For non-\ninteracting (placed at infinite distance one  from another) identical ferrite disks, a and b, one has \npseudo-electric fluxes ()a\npeΞ  and ()b\npeΞ  for a given MDM p: \n                                             . \n                 () ()() q Sd Cd A d iba\nSe ba\nCba\npm\nrba ba ba\nba babaπ θ δδθπ\nθ 2 ]) )( [(,\n,,2\n0*, , ,\n, ,,=Ξ=⋅∈=⋅ = ∇ℜ ∫∫ ∫ℜ=rrrr r\n.           (67) \n \nHere and further we omit the signs ±. \n    Now let us take into account a possible el ectric interaction for two laterally coupled MDM \ndisks. In an assumption about the ability of th e edge function in one location to produce phase \naccumulation in the edge function in another location,  the electric interaction presumes an \nexistence of four pseudo-electric fluxes. We w ill designate a pseudo-electric flux penetrating the \nborder loop of disk a as ()aa\npeΞ  which is connected with a double-valued edge function aaδ via the \nBerry connections ()aa\npmAθr\n as \n \n                                        () ()aa\npe\nCaa\npm\nraa aa a\naa Cd A d i Ξ=⋅ = ∇ℜ∫∫ℜ=π\nθ θ θ δδ2\n0*]) )( [(rr r\n                            (68) \n \n \nand a pseudo-electric flux penetrating the border loop of disk b as ()bb\npeΞ  which is connected with \na double-valued edge function bbδ via the Berry connections ()bb\npmAθr\n as \n \n                                     () ()bb\npe\nCbb\npm\nrbb bb b\nbb Cd A d i Ξ=⋅ = ∇ℜ∫∫ℜ=π\nθ θ θ δδ2\n0*]) )( [(rr r\n.                              (69) \n \nAt the same time, we will designate a pseudo-elect ric flux connected with an edge function of a \nferrite disk b and penetrating the border loop of disk a as ()ab\npeΞ  and a pseudo-electric flux  20connected with an edge function of a ferrite disk a and penetrating the border loop of disk b as \n()ba\npeΞ : \n \n                                    () ()ab\npe\nCab\npm\nrab ab a\naa Cd A d i Ξ=⋅ = ∇ℜ∫∫ℜ=π\nθ θ θ δδ2\n0*]) )( [(rr r\n                                (70) \n \nand \n                                   () ()ba\npe\nCba\npm\nrba ba b\nbb Cd A d i Ξ=⋅ = ∇ℜ∫∫ℜ=π\nθ θ θ δδ2\n0*]) )( [(rr r\n.                                (71) \n \nSuch fluxes are connected with a double-valued edge functions abδ and baδ via the Berry \nconnections ()ab\npmAθr\n and ()ba\npmAθr\n, respectively. \n    The above theory of \"exchange\" interactio n is based on an assumption that an interaction \nbetween MDM ferrite disks is enough weak so th at a mode portrait of a membrane function in \nevery disk, ),(~θηra\np  and ),(~θηrb\np , does not change and is the same as in a separate particle. This \nconservation of mode portraits of membrane functions presumes the conservation of \"spin \nmoments\" ()aeσr and ()beσr of interacting disks. From this statement it follows that to preserve the \nsinglevaluedness of the membrane function of disks a and b we have \n \n                                                   ()()() qa\npeab\npeaa\npeπ2=Ξ=Ξ+Ξ                                                       (72) \n \nand  \n                                                   \n()()() qb\npeba\npebb\npeπ2=Ξ=Ξ+Ξ .                                                     (73) \n \nIt means that fluxes ()aa\npeΞ ,()ab\npeΞ , ()ba\npeΞ , and ()bb\npeΞ  are not characterized by discrete quantities. \nBecause the linearity and reciprocity of ME interaction, we can write  \n \n                                                           ()() qk kpb\npe\npab\npeπ2=Ξ=Ξ                                                   (74) \n \nand  \n                                                           \n()() qk kpa\npe\npba\npeπ2=Ξ=Ξ ,                                                  (75) \n \nwhere pk is the ME interaction coefficient for mode p. For mode p, coefficient k determines a \nfraction of a total pseudo-electric flux of disk a perceiving the border ring of disk b and, equally, a \nfraction of a total pseudo-electric flux of disk b perceiving the border ring of disk a. Evidently, \n1 0≤≤pk . From the above equations one has evident relations: \n \n                                                                  ()()bb\npeaa\npeΞ=Ξ                                                              (76)  21and \n \n                                                                  ()()ba\npeab\npeΞ=Ξ .                                                            (77) \n                                                                   \nIt is useful to note that Eqs. (72) and (73)  correspond to the follo wing integral relations: \n   \n     q d d d\na a a ra a\nrab ab\nraa aaπθ δδθ δδθ δδπ\nθπ\nθπ\nθ 2 ]))( [( ]) )( [( ]) )( [(2\n0*2\n0*2\n0*= ∇= ∇+ ∇ ∫ ∫ ∫ℜ= ℜ= ℜ=r r r\n              (78) \n \nand  \n     \nq d d d\nb b b rb b\nrba ba\nrbb bbπθ δδθ δδθ δδπ\nθπ\nθπ\nθ 2 ]))( [( ]) )( [( ]) )( [(2\n0*2\n0*2\n0*= ∇= ∇+ ∇ ∫ ∫ ∫ℜ= ℜ= ℜ=r r r\n.            (79) \n \n        The pseudo-electric-flux interaction resu lting in redistributions of the double-valued edge \nfunctions δ has no direct influence on the \"exchange \"-interaction mechanism of identical MDM \nferrite disks. Nevertheless, redist ributions of the edge functions δ will lead to redistributions of \nedge magnetic currents in ferrite disks. This can be considered as a certain mechanism of \ninteractions between anapole moments ear of the disks. When the flux of the pseudo-electric field \nin a MDM ferrite disk arises from necessity to pr eserve the single-valued nature of the membrane \nfunctions, the loop magnetic current arises from the demand of conservation of the magnetic flux \ndensity on a border surface of a disk . These effects of conservation, being mutually correlated, are \nimportant for an analysis of the MDM interac tions. Our method, where the MS-potential wave \nfunction of a ME \"molecule\" is created based on the MS-potential wave func tion of isolated MDM \nferrite disks, can be considered as the first- order interaction approach . Taking into account \ninteractions between anapole moments ear of the disks is considered as the second-order \ninteraction approximation.  This second-order a pproximation is beyond the frames of the present \npaper and should be a subject  for a future analysis. \n  \nVII. DISCUSSION AND CONCLUSION \n In this paper, we presented theo retical studies of spectral properti es of literally coupled of MDM \nME disks. We showed that there exists the \"exchange\" mechanism of interaction between the \nparticles, which is distinctive from the magne tostatic interaction between magnetic dipoles. \n    In a quasi-2D ferrite disk with a dominating role of magnetic-dipolar spectra, the oscillating \nspectrum is characterized by energy eigenstates.  Because of the strong influence which the \nboundary geometry has on the energy spectrum of the MDMs, the eigen MS-potential functions \nare characterized by the vortex states.  The vortices  are guaranteed by the chiral edge states which \nresult in appearance of eigen electric mo ments oriented normally to the disk plane. \n   The \"exchange\" interaction be tween coupled MDM ME particles does not represent, certainly, a \ndual case with respect to the r eal exchange interaction between coupled natural complex atoms. \nOne of the main distinctive factors concerns th e symmetry breaking effects of MDM oscillations. \nMDM ferrite disks have evident chiral states and th e near fields of such particles are characterized \nby very specific symmetry properties. Nevertheless,  a certain resemblance with interacting natural \natoms and interacting MDM ferrite disks can be found.      In the simple Heisenberg model each atom is  thought to have a single  electron which interacts \nwith its neighbor and the dominant interaction is c onsidered to arise from a superposition of this  22two-electron interaction. Similarly to the Heisenberg mathematical description of the exchange \ninteraction, we can formally introduce the opera tor characterizing \"excha nge\" interac tion between \nMDM ferrite disks:   \n                                                                \ne ee e\nexchange 2 1 \" \"ˆ σσrr⋅−ℑ=ℵ ,                                                  (80) \n \nwhere eℑ is a certain function of rr – the distance between disk centers – which is chosen so that \nthe eigenvalues of the operator e\nexchage \" \"ˆℵ  (in the space of the \"spin variables\") are equal to the \nenergies ↑↑E and ↑↓E. In Eq. (80), superscripts \" e\" means \"electric\" [21,  23]. The MDM ferrite \ndisks can be coupled to form \"artificial molecu les\" or an extended supe rlattice. Such periodic \narrays of coupled MDM dots – \"artificial crysta ls\" – are interesting both on a fundamental level \nand from a more application-oriented point of vi ew. When we assume that all the disks in an \n\"artificial crystal\" have 21=q , we can write for a lattice: \n \n                                                       ∑\n≠⋅ℑ−=ℵ\nmle\nme\nl lme e\nexchange rσσrrr)(21ˆ\n\" \" .                                           (81) \n \n    In Section VI of the paper, we pointed out  that interaction between  anapole moments of the \ndisks can be considered as the second approxima tion in the analysis. We may treat this anapole-\nanapole type of interaction similar to the cla ssical dipole-dipole interaction between electric \ndipoles [1]. Such an electric-dipole-like  interaction describe d by an operator   \n \n                                      ()()() [ ] ∑\n≠− ⋅⋅−⋅ ∝ ℵ\nmllme\nm lme\nl lme\nme\nl\nlme\nanapole anapole rara raarrrrr rr  3  1ˆ2\n5                           (82) \n \nshould be considered as a ch aracteristic additional to the \"exchange\" interaction. \n \nReferences \n [1] J.D. Jackson, \nClassical Electrodynamics , 2nd ed. (Wiley, New York, 1975). \n[2] E.O. Kamenetskii, arXiv:  cond-mat/0601467; Phys. Rev. E 58, 7965 (1998). \n[3] I.V. Lindell, A.H. Sihvila, S.A. Tretyakov, and A.J. Viitanen, Electromagnetic Waves in Chiral \nand Bi-Isotropic Media  (Artech House, Boston, 1994); M.M. Saadoun and N. Engheta, \nMicrow. Opt. Technol. Lett.  5, 184 (1992); R. Marques et al., Phys. Rev. B 65, 144440 (2002); \nJ. Baker-Jarvis and P. Kabos, Phys. Rev. E 64, 056127 (2003). \n[4] A.P. Cracknell, Magnetism in Crystalline Materials  (Oxford, Pergamon, 1975). \n[5] S. Shastry et al, Phys. Rev. B  70, 064416 (2004). \n[6] D. Fryberger, Foundation of Physics 19, 125 (1989).  \n[7] R. A. Hergstrom et al, Am. J. Phys. 56, 1086 (1988). \n[8] P. Carra, J. Phys. A: Math. Gen. 37, L183 (2004). \n[9] Ya. B. Zel’dovich, Zh. Eksp. Teor. Fiz. 33, 1531 (1957) [Sov. Phys. JETP 6, 1184 (1958)]. \n[10] W. C. Naxton, C.- P. Liu, and M. J. Rumsey-Musolf, Phys. Rev. C 65, 045502 (2002). \n[11] M. A. Bouchiat and C.  Bouchiat, Eur. Phys. J. D 15, 5 (2001). \n[12] R. R. Lewis, Phys. Rev. A 49, 3376 (1994). \n[13] M. Stone, Phys. Rev. D 33, 1191 (1986). \n[14] Q. Niu and L. Klei nman, Phys. Rev. Lett. 80, 2205 (1998).  23[15] R. Gebauer and S. Baroni, Phys. Rev. B 61, R6459 (2000).  \n[16] F. Schütz, M. Kollar, and P. Kopietz, Phys. Rev. Lett.  91, 017205 (2003). \n[17] F. Meier and D. Loss, Phys. Rev. Lett. 90, 167204 (2003). \n[18] J.E. Hirsch, Phys. Rev. B 60, 14787 (1999). \n[19] P. Bruno and V.K. Dugaev, Phys. Rev. B 72, 241302(R) (2005). \n[20] E.O. Kamenetskii, Europhys. Lett. 65, 269 (2004). \n[21] E.O. Kamenetskii, Phys. Rev. E 73, 016602 (2006). \n[22] E.O. Kamenetskii, J. Magn. Magn. Mater. 302, 137 (2006). \n[23] E.O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007).  \n[24] E.O. Kamenetskii, A.K. Sa ha, and I. Awai, Phys. Lett. A 332, 303 (2004). \n[25] A.K. Saha, E.O. Kamenetskii, and I. Awai, J. Phys. D: Appl. Phys. 35, 2484 (2002). \n[26] E.O. Kamenetskii, Phys. Rev. E 63, 066612 (2001). \n[27] P. Politi and M.G. Pini, Phys. Rev. B 66, 214414 (2002). \n[28] M. Grimsditch et al, Phys. Rev. B 70, 054409 (2004); L. Giovannini, F. Montencello, and F. \nNizzoli, Phys. Rev. B 75, 024416 (2007). \n[29] K. Rivkin et al, Phys. Rev. B 70, 184410 (2004); K. Rivkin et al, Phys. Rev. B 75, 174408 \n(2007). \n[30] A. Hubert and R. Schäfer, Magnetic Domains  (Springer, Berlin, 1998).   \n[31] T. Shinjo et al, Science 289, 930 (2000). \n[32] K.Yu. Guslienko et al, Phys. Rev. B 65, 024414 (2001). \n[33] K.Yu. Guslienko et al, J. Appl. Phys 91, 8037 (2002). \n[34] N.A. Usov and L.G. Kurkina. J. Magn. Magn. Mater. 242-245 , 1005 (2002). \n[35] J. Shibata, K. Shigeto, and Y. Otani, Phys. Rev. B 67, 224404 (2003). \n[36] J. Shibata and Y. Otani, Phys. Rev. B 70, 012404 (2004). \n[37] T. Kimura et al, Appl. Phys. Lett. 90, 132501 (2007). \n[38] A.Yu. Galkin, B.A. Ivanov, and C.E. Zaspel, Phys. Rev. B 74, 144419 (2006). \n[39] H. Kogelnik, in Applied Physics Integrated Optics , T. Tamir, Ed. (Springer-Verlag, New \nYork, 1975). \n[40] A. Yariv, IEEE J. Quantum Electron. QE-9 , 919 (1973). \n[41] A.W. Snyder, J. Opt. Soc. Am.  62, 1267 (1972); A.W. Snyder and J.D. Love, Optical \nWaveguide Theory  (Chapman and Hall, London, 1983).  \n[42] A. Hardy and W. Stre ifer, J. Lightwave Technol. LT-3 , 1135 (1985). \n[43] H.A. Haus et al, J. Lightwave Technol. LT-5 , 16 (1987). \n[44] C. Vassallo, J. Lightwave Technol 6, 294 (1988). \n[45] E.O. Kamenetskii, IEEE Tr ans. Microw. Theory Techniq. 44, 572 (1996). \n[46] H.A. Hauss, Waves and Fields in Optoelectronics (Prentice-Hall, N.J., 1984). \n[47] A.B. Matsko and V.S. Ilchenko, I EEE J. Select. Topics Quant. Electron. 12, 3 (2006).  \n[48] M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965). \n[49] H. Miazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000). \n[50] D.R. Rowland and J.D. Love, IEE Proc.-J 140, 177 (1993). \n[51] M. I. Povinelli et al, Optics Express 13, 8286 (2005); T.J. Kippenberg, S.M. Spillane, and K.J. \nVahala, Opt. Lett. 27, 1669 (2002); A. Yariv et al, Opt. Lett. 24, 711 (1999). \n[52] G. Burkard, D. Loss, and D.P. DiVincenzo, Phys. Rev. B 59, 2070 (1999). \n[53] X. Hue and S. Das Sarma, Phys. Rev. A 61, 062301 (2000). \n[54] A. Mizel and D.A. Lidar, Phys. Rev. B 70, 115310 (2004).  \n[55] G. Burkard, G. Seelig, and D. Loss, Phys. Rev. B 62, 2581 (2000); M. Korkusinski and P. \nHawrylak, Phys. Rev. B 63, 195311 (2000). \n[56] R. Q. Yang and J.  M. Xu, Phys. Rev. B 43, 1699 (1991); P. Zhao, Phys. Rev. B 45, 4301 \n(1992). \n[57] E.O. Kamenetskii, M. Sigalov, a nd R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005).   24[58] M.E. Tobar and A.G. Mann, IEEE Trans. Microw. Theory Techniq. 39, 2077 (1991).  \n[59] L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Non- Relativistic Theory , 3rd ed. \n(Pergamon, Oxford, 1977). \n[60] A.S. Davydov, Quantum Mechanics , 2nd ed. (Pergamon, Oxford, 1976). \n[61] S. G. Mikhlin, Variational Metods in Mathematical Physics  (Mc Millan, New York, 1964). \n[62] M. Sigalov. E.O. Kamenetskii, and R. Shavit, arXiv: 0708.2678.  [63] A. Ceulemans, L.F. Chibotaru,  and P.W. Fowler, Phys. Rev. Lett. \n80, 1861 (1998). \n[64] The Berry phase expr essed in Ref. [23] as ()∫⋅\nCmCd Arr\nθ , gives the dimensionless flux of the \npseudo-electric field. The Berry connection mAθr\n is not gauge invariant, but its circulation is \ngauge invariant. Our analysis of  MDMs in quasi-2D ferrite di sks is based on the MS scalar \nand vector potentials but not on th e notions of forces and fields. \n                                                \nFigure captions \n Fig. 1. Two cases, (a) and (b), of identical MD M ferrite disks with diffe rent distributions of \nmembrane functions \nη~ and edge functions δ. \n \nFig. 2. Two cases of coupled MDM ferrite disks with )(~Sη solutions. \n \nFig. 3. Four cases of coupled MDM ferrite disks with )(~Aη  solutions. \n \n                         25 \n   \n                      \n \n        \n  \nFig.1. Two cases, (a) and (b), of  identical MDM ferrite disks w ith different distributions of \nmembrane functions \nη~ and edge functions δ. \n \n          esrear eσr\n)(a+δ\nη~−δ\nη~−\nearesr eσr\n +δ\nη~−−δ\nη~\n)(besreareσresreareσr 26 \n              \n               Fig. 2. Two cases of coupled MDM ferrite disks with \n)(~Sη solutions. \n \n   \n       \n \n                \n           Fig. 3. Four cases of coupled MDM ferrite disks with \n)(~Aη  solutions. \n )(a+δesrear eσr\n+δesrear eσr\n)(b+δesreareσr\n+δesreareσr)(a )(b+δesrear eσr\n−δearesr eσresrear\n+δ−δeσr esreareσr\n)(cesreareσr\n−δ−δesreareσr\n)(desreareσr\n−δ−δesreareσr"    },    {        "title": "1904.02360v1.A_highly_accurate_determination_of_absorbed_power_during_nanomagnetic_hyperthermia.pdf",        "content": "arXiv:1904.02360v1  [physics.app-ph]  4 Apr 2019A highly accurate determination of absorbed power during na nomagnetic hyperthermia\nI. Gresits,1, 2Gy. Thur´ oczy,1O. S´ agi,2I. Homolya,2G. Bagam´ ery,3\nD. Gaj´ ari,3M. Babos,3P. Major,3B. G. M´ arkus,2and F. Simon2\n1Department of Non-Ionizing Radiation, National Public Hea lth Institute, Budapest\n2Department of Physics, Budapest University of Technology a nd Economics and MTA-BME\nLend¨ ulet Spintronics Research Group (PROSPIN), Po. Box 91 , H-1521 Budapest, Hungary\n3Mediso Medical Imaging Systems Ltd., Budapest, Hungary\nAbsorbed power of nanoparticles during magnetic hyperther mia can be well determined from changes in the\nquality factor ( Qfactor) of a resonator, in which the radiofrequency (RF) abs orbent is placed. We present an\norder of magnitude improvement in the Qfactor measurement accuracy over conventional methods by s tudying\nthe switch-on and off transient signals of the resonators. A nuclear magnetic resonance (NMR) console is ideally\nsuited to acquire the transient signals and it also allows to employ the so-called pulse phase-cycling to remove\ntransient artifacts. The improved determination of the abs orbed power is demonstrated on various resonators in\nthe 1-30 MHz range including standard solenoids and also a bi rdcage resonator. This leads to the possibility\nto detect minute amounts of ferrite nanoparticles which are embedded in the body and also the amount of the\nabsorbed power. We demonstrate this capability on a phantom study, where the exact location of an embedded\nferrite is clearly detected.\nPACS numbers:\nIntroduction\nNanomagnetic hyperthermia, NMH,1–7emerged as a poten-\ntial tool for tumor treatment in cancer therapy. It involves a\ntargeted delivery of ferrite nanoparticles to the affected tis-\nsues and its heating with an external RF magnetic field which\nwarms selectively and efficiently the embedding tissue only .\nThe success of NMH relies heavily on several key medical\nfactors3–5,8such as the affinity of the tumor tissue to overtem-\nperature and how specifically the ferrite is delivered to the de-\nsired location. On the physics side, the method depends on th e\naccurate control and knowledge of the power which is dissi-\npated by the ferrite. To obtain this information, most metho ds\ninvolve modeling of the exciting RF magnetic field and this\ninformation is combined with the knowledge of the magnetic\nproperties of the delivered ferrite9–13or the delivered heat is\ndetermined from calorimetry9,11,14–16, which however is an in-\nvasive and inaccurate method.\nWe recently reported17a method to obtain directly the\npower dissipated in the ferrite without any prior knowledge\nabout the RF magnetic field strength or the ferrite propertie s.\nThe method is based on the measurement of the quality factor,\nQ, of an RF resonator with and without the ferrite sample. The\naccuracy of the method for the dissipated power relies on the\naccurate determination of Q. A highly sensitive measurement\ncould lead to e.g. the localization of minute amounts of ferr ite\nand to study its diffusion under in vivo conditions, a better as-\nsessment of specific absorbed power in the NMH materials or\nto study non-linear absorption effects in the ferrites.\nConventional measurement of a resonator Qfactor is per-\nformed by sweeping the excitation frequency and studying\nthe reflected signal18–20. Albeit readily implemented, the fre-\nquency swept method is known to have a low accuracy for\nQand it is limited in measurement time to a few 100 ms\nthus this method does not enable the study of dynamic ab-\nsorption effects (Refs. 18,19,21). Rather than measuring\nin the frequency domain, resonator parameters can be deter-\nmined in time-domain measurements22–25; then the resonator\nis excited with a pulsed carrier signal, whose frequency isclose to the resonator eigen-frequency, f0. Importantly, dur-\ning both the switch-on and off, the resonator oscillates at i ts\neigen-frequency, f0, and the transient decay envelope has a\ntime constant of τ=Q/2πf0. The transient signal can be\nFourier transformed following a superheterodyne detectio n,\nwhich yields directly the resonance profile. This scheme is\nwidely used in the study of high- Qoptical resonators26–29\nand it was also implemented to measure the properties of mi-\ncrowave resonators30,31.\nIn general, the time-domain measurements (like Fourier-\ntransform NMR32and FT-IR spectroscopy) have two ad-\nvantages: improved accuracy (or Connes advantage33) since\nthe measurement is traced back to a stable clock-frequency\nand simultaneous measurement (the Fellgett or multiplex\nadvantage34) of the resonance curve is attained. In fact, the\nresonator transient (also known as resonator ring-down) is\nusually an unwanted side effect and a well-known hindrance\nin low-frequency NMR35. It results in a ”dead-time” in pulsed\nmagnetic resonance and various schemes have been devised\nto reduce it35,36. However, the very same instrumentation of a\nstandard pulsed NMR instrument, known as an NMR console,\nallows a direct measurement of the resonator transients.\nThe present study is motivated by the quest for improved Q\ndetermination accuracy with the goal to improve the absorbe d\npower measurement during hyperthermia. We present that\nstudying transients for RF resonators with f0= 1−30MHz\n(including simple solenoid and MRI birdcage coils) does re-\nsult in an order of magnitude more accurate Qdetermination\nthan the conventional frequency swept methods. We show\nthat a commercial NMR console is readily adapted for this\nstudy without any modifications. Its use even allows to em-\nploy the so-called phase-cycled pulse schemes, which leads\nto the elimination of some transient artifacts. We demonstr ate\nthe low level of noise in actual measurements and also the per -\nformance of the method on a phantom study, which allows to\nlocate a small amount of ferrite.2\nThe instrument setup and its performance\n/s45 /s49/s48/s49\n/s32 \n/s84/s105/s109 /s101 /s32/s40 /s109 /s115/s41/s111 /s110/s45/s114/s101 /s115/s111 /s110/s97/s110/s99/s101 \n/s101 /s120 /s99/s105/s116/s97/s116/s105/s111 /s110\n/s70/s84\n/s48 /s49/s48/s48 /s50/s48/s48/s45 /s49/s48/s49/s82/s101/s115/s111/s110/s97/s116/s111/s114/s32/s116/s114/s97/s110/s115/s105/s101/s110/s116/s32/s40/s97/s114/s98/s46/s117/s46/s41/s111 /s102/s102/s45/s114/s101 /s115/s111 /s110/s97/s110/s99/s101 \n/s101 /s120 /s99/s105/s116/s97/s116/s105/s111 /s110/s32 /s82/s101/s115/s111/s110/s97/s116/s111/s114/s32/s116/s114/s97/s110/s115/s105/s101/s110/s116/s32/s40/s97/s114/s98/s46/s117/s46/s41/s32 /s69/s120 /s99/s105/s116/s105/s110/s103/s32/s80/s117/s108/s115/s101/s32/s69/s110/s118/s101/s108/s111/s112/s101\n/s70/s84/s32/s80/s111/s119/s101/s114/s32/s115/s112/s101/s99/s116/s114/s117/s109/s32/s40/s97/s114/s98/s46/s117/s46/s41\n/s45 /s48/s46/s50 /s48/s46/s48 /s48/s46/s50\n/s32 \n/s73 /s110/s116/s101 /s114/s109 /s101 /s100/s105/s97/s116/s101 /s32/s70/s114/s101 /s113/s117/s101 /s110/s99/s121 /s32/s40/s77 /s72/s122/s41\nFIG. 1: The setup used to determine the resonator Qandf0from the\nswitch on/off transients (upper panel). The NMR console out puts the\nexciting pulse sequences and also detects them. A hybrid jun ction\nacts as duplexer to separate the excitation and the signal re flected\nfrom the resonator which is referenced with respect to 50 Ω. The\ntransient scheme is also shown: for both switch on and off, a t ransient\nsignal is observed (lower panel, left). It is a single expone ntial when\nf=f0but it oscillates when f/negationslash=f0. the corresponding Fourier\ntransform signals are also shown as a function of the interme diate\nfrequency f−f0(lower panel right).\nFig. 1. shows the block diagram of the instrument used\nto measure the resonator quality factor in the time domain.\nA commercial NMR console (obtained from Mediso Medical\nImaging Systems Ltd.) creates the pulses which excite the re s-\nonator and it also detects the reflection from the resonator i n\nthe time domain. A hybrid tee junction (M/A-COM HH-108\nfor 0.2-35 MHz and M/A-COM HH-107 for 2-200 MHz) sep-\narates the exciting and reflected waves from the RF resonator .\nThe NMR console has a digitizing bandwidth of 4 MHz, thus\nit can acquire transients up to this bandwidth. A convention al\nreflectometry setup, which involves a swept frequency sourc e\nand a power detector, which rectifies the RF signal, was used\nfor comparison. Fig. 1. lower panel also depicts the transie nt\ndetection scheme: the resonator is excited with a pulsed car -\nrier signal whose frequency, f, is close to the resonator eigen-\nfrequency, f0. Typical pulses are 100µs long for the irradi-\nation (to achieve steady-state RF excitation in the resonat or),\nfollowed by another 100µs long acquisition, when the switch-\noff transient is detected. These pulse sequences are repeat edafter a delay of a few ms.\nFor both switch on and off, the resonators reflects a transien t\nsignal which differ only in their phase25,30and has a frequency\nf0and decay with τ. Note that the NMR console detects in (or\nRe) and out-of-phase (or Im) signal (also known as quadrature\ndetection) but only one component is shown in the figure to\nretain clarity. The meaningful spectral data is obtained fr om\nthe power spectrum of the FT data, i.e. Re2+ Im2and is\nshown in the figure.\nIn the superheterodyne detection scheme of the NMR con-\nsole, the time-dependent signal is downconverted with f, it\nthus appears as an exponential function when f≈f0or an\noscillating function when f/negationslash=f0. When Fourier transformed,\nboth the switch on and off transients yield a Lorentzian func -\ntion with respect to the intermediate frequency (IF), f−f0.\n/s55/s46/s53 /s55/s46/s54 /s55/s46/s55 /s55/s46/s56 /s55/s46/s57 /s56/s46/s48/s32\n/s32/s32/s112/s111/s119/s101/s114/s32/s100/s101/s116/s101/s99/s116/s111/s114/s82/s101/s115/s111/s110/s97/s116/s111/s114/s32/s114/s101/s115/s112/s111/s110/s115/s101/s32/s40/s97/s114/s98/s46/s32/s117/s46/s41\n/s70/s114/s101/s113/s117/s101/s110/s99/s121/s32/s40/s77/s72/s122/s41/s32/s70/s70/s84/s32/s112/s111/s119/s101/s114/s32/s111/s102/s32/s116/s114/s97/s110/s115/s105/s101/s110/s116\nFIG. 2: Comparison of the Q-factor measurement using the con-\nventional frequency swept power detector detection and the Fourier\ntransformed transient signal. Note the larger noise for the power de-\ntector measurement, this includes the digitalization nois e of the os-\ncilloscope.\nIn Fig. 2., we show the time-dependent resonator transients\nas detected with the NMR console. The detection was per-\nformed in quadrature which allows a Fourier transformation\nof the signal, which yields directly the resonator curve aro und\nthe intermediate frequency, IF. This is also shown on the low er\npanel in Fig. 2. The LO frequency is added to obtain the res-\nonance curve on an absolute frequency scale. We performed\nmeasurements with a conventional, frequency swept method,\nin order to validate the present measurements. The two curve s\nmatch well as demonstrated in Fig. 2. This means that the\ntransient detection methods also yield the same kind of data\nsuch as the conventional measurement technique.\nThe use of the NMR console allows to implement the so-\ncalled phase cycling experiments, which is customary in NMR\nto get rid of the instrumental artifacts. Such artifacts inc lude\na DC offset of the digitizer or an imbalanced amplification in3\n/s98 /s41/s32 /s69/s120/s112/s101/s114/s105/s109/s101/s110/s116/s115/s68/s105/s102/s102/s101/s114/s101/s110/s99/s101/s83/s117/s109/s97 /s41/s32 /s83/s99/s104/s101/s109/s101\n/s48 /s50 /s52\n/s84/s105/s109/s101/s32/s40/s97/s114/s98/s46/s32/s117/s46/s41/s80/s117/s108/s115/s101/s32/s50/s44/s32 /s61/s84/s114/s97/s110/s115/s105/s101/s110/s116/s69/s120/s99/s105/s116/s97/s116/s105/s111/s110\n/s80/s117/s108/s115/s101/s32/s49/s44/s32 /s61/s48\n/s48 /s50 /s52/s39/s80/s97/s114/s97/s115/s105/s116/s101/s39\n/s116/s114/s97/s110/s115/s105/s101/s110/s116\n/s48 /s50 /s52/s39/s84/s114/s117/s101/s39\n/s116/s114/s97/s110/s115/s105/s101/s110/s116/s65/s118/s101/s114/s97/s103/s101/s100\n/s87/s105/s116/s104 /s32/s112/s104/s97/s115/s101/s32/s99/s121/s99/s108/s105/s110/s103/s32/s40/s50/s120/s41\n/s87/s105/s116/s104/s111/s117/s116 /s32/s112/s104/s97/s115/s101/s32/s99/s121/s99/s108/s105/s110/s103\n/s84/s105/s109/s101/s32/s40 /s115/s41\n/s32\n/s45/s50 /s45/s49 /s48 /s49 /s50/s82 /s101/s115/s111/s110/s97/s116/s111/s114/s32/s116/s114/s97/s110/s115/s105/s101/s110/s116/s32/s40/s97/s114/s98/s46/s117/s46/s41/s70/s84\n/s70/s84/s32/s80/s111/s119 /s101/s114/s32/s115/s112/s101/s99/s116/s114/s117/s109 /s32/s40/s97/s114/s98/s46/s117/s46/s41\n/s73/s110/s116/s101/s114/s109/s101/s100/s105/s97/s116/s101/s32/s70/s114/s101/s113/s117/s101/s110/s99/s121/s32/s40/s77/s72/s122/s41/s48 /s53 /s49/s48 /s49/s53 /s50/s48\nFIG. 3: a) The schematics of the phase cycling method as appli ed\nin the present measurement. Two consecutive excitations wi th op-\nposite phase are applied to the resonator, and the resulting transient\ncurves are subtracted to eliminate the unwanted parasitic t ransient\neffects (these are also known as ringing in the NMR literature). b)\nTransients detected with andwithout the phase cycling method. The\nearlier signal is magnified by a factor 2. The corresponding F ourier\ntransformed signals are also shown. Note the effect of the pa rasitic\ntransients on the resulting resonator signal.\nthe two quadrature channels. As an example, the DC offset\nis tackled by exciting the NMR nuclei with pulses in the op-\nposite RF phase and subtracting the signals after digitizat ion.\nImbalances in the quadrature detection are tackled by excit -\ning the nuclei by cycling the RF phase by 90 degrees in con-\nsecutive excitation phases and cycling the phase of the digi tal\ndownconversion by the same value. This scheme leads to the\ngeneric name, phase cycling, of the method.\nIn our case, the dominant artifact is a peak followed by some\nparasitic ”ringing” which appears when the pules are either\nswitched on or off. This can be tackled by alternating the\nRF phase of the exciting pulse by 180 degrees: the parasitic\nsignal is not sensitive to the RF phase, whereas the resonato r\ntransient is also rotated by 180 degrees as it is shown in Fig.\n3a. When the resulting transients are subtracted according ly\nonly the desired transient is observed and the parasitic sig -\nnal is eliminated. The effect of this phase cycling scheme\nis demonstrated in Fig. 3b.: the measured transient signal\nis free from any parasitic signal and its Fourier transform i n\na regular Lorentzian curve. In contrast, the unwanted signa l\nappears without phase cycling and the corresponding Fourie rtransformed signal is also distorted.\nIt was established earlier30,31that the appropriate errors of\nthef0andQdetermination accuracies are the following quan-\ntities:\nδ(Q) :=σ(Q)\nQ;δ(f0) :=σ(f0)\n∆f, (1)\nwhereQand∆fare the mean values of Qand the resonator\nbandwidth ∆f, respectively. Q=f0/∆f, wheref0is the\nresonator frequency30. We note that the error of f0is not\nσ(f0)/f0as it would be intuitive at first sight. This quantity\nwould overestimate the accuracy for an ultra-high frequenc y\nresonator with a moderate Qfactor.\nWhen comparing different measurement methods, a nor-\nmalization with the measurement time is also important and\nwe present data which is normalized to 1 second, thus the\ndata is given in units of 1/√\nHz. We found that the con-\nventional frequency swept method results in about δ(Q)≈\nδ(f0)≈2·10−3·1/√\nHz. In contrast, under the most op-\ntimal settings, the transient detection method results in a bout\n20 times smaller Qandf0determination errors, as small as\nδ(Q)≈δ(f0)≈10−4·1/√\nHz. The details of the most op-\ntimal transient acquisition settings, as well as a discussi on of\nthe error sources in terms of stochastic and drift-like erro rs, is\npresented in the Supplementary Materials.\nApplication to detect a minute amount of buried ferrite\nThe ultra-high sensitivity of the present method opens the\nway for a number of applications in ferrite based hyperther-\nmia of which we envisage a few. First, it allows to detect\nminute amounts of ferrite and the small amount of absorbed\npower in a realistic in vivo animal model study. We previously\ncalculated17that the smallest amount of detectable magnetite\nis 6 mg which is too much for hyperthermia therapy even in\nsmall laboratory animal models. However, as the sensitivit y of\nour method is about 20 times better than our previous one, thu s\nthe lowest detectable ferrite amount is about 0.3-0.5 mg whi ch\nis typically employed in mice animal model studies15,37,38.\nThe high sensitivity of the present method makes it suitable\nto detect non-linear (e.g.: saturation) effects or the chan ge of\nthe absorbed power due to the change of sample parameters\ne.g. the sample temperature. We demonstrate its utility to\ndetect the position of a small amount of ferrite whose locati on\nis otherwise unknown. Locating the ferrite in hyperthermia\nis of great importance in medical applications; it could ass ess\nthe success of drug delivery targeting and it could also allo w\nto better focus the heating RF irradiation.\nWe show in Fig. 4., the variation of Qandf0when a small\namount of magnetite (about 4 mm long, containing 1 mg of\nmagnetite) is moved across the solenoid (with 14 mm length)\nof an RF circuit. We used 2 manual linear translation stages\n(Thorlabs GmbH) to achieve a lateral movement of 50 mm.\nClearly, both circuit parameters are affected by the presen ce\nof the ferrite. Therefore locating an otherwise invisible f er-\nrite with a good accuracy is made possible with the present\ntechnique.4\n/s52/s46/s53/s50/s50/s53/s52/s46/s53/s50/s51/s48/s52/s46/s53/s50/s51/s53/s52/s46/s53/s50/s52/s48\n/s32/s32\n/s83/s97/s109/s112/s108/s101/s32/s108/s101/s110/s103/s116/s104/s102\n/s48/s32/s40/s77/s72/s122/s41/s67/s111/s105/s108/s32/s108/s101/s110/s103/s116/s104\n/s48 /s50/s48 /s52/s48/s51/s54/s46/s52/s51/s54/s46/s53/s51/s54/s46/s54\n/s32/s81\n/s76 /s97/s116/s101/s114/s97/s108/s32/s112/s111/s115/s105/s116/s105/s111/s110/s32/s40/s109 /s109 /s41\nFIG. 4: Variation of f0andQwhen a small ferrite sample (containing\nabout 1 mg of magnetite in solution) is moved across a solenoi d. Each\ndata point was recorded for 1 second. Arrows indicate the len gth of\nthe solenoid and that of the sample. Note that both f0andQdiffer\nslightly on the two sides of the lateral movement due to an asy mmetry\nin the sample holder.Summary\nIn summary, we presented a highly sensitive method to de-\ntermine the power absorbed in nanomagnetic particles durin g\nradio-frequency irradiation. The method is based on moni-\ntoring the transient response of an impedance matched radio -\nfrequency resonant circuit using a conventional nuclear ma g-\nnetic resonance console. The latter technique allows the us e\nof the so-called smart phase cycling schemes, which allows\nthe artefact-free detection of the short transients. The me thod\nyields an unprecedented accuracy of the resonator quality\nfactor and resonance frequency which reduces the amount\nof detectable ferrite during nanomagnetic hyperthermia. W e\ndemonstrate the utility of the method by sensitively detect ing\nthe location of a small amount of ferrite in a test tube.\nAcknowledgements\nSupport by the National Research, Development and In-\nnovation Office of Hungary (NKFIH) Grant Nrs. K119442,\n2017-1.2.1-NKP-2017-00001, and VKSZ-14-1-2015-0151\nand by the BME Nanonotechnology FIKP grant of EMMI\n(BME FIKP-NAT), are acknowledged.\n1Q. Pankhurst, J. Connolly, S. Jones, and J. Dobson, Journal o f\nPhysics D-Applied Physics 36, R167 (2003).\n2M. Kallumadil, M. Tada, T. Nakagawa, M. Abe, P. Southern, and\nQ. A. Pankhurst, Journal of Magnetism and Magnetic Material s\n321, 1509 (2009).\n3C. S. Kumar and F. Mohammad, Advanced Drug Delivery Re-\nviews 63, 789 (2011).\n4M. Angelakeris, Biochimica et Biophysica Acta (BBA) - Gener al\nSubjects 1861 , 1642 (2017).\n5A. J. Giustini, A. A. Petryk, S. M. Cassim, J. A. Tate, I. Baker , and\nP. J. Hoopes, Nano Life 01, 17 (2010).\n6K. M. Krishnan, IEEE Transactions on Magnetics 46, 2523\n(2010).\n7J. Beik, Z. Abed, F. S. Ghoreishi, S. Hosseini-Nami, S. Mehrz adi,\nA. Shakeri-Zadeh, and S. K. Kamrava, Journal of Controlled R e-\nlease 235, 205 (2016).\n8E. A. Perigo, G. Hemery, O. Sandre, D. Ortega, E. Garaio,\nF. Plazaola, and F. J. Teran, Applied Physics Reviews 2(2015).\n9E. Garaio, J. Collantes, J. Garcia, F. Plazaola, S. Mornet, F . Couil-\nlaud, and O. Sandre, Journal of Magnetism and Magnetic Mater i-\nals368, 432 (2014).\n10E. Garaio, J. M. Collantes, F. Plazaola, J. A. Garcia, and\nI. Castellanos-Rubio, Measurement Science and Technology 25,\n115702 (2014).\n11E. Garaio, O. Sandre, J.-M. Collantes, J. A. Garcia, S. Morne t, and\nF. Plazaola, Nanotechnology 26, 015704 (2015).\n12V . Connord, B. Mehdaoui, R. P. Tan, J. Carrey, and M. Respaud,\nReview of Scientific Instruments 85, 093904 (2014).\n13J. Carrey, B. Mehdaoui, and M. Respaud, Journal of Applied\nPhysics 109, 083921 (2011).\n14S. Y . Wang, S. Huang, and D. A. Borca-Tasciuc, IEEE Transac-tions on Magnetics 49, 255 (2013).\n15A. Espinosa, R. Di Corato, J. Kolosnjaj-Tabi, P. Flaud, T. Pe lle-\ngrino, and C. Wilhelm, ACS Nano 10, 2436 (2016).\n16K. H. Bae, M. Park, M. J. Do, N. Lee, J. H. Ryu, G. W. Kim,\nC. Kim, T. G. Park, and T. Hyeon, ACS Nano 6, 5266 (2012).\n17I. Gresits, G. Thur´ oczy, O. S´ agi, B. Gy¨ ure-Garami, B. G. M ´ arkus,\nand F. Simon, Scientific Reports 8, 12667 (2018).\n18A. Luiten, Q-Factor Measurements (John Wiley & Sons, Inc.,\n2005), Encyclopedia of RF and Microwave Engineering.\n19D. Kajfez, Q-Factor (John Wiley & Sons, Inc., 2005), Encyclope-\ndia of RF and Microwave Engineering.\n20D. Kajfez and E. Hwan, IEEE Transactions on Microwave Theory\nand Techniques 32, 666 (1984).\n21P. J. Petersan and S. M. Anlage, Journal of Applied Physics 84,\n3392 (1998).\n22W. Gallagher, IEEE Transactions on Nuclear Science 26, 4277\n(1979).\n23Y . Komachi and S. Tanaka, Journal of Physics E: Scientific Ins tru-\nments 7, 905 (1974).\n24J. Amato, Review of Scientific Instruments 53, 776 (1982).\n25R. W. Quine, D. G. Mitchell, and G. R. Eaton, Concepts in Mag-\nnetic Resonance Part B: Magnetic Resonance Engineering 39B,\n43 (2011).\n26J. Hodges, H. Layer, W. Miller, and G. Scace, Rev. Sci. Instru m.\n75, 849 (2004).\n27J. Hodges and R. Ciurylo, Rev. Sci. Instrum. 76, 023112 (2005).\n28A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz,\nJ. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T.\nHodges, Rev. Sci. Instrum. 82, 063107 (2011).\n29G. W. Truong, D. A. Long, A. Cygan, D. Lisak, R. D. van Zee,\nand J. T. Hodges, J. Chem. Phys. 138, 094201 (2013).5\n30B. Gy¨ ure, B. G. M´ arkus, B. Bern´ ath, F. Mur´ anyi, and F. Sim on,\nReview of Scientific Instruments 86, 094702 (2015).\n31B. Gy¨ ure-Garami, O. S´ agi, B. G. M´ arkus, and F. Simon, Revi ew\nof Scientific Instruments 89, 113903 (2018).\n32R. R. Ernst, Angewandte Chemie-International Edition in En glish\n31, 805 (1992).\n33J. Connes and P. Connes, J. Opt. Soc. Am. 56(1966).\n34P. B. Fellgett, Theory of Infra-Red Sensitivities and its Application\nto Investigations of Stellar Radiation in the Near Infra-Re d (PhD\nthesis). (University of Cambridge, 1949).\n35D. I. Hoult, Review of Scientific Instruments 50, 193 (1979).\n36E. Fukushima and S. Roeder, Experimental pulse NMR: a nuts and\nbolts approach , The Advanced Book Program (Addison-Wesley\nPub. Co., Advanced Book Program, 1981).\n37M. Heidari, N. Sattarahmady, S. Javadpour, N. Azarpira, H. H eli,\nA. Mehdizadeh, A. Rajaei, and T. Zare, Iran J Med Sci 41, 314\n(2016).\n38H. S. Huang and J. F. Hainfeld, Int J Nanomedicine 8, 2521\n(2013).6\nAppendix A: Noise of the measured parameters\n/s48 /s53/s48 /s49/s48/s48/s45 /s52/s48/s45 /s50/s48/s48/s50/s48/s52/s48/s84/s114/s97/s110/s115/s105/s101/s110/s116\n/s115 /s40/s102\n/s48/s41/s61/s49/s49/s32/s72/s122\n/s48 /s53/s48 /s49/s48/s48/s52/s52/s46/s57/s56/s52/s52/s46/s57/s57/s52/s53/s46/s48/s48/s52/s53/s46/s48/s49/s52/s53/s46/s48/s50/s115 /s40/s81 /s41/s61/s48/s46/s48/s48/s54/s51\n/s32 \n/s77/s101/s97/s115/s117/s114/s101/s109/s101/s110/s116/s32/s105/s110/s100/s101/s120/s48 /s53/s48 /s49/s48/s48/s45 /s52/s48/s48/s45 /s50/s48/s48/s48/s50/s48/s48/s52/s48/s48\n/s32 /s115 /s40/s102\n/s48/s41/s61/s56/s49/s32/s72/s122/s102\n/s48/s45/s60 /s102\n/s48/s62/s32/s40/s72/s122/s41/s70/s114/s101/s113/s117/s101/s110/s99/s121/s32/s115/s119/s101/s101/s112\n/s48 /s53/s48 /s49/s48/s48/s53/s48/s46/s52/s53/s48/s46/s54/s53/s48/s46/s56/s53/s49/s46/s48\n/s115 /s40/s81 /s41/s61/s48/s46/s49/s48/s56/s81\nFIG. 5: Noise of the respective parameters as obtained with t he con-\nventional frequency sweep as well as the presented method fo r a mea-\nsurement time of 1 sec/data point. A straight line was subtra cted from\nthef0data due to a linear drift in both types of data and it is shown\nwith respect to the mean values. The standard deviations, σ(f0)and\nσ(Q), are given. We note that these values are about one sixth of\nthe apparent peak-to-peak deviation from the respective me an values.\nNote the different scales for the two types of measurements.In Table I., we show the measurement parameters as well\nas the observed error of the Qdetermination, δQ. We mea-\nsured each data point in Table I. 100 times, in order to obtain a\nstatistically appropriate empirical estimate of the stand ard de-\nviation for both Qandf0:σ(Q)andσ(f0), which is used to\nobtainδ(Q)andδ(f0)as explained in the main text.\nWe also give the error of the Qdetermination normalized\nby two different methods: the first considers the presence of\nthe stochastic noise only and is normalized by the time spent\nwith the acquisition of the transients. The other normaliza -\ntion considers the total amount of time spent to measure each\ndata point, it is therefore a realistic estimate of the error en-\ncountered in a real-life situation. We can draw several con-\nclusions from the table: the value of δQis little affected by\naveraging the transients for 10-100- or 1000 times. This is\nthe result of other than stochastic noise sources (probably drift\neffects). This means that it makes no sense to average the\ntransients for larger than about 10 times. The error is also\nnot improved for measuring the transients for longer times a s\nthe transient decays for a maximum of about 10−20µs and\nin the rest of the measurement, only noise is acquired. The\nactual durations indicate that the spectrometer has a minim al\nacquisition time of about 2 ms for each averaging, which can\nnot be further reduced. Given that our typical transient dur a-\ntion is10−20µs, in principle a perfect instrument with zero\nacquisition- (or dead-) time would allow to improve δQby an\nadditional factor of about 10.7\nNumber of transient\naveragesMeasurement time\n(seconds)Transient duration\n(µs)δQStochastic δQto 1 s\n(in units of 1/√\nHz)RealisticδQto 1 s\n(in units of 1/√\nHz)Type of\nmeasurement\n10 0.025 32.8 2.5·10−44.5·10−64.0·10−5transient\n100 0.22 32.8 1.6·10−49.4·10−67.7·10−5transient\n1000 2.17 32.8 4.6·10−48.3·10−56.8·10−4transient\n10 0.045 262.1 3.3·10−41.7·10−57.1·10−5transient\n100 0.41 262.1 1.5·10−42.4·10−59.5·10−5transient\n1000 4.21 262.1 3.5·10−41.8·10−47.2·10−4transient\n10 0.2 2097.2 3.2·10−44.7·10−51.4·10−4transient\n100 1.98 2097.2 2.5·10−41.1·10−43.5·10−4transient\n1000 1.967 2097.2 3.0·10−44.2·10−48.4·10−4transient\n128 7.37 1000 7.4·10−42.7·10−42.0·10−3Freq. sweep\nTABLE I: The statistics and the errors of the Qdetermination for the transient based and the frequency swe ep methods. The Qvalue was\ntypically 45. The δQquantity is determined according to the definition in the mai n text. This quantity can be normalized by the duration of\nthe transient itself to yield the ”Stochastic δQto 1 s”. Alternatively, the δQcan be normalized by the true measurement time, which yields a\nrealistic estimate of the attainable accuracy of the Qdetermination. E.g. the corresponding data in the first row i s obtained by multiplying the\nrawδQis multiplied by√10·32.8µs and√\n25ms, respectively."    },    {        "title": "2002.04299v2.Diffusion_of_single_active_dipolar_cubes_in_applied_fields.pdf",        "content": "Di\u000busion of single active-dipolar cubes in applied fields\nMartin Kaiser\u0003a, Yeimy Martinezb, Annette M. Schmidtb, Pedro A. S ´anchezc, Sofia S. Kantorovichd,a\naFaculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria\nbChemistry Department, University of Cologne, D-50939 Cologne, Germany\ncHelmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany\ndUral Federal University, Lenin Av. 51, Ekaterinburg 620000, Russian Federation\nAbstract\n“Active matter” refers to a class of out-of-equilibrium systems whose ability to transform environmental energy to\nkinetic energy is sought after in multiple fields of science and at very di \u000berent length scales. At microscopic scales,\nan important challenge lies in overpowering the particles reorientation due to thermal fluctuations, especially in nano-\nsized systems, to create non-random, directed motion, needed for a wide range of possible applications. In this article,\nwe employ molecular dynamics simulations to show that the di \u000busion of a self-propelling dipolar nanocube can be\nenhanced in a pre-defined direction with the help of a moderately strong applied magnetic field, overruling the e \u000bect\nof the thermal fluctuations. Furthermore, we show that the direction of di \u000busion is given by the orientation of the net\ninternal magnetisation of the cube. This can be used to determine experimentally the latter in synthetically crafted\nactive cobalt ferrite nanocubes.\nKeywords: Active Matter, Magnetic Cubes, Molecular Dynamics\n1. Introduction\nThe term “active matter” is a broad concept that ac-\ncounts for any system of one or many entities that con-\nvert environmental energy into kinetic energy, hence\nself-propelled motion. Importantly, such general defi-\nnition applies to any length scale. A paradigmatic ex-\nample is the case of animals, that are active entities\nwhose characteristic sizes span from the macroscopic to\nthe microscopic scale. For the latter case, one can find\nnot only other active biological entities, such as bacteria\nor that biopolymers forming the cytoskeleton of living\ncells, but also artificial systems created with nano- and\nmolecular motors on the nanoscale. Available experi-\nmental techniques have already allowed to explore mul-\ntiple mechanisms to create active microscopic systems,\nparticularly artificial “active particles” that self-propel\nacross an appropriate or taylored environment. Exam-\nples of such environments are as diverse as concentra-\ntion gradients of chemical reactants [1, 2] or the use of\ndefocused lasers to induce self-thermophoresis [3–5].\nThe interest in designed active micro- and nanopar-\nticles has largely grown in recent years due to their\nEmail address: martin.kaiser@univie.ac.at (Martin\nKaiser\u0003)great potential for multiple applications. The relevant\nproperty one harness from such active particles is their\nenhanced kinetic energy compared to simple Brown-\nian particles, leading to fascinating applications such\nas dynamically changing crystal lattices [6–8] or tar-\ngeted drug delivery systems [9–12]. However, many of\nsuch applications require the active component to move\nwithin liquid backgrounds that can not be easily tay-\nlored while facing the e \u000bects of thermal fluctuations,\nwhose relative importance tends to grow as the char-\nacteristic length scale of the system decreases. Rota-\ntional di \u000busion becomes a challenge for the design of\ncertain applications, as it tends to make the direction\nof the active motion unpredictable, particularly at the\nnanoscale [13, 14]. Therefore, to find new ways to con-\ntrol and direct the motion of active micro- and nanopar-\nticles, preferably by means of easily applicable external\nstimuli, is a key aspect for the development of applica-\ntions based on these systems. One of the most inter-\nesting strategies to achieve such a control is based on\nthe use of external magnetic fields. The fact that most\nbiological materials have a negligible response to not\nvery strong fields avoids undesired side e \u000bects, making\nthis approach particularly appealing for biomedical ap-\nplications. The main challenge is the design of artificial\nactive particles with a magnetic response that optimises\nPreprint submitted to (and accepted as per 10.Feb.2020) by Journal of Molecular Liquids February 13, 2020arXiv:2002.04299v2  [cond-mat.soft]  12 Feb 2020the external control of their motion.\nThe idea of gaining control on active systems by de-\nsigning magnetoresponsive active particles is not un-\ncharted waters. There have been several attempts of\nusing external fields to orient the motion of active par-\nticles self-propelled by catalytic reactions, for instance\nby partially covering their surface with thin layers of\nmagnetic materials [15, 16]. Rotating and non-uniform\nmagnetic fields can be employed to not only orient but\nalso to power the self-propulsion of magnetic particles\n[5, 17, 18], that become swimming units. However, de-\nspite the promising properties that magnetic particles\nhave regarding their field induced reorientation, to tay-\nlor and optimise their behaviour as active entities is still\nan open challenge. To this respect, any rationale design\nhas to take into account the current knowledge on the\nproperties of magnetic colloids and nanoparticles.\nIndependently from their potential as active materi-\nals, micro- and nanoparticles composed entirely or par-\ntially of magnetic substances have been studied in the\npast 60 years as the main building blocks of magnetic\nsoft matter systems. Classical examples of magnetic\nsoft matter are ferrofluids and magneto-rheological flu-\nids, that are suspensions of such magnetic particles\nin magneto-passive liquid carriers [19–22], as well as\nmagnetic gels [23–25] and elastomers [26, 27]. The be-\nhaviour of all these materials strongly depends on the\nself-assembly and field-induced assembly processes of\nthe magnetic particles forming them [28–31]. Such as-\nsembly properties are determined by the existence of a\nremanent or field-induced magnetic moment within the\nparticles, with a persistent or changing orientation with\nrespect to their body frame. In the simplest case, cor-\nresponding to monocrystalline spherical particles, the\nmagnetisation orientation mainly depends on internal\nanisotropies associated to the crystalline structure of the\nmaterial [32, 33]. For anisometric ( i.e., non spherical)\nparticles, their shape anisotropy may cause additionally\nan imbalance in the demagnetising fields, generating a\npreferential axis for magnetisation orientation. The im-\nportance of this interplay between internal and shape\nanisotropies is growing with the development of modern\nsynthesis techniques, that allow reproducible manufac-\nturing of micro- and nanoparticles with a broad range of\nanisotropy combinations and magnetic behaviours [34–\n44].\nAmong novel anisometric magnetic particles, mag-\nnetic nanocubes are currently attracting a considerable\nattention due to the strong dependence of their proper-\nties on the relative orientation of their magnetic prefer-\nential axis and their anisometry [45–51]. Such diversity\nof behaviours points magnetic nanocubes as extremelyinteresting test systems for the fundamental study of the\nimpact of anisotropies on active nanoparticles, opening\nup the possibility to find novel and /or optimised config-\nurations for practical applications.\nIn this work we present a preliminary qualitative\nstudy based on computer simulations of a recently syn-\nthesised hybrid active-magnetic nanoparticles. The sys-\ntem is composed of a catalytic active spherical nanopar-\nticle and a single-domain magnetic nanocube rigidly as-\nsembled [52]. The propulsion and the magnetic axes in\nthis hybrid particle are not necessarily co-aligned, hence\nvery di \u000berent behaviours can be obtained depending on\ntheir relative orientation. Employing a coarse-grained\nmodel that accounts for the shape of each component\nand represents the magnetisation of the cube as a point\ndipole fixed in its body frame, we perform extensive\nmolecular dynamics simulations of a single active unit,\nsampling two distinct orientations of the magnetisation\nin an experimentally accessible range of applied mag-\nnetic fields. By thoroughly comparing the active di \u000bu-\nsion properties for both investigated cases, we show that\nan applied field of moderate strength can e \u000bectively di-\nrect the active di \u000busion of these particles. We also show\nthat the intrinsic orientation of the magnetisation is the\ndecisive factor that determines the direction of the active\ndi\u000busion through a measure accessible in experiments.\nOur results indicate that this e \u000bect could be used to de-\ntermine experimentally the actual magnetic axis of any\nindividual active nanoparticle of this type.\nThe structure of the article is the following. In the\nnext Section 2 we introduce the system under study.\nIn Section 2.1 we describe the experimental system,\nwhereas Section 2.2 includes details of the simulation\napproach. In 2.3, we discuss experimental and model\nparameters. Section 3 presents the results, first dis-\ncussing the di \u000busion coe \u000ecients for both studied cases\nin 3.1 and finally the impact of magnetisation orienta-\ntion on the direction of di \u000busion in 3.2. Final conclu-\nsions are summarised in Section 4.\n2. Active magnetic nanocube\n2.1. Experimental system\nThe investigated active particle consists of a single-\ndomain cobalt ferrite (CoFe) nanocube with a smaller\nplatinum (Pt) nanoparticle rigidly attached to one of its\ncorners, as shown in Fig. 1. The synthetic preparation\nof cobalt ferrite-platinum nanostructures entails a sta-\nble interface linkage between the domains via a two-\nstep process [53]. Initially, platinum nanoparticles in a\nsize range of (6 :4\u00060:8)nm are prepared by a modified\n2Figure 1: Left: HR-TEM images of the self-propelled dipolar cubes.\nIn the bright-field images, darker contrast corresponds to platinum,\nwhile lighter contrast corresponds to cobalt ferrite. Right: computa-\ntional ”raspberry” model of the self-propelled dipolar cube. The dark-\ngray particle attached to the corner of the cube represents the active\nplatinum sphere in the experimental system.\nthermal decomposition route [52]. The seed-mediated\ngrowth of the CoFe domain is induced by thermolysis\nand performed in organic phase nucleated from the plat-\ninum counterpart. Next, the capping surface of these\nnanostructures is further modified using a ligand ex-\nchange treatment. In this way, it is possible to obtain\npoly (acrylic acid) capped nanostructures with an edge\nlength of (29 :6\u00063:7)nm. These nanostructures are well-\ndispersible and stable in aqueous media as well as in di-\nluted bu \u000ber solutions at physiological pH. The units are\nactivated through self-di \u000busiophoresis using a coupled\nchemical fuel system based on the platinum catalysed\nreduction of borohydrides. Hence, the propulsion is\ngenerated by a concentration gradient considering both\nfuel and reaction products in the vicinity of the plat-\ninum counterpart. In addition, the dipolar CoFe units\nare railed by a passive magnetic field to reduce the pre-\ndominant rotational di \u000busion a \u000becting for nanometric\nobjects.\nThe actual orientation of the magnetic moment within\nthe cube and with respect to the corner where the active\nparticle is attached is di \u000ecult to determine experimen-\ntally. The crystalline anisotropy suggests that [111] ori-\nentation is the most probable one. However, the orien-\ntation in real systems might di \u000ber or even switch in the\ncourse of the experiment. One of the ways to elucidate\nthe impact of intrinsic magnetisation direction on the\nself-propulsion behaviour in an applied magnetic field\nis to employ simulations, in which, as shown below, it is\nstraightforward to manipulate this parameter and anal-\nyse how it a \u000bects the e \u000eciency of the external field on\ndirecting the active di \u000busion.2.2. Numerical model\nWe perform molecular dynamics simulations in the\ncanonical ensemble to investigate the e \u000bects of the\nanisotropies in the active di \u000busion of the dipolar cube\nunder infinite dilution conditions. All simulations were\nexecuted with the simulation package ESPResSo [54].\nThe fundamental equation which is numerically inte-\ngrated to get a discrete trajectory of the particle is the\nLangevin equation of motion, that for translational de-\ngrees of freedom reads\nmdv\ndt=\u0000\rv\u0000rU(r)+F(t) ;v=dr\ndt; (1)\nincluding the quantities: particle mass m, particle po-\nsition r, particle velocity vector v, friction coe \u000ecient\n\r, the gradient of any interaction potential acting on\nthe particlerU(r) and a random force F(t). The lat-\nter should be Gaussian distributed according to Ornstein\nand Uhlenbeck [55], having independent components\nwith magnitude Dp, and\u000e-correlated time dependence,\nhF(t)i=0;\nhFi(t)Fj(t0)i=2Dp\u000ei;j\u000e(t\u0000t0);(2)\nwhere iandjcan take the indices x;yandzof the spa-\ntial directions. This random force represents implicitly\nthe e\u000bects of the thermal fluctuations of the background\nfluid at a temperature T, providing the possibility to e \u000e-\nciently produce simulation data for a system at constant\nthermal energy kT, being kthe Boltzmann constant. Ex-\npressions analogous to (1) and (2) are also integrated for\nthe rotational degress of freedom.\nThe interaction of the cube magnetic moment, repre-\nsented as a fixed point dipole ~d, with the applied mag-\nnetic field,~H, is given by the classical Zeeman potential\nUZ=\u0000~d\u0001~H; (3)\nIn all cases, the field is applied along the z-axis of the\nsimulation box, that is cubic and has periodic boundary\nconditions in order to represent a pseudo-infinite sys-\ntem.\nExploiting the Langevin-equation, self-propelled mo-\ntion in simulations can be represented by a constant\nforce applied along the propulsion axis of the active par-\nticle. Through a velocity dependent friction, an active\nparticle attains a terminal velocity va(see Table 1). The\nvalue of the latter is defined by the balance of this fric-\ntion and the driving force. This approach is called the\nActive-Brownian-Particle (ABP) model and is used to\nstudy a variety of active matter phenomena in simula-\ntions [56, 57].\n3\f\f\f\f~d\f\f\f\f\f\f\f\f~Hmax\f\f\f\fkT\rmCoFe mPt va\n10 0.1 1 1 56 2 0.1\nTable 1: Dimensionaless parameters used in the simulations: dipole moment of the magnetic cube,\f\f\f\f~d\f\f\f\f; maximum strength of the applied field,\f\f\f\f~Hmax\f\f\f\f; thermal energy, kT; friction coe \u000ecient,\r; mass of the magnetic cube, mCoFe; mass of the catalytic sphere, mPt; terminal velocity of the\nactive force, va. See the main text for their correspondence to experimental values.\ndo=[111]do=[100]fo=[111]\nFigure 2: Schematic of an active-cube unit, with the cube in light-\ngray and the active portion as a dark-gray sphere. The vectors in the\ncenter represent the point dipole in the center in the cube, which has\na direction doaligned with either the [111] (in blue) or the [100] (in\nred) axis of the cubes body. The black vector indicates the orientation\nfo=[111] of the induced active velocity, which is pointing towards\nthe cube center at all times.\nThe approach used to represent the anisometry of\nour system is the so-called “raspberry model” [58–60],\nwhich uses spherical building blocks disposed in a rigid\narrangement to e \u000bectively represent any body shape.\nThis is analogous to the model used by Donaldson et\nal.for simple magnetic nanocubes [50, 61, 62]. The\nsize, shape and mass of the raspberry grains are cho-\nsen in such a way, that the resulting cube characteris-\ntics closely resemble those in experiment. The number\nof grains in the raspberry is not directly a \u000becting the\ndi\u000busion of the particles, but only its geometry. It is\nimportant to mention that once hydrodynamics is taken\ninto account, the choice of size and number of raspberry\ngrains becomes undeniably important. Fig. 1 shows the\nraspberry structure used in our simulations. The point\ndipole is placed in the center of the cube. Its relative ori-\nentation do, defined with respect to the corner at which\nthe active particle is fixed, is either [111] (along one\nmain diagonal of the cube, pointing opposite to the ref-\nerence corner) or [100] (pointing to the center of oneof the faces of the cube that includes the reference cor-\nner). This is depicted in the schematic representation\nshown in Fig. 2. The self-propulsion force of the ac-\ntive sphere sitting at the reference corner is constant and\npointing towards the center of the cube, thus, parallel to\nthe dipole moment for the case [111] and perpendicular\nto it for [100]. The analysis of the simulation trajec-\ntories is performed separatelly for the direction paral-\nlel (z-axis) and perpendicular ( xy-plane) to the applied\nfield.\nIn all simulations the integration time step has been\nchosen to be \u001c=0:005, ensuring stability of the inte-\ngration scheme. The simulation protocol is the follow-\ning. First, a cycle of 2000 \u001cto allow the random reori-\nentation of the raspberry particle from its initial config-\nuration has been performed before the magnetic field is\nswitched on along the z-axis. Another cycle of the same\nlength provides time for the unit to respond to the mag-\nnetic field. The mean-squared displacement (MSD) is\ncalculated after such initial relaxations, for at least 107\u001c\nsteps, to provide su \u000ecient statistics for the range of the\nMSD investigated in this study. Results below were ob-\ntained by averaging over 4 independent simulation runs.\n2.3. Connection to the experiments\nThe parameters used in the model represent CoFe\ncubes of 20 nm side length with a magnetic moment\nof 1:05\u000110\u000018A\u0001m2attached to Pt spheres of 4 nm of\ndiameter. The highest strength of the magnetic field is\nchosen so that the absolute value of the minimum Zee-\nman energy, corresponding to a perfect aligment of the\ndipole with the field, is equal to the thermal energy. This\ncorresponds to a field of approximately 3.9 mT. How-\never, in order to ensure the stability of the numerical\nintegrations, in simulations it is convenient to use a sys-\ntem of dimensionless units that gives parameter values\naround unity. That system can be arbitrary as long as\nit keeps the same ratios for the corresponding relevant\nexperimental parameters. In our case, we set our dimen-\nsionless parameters by considering the experimental ra-\ntios that have been already determined for this system\n[52]. These are the aforementioned ratio between mag-\n4netic and thermal energy, jUZj=kbT=1, and the mass\nratio of the Pt and CoFe components, mCoFe=mPt=28.\nSince here we focus only on qualitative results, arbi-\ntrary values have been chosen for parameters not yet\nmeasured experimentally. Table 1 summarises the di-\nmensionaless values used in this study. The correspon-\ndence between the experimental and computational time\nis not useful due to the absence of explicit hydrodynam-\nics. However, this does not qualitatively a \u000bect the main\nresults reported below.\n3. Results and Discussions\n3.1. Mean-squared displacement and di \u000busion\nIn order to quantify di \u000busion anisotropy, we investi-\ngated the MSD and di \u000busion coe \u000ecient D\u001cfor a range\nof applied field strengths up to jUZj=kbT=1 for a single\nactive unit to see how much its di \u000busion is influenced by\nthe magnetic field. As a reference, the di \u000busion D0(\u001c) of\nonly the active particle without the cube, but otherwise\nsame parameters, is computed by dividing the MSD by\n2\u001cper component. The calculation of the di \u000busion is\nsplit into two parts, with the component Dk\n0being the\ndi\u000busion along the field direction and the component\nD?\n0being the mean of the di \u000busion components per-\npendicular to the field. The di \u000busion, shown in Fig. 3,\nfollows a typical behaviour of a free, unconstrained ac-\ntive particle as in Ref. [2], reaching constant saturation\nvalue after a ballistic regime. In this short time ballistic\nregime, the particle can move in a more or less straight\nline before it is reoriented by random kicks from its sur-\nrounding medium. The duration of this regime is deter-\nmined by the strength of the active force acting on the\nparticle. The fact that both curves are almost identical\nevidences a fully isotropic di \u000busion, as expected.\nTop panel in Fig. 4 shows the split MSD of the whole\nhybrid active-magnetic particle with orientation of the\nmagnetic moment [111] for di \u000berent field strengths,\nwhereas the bottom panel shows its split di \u000busion coef-\nficients divided by the corresponding reference value of\nthe free active sphere, Dk=Dk\n0andD?=D?\n0. Here, dotted\nlines and filled symbols are the average of the two com-\nponents perpendicular to the field and dashed lines with\nempty symbols are the parallel components. To guide\nthe eye, the point \u001cRafter which all perpendicular com-\nponents reached constant di \u000busion, ( dD(\u001c)=d\u001c)\u001c\u0015\u001cR=0,\nand the ratio of perturbed and non perturbed di \u000busion\nequal to unity, D(\u001c)=D0(\u001c)=1, are indicated by dashed\nhorizontal and vertical lines, respectively. The MSD\nreveals that the e \u000bect of particle redirection stemming\nFigure 3: Di \u000busion of an unconstrainted active particle without the\ncube attached, obtained from the computation of the MSD divided\nby\u001c. Dashed lines and empty markers correspond to the component\nparallel to the magnetic field, Dk\n0, dotted lines and filled markers to\nthe mean of the two perpendicular components, D?\n0.\nfrom the interaction of the dipolar cube with the mag-\nnetic field leads to a significant enhancement of the par-\nallel component of the displacement, with an increas-\ning slope at stronger fields. This is equally reflected\nin the di \u000busion coe \u000ecient, where it becomes clear that\nthe perpendicular to the field components saturate to a\nstate of constant di \u000busion while the parallel components\ndo not follow this behaviour and keep growing beyond\nthe investigated time frame. Additionally, the perpen-\ndicular components saturate at a more than 10 times\nsmaller di \u000busion coe \u000ecient than its unperturbed coun-\nterpart, D0. Besides not saturating, the parallel com-\nponents are also only smaller than their counterpart for\nshort time scales, eventually increasing over the point\nwhere D(\u001c)=D0(\u001c)=1. The time at which D(\u001c) and\nD0(\u001c) are equal, depends on the strength of the applied\nfield, and is shorter as the magnetic field strength in-\ncreases.\nFig. 5 shows the same quantities as the just discussed\nFig. 4, but for the case of dipole orientation do=[100].\nQualitatively, the behaviour stays intact, but quantitative\nchanges are observed. Within the same time-frame, the\ndi\u000busion does not grow as high as in the [111] case, and\nonly the parallel component for a magnetic field where\njUZj=kbT=1, manages to reach the point where D(\u001c)\nandD0(\u001c) are equal. This is attributed to the unfavorable\nconfiguration of the active force compared to the dipole\norientation. The dipole remains mostly aligned with the\nmagnetic field – as shown in later parts of this section\n– and the active force can not anymore propagate its\nfull energy onto the e \u000bective di \u000busion direction of the\ncube unit, resulting in an overall slower increase of the\ndi\u000busion over time as compared to the more favourable\n5Figure 4: MSD (upper) and D(\u001c) (lower) of a single active cube unit in\nfields with magnitude as marked by colours and symbol shapes, where\nthe dipole orientation dolies along the [111] axis of the cube. Dashed\nlines and empty symbols correspond to the component parallel to the\nmagnetic field, dotted lines and filled symbols to the mean of the two\nperpendicular components. The vertical bold line indicates \u001cRand the\nhorizontal thin line the point where D(\u001c)=D0(\u001c) is equal to 1.\n[111] case.\nIt may seem surprising that the ratio of in field com-\nponents keep growing with increasing \u001cin Figs. 4 and 5.\nThe reason for this growth is that the distance, traveled\nby the active cube in the direction of the applied field,\nis growing infinitely large with increasing time step,\nin contrast to Fig. 3, where thermal fluctuations force\nthe unbiased active particle to perform random motion,\nleading to the saturation of D0(\u001c). One can understand\nthis by imagining a particle that is moving in one direc-\ntion with a constant velocity. If you measure the dis-\ntance the particle traveled during certain time frames,\none will see that the distance travelled during larger\ntimes is bigger than for smaller ones.\nAt this point we define two additional quantities use-\nful for the discussion: the ratio R=(Dk=D?)\u001c=\u001cRof\nthe parallel and perpendicular components of the dif-\nfusion at point \u001c=\u001cR, and the transport e \u000eciency\nE=1\u0000(D?=Dk)\u001c=\u001cR. The dependence of these pa-\nrameters on the field strength for both dipole orienta-\ntion is shown in the upper and lower panels of Fig. 6,\nFigure 5: MSD (upper) and D(\u001c) (lower) of a single active cube unit in\nfields with magnitude as marked by colours and symbol shapes, where\nthe dipole orientation dolies along the [100] axis of the cube. Dashed\nlines and empty symbols correspond to the component parallel to the\nmagnetic field, dotted lines and filled symbols to the mean of the two\nperpendicular components. The vertical bold line indicates \u001cRand the\nhorizontal thin line the point where D(\u001c)=D0(\u001c) is equal to 1.\nrespectively. Here one can see that, within the inves-\ntigated range of magnetic field strengths, for the [111]\ncase, di \u000busion in direction parallel to the field is up to 16\ntimes higher than di \u000busion of the perpendicular compo-\nnents and the e \u000eciency therefore goes up to 94%. For\nthe [100] case, although not all energy of the active par-\nticle is distributed towards di \u000busion in field direction,\nthe parallel component is still up to 5 times bigger in\nthe same field strength range, topping out at 80% e \u000e-\nciency. The above measures disclose the ability of the\nmagnetic field to direct the active cube and enhance its\ndi\u000busion along its direction. So far unclear, taking into\naccount the geometry of the cube, is whether di \u000busion\nhappens parallel or anti-parallel to the field direction, as\nthe di \u000busion coe \u000ecients alone are not suitable to make\na precise statement about this point.\n3.2. Angular anisotropy and trajectories\nIn order to elucidate the question rised above, in\nFig. 7, we present polar relative probability distribu-\ntions of the track-angle – i.e., the angle between the\n6Figure 6: Ratio (upper) and transport-e \u000eciency (lower) versus H,\ncomputed for the values of DkandD?at\u001c=\u001cr. The results for\nthe dipole orientation do=[100] are shown with circles and for\ndo=[111] with triangles. Dotted lines are guides to the eye.\nvector connecting two consequent points of the trajec-\ntory and the magnetic field vector. To have a deeper in-\nsight into possibly occurring anisotropies, the analysis\nof this distribution is split into the angle that the projec-\ntion of the vector trajectory onto the xy-plane encloses\nwith the magnetic field, and the angle that the corre-\nsponding projection onto the yz-plane encloses with the\nlatter. Here, those two angles are denoted with \u001eand\u0012,\nrespectively. Probability distributions for the values of\nthese angles obtained for three selected field strengths,\nH=0:0;0:06;0:1, are displayed in these plots. The\ndistributions are a representation of the mean direc-\ntion traveled by the particle with respect to the mag-\nnetic field. It is seen that fields of increasing magni-\ntude clearly shift the distribution towards the 0\u000eaxis for\nthe [111] case, showing a clear deviation from the uni-\nform distribution corresponding to an unperturbed ac-\ntive cubic particle at 0 field. Both, \u001eand\u0012, follow this\npattern. The [100] case shows an strikingly opposite\nbehaviour. Here, the particle travels in the opposite di-\nrection of the magnetic field. This observation can be\nexplained in two steps. First, the angle between the ac-\ntive force and the [100] dipole is acute enough, so that\nthe active particle is e \u000bectively pushing in an opposeddirection to which the dipole is pointing (refer back to\nFig. 2 as a visual aid). Second, the force of the active\nparticle is not strong enough to fully break the align-\nment of the dipole and the magnetic field. Those two\nfactors force the active particle to push the unit towards\nthe counter-direction of the dipole, hence the direction\nof the magnetic field, and we therefore get the distribu-\ntions observed in Fig. 7. Furthermore, the distributions\nof the [111] case are more narrow than the ones for the\n[100] case at the same field strength. This stems from\nthe same reason as the magnitude di \u000berence in the dif-\nfusion coe \u000ecient graphs for the two cases: the active\nparticle is not able to fully project its energy onto the\ne\u000bective di \u000busion direction. The track-angle distribu-\ntion is a quantity accessible in experimental set-ups and\ncan therefore act as a guide to determine the internal\norientation of the synthesised CoFe cubes.\n4. Conclusion\nBy performing Langevin Dynamics simulations,\nwe investigated the behaviour of a hybrid magnetic\nnanocube with a smaller active catalytic particle at-\ntached to one of its corners, when placed under the in-\nfluence of an applied homogeneous magnetic field. We\nfound that fields at which the Zeeman energy is equal\nto the strength of the thermal fluctuations are su \u000ecient\nto drastically orient the cube along the magnetic field.\nThis stems from the inability of the active component to\noverpower the reorientation process due to the magnetic\nfield, even if the active force is not directly aligned with\nthe direction of the dipole. The active di \u000busion parallel\nto the field is growing slower for the case of non-aligned\nactive force-dipole orientations, as the active force is not\nfully propagated along the di \u000busion direction of the par-\nticle and some energy is therefore lost. The direction\nof di\u000busion is determined by the internal magnetisation\norientation, showcased for two orientations along the\n[111] and [100] axis of the cube. The [111] case dif-\nfuses parallel to the magnetic field, while the [100] par-\nticle is geometrically constrained to move anti-parallel\nto the field. This can act as a guide to ascertain the mag-\nnetisation orientation of synthetically created magnetic\ncubes, as the observation of this behaviour can also be\ncaptured experimentally, and may furthermore act as a\nsorting procedure to separate cubes with di \u000berent mag-\nnetisation orientations if an active force on the units is\npresent. Regardless, both scenarios are highly suitable\nfor potential applications where field induced redirec-\ntion can be beneficial, as the transport parallel to the\nfield is up to 16 times higher for the [111] and up to 5\ntimes higher for the [100] case. Being these results only\n7do=[111]\ndo=[100]Figure 7: Polar distributions of the track-angle – the angle enclosed between a vector from one trajectory point to another and the magnetic field\nvector (~H, in red, aligned with the 0\u000eline) – for the zx-plane component ( \u0012, in light-blue) or zy-plane component ( \u001e, in light-yellow). The row\nof the figures determines the dipole orientation withing the cube, whichs is either [111] in the upper row or [100] in the lower row. The columns\ndetermine the strength of the applied field ranging from H =0.0 on the left, to H =0.1 on the right.\nfor magnetic fields where the Zeeman energy and ther-\nmal fluctuations are of the same order, we expect a much\nhigher e \u000eciency of the process at stronger fields, which\ncan still be easily achieved in experimental set-ups.\nAcknowledgements\nThis research has been supported by the Russian\nScience Foundation Grant No.19-12-00209. Authors\nalso acknowledge support from the Austrian Research\nFund (FWF), START-Projekt Y 627-N27. Y .M. grate-\nfully acknowledges a Doctoral Scholarship granted by\nthe Deutscher Akademischer Austauschdienst (DAAD).\nA.M.S. acknowledges funding from DFG-SPP 1681,\ngrant number SCHM1747 /10. Computer simulations\nwere performed at the Vienna Scientific Cluster (VSC-\n3).\nReferences\n[1] D. Velegol, A. Garg, R. Guha, A. Kar, M. Kumar, Origins\nof concentration gradients for di \u000busiophoresis, Soft matter 12\n(2016) 4686–4703.\n[2] C. Bechinger, R. Di Leonardo, H. L ¨owen, C. Reichhardt,\nG. V olpe, G. V olpe, Active particles in complex and crowded\nenvironments, Reviews of Modern Physics 88 (2016) 045006.\n[3] R. Piazza, Thermophoresis: moving particles with thermal gra-\ndients, Soft Matter 4 (2008) 1740–1744.[4] M. Yang, M. Ripoll, Simulations of thermophoretic nanoswim-\nmers, Physical Review E 84 (2011) 061401.\n[5] A. Ghosh, P. Fischer, Controlled propulsion of artificial mag-\nnetic nanostructured propellers, Nano letters 9 (2009) 2243–\n2245.\n[6] M. Cates, O. Henrich, D. Marenduzzo, K. Stratford, Lattice\nboltzmann simulations of liquid crystalline fluids: active gels\nand blue phases, Soft Matter 5 (2009) 3791–3800.\n[7] S. Whitelam, K. Klymko, D. Mandal, Phase separation and\nlarge deviations of lattice active matter, The Journal of chemical\nphysics 148 (2018) 154902.\n[8] O. D. Lavrentovich, Active colloids in liquid crystals, Current\nopinion in colloid & interface science 21 (2016) 97–109.\n[9] G. Bonacucina, M. Cespi, M. Misici-Falzi, G. F. Palmieri, Col-\nloidal soft matter as drug delivery system, Journal of pharma-\nceutical sciences 98 (2009) 1–42.\n[10] C. Barbe, J. Bartlett, L. Kong, K. Finnie, H. Q. Lin, M. Larkin,\nS. Calleja, A. Bush, G. Calleja, Silica particles: a novel drug-\ndelivery system, Advanced materials 16 (2004) 1959–1966.\n[11] R. Singh, J. W. Lillard Jr, Nanoparticle-based targeted drug de-\nlivery, Experimental and molecular pathology 86 (2009) 215–\n223.\n[12] D. Needleman, Z. Dogic, Active matter at the interface between\nmaterials science and cell biology, Nature Reviews Materials 2\n(2017) 17048.\n[13] V . Yadav, W. Duan, P. J. Butler, A. Sen, Anatomy of nanoscale\npropulsion, Annual review of biophysics 44 (2015) 77–100.\n[14] I. Santiago, Nanoscale active matter matters: Challenges and\nopportunities for self-propelled nanomotors, Nano Today 19\n(2018) 11–15.\n[15] L. Baraban, D. Makarov, R. Streubel, I. Monch, D. Grimm,\nS. Sanchez, O. G. Schmidt, Catalytic janus motors on microflu-\nidic chip: deterministic motion for targeted cargo delivery, ACS\nnano 6 (2012) 3383–3389.\n8[16] L. Baraban, D. Makarov, O. G. Schmidt, G. Cuniberti, P. Lei-\nderer, A. Erbe, Control over janus micromotors by the strength\nof a magnetic field, Nanoscale 5 (2013) 1332–1336.\n[17] U. K. Cheang, F. Meshkati, D. Kim, M. J. Kim, H. C. Fu, Min-\nimal geometric requirements for micropropulsion via magnetic\nrotation, Physical Review E 90 (2014) 033007.\n[18] V . Lalande, F. P. Gosselin, S. Martel, Experimental demon-\nstration of a swimming robot propelled by the gradient field\nof a magnetic resonance imaging (mri) system, in: 2010\nIEEE /ASME International Conference on Advanced Intelligent\nMechatronics, IEEE, 2010, pp. 103–108.\n[19] R. Hiergeist, W. Andr ¨a, N. Buske, R. Hergt, I. Hilger, U. Richter,\nW. Kaiser, Application of magnetite ferrofluids for hyperther-\nmia, Journal of Magnetism and Magnetic Materials 201 (1999)\n420–422.\n[20] W. Huang, C. Shen, S. Liao, X. Wang, Study on the ferrofluid\nlubrication with an external magnetic field, Tribology Letters\n41 (2011) 145–151.\n[21] S. Odenbach, Colloidal magnetic fluids: basics, development\nand application of ferrofluids, volume 763, Springer, 2009.\n[22] J. de Vicente, D. J. Klingenberg, R. Hidalgo-Alvarez, Magne-\ntorheological fluids: a review, Soft Matter 7 (2011) 3701–3710.\ndoi:10.1039/C0SM01221A .\n[23] T. Shiga, A. Okada, T. Kurauchi, Magnetroviscoelastic behavior\nof composite gels, J. Appl. Polym. Sci. 58 (1995) 787–792.\ndoi:10.1002/app.1995.070580411 .\n[24] M. Zr ´ınyi, L. Barsi, A. B ¨uki, Ferrogel: a new magneto-\ncontrolled elastic medium, Polym. Gels Networks 5 (1997) 415–\n427. doi: 10.1016/S0966-7822(97)00010-5 .\n[25] L. Roeder, P. Bender, M. Kundt, A. Tschope, A. M. Schmidt,\nMagnetic and geometric anisotropy in particle-crosslinked fer-\nrohydrogels, Phys. Chem. Chem. Phys. 17 (2015) 1290–1298.\ndoi:10.1039/C4CP04493B .\n[26] M. R. Jolly, J. D. Carlson, B. C. Mu ˜noz, T. A. Bullions, The\nmagnetoviscoelastic response of elastomer composites consist-\ning of ferrous particles embedded in a polymer matrix, J.\nIntell. Mater. Syst. Struct. 7 (1996) 613–622. doi: 10.1177/\n1045389X9600700601 .\n[27] S. Odenbach, Microstructure and rheology of magnetic hy-\nbrid materials, Arch. Appl. Mech. 86 (2016) 269–279. doi: 10.\n1007/s00419-015-1092-6 .\n[28] M. Klokkenburg, C. V onk, E. M. Claesson, J. D. Meeldijk, B. H.\nErn´e, A. P. Philipse, Direct imaging of zero-field dipolar struc-\ntures in colloidal dispersions of synthetic magnetite, J Am Chem\nSoc 126 (2004) 16706–16707. doi: 10.1021/ja0456252 .\n[29] M. Klokkenburg, B. H. Ern ´e, A. Wiedenmann, A. V . Petukhov,\nA. P. Philipse, Dipolar structures in magnetite ferrofluids stud-\nied with small-angle neutron scattering with and without applied\nmagnetic field, Phys. Rev. E 75 (2007) 051408. doi: 10.1103/\nPhysRevE.75.051408 .\n[30] G. Filipcsei, I. Csetneki, A. Szil ´agyi, M. Zr ´ınyi, Oligomers -\nPolymer Composites - Molecular Imprinting, Springer Berlin\nHeidelberg, Berlin, Heidelberg, 2007, pp. 137–189.\n[31] T. Borb ´ath, S. G ¨unther, D. Y . Borin, T. Gundermann, S. Oden-\nbach, X\u0016CT analysis of magnetic field-induced phase transi-\ntions in magnetorheological elastomers, Smart Mater. Struct. 21\n(2012) 105018. doi: 10.1088/0964-1726/21/10/105018 .\n[32] K. H. J. Buschow, F. R. Boer, et al., Physics of magnetism and\nmagnetic materials, volume 7, Springer, 2003.\n[33] B. D. Cullity, C. D. Graham, Introduction to magnetic materials,\nJohn Wiley & Sons, 2011.\n[34] M. V . Kovalenko, M. I. Bodnarchuk, R. T. Lechner, G. Hesser,\nF. Sch ¨a\u000fer, W. Heiss, Fatty acid salts as stabilizers in size-\nand shape-controlled nanocrystal synthesis: The case of inverse\nspinel iron oxide, J. Am. Chem. Soc. 129 (2007) 6352. doi: 10.1021/ja0692478 .\n[35] L. Rossi, S. Sacanna, W. T. M. Irvine, P. M. Chaikin, D. J. Pine,\nA. P. Philipse, Cubic crystals from cubic colloids, Soft Matter 7\n(2011) 4139–4142. doi: 10.1039/C0SM01246G .\n[36] A. Ahniyaz, Y . Sakamoto, L. Bergstr ¨om, Magnetic field-\ninduced assembly of oriented superlattices from maghemite\nnanocubes, Proc. Natl. Acad. Sci. 104 (2007) 17570. doi: 10.\n1073/pnas.0704210104 .\n[37] S. Disch, E. Wetterskog, R. P. Hermann, G. Salazar-Alvarez,\nP. Busch, T. Br ¨uckel, L. Bergstr ¨om, S. Kamali, Shape in-\nduced symmetry in self-assembled mesocrystals of iron ox-\nide nanocubes, Nano Lett. 11 (2011) 1651. doi: 10.1021/\nnl200126v .\n[38] J.-M. Meijer, D. V . Byelov, L. Rossi, A. Snigirev, I. Sni-\ngireva, A. P. Philipse, A. V . Petukhov, Self-assembly of col-\nloidal hematite cubes: a microradian x-ray di \u000braction explo-\nration of sedimentary crystals, Soft Matter 9 (2013) 10729.\ndoi:10.1039/C3SM51553B .\n[39] M. Yan, J. Fresnais, J.-F. Berret, Growth mechanism of nanos-\ntructured superparamagnetic rods obtained by electrostatic co-\nassembly, Soft Matter 6 (2010) 1997–2005. doi: 10.1039/\nB919992F .\n[40] A. G ¨unther, P. Bender, A. Tsch ¨ope, R. Birringer, Rota-\ntional di \u000busion of magnetic nickel nanorods in colloidal disper-\nsions, J. Phys.: Cond. Matter 23 (2011) F5103. doi: 10.1088/\n0953-8984/23/32/325103 .\n[41] M. Nakade, T. Ikeda, M. Ogawa, Synthesis and properties of\nellipsoidal hematite /silicone core-shell particles, J. Mater. Sci.\n42 (2007) 4815–4823. doi: 10.1007/s10853-006-0761-9 .\n[42] S. Sacanna, M. Korpics, K. Rodriguez, L. Col ´on-Mel ´endez,\nS.-H. Kim, D. J. Pine, G.-R. Yi, Shaping colloids for self-\nassembly, Nature Communications 4 (2013) 1688. doi: 10.\n1038/ncomms2694 .\n[43] P. Tierno, Recent advances in anisotropic magnetic colloids: re-\nalization, assembly and applications, Phys. Chem. Chem. Phys.\n16 (2014) 23515–23528. doi: 10.1039/C4CP03099K .\n[44] J. Donaldson, E. Pyanzina, E. Novak, S. Kantorovich, Ani-\nsometric and anisotropic magnetic colloids: How to tune the\nresponse, Journal of Magnetism and Magnetic Materials 383\n(2015) 267–271. doi: 10.1016/j.jmmm.2014.11.013 .\n[45] X. Liu, G. Qiu, X. Li, Shape-controlled synthesis and properties\nof uniform spinel cobalt oxide nanocubes, Nanotechnology 16\n(2005) 3035.\n[46] Y . Xiong, J. Ye, X. Gu, Q.-w. Chen, Synthesis and assembly\nof magnetite nanocubes into flux-closure rings, J Phys Chem C\n111 (2007) 6998–7003. doi: 10.1021/jp070957p .\n[47] L. Rossi, S. Sacanna, W. T. Irvine, P. M. Chaikin, D. J. Pine,\nA. P. Philipse, Cubic crystals from cubic colloids, Soft Matter 7\n(2011) 4139–4142.\n[48] M. W. Szyndler, R. M. Corn, Self-assembly of flux-closure\npolygons from magnetite nanocubes, J Phys Chem Lett 3 (2012)\n2320–2325. doi: 10.1021/jz300931s .\n[49] E. Wetterskog, M. Agthe, A. Mayence, J. Grins, D. Wang,\nS. Rana, A. Ahniyaz, G. Salazar-Alvarez, L. Bergstr ¨om, Precise\ncontrol over shape and size of iron oxide nanocrystals suitable\nfor assembly into ordered particle arrays, Science and Technol-\nogy of Advanced Materials 15 (2014) 055010. doi: 10.1088/\n1468-6996/15/5/055010 .\n[50] L. Rossi, J. G. Donaldson, J.-M. Meijer, A. V . Petukhov,\nD. Kleckner, S. S. Kantorovich, W. T. Irvine, A. P. Philipse,\nS. Sacanna, Self-organization in dipolar cube fluids constrained\nby competing anisotropies, Soft matter 14 (2018) 1080–1087.\n[51] Z. Li, M. Wang, X. Zhang, D. Wang, W. Xu, Y . Yin, Magnetic\nassembly of nanocubes for orientation-dependent photonic re-\nsponses, Nano Lett. 19 (2019) 6673–6680. doi: 10.1021/acs.\n9nanolett.9b02984 .\n[52] M. E \u000bertz, Formgerichtete Synthese von Hybrid-\nNanostrukturen und Methodenentwicklung zur Echtzeitver-\nfolgung von Sub-Abbe-Partikeln. Doctoral Dissertation.,\nUniversitt zu Kln, Cologne, Germany, 2016.\n[53] H.-T. Zhang, J. Ding, G.-M. Chow, Morphological control of\nsynthesis and anomalous magnetic properties of 3-d branched\npt nanoparticles, Langmuir 24 (2008) 375–378.\n[54] F. Weik, R. Weeber, K. Szuttor, K. Breitsprecher, J. de Graaf,\nM. Kuron, J. Landsgesell, H. Menke, D. Sean, C. Holm,\nEspresso 4.0–an extensible software package for simulating soft\nmatter systems, The European Physical Journal Special Topics\n227 (2019) 1789–1816.\n[55] G. E. Uhlenbeck, L. S. Ornstein, On the theory of the brownian\nmotion, Physical review 36 (1930) 823.\n[56] P. Romanczuk, M. B ¨ar, W. Ebeling, B. Lindner, L. Schimansky-\nGeier, Active brownian particles, The European Physical Jour-\nnal Special Topics 202 (2012) 1–162. doi: 10.1140/epjst/\ne2012-01529-y .\n[57] M. R. Shaebani, A. Wysocki, R. G. Winkler, G. Gompper,\nH. Rieger, Computational models for active matter, 2019.\narXiv:1910.02528 .\n[58] J. de Graaf, T. Peter, L. P. Fischer, C. Holm, The raspberry\nmodel for hydrodynamic interactions revisited. ii. the e \u000bect\nof confinement, The Journal of chemical physics 143 (2015)\n084108.\n[59] L. P. Fischer, T. Peter, C. Holm, J. de Graaf, The raspberry\nmodel for hydrodynamic interactions revisited. i. periodic arrays\nof spheres and dumbbells, The Journal of chemical physics 143\n(2015) 084107.\n[60] V . Lobaskin, B. D ¨unweg, A new model for simulating colloidal\ndynamics, New Journal of Physics 6 (2004) 54.\n[61] J. G. Donaldson, S. S. Kantorovich, Directional self-assembly\nof permanently magnetised nanocubes in quasi two dimen-\nsional layers, Nanoscale 7 (2015) 3217–3228. doi: 10.1039/\nC4NR07101H .\n[62] J. G. Donaldson, E. S. Pyanzina, S. S. Kantorovich, Nanopar-\nticle shape influences the magnetic response of ferro-colloids,\nACS Nano 11 (2017) 8153–8166. doi: 10.1021/acsnano.\n7b03064 .\n10"    },    {        "title": "1907.12767v1.The_effect_of_heating_rate_and_soaking_time_on_microstructure_of_an_advanced_high_strength_steel.pdf",        "content": "1 The effect of heating rate and soaking time on microstructure of an \nadvanced high strength steel  \nM.A. Valde s-Tabernero1, C. Celada -Casero2, I. Sabirov1, A. Kumar2, R. H. Petrov2, 3 \n1 IMDEA Materials Institute, Calle Eric Kandel 2, Getafe 28906, Madrid, Spain  \n2 Department of Materials Science and Engineering, Delft University of Technology, \nMekelweg 2, 2628  CD Delft, The Netherlands  \n3 Department of Electrical Energy, Metals, Mechanical constructions & Systems , Ghent \nUniversity, Technologiepark 46, 9052 Ghent, Belgium  \n \nAbstract  \nThis work  focuses on the effect of soaking time on the microstructure  during ultrafast heat \ntreatment  of a 50% cold rolled low carbon steel with initial ferriti c-pearlitic microstructure . \nDilatometry analysis was used to estimate the effect of heating rate on the phase \ntransformation temperatures and to select an appropriate inter -critical temperature for final \nheat treatments. A thorough qualitative and quantitati ve microstructural characterization of \nthe heat treated samples is performed using  a wide range of characterization techniques . A \ncomplex multiphase, hierarchic al microstructure consisting of ferritic matrix with embedded \nmartensite and retained austenite is formed after all applied heat treatments. In turn, the \nferritic matrix contains recrystallized and non -recrystallized grains. It is demonstrated that \nthe ultrafast heating generally results in finer microstructure compared to the conventional \nheating independently on the soaking time. There is a significant effect of the soaking time \non the volume fraction of martensite of the ultrafast heated material, while in the samples \nheated with  conventional heating rate it remains relatively unchanged during soak ing. \nRecrystallization , recovery and phase transformation s occurring  during soaking are \ndiscussed with respect to the applied heating rate . \nKeywords:  steel, ultrafast heating, microstructure, transmission Kikuchi diffraction , texture   \n Introduction  \n \n                                                 \nCorresponding author : Miguel Angel Valdés Tabernero.  \nPostal address: IMDEA Materials Institute, Calle Eric Kandel 2, Getafe 28906, Madrid, Spain. \nPhone: + 34 91  5493422 . E-mail: miguelangel.valdes@imdea.org  2 Steels have been the most widely used materials all over the world and are likely to remain \na key material of choice in construction and manufacturing. Steel manufacturing is a \nmultistage process, where the heat treatment of (semi -)final product (in form o f sheet, rod, \nwire) to a great extent determines its microstructure and, hence, its properties. The current \napproach for steel heat treatment is based on homogenization of microstructure at elevated \ntemperatures (either at austenitic or intercritical tempe ratures) and cooling with controlled \nrate often followed by further treatment  to form the required microstructure  [1]. In 2011, \nCola et. al . [2] proposed an idea to apply ultrafast heat treatment for manufacturing  advanced \nhigh strength steels ( AHSS ) with microstructures as heterogeneous as those processed via \nconventional heat treatments. This treatment was initially referred to as ‘flash pro cessing’ \n[2], and other terms such as ‘ultrashort annealing’ [3] and ‘ultrafast heating’ [4–7] are widely \nused for this process in the recent literature. Ultrafast heat treatment is based on heating the \nmaterial with the heating rate in the range of 100 to 1000 oC/s to an intercritical temperature, \nvery short soaking at this temperature followe d by quenching.  The whole process lasts just \na few seconds and, therefore, is characterized by significantly reduced energy consumption  \ncompared to the conventional heat treatments  [8]. \nThe current state of the art in the effect of ultrafast heat treatment on the microstructure and \nproperties of steels can be summarized  as follows. The final microstructure of the ultrafast \nheat treated steels is determined by three major heat treatment parameters: heating rate, peak \ntemperature and soaking time. Ultrafast heating typically result s in grain refinement in \ninterstitial free (IF) [9] and low carbon steels [3–5,10,11] , thus, l eading to higher mechanical \nstrength. Increasing heating rate shifts the recrystallization temperature to higher values  than \nthe one measured at conventional heating rates of 10 -20°C/s . Recovery and recrystallization \nprocesses concurrently occur during ult rafast heating, and increasing the heating rate \ndecreases the recrystallized fraction of ferrite for a given temperature [5–7,12–14]. The \nmartensite volume fraction  in the heat treated steel  tends to increase with increasing peak \ntemperature [15]. The initial microstructure strongly influences the properties of steels after \nultrafast heat treatment  [5]. Particularly, the steels with the initial ferritic -pearlitic \nmicrostructure showed lower strength and higher ductility compared to the steels with the \ninitial ferritic -martensitic microstructure [5]. The pre -heating stage at temperatures of 300 -\n400 oC has minor effects on the microstructure evolution during ultrafast heating, though \nincrease of pre -heating temperature results in lower volume fraction of austenite , and hence \nmartensite upon quenching , due to cementite spheroidization [12]. 3 Microstructure evolution in steels during ultrafast heating and short soaking at the peak \ntemperature is a very complex phenomenon, as it involves simultaneously recovery, \nrecrystallization, grain gr owth, phase transformations and diffusion of alloying elements \nwith carbon playing the key role. In most of the basic studies, the isothermal soaking time \nwas taken as short as possible, 0.1 - 0.2 s [5,7,12,13] . Such short soaking times cannot be \nreached during UFH processing of steel on the existing industrial lines  and this is a \nsignificant obstacle for implementation of the ultrafast heating in steel industry . It was \nreported that longer isothermal soaking t ime (30 s) can erase the positive grain refining effect \nof the ultrafast heating [16]. However, in the current literature th ere are no systematic studies \non the effect of the isothermal soaking time at the peak temperature on the microstructure \nand properties of steel after ultrafast heating. Fundamental understanding of microstructure \nevolution is required to enable an easy de termination of the optimum soaking parameters for \nmicrostructural design in the ultrafast heat treated steels. Therefore, the main objective of \nthe present work is to thoroughly study the effect of soaking time on the microstructure \nevolution during ultraf ast heating of a low carbon steel. Conventional heating of the steel \nfollowed by detailed microstructural characterization is also performed for comparison.  \n \n Material and experimental procedures  \n \n Material  \nA low carbon steel with chemical composition of 0.19 % C, 1.61 % Mn, 1.06 % Al, 0.5 % \nSi (in wt. %) was selected for this investigation . Alloys  with this composition are typically \nused in the automotive sector as transformation induced plasticity (TRIP) assisted steels , \nwhic h belong to the 1st generation of AHSS  [17–19]. Two kinds of heating experiment s were \nperformed : a) dilatometry  measurements to determine phase  transformation temperatures , \nand b) annealing tests to the intercritical temperature  with varying soaking time followed by \nquenching . Both types of experiments are described in detail below.  \n Dilatometry experiments  \nAs increasing  heating rate shifts the recrystallization temperature to the higher values  than \nthe equilibrium one or the one measured at conventional heating rates  [5,13] . Dilatometry \nmeasureme nts were carried out to determine  the phase transformation temperatures A C1 and 4 AC3 of the studied steel  as a function of heating rate . For these  experiments, specimens with \ndimensions of 10x5x1 mm3 were machined from the as -received material. Tests were c arried \nout in a Bähr DIL805A/D dilatometer (Bähr -Thermoanalyse GmbH, Hüll-Horst, Germany). \nSpecimens were heated up to 1100 ºC with diff erent heating rates (1, 10, 50  and 200  oC/s) \nand h olding time equal to 0.2 s . Heating rates above 200 ºC/s were not applied due to \ninstability of the system in that range of heating rates. A K-type therm ocouple  was welded \nto the midsection of each specimen to measure their temperature during experiment.  The \nmaterial was then cool ed down to room temperature at -300 ºC/s.  The sample \nexpansion/contraction duri ng heating/cooling was recorded, and the obtained dilatometry \ncurves were analyzed.  The tangent intersection method was applied to determine the start \n(AC1) and finish  (AC3) temper atures of austenite formation.  \n \n Intercritical heat treatments  \nFor the intercritical heat treatments, strips of 100 mm in length and 10 mm in width were \nmachined along the rolling direction and heat treated  in a thermo -mechanical simulator \nGleeble 3800. A K-type thermocouple was spot -welded to the midsection of each specimen . \nTwo different types of heat treatment were applied . In both types , the thermal cycle was \ndivided into five stages. On the first and second stages, the specimens were heated at 10 ºC/s \nto 300 ºC, followed by a so aking period of 30 s at 300 ºC . These stages simulate a preheating \nin some industrial continuous annealing lines to reduce the thermal stresses during heating. \nThe third stage is heating from 300 ºC to the peak temperature of 860 ºC at two different \nheating rates, 10 ºC/s (conventional heating or CH) and 800 ºC/s (ultra -fast heating or UFH) \nfollowed by soaking at 860 ºC for 0.2  s. The processed specimens will be referred to as \nCH10 -0.2s and UFH800 -0.2s, respectively. Such a short soaking time (0.2 s) allows to \neliminate the effect of annealing time on the microstructure  and to focus entirely on the effect \nof heating rate . The last stage was to cool down the material to room temperature at ~160 \nºC/s. The peak temperature of 860 ºC for intercritical annealing was selected based on the \noutcomes of the dilatometry measurements (see Section 3.1). \nTo study the effect of soaking time at both heating rates  (CH and UFH ), additional heat \ntreatments were performed with higher soaking time ( 1.5 s and 30 s). The new generated \nconditions are referred to as CH10 -1.5s and CH10 -30s for the CH treatment , and UFH800 -\n1.5s and  UFH800 -30s for the UFH treatment . All applied thermal cycles are schematically 5 presented in  (Figure 1). In all samples, a minimum length of 10 mm of the homogeneously \nheat treated zone was verified  by microhardness measurements.  \n \nFigure 1: Schematic representation of the different heat treatments applied to the studied material. \n(For interpretation of the references to color in this figure, the reader is referred to the web version \nof this article).  \n \n Microstructural characterization  \nA thorough microstructural characterization of the samples heat treated in a thermo -\nmechanical simulator ( Figure 1) was performed. Specimens for scanning electron \nmicroscopy (SEM) studies were ground and polished to a mirror -like surface applying \nstandard metallographic techniques with final pol ishing using OP -U (colloidal silica). The \npolished specimens were etched with 3 vol.% N ital solution for 10 s . Examination of the \nmicrostructure was performed using a FEI Quanta™ 450 FEG -SEM operating at an \naccelerating voltage of 15 kV. Microstructure was observed on the RD –ND plane.  \nSpecimens for electron backscatter diffraction ( EBSD ) analysis were ground and polished \nfollowing the same procedure as for SEM images. Orientation imaging microscopy (OIM) \nstudies were performed using a FEI Quanta™ Helios NanoLab 600i  equipped with a \nNordlysNano detector controlled by the AZtec Oxford Instruments Nanoanalysis (versi on \n2.4) software. The data were acquired at an accelerating voltage of 18 kV, a working distance \nof 8 mm, a tilt an gle of 70 º, and a step size of 65 nm in a hexagonal scan gri d. The orientation \ndata were post -processed using HKL Post -processing Oxford Inst ruments Nanotechnology \n6 (version 5.1 ©) software and TSL Data analysis version 7.3 software.  Grains were defined as \na minimum of 4 pixels with  a misorientation higher than 5 º. Grain boundaries having a \nmisorientation ≥ 15º were defined as high -angle grain bo undaries (HAGBs), whereas low -\nangle grain boundaries (LAGBs) had a misorientation <  15º. Textures are represented as \norientation distribution functions (ODFs) using Bunge notation  [20]. The ODFs were \nderived from the EBSD scans by superimposing Gaussian distribu tions with a half -width of \n5°. The resulting ODF was represented as a series expansion of spherical harmonics \nfunctions with a maximum rank of the expansion coefficient L =  16. Texture and grain size \ncalculations were made using scans having area of ~ 6000 µm2 which contains at least  1100 \ngrains. The volume fractions of transformed/untransformed grains and \nrecrystallized/ recovered ferritic grains were determined  by a two -step partitioning procedure \ndescribed in  [5,21] . In this procedure, grains with high  (> 70o) and low (≤ 70o) grain average \nimage qualities are separated in a first step, allowing to distinguish between untransformed \n(ferrite) and transformed (martensite) fractions , respectively . In the second step, \nrecrystallized and non -recrystallized ferritic grains are separated using the grain orientation \nspread criterion: Grains with orientation spread below 1 º are defined as the recrystallized \ngrains, while grains wi th an orientation spread above 1 º are defined as  the non-recrystallized  \nones [22]. It should be noted that another grain average misorientation b ased criterion was \nemployed in our recent report  [14] for separation of recrystallized/non -recrystallized grains. \nComparison of these two different criteria via analysis of n umerous EBSD scans carried out \nin this work has shown , that the criteri on utilized  in the present manuscript  yields better \nresults.  The microstructure was characterized on the plane perpendicular to th e sample \ntransverse direction ( the RD–ND plane ). \nX-ray diffraction (XRD) experiments were carried out to determine the retained austenite \nvolume fraction and its carbon concentration. Specimens with a surface of 10 x 5 mm2 were  \nprepared following the same procedure as for the EBSD analysis. The measureme nts were \nperformed using a Bruker D8 Advance diffractometer (Bruker AXS, Karlsruhe, Germany) \nequipped with a VANTEC position sensitive detector and using Co K α radiation ( λ = 1.78897 \nÅ), an acceleration voltage of 45 kV and current of 35 mA. The measuremen ts were \nperformed in the 2θ range from 45º to 130º with a step size of 0.035º and a counting time \nper step of 3 s. The volume fraction of retained austenite was calculated using the Jatczak \nmodel as described in [23]. The austenite carbon concentration, X c, was estimated from its \nlattice paramet er, a γ. The latter  was determined from the austenite peak position as [24]: 7 aγ = 0.3556+0.00453 X c +0.000095 X Mn +0.00056 X Al      (1) \nwhere a γ is the austenite lattice parameter in nm and Xi represents the concentration of the \nalloying element i in wt . %. The effect of silicon and phosphorous is not taken into account , \nas it is negligible  compared to other elements considered  in Eq. (1).  \nIn order to carry out a thorough  characterization of nanoscale constituents  in a rapid manner , \nin 2012 Keller et al.  proposed a novel approach called transmission Kikuchi diffraction \n(TKD)  analysis [25]. It is based on  performing a n EBSD analysis in transmission mode. The \nmethod  requires very thin samples, similar to those  for TEM characterization, and a \nconventional SEM equipped with  EBSD detector.  It can also be combined with transmission \nelectron microscopy ( TEM ) analysis.  Due to  the low thickness of sample, typical SEM \nvoltages are sufficient  for electrons to interact with the material and pass through, to finally \nbe captured by the EBSD detector. TKD offers better spatial resolution (< 10 nm) than \nEBSD, allowing the resolution o f nanoscale microstructural constituents  having 10-30 nm \nin size [26,27] . It has been successfully used to analyze oxides and nitrides in alumin ium \nalloys [28] and stainless steels [29,30] , as well as martensite  and retained austenite in bainitic \nsteels [31]. In this work, for TKD  and TEM  studies , the samples were ground to a thickness \nof 100 µm and disks of 3 mm in diameter were subsequently punched out. The disks  were \nfurther thinned in a Struers Tenupol -5 via twin -jet electropolishing until a central hole \nappeared. The used electrolyte was composed of 4 % vol. HClO 4 in 63 % water -diluted \nCH 3COOH under 21 V at 20 ºC and a flow rate equal to 17. TKD data were collected by an \nEDAX -TSL EBSD system attach ed to a FEI Quanta™ 450 -FEG -SEM  under the following \nconditions : accelerating volt age of 30 kV, working dista nce of 4 mm, tilt angle of - 40°, a \nbeam current of 2.3 nA corresponding to the FEI spot size of 5, aperture size of 30 μm. TKD \nmeasurement s were performed with the step size  of 10 nm. The orientation data were post -\nprocessed using TSL Data analysis version 7.3 software.  TEM images were acquired in a \nJeol (S)TEN JEM -2200FS operated at 200 kV and equipped with an aberration corrector of \nthe objective lens (CETCOR, CEOS GmbH) an d a column electron energy filter (omega \ntype).  XRD, TEM and TKD measurements were performed on samples CH10 -0.2s, \nUFH800 -0.2s, UFH800 -1.5s and UFH800 -30s. \n \n Results and discussion  \n3.1. Dilatometry  8 Figure 2a represents the typical dilatometry curves for the samples tested with different \nheating rates. The A C1 temperature was determined at 5 % volume fraction of the \ntransformed phase calculated by the lever rule ( as shown in  Figure 2b). Such relatively high  \npercentage of the transformed phase was selected as a criterion due to complexity of the \nmicrostructure evolution during heating, which involves various processes (carbide \ndissolution, recovery and recrystallization of ferrite, formation of austenite as observed in \n[32–34] and described in Section 3) resulting in A C1 temperature range.  Once the sample is \nfully austenitic at  the A C3 phase transformation temperature, the expansion becomes linear \nwith the temperature. The martensite start temperature M S corresponds to the point on the \ndilatation curve, where the contraction of austenite during quenching is replaced by \nexpansion due to the formation of martensite. As it is seen from  Table 1, all three \ntransformation temperatures, A C1, AC3 and M S, tend to increase with the increasing heating \nrate. 9  \nFigure 2: a) Dilatometry curves from dilatometry tests with different heating rates ; b) Schematic \ndiagram of an experimental dilatometry curve (measured at 1 oC/s) to calculate A C1 and A C3 \ntemperatures via tangent intersection principle and lever rule . (For interpretation of the references \nto color in this figure, the reader is referred to the web version of this article).  \n \nTable 1: Effect of the heating rate on the  phase transformation temperatures:  AC1, A C3 and M S. \nHeating rate (ºC/s)  AC1 (ºC) AC3 (ºC) MS (ºC) \n1 738 968 483 \n10 760 969 489 \n50 781 971 498 \n200 793 983 530 \n \n10 For the A C1, the pronounced  increase from 738 to 781 oC occurs at the lower heating rates \nranging from 1 ºC/s to 50 ºC/s. On the other hand, the A C3 temperature just  slightly grows  \nfrom 968 to 971 oC in that temperature range jumping up to 983 ºC at 200 ºC/s.  It can be \nhypothesized, that t his variation of the A  C1 temperature is determined mainly by nucleation \nand growth rate of austenitic grains. The nucleation rate at the given elevated temperature \ngrow s with the increasing heating rate, since the latter suppresses the recovery effects, \nresulting in higher density of lattice defects at the given temperature, which, in turn, promote \nphase nucleation . The growth rate of the nucleated austenitic grains is c ontrolled by carbon \ndiffusion [7] and solute drag effect  (by Mn atoms in the studied steel) [35]. Therefore, at the \nearly stages of phase transformation, the austenite volume fraction at the given temperature \ndecreases with increasing heating rate. Both factors result in increasing A C1 temperature with \nrising  heating rate. It should be noted that s imilar results were earlier  published in [36]. In \nthis study, a linear dependency of AC1 on the heating rate ( Figure 3) on the  semi -log plot is \nobserved . Similar tendency of A C1 on the heating rate for ferritic -pearlitic microstructure has \nbeen  reported in [37,38] . The nucleation and growth depend on the heating rate exponentially \n[38]. Moreover , the extrapolation of this behavior to low heating rates (0.2 ºC/s) show s an \nequilibrium temperature of 720 ºC, which is very close  to the theoretical one (723 ºC) , thus \nconfirming the linear character of this dependence . Therefore, this approach can also be used \nto predict the A C1 temperature at high heating rates. Particularly, f or 800 ºC/s , the A C1 \ntemperature is about  808 ºC  (Figure 3). On the other hand, the dependence of A C3 \ntemperature on the heating rate is less pronounced. Similar observations were reported \nearlier in [39]. Therefore, the intercritical temperature of 860 oC was selected as the peak \ntemperature for both CH and UFH treatments (see Section 2.3). 11  \nFigure 3: Effect of heating rate on the A C1 temperature . \nIncreasing heating rate during heat treatment with full  austenitization followed by  immediate  \ncooling leads to increment o f the MS temperature. This effect is produced because the higher  \napplied heating rate results in  the higher amount of defects in the microstructure induced by  \ncold roll ing. As recovery is diffusion controlled [40], higher density of lattice defects is \nretained in the microstructure due to shorter time at elevated temperatures . This effect was \nobserved previously in [41,42] . In addition, at high heating rates carbides remain undissolved \nin the microstructure, leading to a formation of austenite with lower ca rbon content and, \nhence, a higher M S compare d to the conventional heating rates . Therefore, the steepest \nincrement on M S is produced , when heating rate grows  from 50 ºC/s to 200 ºC/s leading to \nan increase of transformation temp erature from 4 98 ºC to 530 º C. On the other hand, in the \nrange of lower heating rates from 1 to 50 ºC/s the MS temperature just slightly  varies . \n \n3.2. SEM characterization  \nThe supplied material shows a typical cold rolled  microstructure consisting of elongated \ngrains of deformed ferrite with volume fraction of 76 % and pearlite with volume fraction \nof 24%  (Figure 4). \n12  \nFigure 4: Initial ferritic -pearlitic microstructure of the steel after 50 % cold reduction, being ferrite \nin grey and pearlitic colonies in white.  \n \nThe microstructure af ter CH treatment  with soaking time of 0.2 s, 1.5 s and 30 s  is presented \nin Figure 5a, b, c, respectively, whereas remaining images  illustrate  the microstructure after \nUFH treatment . In all cases , the material presents a complex microstructure formed by a \nferritic matrix  (consisting of recrystallized and recovered ferritic grains)  with embedded \nmartensite and retained austenite  grains . However, it strongly depends on the applied heat \ntreatment parameters. During  CH treatment, the material presents a similar microstructure \nindependent ly on the soaking time, while the latter has very significant effect on the \nmicrostructure formed after  UFH treatment.  \nCH treatment  generates a ferritic matrix with homogeneous micros tructure consisting of  \nequiaxed grains, as previously observed in [5]. On the other hand, UFH results in  the matrix \nmicrostructure consisting o f fine equiaxed grains and large r elongated  grains surrounded by \nmartensitic grains . The large grains may grow from the heavily deformed ferrite located in \nthe vicinity of pearlite colonies, as the latter are not able to accumulate high plastic strain \nduring rolling.  Hence, the higher energy stored in the heavily deformed ferritic areas leads \nto a faster grain growth  [40]. Some Widmanstätten ferritic grains are also observed in the \n13 UFH samples after soaking for 1.5 and 30 s  (marked by white arrows on Figure 5h, i) \npossibly formed at the early stages of cooling. Those ferrite plates are surrounded by bainite.  \nSpheroi dized cementite  (SC) is also observed in samples UFH -0.2s and UFH -1.5s (marked \nby red dashed arrows o n SEM micrographs presented on Figure 5). It is related to  the short \ntime (0.2 – 1.5 s)  of the heat treatment , as reported previously by Castro  Cerdá et al. [5,43] , \nand fully dissolved  after soaking for 30 s. A very small region with spheroidized cem entite \nparticles was also observed in the CH -0.2s sample, although its amount is negligible ( Figure \n5a). 14  \nFigure 5: SEM micrographs showing the effect of  heating rate (10 and  800 ºC/s) and  soaking time \n(0.2 to 30 s ) on the microstructure : a), b) and c) correspond to 10 ºC/s for 0.2, 1.5 and 30 s , \nrespectively; d), e) and f) correspond to 800 ºC/s for 0.2, 1.5 and 30 s , respectively. Higher \nmagnification i mages g), h) and i) show  microstructures heated at 800 ºC/s for 0.2, 1.5 and 30 s , \nrespectively;  j) higher magnific ation image of spheroidized cementite  (SC)  in the sample heated at  \n800 ºC/s for 1.5 s. Spheroidized cementite is marked by dashed red arrows , while white arrows \n15 indicate Widmanstätten ferrite  (WF) . Ferrite is marked as F, and  M/RA  stands for  martensite/retained \naustenite.  Etched with Nital (3%).  \n \n3.3. EBSD characterization  \nEBSD technique was used to precisely quantify and characterize the different \nmicroconstituents formed in the material after both heat treatments . The results of EBSD \nanalysis are outlined  in Table 2. CH treatment leads to a microstructure mainly formed by a \nferritic matrix, whose volume fraction remains constant ( ~ 86–87 %) and martensite volume \nfraction slightly increas es from 10.6 % to  12.5 %  with the soaking time . As volume fraction \nof ferrite does not vary with  soaking time  (i.e. the amount of intercritical austenite formed \nat the peak temperature does not depend on the soaking time) , the martensite increment can \nbe attributed to the partial transformation of austenite into martensite by deformation during \nsample preparation . This indicates that retaine d austenite is less stable caused by the \nhomogenization  of carbon distribution in its interior after longer soaking times.  Although \nthe UFH process generates similar micro structure with the same microstructural \nconstituents , there are significant variations in the volume fractions of different phases with \nrespect to the CH treatment. The volume fraction  of ferrite  noticeably  decreases with \nincreasing soaking time from 90.9 % at 0.2 s to 75.9 % at 30 s , while the volume fraction of \nmartensite shows the opposite trend . As the volume fraction of retained austenite  remains \nstable  (2.1 – 2.2 %) , it is possible to assure that the decrease of ferrite fraction is directly \nassociated to the formation of martensite.  On the other hand, the difference in ferrite and \nmartensite volume fractions between CH and UFH conditions can be explained by the \nspheroi dization  of cementite  during heating . First, the nucleation of austenite occurs at the \nα/cementite  interface  [44]. With conventional heating  (CH), the cementite  spheroidizes [7] \nreducing the amount of preferable sites for austenite formation  and resulting in longer \nsoaking time  to reach the equilibrium . The main fraction  of the inter-critical austenite is \ntransformed into martensite during cooling. On the other hand, during UFH treatment the \npeak  temperature is reached in less than 1 s  which  dramatically reduc es the amo unt of \nspheroidized  cementite and, thus,  increas es the driving force  for austenite nucleation at the \nmore  favorable α/cementite interfaces.  16 Table 2: Effect of the heating rate and soaking time on the volume fractions of phases present in \nthe studied material.  \nCondition  \n(s) CH UFH  \n0.2 1.5 30 0.2 1.5 30 \nFerrite \n(%) 86.3 ± 2.4  87.4 ± 2.7  85.8 ± 1.6  90.9 ± 4.0  85.3 ± 2.8  75.9 ± 4.6  \nMartensite \n(%) 10.6 ± 1.7  10.8 ± 1.6  12.5 ± 1.6  6.9 ± 3.2  12.6 ± 3.1  22.0 ± 3.0  \nRetained \naustenite \n(%) 3.1 ± 0.7  1.8 ± 0.6  1.7 ± 0.1  2.2 ± 0.4  2.1 ± 0.3  2.1 ± 1.9  \n \nThe morphology of  the ferritic matrix in the CH and UFH heat treated samples also present s \nsignificant  differences.  The EBSD analysis revealed both recrystallized and recovered grains \nin the ferritic matrix.  Figure 6 represents the fraction of recrystallized ferrite in the ferritic \nmatrix for all analyzed conditions. It is seen that, while the CH treatment leads to a \nhomogeneous ferritic matrix, where almost 90 % of ferrite is recrystallized, the UFH \nprocessing generat es a matrix microstructure formed by recrystallized and non -recrystallized \n(i.e. recovered) ferrit ic grains . After UFH treatment, the volume fraction of recrystallized \nferrite increases from ~50 % after 0.2 s to ~67 % after 30 s.  So, while the recrystalliz ation \nprocess is completed during CH treatment already after soaking for 0.2 s , it is delayed during \nUFH process. Similar observations were previously reported in [43,45,46] . This effect is due \nto the competition of different processes, such as austenite formation and further grain \ngrowth, reducing the driving force for recrystallization. For short soaking time (0.2 s), the \nrecrystallization is the co ntrolling process, which results in a very low martensite volume \nfraction ( Table 2), similar to the CH treatment, and a significant volume fraction of  \nrecrystallized ferrite present in the material ( Figure 6). However, after soaking for longer \ntime (1.5 – 30 s) , other processes become dominant over recrystallization, such as the \nnucleation and growth of austenite into ferrite and ferrite grain growth [10,16] . The first \neffect results in the higher volume fraction of  martensite present in the UFH800 -30s ( Table \n2) and the decrease in volume fraction of recrystallized ferrite with increasing soaking time 17 from 1.5 to  30 s ( Figure 6). The latter effect is discussed more in detail below ( Figure 7 and \nFigure 8). \n \nFigure 6: Evolution of volume fraction of recrystallized ferrite with respect to the total fraction of \nferrite with heating rate and soaking time. (For interpretation of the references to color in this \nfigure, the reader is referred to the web version of this article).  \n \nFigure 7 represents the IPF maps for recrystallized  (a, b,  c) and non-recrystallized  (d, e,  f) \nferrite after UFH for 0.2, 1.5 and 30 s , respectively . It is seen in Figure 7a, b, that the vast \nmajority  of the grains are in the early stage of growth, presenting a size ≤ 1.5 µm, although \nit is possible to observe grains which have fully recrystallized a nd grown, i.e. grains without \nLAGBs and with low misorientations in their interior. This observation was also reported by \nCastro  Cerda  et al. [5]. When soaking time increases  to 30 s , the fraction of fine grains \ndecrease s due to their grow th, and the presence of large r grains is more evident  (Figure 7c). \nThe non -recrystallized grains demonstrate significant misorientation in the interior of the \ngrains indicating  formation of substructure independently on the applied soaking time  \n(Figure 7d, e, f). \n18  \nFigure 7: IPF maps after UFH treatment  showing the recrystallized (a, b,  c) and non -recrystallized \n(d, e,  f) ferr ite after 0.2, 1.5 and 30 s,  respectively. HAGBs are shown in black and LAGBs in \nwhite. (For interpretation of the references to color in this figure, the reader is referred to the web \nversion o f this article).  \nThe evolution of the grain size distribution for recrystallized  ferrite is clearly visible and \nquantif ied in Figure 8a, b, c, where  the grain size is plotted vs. the area fraction for the \nUFH800 -0.2s, UFH800 -1.5s and UFH800 -30s, respectively  (blue lines) . It is observed  that \nthe mean peak shifts to higher values  and widens . For instance, in the samples UFH800 -0.2s \nand UFH800 -1.5s the fraction  of grains with a size below 1.5 µm is 52 % and 56 % , \nrespectively, while after longer soaking  it decreases to 36 %  indicating the growth of the \nsmall grain s nucleated at shorter times. A second peak at higher grain size  is noticeable \nindicating th e presence of the large  grains mentioned above. The intensity of the second peak \ndecreases with  soaking  time, as the microstructure become s more homogeneous ( Figure 8 \nc). The histogram of grain size distribution for non-recrystallized  ferritic grains (red lines in \nFigure 8) present s a similar character  in comparison to  the recrystallized ones . The primary \n19 peak shifts to the higher  values becoming wider,  when soaking time is increased. The \nfraction of grains having size above  2.5 µm increases from 59 % at 0.2 s to 68 % at 1.5 s to \n73 % after 30 s. This effect can be produced by the coalescence of grains after partial \nrecrystallization  indicated by the presence of HAGB s. Nevertheless, the non-recrystallized \ngrains  are larger  compared to the recrystallized  ones after all soaking times.  On the other \nhand, the ferritic matrix in the CH condition is formed mainly by recrystallized equiaxed \ngrains , and its microstructure is not affected by soaking time  (Figure 8d). \n \nFigure 8: a), b),  c) Representation of the  equivalent circle  diameter  (ECD)  versus area fraction for \nrecrystallized (RX) and non -recrystallized (Non RX) ferrite after UFH with soaking for 0.2, 1.5 and \n30 s, respectively; d) grain diameter versus area fraction for ferrite after CH treatment. Data are \nobtained from the EBSD measurements. (For i nterpretation of the references to color in this figure, \nthe reader is referred to the web version of this article).  \n \nIt is well known that high heating rates lead to a small er grain size [6,10,13,47,48] , as it is \nshown for the studied steel in Figure 8. This is caused, among other reasons, by the short \ntime given to the α/α interface  to grow. On the one hand, after CH treatment the \nrecrystallization and grain growth processes are completed  independently on the applied \nsoaking time . The grain size is also not affected by soaking time, as intercritical austenitic \n20 grains  act as barr iers for the ferritic grains suppressing  their further growth. On the other \nhand, the  UFH treated conditions show a bim odal distribution of grain size . The presence of \nthe two differentiated regions on the histograms  can be rationalized  by the interplay  of two \nmain effects:  \n(1) the effect of the initial heterogeneous microstructure  related to  different amounts of strain \naccommodate d by individual ferritic grains,  as shown in  Figure 4; \n(2) the effect of heating rate . A higher heating rate results in a recrystallization process taking \nplace  at higher temperatures, as discussed  above , and , thus, in a higher nucleation rate  due \nto the high  density  of defects  [13,43,48] . \nThe nucle i formed within  the highly deformed areas possess high er driving force to grow \nand coalesce due to the high energy stored during cold rolling , resulting in  the large r grains. \nOn the other hand, nucle i generated within  the less deformed regions present r educed driving \nforce for growth. Moreover, due to the short time of the heat treatment, remains of individual \ncementite particles (which were  not completely dissolved  during inter -critical annealing ) \nlocate d at grain boundaries  effectively pin grain boundaries suppressing grain  growth and \ncoalescence [49–51] (Figure 5g, h, i). As the material is heated up to an intercritical \ntemperature, a nother important factor comes into play : Formation of austenite and its growth \ncompetes  for the energy stored in the material . The austenitic grains nucleate  in carbon \nenriched a reas, i.e. within  pearlitic colonies. It can be assumed that t he intensive  nucleation \nof austenitic grains takes place  within p earlitic colonies which were  severely deformed, \nrotate d or broken  during cold rolling , resulting in reduction of  distance between cementite \nplates . As is well known, the austenite nucleation rate is inversely proportional to  the inter -\nlamellar  spacing of pearlite  [12]. The austenite grows firstly into the pearlite until it is \ndissolved and then into ferrite, as it is seen in Figure 5. Competition of a ll these processes \nduring UFH treatment results in  the microstructure with finer  grains  (Figure 5, Figure 8). \nFigure 9 represents the equivalent  circle  diameter of martensite plotted versus area fraction. \nFor the CH  condition , at short soa king time (0.2 s) most of the martensite grains were formed \nfrom ultrafine austenitic grains, as the major peak lies below 1 µm (Figure 9a). Increasing \nsoaking time  up to 1.5 s , the curve shifts to the  right, indicating the growth of the earlier \nformed nucle i. Finally, after annealing for 30 s,  the d ecrease of the main peak intensity is \naccompanied by  increase in the area fraction at 3 µm, displaying that the austenite has \nentered the growth stage after the nucleation after short soaking times. In the case of the 21 UFH 800-0.2s, the curve is similar to the CH  condition with  the same soaking time. However, \nthe fraction of larger grains having a size of 4 -5 µm increases. This behavior can indicate \nthat the austenite nucleation is accompanied by a growth, due to the fact that the material \nhas higher energy compared to the CH condition  because of the  low amount  of spheroidized \ncementite  and the higher carbon gradients  present in the material, both produced by the rapid \nheating. It is more pronounced  after 1.5 s , where the main peak has reduced , but there is a n \nincrease of the fraction of large r grains. The result of this effect is the rise of the martensite \nfraction in the overall microstru cture. Finally, after 30 s  the peak spreads to higher values, \nas it happens in the ferrite, showing an intense growth of t he austenite grains during soaking.  \n \nFigure 9: Martensite ECD  vs area fraction for CH (a) and UFH (b) for different soakin g times: 0.2  \ns, 1.5 s and 30 s . \n \n3.4. Texture analysis  \nTo analyze evolution of the preferable crystallographic orientation of ferritic grains , texture \nanalysis was carried out for all studied conditions . Figure 10a represents the ideal positions \nof the most important texture components in BCC lattice , while Figure 10b shows the \norientation distribution function (ODF) of the initial cold -rolled material. Figure 10c, d, e \ndisplay the ODFs for the CH samples annealed  for 0.2, 1.5 and 30 s , respectively, while \nFigure 10e, f, g represent the UFH conditions soaked for 0.2, 1.5 and 30 s , respectively.  The \ninitial cold -rolled material  is represented by the ND {111} ‹uvw› and RD { hkl}‹110› fibers, \nwith a maxima corresponding to {111} ‹110› components. Similar texture was found \npreviously in cold -rolled low carbon steels [52,53] . On the other hand, the CH samples  \n(Figure 10c, d, e) present an opposite curvature in the ND fiber compared to the initial cold -\nrolled microstructure and lower intensity in the RD fiber . Both effect s can be associated with \n22 the recrystallization in the ferritic matrix  [4]. In the UFH conditions ( Figure 10f, g, h), the \nODFs display texture similar to the initial cold -rolled condition  (Figure 10b), with a strong \nintensity in the ND fiber  components, indicating that complete recrystallization has been \ndelayed . However, its intensity is reduced with increasing soaking time . This effect can be \nattributed to onset of recrystallization during intercritical annealing for >  1.5 s and increasing \nfraction of recrystallized grains with soaking time revealed by EBSD analysis (Figure 6, \nSection 3.3), as the initial ND fiber grains in the cold rolled steel present the higher  stored \nenergy  [54].  \nThe alpha fiber in the UFH treated material is also affected by soaking time. While a \nsignificant  fraction of gamma fiber compone nts recrystallized during UFH due to higher \nenergy stored during cold rolling  (compared to the  alpha fiber components ) [55,56] , a lower  \nfraction of alpha possesses  energy  (i.e. driving force) sufficient for recrystallization . So the \nRD fiber intensity is retained to large extent  during UFH  treatment . 23  \nFigure 10: Effect of heating rate and  soaking time on the orientation distribution function (ODF) of \nthe studied material  for φ2 =45º in the Euler space ; a) Ideal  BCC texture components for φ2 =45º in \nthe Euler space; b) ODF of t he initial cold rolled material, reproduced from [5]; c), d) and e) ODF \ncorrespond ing to the CH conditions annealed for  0.2, 1.5 and 30 s, respectively ; f), g) and h) \ncorrespond to the UFH conditions soaked  for 0.2, 1.5 and 30 s , respectively.  \n \n3.5. XRD  analysis  \nXRD measurements were carried out to analyze the evolution of retained austenite and its \ncarbon content  with soaking time . The results  are listed  in Table 3 and compared to the \nvalues obtained by TKD  (see Section 3.6). \n24 Table 3: Effect of the heating rate and soaking time on the retained austenite volume fraction and \nits carbon content  measured by XRD  and TKD  analysis . \nCondition  XRD  TKD  \n(%) % C (wt.)  (%) \nCH10 -0.2s 7.9 0.77 4.8 \nUFH800 -0.2s 6.6 0.80 8.1 \nUFH800 -1.5s 6.9 0.77 4.9 \nUFH800 -30s 5.2 0.70 4.4 \n \nAfter short annealing  (soaking for 0.2 s), the CH sample present s a higher retained austenite  \nfraction compare d to the UFH condition. The CH treatments  lead to phase fractions closer \nto the ones at the equilibrium condition since there is more time for the austenite to nucleate \nand grow  (Table 2). In the CH10 -0.2s sample, taking into account fractions of both  phases \n(i.e. retained austenite measured by XRD in Table 3 and martensite determined  by EBSD in \nTable 2), the total fraction of austenite formed during  intercritical  annealing  is close to 20 \n%. The effect of soaking time on the retained austenite volume fraction for the UFH samples \nhas two diff erent trends. For short soaking times  (0.2 s, 1.5 s) , both nucleation and growth  \nof intercritical austenite take place , as it is observed  from the martensite fraction (see Section \n3.3). The n, the  volume fraction  of austenite rises  slightly from 6.6 % to 6.9 % with increasing \ntime within  the short range  (Table 3). This effect indicates , that the nucleation stage plays a \nmore important role  compared to the growth stage , as there is a significant austenite fract ion, \nwhich retains  after rapid cooling , with a carbon concentration similar to the CH condition.  \nEventually , when  the soaking time increases up to 30 s, the austenite fraction at the peak \ntemperature increases due to the  longer  time to nucleate  and grow , as there is a significant \nfraction of ma rtensitic grains having a size below 1 µm (Figure 9), but its carbon \nconcentration decreases up to 0. 7 % reducing the amount of retained austenite down  to 5.2 \n%. \nThe volume fraction s of retained austenite m easured by XRD (Table 3) are considerably \nhigher than  the values determined  by EBSD  (Table 2). This effect is produced by the large \ndifference in the depth of the analyzed area being approximately 1 µm for XRD and 50 nm \nfor EBSD  [57]. As is well known, the metastable retained austenite  generates a local increase \nin volume during transformation into martensite [58]. As phase transformatio n on the surface \nallows an easier accommodation of  this volume change , the surface retained austenite grains 25 are more prone to phase transformation during sample preparation, that reduces the amount \nof retained austenite detected by EBSD  [57]. Meanwhile , XRD is able to detect  retained \naustenite  present in the bulk material , which has not transform ed into martensite. Moreover, \nit should be noted that although the spatial resolution of the EBSD is reaso nably high (65 \nnm in step size) , it is not sufficient for detection of the finest  austenite grains present in the \nmicrostructure , revealed by TEM analys is (see  Section 3.6). Similar conclusions were drawn  \nfor other steel grades  containing metastable austenite , such as Q&P steels in [59,60]. \n \n3.6. TEM and TKD  analysis  \nTo study the evolution of microstructure during soaking on nanoscale, TKD analysis \ncombined with TEM characterization were carried out o n CH10 -0.2s and UFH after 0.2, 1.5 \nand 30 s  samples . Figure 11 represents the phase maps of the di fferent samples analyzed by  \nTKD. They are in a good a ccordance with the outcomes of  the EBSD measurements \npresented above (see Section 3.3). Larger ferritic grains are observed in the CH10 -0.2s \nsamples ( Figure 11a) compared to those  seen in the UFH  samples  (Figure 11b, c, d). In \naddition, the CH treatment results in equiaxed ferritic grains without LAGBs in their interior \n(Figure 11a) due to the long er treatment time, while the UFH leads to an inhomogeneous \nmicrost ructure with varying  grain size  and a higher fraction of LAGB s (Figure 11b, c, d).  \nValues of retained austenite volume fraction measured by TKD are provided  in Table 3. \nThey are higher  compared to those  determined  by EBSD. This effect is caused by high er \nspatial resolution of the TKD technique, which enable s to resolve nanoscale microstructural \nconstituents having  10-30 nm in size  [27]. Discrepancies between the volume fractions of \nretained austenite determined by XRD and those  measured by TKD  should also be noted . \nUnlike in the XRD measurements , a very local area is analyzed by TKD which leads to \nstatistically insignificant data . Moreover , the TKD results highly depend on the quality of \nthe studied samples . If the electropolishing step is inhomogeneous, there are significant \ndifferences in the foil thickness t hrough the sample. If a local area is too thick , the electrons \nare unab le to pass through and reach the detector, as their initial energy is orders of \nmagnitud e less compare d to the ones generated in TEM which results in the non-indexed \nareas. Similar effect  occur s when the foil is too thin, as too many electrons cross the \nspecimen and reach  the detector [26,61] . Diffraction patterns were taken from different 26 austenitic regions observed by TKD in all samples, in order to pro ve the presence of austenite \nin the material, as it is shown in Figure 11e). \n \nFigure 11: Phase maps obtained from TKD analysis in a) CH10 -0.2s and UFH for 0.2 s (b &  c), \nand 1.5 s ( d)). Figure c) shows a detailed region in figure b).  Figure e) represents the diffraction \npattern of the austenite marked in figure d).  Ferrite is shown in red and austenite in green. HAGB s \nare represented in black and LAGB s in white. Large regions in black are areas  with a confidence \nindex (CI) l ower than 0.1 . \nFigure 12a, c, e shows  TEM images illustrating microstructure evolution during UFH \ntreatment of the steel within the non -recrystallized areas (as discussed in Sections above). \n27 Figure 12b, d, f illustrate the corresponding KAM maps of the corresponding  region s \nextract ed from the TKD analysis. Formation of dislocation walls and other configurations  is \nobserved after UFH 0.2 s treatment, which  are represented in form of lines with local \nmisorientation <  1o on KAM maps (Figure 12a, b). Dislocation w alls associated to recovery \nwere reported elsewhere [49,62] . Longer soaking time of 1.5 s  allows furthe r dislocation \nclimb and rearrangement  and onset of LAGB s formation ( Figure 12c, d). Finally, annealing \nfor 30 s results in formation of a n energetically favorable substructure in the grain interior \n(Figure 12e) with local misorientation at LAGBs reaching 4o (Figure 12f). In Figure 12e, \nf, enhanced local dislocation density and increased local misorientation are  clearly seen also \nin the ferritic matrix near the martensite/ferrite interface  (marked by white arrows ). It is \nrelated to accommodation of  the plastic micro -strain  induced by the volume expansion  due \nto the austenite/martensite transformation during rapid cooling. This observation was \nreported earlier  for DP steels [63]. 28  \nFigure 12: TEM images after UFH treatment for a) 0.2  s, c) 1.5  s and e) 30  s; KAM maps for b) \n0.2 s, d) 1.5  s and f) 30  s obtained from the TKD analysis.  White dashed arrows indicate the \nincrease in misorientation in the ferritic matrix due to the martensite formation.  (HAGBs in black, \nLAGBs in white).  \nThe outcomes of this study clearly indicate that the microstructure of the low carbon steel is \nvery sensitive to the soaking time at the peak temperature during UFH  treatment. This \nprovides an additional tool for mi crostructural design in carbon steels by manipulating also \nthe soaking time in addition to the heating rate [5] and initial microstructure [12] of steels. \n29 Grain size, volume fraction of martensite, volume fraction of non -recrystallized and \nrecrystallized ferrite can be optimized via the correct balance o f the heat treatment \nparameters, so steels with the excellent com bination of high strength and ductility can be \nmanufactured  [5]. The approach can be applied to all carbon steels.  \n \n Conclusions  \nThe effect of heating rate and soaking  time on the microstructure of the  heat-treated low \ncarbon steel was studied using SEM, E BSD, XRD, TKD and TEM techniques. The \nfollowing conclusions can be drawn.  \n1. A complex multiphase, hierarchic microstructure mainly consisting of ferritic matrix with \nembedded martensite and retained austenite is formed after all applied heat treatments. \nThere is significant effect of soaking time on the microstructure of the UFH treated steel, \nwhile it does not affect  the microstructure evolved in the CH treated material.  \n2. There is a strong effect of heating rate on the microstructure of the ferritic matrix. The \nCH treatment results in the ferritic matrix consisting  mainly of equiax ed recrystallized \ngrains  independently on the soaking time , while fine recrystallized grains and larger non -\nrecrystallized (i.e. recovered) ferritic grains are present in all UFH treated conditions . The \nfraction of recrystallized ferritic grains generally tends to increase with increasing \nsoaking time.  Combined TEM and TKD study proved directly that the recovery process \nstarts with formation of dislocation walls via dislocation climb and rearrangement , which \ngradually transform into LAGBs.  \n3. Volume fraction o f martensite tends to increase with increasing soaking time during UFH \ntreatment due to suppression of cementite spheroidization, which, in turn, reduces the \namount of energetically favorable  sites for austenite nucleation and results in longer \nsoaking tim e to reach the equilibrium at the inter -critical peak temperature.  \n4. Based on the outcomes of the XRD analysis, it is possible to conclude that UFH \ntreatments results in slightly lower amount of retained austenite compared to CH \ntreatment. The amount of reta ined austenite and carbon content therein tend to slightly \ndecrease with increasing soaking time after UFH treatment due to lower carbon gradients \nin the material before rapid cooling.  30 5. TKD analysis allows to precisely identify and analyze the retained aust enite nanograins \nand other nanoscale elements of the complex microstructure  along with the local \nmisorientations due to dislocation generation and rearrangement . \n6. TKD and TEM proved that local volume expansion due to austenite -martensite phase \ntransformation during rapid cooling induces dislocations into the ferritic grains.  \n \nAcknowledgements  \nMAVT acknowledges gratefully the financial support by IMDEA Innovation Award.  \n \nData availability statement  \nThe raw/processed data required to reproduce these findings cannot be shared at this \ntime as the data also forms part of an ongoing study.  \n \nReferences  \n[1] N. Fonstein, Advanced High Strength Sheet Steels: Physical Metallurgy, Design, \nProcessing, and Proper ties, Springer, 2015. doi:10.1007/978 -3-319-19165 -2. \n[2] T. Lolla, G. Cola, B. Narayanan, B. Alexandrov, S.S. Babu, Development of rapid \nheating and cooling (flash processing) process to produce advanced high strength steel \nmicrostructures, Mater. Sci. Tec hnol. 27 (2011) 863 –875. \ndoi:10.1179/174328409x433813.  \n[3] R.H. Petrov, J. Sidor, W.J. Kaluba, L.A.I. Kestens, Grain Refinement of a Cold Rolled \nTRIP Assisted Steel after Ultra Short Annealing, Mater. Sci. Forum. 715 –716 (2012) \n661–666. doi:10.4028/www.sci entific.net/MSF.715 -716.661.  \n[4] R.H. Petrov, J. Sidor, L.A.I. Kestens, Texture Formation in High Strength Low Alloy \nSteel Reheated with Ultrafast Heating Rates, Mater. Sci. Forum. 702 –703 (2012) 798 –\n801. doi:10.4028/www.scientific.net/MSF.702 -703.798.  \n[5] F.M. Castro Cerda, C. Goulas, I. Sabirov, S. Papaefthymiou, A. Monsalve, R.H. \nPetrov, Microstructure, texture and mechanical properties in a low carbon steel after \nultrafast heating, Mater. Sci. Eng. A. 672 (2016) 108 –120. \ndoi:10.1016/j.msea.2016.06.056.  \n[6] F.M. Castro Cerda, F. Vercruysse, T.N. Minh, L.A.I. Kestens, A. Monsalve, R.H. \nPetrov, The Effect of Heating Rate on the Recrystallization Behavior in Cold Rolled \nUltra Low Carbon Steel, Steel Res. 87 (2016) 1 –9. doi:10.1002/srin.201600351.  \n[7] F.M. Castro Cerda, I. Sabirov, C. Goulas, J. Sietsma, A. Monsalve, R.H. Petrov, \nAustenite formation in 0.2% C and 0.45% C steels under conventional and ultrafast 31 heating, Mater. Des. 116 (2017) 448 –460. doi:10.1016/j.matdes.2016.12.009.  \n[8] http://www.flas hbainite.com/, (n.d.).  \n[9] L.A.I. Kestens, A.C.D. Reis, W.J. Kaluba, Y. Houbaert, Grain Refinement and \nTexture Change in Interstitial Free Steels after Severe Rolling and Ultra -Short \nAnnealing, Mater. Sci. Forum. 467 –470 (2004) 287 –292. \ndoi:10.4028/www.sci entific.net/MSF.467 -470.287.  \n[10] V. Massardier, A. Ngansop, D. Fabrègue, S. Cazottes, J. Merlin, Ultra -rapid \nintercritical annealing to improve deep drawability of low -carbon, al -killed steels, \nMetall. Mater. Trans. A. 43 (2012) 2225 –2236. doi:10.1007/s11 661-012-1096 -6. \n[11] P. Gobernado, R.H. Petrov, L.A.I. Kestens, Recrystallized {311}(136) orientation in \nferrite steels, Scr. Mater. 66 (2012) 623 –626. doi:10.1016/j.scriptamat.2012.01.056.  \n[12] F.M. Castro Cerda, C. Goulas, I. Sabirov, L.A.I. Kestens, R.H . Petrov, The effect of \nthe pre -heating stage on the microstructure and texture of a cold rolled FeCMnAlSi \nsteel under conventional and ultrafast heating, Mater. Charact. 130 (2017) 188 –197. \ndoi:10.1016/j.matchar.2017.06.010.  \n[13] M. Ferry, D. Muljoni, D.P . Dunne, Recrystallization Kinetics of Low and Ultra Low \nCarbon Steels during High -rate Annealing, ISIJ Int. 41 (2001) 1053 –1060. \ndoi:10.2355/isijinternational.41.1053.  \n[14] M.A. Valdes -Tabernero, F. Vercruysse, I. Sabirov, R.H. Petrov, M.A. Monclús, J.M. \nMolina -Aldareguia, Effect of Ultrafast Heating on the Properties of the \nMicroconstituents in a Low -Carbon Steel, Metall. Mater. Trans. A. 49 (2018) 3145 –\n3150. doi:10.1007/s11661 -018-4658 -4. \n[15] F. Vercruysse, Third generation advanced high strength steel by ultrafast annealing, \nUniversity of Ghent, 2016.  \n[16] A. Puype, R.H. Petrov, D. De Knijf, J. Sidor, V. Vanroose, Developing of advanced \nhigh strength steel via ultrafast annealing, University of Ghent, 2014.  \n[17] L. Barbé, K. Verbeken, E. Wettinck, Effec t of the Addition of P on the Mechanical \nProperties of Low Alloyed TRIP Steels, ISIJ Int. 46 (2006) 1251 –1257. \ndoi:10.2355/isijinternational.46.1251.  \n[18] E.M. Bellhouse, J.R. McDermid, Effect of continuous galvanizing heat treatments on \nthe microstructure  and mechanical properties of high Al -low Si transformation \ninduced plasticity steels, Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 41 (2010) \n1460 –1473. doi:10.1007/s11661 -010-0185 -7. \n[19] B.C. De Cooman, Structure -properties relationship in TRIP stee ls containing carbide -\nfree bainite, Curr. Opin. Solid State Mater. Sci. 8 (2004) 285 –303. \ndoi:10.1016/j.cossms.2004.10.002.  \n[20] O. Engler, V. Randle, Introduction to texture analysis: macrostructure, microstructure \nand orientation mapping, 2nd ed., CRC Pr ess, Boca Raton, n.d.  \n[21] R.H. Petrov, L.A.I. Kestens, Advanced High -Strength Steels: Electron Backscatter \nDiffraction (EBSD), Encycl. Iron, Steel, Their Alloy. (2015) 46 –69. doi:10.1081/E -\nEISA -120050786.  \n[22] Y. Cao, H. Di, J. Zhang, J. Zhang, T. Ma, R.D.K. Mishra, An electron backscattered \ndiffraction study on the dynamic recrystallization behavior of a nickel – chromium \nalloy (800H) during hot deformation, Mater. Sci. Eng. A. 585 (2013) 71 –85. 32 doi:10.1016/j.m sea.2013.07.037.  \n[23] C.F. Jatczak, Retained Austenite and Its Measurement by X -Ray Diffraction, SAE \nTech. Pap. (1980). doi:10.4271/800426.  \n[24] N.H. van Dijk, A.M. Butt, L. Zhao, J. Sietsma, S.E. Offerman, J.P. Wright, S. van der \nZwaag, Thermal stability of retained austenite in TRIP steels studied by synchrotron \nX-ray diffraction during cooling, Acta Mater. 53 (2005) 5439 –5447. \ndoi:10.1016/j.actamat.2005.08.017.  \n[25] R.R. Keller, R.H. Geiss, Transmission EBSD from 10 nm domains in a scanning, J. \nMicrosc. 245 (2012) 245 –251. doi:10.1111/j.1365 -2818.2011.03566.x.  \n[26] P.W. Trimby, Orientation mapping of nanostructured materials using transmission \nKikuchi diffraction in the scanning electron microscope, Ultramicroscopy. 120 (2012) \n16–24. doi:10.1016/j.ultrami c.2012.06.004.  \n[27] P.W. Trimby, Y. Cao, Z. Chen, S. Han, K.J. Hemker, J. Lian, X. Liao, P. Rottmann, \nS. Samudrala, J. Sun, J.T. Wang, J. Wheeler, J.M. Cariney, Characterizing deformed \nultrafine -grained and nanocrystalline materials using transmission Kiku chi diffraction \nin a scanning electron microscope, Acta Mater. 62 (2014) 69 –80. \ndoi:10.1016/j.actamat.2013.09.026.  \n[28] N. Mortazavi, C. Geers, M. Esmaily, V. Babic, M. Sattari, K. Lindgren, P. Malmberg, \nB. Jönsson, M. Halvarsson, J.E. Svensson, I. Panas, L.G. Johansson, Interplay of \nwater and reactive elements in oxidation of alumina -forming alloys, Nat. Mater. 17 \n(2018) 610 –617. doi:10.1038/s41563 -018-0105 -6. \n[29] N. Mortazavi, M. Esmaily, M. Halvarsson, The capability of Transmission Kikuchi \nDiffraction technique for characterizing nano -grained oxide scales formed on a \nFeCrAl stainless steel, Mater. Lett. 147 (2015) 42 –45. \ndoi:10.1016/j.matlet.2015.02.008.  \n[30] D. Wang, H. Kahn, F. Ernst, A.H. Heuer, “Colossal” interstitial supersaturation in \ndelta ferrit e in stainless steels: (II) low -temperature nitridation of the 17 -7 PH alloy, \nActa Mater. 124 (2017) 237 –246. doi:10.1016/j.actamat.2016.11.004.  \n[31] C. Hofer, V. Bliznuk, A. Verdiere, R.H. Petrov, F. Winkelhofer, H. Clemens, S. \nPrimig, High -resolution cha racterization of the martensite -austenite constituent in a \ncarbide -free bainitic steel, Mater. Charact. 144 (2018) 182 –190. \ndoi:10.1016/j.matchar.2018.07.011.  \n[32] M. Kulakov, W.J. Poole, M. Militzer, The effect of the initial microstructure on \nrecrystalli zation and austenite formation in a DP600 steel, Metall. Mater. Trans. A \nPhys. Metall. Mater. Sci. 44 (2013) 3564 –3576. doi:10.1007/s11661 -013-1721 -z. \n[33] R.R. Mohanty, O.A. Girina, N.M. Fonstein, Effect of heating rate on the austenite \nformation in low -carbon high -strength steels annealed in the intercritical region, \nMetall. Mater. Trans. A. 42 (2011) 3680 –3690. doi:10.1007/s11661 -011-0753 -5. \n[34] J. Huang, W.J. Poole, M. Militzer, Austenite Formation during Intercritical \nAnnealing, Metall. Mater. Trans. A. 35 (2004) 3363 –3375. doi:10.1007/s11661 -004-\n0173 -x. \n[35] J.B. Seol, D. Raabe, P.P. Choi, Y.R. Im, C.G. Park, Atomic scale effects of alloying, \npartitioning, solute drag and austempering on the mechanical properties of high -\ncarbon bainitic –austenitic TRI P steels, Acta Mater. 60 (2012) 6183 –6199. \ndoi:10.1016/j.actamat.2012.07.064.  33 [36] V.N. Gridnev, Y.Y. Meshkov, S.P. Oshkaderov, Austenite Transformation Point in \nRapidly Heated Steel and Iron, Phys. Met. Metallogr. 18 (1964) 135 –136. \n[37] H. Li, K. Gai, L.  He, C. Zhang, H. Cui, M. Li, Non -isothermal phase -transformation \nkinetics model for evaluating the austenization of 55CrMo steel based on Johnson – \nMehl – Avrami equation, Mater. Des. 92 (2016) 731 –741. \ndoi:10.1016/j.matdes.2015.12.110.  \n[38] N. Li, J. Lin , D.S. Balint, T.A. Dean, Experimental characterisation of the effects of \nthermal conditions on austenite formation for hot stamping of boron steel, J. Mater. \nProcess. Technol. 231 (2016) 254 –264. doi:10.1016/j.jmatprotec.2015.12.008.  \n[39] W.L. Haworth, J. G. Parr, The effect of rapid heating on the alpha -gamma \ntransformation of iron, Trans AMS. 58 (1965) 476 –488. \n[40] G. Gottstein, Physical Foundations of Materials Science, 2004. doi:10.1007/978 -3-\n662-09291 -0. \n[41] A.S. Sastri, D.R.F. West, Effect of austen itizing conditions on kinetics of martensite \nformation in certain medium -alloy steels., J. Iron Steel Inst. 203 (1965) 138 –145. \n[42] A. Ankara, Strength of austenite and its effect on martensite transformation, J. Iron \nSteel Inst. 208 (1970) 819 –823. \n[43] F.M. Castro Cerda, L.A.I. Kestens, A. Monsalve, R.H. Petrov, The Effect of Ultrafast \nHeating in Cold -Rolled Low Carbon Steel: Recrystallization and Texture Evolution, \nMetals (Basel). 6 (2016) 288 –299. doi:10.3390/met6110288.  \n[44] G. Speich, A. Szirmae, M.  Richards, Formation of austenite from ferrite and ferrite -\ncarbide aggregates, Trans Aime. 245 (1969) 1063 –1073.  \n[45] J. Stockemer, P. Vanden Brande, Recrystallization of a cold -rolled low -carbon steel \nby cold -plasma -discharge rapid annealin, Metall. Mater . Trans. A. 34 (2003) 1341. \ndoi:10.1007/s11661 -003-0245 -3. \n[46] R.H. Petrov, F. HajyAkbary, J. Sidor, M.J. Santofimia, J. Sietsma, L.A.I. Kestens, \nUltra -Fast Annealing of High Strength Steel, Int. Virtual J. Mach. Technol. Mater. 8 \n(2012) 68 –71. \n[47] D. Mu ljono, M. Ferry, D.P. Dunne, Influence of heating rate on anisothermal \nrecrystallization in low and ultra -low carbon steels, Mater. Sci. Eng. A. 303 (2001) \n90–99. doi:10.1016/S0921 -5093(00)01882 -7. \n[48] T. Senuma, K. Kawasaki, Y. Takemoto, Recrystallization Behavior and Texture \nFormation of Rapidly Annealed Cold -Rolled Extralow Carbon Steel Sheets, Mater. \nTrans. 47 (2006) 1769 –1775. doi:10.2320/matertrans.47.1769.  \n[49] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phen omena, \n2004. doi:10.1016/B978 -008044164 -1/50015 -3. \n[50] G.S. Rohrer, Introduction to Grains, Phases, and Interfaces - an Interpretation of \nMicrostructures, Trans Aime. 175 (1948) 15 –51. doi:10.1007/s11661 -010-0215 -5. \n[51] V. Massardier, A. Ngansop, D. Fabr ègue, J. Merlin, J. Capelle, F. V. Cedex, \nMicrostructure and mechanical properties of low carbon Al -killed steels after ultra -\nrapid annealing cycles, Mater. Sci. Forum. 642 (2010) 3368 –3373. \ndoi:10.4028/www.scientific.net/MSF.638 -642.3368.  \n[52] B. Hutchins on, Development and control of annealing textures in low -carbon steels, \nInt. Met. Rev. 29 (1984) 25 –42. doi:10.1179/imtr.1984.29.1.25.  34 [53] R.K. Ray, J.J. Jonas, R.E. Hook, Cold rolling and annealing textures i~ low carbon \nand extra low carbon steels, Int.  Met. Rev. 39 (1994) 129 –1720. \ndoi:10.1179/imr.1994.39.4.129.  \n[54] I.L. Dillamore, P.L. Morris, C.J.E. Smith, B. Hutchinson, Transition Bands and \nRecrystallization in Metals, Procedings R. Soc. London A. 329 (1972) 405 –420. \ndoi:10.1098/rspa.1972.0120.  \n[55] I. Samajdar, B. Verlinden, P. Van Houtte, D. Vanderschueren, γ -Fibre \nrecrystallization texture in IF -steel: an investigation on the recrystallization \nmechanisms, Mater. Sci. Eng. A. 238 (1997) 343 –350. doi:10.1016/S0921 -\n5093(97)00455 -3. \n[56] J. Kang, B.  Bacroix, H. Réglé, K.H. Oh, H. Lee, Effect of deformation mode and grain \norientation on misorientation development in a body -centered cubic steel, Acta Mater. \n55 (2007) 4935 –4946. doi:10.1016/j.actamat.2007.05.014.  \n[57] G.K. Tirumalasetty, M.A. van Huis, C. Kwakernaak, J. Sietsma, W.G. Sloof, H.W. \nZandbergen, Deformation -induced austenite grain rotation and transformation in \nTRIP -assisted steel, Acta Mater. 60 (2012) 1311 –1321. \ndoi:10.1016/j.actamat.2011.11.026.  \n[58] P.G. Xu, Y. Tomota, Y. Arakaki, S. Harj o, H. Sueyoshi, Evaluation of austenite \nvolume fraction in TRIP steel sheets using neutron diffraction, Mater. Charact. 127 \n(2017) 104 –110. doi:10.1016/j.matchar.2017.02.028.  \n[59] I. De Diego -Calderón, D. De Knijf, J.M. Molina -Aldareguia, I. Sabirov, C. Fö jer, \nR.H. Petrov, Effect of Q&P parameters on microstructure development and \nmechanical behaviour of Q&P steels, Rev. Met. Rev. Metal. 51 (2015) 34 –8570. \ndoi:10.3989/revmetalm.035.  \n[60] D. De Knijf, R.H. Petrov, C. Föjer, L.A.I. Kestens, Effect of fresh ma rtensite on the \nstability of retained austenite in quenching and partitioning steel, Mater. Sci. Eng. A. \n615 (2014) 107 –115. doi:10.1016/j.msea.2014.07.054.  \n[61] S. Suzuki, Features of Transmission EBSD and its Application, J. Minearls, Met. \nMater. Soc. 65  (2013) 1254 –1263. doi:10.1007/s11837 -013-0700 -6. \n[62] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D. Juul Jensen, M.E. \nKassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Current issues in \nrecrystallization: A review, Mater. Sci. Eng . A. 238 (1997) 219 –274. \ndoi:10.1016/S0921 -5093(97)00424 -3. \n[63] M. Calcagnotto, D. Ponge, E. Demir, D. Raabe, Orientation gradients and \ngeometrically necessary dislocations in ultrafine grained dual -phase steels studied by \n2D and 3D EBSD, Mater. Sci. Eng.  A. 527 (2010) 2738 –2746. \ndoi:10.1016/j.msea.2010.01.004.  \n "    },    {        "title": "1801.01266v1.Properties_of_polycrystalline_nanoparticles_with_uniaxial_and_cubic_types_of_magnetic_anisotropy_of_individual_grains.pdf",        "content": "Properties of polycrystalline nanopart icles with uniaxial and cubic types \nof magnetic anisotropy of individual grains \n \nV. A. Bautin1, A. G. Seferyan1, M. S. Nesmeyanov3 and N. A. Usov1,2,3\n \n1National University of Science and Tec hnology «MISiS», 119049, Moscow, Russia \n2Pushkov Institute of Terrestrial Magnetis m, Ionosphere and Radio Wave Propagation,  Russian Academy of Sciences, IZMIRAN, \n142190, Troitsk, Moscow, Russia \n3National Research Nuclear Unive rsity “MEPhI”, 115409, Moscow, Russia \nAbstract \n \nThe influence of the crystal structure inhomogeneitie s on the magnetic properties of cobalt nanoparticles \nwith different aspect ratio and spherical nanopartic les of chromium dioxide, cobalt ferrite and magnetite \nhas been studied by means of numerical simulation. The polycrystalline nanoparticles are modeled by \nmeans of subdivision of the nanoparticle volume into tightly bound single-crystal granules with randomly \ndistributed directions of the easy anisotropy axes. The probability of appearance of quasi uniform and \nvortex states in sufficiently large assemblies of polycrystalline nanoparticles of various types have been calculated depending on the nanoparticle diameter. It is shown that the subdivision of a nanoparticle into \nsingle-crystal granules with different orientations of the easy anisotropy axes substantially reduces the \neffective single-domain diameters for particles with uniaxial type of anisotropy of individual granules. However, for particles with cubic type of magnetic anisotropy the influence of the crystal structure \ninhomogeneities on the equilibrium properties of the particles is not so important even for magnetically \nhard cobalt ferrite nanoparticles. It is practically absent for magnetically soft magnetite nanoparticles. \n \nPACS  75.20.-g; 75.50.Tt; 75.40.Mg \n \nKeywords:   Polycrystalline magnetic nanoparticles, Magnetic anis otropy, Single-domain diameter, Numerical simulation  \n \n \nI. INTRODUCTION \n \nMagnetic nanoparticle assemblies are promising for \nvarious technological and biomedical applications, in particular for magnetic resonance imaging contrast \nenhancement, targeted drug delivery and magnetic \nhyperthermia [1-3]. However, in order to fully understand the magnetic properties of nanoparticles, \ndetailed experimental information on the particle crystal \nstructure is important. Are the magnetic particles single-crystal or do they consist of a set of several \nmonocrystalline grains? In the latter case what the \naverage size of the monocrystalline granules is? What are the type of magnetic anisotropy and the direction of \nthe easy anisotropy axes of individual granules in this \nnanoparticle? Such detailed information is available in some cases for very small nanoparticles with dimensions \non the order of several nanometers [4,5]. But for \nmagnetic nanoparticles of larger sizes experimental \ninformation on the particle crystal structure is scarce. It \nis usually tacitly assumed that magnetic nanoparticles with dimensions on the order of several tens of \nnanometers, which are used in particular in biomedical \napplications [2,3], are monocrystalline. However, it does remain unclear why the properties of these nanoparticles, \nfor example, the saturation magnetization, the magnetic \nanisotropy constants, etc. differ substantially from the corresponding bulk values. \nMeanwhile, the formation of polycrystalline \nparticles in the course of chemical reactions is quite likely [6], if the growth of large nanoparticles occurs as a \nresult of the coalescence of single-crystal nuclei. It has been found recently, that monodisperse iron oxide \nnanoparticles of sufficiently large sizes prepared by \nthermal decomposition of organometallic precursors [7] \nor other methods [8-11] may have complicated \ncrystalline structure. Multi-core nanoparticles [12,13] consisting of monocrystalline magnetic grains can also \nbe considered as polycrysta lline nanoparticles if there is \nexchange interaction of ap preciable value between the \nconstituting grains.  \nIt should be noted that now, due to a significant \nincrease in computer perfor mance, numerical modeling \nmakes it possible to study the equilibrium and kinetic \nproperties of magnetic nanoparticles in all details. \nSingle-domain diameters of different types of magnetic particles can be obtained both with the help of analytical \nestimates [14-18] and using numerical modeling [18-24]. \nIt was shown in particular [23] that effective single-domain diameters of non ellipsoidal nanoparticles, such \nas cube or cylinder, do not differ considerably from \nsingle-domain diameter of an ellipsoid of a proper shape. \nAt the same time, the experi mental values for single-\ndomain diameters of various magnetic nanoparticles, \ntheir dependence on the particle shape, possible \ncomposition variations, crys tal structure, etc., are \npractically unknown. \nInvestigation of the effect of the crystal structure \nheterogeneities on the equilibrium magnetic properties of \nnanoparticles is important also for understanding the behavior of nanoparticles in a quasistatic and alternating \nmagnetic field. Recently [25] , the magnetic properties of \npolycrystalline cobalt nanoparticles of spherical shape \nhave been studied theoretically. In this paper, single-\n 1domain diameters for oblate and elongated single-crystal \ncobalt particles, as well as for spherical nanoparticles of \nchromium dioxide, cobalt ferrite, and magnetite are \ndetermined using numerical simulation. Particles of cobalt and chromium dioxide have uniaxial type of \nmagnetic anisotropy, whereas particles of cobalt ferrite \nand magnetite belong to the cubic type of anisotropy, with a different number of equivalent directions of the \neasy anisotropy axes. In addition, the nanoparticles \nstudied have different magnetic hardness. The latter is characterized by a di mensionless parameter \nK M N ps z22=  [14,17,18], where Nz is the \ndemagnetizing factor of the spheroidal particle along the \nsymmetry axis, Ms is the saturation magnetization, and K \nis the absolute value of the particle anisotropy constant. \nAnalogous calculations have  been also carried out \nfor assemblies of polycrystalline nanoparticles of the \nsame compositions, with different amounts of single-crystal granules in the particle volume. In the absence of \nmore specific information, it is assumed that the easy \nanisotropy axes in various single-crystal granules of a polycrystalline nanoparticle are randomly oriented. It is \nshown that for polycrystalline nanoparticles with \nuniaxial anisotropy the effec tive single-domain diameter \nD\nc,ef is significantly reduced in comparison with that of \nmonocrystalline nanoparticle, Dc0. The difference \nbetween these diameters in creases with increasing \nmagnetic hardness of the nanoparticle, that is, with a decrease in the parameter p. On the other hand, for \nnanoparticles with a cubic type of magnetic anisotropy, a \ndecrease in the effective single-domain diameter was \nobtained only for magnetically hard nanoparticles of cobalt ferrite. It has been found that the diameters D\nc,ef \nand Dc0 coincide for magnetically soft magnetite \nnanoparticles. \n \nII. Numerical simulation \n \nDynamics of the unit magnetization vector ()rrrα  \nof a polycrystalline nanoparticle is described by the \nLandau – Lifshitz - Gilbert (LLG) equation [14,17] \n() ⎟⎠⎞⎜⎝⎛\n∂∂× + × − =∂∂\ntHtefαα κ α γαrrrrr\n, (1)  \nwhere γ is the gyromagnetic ratio  and κ is the \nphenomenological damping constant. The effective \nmagnetic field acting on the unit magnetization \nvector can be calculated as  a derivative of the total \nnanoparticle energy W [14]  efHr\nαrr\n∂∂− =\nsefVMWH ; \n H MwC H Msa\nef s′+ − Δ =r\nrr r\nα ∂∂α  .  (2) \nHere V is the nanoparticle volume, Ms is the \nsaturation magnetization, C = 2 A is the exchange \nconstant, ()αr\naw  is the magneto-crystalline anisotropy \nenergy density, and H′r\n is the demagnetizing field.  For numerical simulation a nanoparticle is \napproximated by a set of small ferromagnetic cubes of \nside b much smaller than the exchange \nlength,s ex M C L= , of the ferromagnetic material. \nTypically, several thousands of numerical cells, N ~ 103 \n– 104, are necessary to appr oximate with sufficient \naccuracy stationary magnetization distributions in \nnanoparticle volume. The equilibrium micromagnetic \nconfigurations in the nanoparticles studied were \ncalculated starting from arbitrary initial micromagnetic \nstate, the magnetic damping parameter being κ = 0.5. In \naccordance with the Eq. (1), the final magnetization state \nis assumed to be stable under the condition \n \n()[ ]6\n, , 1 10 max−\n≤ ≤ < ×i ef i ef i N iH Hrrrα ,  (3) \nwhere iαr and i efH,r\n are the unit magnetization vector \nand effective magnetic field in the i-th numerical cell, \nrespectively. \nTo simulate a distribution of the easy anisotropy \naxes in a polycrystalline magnetic nanoparticle, we first \nselect randomly within a particle volume several seed \ncells, Ng = 4 - 16, which serve as the nuclei of the \nmonocrystalline grains to be constructed. Then we \nconsistently attach the closest numerical cells to every \nembryo until all available numerical cells are connected \nto one of the growing grains . Using such an algorithm \none can generate within the nanoparticle volume the \ndisjoint continuous areas representing the \nmonocrystalline grains of a polycrystalline nanoparticle. \nInterestingly, this algorithm leads to the partition of the \nparticle volume into Ng grains of similar volume. Other \npartitioning algorithms that have been tried lead to similar results.  \nThe directions of the easy anisotropy axes in the \ncrystallites created in such a manner were selected randomly. For a nanoparticle with uniaxial magnetic \nanisotropy the magneto-crystalline anisotropy energy density of the j -th monocrystalline grain is given by  \n \n()()2\n, 1j j a n K wrrα− = ,  j = 1,2, .. N g, (4a) \nwhere K is the uniaxial anisotropy constant and nj is the \nunit vector parallel to the easy anisotropy axis of the given grain. For a nanoparticle with cubic anisotropy the corresponding expression reads  \n \n()()( ) ( )( ) () ( )2\n32\n22\n32\n12\n22\n1 , j j j j j j с j a e e e e e e K wrrrrrrrrrrrrα α α α α α+ + =\n            ( 4 b )  \n \nHere Kc is the cubic magnetic anisotropy constant, \nand ( e1j, e2j, e3j) is a set of orthogonal unit vectors that \ndetermine an orientation of j-th monocrystalline grain of \nthe nanoparticle. One may hope that this numerical model is capable to describe the distribution of the easy \nanisotropy axes in real polycrystalline nanoparticles \ncreated as a result of the coalescence of monocrystalline \nembryos originally formed by  a chemical reaction in a \nsolution [6]. \nFig. 1 shows typical examples of a random \npartitioning of a quasi-spherical nanoparticle into \ndifferent numbers Ng = 4, 8, 16 monocrystalline granules  \n 2 \n \nFig. 1. Examples of a random partition of a spherical \nnanoparticle into 4 (a), 8 (b) and 16 (c) single crystal \ngrains, respectively. \n \nof approximately equal volume obtained by the algorithm described above. It is assumed that the type of the magnetic anisotropy in all granules of the given \nmagnetic nanoparticle is the same. However, as we \nmentioned above the easy anisotropy axes are randomly oriented in different granules of a polycrystalline \nnanoparticle. \nWhen a subdivision of a particle of a given \ndiameter into monocrystallin e granules is carried out, \nand the directions of the easy anisotropy axes are \nassigned to each numerical cell, the stationary \nmagnetization distributions existing in a given \nnanoparticle can be obtained by solving the dynamic LLG Eq. (1). The calculations show that for a given \npolycrystalline nanoparticle in the range of diameters \nstudied only one or two stable stationary micromagnetic states usually exist. They ar e a quasi-uniform state with \naverage magnetization close to the saturation magnetization, and a vortex with relatively small remanent magnetization. In this paper, for each \nnanoparticle of the given type and geometry, a \nsufficiently large number of independent random particle partitions with the fixed number N\ng of monocrystalline \ngranules was generated. Then, for this assembly of polycrystalline nanoparticles the average energy and average magnetization of low-lying micromagnetic states \nwere calculated. \n \nTable. 1. Magnetic parameters of the nanoparticles \nstudied [26,27]. \n \n Ms, \nemu/cm3A, erg/cm K, erg/cm3Lex, \nnm \nCo 1400  1.3×10-6  4.3×106  11.5 \nCrO 2 490  4.37×10-7  3.0×105  19.1 \nCoFe 2O4 420  1.5×10-62.0×106  41.2 \nFe3O4 480 1.0×10-6-1.0×105  29.5 \n \nThe material parameters of various types of the \nnanoparticles studied are given in Table 1. In order to \ninvestigate the effect of comp licated crystal structure on \nthe particle magnetic proper ties, the nanoparticles of \nboth uniaxial (Co, CrO 2) and cubic (CoFe 2O4, Fe 3O4) \ntypes of magnetic anisotropy were considered.  \n III. Results and discussion  \n \nLet us consider the results of numerical simulation \nobtained for polycrystalline magnetic nanoparticles listed in Table 1, in comparison with the properties of \nmonocrystalline nanoparticles of the same composition. \n \nCobalt nanoparticles  \nThe magnetic properties of spherical polycrystalline \ncobalt nanoparticles have been studied in Ref. 25. Meanwhile, in the experiment cobalt nanoparticles of various shapes can be found. Therefore, in this paper \noblate and elongated spheroidal cobalt nanoparticles with \naspect ratios D\nz/D = 2/3 and 3/2, respectively, were also \nstudied for completeness. Here Dz and D are the \nlongitudinal and transverse diameters of a spheroid, respectively. It is assumed that monocrystalline cobalt granules have a hexagonal crystal structure, so that the \nenergy density of magnetic anisotropy of individual \ncobalt granules is given by Eq. (4a) with the \ncorresponding uniaxial anisotropy constant, K = 4.3×10\n6 \nerg/cm3. \n \n \n \nFig. 2. Stationary magnetization distributions in \npolycrystalline cobalt nanoparticles of different \ndiameters with various aspect ratios: a), b), c) Dz/D = \n2/3; d, e) D z/D = 1.5.  \n \nFigs. 2a - 2c show the calculated numerically \nstationary magnetization distributions in polycrystalline \ncobalt nanoparticles with the aspect ratio Dz/D = 2/3. Fig. \n2a shows a quasi-uniform state in a particle with a transverse diameter D = 24 nm. Figs. 2b and 2c show \nvortex states with different directions of the vortex axis \nin particles with diameters D = 56 nm, and D = 44 nm, \nrespectively. Figs. 2d and 2e show the quasi-uniform and vortex states in cobalt nanoparticles with the aspect ratio D\nz/D = 1.5 and with transverse diameters D = 20 nm, and \nD = 32 nm, respectively. It is worth of mentioning that \nthe structures of the quasi-uni form and vortex states in \npolycrystalline nanoparticles are close to analogous \nmagnetization distributions in monocrystalline cobalt \nparticles. However, in polycrystalline particles the directions of the average magnetization of the quasi-\nuniform state, as well as the vortex axis directions \ndepend on the specific distribution of monocrystalline grains over the nanoparticle volume. In addition, the total \nenergies of the stationary states for polycrystalline \nparticles can differ significantly from that for monocrystalline particles of the same geometry. \n \n 324 32 40 48 56 643.54.04.55.05.56.0 6\n543\n2\n  Total energy (106 erg/cm3)\nParticle diameter (nm)1\nDc0 = 41 nmDz/D = 2/3\n(a)\n  \n24 32 40 48 56 640.20.40.60.81.0\nDz/D = 2/3\n(b)PolyCryst\nparticles\n654\n321\n  Me/Ms\nParticle diameter (nm)MonoCrystparticles\n \n \nFig. 3. a) Energy diagram of stationary micromagnetic \nstates in oblate cobalt nanoparticles; b) the total reduced magnetic moment of various states as a function of the \ntransverse diameter D. Curves 1-3 and curves 4 to 6 \ncorrespond to polycrystalline a nd single crystal particles, \nrespectively. \n \nFig. 3a shows the energy diagram of stationary \nmicromagnetic states in monocrystalline and \npolycrystalline cobalt nanoparticles with the aspect ratio D\nz/D = 2/3. Curves 4 - 6 in Fig. 3a correspond to the case \nof a monocrystalline cobalt nanoparticle with easy anisotropy axis parallel to the short diameter of the spheroid, D\nz. In this nanoparticle for all investigated \ndiameters there is a stable uniform state with a magnetization parallel to the easy anisotropy axis (curve 4). The vortex state with the vortex axis oriented \nperpendicular to the easy anisotropy axis competes in energy with the uniform magnetization, (curve 5 in Fig. 3a). Curve 6 in Fig. 3a shows the energy of the vortex \nwhose axis is oriented parallel to the easy anisotropy \naxis. The intersection of the curves 4 and 5 in Fig. 3a determines the single-domain diameter, D\nc0 = 41 nm, of \nthe oblate monocrystalline cobalt nanoparticle with aspect ratio D\nz/D = 2/3. For the oblate particle the \ntransverse vortex remains stable in the range of \ndiameters D ≥ 40 nm. \nCurves 1-3 in Fig. 3a show  the average energies of \nstationary micromagnetic states in assemblies of \npolycrystalline oblate nanoparticles with different amounts of crystalline granules, namely, Ng = 4 for curve \n1, Ng = 8 for curve 2, and Ng = 16 for curve 3, \nrespectively. To obtain statistically reliable results, curves 1-3 were obtained by averaging over 200 – 250 independent realizations of polycrystalline oblate \nnanoparticles of fixed diameter in the range of sizes 24 \nnm ≤ D ≤ 60 nm. The dependence of the average reduced \nmagnetic moment of oblate cobalt nanoparticles on the \ntransverse particle diameter is shown in Fig. 3b. Curves 4 \nand 5 in Fig. 3b give the magnetization of a \nmonocrystalline cobalt nanoparticle in uniform and \ntransverse vortex states, re spectively, Curves 1- 3 \ncorrespond to polycrystalline nanoparticles with various \nnumber of granules N\ng = 4, 8 and 16, correspondingly.  \nComparing the curves 1-3 in Fig. 3a and 3b, one \ncan conclude that the stationary states in polycrystalline particles with the smallest number of granules, N\ng = 4, \n(curves 1), have the smallest average energy and, at the \nsame time, the largest average magnetic moment. With an increase in th e number of granules in the \npolycrystalline nanoparticle, the average particle energy \nincreases, whereas average magnetic moment decreases. \nThis effect is a direct conse quence of a subdivision of the \nnanoparticle volume into the domains with different directions of the easy anisotropy axes. \nThe calculations show that only quasi- uniform \nstates with a reduced magnetic moment M e/Ms > 0.9 are \nrealized for oblate polycrystalline cobalt nanoparticles \nwith diameters D ≤ 28 nm, and only vortex states are \nrealized in the range of diameters D ≥ 52 nm. In the \nintermediate range of sizes, 28 nm  < D < 52 nm, both \nvortex and quasi- uniform micromagnetic states can be \nfound in oblate polycrystallin e nanoparticles.  Based on \nthe results obtained, one can conclude that in oblate \npolycrystalline cobalt nanopa rticles quasi- uniform \nmicromagnetic states arise in the interval of transverse \ndiameters D ≤ 28 nm, regardless of the number of \nmonocrystalline granules in the particle. Accordingly, \nthe value Dc,ef = 28 nm can be taken as the effective \nsingle-domain diameter of the polycrystalline cobalt nanoparticle with aspect ratio D\nz/D = 2/3. The latter is \nthus much smaller than the single-domain diameter,  Dc0 \n= 41 nm, of the oblate monocrystalline cobalt nanoparticle. \nFig. 4 shows the probability of the appearance of \nstationary micromagnetic states with different average magnetization, M\ne/Ms, for oblate polycrystalline cobalt \nnanoparticles in the intermediate range of diameters. As \nFig. 4a demonstrates, for particles with diameter  \n \n0 . 00 . 20 . 40 . 60 . 81 . 00.000.070.140.210.280.35\nD = 32 nm\n  Probability\nMe/Ms(a)\n0 . 20 . 40 . 60 . 81 . 0(c)\n  \nMe/MsD = 48 nm\n0 . 20 . 40 . 60 . 81 . 0(b)\nD = 40 nm\n  \nMe/Ms  \n \nFig. 4. The probability of the appearance of stationary \nmicromagnetic states with different mean magnetization in polycrystalline oblate cobalt nanoparticles of various \ntransverse diameters.  \n 4D = 32 nm, close to the effective single-domain diameter \nDc,ef = 28 nm, a significant fraction of the stationary \nstates still have large average magnetic moments, Me/Ms \n≥ 0.8. For nanoparticles with diameter D = 40 nm (see \nFig. 4b), near the middle of the intermediate range of \ndiameters, the probability of appearance of the vortex \nstates with reduced remanent magnetization Me/Ms = 0.3 \n– 0.5 is nearly the same as for quasi uniform states. \nFinally, as Fig. 4c shows, for nanoparticles with diameter \nD = 48 nm the majority of the stationary micromagnetic \nstates are vortices with reduced remanent magnetization \nMe/Ms = 0.2 – 0.4. These probabilities are calculated for \nan assembly of 200 polycrystalline nanoparticles consisting of N\ng = 4 monocrystalline grains for each \ntransverse diameter studied. Similar results are obtained \nalso for assemblies of oblate polycrystalline cobalt nanoparticles consisting of N\ng = 8 and 16 \nmonocrystalline grains, respectively. \nFig. 5a shows the energy diagram of stationary \nmicromagnetic states of elongated monocrystalline and polycrystalline cobalt nanoparticles with aspect ratio \nD\nz/D = 1.5. Fig. 5b shows the total reduced magnetic \nmoment of these nanoparticles as a function of transverse diameter D. Curves 1-3 correspond to polycrystalline \nelongated nanoparticles with different amounts of single \ncrystal grains. Curve 4 corresponds to a uniform state in  \n20 30 40 50 60 70 802345\n  Total energy (106 erg/cm3)\nParticle diameter (nm)Dc0 = 56 nm123\n4\n5\n(a)Dz/D = 1.51)  Ng = 4\n2)  Ng = 8\n3)  Ng = 16\n \n20 30 40 50 60 70 800.00.20.40.60.81.0\n1)  Ng = 4\n2)  Ng = 8\n3)  Ng = 16Dz/D = 1.5\n(b)\n  Me/Ms\nParticle diameter (nm)MonoCryst\nparticles\nPolyCrystparticles1\n2\n3\n54\n \n \nFig. 5. a) Energy diagram of stationary micromagnetic \nstates in elongated cobalt nanoparticles with aspect ratio \nDz/D = 1.5; b) the total reduced magnetic moment as a \nfunction of the transverse diameter D. Curves 1-3 and \ncurves 4, 5 correspond to polycrystalline and single crystal particles, respectively. a monocrystalline cobalt nanoparticle with an easy anisotropy axis parallel to particle symmetry axis. Curve \n5 corresponds to the vortex with the vortex axis parallel \nto the easy anisotropy axis. As can be seen in Fig. 5a, the single-domain diameter of an elongated monocrystalline \ncobalt nanoparticle with aspect ratio D\nz/D = 1.5 equals \nDc0 = 56 nm. The vortex state in this nanoparticle is \nstable at D ≥ 36 nm. \nDetailed calculations carried out for polycrystalline \ncobalt nanoparticles with aspect ratio Dz/D = 1.5 in the \nrange of transverse diameters 20 nm  ≤ D ≤ 64 nm \nshowed that only quasi-uniform states with reduced \nmagnetic moment close to unity exist in the interval D ≤ \n24 nm, whereas in the range of transverse diameters D ≥ \n44 nm only vortex states are realized. In the intermediate \nrange of diameters, 24 nm  < D < 44 nm, in elongated \npolycrystalline cobalt nanoparticles both vortex and quasi uniform micromagnetic states can be found. Thus, \nthe value D\nc,ef = 24 nm can be taken as the effective \nsingle-domain diameter of polycrystalline cobalt \nnanoparticle with aspect ratio Dz/D = 1.5. \n \nChromium dioxide \nSimilar calculations have been made for spherical \nchromium dioxide nanoparticles with uniaxial type of \nmagnetic anisotropy,  \n30 45 60 75 90 105 1203.003.754.505.256.006.751)  Ng = 4\n2)  Ng = 8\n3)  Ng = 16\n(a)\n  Total energy ( 105 erg/cm3)\nParticle diameter (nm)Dc0 = 60nm123\n4\n5\n \n30 45 60 75 90 105 1200.20.40.60.81.0\n(b)1)  Ng = 4\n2)  Ng = 8\n3)  Ng = 16\n  Me/Ms\nParticle diameter (nm)MonoCryst\nparticlesPolyCrystparticles1\n23\n54\n \nFig. 6. a) Energy diagram of stationary micromagnetic \nstates in chromium dioxide nanoparticles; b) the total \nreduced magnetic moment as a function of particle diameter. Curves 1-3 correspond to polycrystalline \nnanoparticles, and curves 4, 5 to monocrystalline ones, \nrespectively. \n 5but much lower saturation magnetization than that of \ncobalt. \nAs can be seen in Fig. 6a, for a monocrystalline \nparticle of chromium dioxide the single-domain diameter is given by D\nc0 = 60 nm. The calculations of stationary \nmagnetization distributions for polycrystalline chromium dioxide nanoparticles were carried out in the interval of \ndiameters 40 nm  ≤ D ≤ 120 nm. It was found that only \nquasi-uniform states are realized in the range of \ndiameters D ≤ 44 nm, and only vortices exist for D ≥ 60 \nnm. In the transition region, 44 nm < D < 60 nm, both \nvortices and quasi uniform magnetization distributions \nare realized with various probabilities. Based on these \ncalculations, the effective single-domain diameter of \npolycrystalline chromium dioxide nanoparticles was \ndetermined to be D\nc,ef = 44 nm. \n \nCobalt ferrite  \nTo investigate the effect of the type of magnetic \nanisotropy on the magnetic properties of polycrystalline \nnanoparticles, spherical nanop articles of cobalt ferrite, \nwith positive cubic anisotropy constant, Kc = 2.0×106 \nerg/cm3, were considered. \n60 80 100 120 140 1602.03.55.06.58.0\n1)  Ng = 4\n2)  Ng = 8\n3)  Ng = 16\n(a)\nTotal energy (105 erg/cm3)\nParticle diameter (nm)Dc0 = 140 nm123\n4\n5\n \n \n \nFig. 7. a) Energy diagram of stationary micromagnetic \nstates in monocrystalline and polycrystalline cobalt \nferrite nanoparticles; b) – e) probability of the appearance of stationary micromagnetic states with \ndifferent mean magnetization in polycrystalline cobalt \nferrite nanoparticles of various transverse diameters.  Consequently, monocrystalline cobalt ferrite granules have 6 equivalent directions of the easy anisotropy axis. \nThe energy density of magnetic anisotropy of individual \ncobalt ferrite grain is given by Eq. (4b). \nAs Fig. 7a shows, for a monocrystalline cobalt \nferrite nanoparticle the single-domain diameter is given by D\nc0 = 140 nm. The calculations of stationary \nmagnetization distributions for polycrystalline cobalt \nferrite nanoparticles were carried out in the interval of \ndiameters 60 nm  ≤ D ≤ 150 nm. In Figs. 7b - 7e the \nprobabilities of the appearance of stationary \nmicromagnetic states with different mean magnetization \nare shown for polycrystalline cobalt ferrite nanoparticles \nof various diameters consisting of Ng = 4 \nmonocrystalline grains. One can see that for \npolycrystalline cobalt ferrite nanoparticles with diameter \nD = 110 nm most of the stationary micromagnetic states \nhave large average magnetization, Me/Ms > 0.9. The \nsame is true for nanoparticles with diameters D < 110 \nnm. On the other hand, for nanoparticles with diameter D \n≥ 120 the probability of appearance of non-uniform \nmicromagnetic state with average magnetization, Me/Ms \n~ 0.5, increases gradually as a function of the particle diameter. One can conclude safely, that the lower bound for the effective single-domain diameter of \npolycrystalline cobalt ferrite nanoparticles is given by \nD\nc,ef = 110 nm.  \n \nMagnetite \nThe magnetic properties of polycrystalline \nmagnetite nanoparticles are par ticularly interesting, since \nmagnetite nanoparticles are widely used in biomedicine [1-3]. Magnetite nanoparticles also have cubic type of \nmagnetic anisotropy. But unlike cobalt ferrite, the cubic \nanisotropy constant for magnetite is negative, K\nc = - \n1.0×105 erg/cm3. As a result, monocrystalline magnetite \ngranules have 8 equivalent directions of the easy anisotropy axis. Fig. 8 shows the energy of stationary \nmicromagnetic states calculated for spherical \nmonocrystalline and polycrystalline magnetite nanoparticles with different amounts of crystalline \ngranules in the range of diameters 32 nm  ≤ D ≤ 96 nm.  \n30 45 60 75 90 105 1202.02.53.03.54.04.55.01)  Ng = 4\n2)  Ng = 8\n3)  Ng = 16\n  Total energy (105 erg/cm3)\nParticle diameter (nm)123\n4\n5\nDc0 = 64 nm\n \n \nFig. 8. Energy diagram of stationary micromagnetic \nstates in spherical polycrystalline (curves 1-3) and monocrystalline (curves 4, 5) magnetite nanoparticles. \n 6As can be seen in this figu re, the effect of complicated \ncrystal structure on the properties of magnetite \nnanoparticles is insignificant. In particular, single-\ndomain diameters for monocrystalline and polycrystalline magnetite nanoparticles coincide, D\nc0 = \nDc,ef = 64 nm. \nIn Table 2 we present the calculated single-domain \ndiameters, Dc0, of the monocrystalline nanoparticles \nstudied in comparison with the effective single-domain diameters of the polycrystalline ones, D\nc,ef. In addition, \nthe values of the parameter K M N ps z22= , which \ncharacterizes the magnetic hardness of the nanoparticles, are also given in Table 2. Note, that one has p >> 1 and p \n< 1 for particles of soft and hard magnetic types, respectively. First of all, one can see that a noticeable difference between the D\nc0 and Dc,ef  values exists for \nmagnetic nanoparticles with uniaxial type of magnetic anisotropy. Furthermore, this  difference increases with \nincreasing of magnetic hardness of the nanoparticle. The \ngreatest difference between the D\nc0 and Dc,ef diameters \nwas obtained for elongated cobalt nanoparticles with p  = \n0.667. On the other hand, for nanoparticles with cubic anisotropy, relatively small difference in D\nc0 and Dc,ef \ndiameters exists only for cobalt ferrite nanoparticles with a small parameter p = 0.185. For magnetically soft \nmagnetite nanoparticles the single-domain diameters D\nc0 \nand Dc,ef coincide. Obviously, the individual \nmonocrystalline grains with cubic anisotropy have a \nlarge number of equivalent directions of the easy \nanisotropy axis. Therefore, for polycrystalline \nnanoparticle with cubic anisotorpy the probability to get \nan inhomogeneous distribution of easy anisotropy axes over the particle volume is much smaller than for \nparticles with uniaxial type of magnetic anisotropy. As a \nresult, some difference between the D\nc0 and Dc,ef values \nfor polycrystalline nanoparticle with cubic anisotropy \nappears only for small values of parameter p. This gives \na qualitative physical explanation for the results of the \nnumerical simulation presented in Table 2. \n \nTable. 2. The calculated single-domain diameters for \nmono and polycrystalline magnetic nanoparticles. \n \n Dz/D p Dc0, \nnm Dc,ef, \nnm Anisotropy \ntype \nCo 2/3 1.277 41 28 Uniaxial \nCo 1 0.955 45[25] 24[25] Uniaxial  \nCo 1.5 0.667 56 24 Uniaxial \nCrO 2 1 1.676 60 44 Uniaxial \nCoFe 2O4 1 0.185 140 110 Cubic \nFe3O4 1 4.825 64 64 Cubic \n \nIV. Conclusions  \n \nIn this paper the influence of the crystal structure \nheterogeneities on the equilibrium magnetic properties of \ncobalt nanoparticles with different aspect ratio and \nspherical nanoparticles of chromium dioxide, cobalt ferrite and magnetite has been studied using numerical \nsimulation. The nanoparticles studied possess both uniaxial and cubic types of magnetic anisotropy and have \ndifferent magnetic hardness. For monocrystalline \nnanoparticles of these types the single-domain diameters \nD\nc0 have been determined comparing the total energies \nof quasi-uniform and vortex micromagnetic states. The \npolycrystalline nanoparticles are modeled by means of \nsubdivision of the nanoparticle volume into tightly bound single-crystal granules with randomly distributed \ndirections of the easy anisotropy axes. The probability of \nappearance of quasi uniform and vortex states in sufficiently large assemblies of polycrystalline \nnanoparticles of various types have been calculated \ndepending on the nanoparticle diameter. For \npolycrystalline nanoparticles the effective single-domain \ndiameters, D\nc,ef, have been determined under the \ncondition that only quasi-uniform states with reduced \nmagnetic moment Me/Ms > 0.9 exist in the \npolycrystalline nanoparticle of a given type in the range \nof diameters D < Dc,ef.  \nIt is shown that the subdivision of a nanoparticle \ninto single-crystal granules with different orientations of the easy anisotropy axes substantially reduces the \neffective single-domain diam eters for particles with \nuniaxial type of anisotropy. Moreover, for these \nnanoparticles the difference between the diameters D\nc0 \nand Dc,ef increases with increasing of the particle \nmagnetic hardness. At the same time, for particles with cubic type of magnetic anisotropy, the influence of the \ncrystal structure inhomogeneities on the equilibrium \nproperties of the particles is not so important even for magnetically hard cobalt ferrite nanoparticles. It is \npractically absent for magnetically soft magnetite \nnanoparticles. This is a conse quence of the fact that in \nparticles with cubic type of magnetic anisotropy the \nprobability to create an inhomogeneous easy axis \ndistribution over the nanoparticle volume is small due to \nthe presence of a large number  of equivalent directions \nof the easy anisotropy axes in the individual granules. \n \nAcknowledgments \nWe acknowledge funding from Russian Ministry of \nEducation and Science (Grant RFMEFI57815X0128).  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 7References  \n \n[1] Q.A. Pankhurst, N.K.T. Thanh, S.K. Jones, J. \nDobson, J. Phys. D: Appl. Phys. 42 (2009) 224001. \n[2] E.A. Périgo, G. Hemery, O. Sandre, D. Ortega, E. Garaio, F. Plazaola, F.J. Teran, Applied Physics Reviews 2 (2015) 041302. \n[3] A.K.A. Silva, A. Espinosa, J. Kolosnjaj-Tabi, C. Wilhelm, F. Gazeau, Iron Oxides: From Nature to Applications, Ed. D. Faivre, Wiley-VCH Verlag, 2016, \npp 425 – 471. \n[4] Z.L. Wang, J. Phys. Chem. B 104 (2000) 1153–1175. \n[5] L.D. Marks, Reports on Progress in Physics 57 (1994) 603-649. \n[6] J. Baumgartner, A. Dey, P.H.H. Bomans, C.L. \nCoadou, P. Fratzl, N.A.J.M. Sommerdijk, D. Faivre, \nNature Mater. 12 (2013) 310-314. \n[7] B. Luigjes, S.M.C. Woud enberg, R. de Groot, J.D. \nMeeldijk, H.M. Torres Galvis, K.P. de Jong, A.P. Philipse, B.H. Erné, J. Phys. Chem. C 115 (2011) 14598-\n14605. \n[8] M. Levy, A. Quarta, A. Espinosa, A. Figuerola, C. Wilhelm, M. García-Hernandez, A. Genovese, A. Falqui, D. Alloyeau, R. Buonsanti, P.D. Cozzoli, M.A. García, \nF. Gazeau, T. Pellegrino, Chem . Mater. 23 (2011) 4170–\n4180. \n[9] A. Lak, M. Kraken, F. Ludwig, A. Kornowski, D. Eberbeck, S. Sievers, F. J. Litterst, H. Weller, M \nSchilling, Nanoscale 5 (2013) 12286-12295. \n[10] W. Baaziz, B. P. Pichon , S. Fleutot, Y. Liu, C. \nLefevre, J.-M. Greneche, M. Toumi, T. Mhiri, S. Begin-Colin, J. Phys. Chem. C 118 (2014) 3795 −3810. \n[11] J. van Rijssel, B.W.M. Kuipers, B.H. Erné, J. Magn. \nMagn. Mater. 380 (2015) 325-329. \n[12] L. Lartigue, P. Hugounenq, D. Alloyeau, S.P. \nClarke, M. Lévy, J.-C. Bacri, R. Bazzi, D. F. Brougham, C. Wilhelm, F Gazeau, ACS Nano 6 (2012) 10935−10949. \n[13] C. Blanco-Andujar, D. Ortega, P. Southern, Q. A. Pankhurst, N.T.K. Thanh, Nanoscale 7 (2015) 1768 -\n1775. \n[14] W.F. Brown, Jr., Micromagnetics, Wiley-Interscience, 1963. \n[15] W.F. Brown, Jr., J. Appl. Phys. 39 (1968) 993-994. \n[16] W.F. Brown, Jr., Ann. N.Y. Acad. Sci. 147 (1969) 461-488. \n[17] A. Aharoni, Introduction to the Theory of \nFerromagnetism, Clarendon Press, 1996. \n[18] N.A. Usov, J.W. Tucker, Material Science Forum \n373-376 (2001) 429-432.  \n[19] D.R. Fredkin, T.R. Koehler, IEEE Trans. Mag. 25 (1989) 3473-3475. \n[20] M.E. Schabes, J. Magn. Magn. Mater. 95 (1991) \n249-288.  \n[21] H. Kronmuller, R. Hertel, J. Magn. Magn. Mater. 215-216 (2000) 11-17.  \n[22] J. Fidler, T. Schrefl, J. Phys. D: Appl. Phys. 33 \n(2000) R135-R156.  \n[23] N.A. Usov, L.G. Kurkina, J.W. Tucker, J. Phys. D: Appl. Phys 35  (2002) 2081-2085.  \n[24] N.A. Usov, Yu.B. Grebenshchikov, Magnetic \nnanoparticles, edited by Prof . S.P. Gubin, Wiley-VCH, \n2009, Chap. 8. \n[25] V.A. Bautin, A.G. Seferyan, M.S. Nesmeyanov, \nN.A. Usov, AIP Advances 7 (2017) 045103. \n[26] S. Chikazumi, Physics of Magnetism, Wiley, 1964. \n[27] B.D. Cullity, C.D. Graham, Introduction to Magnetic Materials, Wiley, 2009. \n \n 8"    },    {        "title": "2007.14934v1.All_optical_nonreciprocity_due_to_valley_polarization_in_transition_metal_dichalcogenides.pdf",        "content": "All-optical nonreciproc ity due to valley polarization in   \ntransition metal dichalcogenides  \n \nYuma Kawaguchi1*, Sriram Guddala1*, Kai Chen1, Andrea Alù3,2,1, Vinod Menon2,4, and \nAlexander B. Khanikaev1,2,4 \n1Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New \nYork, 140th Street and Convent Avenue, New York, NY 10031, USA.  \n2Physics Program, Graduate Center of the City University of New York, New York, NY 10016, USA.  \n3Photonics I nitiative, Advanced Science Research Center, City University of New York, New York, NY 10031, \nUSA  \n4Department of Physics, City College of New York, 160 Convent Ave., New York, NY 10031, USA  \n \nAbstract  \nNonreciprocity and nonreciprocal optical devices play a vital role in modern photonic technologies \nby enforcing one -way propagation of light. Most nonreciprocal devices today are made from a \nspecial class of low -loss ferrites that exhibit a magneto -optical  response in the presence of an \nexternal  static  magnetic field. While breaking transmission symmetry , ferrites fail to satisfy the \nneed for miniaturization of photonic circuitry  due to weak character of nonreciprocal response s at \noptical wavelengths and  are not eas y to integrate into on-chip photonic systems. These challenges \nled to the emergence of magnetic -free approaches relying on breaking time reversal symmetry, \ne.g. with no nlinear effects modulating optical system in time.  1–5  Here , we demonstrate an all-\noptical approach to nonreciprocity based on nonlinear valley -selective response in transition metal \ndichalcogenides  (TMDs) . This approach  overcomes  the limitations of magnetic materials and it \ndoes not require  an external magnetic field . We provide experimental ev idence of photoinduced \nnonreciprocity in a monolayer WS 2 pumped by circularly polarized light. Nonreciprocity  stems \nfrom valley -selective exciton -exciton interaction s, giving rise to nonlinear circular dichroism \ncontrolled by circularly polarized pump fields. Our experimental results reveal  a significant  effect \neven at room temperature , despite considerable intervalley -scattering , show ing potential for \npractical applica tions in magnet ic-free nonreciprocal platforms . As an example, we propose a \ndevice scheme to realize an optical isolator based on a pass -through silicon nitride (SiN) ring \nresonator integrating the optically biased  TMD  monolayer . \n \nIntroduction  \nNonreciprocal optical devices , such as isolators and circulators , are critical components for \nphotonic system s3–12 at large . Optical isolators enable stable laser operation by blocking reflected \nlight from entering the laser cavity, and circulators facilitate nonreciprocal routing of optical \nsignals in telecommunication networks. However, nonreciprocal devices availab le today rely on \nmagneto -optical materials , whic h have limited possibility of integration into modern photonic \ncircuitry due to chemical incompatibility of materials  and typically require  a bulky  external \nmagnetic bias . In addition, the weak character of m agneto -optical effects prevents miniaturization \nof magneto -optical components , which must be large to provide sufficient nonreciprocal response . \nAlthough  numerous  solutions have been proposed , including  photonic1,5,13 –16 and plasmonic materials17–20 integrating magneto -optical media , these schemes have  not yet been  prove n to be  of \ntechnological relevan ce.  \nIn recent years , magnet -free approach es to nonreciprocity ha ve gained attention , including \nlinear1- and angular -2 momentum biased photonic structures and metamaterials. In such systems , \nparametric phenomena induced by external time -modulated  bias were shown to give rise to \nnonreciprocal response s. However, electro -optical modulation schemes are limited to a few GHz \nspeeds, implying that optical non -reciprocity can be difficultly achieved with these schemes, and \nmost experimental demonstrations with practically relevant metrics of performance have  been \nlimited to radio -frequencies3,22. Nonlinear phenomena combined with  asymmetric field \ndistributions have also been shown to enable nonreciprocity in some regimes23, exploiting the \ntemporal modulations enabled by the signal itself as it propagates through the device24,25. However, \nthis form of self -bias nonreciprocity comes with some drawbacks 22,26 –28that hinder its widespread \napplicability.  In the optical domain , therefore , magnet -free isolators and circulators  remain  elusive, \neven though some important proof -of-concept experimental schemes have been demonstrated4,5. \nNonetheless, some of the  all-optical modulation schemes to break reciprocity  proposed recently \nmay o vercome th e above limitations29. \n In a different context, two-dimensional (2D) Van-der-Waals materials have been shown to \nprovide a promising platform for enhanced light -matter interactions, including enhanced  nonlinear \nresponses in graphene and other 2D materials30–35. A particular class of  2D semiconductors, \nmonolayer transition  metal dichalcogenides (TMDs), has attracted significant attention from the \nresearch community due to their unique valley -dependent optical response36–39. The conservation \nof angular momentum in TMDs enforces circularly polarized light to interact selectively with \nelectronic subsystems at K and K’ valley s, leading to valley -selective absorption of circularly \npolarized light40–43. Valley -polarized ex citons have been shown to support  circularly polarized \nluminesce nce connected with the pump handedness, due to the conservation of the valley degree \nof freedom. A variety of fascinating effects based on such chiral light -mater interaction s have been \ndemons trated recently, including direction al launching of guided waves and surface plasmon -\npolaritons42,44 –46. More recently nonlinear effects  in TMDs  such as saturable absorption47, valley -\ndependent  exciton   bistability48 and valley -dependent second harmonic generation49–51 have been \ndemonstrated  and proposed  for valley optoelectronic applications . \nIn this work , we exploit the enhanced nonlinearity in TMDs, and the valley selectivity in their \nnonlinear response, to  experimentally demonstrate that nonlinear chiral light -matter interaction in \nTMDs open a  route t o all-optical nonreciprocal photonics. We show that valley -selective exciton -\nexciton interactions lead to photoinduced nonreciprocal circular dichroism analogous to the one \nobserved in magneto -optical materials , but in which optical pumping with given hand edness \nreplaces the magnetic bias . \n \nPhotoinduced nonreciprocal circular dichroism  \nThe scheme illustrating the concept of photoinduced nonreciprocity is shown in Fig. 1 a. A TMD \nmonolayer is pumped by a strong  circularly polarized laser radiation, which leads to the selective \nformation of exciton gas at one of the valleys. At high pump field intensities, the increasing density of excitons at the photoexcited valley gives rise  to stronger nonlinear response due t o the exciton -\nexciton interactions52 (Fig. 1 b). Provided the valley polarization of excitons is at least partially \npreserved, it will give rise to a n asymmetric response of the TMD monolayer to weak probe signals \nof opposite handedness , due to the fact that they  selectively interact with one of the two valleys44. \nAs schematically depicted in Fig. 1 a, this effect lead s to a nonreciprocal dichroic response , i.e.,  \nprobe signals of opposite handedness are absorbed and reflected differently  from the optically \npumped TMD monolayer . Since the handedness  of circularly polarized light is locked to the \npropagation direction, and similar  locking of transverse angular -momentum to propagation \ndirection exists for  evanescent electromagnetic fields53–55, this opens  the opportunity for design ing \noptical elements  with inherently nonreciproca l response induced by the circularly polarized  pump \nfield.  Is worth noting here that the circular dichroic response of any planar 2D systems, including \n2D materials, is necessarily nonreciprocal , since reciprocal  circular dichroism, known as optical \nactivi ty, requires nonlocal bianisotropic response, which is possible only in structures with finite \nthickness56,57. \n \nFigure 1 | Photoinduced nonreciprocity in TMDs. a, Schematic illustration of nonreciprocal reflection \ndue to valley -selective response induced by a circularly polarized pump. b, Mechanisms for long-living \ndichroic response and nonlinear saturation as a two -step process with delayed relaxation of free -carriers to \nexcitons and of exciton -exciton interactions.  c, Optical microscope image of encapsulated WS 2 monolayer \non glass substrate . Encircled white and red dotted lines refer to the WS2 monolayer and the thin layer of \nhBN respectively.  \n \nFirst, we investigate the optical response of a WS 2 monolayer under circularly polarized pump, \nexpecting to observe nonreciprocal circular dichroism at large pump intensities. As schematically \nshown in Fig. 1 a, a pump with left -handed circular polarization illuminating from above the \nsample has a counter c lock-wise (CCW) projected helicity on the plane of the 2D material, which \nleads to the formation of excitons at the K valley in WS 2. In the ideal case of no valley scattering, \nthis increased exciton density at one of the valleys leads to exciton -exciton in teractions \n(schematically shown in Fig. 1 b) which affects reflectivity of a probe signal of the same helicity \nas the pump, while the reflectivity of the probe field with opposite helicity remains unaffected. As \na consequence, probe signals illuminating fro m opposite angles  with opposite helicity , time -\nreversed versions of each other,  will experience different  reflectivity 𝑟𝐶𝑊≠𝑟𝐶𝐶𝑊. Since the \nprojected helicity is flipped for opposite propagation directions of the probe signal, as illustrated \nin Fig. 1a, this response is  nonreciprocal 𝑟𝐶𝑊(𝑘∥)≠𝑟𝐶𝐶𝑊(−𝑘∥), and can be used to realize an all -\noptical magnet -free isolator, as shown in the following .  \n \nTheoretical model  \n \nIn order to quantitatively  describe the dichroic  nonreciprocal response  in optically pumped TMDs , \nwe introduce a nonlinear surface conductivity  tensor  \n \n𝜎̂=𝜎𝑁(𝐼)+𝜎̂𝐾(𝐼𝐶𝑊)+𝜎̂𝐾′(𝐼𝐶𝐶𝑊),                                             (1) \n \nwhere 𝜎𝑁 describes the  valley -independen t optical response , 𝜎̂𝐾, 𝜎̂𝐾′ correspond to the  valley -\ndependent response  due to excitations at K and K’ valley, respectively , 𝐼𝐶𝑊, 𝐼𝐶𝐶𝑊 are the \nintensit ies of the circularly polarized pump field s, which make clockwise and counterclockwise \nprojections of the electric field onto the TMD plane,  respectively,  and 𝐼=𝐼𝐶𝑊+𝐼𝐶𝐶𝑊 is the total \npump field . In addition to conventional non -valley polarized optical processes, the first term  in Eq. \n(1), 𝜎𝑁(𝐼), also accounts for valley “depolarization” due to various inter-valley scattering  \nprocesses . It is worth highlighting  that here the notations of CW and CCW specify the handedness \nof the electric field rotation in  the TMD plane , irrelevant of the propagatio n direction , and that \nLCP and RCP polarization/handedness of optical wave s are therefore not in one -to-one \ncorrespondence with CW and CCW . The valley -polarized response is uniquely described by the \nprojected helicity (CW/CCW).  \nThe valley -dependent terms in (1) have the following form , which accounts for the ir chiral \nresponse:  \n \n𝜎̂𝐾=1\n2(𝜎𝐾 𝑖𝜎𝐾\n−𝑖𝜎𝐾 𝜎𝐾) , 𝜎̂𝐾′=1\n2(𝜎𝐾′−𝑖𝜎𝐾′\n𝑖𝜎𝐾′ 𝜎𝐾′),                                 (2) \n \nwhere 𝜎𝐾=𝜎𝐾(𝐼𝐶𝑊) and 𝜎𝐾′=𝜎𝐾′(𝐼𝐶𝐶𝑊) are surface conductivities f or the two valleys in the \ncircularly polarized  (CP)  basis . The form of Eqs.  (2) follows directly from the fact that the response \nof each valley is selective with respect to the handedness of the optical field, and therefore it is \ndescribed by the matrices 𝜎̂𝐾𝐶𝑃𝐵=[𝜎𝐾,0;0,0] and 𝜎̂𝐾′𝐶𝑃𝐵=[0,0;0,𝜎𝐾′] in the circularly polarized  \nbasis  (CBP) . \nIn the case of no optical pump , the two valleys yield the same response 𝜎𝐾(𝐼𝐶𝑊=0)≡\n𝜎𝐾′(𝐼𝐶𝐶𝑊 =0), so that 𝜎̂𝐾+𝜎̂𝐾′=[𝜎𝐾,0;0,𝜎𝐾′ ] and the TMD shows no asymmetry in the  \nresponse with respect to CW and CCW  probe signal s. However, dichroi sm arises as  the pump intensity of a particular handedness  is increased, and the response enters the nonlinear regime such \nthat 𝜎𝐾(𝐼𝐶𝑊)−𝜎𝐾′(𝐼𝐶𝐶𝑊)≠0, yielding an effective response of the form  \n𝜎̂𝑇𝑀𝐷 =(𝜎𝑁+1\n2(𝜎𝐾+𝜎𝐾′)𝑖\n2(𝜎𝐾−𝜎𝐾′)\n−𝑖\n2(𝜎𝐾−𝜎𝐾′) 𝜎𝑁+1\n2(𝜎𝐾+𝜎𝐾′))=(𝜎𝑥𝑥 𝑖𝜎𝑥𝑦\n−𝑖𝜎𝑥𝑦 𝜎𝑥𝑥).          (3) \nThis response is equivalent to the one  of a 2D electron gas in the presence of a dc external magnetic \nbias58,59, showing how the  circularly polarized optical pump can effectively break time -reversal \nsymmetry in TMDs . Indeed, the possibility to use a circularly polarized pump as an effective \nmagnetic field bias has been proposed before in the context of so called Floquet systems and \nFloquet topological insulators have been introduced29,60,61. More recently, the circularly polarized \npump field was used to demonstrate photoinduced quantum Hall effect in graphene62. Here, \nhowever, we report the effect not related to Floquet physics, but originating solely in the valley -\npolarized nonlinear  optical  response of TMDs . \n \nFigure 2|  Experimental demonstration of  photoinduced nonreciprocal circular dichroism in WS 2. a,b, \nReflectivity of the WS 2 monolayer for probe s of opposite helicities as a function of the wavelength and of  \nthe intensity of the pump with C CW helicity . a and b show the cases of CCW and CW probes , respectively . \nThe dark blue (low signal) region on the left is due to optical filter s used to eliminate the pump signal from \nthe probe channel. c, Pump power dependence of the reflectivity for probes with CW and CCW helicities  \nat 𝜆=616 nm, illustrating  the nonreciprocal  dichroic character and saturation. d, Wavelength dependence \nof reflectivity for CW and CCW  probes.  Solid lines show the result of fitting by a modified Fresnel equation  \nwith su rface conductivity described  by a Loren tzian model  (see Methods for details) , and the saturable \nabsorption model described in Supplement A . \n \nExperimental results  \n \nIn order to  experimentally verify the photoinduced dichroic response, we have performed \nmeasurements on a WS 2 monolayer encapsulated in hBN and transferred onto a glass substrate \n(hBN side on top). The image of the sample is shown in Fig. 1 c (details of the sample pr eparation \ncan be found in Methods).  \nThe sample was pumped by 30ps circularly polarized  pulses from a supercontinuum source \n(NKT SuperK SELECT) with 12ns pulse period at the wavelength on the blue -side and as close \nas possible to  the exciton resonance (616 nm) to promote formation of exciton s and their  \ninteractions52. Pumping at higher frequencies was found to lead to decreased nonreciprocal \ndichroic response. The intensity of the circularly polarized  pump was gradua lly increased, and the \nsample reflectivity was probed with low-intensity circularly polarized beams from a halogen light \nsource , collecting the reflected signal  with a  fiber -coupled spectrometer (Spectral Products \nSP400 ). The  experimental results in Fig s. 2a,b,c show that, as the pump intensity  increases , the \nreflected probe signals with opposite projected helicit ies become increasingly different, \nconfirm ing our hypothesis  about photoinduced nonreciprocal optical dichroism . As seen from \nFigs. 2 a,b,d, the dichroism shows the largest  increase at the frequency of the exciton resonance  \n(plotted separately in Fig. 2 c), which farther proves that the  mechanism responsible for \nnonreciprocity  is associated with the difference  in exciton densities at the two valleys . The clear \nsaturable behavior  of the probe signal reflection with respect to pump intensity  can thus be \nattributed to exciton -exciton interactions (indicated by wavy lines  in the schematic in Fig. 1b). \nSuch interactions were previously shown  to yield corrections to both the energy and the lifetime \nof excitons52, giving rise to saturation in the reflectivity for pump frequencies exceeding the one \nof the exciton resonance.  \nTo explain the observed photoinduced nonreciprocal dichroic behavior, we developed an \nanalytical model  based on the Fresnel equations modified by the TMD monolayer , whose optical \nresponse is described by a surface conductivity with Lorentzian dispersion63 (see Supplement A \nfor details) .  In addition, we incorporated the nonlinear effects into the Lorenz model by accounting \nfor an increase in the exciton density as well as for the broadening of the exciton resonance due to \nexciton -exciton interactions52. W e note that the spectral shift was unnoticeable in our \nmeasurements due to the already broad exciton resonance at room temperature , and hence it  was \nneglected in our model.  \nThe proposed  model  was used to fit the experimental data , enabl ing the retrieval of the surface \nconductivity tensor , with result s shown  in Fig. 3 . Since the conductivity for each of the projected \nhelicities is 𝜎𝐾=(𝜎𝑥𝑥−𝜎𝑁)+𝜎𝑥𝑦 and 𝜎𝐾′=(𝜎𝑥𝑥−𝜎𝑁)−𝜎𝑥𝑦, our extracted  photoinduced off-\ndiagonal (dichroic ) component  of the surface conductivity reache s the value 𝜎𝑥𝑦=(𝜎𝐾−\n𝜎𝐾′)/2≈0.059𝜎𝑥𝑥 for the highest  pump power  at the peak reflectivity. This value of dichroic \nresponse is very large  since the measurements are performed at room temperature , where \nintervalley scattering plays a detrimental role and , in addition,  the short 30 ps pulse duration of the \npump signal with 12 ns repetition rate  fundamentally limits the overall nonlinear respo nse. The \nfact that the dichroism does not vanish over such long integration times (compared to pump \nduration) indicates the presence of long-living  valley -polarized excitations in the system. Indeed, while the excitons in TMDs are known to have rather short life times of less than 2  ps, recent time-\nresolved pump -probe experimental studies have suggest ed that the lifetime of photoexcited free \ncarriers  can be as long as  2 ns64 at room temperature, and may exceed values of 10 ns at cryogenic \ntemperatures65. We therefore attribute the large value of the measured dichroism  to the delayed \nrelaxation of the photoexcited valley -polarized free carriers into exciton states with partial \npreservation of the valley -polarization . For strong pump intensities, such  valley -preserving \nrelaxation  of free -carriers leads to a larger density  of excitons  and thus higher rate of exciton -\nexciton interactions at one of the valley , giving rise to an early onset of saturatio n at the respective \nvalley  (blue line in Fig. 2 c). The saturation due to exciton -exciton interaction s at the opposite \n(unpumped) valley  (red line in Fig. 2 c) has a relatively late onset and  it can be  solely attributed to \nnon-valley -preserving relaxation of free-carriers  into the respective valley . The schematic \nmicroscopic picture of the processes responsible for the dichroism  is illustrated in Fig. 1b. \n \nFig. 3 | Measured d ichroic surface conductivity of WS 2 under circularly polarized optical pump . a, \nDiagonal element of the surface conductivity plotted alongside with  the off-diagonal element. b, Ratio of \noff-diagonal  and diagonal surface conductivity tensor components  describing the strength of the \nphotoinduced dichroic response . The dot s in a and b show values extracted from experimentally measured \nreflectivities. The solid lines are the result of fitting by our analytical mode l (Supplement A ). \n \nProposed device scheme of an all-optical isolator  \nTo demonstrate  that the photoinduced circular dichroism phenomenon  can yield nonreciprocal \noperation , we propose a practical design of a magnet -free optical isolator relying on this effect. \nThe proposed device is based on a silicon nitride ring resonator  critically coupled to a waveguide ; \nthis scheme was  recent ly employed for high speed modulation of light with 2D materials, \ngraphene66 and tungsten disulfide WS 2 67. The functionality of the device is illustrated in Figs. 4a, \nb and it is based on spin-orbit  coupling68 due to the non -vanishing transverse angular momentum \nof the evanescent optical field of guided waves53,69. In particular , the mode  guided in the forward \ndirection by a SiN waveguide is evanescent in the cladding, and it is characterized by  CW (CCW)  \nelliptically polarized nearfield s on the left (right) , as schematically shown in the inset to Fig. 4 a. \nIf the propagation direction of the guided wave is reversed,  as in the inset to Fig. 4 b, the \nhandedness of the evanescent field accordingly reverses. Therefore, by placing a dichroic TMD \nmono layer asymmetrically with respect to the waveguide (only on the one side , as in Fig.  3a,b \ninsets /zoom -ins) we expect  different absorption rate s for oppositely propagating guided waves. \nIndeed, due to the  dichroic response in optically pumped TMD , the differen t nearfield overlap of  \nthe guided wave with the surface conductivity of TMD must yield a different absorption rate for \nforward and backward guided modes . Such nonreciprocal absorption can be estimated using  \nelectromagnetic perturbation theory70,71.  \nTaking the electric field 𝑬0 of the guided mode  without the TMD monolayer as the unperturbed \nsolution , and treating the monolayer as a perturbation, the attenuation rate due to the absorption in \nthe TMD  can be estimated to first-order to be  \n 𝐼𝑚(𝛽)=𝛽0\n𝜔𝑊 0∫ 𝑑𝑆[𝑬0∗𝑅𝑒(𝜎̂𝑇𝑀𝐷)𝑬0] 𝑇𝑀𝐷, \n \nFig. 4| All-optical isolator device design and operation principle . a, b SiN ring resonator loaded  \nasymmetric ally by a TMD mono layer (on the inner side of the ring only  to maximize asymmetric  loss), \nwhich explains  nonreciprocal transmission due to different absorption of clockwise and counter -clockwise \nmodes in the ring resonator. c, nonreciprocal transmission trough the waveguide  with forward and backward \ntransmission shown  by blue and red lines , respectively . The ring radius 𝑅=30 µm, therefore the trip distance \n𝐿=2𝜋𝑅,  t = 0. 788 and c. 𝑎+=0.845 ,𝑎−=0.932, which correspond to the surface conductivity tensor \n𝜎𝑥𝑥=2.1× 10−3 and 𝜎𝑥𝑦=1.25×10−4with parameters  𝛼=1.79×104 1/m,𝛿=7.37×103 1/\nm,𝐿𝑇𝑀𝐷 =6.6 μm,the width of the TMD monolayer is 𝑤=50 nm. \n \nwhere 𝛽0 is the unperturbed wavenumber of the guided wave, 𝑆 is the surface area, and 𝑊0=\n2∫𝑑𝑉[|𝐸0(𝑟)|2𝜖0𝜖𝑟(𝑟)]𝑉 is the energy density of the unperturbed guided wave, with the \nintegration performed over the mode volume. In this discussion, we neglect the small material loss \nin the unperturbed waveguide. Decomposing the evanescent field in the TMD region into the CW \nand CCW helicity components 𝑬0=𝑬0𝐶𝑊+𝑬0𝐶𝐶𝑊, we obtain 𝐼𝑚(𝛽)=𝐼𝑚(𝛽0)+𝐼𝑚(𝛽𝐾)+\n𝐼𝑚(𝛽𝐾′)  where 𝐼𝑚(𝛽0)≡𝛼=𝛽0\n𝜔𝑊 0∫ 𝑑𝑆[|𝐸0|2𝜎𝑥𝑥]𝑇𝑀𝐷 and 𝐼𝑚(𝛽𝐾/𝐾′)=\n𝛽0\n𝜔𝑊 0∫ 𝑑𝑆[|𝐸0𝐶𝑊/𝐶𝐶𝑊 |2𝜎𝐾/𝐾′]𝑇𝑀𝐷 are valley independent and valley polarized contributions to the \nattenuation caused by the absorption in the TMD. Since the pumped TMD monolayer has 𝜎𝐾≠\n𝜎𝐾′ and due to the evanescent field of the guided mode is chiral, we obtain a nonzero differential \nattenuation for forward and backward waves: 𝛿≡𝐼𝑚(𝛽(𝑘>0)−𝛽(𝑘<0))/2=\n𝛽0\n2𝜔𝑊 0∫ 𝑑𝑆[(|𝐸0𝐶𝑊|2−|𝐸0𝐶𝐶𝑊 |2)(𝜎𝐾−𝜎𝐾′)]𝑇𝑀𝐷. By applying this analysis to the modal solution \nfor the SiN waveguide obtained with COMSOL Multiphysics, we retrieved 𝐼𝑚(𝛽𝑏𝑎𝑐𝑘𝑓𝑜𝑟𝑑 )=\n9.69×104 1/m and 𝐼𝑚(𝛽𝑓𝑜𝑟𝑤𝑎𝑟𝑑 )=8.22×104 1/m. The magnitude of such nonreciprocal \nattenuation, however, is not large enough to yield sufficient isolation for reasonable propagation \ndistances. We therefore employ a resonant scheme to enhance the  nonreciprocal differential \nabsorption.  \nThe optical isolator layout is shown in Fig. 4 a,b and it consists of a SiN waveguide \nevanescently coupled to a  SiN ring resonator . We place the circularly pumped TMD mono layer \non the inner  side of the ring resonator only, which  ensur es that the modes propagating in opposite \ndirections have different attenuation rate s. Indeed, similar  to the case of the waveguide, the \nevanescent component of the electric field of the mode in the ring resonat or carries angular \nmomentum of opposite handedness on the inner and outer side s of the ring. The handedness of the \nevanescent fields flips when the propagation direction in the ring resonator reverses from CW \npropagating mode to CCW propagating mode, which  again gives  rise to  a differen ce in absorption  \nfor the two modes . \nSuch  different absorption rate for modes propagati ng in opposite directions enables to induce \nselectively critical coupling between the ring resonator and the waveguide72,73 only for  one \npropagation, yielding a strong nonreciprocal response . From here on we will use subscripts +/ – to \nindicate CW  and CCW propagation directions  in the ring resonator to avoid confusion with the \nnotations of the projected handedness of the electric field  of the modes  on the TMD .  \nAccording to coupled mode theory74, the critical coupling condition for the mode propagating \nbackward, i.e. from Port 2 to Port 1 in the SiN waveguide  (Fig. 4 a), and therefore coupling to the \nCW ( +) mode of the ring resonator, is 𝑡=𝑎+.  Here  𝑡 is the self -coupling of the waveguide and \n𝑎+=exp[−(𝛼+𝛿)𝐿𝑇𝑀𝐷] is the round -trip loss coefficient in the ring resonator for the CW(+) \nmode , and 𝐿𝑇𝑀𝐷 is the length of coverage of the ring resonator by the TMD monolayer . This \ncondition cannot be satisfied simultaneously for the waveguide mode propagating in the forward  \ndirection , i.e. from Port 1 to Port 2, thus yielding the nonreciprocal transmission . In the latter case \nthe critical coupling condition is 𝑡=𝑎−, where 𝑎−=exp[−(𝛼−𝛿)𝐿𝑇𝑀𝐷], since the guided mode \nnow couple s to the CCW (-) mode in the ring resonator which has  different round -trip loss \ncoefficient 𝑎−≠𝑎+.  \nTo confirm the functionality of the proposed device , we performed CMT74 modeling with the \nparameters obtained from perturbati on theory using the field profiles 𝑬0 for unperturbed SiN waveguide calculated in COMSOL . For the conductivity parameters retrieved from our  \nexperimental data, we found that an isolation of 3dB can be achieved for an overall forward \ntransmission of ~ 6.8%. The main limiting factor for a stronger  isolation is intervalley scattering , \nwhich gives rise the non-dichroic loss in the device.  Intervalley scattering can be significantly \nreduced by lowering the temperature. As a n alternative app roach , valley -polarization can be \nstabilized by using weak a magnetic field75. Here, as an example, we estimate that the effect of \nlowering  the operating temperature would reduce the intervalley scattering fivefold  (leading to \napproximately fivefold reduction of 𝜎𝑁), in which case the nonreciprocal  response  in WS 2 can be \nsignificantly boosted . The corresponding results showing ( i) forward transmission 𝑆12 (from Port \n1 to Port 2 ) and ( ii) backward transmission 𝑆21 (from Port 2 to Port 1 ) are plotted in Fig. 4 c and \nclearly show strong  nonreciprocal response . Note that one ha ve to operate slightly off the exact \ncritical coupling condition to ensure high transmission  in the forward direction . Thus, f or the \n29.5% transmission in forward  direction, the isolation of 10.0 dB can be readily achieved . We note \nthat higher values of isolation are possible at the expense of lower backward transmission.  Ideally,  \nthe performance  of the proposed isolator  can be farther improved with an  even lower non-valley \nselective component of the surface conductivity  𝜎𝑁, e.g., by combining lower temperature with a \nweak magnetic field, in which case one would  operate closer to the critical coupling condition \nensuring stronger  isolation  and higher transmission in the backward  direction  at the same time . \nEven in this case, the bet ter compatibility and ease of integration of TMD monolayers with \nintegrated photonic systems would render the proposed approach to nonreciprocity more practical \nthan the use of magneto -optical materials  in many applications . \n \nConclusions  \nTo conclude , here we have experimentally demo nstrated the emergence of a nonreciprocal dichroic \noptical response in WS 2 monolayer biased by circularly polarized pump field. The dichroic \nresponse was explained as the result of interaction of light with valley polarized excitons, whose \ninteraction for higher pump intensities le ad to nonlinear saturable behavior of the optical response. \nAn analytical model of this effect was developed, which allowed to explain the experimental data \nand extract the surface conductivity tensor of  the optically biased WS 2 monolayer.  \nThe analogy of the observed dichroic response with the one of 2D electron systems in an \nexternal magnetic field suggest s the  possible use of optically pumped TMDs to produce magnet -\nfree nonreciprocity. A device based on lo cking of transverse angular momentum of the evanescent \nfield with the propagation direction of the guided waves was proposed. Asymmetric  absorption \nrates due to chiral light -matter interactions with a dichroic TMD monolayer was shown to be  the \nmechanism  to achieve unidirectional critical coupling, thus producing optical isolation.  \nWe believe that the recent progress in integration of 2D materials with existing photonic \nmaterials and de vices may facilitate the impact of all -optical nonreciprocal devices base d on the \nproposed photoinduced dichroism  in photonic  system s. We envision a new generation of all -\noptical isolators and circulators integrated into on -chip photonic systems. Moreover, the possibility to control the direction of optical isolation by simply switching the handedness of the optical pump \nbias makes these nonreciprocal devices switchable on the fly, enabling novel applications in \nclassical and quantum photonic frameworks.  \n \nMethods  \nSample fabrication:  \nA monolayer of WS 2 TMD material was exfoliated onto a thick PDMS stamp using standard tape \ntechnique and transferred to 120um thick silica substrate by home build transfer stage. The \nmonolayer annealed at 350oC for 2 hours to remove polymer residue from the transfer process .  \nFurther, the monolayer was encapsulated with a thin hBN layer and annealed again at 350oC for \nanother 2 hours.  \nExperimental set up:  \nHigh -intensity supercontinuum  light-source SuperK  Extreme with connected LLTF Contrast tunable high -\nresolution bandpass filter generated light beam with 2nm bandwidth and the tunable wavelength in the \nrange 0. 4-1.0 µm . The sample was pumped with supercontinuum pulsed laser of 30ps pulse width \nand 12ns pu lse period and wavelength of light was set to 600 nm close to exciton resonance (616 \nnm) at room temperature. The polarization of the excitation beam was set to circular polarization \nby using a combination of linear polarizer and quarter wave plate. A 50X (Olympus) long working \ndistance microscopic objective was used to excite the monolayer WS 2 with 1um spot size at 300 \nangle of incidence. A low intensity white light beam from halogen light source was used as probe \nbeam with circular polariz ation set up by another set of linear polarizer and quarter wave plate. A \nlong working distance 50X microscopic objective (Boli optics) with 1um spot size at the focus \nwas used to probe the sample reflection spectrum. The reflected probe beam from the sample was \npassed through 610 nm long pass filter to cut of the excitation beam and analyzed  the spectrum by \nusing fiber coupled spectrometer (Spectral Product 400).  \nData a vailability  \nData that are not already included in the paper and/or in the Supplementary Information are \navailable on request from the authors.  \n \nAcknowledgements   \nThe work was supported by the National Science Foundation with grants No. DMR -1809915 , \nEFRI -1641069, by the Defense Advanced Research Project Agency  Nascent Program , and by the \nSimons Foundation . \n Author contributions   \nAll authors contributed extensively to the work presented in this paper.  SG and YK contributed \nequally to this work.  \n \nAuthor Information  \nThe authors declare no competing interests.  Correspondence  and requests for materials should be \naddressed  to Alexander B. Khanikaev.  \n  \nReferences  \n1. Yu, Z. & Fan, S. Complete optical isolation created by indirect interband photonic \ntransitions. Nat. Photonics  3, 91–94 (2009).  \n2. Sounas, D. L., Caloz, C. & Alù, A. Giant non -reciprocity at the subwavelength scale using \nangular momentum -biased metamaterials. Nat. Commun.  4, 1–7 (2013).  \n3. Estep, N. A., Sounas, D. L., Soric, J. & Alù, A. Magnetic -free non -reciprocity and isolation \nbased on parametrically modulated coupled -resonator loops. Nat. Phys.  10, 923 –927 \n(2014).  \n4. Tzuang, L. D., Fang, K., Nussenzveig, P., Fan, S. & Lipson, M. Non -reciprocal phase shift \ninduced by an effective magnetic flux for light. Nat. Photonics  8, 701 –705 ( 2014).  \n5. Lira, H., Yu, Z., Fan, S. & Lipson, M. Electrically driven nonreciprocity induced by \ninterband photonic transition on a silicon chip. Phys. Rev. Lett.  109, 033901 (2012).  \n6. Bi, L. et al.  On-chip optical isolation in monolithically integrated non -reciprocal optical \nresonators. Nat. Photonics  5, 758 –762 (2011).  \n7. Bi, L. Materials for nonreciprocal photonics. MRS Bull.  43, 408 –412 (2018).  \n8. Fan, S., Shi, Y. & Lin, Q. Nonreciprocal photonics without magneto -optics. IEEE \nAntennas Wirel. Propag. Lett . 17, 1948 –1952 (2018).  \n9. Jalas, D. et al.  What is -and what is not -an optical isolator. Nature Photonics  vol. 7 579 –\n582 (2013).  \n10. Feng, L. et al.  Nonreciprocal light propagation in a silicon photonic circuit. Science (80 -. ). \n333, 729 –733 (2011).  \n11. Sounas, D. L. & Alù, A. Non -reciprocal photonics based on time modulation. Nature \nPhotonics  vol. 11 774 –783 (2017).  \n12. Figotin, A. & Vitebsky, I. Nonreciprocal magnetic photonic crystals. Phys. Rev. E - Stat. \nNonlinear, Soft Matter Phys.  63, 1–17 (2001).  \n13. Galland, C., Ding, R., Harris, N. C., Baehr -Jones, T. & Hochberg, M. Broadband on -chip \noptical non -reciprocity using phase modulators. Opt. Express  21, 14500 (2013).  \n14. Dötsch, H. et al.  Applications of magneto -optical waveguides in integrated  optics: review. J. Opt. Soc. Am. B  22, 240 (2005).  \n15. Wang, Z. & Fan, S. Broadband optical circulators in two dimensional magneto -optical \nphotonic crystals. in Quantum Electronics and Laser Science Conference (QELS)  vol. 1 \n461–463 (Optical Society of Ame rica, 2005).  \n16. Hafezi, M. & Rabl, P. Optomechanically induced non -reciprocity in microring resonators. \nOpt. Express  20, 7672 (2012).  \n17. Khanikaev, A. B., Mousavi, S. H., Shvets, G. & Kivshar, Y. S. One -way extraordinary \noptical transmission and nonrecip rocal spoof plasmons. Phys. Rev. Lett.  105, 1–4 (2010).  \n18. Chen, J., Chen, Z., Li, Y., Sun, Q. & Xu, J. Nonreciprocal isolator based on a plasmonic \nmagneto -optical resonator. Opt. Commun.  459, 124953 (2020).  \n19. Belotelov, V. I. et al.  Enhanced magneto -optical effects in magnetoplasmonic crystals. \nNat. Nanotechnol.  6, 370 –376 (2011).  \n20. Chin, J. Y. et al.  Nonreciprocal plasmonics enables giant enhancement of thin -film \nFaraday rotation. Nat. Commun.  (2013) doi:10.1038/ncomms2609.  \n21. Arthur R Davoyan and Nader Engheta. Nanoscale plasmonic circulator. New J. Phys.  15, \n083054 –083063 (2013).  \n22. Bernier, N. R.  et al.  Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. \nCommun.  8, 1–8 (2017).  \n23. Khanikaev, A. B. & Steel, M. J. Low -symmetry magnetic photonic crystals for \nnonreciprocal and unidirectional devices. Opt. Express  17, 5265 (2009).  \n24. Sounas, D. L., Soric, J. & Alù, A. Broadband passive isolators based on coupled \nnonlinear resonances. Nat. Electron.  1, 113 –119 (2018).  \n25. Yang, K. Y. et al.  Inverse -designed non -reciprocal pulse router for chip -based LiDAR. \nNat. Photonics  1–6 (2020) doi:10.1038/s41566 -020-0606 -0. \n26. Sounas, D. L. & Alù, A. Fundamental bounds on the operation of Fano nonlinear \nisolators. Phys. Rev. B  97, 115431 (2018).  \n27. Sounas, D. L. & Alù, A. Time -Reversal Symmetry Bounds on the Electromagnetic \nResponse of  Asymmetric Structures. in Physical Review Letters  vol. 118 154302 \n(American Physical Society, 2017).  \n28. Sounas, D. L. & Alu, A. Nonreciprocity based on nonlinear resonances. IEEE Antennas \nWirel. Propag. Lett.  17, 1958 –1962 (2018).  \n29. Duggan, R., Sounas,  D. & Alu, A. Optically driven effective Faraday effect in \ninstantaneous nonlinear media. Optica  6, 1152 (2019).  \n30. Wen, X., Gong, Z. & Li, D. Nonlinear optics of two ‐dimensional transition metal \ndichalcogenides. InfoMat  1, 317 –337 (2019).  \n31. Hu, G. et al. Coherent steering of nonlinear chiral valley photons with a synthetic Au –\nWS2 metasurface. Nat. Photonics  13, 467 –472 (2019).  \n32. Gu, J. et al.  Nonlinear Interaction of Rydberg Exciton -Polaritons in Two -Dimensional \nWSe2. in Conference on Lasers and Elect ro-Optics  FW3M.5 (OSA, 2019). doi:10.1364/CLEO_QELS.2019.FW3M.5.  \n33. Rosa, H. G. et al.  Characterization of the second -and third -harmonic optical \nsusceptibilities of atomically thin tungsten diselenide OPEN. 8, 10035 (2018).  \n34. Woodward, R. I. et al.  Tuna ble Q -switched fiber laser based on saturable edge -state \nabsorption in few -layer molybdenum disulfide (MoS_2). Opt. Express  22, 31113 (2014).  \n35. Smirnova, D. A., Miroshnichenko, A. E., Kivshar, Y. S. & Khanikaev, A. B. Tunable \nnonlinear graphene metasurfaces. Phys. Rev. B - Condens. Matter Mater. Phys.  92, \n161406 (2015).  \n36. Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS 2 monolayers by \noptical pumping. Nat. Nanotechnol.  7, 490 –493 (2012).  \n37. Cao, T. et al.  Valley -selective circular dichroism of monolayer molybdenum disulphide. \nNat. Commun.  3, (2012).  \n38. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polar ization in monolayer \nMoS2by optical helicity. Nat. Nanotechnol.  7, 494 –498 (2012).  \n39. Krasnok, A., Lepeshov, S. & Alú, A. Nanophotonics with 2D Transition Metal \nDichalcogenides. (2018) doi:10.1364/OE.26.015972.  \n40. Sie, E. J. et al.  Valley -selective optic al Stark effect in monolayer WS2. Nat. Mater.  14, \n290–294 (2015).  \n41. Srivastava, A. et al.  Valley Zeeman effect in elementary optical excitations of monolayer \nWSe2. Nat. Phys.  11, 141 –147 (2015).  \n42. Guddala, S., Bushati, R., Li, M., Khanikaev, A. B. & Me non, V. M. Valley selective optical \ncontrol of excitons in 2D semiconductors using a chiral metasurface [Invited]. Opt. Mater. \nExpress  9, 536 (2019).  \n43. Sun, Z. et al.  Optical control of roomerature valley polaritons. Nat. Photonics  11, 491 –496 \n(2017).  \n44. Gong, S. H., Alpeggiani, F., Sciacca, B., Garnett, E. C. & Kuipers, L. Nanoscale chiral \nvalley -photon interface through optical spin -orbit coupling. Science (80 -. ). 359, 443 –447 \n(2018).  \n45. Sun, L. et al.  Separation of valley excitons in a MoS2 monolaye r using a subwavelength \nasymmetric groove array. Nat. Photonics  13, 180 –184 (2019).  \n46. Chervy, T. et al.  Room Temperature Chiral Coupling of Valley Excitons with Spin -\nMomentum Locked Surface Plasmons. ACS Photonics  5, 1281 –1287 (2018).  \n47. Wang, S. et al.  Broadband Few -Layer MoS 2 Saturable Absorbers. Adv. Mater.  26, 3538 –\n3544 (2014).  \n48. Xie, H., Jiang, S., Shan, J. & Mak, K. F. Valley -Selective Exciton Bistability in a \nSuspended Monolayer Semiconductor. Nano Lett.  18, 3213 –3220 (2018).  \n49. Seyler, K. L. et al.  Electrical control of second -harmonic generation in a WSe2 monolayer \ntransistor . Nat. Nanotechnol.  10, 407 –411 (2015).  \n50. Xiao, J. et al.  Nonlinear optical selection rule based on valley -exciton locking in monolayer ws2. Light Sci. Appl.  4, e366 –e366 (2015).  \n51. Hu, G. et al.  Coherent steering of nonlinear chiral valley photons with  a synthetic Au -WS \n2 metasurface. Nat. PHotoNiCS |  13, (2019).  \n52. Scuri, G. et al.  Large Excitonic Reflectivity of Monolayer MoSe2 Encapsulated in \nHexagonal Boron Nitride. Phys. Rev. Lett.  120, 37402 (2018).  \n53. Bliokh, K. Y., Smirnova, D. & Nori, F. Quan tum spin hall effect of light. Science (80 -. ). \n348, 1448 –1451 (2015).  \n54. Van Mechelen, T. & Jacob, Z. Universal spin -momentum locking of evanescent waves: \nsupplemental document. Optica  3, 1–10 (2016).  \n55. Rodríguez -fortuño, F. J., Martínez, A., Wurtz, G. a & Zayats, A. V. Electromagnetic \nGuided Modes. Science (80 -. ). 328, 328 –331 (2013).  \n56. Zhao, Y. & Alù, A. Manipulating light polarization with ultrathin plasmonic metasurfaces. \nPhys. Rev. B - Condens. Matter Mater. Phys.  84, 205428 (2011).  \n57. Khanikaev, A. B. et al.  Experimental demonstration of the microscopic origin of cir cular \ndichroism in two -dimensional metamaterials. Nat. Commun.  7, 1–8 (2016).  \n58. Pan, D., Yu, R., Xu, H. & García de Abajo, F. J. Topologically protected Dirac plasmons \nin a graphene superlattice. Nat. Commun.  8, 1243 (2017).  \n59. Eisenstein, J. P., Pfeiff er, L. N. & West, K. W. Quantum Hall Spin Diode. Phys. Rev. Lett.  \n118, 186801 (2017).  \n60. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor \nquantum wells. Nat. Phys.  5, 1–6 (2011).  \n61. Oka, T. & Aoki, H. Photovoltaic Hall effect in graphene. Phys. Rev. B - Condens. Matter \nMater. Phys.  79, 081406 (2009).  \n62. McIver, J. W. et al.  Light -induced anomalous Hall effect in graphene. Nature Physics  vol. \n16 38 –41 (2020).  \n63. Li, Y. et al.  Measurement of the optical dielectric f unction of monolayer transition -metal \ndichalcogenides: Phys. Rev. B  205422 , 1–6 (2014).  \n64. Yan, T., Yang, S., Li, D. & Cui, X. Long valley relaxation time of free carriers in monolayer \nWSe2. Phys. Rev. B  95, 1–7 (2017).  \n65. Ersfeld, M. et al.   Unveiling Valley Lifetimes of Free Charge Carriers in Monolayer WSe 2 \n. Nano Lett.  (2020) doi:10.1021/acs.nanolett.9b05138.  \n66. Ding, Y. et al.  Effective Electro -Optical Modulation with High Extinction Ratio by a \nGraphene -Silicon Microring Resonator. Nano Lett.  15, 4393 –4400 (2015).  \n67. Datta, I. et al.  Low-loss composite photonic platform based on 2D semiconductor \nmonolayers. Nat. Photonics  (2020) doi:https://doi.org/10.1038/s41566 -020-0590 -44. \n68. Lodahl, P. et al.  Chiral quantum optics. Nature  541, 473 –480 (2017).  \n69. Van Mechelen, T. & Jacob, Z. Universal spin -momentum locking of evanescent waves. \nOptica  3, 118 –126 (2016).  70. Hermann A, H. Haus Waves and Fields in Optoelectronics. Prentice Hall  (1984).  \n71. Amnon, Y. & Pochi, Y. Optical waves in crysta ls: propagation and control of laser \nradiation. Wiley  (1984).  \n72. Menon, V. M., Tong, W. & Forrest, S. R. Control of quality factor and critical coupling in \nmicroring resonators through integration of a semiconductor optical amplifier. IEEE \nPhotonics Techn ol. Lett.  16, 1343 –1345 (2004).  \n73. Bogaerts, W. et al.  Silicon microring resonators. Laser and Photonics Reviews  vol. 6 47 –\n73 (2012).  \n74. Yariv, A. Critical coupling and its control in optical waveguide -ring resonator systems. \nIEEE Photonics Technol. Lett.  14, 483 –485 (2002).  \n75. Smolenski, T. et al.  Tuning valley polarization in a WSe2 monolayer with a tiny magnetic \nfield. Phys. Rev. X  6, 1–7 (2016).  \n \n  Supplement ary information  \n \nAll-optical nonreciprocity due to valley polarization in  \ntransition metal dichalcogenides  \nYuma Kawaguchi1, Sriram Guddala1, Kai Chen1, Andrea Alù3,2,1, Vinod Menon2,4, and \nAlexander B. Khanikaev1,2 \n1Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New \nYork, 140th Street and Convent Avenue, New York, NY 10031, USA.  \n2Physics Program, Graduate Center of the City University of New York, New York, NY 10016, USA.  \n3Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY 10031, \nUSA  \n4Department of Physics, City College of New York, 160 Convent Ave., New York, NY 10031, USA  \n \n \nSupplement A  \nA1. Analytical models to fit the experimental results  \nThe reflectivity spectra for CW and CCW probe at maximum pump power (Fig ure.2d) was fitted \nby the Fresnel equation modified by  sheet conductivity1, \n|𝑟|2=|𝑛2−𝑛1−𝑍0𝜎̃\n𝑛2+𝑛1−𝑍0𝜎̃|2\n.                                                                (A1)  \nFor the CW and CCW probe reflectivities , one consider s the respective sheet conductivities  \n𝜎̃𝐶𝑊=𝜎𝑥𝑥+𝜎𝑥𝑦, 𝜎̃𝐶𝐶𝑊 =𝜎𝑥𝑥−𝜎𝑥𝑦, respectively, which yield  \n|𝑟𝐶𝑊|2=|𝑛2−𝑛1−𝑍0(𝜎𝑥𝑥+𝜎𝑥𝑦)\n𝑛2+𝑛1−𝑍0(𝜎𝑥𝑥+𝜎𝑥𝑦)|2\n,                                                           (A2)  \n|𝑟𝐶𝐶𝑊|2=|𝑛2−𝑛1−𝑍0(𝜎𝑥𝑥−𝜎𝑥𝑦)\n𝑛2+𝑛1−𝑍0(𝜎𝑥𝑥−𝜎𝑥𝑦)|2\n,                                                         (A3)   \nwhere 𝑍0=√𝜇0𝜖0⁄ is the free space impedance , and 𝑛1, 𝑛2 are the respective refractive indices \nof the superstrate and substrate surrounding  the TMDs monolayer. The off -diagonal component \n𝜎𝑥𝑦 gives rise to the difference in reflectivities of the CW and CCW  probes . \nThe optical permittivity  and sheet conductivity of TMD monolayer,  which are the function s of the \nphoton energy 𝐸, were  fitted by Lorentzian dispersion model2, \n𝜖(𝐸)=1+𝑓\n𝐸𝑒𝑥2+𝐸2−𝑖𝐸𝛾,                                                               (A4)  \n𝜎̃(𝐸)=−𝑖𝜖0𝐸𝑑\nℎ[𝜖(𝐸)−1]=−𝑖𝜖0𝐸𝑑\nℎ𝑓\n𝐸𝑒𝑥2+𝐸2−𝑖𝐸𝛾,                                       (A5)  \n where  𝑓 is the  oscillator strength , 𝐸𝑒𝑥 is the exciton resonance energy and 𝛾 is the linewidth of \nthe exciton resonance , and all represent  pump intensity dependent parameters, while  𝑑 is the \nthickness of TMD monolayer  and ℎ is the P lanck constant . The respective parameters for the case \nof maximal pump power are given in Table A1.  \nTable A1 | Fitting parameters  at 𝐼𝐶𝐶𝑊 =0.38 (𝑚𝑊 ) of Lorentzian type model in Fig. 2d \n𝑓 (eV2) 𝐸𝑒𝑥 (eV) 𝛾 (eV) 𝑑 (nm) \n236 2.018  0.15 0.618  \n \nAssuming only linear corrections to the linewidth and oscillator strength due to the pump, i.e. 𝛾=\n𝛾0+𝛾1𝐼𝐶𝐶𝑊 and 𝑓=𝑓0+𝑓1𝐼𝐶𝐶𝑊, and taking into account the lack of dependence of rhe \nresonance position observed in the experiment, we obtain an approximate expression for the \nintensity dependent conductivity , \n𝜎𝑥𝑥,𝑥𝑦=𝐴𝐼𝐶𝐶𝑊\n1+𝛼𝐼𝐶𝐶𝑊+𝜎0.                                                           (A6)  \nThe expression (A6) has the standard form of saturable absorption and has straightforward physical \ninterpretation with the parameter 𝐴 being  the rate of change of exciton  density due to the pump, \nand the parameter  𝛼 reflecting the spectral broadening of the resonance due to the  exciton -exciton \ninteractions . Figure 3a of the main text shows fitting results for the optical sheet conductivities \n𝜎𝑥𝑥 and 𝜎𝑥𝑦 using  equation (A 6), while  Table A 2 gives the corresponding value s of fitting \nparameters at the exciton resonance . The t erm 𝜎0 in (A 6) corresponds to  the optical conductivity \nwithout pumping  and it  is zero for 𝜎𝑥𝑦. \nTable A 2| Fitting parameters of optical sheet conductivities  \n 𝐴 𝛼 𝜎0 \n𝜎𝑥𝑥 0.0073  6.83 0.0013  \n𝜎𝑥𝑦 0.00053  1.99 0 \n \nBy combining the expressions (A1 -A3) and (A 6) we derive the reflectivities , which are saturable \nwith the pumping intensity 𝐼𝐶𝐶𝑊. For the simplest case o f no substrate 𝑛1,2=1, and by considering \nthe negligible value of 𝜎0≈0, after all the substitutions  we obtain the following expression : \n|𝑟|2=|𝑍0(𝐴𝐼𝐶𝐶𝑊\n1+𝛼𝐼𝐶𝐶𝑊)\n2−𝑍0(𝐴𝐼𝐶𝐶𝑊\n1+𝛼𝐼𝐶𝐶𝑊)|2\n=|𝑍0𝐴𝐼𝐶𝐶𝑊\n2(1+𝛼𝐼𝐶𝐶𝑊 )−𝑍0𝐴𝐼𝐶𝐶𝑊|2\n \n=|(𝑍0𝐴𝐼𝐶𝐶𝑊 )2\n4(1+𝛼𝐼𝐶𝐶𝑊 )2−4(1+𝛼𝐼𝐶𝐶𝑊 )(𝑍0𝐴𝐼𝐶𝐶𝑊 )+(𝑍0𝐴𝐼𝐶𝐶𝑊 )2| \n=|(𝑍0𝐴𝐼𝐶𝐶𝑊 )2\n4+(8𝛼−4𝑍0𝐴)𝐼𝑐𝑐𝑤+(4𝛼2−4𝛼𝑍0𝐴+𝑍02𝐴2)𝐼𝐶𝐶𝑊2|.                                               (A7)  \nBy adding a background correction due to the substrate, we arrive at the following expression \ndescrib ing the saturable behavior  for the probes with opposite helicities  |𝑟𝐶𝑊,𝐶𝐶𝑊|2\n𝑚𝑎𝑥=𝐴𝐶𝑊 ,𝐶𝐶𝑊 𝐼𝐶𝐶𝑊\n√4+𝛼𝐶𝑊 ,𝐶𝐶𝑊 𝐼𝐶𝐶𝑊 +𝛽𝐶𝑊 ,𝐶𝐶𝑊 𝐼𝐶𝐶𝑊2+|𝑟0|2 ,                                 (A8)   \nwhere |𝑟0|2is the reflectivit y without CCW pumping  𝐼𝐶𝐶𝑊 =0. The experimentally obtained \nreflectivity spectra for the CW and CCW probe s in Fig. 2 c of main text were  fitted with Eq. ( A8), \nand the respective fitting parameters are given  in Table A 3. \nTable A3 | Fitting parameters of the saturable absorption  \n𝑟0 𝐴𝐶𝑊  𝛼𝐶𝑊 𝛽𝐶𝑊 𝐴𝐶𝐶𝑊 𝛼𝐶𝐶𝑊 𝛽𝐶𝐶𝑊 \n0.0828  6.780  112.6  -21.86  11.97  464.1  597.8  \n \n \nA2. Perturbation theory  for the waveguide interacting with the dichroic 2D \nmaterial  \nThe simulation  of the waveguide was performed in COMSOL Multiphysics.  Experimentally  \nobtained optical conductivities were  then used to obtain t he imaginary part s of the propagation \nconstant in the waveguide 𝛽, which describes the attenuation of the guided wave, and is given by \nthe expression:  \nIm(𝛽)=𝛽0\n𝜔𝑊 0∫ 𝑑𝑆[𝑬0∗𝑅𝑒(𝜎̂𝑇𝑀𝐷)𝑬0] 𝑇𝑀𝐷,                                 (A9)  \nwhere  \n𝑊0=2∫𝑑𝑉[|𝐸0(𝑟)|2𝜖0𝜖𝑟(𝑟)]𝑉,                                     (A10)   \nand 𝑅𝑒(𝜎̂𝑇𝑀𝐷) is the real part of the optical conductivity of the TMDs monolayer , 𝑬0 is the \nabsolute value of the electric field , and 𝑊0 is the energy  density  of the guided wave  (the core plus \nthe cladding) . The imaginary part of the propagation constant 𝛼 due to the diagonal component of \nconductivity tensor, i.e. non -discriminating handedness of the field helicity,  is then given by  \n𝛼=𝛽0\n𝜔𝑊 0∫ 𝑑𝑆[|𝐸0|2𝜎𝑥𝑥]𝑇𝑀𝐷,                                        (A11)   \nwhile the helicity dependent absorption differential is defined by the off -diagonal component of \nconductivity  as \n𝛿=𝛽0\n2𝜔𝑊 0∫ 𝑑𝑆[|𝐸0𝐶𝑊|2−|𝐸0𝐶𝑊|2)(𝜎𝐾−𝜎𝐾′)]𝑇𝑀𝐷.                    (A12)  \n Since the conductivity is uniform across the TMD monolayer, the respective terms can be moved \nout from the integrals and will appear as factors. Then, the integrals defining the nonreciprocal \nabsorption are evaluated from numerically calculated field profiles with v alues given in Table A4.  \n \n Table A4 | Values of the perturbation theory  integrals used for the evaluation of the propagation constant  \nExpression  Evaluated  integration value \n∫ 𝑑𝑆|𝐸0𝐶𝑊|2\n𝑇𝑀𝐷 189.1 V2 \n∫ 𝑑𝑆|𝐸0𝐶𝐶𝑊 |2\n𝑇𝑀𝐷 1029.3 V2 \n∫ 𝑑𝑉|𝐸0(𝑟)|2\n𝑐𝑜𝑟𝑒 0.000419 V2m \n∫ 𝑑𝑉|𝐸0(𝑟)|2\n𝑐𝑙𝑎𝑑 0.00111 V2m \n𝜎𝑥𝑥 0.0021 S  \n𝜎𝑥𝑦 0.00125 S  \n \n \n \n  Supplement B  \n \nB1. Photoinduced nonreciprocal circular dichroism in WS 2 for CW pump  \nThe photoinduced nonreciprocal circular dichroism in WS 2 monolayer measured for the CW pump \nis shown in Fig. S1 . It can be noticed that in this case CW probe reflectivity shows the saturation, \nwhereas  for the case of CCW pump of  the main text , it is the  CCW probe reflectivity shows \nsaturation (Fig.  2 of the main text ).  \n \nFigure S 1| Experimental demonstration of photoinduced nonreciprocal circular dichroism in WS 2 \nfor the CW pump . a,b, Reflectivity of WS 2 monolayer with respect to probe of two opposite helicities as \nthe function of the wavelength and of the intensity of the pump with CW helicity. a and b show the cases \nof CCW and CW probes , respectively . The dark blue (low signal) region on the left is due  to optical filter \nused to eliminate the pump signal from the probe channel. c, pump power dependence of the reflectivity of \nthe probes with CW and CCW helicities at 𝜆=616 nm illustrating dichroic character and saturation. d, \nwavelength dependence of reflectivity for the CW and CCW probes.  \n \n \n \n \n \nB2. Schematic of e xperimental setup  \n \nLP: linear polarizer; LP Filter: Long pass filter.  \n \n \nReferences  \n1. Stauber, T., Peres, N. M. R. & Geim, A. K. Optical conductivity of graphene in the visible \nregion of the spectrum. Phys. Rev. B - Condens. Matter Mater. Phys.  78, 085432 (2008).  \n2. Li, Y. et al.  Measurement of the optical dielectric function of monolayer t ransition -metal \ndichalcogenides: Phys. Rev. B  205422 , 1–6 (2014).  \n \n \n"    },    {        "title": "1502.01071v1.Instability_of_a_ferrimagnetic_state_of_a_frustrated_S_1_2_Heisenberg_antiferromagnet_in_two_dimensions.pdf",        "content": "arXiv:1502.01071v1  [cond-mat.mtrl-sci]  4 Feb 2015Japanese Journal of Applied Physics RAPID COMMUNICATION\nInstability of a ferrimagnetic state of a frustrated S= 1/2\nHeisenberg antiferromagnet in two dimensions\nHiroki Nakano1∗and Toru Sakai1,2\n1Graduate School of Material Science, University of Hyogo, K amigori, Hyogo 678-1297, Japan\n2Japan Atomic Energy Agency, SPring-8, Sayo, Hyogo 679-5148 , Japan\nTo clarify the instability of the ferrimagnetism which is th e fundamental magnetism of ferrite, numerical-\ndiagonalization study is carried out for the two-dimension alS= 1/2Heisenberg antiferromagnet with frus-\ntration. We find that the ferrimagnetic ground state has the s pontaneous magnetizationin small frustration;\ndue to a frustrating interaction above a specific strength, t he spontaneous magnetization discontinuously\nvanishes so that the ferrimagnetic state appears only under some magnetic fields. We also find that, when\nthe interaction is increased further, the ferrimagnetism d isappears even under magnetic field.\nFerrite is a magnetic material that is indispensable in modern society. It is be-\ncause this material is used in various industrial products including mo tors, generators,\nspeakers, powder for magnetic recording, and magnetic heads et c. It is widely known\nthat fundamental magnetism of the ferrite is ferrimagnetism.1–4)The ferrimagnetism is\nan important phenomenon that has both ferromagnetic nature an d antiferromagnetic\nnature at the same time. The occurrence of ferrimagnetism is unde rstood as a mathe-\nmatical issue within the Marshall-Lieb-Mattis (MLM) theorem5,6)concerning quantum\nspin systems. A typical case showing ferrimagnetism is when a syste m includes spins\nof two types that antiferromagnetically interact between two spin s of different types in\neach neighboring pair, for example, an ( S,s)=(1, 1/2) antiferromagnetic mixed spin\nchain, in which two different spins are arranged alternately in a line and coupled by the\nnearest-neighbor antiferromagnetic interaction. The ferrimagn etic state like the above\ncase, in which the spontaneous magnetization is fixed to be a simple fr action of the\nsaturated magnetization determined by the number of up spins and that of down spins\nin the state, is called the Lieb-Mattis (LM) type ferrimagnetism. Ano ther example of\nferrimagnetism is a system including single-type spins that are more t han one in a unit\ncell, although the ferrimagnetism can appear even in a frustrating s ystem including\n∗E-mail: hnakano@sci.u-hyogo.ac.jp\n1/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\n\tB\n \tC\n \nβα\nα\b\nFig. 1. (Color) Network of antiferromagnetic interactions studied in this p aper. The black and red\nbonds represent J1andJ2interactions. Green squares denote finite-size clusters of 24 and 30 sites in\n(a) and (b), respectively. Note that the two-dimensional networ k composed only of the black bonds is\ncalled the Lieb lattice.\nonly a single spin within a unit cell.7,8)\nThe antiferromagnet on the Lieb lattice illustrated in Fig. 1 correspo nds the second\ncase, in which there are three spins in a unit cell. The MLM theorem hold s in the Lieb-\nlattice antiferromagnet. If antiferromagnetic interactions are a dded to this Lieb lattice\nso that magnetic frustrations occur, however, the MLM theorem no longer holds. In this\nsituation, the ferrimagnetic state is expected to become unstable . The problem of how\nthe ferrimagnetism collapses owing to such frustrating antiferrom agnetic interactions is\nan important issue to understand the ferrimagnetism well and to ma ke ferrimagnetic\nmaterials more useful in various products. This problem was studied in theS= 1/2\nHeisenberg antiferromagnet on the spatially anisotropic kagome lat tice,9,10)where the\nexistence of an intermediate phase with weak spontaneous magnet ization is clarified\nbetween the LM type ferrimagnetic phase and the nonmagnetic pha se including the\nisotropic kagome-lattice antiferromagnet. We are then faced with a question: is there\nany other different behavior of the collapse of the ferrimagnetism?\nUnder circumstances, the purpose of this study is to demonstrat e the existence of\na different behavior of collapsing ferrimagnetism in the case of an S= 1/2 Heisenberg\nantiferromagnet on the lattice shown in Fig. 1 to answer the above q uestion. When the\nantiferromagnetic interactions denoted by the red bonds vanish, the system is unfrus-\ntrated and thus it certainly shows ferrimagnetism in the ground sta te. In this study, we\nexamine the case when the red-bond interactions are switched on.\n2/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\nThe model Hamiltonian examined inthis study is given by H=H0+HZeeman, where\nH0=/summationdisplay\ni∈α,j∈βJ1Si·Sj+/summationdisplay\ni∈α′,j∈βJ1Si·Sj\n+/summationdisplay\ni∈α,j∈α′J2Si·Sj, (1)\nHZeeman=−h/summationdisplay\njSz\nj. (2)\nHereSidenotes an S= 1/2 spin operator at site i. Sublattices α,α′, andβand the\nnetwork of antiferromagnetic interactions J1andJ2are depicted in Fig. 1. Here, we\nconsider the case of isotropic interactions. The system size is deno ted byNs. Energies\nare measured in units of J1; thus, we take J1= 1 hereafter. We examine the properties\nof this model in the range of J2/J1>0. Note that, in the case of J2= 0, sublattices α\nandα′are combined into a single sublattice; the system satisfies the above conditions\nof the MLM theorem. Thus, ferrimagnetism of the LM type is exactly realized in this\ncase. In the limit of J2/J1→ ∞, on the other hand, the lattice of the system is reduced\nto a trivial system composed of isolated S= 1/2 spins and isolated dimers of two spins.\nIts ground state is clearly different from the state of the LM-type ferrimagnetism in the\ncase ofJ2= 0. One thus finds that while J2becomes larger, the ground state of this\nsystem will change from the ferrimagnetic one in the case of J2= 0 to another state,\nwhich we survey here.\nNext, we discuss the method we use here, which is numerical diagona lization based\non the Lanczos algorithm.11)It is known that this method is nonbiased beyond any\napproximations and reliable for many-body problems, which are not o nly localized spin\nsystems such as the Heisenberg model12,13)treated in th present study but also strongly\ncorrelatedelectronsystemsincludingtheHubbardmodel14–16)andthet-Jmodel.14,17,18)\nA disadvantage of this method is that the available system sizes are lim ited to being\nsmall. Actually, the available sizes in this method are much smaller than t hose of the\nquantum Monte Carlo simulation19,20)and the density matrix renormalization group\ncalculation;21)however, it is difficult to apply both methods to a two-dimensional (2D )\nfrustrated system like the present model. This disadvantage come s from the fact that\nthe dimension of the matrix grows exponentially with respect to the s ystem size. In\nthis study, we treat the finite-size clusters depicted in Fig. 1 when t he system sizes\nareNs= 24 and 30 under the periodic boundary condition. Note that each o f these\nclusters forms a regular square although cluster (b) is tilted from a ny directions along\n3/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\n–2 0\nh/J 1–1 01M/M sJ2/J 1 = 0.55(b)0 5 10 \nM–10–5 E /J 1Ns = 30\nJ2/J 1 = 0.55(a)\n2\nFig. 2. (Color) Results for J2/J1= 0.55. Lowest energy in each subspace of Mfor the system of\nNs= 30 is shown in panel (a). The magnetization process is depicted in pa nel (b); red and black lines\nrepresent results for Ns= 24 and 30, respectively.\ninteraction bonds.\nWecalculatethelowestenergyof H0inthesubspacecharacterizedby/summationtext\njSz\nj=Mby\nnumerical diagonalizations based on the Lanczos algorithm and/or t he Householder al-\ngorithm. The energy is represented by E(Ns,M), whereMtakes every integer up to the\nsaturation value Ms(=SNs). We here use the normalized magnetization m=M/Ms.\nSome of Lanczos diagonalizations have been carried out using the MP I-parallelized\ncode, which was originally developed in the study of Haldane gaps.22)Note here that\nour program was effectively used in large-scale parallelized calculation s.23–25)\nTo obtain the magnetization process for a finite-size system, one fi nds the magneti-\nzation increase from MtoM+1 at the field\nh=E(Ns,M+1)−E(Ns,M), (3)\nunder the condition that the lowest-energy state with the magnet izationMand that\nwithM+1 become the ground state in specific magnetic fields. Note here th at it often\nhappens that the lowest-energy state with the magnetization Mdoes not become the\n4/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\n–0.2 0\nh/J 1–0.4 –0.2 00.20.4M/M sJ2/J 1 = 0.64(b)\n0010 2 4 6\nM–13–12–11E /J 1Ns = 30\nJ2/J 1 = 0.64(a)\n0.2 3\nFig. 3. (Color) Results for J2/J1= 0.64. Lowest energy in each subspace of Mfor the system of\nNs= 30 is shown in panel (a). The magnetization process is depicted in pa nel (b); red and black lines\nrepresent results for Ns= 24 and 30, respectively. Main panel is a zoomed-in view of its inset wit h a\nwide range. The broken lines represent the results before the Max well construction is carried out.\nground state in any field. The magnetization process in this case is de termined around\nthe magnetization Mby the Maxwell construction.26,27)\nNow, we observe the case of J2/J1= 0.55; results are shown in Fig. 2. Figure 2(a)\ndepicts the lowest energy level in the subspace belonging to MforNs= 30. The levels\nforM= 0 toM= 5 are identical within the numerical accuracy. For M >5, the\nenergies increase with M. This behavior indicates that the spontaneous magnetization\nisM= 5. In Fig. 2(b), we draw the magnetization process determined by eq. (3) in the\nfull range from the negative to the positive saturations. The spon taneous magnetization\nm= 1/3 appears and the state at m= 1/3 shows the plateau with a large width. It is\nobserved that, above m= 1/3, the magnetization grows continuously. These behaviors\nare common with those of the LM ferrimagnetism at the unfrustrat ed case of J2= 0.\nNext, let us examine the case of J2/J1= 0.64; results are shown in Fig. 3. The\nMdependence of the lowest energy belonging to Mis different in M <3 from the\n5/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\ncase ofJ2/J1= 0.55. This difference affects with the disappearance of the spontane ous\nmagnetization, which is shown in Fig. 3(b). This discontinuous disappe arance occurs\natJ2/J1∼0.59 forNs= 24 and at J2/J1∼0.63 forNs= 30. An important point\nis that an intermediate state with smaller but nonzero spontaneous magnetizations is\nabsent between the m= 1/3 state and the nonmagnetic state. This behavior is clearly\ndifferent from the presence of such an intermediate state in the sp atially anisotropic\nkagome lattice.9,10)We speculate that this difference comes from the point that the\ncompeting interaction in the present model has a strong quantum n ature localized\nat pairs of dimerized spins. The discovery of the future third case o f the collapsing\nferrimagnetism would contribute to confirm our speculation. Note a lso that the plateau\natm= 1/3 shows a large width. This suggests that the ferrimagnetic state is realized\nif external magnetic fields are added.\nTo examine the properties of the m= 1/3 states in a more detailed way, we evaluate\nthe local magnetization defined as\nmξ\nLM=1\nNξ/summationdisplay\nj∈ξ/angbracketleftSz\nj/angbracketright, (4)\nwhereξtakesα,α′andβ. Here, the symbol /angbracketleftO/angbracketrightdenotes the expectation value of the\noperator Owith respect to the lowest-energy state within the subspace with a fixed\nMof interest. Recall here that the case of interest in this paper is M=Ms/3. Here\nNξdenotes the number of ξsites. Results are shown in Fig. 4. In the region of small\nJ2/J1,αandα′spins are up and βspin is down, although each of magnetizations is\nslightly deviated from the full moment due to a quantum effect. This s pin arrangement\nis a typical behavior of ferrimagnetism. On the other hand, in the re gion of large J2/J1,\nthe magnetizations at αandα′spins are vanishing and βspin shows almost a full\nmoment up. This marked change in the local magnetizations occurs a tJ2/J1∼1.38 for\nNs= 24 and at J2/J1∼1.40 forNs= 30, which suggests the occurrence of the phase\ntransition around at J2/J1∼1.4. Therefore one finds that, for J2/J1larger than this\ntransition point, the ferrimagnetic state cannot be realized even u nder magnetic fields.\nItisunfortunatelydifficulttodeterminethetransitionpointintheth ermodynamiclimit\nprecisely only from the present two samples of small clusters. For t he determination,\ncalculations of larger clusters are required in future studies. Note here that similar\nobservations of the local magnetizations were reported in Refs. 2 8 and 29, which treated\ntheHeisenberg antiferromagnet ontheCairo-pentagonlattice,30)a2Dnetwork obtained\nby the tiling of single-kind inequilateral pentagons. The same behavio r ofmξ\nLMis also\n6/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\nobserved when the kagome-lattice antiferromagnet31–37)is distorted in the√\n3×√\n3\ntype.25,38)The relationship between these models should be examined in future s tudies.\nNote also that, in the present model, the change around the trans ition point seems\ncontinuous irrespective of whether the system size is Ns= 24 or 30. This aspect is\ndifferentfromtheobservationintheCairo-pentagon-latticeantif erromagnet,28,29)where\nthe change around the transition point seems continuous for Ns= 24 but discontinuous\nforNs= 30. We speculate that whether the change is continuous or discon tinuous in\nfinite-size data is related to whether the number of unit cells in finite- size clusters is an\neven integer or an odd integer. To confirm this speculation, furthe r investigations are\nrequired in future. It will be anunresolved question whether the tr ansitionis continuous\nordiscontinuousinthethermodynamiclimit.Figure5depictsthemagn etizationprocess\natJ2/J1∼1.39. No jumps seem to appear in the process at J2/J1corresponding to\nthe transition point. It is unclear whether the width at m= 1/3 survives or vanishes\nalthough this m= 1/3 width at J2/J1∼1.39 is smaller than those in Figs. 2(b) and\n3(b). Future studies would clarify how themagnetization process b ehaves in the vicinity\nof the transition point.\nIn summary, we have investigated how the ferrimagnetic state of t heS= 1/2\nHeisenberg antiferromagnet onthe 2Dlatticecollapses owing to mag netic frustrationby\nnumerical-diagonalization method. We capture a discontinuous vanis hing of the sponta-\nneous magnetization without intermediate phase showing spontane ous magnetizations\nthat are smaller than that of the Lieb-Mattis ferrimagnetic state w hen a frustrating\ninteraction is increased. We also observe the disappearance of the ferrimagnetic state\nunder magnetic fields for even larger interaction showing frustrat ion. It is known that\norganicmolecularmagnetscanrealizeferrimagnetism.39,40)Sincevarietyoflatticestruc-\ntureleadingtoaninteractionnetworkisavailableinsuchorganicmolec ularmagnets,the\nexperimental confirmation might be done in these magnets more eas ily than metallic-\nelement compounds. Further studies concerning instability of the f errimagnetism would\ncontribute much for our development of more stable ferrimagnetic materials.\nAcknowledgments This work was partly supported by JSPS KAKENHI Grant Numbers 23 340109\nand 24540348. Nonhybrid thread-parallel calculations in numerical diagonalizations were based on\nTITPACK version 2 coded by H. Nishimori. Part of calculations in this st udy were carried out as an\nactivity of a cooperative study in Center for Cooperative Work on C omputational Science, University\nof Hyogo. Some of the computations were also performed using fac ilities of the Department of\nSimulation Science, National Institute for Fusion Science; Center f or Computational Materials\nScience, Institute for Materials Research, Tohoku University; Su percomputer Center, Institute for\n7/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\n0.5 1 1.5\nJ2/J 1–0.4 –0.2 00.20.4L ocal magnetization1.38 1.4 1.4200.5\n2\nFig. 4. (Color) Behavior of local magnetizations vs. the ratio of interactio nsJ2/J1together with a\nzoomed-in view near the transition point in inset. Closed circles and clo sed diamonds denote results\nforαandβforNs= 24, respectively. Results for α′forNs= 24 are identical those for αwithin the\nnumerical accuracy because αandα′are symmetric in the Ns= 24 cluster. Open circle, open\ntriangle, and open squares represent results for α,α′, andβforNs= 30, respectively. Due to the\ntilting for Ns= 30,αandα′are not symmetric, although results of αandα′forNs= 30 are slightly\ndifferent but very similar. To avoid invisibility from overlapping of symbo ls, results of α′are shown\nonly in inset.\n0 1 2 \nh/J 100.51M/M sJ2/J 1 = 1.39\n3\nFig. 5. (Color) Magnetization process for J2/J1= 1.39. Red and black lines represent results for\nNs= 24 and 30, respectively.\nSolid State Physics, The University of Tokyo; and Supercomputing D ivision, Information Technology\nCenter, The University of Tokyo. This work was partly supported b y the Strategic Programs for\nInnovative Research; the Ministry of Education, Culture, Sports , Science and Technology of Japan;\nand the Computational Materials Science Initiative, Japan. We also w ould like to express our sincere\nthanks to the staff of the Center for Computational Materials Scie nce of the Institute for Materials\nResearch, Tohoku University, for their continuous support of th e SR16000 supercomputing facilities.\n8/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\nReferences\n1) N. Ichinose, Jpn. J. Appl. Phys. 5, 461 (1966).\n2) N. Ichinose, Jpn. J. Appl. Phys. 5, 1140 (1966).\n3) A. M. Blanco and F. C. Gonzalez, J. Phys. D 22, 210 (1989).\n4) R. Heindl,R. Deschamps, M. Domine-Berges, and J. Loriers, J. Ma gn. Magn.\nMater.7, 26 (1978).\n5) W. Marshall, Proc. R. Soc. London, Ser. A 232, 48 (1955).\n6) E. Lieb and D. Mattis, J. Math. Phys. (N.Y.) 3, 749 (1962).\n7) T. Shimokawa and H. Nakano, J. Phys. Soc. Jpn. 80, 043703 (2011).\n8) T. Shimokawa and H. Nakano, J. Phys. Soc. Jpn. 80, 125003 (2011).\n9) H. Nakano, T. Shimokawa, and T. Sakai, J. Phys. Soc. Jpn. 80, 033709 (2011).\n10) T. Shimokawa and H. Nakano, J. Phys. Soc. Jpn. 81, 084711 (2012).\n11) C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).\n12) J. B. Parkinson and J. C. Bonner, Phys. Rev. B 32, 4703(1985).\n13) H. Q. Lin, Phys. Rev. B 42, 6561 (1990)\n14) A. Moreo and E. Dagotto, Phys. Rev. B 42, 4786 (1990).\n15) E. Dagotto, A. Moreo, F. Ortolani, D. Poilblanc, and J. Riera, Ph ys. Rev. B 45,\n10741 (1992).\n16) H. Nakano, Y. Takahashi, and M. Imada, J. Phys. Soc. Jpn. 76, 034705 (2007).\n17) M. Ogata, M. U. Luchini, S. Sorella, and F. F. Assaad, Phys. Rev . Lett.66, 2388\n(1991).\n18) H. Tsunetsugu and M. Imada, J. Phys. Soc. Jpn. 67, 1864 (1998).\n19) S. Miyashita, J. Phys. Soc. Jpn. 57, 1934 (1988).\n20) S. Todo and K. Kato, Phys. Rev. Lett. 87, 047203 (2001).\n21) S. R. White and D. A. Huse, Phys. Rev. B 48, 3844 (1993).\n22) H. Nakano and A. Terai, J. Phys. Soc. Jpn. 78, 014003 (2009).\n23) H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 80, 053704 (2011).\n24) H. Nakano, S. Todo, and T. Sakai, J. Phys. Soc. Jpn. 82, 043715 (2013).\n25) H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 83, 104710 (2014).\n26) M. Kohno and M. Takahashi, Phys. Rev. B 56, 3212 (1997).\n27) T. Sakai and M. Takahashi, Phys. Rev. B 60, 7295 (1999).\n28) H. Nakano, M. Isoda, and T. Sakai, J. Phys. Soc. Jpn. 83, 053702 (2014).\n29) M. Isoda, H. Nakano, and T. Sakai, J. Phys. Soc. Jpn. 83, 084710 (2014).\n9/10Jpn. J. Appl. Phys. RAPID COMMUNICATION\n30) I. Rousochatzakis, A. M. L¨ auchli, and R. Moessner, Phys. Re v. B85, 104415\n(2012).\n31) P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and P. Sindzing re, Phys. Rev. B\n56, 2521 (1997).\n32) C. Waldtmann, H.-U. Everts, B. Bernu, C. Lhuillier, P. Sindzingre , P.\nLecheminant, and L. Pierre, Eur. Phys. J. B 2, 501 (1998).\n33) K. Hida, J. Phys. Soc. Jpn. 70, 3673 (2001).\n34) J. Schulenburg, A. Honecker, J. Schnack, J. Richter, and H.- J. Schmidt, Phys.\nRev. Lett. 88, 167207 (2002).\n35) P. Sindzingre and C. Lhuillier, Europhys. Lett. 88, 27009 (2009).\n36) H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 79, 053707 (2010).\n37) T. Sakai and H. Nakano, Phys. Rev. B 83, 100405(R) (2011).\n38) H. Nakano, T. Sakai, Y. Hasegawa, J. Phys. Soc. Jpn. 83, 084709 (2014).\n39) Y. Hosokoshi, K. Katoh, Y. Nakazawa, H. Nakano, and K. Inou e, J. Am. Chem.\nSoc.123, 7921 (2001)\n40) Y. Hosokoshi, K. Katoh, K. Inoue, Synth. Met. 133, 527 (2003).\n10/10"    },    {        "title": "1406.4013v1.An_air_cooled_Litz_wire_coil_for_measuring_the_high_frequency_hysteresis_loops_of_magnetic_samples___a_useful_setup_for_magnetic_hyperthermia_applications.pdf",        "content": "An air-cooled Litz wire coil for measuring the high  frequency hysteresis \nloops of magnetic samples − a useful setup for magnetic hyperthermia \napplications \n \nV. Connord, B. Mehdaoui, R.P. Tan, J. Carrey* and M . Respaud \n \n \nLaboratoire de Physique et Chimie des Nano-objets ( LPCNO) ; Université de Toulouse; INSA; \nUPS; CNRS (UMR 5215) ;  135 avenue de Rangueil, F-3 1077 Toulouse, France \n \nAbstract : \n \nA low-cost and simple setup for measuring the high- frequency hysteresis loops of \nmagnetic samples is described. An AMF in the range 6-100 kHz with amplitude up to 80 mT is \nproduced by a Litz wire coil. The latter is air-coo led using a forced-air approach so no water flow \nis required to run the setup. High-frequency hyster esis loops are measured using a system of \npick-up coils and numerical integration of signals.  Reproducible measurements are obtained in \nthe frequency range of 6-56 kHz. Measurement exampl es on ferrite cylinders and on iron oxide \nnanoparticle ferrofluids are shown. Comparison with  other measurement methods of the \nhysteresis loop area (complex susceptibility, quasi -static hysteresis loops and calorific \nmeasurements) is provided and shows the coherency o f the results obtained with this setup. This \nsetup is well adapted to the magnetic characterizat ion of colloidal solutions of MNPs for \nmagnetic hyperthermia applications. Main Text: \n \n I. Introduction \nMagnetic hyperthermia has been the subject of an in tense research activity in the past \ndecade [1]. This experimental cancer therapy uses t he heat generated by magnetic nanoparticles \n(MNPs) put in an alternating magnetic field (AMF) o f typical frequency in the range 50-300 kHz. \nExperimentally, the heating power value is most of the time determined by measuring the \ntemperature rise of a colloidal solution placed in AMF [2]. Since the heat generated by the MNPs \nduring one cycle equals the area of their hysteresi s loop [1], an alternative method consists in \nmeasuring directly the hysteresis loop. However, si nce the hysteresis loop shape depends \ntremendously on the frequency of the AMF, quasi-sta tic measurements performed in a standard \nmagnetometer are not satisfying; measurements shoul d be done at a frequency similar to the one \nused in magnetic hyperthermia. Measuring the hyster esis loop instead of performing temperature \nmeasurements presents two major advantages: i) the complete hysteresis loop shape contains \nmuch more information than its simple area : inform ation on saturation magnetization, magnetic \ninteractions, aggregation of MNPs, MNP anisotropy c an for instance be deduced from the \nhysteresis loop shape. We and other groups have alr eady shown the interest of this method to get \nan insight into the physics of magnetic hyperthermi a [3, 4, 5, 6]. ii) It is much faster than \ntemperature measurements. A typical temperature mea surement takes in itself around one minute, \nbut the stabilisation of the temperature is much lo nger, so the typical delay between two \nmeasurements is ten minutes. A high-frequency hyste resis loop measurement takes in itself a few \nmicro-seconds, with no need of waiting between two measurements.  \nSo far, only a few groups have reported on the deve lopment of setups permitting such \nmeasurements. Several groups have reported on the b uilding of susceptometers, which provide real and imaginary components of the susceptibility  at low AMF [7]. A hysteresis loop tracer \nworking at a moderate frequency of 2 kHz was report ed in Ref. [8]. Bekovic et al. have built a \nsetup with an objective and an approach similar to ours [6, 9]. However, because of the \ntechnology used for the production of the AMF, the maximum AMF amplitude was only 19 mT \nand the coil had to be water cooled. Finally, a set up with similar functionalities as the one which \nwill be presented here has been built by Garaio et al. [10]. Unfortunately, very few technical and \nbuilding details are provided in this reference, pr eventing anyone to envisage building a similar \nsetup. \n In this article, we present a setup permitting to measure the hysteresis loops of colloidal \nsolutions of MNPs in a frequency range 6-56 kHz and  up to 80 mT. Being based on the use of \nLitz wires, this setup presents the main advantage that a low power is necessary to produce the \nAMF so it can be air-cooled. Measurement results on  typical samples are provided. \n \nII. Description of the setup \n 1. Electric circuit \n This setup is based on a resonant circuit similar to the one described in Ref. [2]. The \nprinciple is to produce an alternating current at a  chosen frequency through a function generator \n(MTX 3240, Metrix) coupled to a voltage amplifier ( HSA 4052, NP Corporation), which can \ndeliver a current of ±2.8 A and voltage of  ±150V a t a maximum frequency of 500 kHz. The \nelectrical circuit is shown in Fig. 1(a). Since the  amplifier maximum current is limited to 2.8 A, a \nhome-made transformer is used to increase the curre nt amplitude. It is composed of 4 commercial \nI-shaped Ni-Zn ferrites assembled in square (Epsos,  material N27). The transformer has 23 turns \nof Litz wire (240×0.05mm, Connect systemes) at the primary and 2.5 turns at the secondary, \nwhich increases the output current amplitude by a f actor 9. To bring the transformer to resonance, a home-made high-voltage ceramic disks adjustable c apacitance C1 is introduced in the primary \nloop; its building has been described in Ref. [2]. A second capacitor C2 is placed into the \nsecondary circuit to bring it to resonance. C2 is composed of several high-voltage ceramic \ncapacitors in series (Vishay, 100 nF, 2500 V). The current in the setup is measured with an AC \ncurrent probe (3274 clamp probe, Hioki). Finally, a  home-made coil which is electrically \nequivalent to a LC parallel circuit is placed into the secondary circuit to produce the AMF.  \n \n 2. Production of magnetic field by the main coil \n The main magnetic coil is composed of Litz wires ( 480x0.071mm, Pack Feindrähte). \nUsing Litz wire is essential to avoid the skin effe ct due to the high frequency current, and to keep \nthe impedance of the coil as low as possible. 120 t urns of wires are rolled up around a PVC \nstructure. Each layer of wire is separated from the  others by a 0.5 mm thick fiberglass mesh to \nprevent electrical breakdown and sparking between t he layers. Thanks to the low impedance of \nthe coil, the heat generated inside it is moderate and can be extracted by a forced air approach. \nFor that purpose, the coil former is pierced of sev eral rectangular holes allowing the air to go \ntrough [see Fig. 1(b)]. The coil is then put on a h ollow holder and connected to a simple vacuum \ncleaner (Ultra Active Green, Electrolux) so the air  is forced from outside the coil to the inside \n[see Figs 2(a) and 2(b)]. This cheap system keeps t he coil temperature stable even if a high \namplitude AMF is applied during hours. AMF amplitud e was calibrated using a pick up coil \ninserted into the main coil. The amplitude of the A MF is calculated using : \n \nfnS Hµ\ncoil πε=max 0  ,  (1)  \nwhere n and Scoil  are the number of turns and surface of the pick-up  coil, f the frequency of the \nAMF and ε the voltage appearing at the coil terminal. Fig. 3 (a) shows the AMF maximum \namplitude as a function of the coil current at a fi xed frequency of 54 kHz. AMF amplitude is \nlinear with the applied current, with a factor of 2 .0±0.1 mT/A. Fig 3(b) shows the evolution of the \nAMF amplitude as a function of the position inside the coil. As expected, the field amplitude \ndecreases on the sides of the coil. There is a 4 cm  depth plateau where AMF does not vary by \nmore than 4%. This 4 cm height zone is used as a wo rking area to put the sample and the \nmeasurement coils (see below). \n Table 1 displays the evolution of the maximum AMF amplitude and current which can be \ngenerated as a function of the working frequency. T he corresponding coil impedance Z(Ω), as \nwell as the C1 and C2 values leading to the circuit resonance are also s hown. Coil impedance \nincreases with the applied frequency inducing a dec rease of the maximum AMF. Simultaneously, \nthis also increases the heat generated inside the c oil, which is compensated by adjusting the \nvacuum cleaner power.  \n \n 3. Hysteresis loop measurements \n Now the home-made system permitting to measure the  high-frequency hysteresis loop of \nmagnetic samples is described. The detection system  is schematized in Fig. 4(a). It consists of \ntwo identical contrariwise-wounded pick-up coils (7  turns of a copper wire, 0.7 mm diameter) \nconnected in series. Let us call coil 2 the pick-up  coil wounded around the sample and coil 1 the \nother one [see Fig. 1(c)]. These pick-up coils are wounded around a PVC holder which maintains \nthe sample and the pick-up coils at a constant heig ht inside the main coil [see Fig. 1(c)]. A tapping and a nut at the top of the sample holder p ermit to adjust precisely its height. Two signals \nare required to measure the high-frequency hysteres is loops: let e1(t) be the voltage at the \nterminals of pick-up coil 1 and e2(t)  the one at the terminals of the two coils in ser ies [see Fig. \n4(a)]. These high-frequency signals are measured by  an oscilloscope (TDS 2022B, Tektronix) \nconnected by USB to a computer and then transmitted  to the latter.                                                                                                   \n The protocol to measure the hysteresis loop of the  sample is the following. First, the \nheight of the empty sample holder is adjusted rough ly to get a maximized signal in coil 1. Then a \nfine adjustment of the height is done by minimizing  e2(t) signal. Each hysteresis cycle \nmeasurement then requires three steps:  \n- Measurement of e1(t) and e2(t)  for a blank sample, which is the same vessel as the  true sample \nfilled with the same quantity of solvent but withou t any magnetic material. \n- Measurement of the true sample \n- Then, the signal e2(t) from the blank sample is substracted from the s ignal e2(t)  obtained from \nthe true sample. \n A typical signal obtained from coil 1 is shown in Fig. 4(b). Signals e2(t) obtained from a \nmagnetic sample and from the blank sample are shown  in Fig. 4(c). To obtain the magnetic field \nand magnetization values,  e 1(t) and e2(t) are integrated numerically using : \n \n( )()\ncoil nS dt te\ntH∫=1\n0µ    (2) \n( )()\nΦ=∫\nsample Snµdt te\ntρσ\n02   (3) \n ( )()\nΦ=∫\nsample nS µdt te\ntM\n02   (4) \nσis the magnetization per unit mass of magnetic mate rial, M its magnetization per unit volume,  \nSsample  the surface of a section of the magnetic sample, Φ the volume concentration of the sample \nand ρ the density of the magnetic material. The numerica l integration is performed on data \ncoming from a single period of the AMF; the average  value of the signal on this period is \nsubstracted from the signal before integration. The  hysteresis loop is obtained by plotting σ or M \nas a function of µ0H, as shown in Fig. 4(d). \n \n III. Measurement examples. \n 1. Ferrite cylinders \n To validate our setup, we have performed measureme nts on commercial ferrite cylinders. \nIn Fig. 5, measurements of ferrites cylinders (Ferr oxcube ROD8/2563S3, 8 mm diameter) at \nfixed frequency as a function of AMF amplitude are shown. Raw signals in coils 1 and 2 are \nshown in Figs. 5(a) and 5(b) for a 2.5 cm long ferr ite cylinder. Corresponding hysteresis loops \nobtained after numerical calculation are shown in F ig. 5(c). These ferrite cylinders display a \nnegligible coercive field, which explains why the v arious hysteresis loops all collapse on a single \nreversible curve. The ferrite saturation is clearly  observed. On this experiment, the hysteresis \nloop could not be measured at larger field because e2(t) became too large to be measured by the \noscilloscope. The approximate saturation value ( ≈ 0.25 T) matches the one expected for this \nferrite (0.32 T from constructor). A low AMF, the c ycles display a linear part, the slope of which \ncorresponds to the external magnetic susceptibility  χext , which in this case equals 10.5.   External susceptibility χext  is directly linked to the demagnetizing factor of the cylinder, \nitself being related to the cylinder length. To che ck the influence this parameter, we have \nmeasured the response of ferrite cylinder of differ ent lengths [see Fig. 5(d)]. As expected, χext  \nstrongly diminishes when shorter cylinders are meas ured. Three different theoretical values of \nχext  have been calculated. χm and χf are derived from the magnetometric and fluxmetric \ndemagnetizing factors extracted from the tables of Ref. [11]. χBoz  is another calculation derived \nfrom fluxmetric demagnetizing factors by R. M. Bozo rth [12].  Comparison between these \ntheoretical values and the experimental are shown i n Table 2. The agreement between the \nexperimental value and the theoretical one is accep table for short ferrites, since there is a factor o f \n2 between both. The discrepancy increases significa ntly for longer samples, probably because \nlong samples have a significant part out of the wor king area and are thus submitted in average to \na lower AMF. However, both the reversible hysteresi s loops and the saturation value expected for \nthese ferrite cylinders are first signs of our setu p validity.  \n \n 2. Measurements on an iron oxide nanoparticle ferr ofluid. \n a) Hysteresis loop measurements. \n The samples studied in this work were colloids of magnetite/maghemite prepared by a \nmodified version of the well known co-precipitation  method originally due to Kalafallah and \nReimers [13].  The samples were prepared by precipi tation of the oxyhydroxides from molar \nsolutions of ferrous (Fe 2+ ) and ferric (Fe 3+) salts.  The precipitation was undertaken using \nammonia. Following the initial precipitation gentle  warming was used to convert the \noxyhydroxides nominally to magnetite (Fe 3O4) but due to the alkalinity of the solution partial  \noxidation to maghemite (Fe 2O3) occurred.  Subsequently using closely controlled conditions of temperature and pH a controlled growth process (CGP ) was used to produce a system with a \nnarrow particle size distribution. The particle siz e distribution was measured using a JEOL 2011 \nTEM with a resolution of about 0.3 nm.  Particle si zes were measured using a Zeiss particle size \nanalyser which is essentially a light box such that  the diameter of individual particles is obtained \nby an equivalent circle method.  To ensure good sta tistics over 500 particles were measured and \nas expected a good fit to a lognormal distribution function was found.  Figs. 6(a) and 6(b) show a \ntransmission electron micrograph of the particles a nd the subsequent size distribution. The \nparticles were dispersed in water using DMSA at a c oncentration of 5 mg of Fe per ml of water.  \nAs can be seen from the TEM image the particles wer e relatively well dispersed with little \naggregation.  The colloid was dialysed to remove re maining traces of the initial salt solutions. \n To measure the sample, we put 0.5 mL of colloidal solution inside a 5 mm in diameter \nvessel. The measurement process here is exactly the  same as for the ferrite samples except that, at \nthe end of the measurement, Equ. (3) is used instea d of Equ.(4) so the magnetization per mass of \nMNPs σ  is obtained.  In Fig. 7 hysteresis loops measurements as a functi on of the AMF \namplitude and for four frequencies in the range of our setup (19, 32, 56 and 92 kHz) are shown. \nFor each frequency, all the cycles are plotted on t he same graph. Measurements at the three lower \nfrequencies show a very high coherency, all the cur ves being interlocked one inside the others. At \nthe largest frequency (92 kHz), the observed lack o f coherency reflects a lack of reproducibility \non the measurements. This is due to the fact that, at large frequencies, the signal is more sensitive \nto even slight modification of the position of the sample inside the sample holder. As a \nconsequence, when this setup was used for measuring  various nanoparticle systems, we have \nalways restricted our frequency to a maximum value of 56 kHz [3, 4, 5].  \n  b) Comparison between our setup and other measurem ent methods. \n To check the validity and coherency of the results obtained using our setup, we have \ncompared it to three other measurement approaches. First, at low AMF, any magnetic system \nresponds linearly with the applied magnetic field s o its magnetic response is completely \ncharacterized by its complex susceptibility χ~. In this regime, the hysteresis loop is an ellipse , the \narea of which can be calculated using [1]: \n,2\nmax χπ′ ′ =HA    (5) \nwhere χ′′ is the imaginary component of χ~. In Fig. 8(a), we show that the hysteresis loops \nmeasured between 2 and 30 mT at 56 kHz are all elli pses with the same shape once normalized. \nThe data are perfectly fitted with an ellipse using  Equs. (30) and (31) of Ref. 1. From this fit, χ~, \nϕ (the phase delay between the AMF and the magnetiza tion) and so ϕχχsin ~=′ ′  were \ndetermined. The hysteresis area calculated using Eq u.(5) and χ′′ determined this way are shown \nin Fig. 8(b) along with the area resulting from the  integration of the individual hysteresis loops; \nboth are logically in good agreement. In this regim e where the linear response theory is valid, \nstandard ac susceptibility measurements are in prin ciple sufficient to determine the hysteresis \narea. To check it, we have connected the output of the pick-up coils to a lock-in amplifier (SR830 \nDSP, Stanford Research Design). As expected, phase values obtained from the lock-in amplifier \nare independent of the AMF amplitude in the range 2 -23 mT , leading to a phase value of ϕ = \n8.7 ±2.6°. This means that at low magnetic, the results given by our setup matches what would be \nobtained with a standard susceptometer. \n Second, we have compared the hysteresis loop obtai ned on our setup with the one \nobtained using a vibrating sample magnetometer (VSM ) measuring the static hysteresis loop. For \nthat purpose, a dried powder issued from the ferrof luid was measured. In Fig. 8(c), both measurements are compared. The static hysteresis lo op measured at the VSM has a negligible \ncoercive field whereas the high-frequency one displ ays an opened hysteresis loop. In spite of this \nnon-surprising difference due to the frequency depe ndence of the coercive field, we notice that \nthe amplitude of the magnetization and the curvatur e of the hysteresis loop are very similar in \nboth setups, which is another sign of the validity of our setup. \n Finally, we compare the obtained hysteresis loop w ith a calorific method. Indeed, the \nhysteresis area is related to the specific absorpti on rate (SAR) of MNPs by equation [1]: \n.Af SAR =      (6) \nWe have thus performed SAR measurements using the p rotocol and analysis method described in \nRef. [2]. Briefly, it consists in measuring the tem perature rise of the colloidal solution when the \nAMF is put on. We have performed these measurements  i) directly inside the present setup using \nthe sample holder as a calorimeter, and ii) inside the electromagnet described in Ref. [2]. The \nhysteresis area deduced from these temperature meas urements are plotted in Fig. 8(d) along with \nthe values obtained after integrating the hysteresi s loops. Hysteresis area deduced from \ntemperature measurements on the electromagnet are i n very good agreement with the one \nobtained from integration, which is a last confirma tion of the validity of our setup. However, it is \nobvious from data shown in Fig. 8(d) that the prese nt setup is not adapted to perform temperature \nmeasurements; it is very likely that, due to the pr esence of a strong air flow inside the setup to \ncool down the coil, the calorimeter losses are very  large and prevent to perform any correct \ncalorimetric measurements inside the setup. This po int could be improved by inserting an \nadiabatic chamber inside the sample holder to insul ate thermally the sample from the remaining \nof the setup. \n  \n IV. Conclusion \n We designed a Litz wire coil able to generate an A MF in the range 6-100 kHz with \namplitude up to 80 mT. This coil is air-cooled so n o water flow is required to run the setup. \nMagnetic hysteresis loops are obtained using contra ry-wide wounded pick-up coils inserted in a \ncoil space where the AMF is homogeneous. Pick-up co ils signals are acquired by an oscilloscope \nand then numerically integrated. Reproducible and s table hysteresis loops are obtained up to \nfrequency of 56 kHz. At low AMF, when the system re sponds linearly to the AMF, connecting \nthe coils to a lock-in simply transforms the setup into a standard susceptometer. In these \nconditions, hysteresis area analysis and complex su sceptibility measurements give identical \nresults with respect to the magnetic response of th e system. Comparison with VSM and \ntemperature measurements indicates the coherency of  the our measurement results. The present \nsetup permits an insight on the physics of magnetic  hyperthermia and has proven its utility in \npreviously published articles [3, 4, 5].  Acknowledgements :  \nThis research was partly funded by the European Com munity’s Seventh Framework Programm \nunder grant agreement no. 262943 “MULTIFUN”. We ack nowledge Liquids Research for \nsupplying the magnetic nanoparticles through the MU LTIFUN Project.  We thank A. Khalfaoui \nand B. Simonigh for machining the setup. \n \nReferences : \n* Correspondence should be addressed to J.C. (julia n.carrey@insa-toulouse.fr) \n                                                   \n[1] J. Carrey, B. Mehdaoui and M. Respaud, J. Appl.  Phys. 109, 083921 (2011) \n[2] L.-M. Lacroix, J. Carrey, M. Respaud, Rev. Sci.  Instrum. 79 , 093909 (2008) \n[3] B. Mehdaoui, J. Carrey, M. Stadler, A. Cornejo,  C. Nayral, F. Delpech, B. Chaudret and M. \nRespaud, Appl. Phys. Lett. 100 , 052403 (2012) \n[4] A. Meffre, B. Mehdaoui, V. Kelsen, P. F. Fazzin i, J. Carrey, S. Lachaize, M. Respaud and B. \nChaudret, Nanoletters 12 , 4722 (2012) \n[5] B. Mehdaoui, R. P. Tan, A. Meffre, J. Carrey, S . Lachaize, B. Chaudret and M. Respaud \nPhys. Rev. B 87 , 174419 (2013) \n[6] M. Bekovic, M.Trlep, M. Jesenik,V. Gorican, A. Hamler, J. Magn. Magn. Mater. \n[7] M. Alderighi, G. Bevilacqua, V. Biancalana, A. Khanbekyan, Y. Dancheva and L. Moi, Rev. \nSci. Instr. 84 , 125105 (2013) \n[8] S. B. Slade, G. Kassabian, and A. E. Berkowitz,  Rev. Sci. Instrum. 67 , 2871 (1996) \n[9] M. Bekovic and A. Hamler, IEEE Trans. Mag. 46 , 552 (2010) \n[10] E. Garaio, J.M. Collantes, J.A. Garcia, F. Pla zaola, S. Mornet, F. Couillaud and O. Sandre, J. \nMagn. Magn. Mater., in press, http://dx.doi.org/10. 1016/j.jmmm.2013.11.021                                                                                                                                                                      \n[11] D.-X. Chen, J. A. Brug and R. B. Goldfarb, IEE E Trans. Mag. 27, 3601 (1991) \n[12] Ferromagnetism , by Richard M. Bozorth, pp. 99 2. ISBN 0-7803-1032-2. Wiley-VCH , \nAugust 1993. \n[13] S.E. Khalafalla and G.W. Reimers, IEEE Trans. Mag. 16, 178 (1980)   \nTables:  \n \n \nf (kHz) C1 (nF)  C2 (nF)  I (A)  Z ( Ω) µ0Hmax  (mT)  \n6.8 2200 1100 40 0.25 80 \n13.5 657 560 40 0.2 75 \n22.5 200 200 40 0.2 75 \n31.9 111 100 40 0.28 75 \n45.0 53.1 50 40 0.33 75 \n55.2 34.1 33 40 0.4 75 \n63.7 24 25 35 0.45 65 \n71.1 20 20 33 0.5 61 \n84.1 7.8 14.3 28 0.6 52 \n95.4 4 11.1 25 0.63 46 \n \n \nTable 1: Electrical and magnetic properties of the main coil as a function of the working \nfrequency f. Values of capacitor in the primary and secondary circuit ( C1 and C2), of the \nmaximum current I, of the impedance Z and of the magnetic field µ0Hmax  are provided.   \nLength \n(mm) χext  χf χm χBoz  \n6.25 1.9 4.329 4 4.35 \n12.5 3.9 12.48 7.87 9.09 \n25 8.1 31.25 17.24 25 \n50 19.2 104.17 35.71 66.7 \n75 22.1 177.3 71.43 833 \n \n \nTable 2: Comparison between the external value of t he susceptibility χext  and different theoretical \nvalues. χBoz  is extracted from Ref. [12].  χf and  χm are extracted from Ref. [11]. The constructor \nvalue for the ferrite magnetic permeability µ = 350 was used.  \n \n \nFigures :  \n \n \n \n \nFigure 1 (color online) : (a) Electric schematic of  the setup. C1 (C 2) is a variable capacitor \npermitting the resonance of the primary (secondary)  circuit. The main coil is schematized by a \nparallel L 0C0 circuit. (b) Technical drawing of the main coil ho lder. (c) Technical drawing of the \nsample holder.  \n \n \n \nFigure 2 (color online): (a) Technical drawing of t he complete setup (b) Picture of the complete \nsetup.  \n \nFigure 3 (color online): (a) AMF measured as a func tion of the ac current sent through the main \ncoil. (b) AMF amplitude as a function of the positi on inside the coil. Vertical dashed lines show \nthe limits of the coil. Dotted lines delimitate the  working zone, where the pick-up coils and the \nsample are placed.  \n \nFigure 4 (color online): (a) Schematic illustrating  the detection principle using pick-up coils. (b) \nTypical measurement of voltage signal e1(t) measured on coil 1. (c) Typical measurement of \nvoltage signal e2(t) measured on coil 1 and coil 2 in series. Dots cor respond to the signal obtained \nwhen a blank sample is inserted. Plain line corresp onds to the signal obtained when a typical \nmagnetic sample is put inside the setup. (d) Hyster esis loop obtained after subtracting the blank \nsample signal from the sample one, and subsequent n umerical integration.    \n \n \n \n \nFigure 5 (color online): Measurements of ferrite cy linder samples. (a)(b) Signals e1(t) and  e2(t)   \nwhen the AMF is increase from 0 to 50 mT at a frequ ency of 56 kHz. A 2.5 cm long ferrite \nsample is measured (c) Hysteresis loops obtained fr om the previous signals. All curves all \nsuperimposed on a single one. (d) Hysteresis loops obtained for ferrite samples of varying length \nL.    \n \n \n \nFigure 6 : (a) Transmission electron microscopy of the synthesized MNPs. (b) Size distribution of \nthe MNPs fitted by a log-normal distribution.  \n \n \nFigure 7 (color online): Measurements on an iron ox ide nanoparticle ferrofluid. The figures show \nthe hysteresis measurements as a function of the AM F at frequencies of a) 19 kHz, b) 32 kHz, c) \n56 kHz, and d) 92 kHz.  \n \n \n \n \nFigure 8 (color online): Comparison between various  measurement methods. (a) Normalized \nhysteresis loops measured at 56 kHz for µ0Hmax  ranging from 2 to 18 mT.  (b) Area calculated at \nlow AMF by two methods: ( ■) by integration of the hysteresis loop. ( ●) by using Equation (5). \n(c) Comparison between the hysteresis loop measured  using our setup (plain line) and VSM \n(dashed line). (d) The hysteresis area is calculate d using ( ■) temperature measurements inside our \nsetup, ( ●) temperature measurement inside an electromagnet, ( ▲) integration of hysteresis loops.  "    },    {        "title": "1307.4881v1.Interaction_effect_detected_by_compared_of_the_irreversible_and_remanent_initial_magnetization_curves_in_Ni_Cu_Zn_ferrites.pdf",        "content": " \n1\n \nINTERACTION EFFECT DETECTED BY COMPARED \nOF THE \nIRREVERSIBLE AND REMANEN\nT INITIAL MAGNETIZATION \nCURVES IN Ni\n-\nCu\n-\nZn FERRITES\n \nG. GOEV, V. MASHEVA\n \nFaculty of Physics, “St. Kliment\n \nOhridski” University of Sofia, James Boucher 5, 1164\n-\nSofia, \nBulgaria\n \ne\n-\nmail: gog\no@phys.uni\n-\nsofia.bg\n,\n \nvmash@phys.uni\n-\nsofia.bg\n.\n \nAbstract. \nA new technique for estimation of \nmagnetic \ninteraction\n \neffects\n \nof \ninitial magnetization\n \ncurves \nhas been \nproposed\n.\n \nIt deal\ns\n \nwith\n \nremanence\n,\n \n(\n)\nH\nIRM\nM\nr\n, and\n \ninitial irreversible \nmagnetizatio\nn\n,\n \n)\n(\nirr\nH\ni\nM\n, curves\n. The \nmethod\n \nis applied for\n \ns\ningle\n-\nphase polycrystalline \n             \nNi\n0.85\n-\nx\nCu\n0.15\nZn\nx\nFe\n2\nO\n4\n,\n \n(x = 0, 0.2, 0.4 and 0.6)\n, which\n \nwere synthesized by a standard ceramic \ntechnology. \nA study of the initial \nreversible and irrever\nsible \nmagnetization processes in ferrite \nmaterials was carried out\n.\n \nThe field dependence of the irreversible\n, \n)\n(\nirr\nH\ni\nM\nand reversible, \n)\n(\nrev\nH\ni\nM\nmagnetizations was determined by magnetic losses of minor hysteresis loops obtained fr\nom \ndifferent points of\n \nan\n \ninitial magnetization curve. \nThe influence of Zn\n-\nsubstitutions\n \nin Ni\n-\nCu ferrites \nover irreversible magnetization processes and interactions in magnetic systems has been analyzed.\n \n \nKeywords\n: \nMagnetic i\nnteraction effects, r\neversible\n \nand irreversible magnetizations, magnetization \ncurves,\n \nhysteresis magnetic losses, Ni\n-\nCu\n-\nZn ferrites.\n \nPACS: 75.60.Jk, 75.60.Ej, 87.50.C\n \n \n1.\n \nINTRODUCTION\n \nThe\n \neffect\ns\n \nof magnetic interaction\ns can \nchange \nsubstantially the\n \nmagnetic \ncharacteristic of \nthe \nmaterial\ns. These effects are \nresults of different\n \nphenomena\n \nand \nthere \nexist several \nmethods of approach\n \nthem\n \n[\n1\n]\n. \nOne of\n \nthem \ninvestigates\n \ninteraction effects \nwith\n \nestablished \n∆\nM\n \ntechnique, comparing remanen\nce\n \nmagnetization,\n \n(\n)\nH\nIRM\nM\nr\n,\n \nand dc \ndemagnet\nization remanence, \n(\n)\nH\nDCD\nM\nd\n \ncurves\n \n[\n2\n]\n.\n \nThe remanence \ncurves are determined\n \nby purely irreversible magnetic \nchanges\n, but the measurements of the remanences are in zero field. \n \nAn initial magnetization curve of a virgin sample can be experimen\ntally \nobtained by the edges of minor hysteresis loops, plotted in AC magnetic field with \nprogressively increasing amplitude\n \n[\n3\n]\n.\n \nA method\n, how\n \nthe information for \nirreversible processes of initial magnetization could be derived by the \ndetermination \nof magn\netic losses \nfrom\n \neach minor hysteresis loops\n,\n \nwas proposed \nin Ref. 4\n. \nSimilar method for irreversible processes of maj\nor hysteresis loop can \nalso \nbe applied \nto\n \nRef. \n5\n. \nThe method\ns\n \nw\ne\nre\n \nproved on a Stoner\n–\n \nWohlfarth model \nsystem consisting of disordered non\n-\ninteracting single\n-\ndomain uniaxial particles\n \n[\n6\n]\n \nand compared\n \nwith the results by the remanence curve method\n \n[\n7\n,\n \n8\n]\n. \n \nNi\n-\nCu\n-\nZn ferrites are\n \npertinent magnetic materials for the multiplier chip \ninductors at high frequencies, which are important components \nin many electronic This watermark does not appear in the registered version - http://www.clicktoconvert.com \n2\n \ndevices\n \n[\n9\n,10\n]\n. The magnetic properties of those ferrites\n \nare highly sensit\nive to the \nsintering conditions\n.\n \nSee Refs. \n11\n-\n1\n4\n \nfor more \ndetails.\n \nThe \naim of the present paper is\n:\n \n(i)\n \nto estimate the \nfield dependence of the \nreversible and irrever\nsible \nsusceptibility and magnetizations by using the initial magnetization curve \nof the \npolycrystalline \nsamples\n,\n  \nNi\n0.85\n-\nx\nCu\n0.15\nZn\nx\nFe\n2\nO\n4\n \n(\nx\n \n= 0, 0.2, 0.4\n \nand 0.6)\n,\n \n(ii)\n \nto \nobtain\n \n(\n)\nH\nM\ni\nD\n \n–\n \nplot, describing\n \ninteraction effects\n \nof \ninitial \nmagnetiza\ntion.\n \n2.\n \nEXPERIMENT\n \nZinc substituted Nickel\n-\nCopper ferrites of the composition \n                    \nNi\n0.85\n-\nx\nCu\n0.15\nZn\nx\nFe\n2\nO\n4\n \n(\nx\n \n= 0, 0.2, 0.4, 0.6) were synthesized following the standard \nce\nramic technology described in \nRef.\n \n9\n. The obtained ferrite powders were \npressed \nin ring\n-\nforms with outer and inner diameters of 16.5 mm and 10.2 mm respectively, \nand thickness of 4.6 mm. The final sintering of the rings was carried out at \ntemperature 1125\no\nC for 4 h in air.\n \nThe main magnetic parameters such as saturation \nmagnet\nization, remanence, coercivity and initial permeability\n \nat room temperature\n, \nmeasured from the entire hysteresis loops \nand the scanning electron microscopy \n(SEM) \nof the sam\ne four samples were reported in \nRef. 9\n.\n \nThe minor hysteresis \nloops of toroidal sampl\nes were plotted by using a Ricken\n-\nDenshi AC B\n-\nH Curve \nTrac\ner in field with a frequency of\n \n2 kHz at room temperature\n.\n \n3.\n \nTHE METOD\n \nBoth reversible and irreversible processes occur during magnetization along \nan initial magnetization curve. They can be character\nized by the corresponding \nmagnetizations, \ni\nM\nrev\n \nand \ni\nM\nirr\n, and differential magnetic susceptibilities, \ni\nrev\nc\n \nand \ni\nirr\nc\n \nrespectively. \ni\nM\nirr\n, \ni\nirr\nc\n, and the\n \nenergy, \ni\nW\nirr\n, associated with the \nirreversible magnetization processes.\n \nThe hysteresis losses, \n)\n(\nhyst\nirr,\nH\nW\np\n, can be calculated via the hysteresis loop \narea technique. Where \n)\n(\nhyst\nirr,\nH\nW\np\n \nis the hysteresis loss for the \ngiven “\np\n” minor \nloop\n.\n \nIn the present work, the losses of the minor loops of the initial magnetization \ncurve are obtained by using the Fourier decomposition of the curves, as described \nearlier\n \n[\n1\n5\n,1\n6\n]\n.\n \nThe irreversible energy, \n)\n(\nirr\nH\nW\ni\n,\n \nsuscep\ntibility,\n)\n(\nirr\nH\ni\nc\n,\n \nand  \nmagnetization, \n)\n(\nirr\nH\nM\ni\n, \nare\n \ncalculated, as \nit has been shown \nin \nRef. 4\n.\n \n \nRemanence magnetizations are equal to \n(\n)\nH\nM\nIRM\nr\n \nand they are obtained \nfrom minor hysteresis loops in zero fields. \n \nIn\n \nmacroscopic\n \ndescription,\n \nmagnetization energy per unit volume of \npolycrystalline ferromagnetic material consists of many parts. The most important This watermark does not appear in the registered version - http://www.clicktoconvert.com \n3\n \nare the exchange energy, which causes the spontaneous magnetization, the \nmagentocrystalline energy, related \nto the orientation of the magnetization to \ncrystallographic axes, the energy of mechanical strain etc. These energies, together \nwith the magnetic energy in the external field contribute to the irreversible \nmagnetization,\n \n)\n(\nirr\nH\nM\ni\n. When measur\ned in zero field of the remanent \nmagnetization,\n(\n)\nH\nM\nIRM\nr\n, the energies change. The resulting difference of the \nmagnetizations, \n)\n(\nH\nM\ni\nD\ncould describe the effects of interaction in the magnetic \nsystem\n:\n \n(\n)\n(\n)\n(\n)\nH\nM\nH\nM\nH\nM\ni\nIRM\ni\nirr\nr\n-\n=\nD\n.  \n   \n       \n \n                \n  \n \n(\n1\n)\n \n \nIt is found that the difference, \n)\n(\nH\nM\ni\nD\n, \nis equal to zero\n4\n, for Stoner\n-\nWolfarth model system, which \nis \nwithout interaction.\n \n4.\n \n \nRESULTS AND DISCISSION\n \nAn initial magnetization curve, \n)\n(\nH\nM\ni\n, and \nminor hysteresis loops, \n)\n(\nH\nM\np\n,\n \nmeasured for a sample of Ni\n0.85\nCu\n0.15\nFe\n2\nO\n4\n \nare shown in Fig. 1. For the \nother investigated samples the curves are similar.\n \n \n \n \nFigure\n \n1.\n \nAn i\nnitial magnetization curve, \n)\n(\nH\ni\nM\n(circles)\n, and mi\nnor hysteresis loops, \n)\n(\nH\np\nM\n,\n \nmeasured for a sample of Ni\n0.85\nCu\n0.15\nFe\n2\nO\n4\n.\n \n This watermark does not appear in the registered version - http://www.clicktoconvert.com \n4\n \n \n \nFigure\n \n2.\n \nField dependencies of total differential magnetic susceptibility,\ni\ndiff\nt,\nc\n(crosses), \nirreversible susceptibility, \ni\nirr\nc\n \n(t\nriangles) and reversible susceptibility, \ni\nrev\nc\n \n(circles) of the initial \nmagnetization curve\n.\n \n \nField dependence of the magnetic susceptibilities, are shown in Fig. 2. \n    \nThe following peculiarities are observed:\n \n(i)\n \nThe \ntotal differential susc\neptibility and the irreversible susceptibility change \nalmost simultaneously for the samples with Zn\n-\nsubstitution (Fig. 2b, c, d). They \nhave maximum \nin the region of\n \nthe \ncoercivity for all samples.\n \nThe maximum value \nincreases almost linearly with increasing\n \nx\n \nup to 0.4, but it increases sharply for\n    \n \nx\n \n= 0.6. Almost the same dependence has the initial permeability of the samples\n \n[\n9\n]\n.   The field of the maximum susceptibility decreases linearly with increasing \nx\n.\n \n(ii)\n \nThe reversible susceptibility has minimum in\n \nthe region of\n \nthe \ncoercivity \nfor samples with \nx\n \n= 0 and \nx\n \n= 0.2 and for \nx\n \n= 0 it even changes its sign (Fig. 2a, \nb).\n \nThe reversible processes predominate in the fields smaller than coecivity. The \nirreversible magnetization can sharply increase after then \nat the expense of the \nreversible magnetization. The reversible susceptibility can occur with negative \nvalues.\n \n(iii)\n \nThe maximum of total, irreversible and reversible susceptibility and the \nminimum of only reversible susceptibility are before coercivity (H\nc \n= 3.2\n \nOe) for \nthe sample with x\n \n= 0 (Fig. 2a). For the sample with \nx\n \n= 0.2 the maximum of This watermark does not appear in the registered version - http://www.clicktoconvert.com \n5\n \nsusceptibilities and minimum of reversible susceptibility are after\n \nH\nc \n= 1.4 Oe \n  \n(Fig. 2b). The coercivity of the sample with Zn concentration \nx\n \n= 0.4 is 0.8 Oe and \nthe m\naximum of susceptibilities are in same field. The maximum of \ni\ndiff\nt,\nc\n, \ni\nirr\nc\nand \ni\nrev\nc\n \nfor  \nx\n \n= 0.6 are before coercivity (\nH\nc \n= 0.2 Oe) (Fig.2d).\n \nThe magnetizations obtained for studied Ni\n-\nCu\n-\nZn ferrites are s\nhown in \n  \nFig. 3. The reversible magnetization have maximum and minimum for a sample \nwith x = 0 only   (Fig. 3a). It increases monotonically after the coercivity. The \ninitial magnetization, the irreversible and reversible magnetization increase \nmonotonical\nly with increasing magnetic field for samples with x = 0.2, 0.4 and 0.6 \n(Fig.3b, c, d).\n \nOn Fig. 3 are shown IRM curves for all samples too. With IRM method \nseparate effects of \nH\n \nand \ni\nM\nirr\n \non\n \ni\nM\nrev\n \ncannot be directly determ\nined\n \n[\n4\n]\n.\n \n \n \n \nFigure\n \n3.\n \nField dependencies of the initial magnetization, \n)\n(\nH\ni\nM\n(crosses), the irreversible\n \nremanent \nmagnetization, \n)\n(\nr\nH\nIRM\nM\n(triangles), the irreversible magnetization, \n)\n(\nirr\nH\ni\nM\n(diamonds) and the \nr\neversible magnetization, \n)\n(\nrev\nH\ni\nM\n(squires)\n.\n \n \n \n This watermark does not appear in the registered version - http://www.clicktoconvert.com \n6\n \nThe curves of the irreversible magnetization obtained by our method and \nIRM curves \ndo\n \nnot coincided.\n \nThe difference\ns\n \n(\n)\nH\ni\nM\nD\n \nfor\n \nthe\n \nfour samples are \nshown in Fig. 4.\n \nIt is seen th\nat \ninteraction effects \nare exclusively positive \nfor samples with\n    \n \nx = 0.0 and 0.2 (Fig.4a,b). Positive interactions assist the magnetization process.\n \n(\n)\nH\ni\nM\nD\n-\n \nplot\n \nhas maximum and minimum in the region of\n \nthe \ncoercivity like \nreversible ma\ngnetization for sample with x = 0 only (Fig.3a, and 4a). For sample \nwith least Zn\n-\nsubstitution x = 0.2, \n(\n)\nH\ni\nM\nD\n \n-\n \nplot is insignificant in \nthe \nregion of \nthe \ncoercivity then it increases wit\nh \napplied field\n. \n \nFor sample with x = 0.4 and x = 0.\n6\n,\n \n(\n)\nH\ni\nM\nD\n \n-\n \nplot is negative and \nhas \nminimum before coercivity. In this region interactions hinder magnetization \nprocess. \nAfter coercivity magnetic interactions increase monotonically and change \ntheir\n \nsign (Fig. 4c,\nd).\n \nThe remanent\n \nmagnetiz\nation, measured in zero field can be \nsmaller or bigger than the irreversible magnetization. The magnetic interactions in \na field influence the irreversible magnetization.\n \nOn Fig. 4b, 4c and 4d \nis \nshown that interactions effect is positive and \ndecrease with\n \nincreasing Zn\n-\nsubstitution after region of the coercivity\n.\n \n \n \n \nFigure\n \n4.\n \nField dependencies of the magnetization,\n \n(\n)\nH\ni\nM\nD\n.\n This watermark does not appear in the registered version - http://www.clicktoconvert.com \n7\n \n5.\n \nCONCLUSION\n \nThe irreversible susceptibilit\nies\n \nand magnetization\ns\n, the reversible \nsuscep\ntibilities and magnetizations o\nf\n \ninitial magnetization curve\ns\n \nwere determined \nby measuring sets of magnetic losses on minor hysteresis loops\n \nfor \nsamples of \npolycrystalline Ni\n-\nCu\n-\nZn ferrites\n. \nThe\n \nmethod \nused \nfor \nthe \nestimation of the \nirreversible susceptibility of an initial magnetizatio\nn curve \nis very sensitive and \ndeals with the energy \nof magnetization \nonly, \nand\n \nnot with the magnetization \nmechanisms.\n \nThe reversible susceptibility \nhas minimum\n \nfor sample\n \nwith\n \nZn \nconcentrations, \nx\n \n=\n \n0.2\n \nand for sample Ni\n0.85\nCu\n0.15\nFe\n2\nO\n4\n \nonly and \neven change\ns its \nsign.\n \n \nWe h\nave demonstrated that using\n \n(\n)\nH\ni\nM\nD\n-\n \nplot initial \nmagnetization \ninteraction\ns can\n \nbe\n \neasily quantified. The results obtained \nshow \nthat for s\na\nmple \nwith Zn concentrations, \nx = \n0.4 and 0.6 \ninteraction effects \nare\n \nnegative and \npo\nsitive.\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n This watermark does not appear in the registered version - http://www.clicktoconvert.com \n8\n \nREFERENCES \n \n \n[1]\n \nJ. Geshev, V. Masheva and M. Mikhov, \nIEEE Trans. Magn\n., \n30\n, 863\n \n-\n \n865\n \n(1994).\n \n[2]\n \nP. E. Kelly, K. O’Grady, P. I. Mayo and R. W. Chantrell, \nIEEE Trans. Magn.\n, \n25\n, 388\n0 \n-\n \n3883\n \n(1989).\n \n[3]\n \nH. Morrish, \nThe Physical Pri\nnciples of Magnetism\n \n(John Willey & Sons Inc., \n1996), p. 403.\n \n[4]\n \nG. Goev, V. Masheva and M. Mikhov, \nInternational Journal of Modern \nPhsysics B\n \n21\n, 3707\n \n–\n \n3717\n \n(2007).\n \n[5]\n \nG. Goev, V. Masheva and M. Mikhov\n, Romanian Journal of Physics \n56,\n \n158\n \n-\n164\n \n(2011).\n \n[6]\n \nE. C. St\noner and E. P. Wolfarth,  \nPhil. Trans. R. Soc\n., \nA240\n, 599 \n \n-\n \n642 \n(1948).\n \n[7]\n \nS. Thamm, J. Hesse, \nJ. Magn. Magn. Mater\n.,\n154\n, 254 \n-\n \n262\n(1996)\n.\n \n[8]\n \nA. M. \nd\ne Witte, K. O’Grady, G. N. Coverdale and R. W. Chantrell, \nJ. Magn. \nMagn. Mater\n., \n88\n, 183\n \n-\n \n193\n \n(1990).\n \n[9]\n \nG. Goev, \nV. Masheva\n, L. Ilkov, D. Nihtianova\n \nand M. Mikhov, \nBPU\n-\n5 SPO6\n-\n047\n, 687\n \n–\n \n690 \n \n(2003).\n \n[10]\n \nTatsuya Nakamura, \nJ. Magn. Magn. Mater\n., \n168\n, 285\n \n-\n \n291\n \n(1997).\n \n[11]\n \nK. Kawano, M. Hachiya, Y. Iijima, N Sato and Y Mizuno,\n \nJ. Magn. Magn. \nMater\n., \n321\n, \n2488\n-\n \n2493\n \n(2009).\n \n[12]\n \nO. F\n. Caltun, L. Spinu, Al. Stancu, L. D. Thung, W. Zhou, \nJ. Magn. Magn. \nMater\n., \n160,\n \n242 \n-\n \n245\n \n(2002).\n \n[13]\n \nX. Tang, H. Zhang, H. Su, Zh. Zhong, F. Bai, \nIEEE Trans. Magn.,\n \n47,\n \n4332\n \n-\n4335\n \n(2011).\n \n[14]\n \nM. F. Huq, D. K. Saha, R. Ahmed and Z. H. Mahmood  \nJ. Sci. Res.\n \n5\n \n(2) 215\n \n-\n233\n \n(2013\n).\n \n[15]\n \nG. Goev, V. Masheva and M. Mikhov, \nIEEE Trans. Magn\n., \n39\n,\n \n1993 \n–\n \n1996 \n(2003).\n \n[16]\n \n \nV. Masheva, J. Geshev and M. Mikhov, \nJ. Magn. Magn. Mater\n., \n137\n, 350\n \n-\n \n357\n \n(1994).\n \n This watermark does not appear in the registered version - http://www.clicktoconvert.com"    },    {        "title": "1510.05888v1.First_principles_investigation_of_boron_defects_in_nickel_ferrite_spinel.pdf",        "content": "1 \n \n \n First -principles investiga tion of boron defects in nickel ferrite spinel  \nZs. R ák1, C. J. O’Brien, and D. W. Brenner  \nDepartment of Materials Science and Engineering, North Carolina State University,  \nRaleigh, 27695 -7907  \n \nAbstract  \nThe accumulation of boron within the porous nickel ferrite (NiFe 2O4, NFO) deposited  on \nfuel rods is a major technological problem with important safety and economical implications. In \nthis work t he electronic structure of nickel ferrite is investigated using first -principles method s, \nand the results are combined with experimental data to analyze  B incorporation into the  NFO  \nstructure . Under thermodynamic equilibrium the calculations predict that the incorporation of B \ninto the NFO structure  is unfavorable . The main limiting factors  are the narrow stability domain \nof NFO and the precipitation of B 2O3, Fe 3BO 5, and Ni 3B2O6 as secondary phases. In n -type \nNFO, the most stable defect is Ni vacancy \n2\nNiV  while in p -type material lowest the formation \nenergy belongs to tetrahedrally coordinated interstitial B\n2\nTB . Because of these limiting \nconditions it is more thermodynamically favorable for B to form secondary phases with Fe, Ni \nand O than it is to form point defects in  NFO.     \n \n1. Introduction  \nBecause of  the increasing cost of fossil fuel based energy and the pressure to reduce \ngreenhouse gases , energy policy in the United States currently encourages research and \ndevelopment in nuclear  energy  [1]. To allow longer lifetime s and higher power output from a \n                                                           \n \n \n1 Corresponding author:  \nDepartment of Materials Science and Engineering,  \nNorth Carolina State University,   \n911 Partners Way, EB 1 BOX 79 07 \nRaleigh, NC 27695 -7907  \nEmail: zrak@ncsu.edu  (Zs. Rak)  \n 2 \n \n \n nuclear reactor, a major technical issue that has to be conquered  is the corrosion and corrosion -\nrelated failure of nuclea r fuel. CRUD  (Chalk River Unidentified Deposits) is the name given to \ncorrosion product s that accumulate  on the hot surface of the fuel cladding . In a pressurized water \nreactor (PWR) CRUD  is produced from dissolved metal cations and particulate corrosion \nproducts  originating from the surfaces of the reactor coolant system , and  consists mainly of \nnickel  ferrite  spinel  (NiFe 2O4, NFO ), nickel  oxide  (NiO). [2, 3] Although a thin layer of CRUD  \non the cladding  surface  can enhance heat transfer,  thicker deposits have  a negative  effect  on fuel \nperformance  and generate operational challenges . Thick CRUD , usually deposited on the upper \npart of the fuel rods,  reduces the heat transfer  in the reactor core and raises the local surface \ntemperature of the cladding,  which  increas es the corrosion  rate. Furthermore,  boron  (B) can \naccumulate in thick  CRUD , which  can trigger fluctuations in the neutron flux and  cause a shift  in \nthe power output from the top half to the bottom half of the core . This phenomenon, known as \nthe axial offset anomaly (AOA), has important safety implications  and could  lead to down -rating \nof a power plant with significant economic consequences . Therefore, it is crucial to understand \nand predict the mechanism s of CRUD  formation and B  accumulation within the CRUD .   \nEven though it is clear that the key factors necessary for AOA to manifest are (i) sub-\ncooled nucleate boiling, (ii) thick CRUD , and (iii) sufficient B in the coolant, many details about \nthe root cause of AOA are not fully understood.  For example, l ittle is known about the role \nplayed by the coolant chemistry in AOA development or about the precise mechanism of B \ndeposition . Within the EPRI/WE C (Electric Power Research Institute/Westinghouse Electric \nCompany)  simulation models  B uptake by CRUD  is considered to take place  via lithium borate s \nin the form of LiBO 2, Li2BO 7, and Li 2B4O7.[4-7] However, because  these  compounds exhibit \nretrograde solubility  with respect  to temperature , they are difficult to observe in PWR CRUD  \nscrapes , but they have been observed in simulated CRUD. [8] Sawicki  analyzed the corrosion \ndeposits found on the fuel  assemblies in various  PWR s and identified the formation of Ni 2FeBO 5 \n(mineral bonnacordite)  as a new mechanism  for B retention. [9, 10] The results of Sawicki’s work  \nhave triggered new modeling efforts to describe the chemistry of borated fuel CRUD. [11] \nMesoscale CRUD models under development  within the CASL  program  (Consortium for \nAdvanced Simulation of Light Water Reactors)  assume precipitation of boron oxide (B 2O3) as a \npossible B deposition mechanism in the porous CRUD. [12]   3 \n \n \n Although current research is moving towa rd a better description of CRUD properties and \nits behavior in PWRs, more work is needed to elucidate the mechanisms through which B or \nboron -containing solids are deposited on the fuel rods . In this work  we carry out  electronic \nstructure calculations  to investigate the possibility of B incorporation into crystalline NFO . To do \nthis, we treat B as either a substitutional or interstitial point defect in the NFO  structure  and use \nfirst-principles -based thermodynamics to analyze the stability of B inside the structure.   \n       \n2. Crystal  and defect  modeling  \nThe spinel atomic arrangement  is shared by many transition metal oxides with formula \nAB 2O4 (Fd3m ), where A and B are divalent (A2+) and trivalent (B3+) ions, respectively. In the \nnormal structure  the oxygen  ions form a face centered cubic array and the A2+ and B3+ ions sit in \ntetrahedral (1/8 occupied) and octahedral (1/2 occupied) sites in the lattice, giving a u nit cell with \n8 A's, 16 B's and 32 O's.  The inverse spinel is an alternative arrangement where the divalent ions \nswap with half of the trivalent ions so that the A2+ ions occupy octahedral sites . Therefore, the \ngeneral formula of an inverse spinel can be written as  B3+(A2+B3+)O4. \nNickel ferrite cry stallizes in the inverse spinel structure, with half of the Fe3+ ions \noccupying the tetrahedral sites while  Ni2+ and the remaining Fe3+ are randomly  distributed over \nthe octahedral sites . Because of the periodic boundary conditions employed in our calculations,  \nany atomic distribution  within a supercell corresponds to a n array of cations with  long-range \norder. In theory, the cation  distribution could be modeled  using a special quasi -random  \nstructure ;[13, 14] however , the large unit cells required for such simulation would lead to \nprohibitively ex pensive computational efforts. In this work w e employ the structural model used \nby Fritsch and Ederer, where the Ni and Fe cations are distributed over the octahedral sites such \nthat the symmetry is reduced from cubic ( Fd3m ) to orthorhombic ( Imma ).[15] The same \nstructure has been used by O’Brien et al.[16] to investigate the  thermodynamic properties of NFO  \nsurfaces under conditions  typical to PWR coolant.  \nThe point defects that are investigated in the present wor k are Ni and Fe vacancies as \nwell as substitutional and interstitial B impurities. The vacancies can be of three types depending \non the site from which the atom is removed: tetrahedral and octahedral Fe vacanc ies (\nT\nFeV and 4 \n \n \n \nO\nFeV), and octahedral Ni vacancy  (\nO\nNiV). Similarly, depending on which atom is replaced by B, \nthere are three types of substitutional  impurities: boron can substitute for a Fe atom at a \ntetrahedral or an octahedral site (\nT\nFeB and \nO\nFeB ) or one  Ni atom at an octahedral (\nO\nNiB). The \ninterstitial B can be located either at an empty octah edral or at a n empty  tetrahedral  site. \nAssuming a random Ni distribution, all unoccupied octahedral sites are equivalent , while  there \nare two types of unoccupied tetrahedral sites . The three possible interstitial atomic configura tions \nare illustrated in Fig. 1, where the two t etrahedral sites are denoted T1 and T2 . \n \n3. Computational parameters  \nThe calculations were  performed using the projector augmented wave (PAW) [17, 18] \nmethod within density functional theory (DFT) [19, 20] as implemented in the Vienna Ab initio \nSimulation Package (VASP) .[21-24] The exchange -correlation potential was approximated by \nthe generalized gradient approximation (GGA), as parameterized by Perdew, Burke, and \nErnzerhof ( PBE) .[25]. The standard PAW potentials, supplied with the VASP package, were \nemployed in the calculations .[17, 18] The 3d and 4 s states of Ni and Fe as well as the 2 s and 2 p \nstates of B and O are considered as valence states while the rest are treated as core states. The \ncut-off energy for th e plane wave basis was set to 550 eV   and the convergence of self -consistent \ncycles was assumed when the energy difference between two consecutive cycle was less than 10-\n4 eV. The Brillouin -zone was sampled by the Г -point  in all calculations  and a Gaussian smearing \nof 0.1 eV  was used . The int ernal structural parameters were relaxed until the total energy and the \nHellmann -Feynman forces on each n ucleus  were less than 0.02 eV/Å . To minimize the \ninteraction between periodic images of defects, all defect calculations have been performed on \n2×2×2 s upercells conta ining  448 atoms, using the calculated  lattice constant of pure NFO  (a = \n8.41 Å ).[26] \nTo describe the behavior of th e localized Fe 3 d and Ni  3d states, the orbital -dependent, \nCoulo mb potential (Hubbard U) and the exchange parameter J  were included in the calcul ations \nusing  the DFT+ U formalism. [27] The simplified, rotationally invariant  approach  introduced by \nDudarev et al[28] was used.  The value of the Hubbard U parameter can be estimated from band -\nstructure calculations in the super cell approximation with different d and f occupations [29] or 5 \n \n \n from calculations base d on a constrained random -phase approximation .[27, 30] Here  U and J are \ntreated as parameters with values U(Fe d) = 5.5 eV with the corresponding J(Fe d) = 1.0  eV, and \nU(Ni d) = 7.0 eV with J(Ni d) = 1.0 eV. These values are physically reasonable and are within the \nrange of the previous values in the literature .[16, 31-33]  \n \n4. Thermodynamics of B incorporation  intro nickel ferrite  \nThe formation of a defect in a crystalline solid can be regarded as an exchange of atoms \nand electrons between the host material and chemical reservoirs. Therefore the formation energy \nof a defect D in charge state q can be written as: [34, 35] \n \nqq\nf i i F\niH D E D n qE       , (1) \nwhere  \n \n 0qq\ni i VBM\niE D E D E n E qE         (2) \nIn Eq s. (1) and (2)\nqED  and \n0E  are the total energies of the def ect-containing a nd defect free \nsolids. The second  term on the right side of  Eq. (1) represents the change in energy due to the \nexchange of particles between the host compound and the chemical reservoir , where  \niare the \nchemical potential of the atomic species i (i = Ni, Fe, or B ) referenced to the elemental solid/ gas \nwith energy \niE  and \nin are the number of atoms added to \n0in  or removed from \n0in  the \nsupercell. The quantity\nFE is the Fermi energy referen ced to the energy of the valence band \nmaximum (VBM), \nVBME . This value is calculated as the VBM energy of the pure NFO , corrected \nby aligning the core potential of atoms far away from the defect in the defect -containing \nsupercell with that in the defect free supercell. [35]The quantity\nq  represents the charge state of \nthe defect, i. e. the number of electrons exchanged with the electron reservoir with chemical \npotential \nFE . \nEquation (1) shows that, in principle, by adjusting the atomic chemical potential of the \nconstituents and by tuning the electronic Fermi energy, one can control the de fect formation \nenergy and , consequently , the solubility of the dopant in the host matrix. Under thermodynamic \nequilibrium, the achievable values of the chemical potentials are limited by several condition s:  6 \n \n \n (i) to avoid elemental precipitations, the chemical potentials are bound by  \n \n0, 0, 0, and 0Ni Fe O B        (3) \n(ii) to maint ain a stable NFO  host the \ni ’s must satisfy  \n \n24 2 4 NiFe O (NFO)Ni Fe O HH        (4) \nwhere \n(NFO)H is the formation enthalpy of NiFe 2O4, \n(iii) to avoid formation of competing  phases, such as iron oxides ( Wüstite, hematite and \nmagnetite)  and nickel  oxide s, the following conditions must apply  \nnmFe OFe On m H \n, where \n n,m 1,1 , 2,3 ,and 3,4                (5) \n Ni ONi O n mn m H \n, where  \n n,m 1,1 and 2,3                      (6) \nFurther constraints on the chemical potential are  posed by the possibility of forming  \nsecondary phases  between boron and the host elements. In this work we consider the following \ncompounds  as possible secondary phases : B 2O3, NiB, Ni 2B, Ni 4B3, FeBO 3, Fe 3BO 5, Fe 3BO 6, \nNiB 2O4, Ni 3B2O6, and Ni2FeBO 5. To avoid the formation of these compounds, the chemical \npotentials of B, Ni, Fe, and O must satisfy conditions similar to (5) and (6).     \n \n5. Formation enthalpies and elemental reference energies  \nThe theoretical enthalpy (heat) of formation of a compound \n...nmAB  can be calculated as:  \n( ...) ( ...) ...theor\nn m n m A B H A B E A B nE mE    \n                       (7) \nwhere \n( ...)nmE A B  is the total energy per form ula unit (f. u.) of the compound and \n, ,...ABEE   are \nthe total energies per atom of the elements in their standard state. According to Eq. (7), to predict \nthe enthalpies of formation  required by  conditions (ii)-(iii), it is necessary to compute the \ndifferences between the total energies of  the compound\n...nmAB and their elemental constituents  A, \nB, …  in the standard state. If the compound and the elemental materials are chemically similar, \nEq. (7) yields very accurate results because the DFT errors will cancel out when calculating the \ntotal energy differences. In our case the compounds are t he insulating or semiconducting  \nmaterials, such as  NFO, FenOm, or NinOm, while the elemental phases include the  metallic form \nof the cations (Ni , Fe, and semimetallic B ) and the gaseous anion (O 2). These are chemically and 7 \n \n \n physically dissimilar systems, where  the cancellation of the DFT errors  is known to be \nincomplete. [36, 37] Furthermore, to reproduce the correct electronic structures of the Ni - and Fe -\ncontaining  systems it is essential to include the Hubbard U correction for the Ni and Fe 3d states. \nThe values of the U parameters used for the non -metal compounds, however, are  different from  \nthose used for metallic phases, which can lead to large errors in the formation enthalpy \ncalculations. One way to overcome these issues is to utilize the experimental enthalpies of \nformation \nexpH  in Eqs. (4)-(6). However, this approach cannot be used because the \nexperimental value of the  formation enthalpy of the ternary compounds  from the elemental \nconstituents is not available.  \nTo compute the formation enthalpies we use an approach, [16, 32, 38-40] in which the \nelemental energies \n, ,...ABEE  are approximated from the system of linear equations:  \nexp( ...) ( ...) ...n m n m A B H A B E A B nE mE    \n                             (8) \nWe calculate the DFT energies of 10  binary compounds that can  be formed from Ni , Fe, O, and \nB, for which the \nexpH values are available ,[41, 42]  and then we solve the overdetermined \nsystem of equations Eq. (8) in the least-squares approach. This way we obtain  the elemental \nenergies,\n, ,...ABEE , without directly calculating the DFT energies of the elements in their \nstandard metallic or gaseous state. The obtained values are used as the  elemental reference \nenergies  to calculate the defect formation energies in Eq. (1) and the  enthalpies of formation \nrequired in Eqs. (4)-(6). The experimental and theoretical values of the formation enthalpies are \nlisted in Table 1 , along with the DFT total energies of the compounds and the fitted elemental \nreference energies  are listed in Table 2 .  \n \n6. Results and discussions  \nTo assess the possibility of B incorporation into  NFO,  we calculate the electronic \nstructure of NFO, evaluate  the formation energies of B -related defects and use the \nthermodynamic scheme described above  to estimate the defect stability with reference to the \nformation of Ni -Fe-B compounds as secondary phases.   \n \n6.1 Pure NFO  8 \n \n \n Nickel ferrite spinel is a ferrimagnetic ins ulator  with hig h Curie temperature (870K) [43] \nand, therefore, it has  a great potential for technological applications especially in the area of \nspintronics. [44] However, because in this work we do not focus on device applications of NFO, \nwe only give a brief description of the c alculated electronic structure of NFO, comparing our \nresults with data available in the literature.  \nThe total electronic density of states (DOS), along with the DOS projected on the d-states \nof Fe and Ni ions  are illustrated in Fig. 2. Because the Fe ions in NFO are in the 3+ oxidation \nstate, the Fe 3 d shells are half filled. Fig. 2 (a) and (b) reveal  that all Fe’s are in the high spi n \nstate, with one spin projection completely occupied  (states between -6.5 and -8.0 eV) and the \nother  spin projection completely empty (states between 1.5 and 3.0 eV).  The Fe d states are \nstrongly localized; they are separated from other valence band (VB) and conduction band (CB) \nstates. In contrast, the strong hybridization between the  Ni 3 d and O 2 p states ( Fig. 2 (c) ), \nproduces a VB that displays both Ni d and O p character  across the energy range from -6.0 eV to \nFE\n. The hybridization takes place mainly between the Ni t2g and O 2 p states, while the Ni eg \nstates remain more separated and localized.        \nFigure 2 also illustrates  the origin of the ferrimagnetism in NFO ; the magnetic moments \nof the octahedral Fe3+ and Ni2+ cations are par allel and they couple antiferromagnetically with \nthe tetrahedral Fe3+ moments. Given that there are equal number s of Fe3+ on the octahedral and \ntetrahedral sites, the Fe3+ magnetic moments are compensated , so the net moment is attributable \nmainly to the octahedral Ni2+ cations.  The calculated spin magnetic moments , listed i n Table III , \nare consiste nt with this magnetic structure and are in fairly good agreement with earlier \nexperimental [45] and theo retical values. [15, 46]    \nThe calculated band gap measured from the VBM to the conduction band minimum \n(CBM) is 1.3 eV, somewhat  larger than the gaps of 0.97, 0.99. and 1.1 eV, obtained with the \nDFT+ U method by Fritsch and Ederer [15], Antonov et al. [46], and Sun et al. [47], respectively.  \nThe slightly increased band gap in our calculations is the  result of a  larger on-site Coulomb \ninteraction ( Ueff parameter ) applied to the Ni d states  compared  with previously used values  in \nthe literature .[15, 46, 47] Because  the VBM displays a mixture of O p and Ni  d character,  an 9 \n \n \n increase in the Ni d-d correlation shifts the occupied Ni d  states, and therefore the VBM, to \nlower energies relative to the CBM.   \n \n6.2 Stability of NFO  \nAs described in Section 4, the  achievable values of Ni, Fe and O chemical potentials  are \nbound by the conditions to maintain a stable NFO and avoid formation of competing phases \n(including  elemental solids /gases ). The calculated chemical potential domain  based on Eqs. (3)-\n(6), where NFO is stable , is illustrated by the dark area in Fig. 3.  Under thermodynamic \nequilibrium, the vertices of the triangle in Fig. 3 repr esent the achievable limits of the Ni and Fe \nchemical potentials ; A corresponds to the Fe-rich, Ni -rich (\n0Fe Ni ) limit, B corresponds to \nthe Ni-rich, Fe -poor (\n0, 5.71eVNi Fe  ) limit, and C  is the Ni -poor, Fe -rich (\n11.411eV, 0Ni Fe \n) limit. As is apparent from Fig. 3, the domain of the allowed chemical \npotentials for stable NFO is relatively narrow. In the white areas, NFO is unstable with respect to \ncompeting phases ; the lower part of the triangle represents the region where iron oxides (FeO, \nFe2O3, and Fe 3O4) form, while the upper region is excluded due to precipitation of nickel oxides \n(NiO and Ni 2O3). Figure 3 also illustrates that under Fe - or Ni -rich conditions  (\n0 or 0Fe Fe\n) NFO is not stable. The highest achievable value s of \nFe and \nNi for stable NFO are defined by \nthe intersection of the lines that set the limit for Fe 3O4 and NiO  in the (\nFe ,\nNi) plane . At this \npoint, represented as X in Fig. 3, the  calculated  Fe and Ni chemical potentials are \n1.09 eVFe\n and \n0.70 eVNi . According to Eq.  (4), at point X , the O chemical potential \nis\n2.13 eVO . This is also the lowest possible value of \nO that that still assures a stable NFO.  \nThe lowest achievable values of\nFe and\nNi for stable NFO are defined by the intersection \nof the O -rich line (BC segment on Fig. 3) with the lines that limit the formation NiO and Fe 2O3, \nrespectively. These intersecti ons are denoted as Y and Z on Fig. 3. The calculated values of the \nchemical potentials at Y and Z are\n4.29 eVFe , \n2.83 eVNi and\n4.20 eVFe , \n3.01eVNi\n, respectively.  \n 10 \n \n \n 6.3 Fe and Ni vacancies  \nAccording to Eq.  (1) and (2) the formation energy of a defec t D in charge state q is equal  \nto the difference between  the energies of the defect -containing and defect free supercells, \ncorrected by the chemical potentials of the atomic and electronic reservoirs with which the \nsystem exchanges particles (atoms and el ectrons).  In the  case of Fe or Ni vacancies (VFe/Ni) the \nformation energies are given by\n / / /qq\nf Fe Ni Fe Ni Fe Ni FH V E V qE      . The first term on the \nright -hand side represents the energy difference between the vacancy -containing  and pristine \nsystems , corrected by the elemental reference energies and VBM energy (Eq. (2)). The \ncalculated values of  \nqED , listed in Table 4 , can be used to assess the defect formation in \nNFO under the conditions defined by (i)-(iii). \nTo make the formation of Fe /Ni vacancy favorable, we have to create Fe /Ni-poor \nconditions, that is we have to minimize the chemical potential of Fe/Ni . As calculated  in the \nprevious section, the lowest possible value s of μFe and μNi that satisfie s conditions (i) - (iii) are -\n4.29 and -3.01 eV, respectively . At th ese chemical potential s the formation energies of \ntetrahedral and octahedral Fe and octahedral Ni vacancies i n neutral charge states  are \n0\nT f FeHV\n= 7.73 – 4.29 = 3.44 eV,  \n0\nO f FeHV  = 7.46 – 4.29 = 3.17 eV, and \n0\nO f NiHV  = 5.12 – 3.01 = \n2.11 eV . These values are moderately high, indicating that formation of neutral vacancies in \nNFO is unlikely.  \nIn the case of the cha rged defects, the formation energy depends on the Fermi level, \nbecause to ionize a defect , electrons must be added to or taken from an electron reservoir with \nenergy EF. Figure 4 illustrates the vacancy formation energies  as a function of EF,   calculated for \ndifferent charge states , under Fe -poor and Ni -poor conditions. We observe that the Ni and Fe \nvacancies display similar behavior ; when EF is tuned closer to the VBM or CBM, the vacancies \nbecome charged and the formation energies decrease con siderably. This effect is stronger in n -\ntype NFO ( EF closer to CBM), where the formation energy of Ni vacancy drops to \napproximately 0.5 eV. Figure 4 also illustrates that for all values of EF within the band gap, the \nformation energy of Ni vacancy is the lowest, suggesting that under appro priate conditions, Ni \nvacancy could be  the dominant intrinsic defect in NFO.   11 \n \n \n   \n6.4 Substitutional B defects  \nThere are three types of su bstitutional B defects in NFO ; boron can occupy a tetrahedral \nor octahedral Fe site (B FeT or B FeO) or it can substitute for an octahedral Ni ion (B NiO). Given that \nthe methodology of the formation  energy calculations are the same for the Fe - and Ni -site \ndefects, here we describe the details of Fe -site defect calculations  while for the Ni -site defect we \nonly present the results.  \n   The formation energy of  substitutional B at the Fe site is given by \n //T O T Oqq\nf B Fe F Fe FeH B E V qE      \n. Even though the O and Ni chemical potentials do not \nappear explicitly in this expression, the form ation energy depends indirectly on μNi and μO \nthrough conditions (ii) and (iii), as described in Section 4. To make B incorporation energetically \nfavorable, μFe has to be minimized and μB maximized  As described earlier , the lowest possible \nvalue of μFe that maintains a stable NFO is -4.29 eV, represented by the Y point on Fig. 3 . At this \npoint the chemical potentials of O and Ni are zero and -2.83 eV, respectively. Using these values \nin setting up the conditions to avoid formation of secondary phases, we find that the highest \npossible value of μB is -6.60 eV due to the  restriction  to avoid Ni 3B2O6. Under these conditions, \nthe formation energies of neutral B FeT and B FeO are \n0\nT f FeHB  = – 0.08 + 6.60 – 4.29 = 2.23 eV \nand \n0\nO f FeHB  = 1.93 + 6.60 – 4.29 = 4.24 eV.  These values are relatively high, indicating that , \nunder Fe -poor conditions, B incorporation at the Fe site in NFO is limited by the formation of \nNi3B2O6 as a secondary phase.  \nBecause the formation energies of substitutional B depend indirectly on μNi and μO, \ninstead of limiting the investigation to Fe -poor conditions, we have to explore the entire range of \nchemical potentials where NFO is stable. Within the limits of condition (iii), reduced values of \nμNi and μO allow for larger μB which, in turn,  decreases the formation energies. The minimal \nvalue of μO (O-poor condition) is obtained at the X point in Fig. 3 and it is -2.13 eV. At this point \nμFe = -1.09 eV and μNi = -0.70 eV. The maximum value of μB is obtained by imposing condition \n(iii) on all possible secondary phases. In this case, the limiting condition is given by Fe 3BO 5 \nresulting i n a value of μB that must be less than  -3.63 eV. Therefore, under O -poor conditions  the 12 \n \n \n formation energies of neutral B FeT and B FeO are \n0\nT f FeHB  = – 0.08 + 3.63 – 1.09 = 2.46 eV \nand \n0\nO f FeHB  = 1.93 + 3.63 – 1.09 = 4.47 eV. Similar calculations can be carried out under \nNi-poor conditions, corresponding to point Z in Fig. 3, where μNi  = -3.01 eV , μFe = -4.20 eV, and \nμO = 0. In this case the chemical potential of B is μB ≤ -6.42 eV , and limited by the formation of \nB2O3. The formation energies of  substitutional B impurities at Ni -poor conditions are calculated \nas \n0\nT f FeHB  = 2.14 eV  and  \n0\nO f FeHB  = 4.15 eV .       \nIn the case of the substitutional B impurity at the Ni site, after exploring the entire \nstability domain of NFO, the lowest defect formation energy was obtained at Fe -rich conditions \n(point X in Fig. 3), where μNi  = -0.70 eV, μFe = -1.09 eV, μO = -2.13 eV. The calculated \nformation energy of neutral BNiO is \n0\nO f NiHB  = 4.91 eV.  \nFigure 5 illustrates the lowest formation energies of substitutional B impurities as a \nfunction of EF, calculated  for various charge states. For all values of EF within the band gap, the \nlowest energy belongs to the substitutional B impurity at the tetrahedral Fe site. If the Fermi \nlevel is tuned closer to the VBM, B FeT becomes positively charged and its formation energy \ndecreases , reaching the lowest value of approximately 1.3 eV at the VBM ( EF = 0).  \nAll of the calculated formation energies of substitutional B impurities in NFO are \npositive and moderately high. This suggests that the incorporation of B into the NFO structure as \na substitutional defect is unlikely, the limiting conditions being the formation of Ni3B2O6, B2O3, \nor Fe 3BO 5 as secondary phases . The compositions of these phases are very close to those \nconsidered by Sawicki [9] in a r ecent Mössbauer analysis  of CRUD scrapes  from fuel assemblies \nexhibiting AOA ; the compound include iron borate (FeBO 3), iron orthoborate ( Fe3BO6) and \nbonnacordite (Ni 2FeBO 5).        \n \n6.5 Interstitial  B defects   \nAs illustrated  in Fig. 1, in the spinel structure there are  three interstitial sites which can \naccommodate impurities : two tetrahedral sites, denoted T1 and T2 and one octahedral site, \ndenoted O in Fig. 1. According to Eq. (1), the formation energy of an interstitial B defect can be \ncalculated as\n //qq\nf T O T O B FH B E V qE      . To make incorporation of B favorable, μB must 13 \n \n \n be maximized while avoiding formation of secondary phases. Using the calculated formation \nenthalpies, listed in Table 1, within the limits of NFO stability domain shown in Fig. 3, we find \nthat the maximum possible μB is -3.63 eV and it is limited by the formation of Fe3BO 5. Figure 6 \nillustrates the formation energies of the interstitial B defects in NFO  as a function of EF. The \nmost stable position for B is the tetrahedral interstitial site (T2), with a formation energy that is \nclose to 0.15 eV as the EF approaches the VBM.  Even though this value is considerably lower \nthan all other formation energies, the calculations indicate that it is energetically more favorable \nfor B to form Fe 3BO 5 instead of entering the NFO structure as an interstitial impurity.  \n \n7. Summary     \nUsing first -principles methods, we have investigated the electronic structure of NFO and \ncombined thermodynamical  data with theoretical results to analyze the possibility of B \nincorporation into the spinel structure of NFO. The point defects u nder investigation include \nsubstitutional and interstitial B impurities as well as Ni and Fe vacancies.  \nUnder thermodynamic equilibrium, assuming solid -solid equilibrium between NFO and \natomic reservoirs of Ni and Fe, it is unlikely that B is incorporated  into the NFO structure. The \nmain factors that limit B incorporation are the narrow chemical potential domain where NFO is \nstable and the precipitation of various Fe -Ni-B-O compounds as secondary phases. Among these \nphases the most prevalent appears to be B2O3, Fe 3BO 5, and Ni 3B2O6.  \nThe incorporation energies depend sensitively on the electron chemical potential ( EF) and \nthe charge state of the defect. In n-type NFO, the most stable defect appears to be the Ni vacancy \n2\nNiV\n while in p -type material  the lowest formation energy belongs to the interstitial B \noccupying a tetrahedrally coordinated site\n2\n2TB . Because of the limiting conditions mentioned \nabove, it is more likely that B will form secondary phases with Fe, Ni  and O instead of entering \nin the NFO structure as a point defect.  \n \nAcknowledgement s \nThis research was supported by the Consortium for Advanced Simulation of Light Water \nReactors ( http://www.casl.gov ), an Energy Innovation Hub ( http://www.energy.gov/hubs ) for Modeling 14 \n \n \n and Simulation of Nuclear Reactors under U.S. Department of Energy Contract No. DE -AC05 -00OR22725.  \nThe computational work has been perfor med at NERSC, supported by the Office of Science of \nthe US Department of Energy under Contract No. DE-AC02 -05CH11231 .     \n  \n \nReferences  \n[1] N.R.C. Committee on Review of DOE's Nuclear Energy Research and Development Program, Review \nof DOE's Nuclear Energy Research and Development Program, The National Academies Press, 2008.  \n[2] R. Castelli, Nuclear Corrosion Modeling: The Nature of CRUD, Elsevier, Amsterdam, 2010.  \n[3] J.W. Yeon, I.K. Choi, K.K. Park, H.M. Kwon, K. Song, Chemical analysi s of fuel crud obtained from \nKorean nuclear power plants, J Nucl Mater, 404 (2010) 160 -164.  \n[4] Rootcause Investigation of Axial Power Offset Anomaly, EPRI Report, Palo Alto, CA: 108320, (1997).  \n[5] Modeling PWR Fuel Corrosion Product Deposition and Growth  Processes, EPRI Report, Palo Alto, CA: \n1009734 (2004).  \n[6] Axial Offset Anomaly (AOA) Mechanism Verification in Simulated PWR Environments, EPRI Report, \nPalo Alto, CA: 1013423, (2006).  \n[7] Pressurized Water Reactor (PWR) Axial Offset Anomaly Mechanism Ver ification in Simulated PWR \nEnvironments, EPRI Report, Palo Alto, CA: 1021038, (2010).  \n[8] S. Uchida, Y. Asakura, H. Suzuki, Deposition of boron on fuel rod surface under sub -cooled boiling \nconditions -An approach toward understanding AOA occurrence, Nucl En g Des, 241 (2011) 2398 -2410.  \n[9] J.A. Sawicki, Evidence of Ni2FeBO5 and m -ZrO2 precipitates in fuel rod deposits in AOA -affected high \nboiling duty PWR core, J Nucl Mater, 374 (2008) 248 -269.  \n[10] J.A. Sawicki, Analyses of crud deposits on fuel rods in PWRs  using Mossbauer spectroscopy, J Nucl \nMater, 402 (2010) 124 -129.  \n[11] J. Henshaw, J.C. McGurk, H.E. Sims, A. Tuson, S. Dickinson, J. Deshon, A model of chemistry and \nthermal hydraulics in PWR fuel crud deposits, J Nucl Mater, 353 (2006) 1 -11. \n[12] M.P. Sho rt, D. Hussey, B.K. Kendrick, T.M. Besmann, C.R. Stanek, S. Yip, Multiphysics modeling of \nporous CRUD deposits in nuclear reactors, J Nucl Mater, 443 (2013) 579 -587.  \n[13] A. Zunger, S.H. Wei, L.G. Ferreira, J.E. Bernard, Special Quasirandom Structures, Phy s Rev Lett, 65 \n(1990) 353 -356.  \n[14] S.H. Wei, L.G. Ferreira, J.E. Bernard, A. Zunger, Electronic -Properties of Random Alloys - Special \nQuasirandom Structures, Phys Rev B, 42 (1990) 9622 -9649.  \n[15] D. Fritsch, C. Ederer, Epitaxial strain effects in the spin el ferrites CoFe2O4 and NiFe2O4 from first \nprinciples, Phys Rev B, 82 (2010) 104117.  \n[16] C.J. O'Brien, Z. Rak, D.W. Brenner, Free energies of (Co, Fe, Ni, Zn)Fe2O4 spinels and oxides in water \nat high temperatures and pressure from density functional theor y: results for stoichiometric NiO and \nNiFe2O4 surfaces, J Phys -Condens Mat, 25 (2013) 445008.  \n[17] P.E. Blochl, Projector Augmented -Wave Method, Phys Rev B, 50 (1994) 17953 -17979.  \n[18] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector  augmented -wave method, \nPhys Rev B, 59 (1999) 1758 -1775.  \n[19] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys Rev B, 136 (1964) B864 -&. 15 \n \n \n [20] W. Kohn, L.J. Sham, Self -Consistent Equations Including Exchange and Correlation Effects, Physical \nReview, 140 (1965) 1133.  \n[21] G. Kresse, J. Furthmuller, Efficient iterative schemes for ab initio total -energy calculations using a \nplane -wave basis set, Phys Rev B, 54 (1996) 11169 -11186.  \n[22] G. Kresse, J. Furthmuller, Efficiency of ab -initio total energy calcu lations for metals and \nsemiconductors using a plane -wave basis set, Comp Mater Sci, 6 (1996) 15 -50. \n[23]  G. Kresse,   J. Hafner, Abinitio Molecular -Dynamics for Liquid -Metals, Phys Rev B, 47 (1993) 558 -561.  \n[24] G. Kresse, J. Hafner, Ab -Initio Molecular -Dynamics Simulation of the Liquid -Metal Amorphous -\nSemiconductor Transition in Germanium, Phys Rev B, 49 (1994) 14251 -14269.  \n[25] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys Rev \nLett, 77 (1996) 3865 -3868.  \n[26] D.A . Drabold, S. Estreicher, Theory of Defects in Semiconductors, in, Springer, Berlin/Heidelberg, \n2007.  \n[27] V.I. Anisimov, J. Zaanen, O.K. Andersen, Band Theory and Mott Insulators - Hubbard -U Instead of \nStoner -I, Phys Rev B, 44 (1991) 943 -954.  \n[28] S.L. Du darev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electron -energy -loss spectra \nand the structural stability of nickel oxide: An LSDA+U study, Phys Rev B, 57 (1998) 1505 -1509.  \n[29] V.I. Anisimov, O. Gunnarsson, Density -Functional Calculation o f Effective Coulomb Interactions in \nMetals, Phys Rev B, 43 (1991) 7570 -7574.  \n[30] V.I. Anisimov, I.S. Elfimov, N. Hamada, K. Terakura, Charge -ordered insulating state of Fe_{3}O_{4} \nfrom first -principles electronic structure calculations, Phys Rev B, 54 (1 996) 4387 -4390.  \n[31] H.B. Guo, A.S. Barnard, Modeling the iron oxides and oxyhydroxides for the prediction of \nenvironmentally sensitive phase transformations, Phys Rev B, 83 (2011) 094112.  \n[32] A. Jain, G. Hautier, S.P. Ong, C.J. Moore, C.C. Fischer, K.A. Persson, G. Ceder, Formation enthalpies \nby mixing GGA and GGA plus U calculations, Phys Rev B, 84 (2011) 045115.  \n[33] D.A. Andersson, C.R. Stanek, Mixing and non -stoichiometry in Fe -Ni-Cr-Zn-O spinel compounds: \ndensity functional theory calculations, Phys Chem Chem Phys, 15 (2013) 15550 -15564.  \n[34] S.B. Zhang, J.E. Northrup, Chemical -Potential Dependence of Defect Formation Energies in Gaas - \nApplication to Ga Self -Diffusion, Phys Rev Lett, 67 (1991) 2339 -2342.  \n[35] S.B. Zhang, The microscopic origin of the  doping limits in semiconductors and wide -gap materials \nand recent developments in overcoming these limits: a review, J Phys -Condens Mat, 14 (2002) R881 -\nR903.  \n[36] L. Wang, T. Maxisch, G. Ceder, Oxidation energies of transition metal oxides within the GGA+ U \nframework, Phys Rev B, 73 (2006) 195107  \n[37] R.O. Jones, O. Gunnarsson, The Density Functional Formalism, Its Applications and Prospects, Rev \nMod Phys, 61 (1989) 689 -746.  \n[38] S. Lany, Semiconductor thermochemistry in density functional calculations, Phys Rev B, 78 (2008) \n245207.  \n[39] V. Stevanovic, S. Lany, X.W. Zhang, A. Zunger, Correcting density functional theory for accurate \npredictions of compound enthalpies of formation: Fitted elemental -phase reference energies, Phys Rev \nB, 85 (2012) 115104.  \n[40] H.B. Guo, A.S. Barnard, Thermodynamic modelling of nanomorphologies of hematite and goethite, J \nMater Chem, 21 (2011) 11566 -11577.  \n[41] O. Kubaschewski, C.B. Alcock, P.J. Spencer, Materials Thermochemistry, in, Pergamon Press, New \nYork, 1993.  16 \n \n \n [42] G.K. Johnson, The Enthalpy of Formation of Fef3 by Fluorine Bomb Calorimetry, J Chem Thermodyn, \n13 (1981) 465 -469.  \n[43] S. Krupicka, P. Novak, Oxide Spinels, North -Holland, Amsterdam, 1982.  \n[44] U. Luders, A. Barthelemy, M. Bibes, K. Bouzehouane, S. Fusil, E. Jacquet, J.P. Contour, J.F. Bobo, J. \nFontcuberta, A. Fert, NiFe2O4: A versatile spinel material brings new opportunities for spintronics, Adv \nMater, 18 (2006) 1733 -+. \n[45] S.I. Youssef, M.G. Natera, R.J. Begum, Srinivas.Bs, N.S.S. Murthy, Polarised Neutron  Diffraction \nStudy of Nickel Ferrite, J Phys Chem Solids, 30 (1969) 1941 -&. \n[46] V.N. Antonov, B.N. Harmon, A.N. Yaresko, Electronic structure and x -ray magnetic circular dichroism \nin Fe3O4 and Mn -, Co-, or Ni -substituted Fe3O4, Phys Rev B, 67 (2003) 02441 7. \n[47] Q.C. Sun, H. Sims, D. Mazumdar, J.X. Ma, B.S. Holinsworth, K.R. O'Neal, G. Kim, W.H. Butler, A. \nGupta, J.L. Musfeldt, Optical band gap hierarchy in a magnetic oxide: Electronic structure of NiFe2O4, \nPhys Rev B, 86 (2012) 205106.  \n 17 \n \n \n   \nTABLE 1. Calculated DFT energies per formula unit of the competing and secondary phases \nused in Eq. (1)-(8) along with the experimental and theoretical enthalpies of formation.  \nCompound  DFT energy/f.u. (eV)  \nexpH (eV) \ntheorH (eV) \nB2O3 -40.13   -12.83   -12.85   \nFeB -12.01   -0.76  -0.38  \nFeO -12.83   -2.73  -2.45  \nFe2O3 -34.14   -8.53  -8.40  \nFe3O4 -47.92   -11.49   -11.80   \nNiB -9.22  -0.48  -0.66  \nNi2B -11.45   -0.66  -0.52  \nNi4B3 -30.01   -1.86  -1.95  \nNiO -10.16   -2.48  -2.83  \nNi2O3 -24.36   -5.07  -4.75  \nNiFe 2O4 -44.47   -  -11.41   \nFe3BO 5 -64.84   -  -17.55   \nFe3BO 6 -70.77   -  -18.52   \nFeBO 3 -37.05   -  -10.54   \nNiB 2O4 -50.34   -  -15.74   \nNi3B2O6 -70.94   -  -21.69   \nNi2FeBO 5 -57.75   -  -10.40   \n \n \nTABLE 2. The fitted elemental reference energies calculated with Eq. (8). Values are given in \neV.   \nElement  Fe Ni O B \nFitted elemental energy  -5.43 -2.36 -4.96 -6.20 \n \n \nTABLE 3. Experimental magnetic moments and theoretical  spin magnetic moments (in μ B) \ncalculated using different Hubbard U parameters.  \n FeT FeO NiO Ueff(FeT) Ueff(FeO) Ueff(NiO) \nRef. [45] -4.86 4.73 2.22 - - - \nRef. [46] -3.99 4.09 1.54 4.5 4.5 4.0 \nRef. [15] -3.97 4.11 1.58 3.0 3.0 3.0 \nPresent  work  -4.13 4.22 1.71 4.5 4.5 6.0 \n \n \n 18 \n \n \n  \n \n \nTABLE 4. Calculated defect formation energies in NFO for different charge states. In the case of \nsubstitutional B at the T2 and O sites no convergent results were obtained for q = -1 and -2. \nValues are given in eV.  \nDefect  Charge state  \nq = -2   q = -1  q = 0  q = 1  q = 2  \nVFeT 9.10  8.30 7.73 7.26 6.88 \nVFeO 8.46 7.92 7.46 7.08 6.76 \nVNiO 6.13 5.56 5.12 4.75 4.41 \nBFeT 3.41 1.91 -0.08 -0.55 -0.93 \nBFeO 3.76 4.09 1.93 1.46 1.08 \nBNiO 5.54 3.46 1.94 -0.08 -0.53 \nBT1 5.03 3.17 1.45 -0.32 -1.08 \nBT2 - - -0.92 -2.43 -3.48 \nBO - - 0.09 -1.08 -2.11 \n \n \n \n \n \nFigure 1. Illustration of t he spinel structure  indicating  the two tetrahedral (T1, T2)  and  \noctahedral (O) interstitial sites.  \n \n19 \n \n \n  \nFigure 2. Spin polarized DOS  of nickel ferrite projected on the Fe and Ni  d states . Total DOS is \nalso shown as the grey b ackground area. The d states  of the octahedral cations are separated into \nt2g and eg components and the tetrahedral Fe d states are separated into t2 and e components.  \n \n \n20 \n \n \n  \nFigure 3. Calculated stability domain (dark area) of NFO in the (μ fe, μNi) plane.  The white \nregions represent  domains of the chemical potentials where secondary phases form.    \n \n \n21 \n \n \n  \nFigure 4. Formation energies of Fe and Ni vacancies in NFO as a function of EF, under Fe - and \nNi-poor conditions.  The slope of the lines represent s the charge state of the defect and the value \nof EF where the slope changes represents the charge transition level (ionization level). The most \nstable defect is the Ni vacancy.  \n \n \nFigure 5. Formation energies of substitutional B defects in NFO as a function of EF.  \n \n22 \n \n \n  \nFigure 6. Formation energies of substitutional B defects in NFO versus EF. In p-type NFO, t he \nmost stable location of B is the tetrahedral interstitial site (T2).   \n \n \n"    },    {        "title": "0909.5294v1.First_principles_study_of_ferroelectric_domain_walls_in_multiferroic_bismuth_ferrite.pdf",        "content": "First-principles study of ferro electric domain w alls in m ultiferroic bism uth ferrite\nAxel Lubk,1S. Gemming,2and N. A. Spaldin3\n1Institute for Structur e Physics, T e chnische Universitaet Dr esden, D-01062, Germany\u0003\n2Institute of Ion-Be am Physics and Materials R ese ar ch, FZ Dr esden-R ossendorf, D-01328 Dr esdeny\n3Materials Dep artment, University of California, Santa Barb ar a, CA, 93106-5050, USAz\n(Dated: Marc h 4, 2022)\nW e presen t a \u001crst-principles densit y functional study of the structural, electronic and magnetic\nprop erties of the ferro electric domain w alls in m ultiferroic BiF eO 3 . W e \u001cnd that domain w alls\nin whic h the rotations of the o xygen o ctahedra do not c hange their phase when the p olarization\nreorien ts are the most fa v orable, and of these the 109\u000edomain w all cen tered around the BiO plane\nhas the lo w est energy . The 109\u000eand 180\u000ew alls ha v e a signi\u001ccan t c hange in the comp onen t of\ntheir p olarization p erp endicular to the w all; the corresp onding step in the electrostatic p oten tial\nis consisten t with a recen t rep ort of electrical conductivit y at the domain w alls. Finally , w e sho w\nthat c hanges in the F e-O-F e b ond angles at the domain w alls cause c hanges in the can ting of the F e\nmagnetic momen ts whic h can enhance the lo cal magnetization at the domain w alls.\nP A CS n um b ers: 77.80.Dj, 77.84.Dy , 75.50.Ee\nI. INTR ODUCTION\nP ero vskite-structured bism uth ferrite, BiF eO 3 , is the\nsub ject of m uc h curren t researc h b ecause of its large\nro om temp erature ferro electric p olarization and sim ul-\ntaneous (an tiferro-)magnetic ordering. Suc h multiferr oic\nmaterials sho w a w ealth of complex ph ysical prop erties\ncaused b y their co existing electrical and magnetic order\nparameters, whic h in turn suggest p oten tial applications\nin no v el magneto electronic devices: Recen t rep orts of\nelectric-\u001celd induced switc hing of magnetization through\nexc hange bias of ferromagnetic Co to BiF eO 3 are particu-\nlarly promising [1, 2]. In addition, the large ferro electric\np olarization [3], driv en b y the stereo c hemically activ e\nBi3+lone pair [4], is motiv ating in v estigation of its\npurely ferro electric b eha vior for p ossible applications in\nferro electric memories.\nThe suitabilit y of ferro electric materials for appli-\ncations is determined not only b y the magnitude of\ntheir ferro electric p olarization, but also b y factors\nsuc h as switc habilit y , fatigue and loss. These are in\nturn in\u001duenced b y the structure of the domains and\nparticularly b y the b oundaries b et w een them. The\ndetailed structure and formation energies of domain\nw alls in some con v en tional ferro electrics are no w w ell\nestablished (see for example Refs. 5, 6 for exp erimen tal\nstudies and Refs. 7, 8 for calculations). F or BiF eO 3 ,\nho w ev er, the \u001crst exp erimen tal study of domain w alls\nw as only recen tly rep orted [9], and a detailed theoretical\nstudy is lac king. The additional consideration of the\ne\u001bect of the ferro electric domain w all on the electronic\nand magnetic degrees of freedom mak es suc h a study\nparticularly comp elling.\nIn this w ork w e use densit y functional theory within\nthe LSD A +U metho d to calculate the structure, stabilit y\nand prop erties of the ferro electric domain w alls in\nBiF eO 3 . W e b egin this man uscript b y reviewing thestructure of bulk BiF eO 3 (Section I I), so that w e can use\nthe bulk symmetry to determine the allo w ed energetically\nfa v orable domain w all orien tations (Section I I I). In\nSection IV w e describ e the tec hnical details of our densit y\nfunctional calculations. The main part of the pap er\n\u0015 Section V \u0015 con tains our results: W e p erform full\nstructural optimizations of the atomic p ositions for the\nenergetically fa v orable domain w all orien tations, and\ncalculate and compare their total energies to determine\nwhic h w alls are most lik ely to o ccur. W e then calculate\nthe electronic and magnetic prop erties of the w alls,\npa ying particular atten tion to ho w c hanges in structure at\nthe b oundaries in\u001duence the electronic densities of states,\np oten tial pro\u001cle and spin can ting. The implications\nof our \u001cndings for domain w alls in m ultiferroics, and\nsuggestions for future directions are summarized in\nSection VI.\nI I. STR UCTURE OF BiFeO 3\nBiF eO 3 is a rhom b ohedral p ero vskite with space group\nR3c (Fig. 1). The ground state structure is reac hed\nfrom the ideal cubic p ero vskite ( Pm\u00163m ) b y imp osing\nt w o symmetry-adapted lattice mo des: (1) a non-p olar R -\np oin t mo de whic h rotates successiv e o xygen o ctahedra in\nopp osite sense around the [111] -direction, and (2) a p olar\n\u0000\u0000\n4 distortion, consisting of p olar displacemen ts along\nthe[111] -direction as w ell as symmetric breathing of\nadjacen t o xygen triangles [10]. The rhom b ohedral lattice\nconstan t is 5.63 Å (with corresp onding pseudo cubic\nlattice constan t, a0= 3:89 Å), and the rhom b ohedral\nangle,\u000b= 59:35\u000eis close to the ideal v alue of 60\u000e[11].\nFirst-principles densit y functional calculations ha v e b een\nsho wn to accurately repro duce these v alues [4].\nThe magnetic ordering is w ell established to b e G-\nt yp e an tiferromagnetic [12], with a long w a v elengtharXiv:0909.5294v1  [cond-mat.mtrl-sci]  29 Sep 20092\nFIG. 1: Crystal structure of bulk BiF eO 3 . T w o simple\np ero vskite unit cells are sho wn to illustrate that successiv e\no xygen o ctahedra along the p olar [111] axis rotate with\nopp osite sense around [111] . The red arro ws on the F e atoms\nindicate the orien tation of the magnetic momen ts in the (111)\nplane.\nspiral of the an tiferromagnetic axis [13]. First-\nprinciples densit y functional computations [14] and\nsymmetry considerations [15] indicate a lo cal can ting of\nthe magnetic momen ts to yield a w eak ferromagnetic\nmomen t; this can ting is symmetry allo w ed b ecause of\nthe presence of the non-p olar R p oin t rotations of the\no xygen o ctahedra. Since the orien tation of the w eak\nferromagnetic momen t follo ws the axis of the long-range\nspiral no net magnetization results.\nThe ferro electric p olarization is large, \u0018 90\u0016 C/cm2\n[3], and can p oin t along an y of the eigh t pseudo-cubic\nh111i directions [11]. Simple geometrical considerations\ntherefore suggest angles of \u000671\u000e,\u0006109\u000eor180\u000e\nb et w een allo w ed p olarization orien tations of the ideal\nrhom b ohedral system ( \u000b= 60\u000e) [16]; w e will lab el\nour domain w alls using these angles in the follo wing.\nExp erimen tally , suc h relativ e domain orien tations and\nre-orien tation angles ha v e indeed b een observ ed [1].\nCurren tly nothing is kno wn ab out the b eha vior of the\no ctahedral rotations or the magnetism at the domain\nb oundaries.\nI I I. SYMMETR Y ANAL YSIS OF DOMAIN\nW ALLS\nIn general, the energetically fa v orable domain w all\ncon\u001cgurations for a particular symmetry are thoseorien tations whic h can b e free of b oth stress and\nspace c harge. F or the rhom b ohedral symmetry of\nBiF eO 3 , these conditions lead to the follo wing lik ely\ndomain w all orien tations for \u000671\u000e,\u0006109\u000eand 180\u000e\norien tations resp ectiv ely: f011g ,f001g andf011g (in\npseudo-cubic co ordinates) [16]. F or eac h of these w all\norien tations, there is a c hoice of atomic plane ab out\nwhic h the initial domain w all can b e cen tered (for\nexample around a BiO or F eO 2 plane in the 109\u000ecase).\nIn addition, since the rotations of the o xygen o ctahedra\nare uncoupled from the orien tation of the p olarization,\ndi\u001beren t relativ e orien tations of o xygen o ctahedra on\neither side of the domain w all are p ossible. In order\nto surv ey all p ossibilities w e in v estigate the follo wing\ndomain b oundaries:\n1.71\u000e: W e construct the domain w all in the (011)\nplane with the electric p olarization c hanging from\nthe[111] direction on one side of the domain w all\nto[\u0016111] on the other (Fig. 2(a)). W e study\nt w o con\u001cgurations of the rotations of the o xygen\no ctahedra, whic h w e refer to as either c ontinuous\nor changing . In the con tin uous case, the phase of\nthe o xygen o ctahedral rotations remains unc hanged\nalong an in tegral curv e of the p olarization v ector\n\u001celd; in the c hanging case the phase rev erses at\nthe domain w all. In principle the w all could b e\ncen tered around either a BiF eO or O 2 plane (or an y\nin termediate plane). Ho w ev er, since the domain\nw all lo cation is not \u001cxed b y symmetry and the\ndistance b et w een the t w o planes is small, the fully\nrelaxed domain b oundary will lik ely b e cen tered\nclose to the O 2 plane indep enden t of the initial\ncon\u001cguration (as found in Ref. [8]).\n2.109\u000e: W e use the (001) plane for the domain w all,\nwith p olarization c hanging from the [111] to the\n[\u00161\u001611] direction (Fig. 2(b)). Again w e explore\nt w o con\u001cgurations of the o ctahedral rotations, with\ncon tin uous or c hanging phase along the in tegral\ncurv e of the p olarization v ector \u001celd. In this\ncase w e w ere able to separately resolv e domain\nw alls cen tered on F eO 2 and BiO planes, since their\nseparation isp\n2 times that of the BiF eO and O 2\nplanes in the 71\u000ecase.\n3.180\u000e: W e use the (0\u001611) plane for the domain w all,\nwith p olarization c hanging b et w een [111] and[\u00161\u00161\u00161]\ndirections (Fig. 2(c)). Again w e explore t w o\no ctahedral tilt patterns, with the phases along the\np olarization direction either con tin uous or c hanging\nacross the b oundary . As in the 71\u000ecase, w e do not\ndistinguish b et w een the BiF eO- and O 2 -cen tered\ndomain w alls.3\n(a)\n(b)\n(c)\nFIG. 2: (a) 71\u000edomain b oundary with con tin uous o xygen\no ctahedral rotations. (b) 109\u000edomain b oundary with\ncon tin uous o xygen o ctahedral rotations cen tered on the F eO 2\nplane. (c) 180 ° domain b oundary with con tin uous o xygen\no ctahedral rotations. Note that only half of the sup ercell is\nsho wn.\nIV. COMPUT A TIONAL DET AILS\nW e p erformed densit y functional (DFT) calculations\nusing the Vienna ab-initio sim ulation pac k age, V ASP\n[17]. W e used the pro jector augmen ted w a v e metho d\n[18, 19] with the default V ASP P A W p oten tials including\nsemi-core states in the v alence manifold (core states Bi:\n[Kr], F e: [Ne] 3s2, O: 1s2). W e used the rotationally\nin v arian t implemen tation [20] of the LSD A+U metho d\n[21] to describ e the exc hange-correlation functional with\nv alues ofU= 3 e V andJ= 1 e V that w ere sho wn\npreviously to accurately repro duce the exp erimen tally\nobserv ed structural and electronic prop erties of bulk\nBiF eO 3 [4, 14, 22].\nW e constructed sup ercells con taining t w o domains\nseparated b y domain w alls, with a total of 120 atoms(60 atoms p er domain); the width of eac h domain w as\nthen six pseudo cubic unit cells. W e used the lattice\nparameters obtained from calculations for bulk BiF eO 3\n(see Ref. 4), with a sligh t c hange: the rhom b ohedral\nangle,\u000b , w as tak en to b e exactly 60\u000eto allo w us to\nincorp orate b oth domains in one sup ercell. While the\nelectronic structure of bulk BiF eO 3 at\u000b= 60\u000eis\nindistinguishable from that at the exp erimen tal \u000b=\n59:35\u000e[4], w e p oin t out that this constrain t migh t\nin\u001duence the strain pro\u001cle at the domain b oundary .\nThe total energy di\u001berence of bulk BiF eO 3 with\u000b=\n60\u000eand with\u000b= 59:35\u000eis b elo w 1 me V, hence w e\nconclude, that the e\u001bect ma y b e neglected in the further\ndiscussion. W e initialized the magnetic ordering to the\nG -t yp e an tiferromagnetic arrangemen t kno wn to o ccur in\nthe bulk.\nF ull structural optimizations of the atomic p ositions\n(un til the forces on eac h ion w ere b elo w 0.03 e V p er\nÅ) and cell parameters (un til energy di\u001berences w ere\nb elo w 0.01 e V) w ere then p erformed for all of the domain\ncon\u001cgurations describ ed in Section I I I. No symmetry\nconstrain ts w ere imp osed. The cell parameter relaxations\nw ere necessary b ecause the in terla y er distance in all three\ndomain w alls is sligh tly larger (b y around 0.1 Å) than\nthat in the bulk. The rather large remaining forces\no ccur due to a com bination of the complicated crystal\nstructure of BiF eO 3 and the large n um b er of atoms in\none sup ercell, leading to a \u001dat energy surface and a\nparticularly slo w structural con v ergence. A dditionally ,\nsp ecial care had to b e tak en with resp ect to the starting\nconditions of the structure optimization, i.e. sev eral\ndi\u001beren t initializations of the initial spin con\u001cguration\nand ion p ositions w ere p erformed for eac h con\u001cguration\nto reduce the probabilit y of b eing trapp ed in lo cal\nminima. W e used 5 \u0002 3\u0002 1 (71\u000eand 180\u000e) and 5\u0002 5\u0002 1\n(109\u000e) k -p oin t samplings; these corresp ond to v alues\nthat ha v e b een sho wn to giv e go o d con v ergence for bulk\nBiF eO 3 , with a denser sampling along the long axis of\nthe sup ercell. The plane w a v e energy cut-o\u001b w as set to\n550 e V.\nFinally , for the calculated lo w est energy 109\u000eb ound-\nary , w e p erformed additional non-collinear magnetic\ncalculations with spin-orbit coupling included.\nV. RESUL TS\nA. Structure and energetics\nIn all cases our sup ercells relaxed to con tain t w o\ndistinct domains, with the la y ers in the middle of eac h\ndomain ha ving similar structure to that of bulk BiF eO 3 ;\nthis suggests that the sup ercells w ere large enough to\nminimize in teractions b et w een the domain w alls.\nIn T able I w e list our calculated domain w all energies\nfor all of the con\u001cgurations describ ed in the previous4\n71\u000ec71\u000ed109\u000eBc109\u000eBd109\u000eF c109\u000eF d180\u000ec\n363 436 205 896 492 1811 829\nT ABLE I: Calculated domain w all energies (mJ/m2) for 71\u000e,\n109\u000eand 180\u000ew alls. B and F indicate the BiF eO- and F eO 2 -\ncen tered planes, c and d lab el the con tin uous or discon tin uous\no xygen o ctahedral rotations.\nsection. It is clear that, in all cases, the con\u001cguration\nwith the least p erturbation to the phase of the o ctahedral\nrotations is lo w est in energy . Indeed, in the 180\u000ecase\nw e w ere unable to obtain a con v erged solution for the\ncase with rev ersal of the o ctahedral rotations at the\ndomain b oundary . The large di\u001berences b et w een the\ncon tin uous and discon tin uous o xygen o ctahedra rotations\nis a p eculiarit y of the BiF eO 3 structure and indicates the\nimp ortance of the F e-O-F e b onding angles in determining\nthe structural stabilit y . The 109\u000ew all is energetically the\nmost stable of the three orien tations. It is somewhat\nsurprising that the 109\u000ew all is lo w er in energy that\nthe 71\u000ew all; since the c hange in orien tation of the\nelectric p olarization v ector is smaller in the latter, one\nw ould also exp ect the p erturbation to the structure to\nb e smaller. (Previous calculations for PbTiO 3 found\nthe 90\u000ew all to b e lo w er in energy than the 180\u000ew all,\nconsisten t with this argumen t [8]). W e b eliev e that\nthis rev ersal is caused b y the fa v orable arrangemen t of\nthe o xygen o ctahedra at the 109\u000ew all b oudary: since\nthe 109\u000ew all lies in the f001g plane, it is orien ted\nalong the apices of the o xygen o ctahedra (Fig. 2(b)\nupp er panel), whereas the 71\u000eand 180\u000ef011g w alls are\norien ted along the o ctahedral edges (Figs. 2(a) and 2(c)\nupp er panels) giving them less freedom to accommo date\nthe c hanges in p olarization direction. The 109 ° BiO-\ncen tered w all is lo w er in energy than the F eO 2 -cen tered\nw all, consisten t with previous studies for other p ero vskite\nferro electric domain b oundaries whic h also found A O-\ncen tered w alls to b e more stable [8]. The 180\u000ecase\nhas the highest domain w all energy , consisten t with its\nha ving the largest c hange in the p olarization orien tation.\nFinally , w e note that the domain w all energies in BiF eO 3\nare signi\u001ccan tly larger than those calculated for PbTiO 3 ,\nwhic h in turn are larger than the BaTiO 3 v alues (T able\nI I). The large increase from BaTiO 3 to PbTiO 3 suggests a\ncorrelation b et w een p olarization magnitude and domain\nw all energy . While c hanges in p olarization w ould predict\nsomewhat larger domain w all energies for BiF eO 3 , there\nis a large additional increase whic h is lik ely a result of\nthe additional deformations caused b y the o ctahedral\nrotations (see discussion ab o v e). It is also p ossible that\nthe magnetic energy cost asso ciated with p erturbing\nthe F e-O-F e b ond angles further raises the domain w all\nenergies in BiF eO 3 .\nAs a measure of the amoun t of structural distortion, in\nFigure 3 w e plot the F e-O-F e angles in eac h la y er acrossangle BaTiO 3PbTiO 3\n90 ° N/A 35.2\n180 ° 7.5 132\nT ABLE I I: Lo w est calculated domain w all energies (mJ/m2)\nfor 90 ° and 180 ° domain w alls in BaTiO 3 and PbTiO 3 , from\nRef. 8.\n−3−2−10123150°152°154°156°158°\ndistance from domain wall [a0]FeOFe angle\n  \n71°\n109°\n180°\nFIG. 3: F e-O-F e angles in eac h la y er of the sup ercell. The\nbulk v alue of 152.9\u000eis indicated b y the dashed line. Note the\nc hanges in angle in the domain w all region.\nthe sup ercells. Within the cen tral region of the domain\nthe bulk v alue of 152.9\u000eis regained as exp ected. Indeed\nthe bulk b eha vior is reco v ered within one or t w o la y ers of\nthe domain w all b oundary , consisten t with earlier studies\non PbTiO 3 domain w alls [8]. The angles c hange b y up\nto\u0018 4\u000ein the w all region to accommo date the c hanges in\nstructure asso ciated with the p olarization reorien tation.\nHo w ev er, the F e-O-F e angles remain far from 180\u000ein\nall cases, indicating that the structure within the w alls\nis far from an ideal cubic p ero vskite structure. Since\nthe F e-O-F e angle strongly in\u001duences the sup erexc hange\nin teractions and the lo cal anisotrop y , w e an ticipate that\nthese c hanges in angles migh t in\u001duence the magnetic\nprop erties; w e return to this p oin t later.\nB. Ev olution of the p olarization across the domain\nw alls\nIn order to b etter understand the c hange in structure\nacross the domain w all w e p erformed a la y er-b y-la y er\nanalysis of the lo cal p olarization b y summing o v er the\ndisplacemen ts of the atoms in eac h la y er from their\nideal cubic p ero vskite p ositions, m ultiplied b y their Born\ne\u001bectiv e c harges (BECs). While there is not a unique\nw a y to partition the la y ers, w e \u001cnd that our results\nfrom di\u001beren t decomp osition sc hemes are similar, and so\nw e use the narro w est p ossible la y er partition in order\nto optimize the resolution. W e used the BECs of the\nR3c structure calculated in a previous study [4] using\nthe same computational parameters as w e use here;5\n−3−2−10123405060708090100\ndistance from domain wall [a0]polarization [µC/cm2]\n  \n71°\n109°\n180°\nFIG. 4: La y er-b y-la y er p olarization calculated from the sum\nof the displacemen ts of the ions from their ideal p ositions\nm ultiplied b y the Born e\u001bectiv e c harges.\nnote that the actual BECs migh t deviate sligh tly from\nthese v alues. This tec hnique w as used previously to\nanalyze the p olarization ev olution across PbTiO 3 domain\nw alls [8]. W e are particularly in terested in t w o factors:\nFirst whether the p olarization reorien tation tak es place\nthrough a rigid rotation of the lo cal p olarization, without\na reduction in its lo cal magnitude (analogous to the\nrotation of a magnetic momen t in a Blo c h w all in\na ferromagnet). And second, whether a c hange in\np olarization in the direction p erp endicular to the w all\ndev elops. This is of particular in terest since, as discussed\nin earlier w ork [8], it giv es rise to a p oten tial step at\nthe b oundary whic h, if screened b y a dip ole la y er in the\nc harge densit y , could giv e rise to in triguing e\u001bects suc h\nas enhanced conductivit y at the b oundary .\nFirst, in Fig. 4 w e sho w the magnitudes of the\ncalculated la y er-b y-la y er p olarizations for all three w all\nt yp es. It is clear that in the 71\u000eand 180\u000ew alls, the\nmagnitude of the p olarization remains appro ximately\nconstan t across the w all, indicating a rigid rotation of\nthe p olarization in the manner of a magnetic Blo c h w all.\n(Note that the scatter in the lo cal p olarization esp ecially\nat the 180\u000eresults from our fairly high force tolerance of\n0.03 e V p er Å.) In con trast, the 109\u000ew all has a mark ed\nreduction in the lo cal p olarization in the w all region;\nthis lik ely results from the greater structural \u001dexibilit y\npro vided b y the orien tation of the 109\u000ew all relativ e to\nthe corners of the o ctahedra.\nNext w e analyze the lo cal p olarization b y decomp osing\nit in to the comp onen ts parallel and p erp endicular to the\nplanes of the domain w alls. (Figs. 5(a), (b) and (c) for\nthe 71\u000e, 109\u000eand 180\u000ew alls resp ectiv ely .) The total\np olarization in the mid-domain regions is \u001890\u0016 C/cm2\nin all cases, in go o d agreemen t with previously rep orted\nbulk v alues [4]. In all cases the comp onen t parallel\nto the domain w all c hanges from its full mid-domain\nv alue in one orien tation to the full v alue in the other\norien tation within t w o or three la y ers. The magnitude\nof the c hange in p olarization comp onen t p erp endicular\n−3−2−10123−100−80−60−40−20020406080100\ndistance from domain wall [a0]Polarization [µC/cm2]\n  \n−0.25−0.2−0.15−0.1−0.050\nelectrostatic potential [eV]\n  \nVP⊥\nP||(a)\n−3−2−10123−100−80−60−40−200  20 40 60 80 100 Polarization [µC/cm2]\n  \ndistance from domain wall [a0]−0.25−0.2−0.15−0.1−0.050\nelectrostatic potential [eV]\n  \nVP⊥\nP||\n(b)\n−3−2−10123−100−80−60−40−20020406080100\ndistance from domain wall [a0]Polarization [µC/cm2]\n  \n−0,25−0,2−0,15−0,1−0,050\nelectrostatic potential [eV]\n  \nP⊥\nP||\nV\n(c)\nFIG. 5: P arallel and normal comp onen ts of the p olarization,\nPk and P? , and the macroscopically and planar a v eraged\nelectrostatic p oten tial, V for (a) 71\u000edomain b oundary with\ncon tin uous o xygen o ctahedral rotations, (b) 109\u000edomain\nb oundary with con tin uous o xygen o ctahedral rotations\ncen tered on the F eO 2 plane and (c) 180 ° domain b oundary\nwith con tin uous o xygen o ctahedral rotations. Note that only\nhalf of the sup ercell is sho wn.\nto the w all, ho w ev er, dep ends strongly on the domain\nw all t yp e. In Figs. 5(a), 5(b) and 5(c) w e also plot\nthe planar and macroscopically a v eraged electrostatic\np oten tial (extracted as in Ref. [8]) across the sup ercell to\nillustrate the p oten tial step asso ciated with this c hange\nin p erp endicular comp onen t of the p olarization. F or the6\n71\u000ew all the c hange in p erp endicular comp onen t and\ncorresp onding p oten tial step are small; the magnitude of\nthe p oten tial step is \u0018 0.02 e V. In the 109\u000ecase the c hange\nthe in out-of-plane comp onen t is considerable, and the\ncorresp onding step is signi\u001ccan t (0.15 e V). This b eha vior\nis analogous to that rep orted previously in calculations\nfor 90\u000edomain w alls [8]. P erhaps surprisingly , the 180\u000e\nb oundary sho ws the largest p oten tial step, of 0.18 e V.\n(Earlier studies of 180\u000edomain b oundaries in tetragonal\nPbTiO 3 [8] included an in v ersion cen ter at the domain\nw all and therefore obtained no c hange in p erp endicular\ncomp onen t). The follo wing analysis of the ev olution\nof the p olarization through successiv e corners of the\npseudo cub e explains the loss of in v ersion symmetry and\nthe c hange in the p erp endicular comp onen t in the 180\u000e\ncase.\nIn terestingly , the presence of the large p oten tial steps\nat the 109\u000eand 180\u000ew alls, and the absence of a step\nat the 71\u000ew all, correlate with an in triguing recen t\nobserv ation of electrical conductivit y at the 109\u000eand\n180\u000ew alls, and its absence at the 71\u000ew all [9]. A\np ossible explanation of the observ ed conductivit y is the\ngeneration of a space c harge la y er in the region of the\nw all to screen this otherwise energetically unfa v orable\np oten tial discon tin uit y .\nFinally , to help with visualizing the c hange in\np olarization across the domain w alls, in Fig. 6 w e\nindicate the lo cal p olarization v ectors in eac h la y er of\nthe sup ercells as blue arro ws sho wing the magnitude\nand orien tation. In the 71\u000ecase w e can clearly see\nthat the p olarization rotates from one corner of the\npseudo cubic unit cell, through the cen ter of the edge\nto the adjacen t corner, accompanied b y the small\natten uation in magnitude whic h w e sa w earlier in Fig. 4.\nAs already seen in Fig. 5(a), this geometry allo ws\nthe p erp endicular comp onen t of p olarization to remain\nconstan t across the w all. The analogous carto on for\nthe 180\u000ew all (Fig. 6(c)) sho ws that the p olarization\nv ector rotates b et w een successiv e corners of the pseudo-\ncubic unit cell whic h are the stable orien tations of\nthe p olarization in R3c BiF eO 3 . A t the la y er-b y-la y er\nlev el of resolution w e see a jump b y 71\u000efollo w ed b y a\njump of 109\u000e; b oth in termediate orien tations ha v e small\ncomp onen ts p erp endicular to the domain w all. Note that\nimp osition of an in v ersion cen ter during the structural\nrelaxation, whic h migh t b e an ticipated for a 180\u000ew all,\nw ould not ha v e allo w ed this ground state to dev elop. In\ncon trast, the c hange in orien tation of the p olarization\nacross the 109\u000ew all is accompanied b y a rather large\natten uation of the total p olarization (see Fig. 4 and\nFig. 6(b)).\n(a)\n(b)\n(c)\nFIG. 6: Ev olution of the lo cal p olarization across (a) the\n71 ° , (b) the 109 ° and (c) the 180 ° domain w all. The blue\narro ws represen t the magnitude and orien tation of the lo cal\np olarization.\nC. Electronic prop erties of the domain w alls\nIn ligh t of the in triguing rep orted electrical conduc-\ntivit y men tioned ab o v e, w e next analyze the electronic\nprop erties of the domain w alls. W e lo ok particularly\nat the la y er-b y-la y er densities of states, to see if the\nstructural deformations in the w all region lead to a\nclosing of the electronic band gap. Indeed, earlier\nDFT calculations for bulk BiF eO 3 [4] indicated a strong\ndep endence of the electronic band gap on the structure.\nIn particular the ideal cubic structure, in whic h the\n180\u000eF e-O-F e b ond angles maximize the F e 3d - O\n2p h ybridization and hence the bandwidth, has a\nsigni\u001ccan tly reduced band gap compared with the R3c7\n−8−6−4−20 2 405101520\nE−Ef [eV]DOS\n  \nbulk DOS\nmid−domain DOS\nFIG. 7: Comparison of calculated bulk DOS for BiF eO 3\n(dashed line) with the lo cal densit y of states of a mid-domain\nla y er in the sup ercell with a 109\u000edomain w all. The sum of\nb oth spin c hannels is sho wn.\nstructure and is ev en metallic within the LSD A.\nFirst, in Figure 7 w e compare the lo cal densit y of\nstates (LDOS) for a la y er in the cen ter of a domain with\nour calculated densit y of states for bulk BiF eO 3 . The\nmid-domain LDOS sho wn is for the sup ercell con taining\nthe 109\u000ew all; those of the 71\u000eand 180\u000esup ercells\nare indistinguishable. As found in prior w ork [4], the\nbulk v alence band consists of O 2p - ma jorit y spin\nF e3d h ybridized states, while the b ottom part of the\nconduction band is formed of minorit y spin F e 3d states\nand Bi 6p states. The LSD A+ U band gap is 1.4 e V for\nour c hosen v alues of U andJ . The electronic structure in\nthe mid-domain region fully reco v ers the bulk b eha vior.\nIn the domain w all, deformation of the F e-O-F e angles\ncauses c hanges in the h ybridization whic h a\u001bect the F e\neg states, resulting in shifts of the band edges. These are\nstrongest at the 180\u000eb oundary where the deformations\nare largest and the F e-O-F e angles are strongly increased.\nFig. 8 compares the mid-domain and domain w all LDOSs\nfor the three w all orien tations. The increasing do wn w ard\nshift in the conduction band edge from 71\u000eto 109\u000eto\n180\u000ew alls, correlating with the increasing c hange in F e-\nO-F e band angle is clearly visible. A t the 180 ° w all\nthere is an additional shift of the top of the v alence band\n(consisting of O 2p - F e3d h ybridized states) up w ards in\nenergy . These band edge shifts in turn cause a reduction\nin the lo cal band gap, whic h is plotted in Fig. 9. Again\nthe c hange is smallest for the 71 ° w all and largest for the\n180 ° w all.\nIn Fig. 9 w e sho w the lo cal band gap extracted from\nthe la y er-b y-la y er densities of states across the three w all\nt yp es. In all cases w e see a reduction in the band gap\nin the w all region, with the 180\u000ew all again sho wing the\nlargest e\u001bect. In no case, ho w ev er, do es the gap approac h\nzero in the w all region.\nFinally , to pro vide a quan titativ e measure of the exten t\nof lo calization of the states near the conduction band\nedge, w e calculate the pro jection of the lo w est energy\n−2 −1 0 1 200.10.20.30.40.5\nE−Ef [eV]local DOS\n  \n1.2 1.4  mid−domain\ndomain wall(a)\n0.05 eV(a)\n−2 −1 0 1 2 00.10.20.30.40.5\nE−Ef [eV]local DOS\n  \n1.2 1.4  mid−domain\ndomain wall(b)\n0.1 eV\n(b)\n−2 −1 0 1 200.10.20.30.40.5\nE−Ef [eV]local DOS\n  \n1.21.4  mid−domain\ndomain wall(c)\n0.2 eV\n(c)\nFIG. 8: Comparison of the calculated F e LDOS in the mid-\ndomain and domain w all regions for (a) 71 ° , (b) 109 ° and (c)\n180 ° w alls. Note the do wn w ard shifts in the conduction band\nedges, particularly in the 109 ° and 180 ° cases. The 180 ° case\nalso sho ws a small up w ard v alence band edge shift.\nconduction band on to eac h la y er of the sup ercell; our\nresults are sho wn in Figure 10. It is clear that the\nconduction band edge is dominated b y states in the\ndomain w all, more so in the 109 ° w all (on thef100g\nplane) than in the 71 ° and 180 ° w alls (whic h are b oth in\nf110g planes). Again, this implies that electron carriers\nin the system, whic h will o ccup y the lo w est conduction\nband states, will accum ulate at the domain b oundary\nregions.8\n−4−3−2−101231.11.21.31.4\ndistance from domain wall [a0]local band gap [eV]\n  \n71°\n109°\n180°\nFIG. 9: Lo cal band gap extracted from the la y er-b y-la y er\ndensities of states.\n−3−2−1012302468\ndistance from domain wall [a0]partial band occupation [a.u.]  \n71°\n109°\n180°\nFIG. 10: La y er-b y-la y er pro jection of the lo w est conduction\nband (partial band o ccupation) for 71 ° , 109 ° and 180 ° domain\nw alls. The in tegrated partial band o ccupation is equal to one.\nD. Magnetic prop erties\nIn bulk BiF eO 3 , the magnetic ordering is G-t yp e\nan tiferromagnetic with a long w a v elength ( \u0018620 Å)\nspiral of the AFM axis [13]. The spiral is kno wn to\nb e suppressed b y doping [23] and imp ortan tly for this\nw ork is b eliev ed to b e suppressed in thin \u001clms [24]. Our\nearlier \u001crst-principles calculations sho w ed that the AFM\nv ector lies in one of six easy axes within the magnetic\neasy plane whic h is p erp endicular to the p olar axis.\nW e found a spin-orbit driv en can ting of the magnetic\nmomen ts of\u0018 1\u000e[14] whic h, in the absence of a spiral,\nresults in a net w eak ferromagnetism of 0.05 \u0016B p er F e\nion. The can ting is symmetry allo w ed b ecause of the\no ctahedral rotations; a h yp othetical R3m p olar structure\nwithout o ctahedral rotations could not sho w w eak\nferromagnetism. Recen t magneto-optical measuremen ts\nsho w ed the an tiferromagnetism can b e con trolled using\nan electric \u001celd b ecause its orien tation is determined b y\nthe direction of the ferro electric p olarization [1].\nIn this \u001cnal section w e include spin-orbit coupling\nin our calculations in order to explicitly calculate the\norien tation of the magnetic momen ts relativ e to thep olarization v ector, and to allo w an y spin-orbit driv en\ncan ting to manifest. Consisten t with Ref. [24] and\nfor computational feasibilit y , w e use the ideal G-t yp e\nstructure with initial spin p olarization axis set to the\npseudo cubic [1\u001610] direction, whic h w as c hosen b ecause\nit is p erp endicular to the electric p olarization v ectors on\nb oth sides of the domain w all ( [111]=[\u00161\u001611] in the 109\u000e\ncase) as our starting p oin t; w e do not allo w the long\nw a v elength spiral. Since the non-collinear calculations\nwith spin-orbit coupling are so computationally in tensiv e,\nw e are only able to study one w all orien tation. W e\nc ho ose to study the 109\u000ew all since it is accompanied b y\na reorien tation of the an tiferromagnetic easy plane across\nthe b oundary; our \u001cndings migh t also b e applicable\nto the 71\u000edomain w all in whic h the easy plane also\nreorien ts across the b oundary . (A t the 180\u000edomain\nw all the p olarization rev erses direction and so w e exp ect\nthe easy plane of magnetization, whic h is p erp endicular\nto the p olarization, to remain unc hanged across the\ndomain w all. In addition, since our structural studies\ndescrib ed ab o v e found that the phase of the o ctahedral\nrotations \u0015 whic h determines the orien tation of the\ncan ting \u0015 is unc hanged across the domain w all, w e\ndo not exp ect a rev ersal of the w eak ferromagnetic\nv ector.) W e exp ect that c hanges in the lo cal symmetry\nat the w all migh t signi\u001ccan tly a\u001bect the can ting angles;\nin addition if the p erturbations in the F e-O-F e b ond\nangles are large enough w e could ev en see a c hange\nfrom an tiferromagnetic to ferromagnetic sup erexc hange\n[25, 26, 27].\nIn Fig. 11 w e sho w the net lo cal magnetization\nresulting from the can ting of the F e magnetic momen ts\nin eac h la y er across the 109\u000edomain w all. In the mid-\ndomain regions the orien tation of the lo cal momen t is\n[11\u00162] on one side and [112] on the other side of the w all.\nThe magnitude of the lo cal momen t is consisten t with\nthat calculated for bulk BiF eO 3 . The reorien tation of\nthe AFM plane consisten t with the reorien tation of the\np olarization is eviden t. Imp ortan tly , w e see that the lo cal\ncan ting incr e ases b y\u0018 33% in the w all la y er, consisten t\nwith the larger deviation of the F e-O-F e angles from\n180\u000e. This b eha vior could explain the in triguing recen t\nobserv ation that the magnitude of the exc hange bias in\nBiF eO 3 /Co m ultila y ers is a\u001bected b y the ferro electric\ndomain structure in BiF eO 3 [28].\nVI. SUMMAR Y\nIn summary , w e ha v e used the LSD A +U metho d of\ndensit y functional theory to calculate the structural,\nelectronic and magnetic prop erties of the ferro electric\ndomain w alls in m ultiferroic BiF eO 3 . W e ha v e iden ti\u001ced\nthe w all orien tations that are most lik ely to o ccur based\non their relativ e energy costs; in particular w e ha v e sho wn\nthat w alls in whic h the rotations of the o xygen o ctahedra9\n−3−2−10123−0.1−0.075−0.05−0.04−00.0250.050.0750.1\ndistance from domain wall [a0]magnetization [ µB]\n  \nM⊥\nM||\n|M|\nFIG. 11: La y er-b y-la y er lo cal magnetic momen t across the\n109 ° domain b oundary . (a) Sho ws the lo cal magnetization\nv ectors (small red arro ws) resulting from the can ting of the\nF e magnetic momen ts in eac h la y er, whic h is p erp endicular to\nthe lo cal electric p olarization (big blue arro w), (b) sho ws the\nlo cal comp onen t of the magnetization pro jected parallel and\np erp endicular to the w all plane, and the lo cal magnitude.\ndo not c hange their phase when the p olarization reorien ts\nare signi\u001ccan tly more fa v orable than those with rotation\ndiscon tin uities. Our analysis of the lo cal p olarization\nand electronic prop erties rev ealed p oten tial steps and\nreduction in lo cal band gaps at the 109\u000eand 180\u000ew alls;\nthese correlated with recen t measuremen ts of electrical\nconductivit y at these b oundaries. Finally , w e sho w ed\nthat c hanges in structure at the domain w alls cause\nc hanges in can ting of the F e magnetic momen ts whic h\ncan enhance the lo cal magnetization at the domain w alls.\nThe latter suggests p ossible new routes to electric \u001celd-\ncon trol of magnetism in BiF eO 3 .\nVI I. A CKNO WLEDGMENTS\nSpaldin w as supp orted b y the National Science\nF oundation under A w ard No. DMR-0605852. Calcula-\ntions w ere p erformed at the San Diego Sup ercomputer\nCen ter, and at the National Cen ter for Sup ercomputer\nApplications. W e furthermore ac kno wledge the DF G\nfor funding through F OR 520 and Ge 1202/5-1 and the\nBMBF for funding via the P akt fuer F orsc h ung und\nInno v ation.\u0003Electronic address: axel.rother@trieb en b erg.de\nyElectronic address: s.gemming@fzd.de\nzElectronic address: nicola@mrl.ucsb.edu\n[1] T. Zhao, A. Sc holl, F. Za v alic he, K. Lee, M. Barry ,\nA. Doran, M. P . Cruz, Y. H. Ch u, C. Ederer, N. A.\nSpaldin, et al., Nature Mater. 5 , 823 (2006).\n[2] Y.-H. Ch u, L. W. Martin, M. B. Holcom b, M. Ga jek,\nS.-J. Han, Q. He, N. Balk e, C.-H. Y ang, D. Lee, W. Hu,\net al., Nature Mater. 7 , 478 (2008).\n[3] J. W ang, J. B. Neaton, H. Zheng, V. Nagara jan, S. B.\nOgale, B. Liu, D. Viehland, V. V aith y anathan, D. G.\nSc hlom, U. V. W aghmare, et al., Science 299 , 1719\n(2003).\n[4] J. B. Neaton, C. Ederer, U. V. W aghmare, N. A. Spaldin,\nand K. M. Rab e, Ph ys. Rev. B 71 , 014113 (2005).\n[5] S. Stemmer, S. K. Strei\u001ber, F. Ernst, and M. Rühle,\nPhilos. Mag. A 71 , 713 (1995).\n[6] N. Flo quet and C. V alot, F erro electrics 234(1-4) , 107\n(1999).\n[7] J. P adilla, W. Zhong, and D. V anderbilt, Ph ys. Rev. B\n53 , R5969 (1996).\n[8] B. Mey er and D. V anderbilt, Ph ys. Rev. B 65 , 104111\n(2002).\n[9] J. Seidel, L. W. Martin, Q. He, Q. Zhan, Y.-H. Ch u,\nA. Rother, M. E. Ha wkridge, P . Maksymo vyc h, P . Y u,\nM. Ga jek, et al., Nat Mater 8 , 229 (2009), ISSN 1476-\n1122, URL http://dx.doi.org/10.1038/nmat2373 .\n[10] C. J. F ennie, cond-mat/0807.0472 (2008).\n[11] F. Kub el and H. Sc hmid, A cta Crystallogr. B 46 , 698\n(1990).\n[12] P . Fisc her, M. P olemsk a, I. Sosno wsk a, and M. Szy-\nma«ski, J. Ph ys. C 13 , 1931 (1980).\n[13] I. Sosno wsk a, T. P eterlin-Neumaier, and E. Streic hele,\nJ. Ph ys. C 15 , 4835 (1982).\n[14] C. Ederer and N. A. Spaldin, Ph ys. Rev. B 71 , 060401(R)\n(2005).\n[15] C. J. F ennie, Ph ys. Rev. Lett. 100 , 167203 (2008).\n[16] S. K. Strei\u001ber, C. B. P ark er, A. E. Romano v, M. J.\nLefevre, L. Zhao, J. S. Sp ec k, W. P omp e, C. M. F oster,\nand G. R. Bai, Journal of Applied Ph ysics 83 Nr. 5 ,\n2742 (1998).\n[17] G. Kresse and J. F urthmüller, Comput. Mater. Sci. 6 , 15\n(1996).\n[18] P . E. Blöc hl, Ph ys. Rev. B 50 , 17953 (1994).\n[19] G. Kresse and D. Joub ert, Ph ys. Rev. B 59 , 1758 (1999).\n[20] A. I. Liec h tenstein, V. I. Anisimo v, and J. Zaanen, Ph ys.\nRev. B 52 , R5467 (1995).\n[21] V. I. Anisimo v, F. Ary asetia w an, and A. I. Liec h tenstein,\nJ. Ph ys.: Condens. Matter 9 , 767 (1997).\n[22] C. Ederer and N. A. Spaldin, Ph ys. Rev. B 71 , 224103\n(2005).\n[23] I. Sosno wsk a, W. Sc häfer, W. K o c k elmann, K. H.\nAndersen, and I. O. T ro y anc h uk, Appl. Ph ys. A 74 ,\nS1040 (2002).\n[24] F. Bai, J. W ang, M. W uttig, J. Li, N. W ang, A. P . P .\ndn A. K. Zv ezdin, L. E. Cross, and D. Viehland, Appl.\nPh ys. Lett. 86 , 32511 (2005).\n[25] J. Kanamori, J. Ph ys. Chem. Solids 10 , 87 (1959).\n[26] P . W. Anderson, in Magnetism , edited b y G. T. Rado\nand H. Suhl (A cademic Press, 1963), v ol. 1, c hap. 2, pp.\n25\u001583.10\n[27] J. B. Go o denough, Magnetism and the Chemic al Bond\n(In terscience Publishers, New Y ork, 1963).\n[28] L. W. Martin, Y.-H. Ch u, M. B. Holcom b, M. Huijb en,P . Y u, S.-J. Han, D. Lee, S. X. W ang, and R. Ramesh,\nNanoletters 8 , 2050 (2008)."    },    {        "title": "2101.12114v1.Prediction_of_new_low_energy_phases_of_BiFeO__3__with_large_unit_cell_and_complex_tilts_beyond_Glazer_notation.pdf",        "content": "Prediction of new low-energy phases of BiFeO 3with large unit cell and complex\ntilts beyond Glazer notation\nBastien F. Grosso\u0003and Nicola A. Spaldin\nMaterials Theory, ETH Zürich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland\n(Dated: January 29, 2021)\nBismuth ferrite is one of the most widely studied multiferroic materials because of its large ferro-\nelectric polarisation coexisting with magnetic order at room temperature. Using density functional\ntheory (DFT), we identify several previously unknown polar and non-polar structures within the\nlow-energy phase space of perovskite-structure bismuth ferrite, BiFeO 3. Of particular interest is a\nseries of non-centrosymmetric structures with polarisation along one lattice vector, combined with\nanti-polar distortions, reminiscent of ferroelectric domains, along a perpendicular direction. We dis-\ncuss possible routes to stabilising the new phases using biaxial heteroepitaxial strain or interfacial\nelectrostatic control in heterostructures.\nI. INTRODUCTION\nBismuth ferrite, BiFeO 3, is one of the few materi-\nals that combines magnetic order and ferroelectricity in\nthe same phase at room temperature, making it one the\nmost well-studied multiferroics. The structural ground\nstateofBiFeO 3isadistorted R3c-symmetryperovskite,\nwith anti-ferrodistortive rotations of the oxygen octahe-\ndra around the pseudo-cubic [111] axis, combined with\na large polarisation ( \u001890\u0016C/cm2) along the [111] di-\nrection caused by the 6s2lone pairs of electrons on the\nBi3+ions [1]. The strong superexchange between the\nFe3+3d5electrons gives robust antiferromagnetism.\nWhile theR3cstructural ground state is both the-\noretically [1] and experimentally [2] well established,\nthe low-energy structural phase space of BiFeO 3is\nknown to be very rich. Under compressive strain\nimposed by coherent heteroepitaxy, polar monoclinic,\ntetragonal-like and tetragonal structures can be stabi-\nlized [3–6], whereas under tensile strain or hydrostatic\npressure it adopts a polar orthorhombic structure [7–\n9]. More recently, heteroepitaxy has been exploited to\nform antipolar phases of BiFeO 3in superlattices with\nLa0:7Sr0:3MnO 3[10] and La 0:4Bi0:6FeO 3[11], where the\nstability of the antipolar phase was attributed to mag-\nnetic coupling and control of the electrostatic bound-\nary conditions respectively. Furthermore, a systematic\ndensity functional theory (DFT) study revealed a large\nnumber of low-energy metastable structures within unit\ncells up to a size of 40 atoms [12].\nMotivated in particular by the recent observations of\nultra-largeunitcellphasesinthin-filmheterostructures,\nwe present a detailed computational study of the low-\nenergystructuralphasespaceofBiFeO 3,withafocuson\nlarge-unit-cell structures. Our approach is to start from\nthepreviouslyidentifiedphasesofRef.12andsearchfor\n\u0003Correspondence email address: bastien.grosso@mat.ethz.chunstable phonon modes that indicate structural insta-\nbilities. We then increase the unit cell size to accommo-\ndate the corresponding energy lowering structural dis-\ntortion. With this approach, we find that the apparent\nmetastability of many of the previously identified struc-\ntures, for example PbamandPmc 21, was an artifact of\nthe 40-atom unit cell size, and in fact their energy is\nlowered by large period structural distortions. Finally,\nwe demonstrate how these new phases can be stabilized\nrelativetothebulk R3cgroundstatethroughcarefulen-\ngineering of the electrostatic and strain boundary con-\nditions, facilitating the rational design of BiFeO 3-based\nheterostructures with new functionalities.\nThe remainder of this paper is organized as follows:\nIn section II, we present the technical details of the\nsimulations and introduce a generalisation to the stan-\ndard Glazer notation [13], that allows the description of\nmore complex oxygen octahedral tilt patterns. In sec-\ntion IIIA, we present the new phases that we identify\nin this work and describe their structures in terms of\ntheir main distortion modes. In section IIIB, we con-\nsider a series of structures obtained by increasing the\nunit cell length along one direction and compare this\nseries of structures with the formation of domains. In\nsection IV, we study the possible stabilisation of the\nnew phases using strain or control of the electrostatic\nboundary conditions. Finally, in section V, we summa-\nrize our study.\nII. METHODS\nA. Computational details\nThe calculations were performed using density-\nfunctional theory (DFT) [14] with the projector aug-\nmented wave (PAW) method [15] as implemented in\nthe Vienna ab initio simulation package (VASP 5.4.4)\n[16]. We used a 12x12x12 k-point \u0000-centered mesh to\nsample the Brillouin zone corresponding to a 5-atomarXiv:2101.12114v1  [cond-mat.mtrl-sci]  28 Jan 20212\nunit cell, and chose and energy cutoff of 850 eV for\nthe plane-wave basis. The following valence electron\nconfigurations where used1:5d106s26p3for bismuth,\n3p63d74s1for iron and 2s22p4for oxygen. We used the\nPBEsol +Ufunctional form of the generalized gradient\napproximation [17], with a commonly used value of Ueff\n= 4 eV for the Fe 3dorbitals, according to Dudarev’s\napproach[18].\nB. Phonons and symmetry\nIn order to identify new metastable phases, we start\nfrom the following experimentally stabilized, or com-\nputationally predicted polymorphs of BiFeO 3:Pmc 21\n(20 atoms/unit cell (u.c.)), Pbam(40 atoms/u.c.) and\nPnma(20 atoms/u.c.) [7, 9, 19]) and explore the\nphonon instabilities along various reciprocal directions.\nWe use the frozen-phonon method, as implemented in\nthePHONOPY package [20] to look for imaginary\nphonon frequencies at selected symmetry points corre-\nsponding to supercells up to 160 atoms per unit cell.\nIn practice, for a given starting phase, we construct\nall different possible supercells within our limit on the\nnumber of atoms and compute the phonon frequencies\nto look for instabilities. Once an instability is found\nwe freeze the distortions given by the eigenvector cor-\nresponding to that imaginary frequency and fully re-\nlax the structure; if this procedure identifies a new\n(meta)stable phase, we repeat the procedure on that\nphase iteratively. We restrict our subsequent analysis\nto metastable phases with an energy up to 100 meV/f.u.\nabove theR3cground state. We further test the stabil-\nity of the relaxed structures (up to 80 atoms per unit\ncell) by computing the phonons at the zone center and\nspecify the cases where an instability remains. We anal-\nyse each fully relaxed structure to determine the combi-\nnationofphononmodesthatcontributetoitsstructural\ndistortion from the reference cubic perovskite struc-\nture, using the ISODISTORT [21, 22], AMPLIMODES\n[23, 24] and Pymatgen [25] packages.\nC. Born effective charges and Polarisation\nSince Berry phase calculations of the polarisation\nare prohibitively expensive for very large unit cells, we\ncompute polarisations by summing the displacement of\nthe ions from a high-symmetry non-polar parent struc-\nture multiplied by their Born effective charges. We use\n1The Bi, Fe and O PAWs are dated respectively from April 8\n2002, September 6 2000 and April 8 2002.an averaged Born effective charge per atom type ob-\ntainedfromaveragingoverthetensorcomponentsfor15\nstructures, including all phases presented in this work\nwith 80-atom unit cells or less and other higher energy\nphases, computed in this work but not reported, to ob-\ntain one value per atom species. This procedure results\nin the following values: 4.86 [e] for Bi, 3.99 [e] for Fe\nand -2.95 [e] for O in units of the electronic charge mag-\nnitude, consistent with the literature. [26] We observe\nthat the Born effective charges decrease substantially\nwith structural distortions to more stable structures as\nthe band gap energy increases.\nD. Extended Glazer notation for complex tilting\nGlazer introduced a convenient and widely used\nmethod for describing octahedral tilting in perovskites\n[13], which consists of a letter ( a,borc) indicating the\namplitude of tilting along each of the cartesian direc-\ntions and a superscript +,\u0000or 0, to indicate whether\nthe relative tilts between consecutive octahedra are the\nsame, opposite or zero about the respective axis. This\nnotation is restricted to tilt patterns with wave-vectors\nk= 0or\u0019\na, whereais the lattice vector along the con-\nsidered direction. More complicated tiltings, not cap-\nturedbythecurrentGlazernotationhavebeenreported\n[27, 28] and are prevalent in this work. We propose\nthe following extension to Glazer notation suitable for\ngeneric tilting: we retain the a,bandcnotation refer-\nring to each lattice vector, but we replace the +,\u0000or\n0 superscripts by a series of Greek letters (\u000b;\f;\r;::: )\nindicating the magnitude of rotation of each octahe-\ndron around the pseudo-cubic direction considered. An\nover-line then indicates clockwise rotations, no overline\nindicates anti-clockwise and a ;no rotation. The num-\nber of superscripts indicates the number of octahedra\nin the periodic repeat unit and letters are repeated in\nthe series if the rotation amplitudes of different octahe-\ndra are equal. If the exact same sequence of amplitude\nof the tilts is observed along different directions, the a\norbare repeated along with the series of superscripts.\nDue to the periodicity of these series in a crystal, there\nare multiple ways to write the same sequence; we make\nthe choice to always start the sequence by a clockwise\nrotation, if there is one.\nFor simple tilt patterns the connection between the\ntraditionalGlazernotationandtheextendedGlazerno-\ntation can be easily made, for example:\nPnma a\u0000a\u0000c+()a\u0016\u000b\u000ba\u0016\u000b\u000bc\u0016\u000b\u0016\u000b\nR3c a\u0000a\u0000a\u0000()a\u0016\u000b\u000ba\u0016\u000b\u000ba\u0016\u000b\u000b\nImmm a0b+c+()a;b\u0016\u000b\u0016\u000bc\u0016\u000b\u0016\u000b\nPm\u00163m a0a0a0()a;a;a;\nIn this case, the extended notation offers no advantage3\nover the traditional one. For more complicated tilts,\nwith different amplitudes or complex sequences, it pro-\nvidesaconvenientnotation. Forexample, atiltingchar-\nacterized along two directions by a wave-vector of\u0019\n4a,\nwith two octahedra tilted in one direction (with same\namplitude), the next pair tilted in the opposite direc-\ntion with a different tilting angle from the first pair\n(and with different amplitudes among the pair) and a\nsimple opposite tilting (with same amplitude) along the\nthird direction is written a\u0016\u000b\u0016\u000b\f\ra\u0016\u000b\u0016\u000b\f\rc\u0016\u000b\u000bin this nota-\ntion. Notice that one could use different Greek letters\nalong different directions to signal different (or similar)\nrotational amplitudes if this extra information were of\ninterest, but we make the choice not to distinguish the\namplitudes along different directions.\nWe report the tilt patterns for the phases that were\nidentified in this study, using this extended notation in\nTable I.\nIII. RESULTS\nA. Phases and distortions\nWenowfollowtheproceduredescribedinsectionIIto\nidentify various new polymorphs of BiFeO 3. We extend\nprevious studies [29], by exploring unit cells up to 160\natoms in size, and of variable shape; this allows us to\nincorporate phonon instabilities at lower symmetry q-\npoints in the Brillouin zone.\nIn Table I we show the list of newly identified phases\nthat have an energy difference of less than 100 meV/f.u.\nfrom theR3cground state, and report the lattice pa-\nrameters, energy relative to the ground state, band gap\nand polarisation along each lattice vector for each case.\nIn Table II, we decompose each phase into its main irre-\nducible distortion modes and report its tilting pattern\nin terms of the traditional Glazer notation when pos-\nsible and in terms of the extended notation introduced\nearlier (all cases). For reference we include the ground\nstate (R3c) and the lowest energy non-polar ( Pnma)\nphase in both tables. In Figure 1 we present the unit\ncells of the five lowest energy new phases, and in Fig-\nure 2, the dominant distortion modes that make up the\nstructures, with the presiding distortions highlighted by\narrows.\nBefore starting the analysis of the new phases iden-\ntified in the current study, we summarize briefly the\nwell-established reference phases for BiFeO 3. TheR3c\nground state is reached from the ideal cubic perovskite\nstructure via a polar displacement along the [111]pcdi-\nrection( \u0000\u0000\n4mode)andatiltingoftheoctahedraaround\nFigure1.Crystalstructuresofnewlow-energyphases\nidentified by full relaxation using DFT - The vertical\naxis indicates the energy relative to the ground state. We\norientate the structures such that the z axis stands along\nthe usual [001] growth orientation. The Bi atoms are rep-\nresented in red, the Fe atoms in blue and the O atoms in\ngrey.\nthe same direction ( R\u0000\n5mode) resulting in an a\u0000a\u0000a\u0000\ntilt pattern. At high temperature, BiFeO 3adopts the\nGdFeO 3-likePnmaphase,[30] characterised by antipo-\nlar displacements of the Bi atoms accompanied by anti-\nphase in-plane rotations and in-phase out-of-plane tilt-\ningsoftheoctahedra,resultingina a\u0000a\u0000c+tiltpattern.\nThis phase is generally calculated to be the lowest- en-\nergymetastablephaseforBiFeO 3[12,29,31]), although\ncompeting phases can be lower energy depending on the\nchoice of exchange-correlation functional [12].\nWe begin by searching for instabilities at the zone\nboundaries of the 20-atom Pnma(GdFeO 3structure)\nandPmc 21, and the 40-atom Pbamunit cells, and con-\nstruct the corresponding supercells by doubling them\nin one or two directions, resulting in unit cells of 40\nor 80 atoms; larger unit cells will be presented in the\nnextsection. The Pnmastartingstructuredidnotyield\nany new phases in this procedure, suggesting that it is\nlikely a true metastable phase. We describe the struc-\ntures generated from the Pmc 21andPbamstarting\ncells next. When different structures share the same4\nsymmetry, we will label them with the symmetry fol-\nlowed by an index.\nFigure 2.Main distortion modes - (a) Polar mode dom-\ninated by off-centering of the Bi atom relative to the other\natoms in the unit cell. Here we show the displacement along\nthe[011]pcdirection; displacements along [001]pc(as in the\nP4mmsuper- tetragonal phase) and along [111]pc(as in the\nR3cphase) are also known. (b) Antipolar modes, in which\npairs of Bi atoms displace with opposite direction and the\nsame amplitude. (c) Rotational and tilting modes, in which\nthe main distortion is the rotation or tilt of the octahedra.\nThe inset shows the orientation of the axes related to the\npseudo cubic directions and the dominant distortions are\nhighlighted by arrows.1.Pmc 21as starting cell\nWe start from a 20-atom unit cell with Pmc 21sym-\nmetry and find a zone boundary instability along a\nlong and a short lattice vector. Doubling its unit cell\nalong the long lattice vector and subsequent relaxation\nof the atomic positions yields the 40-atom unit cell Pc\n(1) structure (see Figure 1 lower left), which is only\n23 meV/f.u. above the ground state and 2 meV/f.u.\nabovePnma. It is a polar phase with an out-of-plane\n([001]pc) polarisation of around 54 \u0016C/cm2and an in-\nplane ( [110]pc) polarisation of about 39 \u0016C/cm2. The\npolarisation is mainly due to the displacement of the\neight Bi atoms, six of which shift along the [1\u001611]pcdi-\nrection and two along the [\u0016111]pcdirection resulting in\na larger out-of-plane than in-plane polarisation.\nBy doubling the 20-atom Pmc 21unit cell along\n[\u0016110]pc(short lattice vector), we identify a 40-atom unit\ncell polymorph with the same symmetry, Pmc 21(2),\nwhich has a large polarisation along the [110]pseudo-\ncubic direction. It is the highest energy phase that\nwe identify here, with 76 meV/f.u. above the ground\nstate and calculation of its phonon band structure in-\ndicates that this phase is unstable. Note that there is\nno zone boundary instability to motivate doubling the\nother short lattice vector.\nFurther doubling the Pmc 21(2) unit cell along\n[001]pc, we find a zone boundary instability. We sub-\nsequently relax the atomic positions and identify a\nmetastablestructureof Cmc 21symmetrywith80atoms\nper unit cell (central right panel of Figure 1). There ex-\nists another larger unit cell with 80 atoms, Pmc 21(1),\nobtained by doubling the unit cell of the original Pmc 21\nsimultaneously along [001]pcand[110]pc(lower right of\nFigure 1). Pmc 21(1) has a lower polarisation than\nPmc 21(2) (16\u0016C/cm2instead of 76 \u0016C/cm2, due to\na smaller amplitude of the \u0000\u0000\n4mode), and lower energy\n(32 meV/f.u. instead of 76 meV/f.u.). The structural\ndifference between Cmc 21andPmc 21(1) lies in the\npresence of an extra antipolar displacement along x in\nthe case of Pmc 21(1) that brings the central layer of\nBi atoms (third layer of atoms along the z direction) to\nbe almost aligned (see Figure 1). This difference is due\nto the absence of a \u00062mode (see Figure 2b) in Cmc 21.\nMoreover, the amplitude of the polar mode is larger in\nCmc 21resulting in a larger polarisation than Pmc 21\n(1).\n2.Pbam as starting cell\nCalculating the phonon band structure of the Pbam\n(ground state for PbZrO 3[32, 33]) phase, we first iden-\ntify an unstable mode at the center of the Brillouin\nzone. Following this unstable mode, we obtain a non-5\npolar phase, with P21=csymmetry and an energy of 46\nmeV/f.u. above the ground state (upper left of Figure\n1). In this phase \u00062and\u00063distortions are present,\nresulting in an up/down displacement of the Bi atoms\nboth in-plane and out-of-plane and no net polarisation\n(see figure 2).\nDoubling the Pbamunit cell along [001]pcand subse-\nquentlyrelaxingtheatomicpositions, weobtaintwo80-\natom structures. First, the Pnma(1) phase, which was\npreviously identified and shown experimentally to be\nantiferroelectricinRef.11. Andsecond, anothervariant\nof the same symmetry, Pnma(2), which is metastable,\nbut has much higher energy (70 meV/f.u.).\nIt was shown that the Pbamstructure of PbZrO 3can\nbe described in termes of three main distortion modes\nfrom the ideal cubic perovskite structure, \u00062,S2and\nR\u0000\n5, whichcouplecooperativelytolowertheenergy[34].\nPnma(1) andPnma(2) share the three modes inher-\nited from their Pbamparent structure, but also share\ntwo additional modes, \u00033andT2. While the amplitudes\nof the three first modes are comparable in Pnma(1)\nandPnma(2), those of \u00033andT2differ, representing\nrespectively, 14 %and 17 %of the entire displacement\nfrom the cubic phase for Pnma(1) and 2 %and 12 %\nforPnma(2).\nB. Long-wavelength structures\nHaving explored the phase space of 40- and 80-atom\nunit cells in the previous section, we next extend our\nsystematicsearchtoinstabilitiesatlowerq-pointsofthe\n20-atomPmc 21unit cell, and correspondingly larger\nunit-cell structures.\nWe built a series of supercells, obtained by repeat-\ning thePmc 21unit cell from 4 to 8 times along the\n[110]pcdirection. Note that this is the direction for\nwhich no instability was found halway to the Brillouin\nzone boundary (see section IIIA1). We also found no\ntripling imaginary zonecenter phonon modes in super-\ncells built by the Pmc 21unit cell in that direction. We\nfind, that an anti-polar distortion mode with \u00063sym-\nmetry is unstable in the starting supercells across the\nseries, and is associated with a progressively smaller q-\npoint in the Brillouin zone of the original Pmc 21phase\nas the supercell size is increased (see Figure 3a). In\naddition to this antipolar mode, we observe another\nwavevector-dependent mode, responsible for rotations\nof the octahedra, with S4symmetry (see Figure 3b). To\nemphasize the wavevector dependence of these modes\nwe label them \u0006q\n3andSq\n4. As previously, we freeze in\nthe distortion eigenvectors corresponding to these and\nthe other unstable modes and fully relax the structures.\nWe find a series of structures with Pcsymmetry\nin unit cells with the long lattice vector ranging from\n22.46 Å to 44.78 Å (corresponding to 80 and 160 atomsper unit cell, respectively). Each structure can be de-\ncomposed into four primary distortions: two modes al-\nready discussed in the previous section ( R\u0000\n5and\u0000\u0000\n4)\nand the two new modes introduced above ( \u0006q\n3andSq\n4).\nTheR\u0000\n5mode is responsible for the tilts of the octahe-\ndra and is present in all the new structures identified in\nthis work, including the Pcseries we discuss here. The\n\u0000\u0000\n4mode displaces all the Bi atoms in the same direc-\ntion relative to the other atoms, inducing polarisation\nin all polar structures. In contrast to the R3cphase, the\ndisplacement in the new Pcphases is not along [111] pc\nbut along [110] pc, resulting in purely in-plane polarisa-\ntion. In Figures 3 a-b, we show the new \u0006q\n3andSq\n4\nmodes for a 33 Å long unit cell. Both modes have dis-\ntortions with periodicity related to the size of their unit\ncell. \u0006q\n3is an antipolar mode, that moves the Bi atoms\nalong the [001] direction. This mode has a wavevector\nofq= [1=2 1=2 0]\u0001\u0019\nN\u0001a, whereais the lattice vector of\nthe parentPmc 21structure and Nthe number of times\nit was repeated to generate the supercell. It is associ-\nated with an “ Nup -Ndown” distortion pattern of the\nBi atoms, with NBi atoms moving up and Nmoving\ndown, with the displacement amplitude modulated by\nthe position along [110]pcby a sinusoid. The last mode,\nSq\n4, is a rotational mode that creates pairs of anticlock-\nwise rotated octahedra along the [001] direction, with\nan amplitude of rotation modulated by a clipped sin\nwave along its long lattice vector (Figure 3b).\nThe structure with 120 atoms is shown in Figure 3c\nand for comparison, the R3cphase in the same unit\ncell is displayed in Figure 3d. Comparing carefully the\nanti-polar distortions in Figure 3a and Figure 3c, one\ncan notice that the smooth wavy displacement due to\nthe\u0006q\n3modeisnotexactlyconservedatthecenterofthe\nunit cell in the latter. We observe that additionally to\nthe\u0006q\n3mode with wavevector of q= [1=2 1=2 0]\u0001\u0019\nN\u0001aas\ndefinedearlier, eachstructureacrosstheserieshasaddi-\ntional \u0006iq\n3modes with i= 3;5;7;:::;N. For instance in\nthe structure with q= [1=2 1=2 0]\u0001\u0019\n6\u0001a, two additional\nmodes with i= 3andi= 5exist. These additional\nmodes have a decreasing amplitude as iincreases and\nthey explain the deviation of the displacements of the\nBi atoms from a smooth sinusoid as additional modes\nwith shorter periods are superimposed (see Figure 3e).\nIn order to better understand the distortion trends\nin this series of structures, we plot in Figure 4a the\ncomputed polarisation projected on the [110]pcdirec-\ntion and the energy relative to the energy of the R3c\nphase constrained to the same lattice vectors as a func-\ntion of the inverse of the long lattice vector. We observe\nthat both values decrease and tend to the R3cvalues as\nthe unit cell size increases. This suggests that the series\ncould converge to an analogue to the R3cphase with\nin-plane polarisation. In Figure 4b we plot the maxi-\nmumdisplacementoftheBiatomsalong [001]pcandthe6\nLattice parameters Energies Polarisation\nPhase a [Å] b [Å] c [Å] Energy [meV/f.u.] Band Gap [eV] Pa[\u0016C/cm2]Pb[\u0016C/cm2]Pc[\u0016C/cm2]\nPmc 21(2) 7.79 11.11 5.56 76 2.119 0 0 76.1\nPnma(2) 5.57 15.43 11.22 70 2.296 - - -\nP21=c 7.75 11.19 5.57 46 2.205 - - -\nCmc 21 15.67 11.01 5.54 36 1.993 0 0 31.7\nPnma(1) 5.53 15.65 11.16 35 2.108 - - -\nPmc 21(1) 15.60 10.93 5.58 32 1.959 0 0 16.0\nPc(1) 15.74 5.48 5.58 23 2.055 54.4 0 39.8\nPnma 5.63 7.73 5.40 21 1.825 - - -\nR3c(hexag.) 5.54 5.54 13.72 0 2.141 0 0 100.4\nTable I. Computed lattice parameters, energy compared to the ground state, band gap energy and polarisation for newly\nidentified structures within 100 meV of the R3cground state. In all cases the calculated angles between the lattice vectors\nare equal or very close to 90\u000e. The lattice parameter value in italics indicates the axis along the cartesian zaxis; we refer to\nthis as the out-of-plane axis in the context of our later discussion of thin-film heterostructures. The polarisation is computed\nby summing over an average value of the Born effective charge for each ion multiplied by its displacement from its position\nin the high-symmetry reference structure. We show the values for the ground-state R3c(in the hexagonal setting, in which\nthecaxis corresponds to the [111]pcdirection) and for the high-temperature Pnmastructures for reference.\nMain structural distortions Octahedral tilts\nPhase Polar modes Anti-polar modes Rotational/Tilting modes Glazer Extended Glazer notation\nPmc 21(2) \u0000\u0000\n4 \u00062,S1 R\u0000\n5,M+\n2 -a\u0016\u000b\f\u0016\r\u000ea\u0016\u000b\f\u0016\r\u000ec\u0016\u000b\u0016\u000b\nPnma(2) - \u00062,S2 R\u0000\n5,T2 -a\u0016\u000b\f\u0016\r\u000ea\u0016\u000b\f\u0016\r\u000ec\u0016\u000b\u0016\u000b\f\f\nP21=c - \u00062,\u00063,S2 R\u0000\n5 -a\u0016\u000b\f\u0016\r\u000ea\u0016\u000b\f\u0016\r\u000ec\u0016\u000b\f\nCmc 21 \u0000\u0000\n4 \u00033,X\u0000\n5 R\u0000\n5,M+\n2 -a\u0016\u000b\f\u0016\r\u000ea\u0016\u000b\f\u0016\r\u000ec\u0016\u000b\u0016\f\u0016\f\u0016\u000b\nPnma(1) - \u00062,\u00033,S2 R\u0000\n5,T2 -a\u0016\u000b\f\u0016\r\u000ea\u0016\u000b\f\u0016\r\u000ec\u0016\u000b\u0016\u000b\f\f\nPmc 21(1) \u0000\u0000\n4 \u00033,\u00015,X\u0000\n5,\u00062R\u0000\n5,M+\n2 -a\u0016\u000b\f\u0016\r\u000ea\u0016\u000b\f\u0016\r\u000ec\u0016\u000b\u0016\f\u0016\f\u0016\u000b\nPc(1) \u0000\u0000\n4 \u00015,X\u0000\n5 R\u0000\n5,M+\n2,T2 -a\u0016\u000b\fa\u0016\u000b\fc\u0016\u000b\f\u0016\r\u0016\u000e\nPnma - X\u0000\n5 R\u0000\n5,M+\n2 a\u0000a\u0000c+a\u0016\u000b\u000ba\u0016\u000b\u000bc\u0016\u000b\u0016\u000b\nR3c \u0000\u0000\n4 - R\u0000\n5 a\u0000a\u0000a\u0000a\u0016\u000b\u000ba\u0016\u000b\u000ba\u0016\u000b\u000b\nTable II. Dominant structural distortions and octahedral tilt patterns for the newly identified low-energy phases. The\ndistortion modes are reported with respect to the ideal cubic perovskite structure ( Pm\u00163m) in all cases. We separate the\nmodes into three categories: Polar, Anti-polar or Rotational/Tilting, and we only report the modes contributing to at least\n4%of the total distortion for each structure. An exception is made for the Polar modes, which are always reported to\ndistinguish between polar and non-polar phases. The octahedral tilt patterns are given in terms of the traditional Glazer\nnotation where possible, and the extended notation for all cases. We align the out-of-plane axis reported in Table I with\nthe third axis in the Glazer notation.\nmaximum rotation of the octahedra as a function of the\ninverse of the long lattice vector. We see that, as the\nunit cell size is increased, the maximum rotation value\nindeed tends to the value in the R3cground state. On\nthe other hand, the maximum displacement of the Bi\natoms along [001]pc(antipolar displacements) increases\nfrom the bulk R3cvalue (polar displacements) as the\ncell size is increased. These trends are explained by the\nincrease of both \u0006q\n3andSq\n4modes when qdecreases.\nIn a simple picture, as the octahedra have larger am-\nplitudes of rotation, more space is left for the Bi atoms\nto move. These observations further indicate that the\nseries in fact converges to a structure distinct from the\nR3cground state, although it is likely to be quite closein energy. Note that each half is also different than R3c.\nWe analyze the distortions further by plotting in Fig-\nure 4c the displacements of each Bi atom along [001]pc\nas well as the rotation of each octahedron around the\nsame direction, in the 160-atom unit cell. The values\nfor theR3cstructure are shown with the dashed lines\nfor comparison. In the case of R3c, all Bi atoms are dis-\nplaced in the same direction (whether up or down) and\nthe octahedra rotate clockwise in one (111) layer and\nanticlockwise in the next (111) layer (below or above\nthe Bi atoms). In the Pcphase, at the center of the unit\ncell, at around 20 Å, one can see the crossover between\nup and down displacements of the Bi atoms, whereas at\nthe center of the cell, there is almost no distortion: the7\nFigure 3. The long wavelength structural distortions and fully relaxed structure of the 33 Å long (120-\natom)unit cell - (a) Antipolar \u0006q\n3mode with sinusoidal displacement of the Bi atoms. (b) Rotational Sq\n4mode. (c) Fully\nrelaxed structure with Pcsymmetry. (d) R3csymmetry in the unit cell with same lattice vectors as (c) visualised from\nthe top (upper panel) or from the side (lower panel). (e) Extra \u0006iq\n3modes with i = 1,3,5, individually presented (orange\nboxes) or combined together (red box). The structure in (c) can be decomposed into the modes presented in (a), (b) and\n(e) combined with a \u0000\u0000\n4polar mode and an R\u0000\n5tilting mode. Each unit cell is defined with respect to a common origin, in\norder to help the comparisons and the orientation relative to the pseudo-cubic axes is indicated on the bottom left.\nBi atom sits at the center of the cell (vertically) and the\noctahedra above and below are almost not rotated ( a0-\nlike in Glazer notation). Going away from the center,\nthe octahedra rotate in opposite directions to the left\nor to the right of the unit cell (with opposite rotations\nof the top and bottom layers) and the Bi atoms move\nup in the right and down in the left side of the unit cell.\nThe bulk behavior is recovered, with displacements and\nrotations close to the R3cvalues, midway between the\ncenter and the edges of the supercell, with opposite dis-\nplacements / rotations in each half of the supercell.\nAs the unit cell size is increased, the amplitudes of\nthe\u0006q\n3andSq\n4modes grow. The rotations approach\nthe ground-state R3cvalue. The displacements become\nprogressively larger, resulting in displacements larger\nthan the bulk values. We attribute the lowering of\nthe energy with increasing cell size to the smoother\ntransition between consecutive octahedra, confirming\nprevious studies [35, 36], and anticipate that the en-\nergy would continue decreasing with increasing cell size.\nSince the amplitude of the anti-polar displacements in-\ncreases with the size of the unit cell, we expect large\nanti-polar distortions in the large unit cell limit. This\ncould be interpreted as opposite domains of polarisa-\ntion along [001]pc, while preserving the in-plane compo-\nnents. Each domain keeps the Pcsymmetry but with\ndisplacements along [001]pcaveraging to the R3cvalue\nand resulting in a similar polarisation value.In summary, we have identified a series of structures\nthat allow rotation of the polarisation away from the\n[111]pcdirection and into the (110) plane at minimal\nenergy cost. This behavior is relevant for BiFeO 3thin-\nfilms and heterostructures in which the electrostatic\nboundary conditions might favor phases with no out-\nof-plane polarisation. We explore this scenario next.\nIV. STABILITY AND HETEROSTRUCTURES\nFinally, in this section we explore two possible routes\nto stabilizing the various phases identified above. The\nfirst is biaxial strain, which can be imposed by a sub-\nstrate of different lattice constant through coherent het-\neroepitaxy. Since the different structures have different\nunit cell sizes and shapes, we expect that their rela-\ntive stabilities will be modifiable by careful choice of in-\nplane lattice parameter lengths and orientations. The\nsecond is through exploiting the electrostatic boundary\nconditionsattheinterfacesinheterostructuresorsuper-\nlattices with non-polar III-III perovskite oxides. Since\nthere is an electrostatic energy cost associated with a\npolar discontinuity, such an arrangement destabilizes\nphases with an out-of-plane polarisation component, in-\ncluding the ground-state R3cphase in the usual [001]\ngrowth orientation [37].\nWe continue the convention of Figures 1 and 2 in8\nFigure 4. Energy, polarisation, Bi displacements and oxygen octahedral rotations across the Pcseries, and\ndistortions within the 160-atom u.c. (a) Polarisation (top) and energy (bottom) as a function of the inverse of the\nlong lattice vector. (b) Maximum displacement of the Bi atoms along [001]pc(top) and maximum rotation of the octahedra\n(bottom) as a function of the long lattice vector. (c) Layer-by-layer displacement of each Bi atom (top) and rotation of\neach octahedron (bottom) in the 160-atom unit cell. The orange and blue dots represent octahedra above (blue) or below\n(orange) the Bi atoms of the top panel. The dotted lines indicate the behavior of the R3cin the same unit cell as the\n160-atom unit cell.\nwhich we oriented the usual [001]pcgrowth orientation\nalong the cartesian z direction for all the structures. We\ntherefore refer to the axis parallel to the z direction as\nthe out-of-plane axis, and we apply in-plane strain it.\nA. Strain\nIn Figure 5a, we show the calculated energies for the\nphasesofTableIasafunctionoftheirin-planeaveraged\nlattice parameters. We make the choice to keep the an-\ngles between the lattice vectors fixed and average the\npseudo-cubic in-plane lattice constants before applying\nthe compressive or tensile strain, which increases the\nenergy of the unstrained structures (full markers) com-\npared to the values reported in Table I.\nWe find that, in the range of in-plane lattice param-\neters that we consider, none of the low-energy phases is\nstabilised by strain over the R3cground state. The\nenergy difference between the low-energy competing\nphases and the ground state is sometimes substantially\nreduced on typical substrates however. For instance,the energy difference between Pc(1) andR3cis re-\nduced from 28 meV/f.u. at the lattice constant of\nTbScO 3(TSO) to 21 meV/f.u. at the lattice constant\nof SrTiO 3(STO). The results shown in Figure 5 show\nthat, while moderate strain alone is insufficient to sta-\nbilize metastable phases, it makes a difference quantita-\ntively and should not be neglected. Note that we only\nconsider here strain values of less than 2%(compressive\nor tensile) with respect to the lattice of the ground state\n,whichareexperimentallyaccessibleforfilmthicknesses\nup to around 20 nm.\nB. Electrostatics and polar discontinuity\nAccording to Gauss’s law, an electric charge causes\na divergent electric displacement field with divergence\nequal to the charge density. Therefore, the bound\ncharge at an interfacial polar discontinuity between a\npolar and a non-polar material will induce an electric\nfield, with divergence proportional to the density of\ncharge at the interface. This scenario is energetically\nunfavorable and is well known to be responsible for\nthe critical thickness below which a ferroelectric ma-\nterial loses its net polarisation [38]. In order to re-\nduce its electrostatic energy, an unscreened ferroelec-9\nFigure 5. Strain and electrostatics - (a) Energy as a function of the average in-plane lattice parameter. We consider\neach phase presented in Table I and the Pcphase presented in Figure 4. For each case, we average the in-plane lattice\nconstants and relax the out-of-plane vector as well as the positions of the ions. We indicate the resulting energies and\nlattice constants with full diamonds, full circles or full stars, for polar, non-polar and R3cphases respectively. For the R3c\nphase we used a 10-atom unit cell and kept the rhombohedral angle to be 60\u000eas described in Ref. 6. We then apply\na1%compressive and tensile strain to each structure and fit the data points with a parabola. The vertical dashed lines\nrepresent the lattice vectors calculated in this work of common substrates: SrTiO 3(STO), DyScO 3(DSO) and TbScO 3\n(TSO). (b) Cartoon of the heterostructure considered for (c). We consider a superlattice of BFO surrounded by a non-polar\nIII-III material (e.g. LaFeO 3) separated from the substrate (bottom) by a metallic electrode. (c) Energy as a function of\nthe thickness of the BFO layer. We consider each of the phases presented in (a) and assume that they are surrounded by\na III-III non-polar material with a strain imposed by the substrate (STO, DSO or TSO, respectively from top to bottom\npannel). We report the energy density relative to the lowest non-polar phase. The colors are consistent with (a) and we\nindicate with dashed lines the phases that have zero component of the polarisation perpendicular to the interface. The\nvolume and energy for each phase for a given substrate is extracted from (a).\ntric material usually splits into domains of alternating\nup and down polarisation, resulting in a globally zero\nnet polarisation. However, if a low-energy non-polar\nphase, or a phase with polarisation oriented in a plane\nparallel to the interface exist, a transition to a new\nphase could be more favorable than domain formation.\nThis behavior was demonstrated for superlattices of\nBiFeO 3/(La,Bi)FeO 3, in which the phase labeled Pnma\n(1) in this work was stabilized in the BiFeO 3layers.\nNext, weexplorewhethertheotherlow-energyphases\nidentified in this work can be stabilized relative to the\nR3cground state with experimentally accessible elec-\ntrostatic boundary conditions.The bound charges induce a depolarising field, given\nbyEd=\u0000P\n\u000f0\u000fr, in the opposite direction to the polarisa-\ntion, where \u000f0is the permittivity of the free space and\n\u000frthe relative permittivity of the material in which the\nelectric field is created. The depolarising field then cou-\npleswiththepolarisation, givinganelectrostaticenergy\ncost of1\n2P2\n\u000f0\u000fr[39]. Note that this electrostatic energy\ncost is proportional to the interfacial area, whereas the\ninternal energy, given by the energy difference between\nthe two bulk phases at the appropriately strained in-\nplane lattice constant, is proportional to the volume.\nTherefore we expect a cross-over in their relative con-\ntributions with film thickness, with the electrostatic en-10\nergy dominating in thin-films [37].\nWe consider a heterostructure of BiFeO 3surrounded\nby a non-polar material (e.g. LaFeO 3) separated from\na substrate (STO, TSO or DSO) by a metallic elec-\ntrode (see Figure 5b). In Figure 5c, we show the cal-\nculated energies of thin-films of the various phases of\nBiFeO 3as a function of thickness, with the lattice con-\nstant fixed to that of the STO, TSO or DSO substrate,\nand the electrostatic boundary conditions set by impos-\ning zero electric displacement field outside the BiFeO 3\nlayer. The calculated total energy consists of three con-\ntributions: the internal energy relative to the R3cphase\n(including the effect of strain from the substrate), the\nelectrostatic energy from the polar discontinuity at the\ninterface,andascreeningenergytodecreasetheamount\nof bound charge at the interface and reduce the electro-\nstatic energy. As in Ref. 11, we assume that the system\nis single domain and take generation of electron-hole\npairs across the band gap as the screening mechanism;\nthis is likely to provide an upper bound value on the\nscreening energy cost.\nAmong the polar phases reported in Figure 5a, only\nPc(1) andR3chave an out-of-plane component of the\npolarisation, 54 \u0016C/cm2and 58\u0016C/cm2respectively,\nso their energy density decreases as a function of the\nthickness, while all other phases have a constant en-\nergy density, given by the internal energy. We find that\nPc(1) is unlikely to be stabilised on the considered sub-\nstrates,asthesmallerpolarisationisnotenoughtocom-\npensate the strain energy compared to R3c. On STO,\ntwo phases with in-plane polarisation, Pmc 21(1) and\nCmc 21, are more stable than R3cat low thicknesses.\nOn the other hand, the largest structure from the se-\nries ofPcphases is more stable than R3con DSO and\nTSO. We see that as expected, the critical thicknesses\nat which the phase with zero out-of-plane polarisation\nbecomes stable is smaller when the difference in strain\nenergy between the polar ground state and the lowest\nnon-polar phase is smaller.\nWe predict that BiFeO 3on the different substrates\nconsidered would recover its bulk behavior only for\nthicknesses larger than 10 nm. As we mention, the elec-\ntrostatic model that we chose is likely an upper bound\nestimationofthescreeningcost, whichresultsinalikely\noverestimation of the electrostatic energy and critical\nthickness. Note also that due to the prohibitive cost\nof DFT calculations, we do not consider the competing\nmechanism of domain formation. This would be a fruit-\nful direction for future second-principles or phase-field\ncalculations. Nevertheless, our predictions give new\nroutes to stabilizing new phases in BiFeO 3-based oxide\nheterostructures, and in general, as we showed that the\ncontrol of the electrostatics at the interface can provide\nan extra control parameter, additional to the choice of\nsubstrate.V. SUMMARY AND CONCLUSION\nIn summary, we used first-principles density func-\ntional theory to explore the low-energy phase space of\nBiFeO 3systematically. Weconsideredwell-knownpoly-\nmorphs of BiFeO 3and computed the phonon frequen-\ncies at high symmetry q-points to identify instabilities\nindicating structures of lower energy. Using this pro-\ncedure, we showed that the previously discussed Pbam\nandPmc 21phases are in fact unstable. We first showed\nthat several new metastable phases exist within an en-\nergy range of 50 meV/f.u. above the ground state in\na unit cell of 80 atoms. These phases exhibit complex\ndistortions and tilts that are beyond the scope of the\ntraditional Glazer notation. We proposed an extension\nto the Glazer notation making it suitable for general tilt\npatterns. We then extended our study to larger unit-\ncell sizes by increasing the size of the original Pmc 21\nunit cell along one lattice vector up to a total cell size\nof 160 atoms. We discovered the existence of a series\nof non-centrosymmetric structures that are polar in the\npseudocubic x-y plane, and antipolar in the perpendic-\nular direction. We showed that the antipolar mode is\nmodulated by the size of the unit cell and couples to\na rotational mode that is similarly modulated. In the\nlarge supercell limit these phases are reminiscent of op-\nposite domains of polarisation along the out-of-plane\ndirection. Finally, we discussed the possibilities for sta-\nbilising these phases experimentally and showed that\nthe lowest energy phases without out-of-plane polari-\nsation could in principle be stabilised using a combina-\ntion of strain and electrostatics at the interface between\nBiFeO 3and a non-polar III-III perovskite. Future work\ncould include an analysis of the role of other interfa-\ncial features such as matching of the tilt patterns of the\noxygen octahedra in determining phase stability.\nOur approach of using phonon instabilities in a sys-\ntematic way to explore the phase space of BiFeO 3, is\nof course broadly applicable to any material. It is lim-\nited, however, by the computational cost of the subse-\nquent structural relaxations in the large unit cells. We\nhope, therefore, that our identification of many large-\nunit-cell low-energy phases will motivate further theo-\nretical studies of the phase space of BiFeO 3and related\nmaterials with modern tools such as machine learning\nor second-principles methods. These could reveal ad-\nditional polymorphs with desirable properties such as\nantiferroelectricity. An extension to predict detailed\nmagnetic properties would also be of interest, in par-\nticular to search for phases with a large net magnetic\nmoment.\nOn the experimental front, we identified several new\nlow-energy structures in BiFeO 3, as well as routes for\nstabilizing them, which we hope will be helpful in the\ndesignofnewheterostructureswithtargetedproperties.11\nIn particular, our study of the series of phases with Pc\nsymmetry showed that for large unit cells, reorienta-\ntion of the polarisation is possible with minimal energy\ncost, and the distinction between phase and domains\nbecomes blurred. The Pcphases could therefore pro-\nvide a starting point for engineering polar vortices [40]\nin BiFeO 3-based oxide heterostructures.\nACKNOWLEDGMENTS\nWe acknowledge financial support from ETH Zürich\nand the Körber foundation. Computational resourceswere provided by ETH Zürich and the Swiss National\nSupercomputing Center (CSCS), Project ID No. s889.\nThe visualisations of the structures were done with\nVESTA [41] and we used Agate2to compute the rota-\ntion angles for the octahedra. We thank Kane Shenton\nfor helpful comments on the manuscript.\n[1] J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B.\nOgale, B. Liu, D. Viehland, V. Vaithyanathan, D. G.\nSchlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe,\nM. Wuttig, and R. Ramesh, Science 299, 1719 (2003).\n[2] F. Kubel and H. Schmid, Acta Cryst. B46, 698 (1990).\n[3] H. Béa, B. Dupé, S. Fusil, R. Mattana, B. Warot-\nFonrose, F. Wilhelm, A. Rogalev, S. Petit, V. Cros,\nA. Anane, F. Petroff, K.Bouzehouane, G. Geneste,\nB. Dkhil, S. Lisenkov, I. Ponomareva, L. Bellaiche,\nM. Bibes, and A. Barthélémy, Phys. Rev. Lett. 102,\n217603 (2009).\n[4] R. J. Zeches, M. D. Rossell, J. X. Zhang, A. J. Hatt,\nQ. He, C.-H. Yang, A. Kumar, C. H. Wang, A. Melville,\nC. Adamo, G. Sheng, Y.-H. Chu, J. F. Ihlefeld, R. Erni,\nC.Ederer, V.Gopalan, L.Q.Chen, D.G.Schlom, N.A.\nSpaldin, L. W. Martin, and R. Ramesh, Science 326,\n977 (2009).\n[5] H. M. Christen, J. H. Nam, H. S. Kim, A. J. Hatt, and\nN. A. Spaldin, Phys. Rev. B 83, 144107 (2011).\n[6] A. J. Hatt, N. A. Spaldin, and C. Ederer, Phys. Rev.\nB81, 054109 (2010).\n[7] Y. Yang, W. Ren, M. Stengel, X. H. Yan, and L. Bel-\nlaiche, Phys. Rev. Lett. 109, 057602 (2012).\n[8] J.C.Yang, Q.He, S.J.Suresha, C.Y.Kuo, C.Y.Peng,\nR. C. Haislmaier, M. A. Motyka, G. Sheng, C. Adamo,\nH. J. Lin, Z. Hu, L. Chang, L. H. Tjeng, E. Arenholz,\nN. J. Podraza, M. Bernhagen, R. Uecker, D. G. Schlom,\nV. Gopalan, L. Q. Chen, C. T. Chen, R. Ramesh, and\nY. H. Chu, Phys. Rev. Lett. 109, 247606 (2012).\n[9] D. P. Kozlenko, A. A. Belik, A. V. Belushkin,\nE. V. Lukin, W. G. Marshall, B. N. Savenko, and\nE. Takayama-Muromachi, Phys. Rev. B. 84, 094108\n(2011).\n[10] W. Dong, J. J. P. Peters, D. Rusu, M. Staniforth,\nA. E. Brunier, J. Lloyd-Hughes, A. M. Sanchez, and\nM. Alexe, Nano Lett. 20, 6045 (2020).\n[11] J. A. Mundy, C. A. Heikes, B. F. Grosso, D. F. Segedin,\nZ. Wang, B. H. Goodge, Q. N. Meier, C. T. Nelson,\n2https://github.com/piti-diablotin/agatehttps://github.com/piti-\ndiablotin/agateB. Prasad, L. F. Kourkoutis, W. D. Ratcliff, N. A.\nSpaldin, R. Ramesh, and D. G. Schlom, ArXiv e-prints\n(2018), arXiv:1812.09615, 1812.09615.\n[12] O.Diéguez, O.E.González-Vázquez, J.C.Wojdel, and\nJ. Íñiguez, Phys. Rev. B. 83, 094105 (2011).\n[13] A. M. Glazer, Acta. Cryst. B20, 3384 (1972).\n[14] W.KohnandL.J.Sham,PhysRev. 140,A1133(1965).\n[15] P. E. Blöchl, Phys Rev. B 50, 17953 (1994).\n[16] G. Kresse and J. Furthmüller, Phys Rev. B 54, 11169\n(1996).\n[17] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys Rev.\nLett.77, 3865 (1996).\n[18] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J.\nHumphreys, and A. P. Sutton, Phys Rev. B 57, 1505\n(1998).\n[19] A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D.\nRichards, S. Dacek, S. Cholia, D. Gunter, D. Skinner,\nG. Ceder, and K. A. Persson, APL Mater. 1, 011002\n(2013).\n[20] A. Togo and I. Tanaka, Scr. Mater. 108, 1 (2015).\n[21] T. Stokes, D. M. Hatch, and B. J. Campbell,\niso.byu.edu .\n[22] B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M.\nHatch, J. Appl. Cryst. 39, 607 (2006).\n[23] D. Orobengoa, C. Capillas, M. I. Aroyo, and J. M.\nPerez-Mato, J. Appl. Cryst. 42, 820 (2009).\n[24] J. M. Perez-Mato, D. Orobengoa, and M. I. Aroyo,\nActa Cryst. A66, 558 (2010).\n[25] S. P. Ong, W. D. Richards, A. Jain, G. Hautier,\nM. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A.\nPersson, and G. Ceder, Comput. Mater. Sci. 68, 314\n(2013).\n[26] J. B. Neaton, C. Ederer, U. V. Waghmare, N. A.\nSpaldin, and K. M. Rabe, Physical Review B 71,\n014113 (2005).\n[27] M. D. Peel, S. P. Thompson, A. Daoud-Aladine, S. E.\nAshbrook, and P. Lightfoot, Inorg. Chem. 51, 6876\n(2012).\n[28] B. Xu, D. Wang, J. Íñiguez, and L. Bellaiche, Adv.\nFunct. Mater. 25, 552 (2014).\n[29] O.DiéguezandJ.Íñiguez,Phys.Rev.Lett. 107,057601\n(2011).12\n[30] S. Geller, The Journal of Chemical Physics 24, 1236\n(1956).\n[31] S. Prosandeev, D. Wang, J. Íñiguez, and L. Bellaiche,\nAdv. Funct. Mater. 23, 234 (2012).\n[32] E. Sawaguchi, H. Maniwa, and S. Hoshino, Phys. Rev.\n83, 1078 (1951).\n[33] E. S. G. Shirane and Y. Takagi, Phys. Rev. 84, 476\n(1951).\n[34] J. Íñiguez, M. Stengel, S. Prosandeev, and L. Bellaiche,\nPhys. Rev. B 90, 220103(R) (2014).\n[35] A. Lubk, S. Gemming, and N. A. Spaldin, Phys. Rev.\nB80, 104110 (2009).[36] O. Diéguez, P. Aguado-Puente, J. Junquera, and\nJ. Íñiguez, Phys. Rev. B 87, 024102 (2013).\n[37] M. Stengel and J. Íñiguez, Physical Review B 92,\n235148 (2015).\n[38] J. Junquera and P. Ghosez, Nature 422, 506 (2003).\n[39] M. Marvan and J. Fousek, Phys. Stat. Sol. 208, 523\n(1999).\n[40] A. K. Yadav, C. T. Nelson, S. L. Hsu, Z. Hong,\nJ. D. Clarkson, C. M. Schlepütz, A. R. Damodaran,\nP. Shafer, E. Arenholz, L. R. Dedon, D. Chen, A. Vish-\nwanath, A. M. Minor, L. Q. Chen, J. F. Scott, L. W.\nMartin, and R. Ramesh, Nature 530, 198 (2016).\n[41] K. Momma and F. Izumi, J. Appl. Cryst. 44, 1272\n(2011)."    },    {        "title": "1907.11611v2.Stabilization_of___varepsilon__Fe__2_O__3__epitaxial_layer_on_MgO_111__GaN_via_an_intermediate__γ__Fe__2_O__3__phase.pdf",        "content": "Stabilization of \"-Fe 2O3epitaxial layer on MgO(111)/GaN via an intermediate \r-phase\nVictor Ukleev,1Mikhail Volkov,2Alexander Korovin,2Thomas Saerbeck,3Nikolai Sokolov,2and Sergey Suturin2\n1Laboratory for Neutron Scattering and Imaging (LNS),\nPaul Scherrer Institute (PSI), CH-5232 Villigen, Switzerland\u0003\n2Io\u000be Institute, 194021 Saint-Petersburg, Russia\n3Institut Laue-Langevin, 71 Avenue des Martyrs, 38042 Grenoble, France\nIn the present study we have demonstrated epitaxial stabilization of the metastable magnetically-\nhard\"-Fe2O3phase on top of a thin MgO(111) bu\u000ber layer grown onto the GaN (0001) surface. The\nprimary purpose to introduce a 4 nm-thick bu\u000ber layer of MgO in between Fe 2O3and GaN was to\nstop thermal migration of Ga into the iron oxide layer. Though such migration and successive for-\nmation of the orthorhombic GaFeO 3was supposed earlier to be a potential trigger of the nucleation\nof the isostructural \"-Fe2O3, the present work demonstrates that the growth of single crystalline\nuniform \flms of epsilon ferrite by pulsed laser deposition is possible even on the MgO capped GaN.\nThe structural properties of the 60 nm thick Fe 2O3layer on MgO / GaN were probed by electron\nand x-ray di\u000braction, both suggesting that the growth of \"-Fe2O3is preceded by formation of a thin\nlayer of\r-Fe2O3. The presence of the magnetically hard epsilon ferrite was independently con\frmed\nby temperature dependent magnetometry measurements. The depth-resolved x-ray and polarized\nneutron re\rectometry reveal that the 10 nm iron oxide layer at the interface has a lower density\nand a higher magnetization than the main volume of the \"-Fe2O3\flm. The density and magnetic\nmoment depth pro\fles derived from \ftting the re\rectometry data are in a good agreement with the\npresence of the magnetically degraded \r-Fe2O3transition layer between MgO and \"-Fe2O3. The\nnatural occurrence of the interface between magnetoelectric \"- and spin caloritronic \r- iron oxide\nphases can enable further opportunities to design novel all-oxide-on-semiconductor devices.\nThe magnetic-on-semiconductor heterostructures at-\ntract a lot of interest nowadays due to the vast oppor-\ntunities they provide for designing novel functional spin-\ntronic devices for magnetic memory applications and bio-\ninspired computing1{7. Placing a multiferroic layer with\ncontrollable magnetization/polarization in contact with\na semiconductor adds the functionality of controlling\noptical, electronic and magnetic properties of the het-\nerostructure by applied voltage8{11. One of the rare ex-\namples of material with spontaneous room-temperature\nmagnetization and electric polarization is the metastable\niron(III) oxide polymorph \"-Fe2O312{15. Quite recently,\nthe crystalline layers of \"-Fe2O3have been successfully\nsynthesized on a number of oxide substrates12,16{20and\nGaN(0001)21. The structural and magnetic properties\nof the iron oxide \flms drastically depend on the com-\nposition of the neighboring bu\u000ber layer, the chosen sub-\nstrate and the growth temperature. The feasibility to\nsynthesize as much as four di\u000berent iron oxide phases:\n\"-Fe2O3, Fe3O4,\u000b-Fe2O3and\r-Fe2O3on GaN(0001) by\n\fne adjustment of growth parameters has been recently\ndemonstrated21. It has been shown that stabilization of\nthe\"-Fe2O3phase requires elevated growth temperature\nthat leads to formation of a few nanometer-thick Ga-rich\nmagnetically soft transition layer at the interface between\nthe iron oxide \flm and the GaN substrate22. Later on,\na very similar Ga/Fe substitution phenomena have been\nobserved in yttrium iron garnet (YIG) \flms grown at\nabove 700\u000eC onto a gadolinium gallium garnet (GGG)23.\nAlthoughPna21Ga-substituted epsilon-ferrite GaFeO 3\nis isostructural to \"-Fe2O324and promotes further growth\nof the desired phase, its magnetic ordering temperature\nand coercivity \feld are somewhat lower than those of\"-Fe2O314. This can potentially reduce the magnetoelec-\ntric and magnetooptical performance of the functional\ndevices based on the \"-Fe2O3/ GaN heterostructures.\nIn the present study, we have successfully introduced\nan epitaxial MgO bu\u000ber between the \"-Fe2O3and GaN\nlayers to eliminate Ga migration into the iron oxide \flm.\nThe resulting structural and magnetic properties of the\nfabricated heterostructure were probed by complemen-\ntary x-ray di\u000braction (XRD), x-ray re\rectometry (XRR),\nvibrating sample magnetometry (VSM), and polarized\nneutron re\rectometry (PNR). An outcome of the epitax-\nial stabilization of \"-Fe2O3on the MgO bu\u000ber is a tech-\nnological advantage that provides further opportunities\nto integrate the promising epsilon ferrite into epitaxial\nFe4,25{28, Fe 3O429{33,\u000b-Fe2O331,32,34and\r-Fe2O331,33\nheterostructures and superlattices grown on MgO sub-\nstrates.\nThe substrates used in this work were commercial sap-\nphire Al 2O3(0001) wafers with a 3 \u0016m-thick Ga termi-\nnated GaN (0001) layer grown on top by means of met-\nalorganic vapour-phase epitaxy (MOVPE). The GaN sur-\nface showed a step-and-terrace surface morphology (Fig.\n1) as con\frmed by atomic force microscopy (AFM). The\noxide layers were grown by pulsed laser deposition (PLD)\nfrom MgO and Fe 2O3targets ablated using a KrF laser.\nThe crystallinity and epitaxial relations of the grown lay-\ners were controlled by in-situ high energy electron di\u000brac-\ntion (RHEED) reciprocal space 3D mapping. With this\ntechnique35one obtains a 3D reciprocal space map from\na sequence of conventional RHEED images taken during\nthe azimuthal rotation of the sample. Thus obtained se-\nquence of the closely spaced spherical cuts through the\nreciprocal space can be then compiled into a uniform 3DarXiv:1907.11611v2  [cond-mat.mes-hall]  5 Aug 20192\nFIG. 1. (Color online) Atomic force microscopy images of\nthe surface morphology at consecutive growth stages (from\nbottom to top): GaN, MgO/GaN and \"-Fe2O3/MgO/GaN.\nmap and shown in the easy interpreted form of planar\ncuts and projections. The side cuts and plan views of\nthe reciprocal space maps obtained at each growth stage\nare shown in the same scale in Fig. 2. The expected po-\nsitions of the reciprocal lattice nodes are indicated with\ncircles on the the left halves of the maps.\nThe 4 nm thick MgO layer was deposited onto GaN\nin 0.02 mbar of oxygen at the substrate temperature of\n800\u000eC. As con\frmed by atomic force microscopy (Fig.\n1), the MgO coverage on GaN is smooth and su\u000eciently\nuniform to serve as a di\u000busion barrier. The epitaxial rela-\ntions extracted from RHEED are as follows: GaN(0001)\njjMgO(111); GaN[1-10] jjMgO\u0006[11-2] (Fig. 2). The two\npossible MgO orientations arise due to the symmetry re-\nduction occuring at the interface: from GaN(0001) C 6to\nMgO(111) C 3. Re\rections on the RHEED map of MgO\nare streaky corresponding to the semi-\rat surface.\nA 60 nm thick iron oxide layer was grown onto the sur-\nface of MgO(111) in 0.2 mbar of oxygen at the substrate\ntemperature of 800\u000eC following the approach described\nin our previous report21. It was discovered that unlike\nwhen grown directly on GaN, the iron oxide layer on MgO\nnucleates in gamma rather than in epsilon phase. Upon\ndeposition of 3-5 nm of iron oxide, the RHEED recipro-\ncal space maps start showing a distinct 2 \u00022 pattern of\nstreaks characteristic for the spinel \r-Fe2O3lattice (Fig.\n2) oriented with the [111] axis perpendicular to the sur-\nface and the [11-2] axis parallel to MgO [11-2] and GaN[1-\n10]. The di\u000braction map remains streaky corresponding\nto the still \rat surface.\nThe preference of the \r-Fe2O3over\"-Fe2O3is nat-\nurally related to the cubic symmetry of both lattices.\nThe phase choice mechanisms for the Fe 2O3/ MgO(111)\nsystem might be similar to those of the Fe 2O3/ MgO\nFIG. 2. (Color online) In-situ re\rection high-energy\nelectron di\u000braction maps obtained at consecutive growth\nstages: MgO/GaN, \r-Fe2O3/MgO/GaN and \"-Fe2O3/\r-\nFe2O3/MgO/GaN. Shown in the same scale are the side cuts\n(top) and plan view projections (bottom) of the reciprocal\nspace. The modeled re\rection positions are shown with cir-\ncles.\n(001) system where \r-Fe2O3is known to be the dom-\ninant phase31,36,37. It is noteworthy that a thin \r-like\ntransition layer was also observed during the nucleation\nof\u000b- and\"-Fe2O3directly on GaN21. Though the di\u000brac-\ntion patterns of that layer bore resemblance to FeO, the\nspacing between the adjacent (111) layers of oxygen was3\nFIG. 3. (Color online) The XRD reciprocal space maps measured along the \"-Fe2O300N and 20N re\rection chains in the\n\"-Fe2O3/\r-Fe2O3/MgO/GaN/Al 2O3sample. The specular intensity pro\fle derived from the 00N map is shown on top. The\ninsets show in-plane and out-of-plane widths of the \r-Fe2O3444 and\"-Fe2O3008 re\rections. The re\rections of each compound\nare labeled on the maps with triangles.\nvery similar to \r-Fe2O3.\nWhen the total thickness of the iron oxide reaches\nabout 10 nm, the 2 \u00022 streak pattern gets gradually re-\nplaced by the 6\u00021 streak pattern which is an unmis-\ntakable \fngerprint of the \"-Fe2O3phase. This pattern\npersists until the growth is stopped at 60 nm of the iron\noxide total thickness (Fig. 2). The pattern is dotty rather\nthan streaky in agreement with the few nm surface rough-\nness measured by AFM (Fig. 1). The \"-Fe2O3lattice is\noriented with the polar [001] axis perpendicular to the\nsurface and the easy magnetization [100] axis parallel to\nthe one of the three equivalent GaN [1-10] in-plane direc-\ntions resulting in three crystallographic domains at 120\u000eto each other. It is essential that the growth temperature\nat this stage is no less than 800\u000eC otherwise nucleation\nof\"-Fe2O3phase does not occur.\nTo accurately study the crystal structure of the \flm\nvolume we have applied X-ray di\u000braction in addition to\nthe surface sensitive RHEED. The XRD measurements\nwere carried out at the BL-3A beamline, KEK Photon\nFactory (Tsukuba, Japan). The 3D reciprocal space\nmaps were compiled from a series of di\u000braction patterns\ntaken with a Pilatus 100K two-dimensional detector dur-\ning a multi-angle rotation performed on a standard 4-\ncircle Euler di\u000bractometer. The linear and planar cuts\nthrough the 3D maps obtained across the reciprocal space4\nspecular region are shown in Fig. 3. The series of \"-Fe2O3\n002\u0001N and\r-Fe2O3111\u0001N re\rections are easily identi\f-\nable in addition to the re\rections of the underlying Al 2O3\nand GaN. We do not observe distinctly the re\rections of\nMgO as they considerably overlap with those of \r-Fe2O3.\nMoreover the MgO layer is 15 times thinner than Fe 2O3\nand has about 1.5 times lower scattering length density\nfor x-rays.\nThe derived out-of-plane lattice constant of epsilon fer-\nritec= 9:43\u0017A is in agreement with our earlier studies\nof\"-Fe2O3/ GaN21. The (111) interplane distance in\n\r-Fe2O3is in agreement with the bulk lattice constant\nof\r-Fe2O3a= 8:33\u0017A. The in-plane lattice arrangement\nbecomes clear from the analysis of the reciprocal space re-\ngion containing the o\u000b-specular \"-Fe2O320N re\rections.\nThe\"-Fe2O3lattice shows a 1% in-plane expansion to-\nwardsa= 5:14\u0017A andb= 8:86\u0017A. The\r-Fe2O3lattice\nshows a 1.5 % lattice expansion towards the equivalent\ncubic lattice constant of a= 8:47\u0017A. The in-plane expan-\nsion is not surprising taking into account the fact that the\nin-plane periodicity in GaN is about 8.5% larger than in\nFe2O321. The observed in-plane and out-of-plane re\rec-\ntion widths may be used to judge on the strain relaxation\nand minimal crystallographic domain size in the grown\n\flms. The strain relaxation if present would involve a dis-\ntribution of lattice parameters in the system and would\ncause re\rection broadening that is proportional to the\nmagnitude of the wave vector Qz. Even if such a broad-\nening is present in our system, it is below the experimen-\ntal resolution as all the observed re\rections are of the\nsame shape and width. Such e\u000bect can be attributed to\nthe \fnite size of the coherent crystallographic domains\nwithin the crystal lattice and is typical for the nanos-\ntructured samples. Measuring the in-plane and out-of-\nplane re\rection widths (see the insets in Fig. 3) one can\nconclude that the minimal coherent domains of \"-Fe2O3\nare shaped as (width \u0002height) 14 nm\u000235 nm columns\n(in agreement with Ref.22) while those of \r-Fe2O3look\nlike 33 nm\u000210 nm disks. The reduced coherent thick-\nness of\"-Fe2O3\flm suggests that a transition layer with\na mixed lattice structure exist at the \r-Fe2O3/\"-Fe2O3\ninterface. The lateral coherence between the the adja-\ncent nucleation sites is substantially reduced because the\nsurface cell of the iron oxides is larger than that of MgO.\nCompared to \r-Fe2O3the coherent domain of \"-Fe2O3\nis smaller because of the larger surface cell and the lack\nof the C 3symmetry. Thus the antiphase boundaries are\nformed more frequently in \"-Fe2O3.\nThe magnetometry measurements were carried out us-\ning a Quantum Design PPMS vibrating-sample magne-\ntometer (VSM). The magnetic \feld was applied in the\nsample plane along the [100] easy magnetization axis of\none of the three \"-Fe2O3domains. Fig. 4 shows the\nhysteresis loops measured in the temperature range of\n5-400 K and corrected for the linear diamagnetic contri-\nbution of the substrate. The observed values of satura-\ntion magnetization were about 130 emu/cm3atT= 5 K\nand 100 emu/cm3atT= 400 K which is consistent with\nFIG. 4. (Color online) In-plane hysteresis M(B) curves of\n70 nm-thick \"-Fe2O3/MgO \flm measured at 5-400 K. Shown\nare curves (a) as measured and (b) decomposed to the\nhard and soft components. To express the magnetization in\nemu/cm3the curves in (a) are normalized to the expected \flm\nthickness of 70 nm. The hard and soft component curves in\n(b) are normalized to the thicknesses of 60 nm corresponding\nto the thickness of \"-Fe2O3layer and 70 nm corresponding to\nthe total thickness of the sample.\nwhat was reported for \"-Fe2O3nanoparticles38and\"-\nFe2O3thin \flm grown on SrTiO 3(STO)12, YSZ19,39and\nGaN22, and predicted from ab-initio calculations15.\nThe wasp-waist magnetization loops shown in Fig.\n4a are typical for \"-Fe2O3\flms and nanoparticles and\ncan be qualitatively decomposed to hard and soft com-\nponent loops (Fig. 4b) by subtracting 2 Msoft=\u0019\u0001\narctan(B/Bsoft) function with temperature-independent\nMsoft= 71 emu/cm3andBsoft= 62 mT. These param-\neters were unambiguously derived from manual optimiza-\ntion aimed at making the remaining hard component\nsmooth and monotonous in the vicinity of zero magnetic\n\feld.\nThe value of Msoft = 71 emu/cm3observed for the\nsoft magnetic component is in general agreement with the\npresence of \r-Fe2O3sublayer buried below the main layer\nof\"-Fe2O3as observed by XRD, RHEED and PNR. The5\nFIG. 5. (Color online) (a) Measured (symbols) and \ftted (solid lines) x-ray and neutron re\rectivity curves as a function of\nmomentum transfer ( Qz) on a logarithmic scale. The curves are shifted along vertical axis for clarity. (b) X-ray scattering length\ndensity (SLD) \u001ae(green line), and neutron nuclear SLD \u001an(red line) of \"-Fe2O3/MgO/GaN \flm as a function of the distance\nfrom the GaN layer surface ( z) obtained from the \ftting routine. X-ray SLD \u001aeis given in the units of the classical electron\nradiusre= 2:81794:::\u000210\u000015m. (c) PNR spin-asymmetry ratio ( R+\u0000R\u0000)=(R++R\u0000) at applied magnetic \feld B= 2 T\nandB= 0:5 T after magnetization reversal obtained from experimental data (symbols) and \ftted models (solid curves). (d)\nNeutron magnetic SLD \u001ampro\fle atB= 2 T,B= 0:025 T before and at B= 0:025 T,B= 0:5 T after magnetization reversal,\ncorresponding to the characteristic points (1 \u00004) of theM(B) loop shown in Fig.4.\nmagnetization plotted in Fig. 4b is normalized to the\ntotal \flm thickness of 70 nm. Taking into account the\nreported values of Ms=300-400 emu/cm3for\r-Fe2O3/\nMgO, the soft loop can be attributed to a layer of \r-\nFe2O3having thickness of 12-14 nm. This is comparable\nthough slightly higher than the thickness estimated from\nRHEED and PNR (see the details below).\nThe hard component hysteresis loops show a large sat-\nuration \feld of 1.2-1.8 T characteristic of \"-Fe2O3. The\ncoercive \feld gradually increases as the sample is cooled\ndown - from 0.27 T at 400 K to 0.66 T at 5 K. The loop\nshape is typical for the system with three uniaxial do-\nmains at 120 deg to each other. At saturation the mag-\nnetization is collinear to the \feld in all three domains\nMsum\ns= 3\u0001Ms. From saturation to zero \feld the mag-\nnetization gradually decreases to 2 =3\u0001Msum\ns as the the\nmagnetization in the two non collinear domains returnsto the equilibrium state at 120 deg to the \feld. From this\nstate the magnetization reversal is gradually completed\ntowards the negative saturation. Notably, the magnetic\nphase transition to an incommensurate state that is often\nobserved in \"-Fe2O3nanoparticles, as dramatic shrink-\nage of the loop at T\u0019100\u0000150 K40{43, has not been\nobserved in \"-Fe2O3\flms - neither on GaN nor on the\nother substrates. The absence of a sharp phase transition\nin \flms can be caused by the variation of the magnetic\nproperties across the \flm depth. Thus, a temperature-\ndependent investigation of the depth resolved magnetic\nstructure of \"-Fe2O3\flms by neutron or resonant x-ray\ndi\u000braction is highly desired to address this issue.\nThe XRR measurement was performed on the Pana-\nlytical X'Pert PRO x-ray di\u000bractometer at room tem-\nperature using Cu K\u000b(1.5406 \u0017A) radiation to determine\nthe electron scattering length density (SLD) pro\fle \u001aeof6\nthe \flm as a function of distance from the GaN surface\nz. The specular re\rectance was measured in the range\nof incident angles between 0.5 to 3.5 degrees covering the\nQzrange from 0.075 to 0.5 \u0017A\u00001.\nThe neutron re\rectometry experiments were per-\nformed at the D17 setup44,45(ILL, Grenoble, France)\nin polarized time-of-\right mode. Sample temperature\nand magnetic \feld were controlled by an Oxford In-\nstruments 7 T vertical \feld cryomagnet equipped with\nsingle-crystalline sapphire windows. Neutrons with wave-\nlengths of 4\u000016\u0017A were used to ensure the constant\npolarization of P0>99%. Three di\u000berent incident\nangles (0.8, 1.5 and 3.7 degrees) were chosen to access\ntheQzrange from 0.017 to 0.17 \u0017A\u00001. Intensity of the\nre\rected beam was collected by two-dimensional3He\nposition-sensitive detector. The data was integrated us-\ning a method taking into account the sample curvature\nor beam divergence44,46. Non-spin-\rip re\rectivities R+\nandR\u0000, where +(-) denotes the incident neutron spin\nalignment parallel (antiparallel) to the direction of ap-\nplied magnetic \feld, were acquired without polarization\nanalysis. The detailed description of the re\rectometry\ntechniques can be found elsewhere47,48.\nFigure 5a shows x-ray re\rectivity (room temperature)\nand neutron re\rectivity ( T= 5 K) curves plotted as a\nfunction of momentum transfer Qz. The neutron re\rec-\ntivity curves were measured at the characteristic char-\nacteristic points of the M(B) loop marked as (1 \u00004) in\nFig.4. The PNR curves shown in Fig. 5a are measured\nin applied magnetic \felds of B= 0:025 T (state 1 in re-\nmanence) and B= 2 T (state 3 in saturation). The XRR\nand PNR curves were simultaneously \ftted using GenX\nsoftware49. The simplest model, for which the \ftting\nroutine converges, corresponds to a stack consisting of\nthe GaN substrate, the MgO bu\u000ber, the transition iron\noxide layer with an unspeci\fed density and the main \"-\nFe2O3layer. The depth-pro\fles of the x-ray ( \u001ae) and\nnuclear neutron ( \u001an) scattering length densities (SLDs)\nextracted from the re\fned model are shown in Fig. 5b.\nThe pro\fles re\rect the chemical composition and den-\nsity of the layers as well as the structural roughness of\nthe interfaces. The root mean square (RMS) roughness\nof all the interfaces is below 15 \u0017A. Notably, we observe\nthe transition layer at the iron oxide/MgO interface with\nthickness of 105\u000610\u0017A and reduced x-ray and neutron\nnuclear SLDs compared to the main \"-Fe2O3volume of\nthe \flm. This looks natural as \r-Fe2O3having the same\nchemical formula as \"-Fe2O3is by 3.4 % less dense due\nto the presence of iron vacancies in the inverted spinel\nstructure. The comparably low SLD of the MgO layer\ngives a few nm wide reduction of \u001aeand\u001anlocated on\nthe SLD pro\fle at z= 0.\nThe magnetization pro\fle of the heterostructure is\nencoded in the dependence of the spin-asymmetry ra-\ntio (R+-R\u0000)/(R++R\u0000) onQz. Fitting it against the\nmodel gives the depth pro\fle of the magnetic contribu-\ntion to the neutron SLD \u001am(\u0017A\u00002) which can be con-\nverted to magnetization M(emu/cm3) using the fol-lowing formula: M= 3505\u0001105\u0001\u001am50. The mea-\nsured and \ftted spin-asymmetry ratios are shown in Fig.\n5c for the two magnetic states 2 and 3 on the lower\nbranch of the hysteresis loop (see Fig. 4): with partially\nswitched magnetization ( B= +0:5 T) and in full satu-\nration (B= +2 T). The \ftted model suggests that the\niron oxide \flm is divided into two magnetically di\u000berent\nsub-systems: the main \"-Fe2O3layer with a saturation\nmagnetization of Ms1\u001956 emu/cm3and an interfacial\nlayer withMs2\u001970 emu/cm3(Fig. 5d). Using the PNR\ndata obtained at 5 K we are able to track the magneti-\nzation behavior of individual sublayers as the system is\nmagnetized from the negative remanence (state 1) to full\nsaturation (state 3) and back to the positive remanence\n(state 4). As shown in (Fig. 5d) the magnetization of the\nsofter interface layer is switched between B= 0:025 T\n(state 1) and B= 0:5 T (state 2) and reaches satura-\ntion of 70 emu/cm3atB= 2 T. The magnetization of\nthe much harder \"-Fe2O3layer switches somewhere be-\ntweenB= 0:5 T (state 2) and B= 2 T (state 3). As\nthe magnetically hard component of the hysteresis loop\nis not completely closed in the maximum applied positive\nof 2 T (Fig. 4b), the PNR curves measured at B= 2 T\n(state 3) and B= 0:025 T (state 4) belong to the minor\nbranch of the hysteresis. Magnetization of 56 emu/cm3\nis found at B= 2 T, which is slightly smaller that the\nsaturation moment. Going back to positive remanence\nof the minor loop (state 4), the magnetization of both\ninterface and bulk layers start slowly decreasing (faster\nfor the interface layer).\nSequential switching of interface \r- and main \"- lay-\ners in principle re\rects a step-like shape of the hysteresis\nloops observed by VSM magnetometry (Fig. 4). It must\nbe noted that the maximum magnetization for \"-Fe2O3\nlayer derived from PNR is about twice lower than the\nhighest reported values for \"-Fe2O3but in good agree-\nment with the maximum magnetization observed in the\ndecomposed VSM loop shown in Fig. 4b. The maxi-\nmum magnetization of the \r-Fe2O3layer derived from\nPNR is about 5 times lower than the expected 300-\n400 emu/cm3reported for \r-Fe2O3/MgO layers31,36,37,\nand cannot completely explain the soft-magnetic com-\nponent observed by VSM. Magnetic degradation of the\ntransition\r-Fe2O3layer can be possibly explained by the\nsize e\u000bect51, epitaxial strain52{54or large number of the\nantiphase boundaries55,56between the nano-columns in\nthe plane of the layer and at the interface with main \"-\nFe2O3\flm.\nThe much higher magnetization of the soft magnetic\ncomponent observed in VSM suggests that another soft\nmagnetic phase is likely present in the sample that cannot\nbe distinguished in the PNR experiment. Similar e\u000bect\nwas also observed in \"-Fe2O3grown directly on GaN22.\nThe most plausible candidates are homogeneously dis-\ntributed minor fractions of polycrystalline \r-Fe2O3and\nFe3O457{59not pronounced in XRD data. Again, one\nmust also take into account the columnar structure of\nthe\"-Fe2O3\flms containing considerable concentration7\nof the antiphase boundaries. As was pointed out in Ref.60\nthe antiphase boundaries in iron oxides may account for\nthe soft magnetic behavior. The magnetic moments lo-\ncated in minor phase fractions of small volume, or at\nthe antiphase boundaries in the sample plane that can-\nnot be resolved with PNR, which is a laterally averaging\ntechnique, because the disordered moments at bound-\naries and minor phase fractions are highly diluted, but\nintegrated into the magnetization measured by VSM. We\nsuggest that the deposition of small ( \u0016m-scale) iron par-\nticulates ejected from the PLD target is the most plausi-\nble scenario, that have been also observed for other PLD\n\flms61{63.\nIn conclusion, we have demonstrated the possibil-\nity to epitaxially grow single crystal \"-Fe2O3thin \flm\non MgO(111) surface by pulsed laser deposition. In\ncontrast to the previously investigated non-bu\u000bered \"-\nFe2O3/GaN(0001) system, where the interfacial GaFeO 3\nmagnetically degraded layer was reported to form due\nto Ga di\u000busion22from GaN, the \"-Fe2O3/ MgO / GaN\nsystem has advantage of exploiting the di\u000busion block-\ning MgO barrier. Though formation of the orthorhombic\nGaFeO 3was supposed earlier to be a potential trigger of\nthe nucleation of the isostructural \"-Fe2O3, the present\nwork demonstrates that the growth of single crystalline\nuniform \flms of epsilon ferrite by pulsed laser deposition\nis possible even without the aid of Ga. Still the aid of Gaseems important as on GaN the \"-Fe2O3layer could be\nnucleated with a transition layer of few angstrom thick-\nness while on MgO the growth of \"-Fe2O3\flm is preceded\nby nucleation of a 10 nm thick layer of another iron oxide\nphase. A complimentary combination of electron and x-\nray di\u000braction, x-ray re\rectometry and polarized neutron\nre\rectometry techniques allowed unambiguous identi\fca-\ntion of this phase as P4132 (P4332) cubic\r-Fe2O3. This\nphase is known to show magnetoelectric functionality64\nand spin Seebeck e\u000bect65and can enable further opportu-\nnities to design the novel all-oxide heterostructure mag-\nnetoelectric and spin caloritronic devices.\nWe are grateful to Institut Laue-Langevin for pro-\nvided neutron and x-ray re\rectometry beamtime (pro-\nposal No.: 5-54-24445). Synchrotron x-ray di\u000braction ex-\nperiment was performed at KEK Photon Factory as a\npart of the proposal No. 2018G688. We thank Dr. Tian\nShang for the assistance with magnetization measure-\nments. The part of the study related to PNR and XRR\nwas partially supported by SNF Sinergia CRSII5-171003\nNanoSkyrmionics. The part of the study related to\ngrowth technology and di\u000braction studies was supported\nby Russian Foundation for Basic Research grant №18-02-\n00789. The open access fee was covered by FILL2030, a\nEuropean Union project within the European Commis-\nsion's Horizon 2020 Research and Innovation programme\nunder grant agreement No. 731096.\n\u0003victor.ukleev@psi.ch\n1G. A. Prinz, Science 250, 1092 (1990).\n2Y. Ohno, D. Young, B. Beschoten, F. Matsukura, H. Ohno,\nand D. Awschalom, Nature 402, 790 (1999).\n3S. Wolf, D. Awschalom, R. Buhrman, J. Daughton,\nS. Von Molnar, M. Roukes, A. Y. Chtchelkanova, and\nD. Treger, Science 294, 1488 (2001).\n4S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, and\nK. Ando, Nature Materials 3, 868 (2004).\n5A. D. Kent and D. C. Worledge, Nature Nanotechnology\n10, 187 (2015).\n6J. Grollier, D. Querlioz, and M. D. Stiles, Proceedings of\nthe IEEE 104, 2024 (2016).\n7B. Dieny and M. Chshiev, Reviews of Modern Physics 89,\n025008 (2017).\n8J. Scott, Nature Materials 6, 256 (2007).\n9M. Gajek, M. Bibes, S. Fusil, K. Bouzehouane, J. Fontcu-\nberta, A. Barth\u0013 el\u0013 emy, and A. Fert, Nature Materials 6,\n296 (2007).\n10N. Ortega, A. Kumar, J. Scott, and R. S. Katiyar, Journal\nof Physics: Condensed Matter 27, 504002 (2015).\n11J.-M. Hu, C.-G. Duan, C.-W. Nan, and L.-Q. Chen, NPJ\nComputational Materials 3, 18 (2017).\n12M. Gich, I. Fina, A. Morelli, F. S\u0013 anchez, M. Alexe,\nJ. G\u0012 azquez, J. Fontcuberta, and A. Roig, Advanced Ma-\nterials 26, 4645 (2014).\n13S.-I. Ohkoshi, A. Namai, K. Imoto, M. Yoshikiyo,\nW. Tarora, K. Nakagawa, M. Komine, Y. Miyamoto,\nT. Nasu, S. Oka, and H. Tokoro, Scienti\fc Reports 5,\n14414 (2015).14T. Katayama, S. Yasui, Y. Hamasaki, T. Osakabe, and\nM. Itoh, Journal of Materials Chemistry C 5, 12597 (2017).\n15K. Xu, J. Feng, Z. Liu, and H. Xiang, Physical Review\nApplied 9, 044011 (2018).\n16M. Gich, J. Gazquez, A. Roig, A. Crespi, J. Fontcuberta,\nJ. Idrobo, S. Pennycook, M. Varela, V. Skumryev, and\nM. Varela, Applied Physics Letters 96, 112508 (2010).\n17T. M. N. Thai, D. T. Nguyen, N.-S. Lee, J.-S. Rhyee,\nJ. Song, and H.-J. Kim, Journal of Applied Physics 120,\n185304 (2016).\n18Y. Hamasaki, T. Shimizu, S. Yasui, T. Shiraishi,\nA. Akama, T. Kiguchi, T. Taniyama, and M. Itoh, Journal\nof Applied Physics 122, 015301 (2017).\n19L. Corbellini, C. Lacroix, C. Harnagea, A. Korinek, G. A.\nBotton, D. M\u0013 enard, and A. Pignolet, Scienti\fc Reports 7\n(2017).\n20V. Q. Viet, S. Y. Adeyemi, W. H. Son, J.-S. Rhyee, N.-S.\nLee, and H.-J. Kim, Crystal Growth & Design 18, 3544\n(2018).\n21S. Suturin, A. Korovin, S. Gastev, M. Volkov, A. Sitnikova,\nD. Kirilenko, M. Tabuchi, and N. Sokolov, Physical Re-\nview Materials 2, 073403 (2018).\n22V. Ukleev, S. Suturin, T. Nakajima, T.-h. Arima,\nT. Saerbeck, T. Hanashima, A. Sitnikova, D. Kirilenko,\nN. Yakovlev, and N. Sokolov, Scienti\fc Reports 8, 8741\n(2018).\n23S. Suturin, A. Korovin, V. Bursian, L. Lutsev,\nV. Bourobina, N. Yakovlev, M. Montecchi, L. Pasquali,\nV. Ukleev, A. Vorobiev, A. Devishvili, and N. Sokolov,\nPhysical Review Materials 2, 104404 (2018).8\n24S. Abrahams, J. Reddy, and J. Bernstein, The Journal of\nChemical Physics 42, 3957 (1965).\n25Y. V. Goryunov, N. Garifyanov, G. Khaliullin, I. Gari-\nfullin, L. Tagirov, F. Schreiber, T. M uhge, and H. Zabel,\nPhysical Review B 52, 13450 (1995).\n26M. Klaua, D. Ullmann, J. Barthel, W. Wulfhekel,\nJ. Kirschner, R. Urban, T. L. Monchesky, A. Enders, J. F.\nCochran, and B. Heinrich, Physical Review B 64, 134411\n(2001).\n27H. Raanaei, H. Lidbaum, A. Liebig, K. Leifer, and\nB. Hj orvarsson, Journal of Physics: Condensed Matter 20,\n055212 (2008).\n28R. Moubah, F. Magnus, T. Warnatz, G. K. P\u0013 alsson, V. Ka-\npaklis, V. Ukleev, A. Devishvili, J. Palisaitis, P. Persson,\nand B. Hj orvarsson, Physical Review Applied 5, 044011\n(2016).\n29J. Anderson, M. Kuhn, U. Diebold, K. Shaw, P. Stoyanov,\nand D. Lind, Physical Review B 56, 9902 (1997).\n30D. Margulies, F. Parker, M. Rudee, F. Spada, J. Chapman,\nP. Aitchison, and A. Berkowitz, Physical Review Letters\n79, 5162 (1997).\n31Y. Gao, Y. Kim, S. Thevuthasan, S. Chambers, and P. Lu-\nbitz, Journal of Applied Physics 81, 3253 (1997).\n32Y. Kim, Y. Gao, and S. Chambers, Surface Science 371,\n358 (1997).\n33F. Voogt, T. Fujii, P. Smulders, L. Niesen, M. James, and\nT. Hibma, Physical Review B 60, 11193 (1999).\n34Y. Gao, Y. Kim, S. Chambers, and G. Bai, Journal of\nVacuum Science & Technology A: Vacuum, Surfaces, and\nFilms 15, 332 (1997).\n35S. M. Suturin, A. M. Korovin, V. V. Fedorov, G. A.\nValkovsky, M. Tabuchi, and N. S. Sokolov, Journal of\nApplied Crystallography 49, 1532 (2016).\n36X. Huang, Y. Yang, and J. Ding, Acta Materialia 61, 548\n(2013).\n37B. Sun, W. Zhao, Y. Xiong, Y. Lin, and P. Chen, Metal-\nlurgical and Materials Transactions A 45, 5245 (2014).\n38J. Jin, S.-i. Ohkoshi, and K. Hashimoto, Advanced Mate-\nrials 16, 48 (2004).\n39K. Kn\u0013 \u0010\u0014 zek, M. Pashchenko, P. Levinsk\u0012 y, O. Kaman,\nJ. Houdkov\u0013 a, P. Ji\u0014 r\u0013 \u0010\u0014 cek, J. Hejtm\u0013 anek, M. Soroka, and\nJ. Bur\u0014 s\u0013 \u0010k, Journal of Applied Physics 124, 213904 (2018).\n40M. Gich, C. Frontera, A. Roig, E. Taboada, E. Molins,\nH. Rechenberg, J. Ardisson, W. Macedo, C. Ritter,\nV. Hardy, et al. , Chemistry of Materials 18, 3889 (2006).\n41Y.-C. Tseng, N. M. Souza-Neto, D. Haskel, M. Gich,\nC. Frontera, A. Roig, M. Van Veenendaal, and J. Nogu\u0013 es,\nPhysical Review B 79, 094404 (2009).\n42J. L. Garc\u0013 \u0010a-Mu~ noz, A. Romaguera, F. Fauth, J. Nogu\u0013 es,\nand M. Gich, Chemistry of Materials 29, 9705 (2017).\n43S.-i. Ohkoshi, K. Imoto, A. Namai, S. Anan, M. Yoshikiyo,\nand H. Tokoro, Journal of the American Chemical Society\n139, 13268 (2017).\n44T. Saerbeck, R. Cubitt, A. Wildes, G. Manzin, K. H. An-\ndersen, and P. Gutfreund, Journal of Applied Crystallog-\nraphy 51, 249 (2018).45V. Ukleev, A. Chumakov, T. Saerbeck, and A. Voro-\nbiev, \\Magnetism and structure of \"-Fe2O3\flms grown\non gallium nitride bu\u000ber layer,\" Institut Laue-Langevin\n(ILL) http://dx.doi.org/10.5291/ILL-DATA.5-54-244\n(2018).\n46R. Cubitt, T. Saerbeck, R. A. Campbell, R. Barker,\nand P. Gutfreund, Journal of Applied Crystallography 48\n(2015).\n47J. Ankner and G. Felcher, Journal of Magnetism and Mag-\nnetic Materials 200, 741 (1999).\n48H. Zabel, K. Theis-Brohl, M. Wol\u000b, and B. Toperverg,\nIEEE Transactions on Magnetics 44, 1928 (2008).\n49M. Bj orck and G. Andersson, Journal of Applied Crystal-\nlography 40, 1174 (2007).\n50Y. Zhu, Modern Techniques for Characterizing Magnetic\nMaterials (Springer Science & Business Media, 2005).\n51J. Orna, P. A. Algarabel, L. Morell\u0013 on, J. Pardo,\nJ. de Teresa, R. L. Ant\u0013 on, F. Bartolom\u0013 e, L. Garc\u0013 \u0010a, J. Bar-\ntolom\u0013 e, J. Cezar, et al. , Physical Review B 81, 144420\n(2010).\n52F. Yang, N. Kemik, M. D. Biegalski, H. M. Christen,\nE. Arenholz, and Y. Takamura, Applied Physics Letters\n97, 092503 (2010).\n53J. Bertinshaw, S. Br uck, D. Lott, H. Fritzsche, Y. Khay-\ndukov, O. Soltwedel, T. Keller, E. Goering, P. Audehm,\nD. L. Cortie, et al. , Physical Review B 90, 041113 (2014).\n54M. Gibert, M. Viret, A. Torres-Pardo, C. Piamonteze,\nP. Zubko, N. Jaouen, J.-M. Tonnerre, A. Mougin, J. Fowlie,\nS. Catalano, et al. , Nano Letters 15, 7355 (2015).\n55F. Rigato, S. Estrad\u0013 e, J. Arbiol, F. Peir\u0013 o, U. L uders,\nX. Mart\u0013 \u0010, F. S\u0013 anchez, and J. Fontcuberta, Materials Sci-\nence and Engineering: B 144, 43 (2007).\n56A. V. Ramos, S. Matzen, J.-B. Moussy, F. Ott, and\nM. Viret, Physical Review B 79, 014401 (2009).\n57J. Jin, K. Hashimoto, and S.-i. Ohkoshi, Journal of Ma-\nterials Chemistry 15, 1067 (2005).\n58J. L\u0013 opez-S\u0013 anchez, A. Mu~ noz-Noval, A. Serrano, M. Abu\u0013 \u0010n,\nJ. de la Figuera, J. Marco, L. P\u0013 erez, N. Carmona, and\nO. R. de la Fuente, RSC Advances 6, 46380 (2016).\n59L. Corbellini, C. Lacroix, D. M\u0013 enard, and A. Pignolet,\nScripta Materialia 140, 63 (2017).\n60R. So\fn, H.-C. Wu, and I. Shvets, Physical Review B 84,\n212403 (2011).\n61S. Haindl, K. Hanzawa, H. Sato, H. Hiramatsu, and\nH. Hosono, Scienti\fc Reports 6, 35797 (2016).\n62X. Zhai, A. J. Grutter, Y. Yun, Z. Cui, and Y. Lu, Physical\nReview Materials 2, 044405 (2018).\n63J. A. Grant-Jacob, J. J. Prentice, S. J. Beecher, D. P.\nShepherd, R. W. Eason, and J. I. Mackenzie, Materials\nResearch Express 5, 036402 (2018).\n64B. Cheng, H. Qin, J. Pei, L. Liu, S. Ren, and J. Hu,\nApplied Physics Letters 108, 212402 (2016).\n65P. Jim\u0013 enez-Cavero, I. Lucas, A. Anad\u0013 on, R. Ramos, T. Ni-\nizeki, M. Aguirre, P. Algarabel, K. Uchida, M. Ibarra,\nE. Saitoh, et al. , APL Materials 5, 026103 (2017)."    },    {        "title": "2403.04741v1.Effects_of_mechanical_stress__chemical_potential__and_coverage_on_hydrogen_solubility_during_hydrogen_enhanced_decohesion_of_ferritic_steel_grain_boundaries__A_first_principles_study.pdf",        "content": "Effects of mechanical stress, chemical potential, and coverage on\nhydrogen solubility during hydrogen enhanced decohesion of\nferritic steel grain boundaries: A first-principles study\nAbril Az´ ocar Guzm´ an ,1,2∗and Rebecca Janisch1†\n1Interdisciplinary Centre for Advanced Materials Simulation (ICAMS),\nRuhr-Universit¨ at Bochum, 44801 Bochum, Germany\n2Current Address: Institute for Advanced Simulations – Materials Data Science and Informatics (IAS-9),\nForschungszentrum J¨ ulich GmbH, 52425 J¨ ulich, Germany\n(Dated: March 8, 2024)\nHydrogen enhanced decohesion (HEDE) is one of the many mechanisms of hydrogen embrittle-\nment, a phenomenon which severely impacts structural materials such as iron and iron alloys. Grain\nboundaries (GBs) play a critical role in this mechanism, where they can provide trapping sites or act\nas hydrogen diffusion pathways. The interaction of H with GBs and other crystallographic defects,\nand thus the solubility and distribution of H in the microstructure, depends on the concentration,\nchemical potential and local stress. Therefore, for a quantitative assessment of HEDE, a general-\nized solution energy in conjunction with the cohesive strength as a function of hydrogen coverage is\nneeded. In this work, we carry out density functional theory calculations to investigate the influence\nof H on the decohesion of the Σ5(310)[001] and Σ3(112)[1 ¯10] symmetrical tilt GBs in bcc Fe, as\nexamples for open and close-packed GB structures. A method to identify the segregation sites at\nthe GB plane is proposed. The results indicate that at higher local concentrations, H leads to a\nsignificant reduction of the cohesive strength of the GB planes, significantly more pronounced at\nthe Σ5 than at the Σ3 GB. Interestingly, at finite stress the Σ3 GB becomes more favorable for H\nsolution, as opposed to the case of zero stress, where the Σ5 GB is more attractive. This suggests\nthat under certain conditions stresses in the microstructure can lead to a re-distribution of H to\nthe stronger grain boundary, which opens a new path to designing H-resistant microstructures. To\nround up our study, we investigate the effects of typical alloying elements in ferritic steel, C, V, Cr\nand Mn, on the solubility of H and the strength of the GBs.\nI. INTRODUCTION\nHydrogen embrittlement (HE) is a fundamental prob-\nlem in materials science. In particular, it is known to\nhave a detrimental effect on the mechanical properties\nof structural materials such as iron and iron alloys. For\nover a century researchers have striven to understand the\nmechanisms of HE, still, many questions remain open [1].\nThis is mainly due to the fact that hydrogen changes the\nproperties of several defects in the material, often at the\nsame time. Common to all, however, is the adsorption\nof hydrogen in the first place. Therefore it is important\nto understand and to be able to predict the solution, re-\nspectively trapping of H at vacancies, dislocations, grain\nboundaries, and in areas of residual strain in the mi-\ncrostructure or the stress field of crack tips. At the same\ntime, there is the need to investigate the effects that H\nis causing at these defects. Only with a thorough un-\nderstanding of these phenomena, multi-scale mechanical\nmodels of hydrogen transport and embrittlement, and\nthus methods to prevent H embrittlement can be devel-\noped.\nAb initio density functional theory (DFT) calculations\nare a powerful tool to determine solution and trapping\nenergies and interpret them in terms of the electronic\n∗a.azocar.guzman@fz-juelich.de\n†rebecca.janisch@rub.destructures. Several DFT studies have confirmed the ten-\ndency of H to segregate to grain boundaries and the effect\nof alloying elements thereon, e.g [2–7], or investigated the\ntrapping of H in vacancies in the bcc [8, 9] and fcc Fe\n[10] lattice. The latter studies also discuss the maximum\nsolubility of H at these defects. Even the solubility of\nH at dislocation cores can be estimated [11] and com-\npared to those at other defects. However, the resulting\npartitioning should depend significantly on the H chem-\nical potential and other factors, such as stresses in the\nmicrostructure. These two aspects have so far been ne-\nglected in the literature.\nIn the study at hand, the focus is on grain bound-\naries, which play several roles in the context of mechan-\nical properties of the material, even without hydrogen.\nThey are known to have a significant impact on the de-\nformability, strength, and fracture toughness of struc-\ntural materials, such as iron and iron alloys. In hydrogen\ncharged systems, they provide trapping sites and thus re-\nmove mobile hydrogen from the grain interior, but they\ncan also act as diffusion paths. Furthermore, they are\nexpected to be prone to hydrogen enhanced decohesion\n(HEDE), leading to intergranular fracture. The HEDE\nmechanism is mostly attributed to a weakening of inter-\natomic bonds, due to the charge transfer between H and\nthe host metal atom [12, 13]. Again, electronic structure\ncalculations represent a robust method to elucidate this\nmechanism at the atomic and electronic scale.\nThe decohesion of cleavage planes in bcc Fe due to HarXiv:2403.04741v1  [cond-mat.mtrl-sci]  7 Mar 20242\npresence was investigated by Katzarov and Paxton [14],\nwhere a reduction of the cohesive strength from 33 GPa\nto 22 GPa (approximately 33%) was reported. How-\never, similar studies in symmetrical tilt grain boundaries\n(STGBs) did not find a such a strong reduction, although\nHEDE is expected to occur at GB planes, promoting in-\ntergranular fracture. Tahir et al. [5] reported only a\nreduction of 6% at the Σ5(310)[001]; while, Momida et\nal.[15] found a 4% reduction of the Σ3(112)[1 ¯10] ideal\nstrength. The methodological differences between the\ntechniques used to calculate the cohesive properties were\naddressed and reconciled in [16], where it is shown that\nif the excess elastic energy which occurs during the sepa-\nration process is taken into account, there is a significant\nreduction of the GB strength by the presence of H, but it\nis not higher than that of the bulk (001) and (111) cleav-\nage planes in the investigated range of H concentration\nat the GB.\nThis introduces the next aspect, since, as will be shown\nin the paper at hand, it is not only important to correctly\ndetermine the excess elastic energy during separation of\nthe grain boundary, but also to consider much higher lo-\ncal concentrations of H at the GB plane than what is\nusually studied in DFT calculations, when only one seg-\nregation site per structural unit is assumed for hydrogen\natoms. In this work, we propose a method to identify the\ninitial configurations of H atoms at higher coverage of the\nGB, based on an algorithm that determines the voids in\nthe atomic structure and the possible segregation sites.\nThe solution energies then show that, similar to the va-\ncancies, [10] most GB structural units can capture several\nH atoms, leading to an even more pronounced reduction\nin strength.\nTo add to the complexity, it must be noted that the\nconcentration-dependent solution energies also vary with\na variation of the H chemical potential, and, most im-\nportantly for HEDE, they depend on the separation at\nthe GB plane, i.e. the stress-dependent excess volume of\nthe GB. In other words, the solution energy is a function\nof the reference H chemical potential, the local concen-\ntration, and the local stress. All these quantities can be\ncoupled in a thermodynamic framework as introduced by\nMishin [17] and Van der Ven and Ceder [18, 19], but to\nthe best of our knowledge has not been implemented for\nGBs so far.\nFurthermore, Hirth and Rice [20, 21] formalized the\nthermodynamic limits of the fracture process: (i) the\nlimit of constant composition: the separation is faster\nand the interfaces may have empty segregation sites and\n(ii) limit of constant chemical potential: a slower separa-\ntion that occurs at a time scale that allows diffusion of the\nsolute atoms to the interface. In-situ hydrogen charged\ntensile tests of high-strength steels were performed by\nDepover et al. [22], finding that HE increased at lower de-\nformation speeds. Further numerical methods elucidated\nthat the stress dependency of the diffusion coefficient lead\nto different H concentration profiles [23]. In this study\nwe address both scenarios by calculating solution energiesfor several constant compositions, but also as a function\nof the H chemical potential for different coverage at the\ngrain boundary and relating them to the local stress at\nthe GB. This recipe on the one hand allows to predict\nthe effective strength as a function of chemical poten-\ntial by equilibrating the concentration during the sepa-\nration process, as demonstrated for bulk cleavage planes\nby Katzarov et al [14]. On the other hand, it can also be\nused to analyse the partitioning of H between different\ndefects in the microstructure during mechanical loading,\nas e.g. between the Σ5 and Σ3 STGB in this study. With\nthis, a complete picture of the hydrogen distribution in a\nmicrostructure under various conditions can be obtained.\nThis paves the way to identify the weakest links of a de-\nformed microstructure and investigate ways to stabilize\nthem. The latter point is addressed exemplarily by a\nstudy of the influence of the alloying elements C,V,Cr,\nand Mn in this paper.\nII. METHODOLOGY\nA. Technical details\nWe investigate the effect of the segregation of hydro-\ngen together and without additional alloying elements to\ngrain boundaries in bcc Fe. Total energies have been\ncalculated using density functional theory (DFT) as im-\nplemented in the Vienna Ab Initio Simulation Package\n(VASP) [24, 25], in a spin-polarized fashion. The elec-\ntron exchange-correlation was estimated with the gen-\neralized gradient approximation (GGA) of the Perdew-\nBurke-Ernzerhof (PBE) [26] form and the core-valence\ninteraction with the projector augmented-wave (PAW)\nmethod [27, 28]. The convergence criteria for the elec-\ntronic iteration was set to 10−6eV and the equilibrium\nstructures were relaxed until the forces on each atom were\nbelow 10−3eV/˚A. The k-point mesh was generated using\nMonkhorst-Pack grids [29].\nTwo symmetrical tilt grain boundaries (STGB) struc-\ntures were chosen: Σ5(310)[001] 36.9◦and Σ3(112)[1 ¯10]\n70.53◦. The constructed supercells are shown in Fig.\n1(a) and 1(b), respectively. The Σ5 STGB supercell\nhas 40 bcc Fe atoms, 20 atomic layers, and lattice vec-\ntors: 3 a0[310]×1.5a0[¯130]×a0[001]. The Σ3 STGB has\n96 bcc Fe atoms, 24 atomic layers, and lattice vectors:\n4a0[112] ×a0[11¯1]×2a0[1¯10]. The value of a0is 2.837\n˚A for Fe, in agreement with the literature [30]. For these\ncells of pure iron, the k-point grids consist of 2 ×4×8 (Σ5)\nand 4 ×2×4 (Σ3), and are scaled accordingly if the cell\nsize is changed.\nFor the cases with C segregation, due to long-range\ninteraction of the C atoms, an additional cell was con-\nstructed with 30 atomic layers (60 bcc Fe atoms), ex-\ntending the lattice vector in the [310] direction to 4 .5a0.\nFor both H and C cases, the supercell was doubled along\nthe [001] direction in order to access lower concentrations.\nThe stable configurations of the GB supercells were ob-3\ntained by optimization in the direction perpendicular to\nthe GB plane, in order to accommodate the excess length\nof the GB [31]; which is 0.31 ˚A for Σ5 and 0.16 ˚A for\nΣ3. The calculated GB energy for the Σ5 GB is higher\nthan for the Σ3, 1.58 J/m2and 0.43 J/m2, respectively.\nSimilarly, the excess length is higher in the case of the Σ5\n(0.31 ˚A and 0.16 ˚A , respectively), which is attributed to\nthe local atomic environment being more closed-packed\nat the Σ3 GB plane.\nFIG. 1. Structure of the (a) Σ5(310)[001] and (b)\nΣ3(112)[1 ¯10] STGBs. The Fe atoms are indicated in blue,\nwith the atoms of the structural unit of the GB delineated in\ngrey.\nB. Solution energy\nThe solution energy, Esol, per interstitial atom can be\nobtained using the calculated total energies with different\nconcentrations of H and C at the GB, as follows:\nEsol=EGB+X\ntot −EGB\ntot−P\nX=H,X=CNXµX\nNH+NC(1)\nwhere EGB+X\ntot is the total energy of the GB, either\nin pure iron, or with segregated substitutional elements\nCr, V, or Mn, and containing NH+NCsegregated in-\nterstitials of type X=H and/or X=C. Correspondingly,\nEGB\ntotis the total energy of the GB, either in pure Fe or\nwith segregated substitutional elements Cr, V, or Mn,\nbut without any interstitial elements. The chemical po-\ntential of H or C, µX, refers to the reference value of H\nin a H 2molecule (-3.385 eV) or C in diamond (-9.120\neV). Finally, NXis the number of interstitial atoms in\nthe supercell.C. Ab initio tensile tests and the first principles\ncohesive zone model\nA full characterisation of the GB cohesion requires, be-\nsides the work of separation, also the calculation of the\ntensile strength of the interface [32]. The decohesion pro-\ncess can be studied through the so-called ab initio tensile\ntest. Although it has been extensively used for calculat-\ning cohesive strength of material systems [33], there are\ncertain intricacies that require careful implementation.\nThe different approaches are described and compared in\ndetail in [16]. One way to perform such a test is to intro-\nduce a certain displacement, ∆, in the supercell between\nthe two grains defining the GB plane (or the bulk cleavage\nplane) and calculating the energy, E, while keeping the\npositions of the atoms fixed. The energy-displacement\ndata can be fitted using the universal binding energy re-\nlationship (UBER) [34] and the ideal cohesive or frac-\nture stress, σcoh, can be obtained from σcoh=∂E/A∂ ∆,\nwhere A is the area perpendicular to the cleavage plane.\nThe maximum value of the stress corresponds to the co-\nhesive strength.\nThe case of the rigid tensile test describes ideal brit-\ntle cleavage under loading mode I. However, the alterna-\ntive approach, a tensile tests in which the relaxation of\natomic positions is allowed, is required to correctly pre-\ndict segregation sites under stress and understand the\neffect of segregating atoms on the structural changes. In\nthis case, due to the release of elastic energy, the output\nscales with system size, as shown by Nguyen and Ortiz\n[35] and Hayes et al. [36] A solution was proposed by Van\nder Ven and Ceder [18, 37], the first-principles cohesive\nzone model, which allows the derivation of a traction-\nseparation law independent of the size of the system by\nusing not the total, but excess energies. This approach\nhas been extended to systems with GB planes and it is\nimplemented in the present work, the detailed description\nof the method can be found in [16].\nTwo different types of calculations are required for this\nexcess energy approach: rigid grain shifts with subse-\nquent relaxation (RGSrel) of the GB cell and a homoge-\nneous elongation of a single crystal (HEC) in the same\norientation as the grain boundary cell. The latter serves\nto determine the stress as a function of interplanar spac-\ning in the bulk. This information can then be used to\nidentify the stress in a GB supercell. The excess energy\nand length are calculated through the difference between\nRGSrel and HEC at the same stress. In the case of the\ncohesive zone containing a segregated GB plane, the ex-\ncess energy and length with a defect (impurity and GB),\neD\nexandlD\nex, are calculated as follows:\neD\nex(σ) =\nEGB+X\nRGSrel(σ)\nA−(np−1)Ebulk\nHEC(σ)\nA−NXµX(2)4\nlD\nex(σ) =\n1\n2\u0002\nLGB+X\nRGSrel(σ)−(np−1)LFe\nHEC(σ)\u0003\n−∆LGB(3)\nEGB+X\nRGSrelis the total energy of the GB supercell with\nNinterstitial segregants, obtained from the RGS with\nrelaxation. Ebulk\nHEC is the total energy per atomic plane\nfrom the HEC pure Fe bulk calculation. The number\nof atomic planes perpendicular to the tensile axis is de-\nnoted by npandAis the area projected onto the cohesive\nzone. Both energies are at the same stress, σ, obtained\nvia the interplanar spacing. In equation (3), LFeGB +X\nRGSrel\nis the total length of the GB supercell in the direction\nof elongation and LHEC is the spacing between two ad-\njacent planes in the HEC pure Fe bulk case. ∆ LGBis\nthe excess length of the pure Fe grain boundary at zero\nstress.\nFinally, the opening of the cohesive zone, δ, can be\nobtained from δ=lex−d0, with d0being the equilibrium\ninterplanar distance at zero stress. The excess energy\nvs. the opening of the cohesive zone can again be fitted\nto an UBER curve, and the derivative corresponds to the\ntheoretical cohesive stress, as per the following equation,\nσcoh=1\nA∂eD\nex\n∂δ(4)\nThe difference between the definition of excess length\nin equation (3) and the original one in [18] is the addi-\ntional ∆ LGB, which defines the opening of the cohesive\nzone as zero if the GB is free of segregated atoms and\nfully relaxed. Without this addition, even the pure GB\nwould have a finite opening, even if it was stress-free.\nHowever, this is a mere convention and does not change\nthe derivative, i.e. the cohesive stress vs. opening of the\ncohesive zone.\nIn all tensile tests performed in the present work, the\nPoisson contractions are suppressed, which means uniax-\nial strain loading. From this, a traction-separation law\nfor continuum fracture simulations under mode I loading\nand plane strain conditions can be derived. Under such\na fracture mode, a triaxial state at the crack tip occurs\n[38], equivalent to the one obtained with the tensile tests\nof this work.\nD. Identifying segregation sites\nOne of the open questions of H embrittlement mecha-\nnisms is how to predict the local concentration of H at\ndifferent defects, specifically grain boundaries in the case\nof HEDE; and how the local concentration fo H changes\nunder mechanical load. In order to identify the possible\nsegregating sites for H atoms at the Σ5 STGB, we have\ncalculated the solution energy surface of one H atom in\nand in the vicinity of the structural units which definethe GB, at equilibrium and under strain. The solution\nenergy surface is obtained as the difference between the\nrigid energy of the system with H placed anywhere in\nthe a selected volume and the total energy of the most\nfavorable configuration of 1 H atom at the GB.\nFigure 2 shows the solution energy surface in a plane\nperpendicular to the grain boundary at z= 0 with excess\nlengths corresponding to 0, 3 and 10 % elongation. In the\nequilibrium GB (2(a)), the minimum is located in the\ncenter of the trigonal prism created by the Σ5 structural\nunit, which is in agreement with the selected sites for H\nin this system found in the literature [5–7, 15, 16]. The\nmost energetically favorable region is extended as the GB\nis strained up to 3% (2(b)). However, when higher values\nof strain are reached (2(c)), the minimum separates into\ntwo distinct regions and more minima emerge around the\ncentral Fe atom (highlighted by red arrows). This means\nmore H segregating sites are available in the Σ5 STGB as\nit expands. These sites can be identified through such en-\nergy surface calculations, but this approach is extremely\ntime-consuming.\nAn alternative method for identifying the segregating\nsites is proposed based on the algorithm of a polyhedral\nunit model by Banadaki and Patala[39]. This algorithm\nidentifies fcc GB atomic structures by creating a three-\ndimensional array of polyhedra from the Voronoi vertices\npresent in the structure, using a clustering technique it\nis possible to classify the geometries of the observed GB\npolyhedral units by comparing with a database of hard-\nsphere packings. Here, we have implemented this algo-\nrithm for bcc lattices and analysed the individual voids in\nthe structure available for segregation. The python im-\nplementation of the algorithm is based on the Voro++ [40]\nandpyscal [41] software, the void analysis code is avail-\nable in a public repository [42]. The identified voids for\nsegregation of atoms at the GB are compared with the\nmost favorable positions found with the energy surface\ncalculations. At 10% elongation, in both Fig. 2(c) and\n3(a), comparable results from both techniques are ob-\ntained: two distinct minima can be observed inside the\ntrigonal prism of the structural unit and several smaller\nsites around the center Fe atom. Yet, the void analy-\nsis from the polyhedral unit model is substantially more\nefficient.\nThe concentrations of H and C chosen for the deco-\nhesion study were selected from the numbered sites in\nFig. 3(a),(b) and 3(c),(d), respectively. For Σ5 STGB:\nFe80H2, Fe 80H4, Fe 80H6and Fe 40H4with only 1 H per\nstructural unit; Fe 40H6as a mixed case and increasing\nup to 4 H atoms per unit Fe 40H8, Fe40H12and Fe 40H16.\nSince C is a bigger atom, the void analysis was performed\nwith an already segregated C at the GB (Fig. 3(b))\nand the chosen concentrations are: Fe 120H2, Fe 120H4,\nFe120H6, Fe60H4and Fe 60H8. And finally for Σ3 STGB:\nFe96H8, Fe 96H16, Fe 96C4and Fe 96C8. These concentra-\ntions are translated to a GB coverage value, θ, calculated\nas the ratio of H or C atoms per Fe at the GB. It can be\nobserved in Fig. 1(c) and (d) that the GB layers can be5\nFIG. 2. Cross-section of the solution energy surface of the structural unit of Σ5 STGB in the Fe+H system. The H atom is\nplaced in a range of ±2˚A from the GB plane in the x direction. The H atom is placed every 0 .25˚A in x=[310] and y=[ ¯130]\ndirections. The [001] direction is kept constant at z= 0. The H atom was placed at a distance no closer than 1 ˚A from the\nin-plane Fe atoms.\nFIG. 3. Void analysis at 10% elongation of the pure Fe GB ((a) and (b)) and the GB with segregated C atoms ((c) and (d)).\nVoids are identified with blue color, grey atoms are Fe, and red C. The Σ5 Fe STGB corresponds to Fig. (a) and (c) and Σ3\nFe STGB (b) and (d).\nidentified from the interlayer spacing deviation from the\ngrain interior; from this, the Fe GB atoms are selected\nas 6 atoms for Σ5 and 4 atoms for Σ3.\nIII. RESULTS\nA. Decohesion at constant concentrations of H\nInitially, the tensile test is carried out for several fixed\nconcentrations of H at the GBs. This is done by step-wise\nplacing a H atom in each structural unit, until all units\nare occupied by one atom, then increasing the number of\nH per structural unit. The sites were chosen according to\nthe void analysis described in Section II D. The coverageof the GB with solute atoms then is the ratio of the solute\natoms per GB Fe atom, where GB atoms are those which\ndefine the structural units. The corresponding area con-\ncentrations and number of atoms per structural unit are\nfound in Appendix A.\nThe excess energy and opening of cohesive zone calcu-\nlated from Equations 2 and 3 are plotted in Fig. 4(a).\nThe work of separation ( Wsep) is significantly reduced\nwith increasing H coverage; from 3.4 J/m2to 1.2 J/m2\nat 1.33 coverage. From the UBERfit of the excess en-\nergy curves the cohesive stress is calculated and shown\nin Fig. 4 (b). Similarly to the work of separation, the\ncohesive strength is significantly reduced with increasing\nH coverage, from 20.6 GPa to 8.2 GPa at 1.33 coverage.\nThe same recipe was applied to the Σ3 STGB. The6\nFIG. 4. (a) Excess energy and (b) Cohesive stress as a func-\ntion of the opening of the cohesive zone for the Σ5 STGB\nwith varying H coverage (ratio of H/Fe atoms) at the GB.\nresulting excess energy and cohesive stress curves as a\nfunction of opening of the cohesive zone are shown in\nAppendix B.\nFrom the stress as a function of opening, one can ob-\ntain the maximum, which is the cohesive strength of the\ngrain boundary for this particular coverage. The cohe-\nsive strength as function of coverage is shown in Fig. 5\nfor both grain boundaries. For comparison, the equiva-\nlent results for the completely rigid scheme are shown as\nwell, where the ideal cohesive stress is calculated accord-\ning to equation (4).\nAlthough the difference between the rigid and relaxed\ntensile tests can be up to 6 GPa, the general trends iden-\ntified in both cases coincide. There are two different\nregimes, related to the occupancy of H in the same GB\npolyhedral unit, or structural unit. Up to 0.5 H coverage,\nonly one H atom occupies the structural unit and the re-\nduction of strength is weak. While between 0.5 and 1.33\nthe H occupancy is increased, leading to a much more\nsignificant reduction in strength. Also note that even for\nthe highest value of H coverage, the Σ3 grain boundary\nremains stronger than the Σ5.\nFIG. 5. Cohesive strength (= peak value of the cohesive\nstress) wrt. H coverage, obtained via different schemes (re-\nlaxed and rigid calculations) for Σ5 and Σ3 STGBs.\nFIG. 6. GB solution energy of H and C atoms at equilibrium\nwith varying coverage, for (a) Σ5 and (b) Σ3 STGBs.\nB. Hydrogen solubility at zero stress and constant\nchemical potential\nIn order to estimate if the coverage values that were\nused in the previous section are realistic, i.e. energeti-\ncally favorable, the solution energy of the solute atoms\nfor relaxed atomic positions were calculated according to\nequation (1), i.e. for zero opening of the cohesive zone\nand the chemical potential of H in a H molecule. The\nresult is shown in Fig. 6.\nRegarding the Σ5 GB in Fig. 6(a), it can be seen that\nall chosen coverage values of H and C at the GB have\na negative solution energy, meaning it is more favorable\nfor the atoms to be at the GB than at their respective\nreservoirs. At lower concentrations of C the solution en-\nergy is more negative than that of H, but at increasing\nconcentrations they become comparable. In the Σ3 case,\nhowever, due to a more closed-packed structure at the\nGB with less available space for segregation, when there\nis more than one atom in the structural unit the solubility\nof H is not favorable.7\nFIG. 7. Solution energy of H at the Σ5 STGB at (a) 0 GPa\nand (b) 20 GPa, as a function of the chemical potential dif-\nference, ∆ µH. The dashed lines indicate different values of H\ncoverage θat the GB.\nC. Solution energy as function of stress and\nchemical potential\nTo estimate the effect of residual or applied stresses\non the hydrogen distribution, as well as to see how much\nit can be influenced by varying the chemical potential\nof H, the solution energy is calculated as defined in the\nfollowing equation:\nEGB\nsol,H(σ) =EFe+H\ntot (σ)−EFe\ntot(σ)−nHµH\n2A(5)\nHere, the total energies of the pure Fe and Fe+H\nGB systems are subtracted at the same stress, utilizing\nthe excess energy from the first-principles cohesive zone\nmodel, defined in equation (2). The chemical potential,\nµHis now a variable which decreases from the value of\nthe reference chemical potential, µH2\nH, which is that of the\nhydrogen molecule down to −0.4eV+µH2\nH. Figure 7(a)\nshows the solution energy as calculated in equation (5)\nat the Σ5 in the style of a defect phase diagram [43]. It\ncan be seen how the H coverage increases with increasing\nchemical potential.\nWe have added a third dimension to such a defect\nphase diagram by repeating this calculation at different\nvalues of stress. This allows us to estimate how much\nthe two grain boundaries compete for H under mechani-\ncal loading. For demonstration, in Fig. 7(b) the case ofthe Σ5 STGB for 20 GPa is shown, which corresponds\nto the stress just before the cleavage of the GB plane oc-\ncurs. The equivalent diagrams for the Σ3 STGB can be\nfound in the appendix B (Fig. 13).\nIn Fig. 8, the two boundaries and stress states are com-\npared, it shows the resulting solution energy at the GB\nwrt. the chemical potential difference at different values\nof applied stress. In each case the concentration increases\n(solution energy decreases) with increasing chemical po-\ntential, indicating the sequential filling of the available\nsegregation sites at the GB plane. Note, however, that\nat the Σ5 STGB, the solution energy increases, as the\nstress increases, while for the Σ3 STGB, we observe the\nopposite. Thus, the maximum coverage of the Σ5 at\nhigher applied stress is reduced to θ= 0.08, while at zero\nstress it reaches θ= 1.00. This leads to the important\nphenomenon, that with increasing stress, the most favor-\nable GB for H segregation is the Σ3 instead of the Σ5,\nopposite to the situation at zero stress, as observed also\nin Fig. 6.\nD. Cohesion enhancing effect of carbon\nIn the case of steels, it is necessary to study the influ-\nence of carbon to understand the embrittlement mecha-\nnisms and whether the cohesion enhancing effect of C can\ncounter the detrimental impact of H. Figure 9 presents\nthe results of the calculated cohesive strength as a func-\ntion of the C coverage. The strength of the Σ5 STGB in-\ncreases linearly with a higher local C concentration at the\nGB plane. The increase from 20 .6 GPa up to 29 .8 GPa\nrepresents a maximum of 45%. Although the pure Fe Σ3\nhas a higher strength than Σ5, the cohesion enhancing\neffect of C is limited to a 17% increase, from 29 .1 GPa\nto 33 .9 GPa, with a negligible difference between both C\ncoverage values studied. The resulting cohesive strength\nof the ab initio tensile test using rigid grain shifts is also\nreported, labeled as “rigid energy”, while there is negli-\ngible difference between both procedures for the Σ3, the\nFIG. 8. Solution energy of H at the Σ5 and Σ3 STGB as\nfunction of the chemical potential difference for selected stress\nstates. The coverage values are the maximum values reached\nfor the corresponding applied stress.8\nFIG. 9. Cohesive strength (= peak value of the cohesive\nstress) wrt. C coverage, obtained via different schemes (from\nexcess and rigid energies) for Σ5 and Σ3 STGBs.\nmore open Σ5 has a considerable difference of 10 GPa.\nThis indicates that the energy relaxation is needed to\nfully understand the effect of segregating atoms at the\nGB and is crucial in the case of defects which allow more\navailable space for segregation [16].\nAnother mechanism of interest in the case of ferritic\nsteels is the C and H interaction. In order to under-\nstand the co-segregation effect of C and H on the co-\nhesive properties of the Σ5 STGB, two different cases\nwere investigated. In the first case, the supercell was\nconstructed with a coverage θ= 0.33 and the number of\natoms segregating to the structural unit was limited to\none. The resulting cohesive strength of the varying C and\nH co-segregation cases can be observed in Fig. 10(a). In\nthe second co-segregation case studied two atoms sit in\nthe structural unit with a total coverage θ= 0.67 (Fig.\n10(b)). The cohesive strength in both cases is reduced\nwith increasing H presence at the GB. In the first case,\nthe co-segregation behavior falls in the expected mix-\ning behavior at higher H and C concentrations, while in\nthe case at higher solute coverage, the results indicate\na slightly detrimental effect, where the strength of the\npure Fe GB is reduced 1 .6 GPa. This effect is only no-\nticed when the full structural relaxation of the cohesive\nzone is allowed, when the energies are obtained rigidly,\nthe strength reduces linearly.\nE. Effect of substitutional alloying elements\nUnderstanding the embrittlement mechanism of H in\nferritic steels requires insight into the effect of common\nalloying elements and impurities often found in steels. In\nthe present work substitutional transition metals V, Cr\nand Mn are introduced in the Fe+H Σ5 STGB system.\nThe supercell creation and optimized configurations can\nbe found in the work of Subramanyan et al. [6]. The\ncomposition of the substitutional elements in the Fe su-\npercell corresponds to Fe 38X2with X = V, Cr, or Mn.\nFIG. 10. Cohesive strength vs. different H and C co-\nsegregation cases for Σ5 STGB with varying H and C fraction\nper structural unit (SU): in (a) the maximum number of so-\nlute atoms per SU is one, total solute coverage = 0 .33 and in\n(b) one SU contains two solute atoms, total solute coverage\n= 0.67.\nThe V substitutes an Fe atom sitting at the GB plane,\nwhile Cr and Mn substitute a matrix atom that sits in\nthe layer next to the GB. The chosen coverage values of\nthe H atom are : 0 .33, 0 .67 and 1 .33, corresponding to\n1H, 2H and 4H at the structural unit of the GB.\nThe effect of the co-segregation of substitutional ele-\nments and H atoms on the solution energy of H and the\ncohesive strength can be observed in Fig. 11. When only\none atom sits at the structural unit, the influence of the\nsubstitutional elements on the H solubility at the GB is a\nreduction of up to 0 .04 eV/atom wrt. the pure Fe GB, as\nobserved in [6]. However, at the highest H coverage the\neffect is enhanced, reducing the solubility of H by 0 .12\neV/atom, in the case of V. On the other hand, at a high\nlocal concentration of H at the GB, the strengthening\neffect of the substitutional atoms is considerable, vana-\ndium increases the strength by 5 .5 GPa, chromium at the\nGB increases the strength by 9 .8 GPa; and, manganese\nincreases the cohesive strength by 10 .1 GPa.\nIV. DISCUSSION\nThe present work investigates hydrogen enhanced de-\ncohesion (HEDE) in bcc Fe symmetrical tilt grain bound-\naries (STGBs): Σ5(310)[001] 36.9◦and Σ3(112)[1 ¯10]9\nFIG. 11. (a) Solution energy of H at GB and (b) cohesive\nstrength vs. H coverage of a GB decorated with alloying ele-\nments: V, Cr and Mn.\n70.53◦.\nThe cohesive properties of the GBs are calculated\nthrough ab initio tensile tests. However, stress and strain\nin the microstructure do not only change the trapping\nstrength of the solute atoms, but also the number and\narrangement of trapping sites at the GB (see energy sur-\nface of the Fe+H system in Fig. 2). Thus, a novel method\nfor identifying relevant trapping sites in the structure has\nbeen proposed, based on the voids of the polyhedral unit\nat the GB [39]. The sites obtained through the void anal-\nysis method were compared with the sites obtained ac-\ncording to the energy surface and the proposed method\nproved to be a more efficient option. Once the trap-\nping sites were found, the solubility of H calculated at\nzero stress indicated that the concentration of the solute\natoms can be increased locally at the GB; considering\nthan more that one H atom can sit in the same struc-\ntural unit.\nOne of the key findings of this work is that the pres-\nence of H can reduce the cohesive strength of the Σ5 GB\nup to 60% and Σ3 GB up to 16% (see Fig. 5). Such a\nstrong effect has not been reported in literature of first-\nprinciples studies of HEDE in GBs. The work of Tahir et\nal.[5] found that a monolayer of H reduced the strength\n6%, at a coverage of one H atom per structural unit of\nthe Σ5 GB. Similarly, Momida et al. [15] reported a\n4% reduction of the Σ3(112) ideal strength. In contrast,\nKatzarov, and Paxton [14] calculated a decrease from 33\nGPa to 22 GPa with increasing H concentration in the(111) cleavage plane in bcc Fe, using tight-binding cal-\nculations. The strong reduction of the cohesive strength\nat the GB plane is only observed at higher local concen-\ntrations of H when more than one solute atom sit at the\nstructural unit.\nRegarding the difference between the STGBs, it was\nobserved that Σ5 had a considerable effect of H as com-\npared to the Σ3. Although in both cases the hydrogen\nembrittlement mechanism is due to the charge transfer\nbetween the Fe host and the H, the difference between\nboth GBs is attributed to the local atomic environment\nand the amount of host atoms the H impurities interact\nwith at the interface. The Σ5 was chosen as a sample of\nstructures with a more open atomic environment, with\na higher excess length (0 .31˚A) and higher energy (1 .58\nJ/m2) than the Σ3. Meanwhile, the Σ3 is chosen as an\nexample of a close-packed structure with bulk-like envi-\nronment and lower excess length and energy (0 .16˚A and\n0.43 J/m2, respectively). The local atomic environment\nat the GB is associated to the bond length and excess\nvolume, this geometric criterion has been proposed for\nC segregation to bcc Fe GBs [44] and for H segregation\nto Ni GBs [45]. This observation can be further clarified\nand formalized, in this work, the GB criterion is defined\nin terms of the number of sites available for segregation\nat the GB and the size of the interstitial voids identified.\nThe cohesive properties of the segregated grain bound-\naries also strongly depend on the thermodynamic limits\nof the separation process. According to Hirth and Rice\n[20, 21], these properties vary between the limit of con-\nstant composition, and of constant chemical potential.\nThe results presented in Section III A correspond to con-\nstant composition, where the separation is faster than the\ndiffusion of the H atoms. Contrarily, the limit of constant\nchemical potential refers to a slower separation of the in-\nterface, where some segregation sites can be filled, thus\nchanging the composition. In Section III C, the solution\nenergy is calculated under mechanical load in order to\nelucidate the effect of the chemical potential on the co-\nhesive properties. The comparison shows another key\nfinding of this work: The solubility of H at the Σ3 STGB\nis significantly less sensitive to both, changes in the chem-\nical potential and an increase of the applied stress than at\nthe Σ5. In the latter case, it decreases drastically as the\ncohesive strength of 20 GPa of the grain boundary is ap-\nproached. Also, there is a cross-over of solubility energies\nbetween Σ5 and Σ3 in Fig. 8, with an increasing advan-\ntage for the Σ3 as the chemical potential is increased.\nThis means that for a suitably chosen µH, the whole sys-\ntem can be stabilized by driving the H towards the Σ3\nas the stress increases. This is further enabled by the\nfact that the energy barriers at the Σ5 GB decrease with\nincreasing separation, as can be seen in Fig. 2, which\nmeans that the traps become more shallow. Of course,\nconsidering only two grain boundaries as potential traps\nis a very artificial scenario, but the study demonstrates\nhow the stresses in the microstructure and the chemical\npotential of H can completely change the picture which is10\nobtained for DFT calculations at constant coverage, see\nFig. 5.\nIf the fracture is fast, in the sense that H will not re-\ndistribute, a high coverage at the weaker grain boundary\nand significant embrittlement must be expected. Thus,\nanother important factor to consider is how the cohesion\nof the GB can be stabilized by adding alloying elements.\nThe first element that comes to mind when talking about\nsteel is C, but also the substitutional atoms V,Cr, and\nMn are interesting candidates. The interplay of these el-\nements has been investigated already in [6], but at rather\nlow concentrations of H. However, as we know now, that\ncoverage range underestimates the effect of segregation.\nThus, in the study at hand the range of coverage values\nstudied was increased.\nWe started with the segregation of C, as well as the\nco-segregation of C and H, where both solutes compete\nfor interstitial sites at the GB plane. Carbon is known\nto have a cohesion enhancing effect on the Σ5 STGB,\nas reported in previous works [5, 6, 16]. In the present\nstudy, C was found to increase the strength of the Σ5\nGB from 20 .6 GPa to 29 .8 GPa (up to 45%) and that\nof the Σ3 GB from 29 GPa to 33 .9 GPa (up to 17%).\nThe cohesion enhancing effect of C is limited at higher\nconcentrations of C at the GB, carbide formation was not\nconsidered in this study.\nAnother aspect that was investigated was if the pres-\nence of C in the Fe+H system is able to counteract the\ndetrimental effect of H on the cohesive properties of the\nGB (see Fig. 10). Two cases of the co-segregation of\nC and H were selected, based on the total solute cover-\nage. In neither of the cases the presence of C was able to\novercome the negative effect of the H segregation.\nA different story is the co-segregation of H with sub-\nstitutional alloying elements commonly present in ferritic\nsteel, such as V, Cr and Mn. The influence of these ele-\nments in the cohesive strength of the Σ5 STGB is limited\nat lower coverage of H ( θ= 0 and 0 .33), and only when\nthe H coverage increases up to 1 .33 is a considerable ef-\nfect observed. At the highest H coverage, the strength\nof the pure Fe GB is reduced by 60%, when Cr and Mn\ndecorate the GB the reduction of the strength is of 13 .8%\nand 12 .1%, respectively. Mn is found to be the alloying\nelement which leads to the least reduction of strength\nin the presence of H. This finding is in agreement with\nKhanchandani and Gault [46], where an atom probe to-\nmography study on Twinning-Induced Plasticity (TWIP)\nsteels found increased HEDE in Mn-depleted GBs. On\nthe other hand, the presence of V at the GB signifies\na strength 35% lower than the pure Fe GB, having an\noverall beneficial effect considering the solubility of H is\n−0.05 eV/atom, higher than Cr and Mn. Although the\nimpact of these substitutional elements at the GB is not\ncompletely negate the detrimental effect of H at the Fe\nSTGB, the co-segregation of such elements significantly\ncounteract the influence of H. Thus, it is necessary to\ndiscern the role of the H interaction with other alloying\nelements at the GB, specially at higher local concentra-tions of H, where a higher impact is expected.\nV. CONCLUSIONS\nFirst-principles calculations have been carried out\nto investigate the segregation of H and C to bcc Fe\nsymmetrical tilt grain boundaries: Σ5(310)[001] and\nΣ3(112)[1 ¯10]. In order to identify the trapping sites at\nthe GB a novel method has been implemented, based on\nthe polyhedral unit model. This method is compared\nwith the solution energy surfaces of H at the Σ5 GB un-\nder strain and it proves accurate and more efficient as\na site identification technique. Employing this method\nallowed the increase of the local H concentration at the\nGB in order to further understand HE at Fe GBs.\nThe hydrogen enhanced decohesion (HEDE) mecha-\nnism is observed in both studied GBs. The Σ3 GB was\nobserved to have a lower susceptibility to H embrittle-\nment, opposed to the Σ5 GB. This observation is associ-\nated with the GB geometry, where the more open local\natomic of the Σ5 GB translates to a detrimental effect on\nthe cohesive properties by the presence H. Future works\ncould consider a formalization of the relationship between\nthe GB geometry and the cohesive properties, specifically\nthe GB geometry in terms of the available space for the\nsegregation of H atoms.\nThe hydrogen solution energy, and thus the expected\nH coverage at a specific grain boundary depends on the\nlocal stress as well as the chemical potential. This de-\npendency is very pronounced for the Σ5 STGB, while\nthe Σ3 GB is only weakly affected. As a consequence,\nassuming fast diffusion of H in the microstructure, there\nis a range of chemical potential for which H atoms should\nre-distribute, depleting the weaker Σ5 STGB and enrich-\ning the stronger Σ3 STGB. This would make the effect\nof H less detrimental. Note that the prediction of this\nrather unexpected effect is only possible due to the ad-\ndition of a third dimension, i.e. the stress acting at the\nboundary, to the defect phase diagram that describes the\nhydrogen solution at the boundaries.\nIf diffusion is slow or hindered, the H distribution\nat zero stress will remain and the Σ5 STGB will fail\nfirst, at a critical stress which can be reduced by 60%\nin comparison to the pure Fe STGB. To prevent HEDE\nat slow diffusion levels, alloying elements can help. In\nthe case of co-segregation of C and H to the GB, C\nexhibited cohesion enhancing properties, although the\neffect is limited at higher local concentration. However,\nthe positive influence of the segregation of substitutional\nelements (Cr, V and Mn) to the Σ5 GB on the cohesive\nstrength of the GB plane is much more pronounced and\nespecially Mn can counteract the effect of H completely.\nThis case study shows the importance of studying\nHEDE at grain boundaries at higher local hydrogen cov-\nerage and at finite stress values. To be able to predict\nthe concentration, the solution energy as a function of11\nstress, chemical potential, and coverage. Only then, the\nproper recipes to prevent HEDE via alloying strategies\nand/or by manipulating the chemical potential of H can\nbe developed.\nACKNOWLEDGMENTS\nThis research has been supported by the German Re-\nsearch Foundation (DFG), projects number 414750139\nand 535248809. The authors acknowledge the com-\nputer resources provided by the Center for Interface-\nDominated High Performance Materials (ZGH, Ruhr-\nUniversit¨ at Bochum) and the Interdisciplinary Cen-\nter for Advanced Materials Simulation (ICAMS, Ruhr-\nUniversit¨ at Bochum).\nAppendix A: H coverage at the grain boundary\nThe coverage of the interstitial sites at the GB is calcu-\nlated based on the ratio of interstitial atoms with respect\nto the matrix Fe atom in the structural unit that defines\nthe GB. The corresponding areal concentration values of\neach configuration considered in this study are presented\nin Table I.\nTABLE I. Coverage, atoms per structural unit (SU) and areal\nconcentration at the Σ5 and Σ3 STGBs.\nSTGB Coverage Atom/SU Areal concentration\n(at/˚A2)\nΣ50.08 - 0 .02\n0.17 - 0 .04\n0.25 - 0 .06\n0.33 1 0 .08\n0.50 - 0 .12\n0.67 2 0 .16\n1.00 3 0 .24\n1.33 4 0 .31\n1.67 5 0 .39\nΣ31.0 1 0 .10\n1.5 - 0 .15\n2.0 2 0 .20\nFIG. 12. (a) Excess energy and (b) Cohesive stress as a func-\ntion of the opening of the cohesive zone for Σ3 STGB with\nvarying H coverage at the GB.\nAppendix B: Decohesion of the Σ3 STGB\nThe excess energy as a function of the opening of\nthe cohesive zone, calculated using equations 2 and 3 is\nshown for the Σ3 STGB in Fig. 12(a). From the deriva-\ntive of the UBER fit w.r.t. the opening, the cohesive\nstress curves shown in Fig. 12(b) are obtained. Accord-\ning to Fig. 6, the coverage θ= 2.0 has a positive solution\nenergy at zero stress.\nThe solution energy curves in Fig. 7 are produced in a\nsimilar fashion as the defect phase diagrams construction\nfrom ab initio calculations [43]. The calculation of the\ndefect phase diagram concept aims to understand a defect\nphase and the transition between phases upon changes\nin the (local) chemical potential. We have added the\nstress in the microstructure as a third dimension. The\ntwo exemplary cases of zero and 20 GPa applied stress\nfor the Σ3 STGB are shown in Fig. 13.12\nFIG. 13. Solution energy of H at the Σ3 STGB as a function of the chemical potential difference, ∆ µH. The dashed lines\nindicate different values of H coverage θat the GB. The applied stress is (a) 0 GPa and (b) 20 GPa.\n[1] M. L. Martin, M. J. Connolly, F. W. DelRio, and A. J.\nSlifka, Hydrogen embrittlement in ferritic steels, Appl.\nPhys. Rev. 7, 041301 (2020).\n[2] Y. A. Du, L. Ismer, J. Rogal, T. Hickel, J. Neugebauer,\nand R. Drautz, First-principles study on the interaction\nof h interstitials with grain boundaries in α- and γ-fe,\nPhys. Rev. B 84, 144121 (2011).\n[3] Z. X. Tian, J. X. Yan, W. Hao, and W. Xiao, Effect of\nalloying additions on the hydrogen-induced grain bound-\nary embrittlement in iron, J. Phys.: Condens. Matter 23,\n015501 (2011).\n[4] B. He, W. Xiao, W. Hao, and Z. Tian, First-principles\ninvestigation into the effect of Cr on the segregation of\nmulti-H at the Fe Σ3 (111) grain boundary, J. Nucl.\nMater. 441, 301 (2013).\n[5] A. Tahir, R. Janisch, and A. Hartmaier, Hydrogen em-\nbrittlement of a carbon segregated Σ5(310)[001] symmet-\nrical tilt grain boundary in α-Fe, Mater. Sci. Eng. A 612,\n462 (2014).\n[6] A. P. A. Subramanyam, A. Az´ ocar Guzm´ an, S. Vincent,\nA. Hartmaier, and R. Janisch, Ab initio study of the com-\nbined effects of alloying elements and H on grain bound-\nary cohesion in ferritic steels, Metals 9, 291 (2019).\n[7] X. Huang and R. Janisch, Partitioning of interstitial seg-\nregants during decohesion: A DFT case study of the Σ3\nsymmetric tilt grain boundary in ferritic steel, Materials\n12, 2971 (2019).\n[8] Y. Tateyama and T. Ohno, Stability and clusterization\nof hydrogen-vacancy complexes in α−Fe : An ab initio\nstudy, Phys. Rev. B 67, 174105 (2003).\n[9] E. R. M. Davidson, T. Daff, G. Csanyi, and M. W. Finnis,\nGrand canonical approach to modeling hydrogen trap-\nping at vacancies in α−Fe, Phys. Rev. Mater. 4, 063804\n(2020).\n[10] R. Nazarov, T. Hickel, and J. Neugebauer, First-\nprinciples study of the thermodynamics of hydrogen-\nvacancy interaction in fcc iron, Phys. Rev. B 82, 224104\n(2010).\n[11] A. S. Kholtobina, R. Pippan, L. Romaner, D. Scheiber,\nW. Ecker, and V. I. Razumovskiy, Hydrogen trapping in\nbcc iron, Materials 13, 2288 (2020).\n[12] L. B. Pfeil and H. C. H. Carpenter, The effect of occluded\nhydrogen on the tensile strength of iron, Proc. R. soc.Lond. Ser. A-Contain. Pap. Math. Phys. Character 112,\n182 (1926).\n[13] A. R. Troiano, The role of hydrogen and other intersti-\ntials in the mechanical behavior of metals, Trans. Am.\nSoc. Met. 52, 54–80 (1960).\n[14] I. H. Katzarov and A. T. Paxton, Hydrogen embrittle-\nment II. analysis of hydrogen-enhanced decohesion across\n(111) planes in α-Fe, Phys. Rev. Mat. 1, 033603 (2017).\n[15] H. Momida, Y. Asari, Y. Nakamura, Y. Tateyama, and\nT. Ohno, Hydrogen-enhanced vacancy embrittlement of\ngrain boundaries in iron, Phys. Rev. B 88, 144107 (2013).\n[16] A. A. Guzm´ an, J. Jeon, A. Hartmaier, and R. Janisch,\nHydrogen embrittlement at cleavage planes and grain\nboundaries in bcc iron — revisiting the first-principles\ncohesive zone model, Materials 13, 5785 (2020).\n[17] Y. Mishin, P. Sofronis, and J. Bassani, Thermodynamic\nand kinetic aspects of interfacial decohesion, Acta Mater.\n50, 3609 (2002).\n[18] A. Van der Ven and G. Ceder, The thermodynamics of\ndecohesion, Acta Mater. 52, 1223 (2004).\n[19] A. Van der Ven and G. Ceder, Impurity-induced van der\nWaals transition during decohesion, Phys. Rev. B 67,\n060101 (2003).\n[20] J. R. Rice, Effect of hydrogen on behavior of materials\n(The Metallurgical Society of AIME (The Metallurgical\nSociety of AIME). Edited by Thompson, A W and Bern-\nstein, I M, 1976).\n[21] J. P. Hirth and J. R. Rice, On the thermodynamics of ad-\nsorption at interfaces as it influences decohesion, Metall.\nMater. Trans. A 11, 1501 (1980).\n[22] T. Depover, E. Wallaert, and K. Verbeken, Fractographic\nanalysis of the role of hydrogen diffusion on the hydrogen\nembrittlement susceptibility of DP steel, Mater. Sci. Eng.\nA649, 201 (2016).\n[23] S. Vander Vennet, K. Verbeken, and T. Depover, A com-\nbined numerical–experimental approach for the critical\nhydrogen diffusion depth in steel, Steel Res. Int. 94,\n2200873 (2023).\n[24] G. Kresse and J. Hafner, Ab initio molecular dynamics\nfor open-shell transition metals, Phys. Rev. B 48, 13115\n(1993).\n[25] G. Kresse and J. Furthm¨ uller, Efficient iterative schemes\nfor ab initio total-energy calculations using a plane-wave13\nbasis set, Phys. Rev. B 54, 11169 (1996).\n[26] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized\ngradient approximation made simple, Phys. Rev. Lett.\n77, 3865 (1996).\n[27] P. E. Bl¨ ochl, Projector augmented-wave method, Phys.\nRev. B 50, 17953 (1994).\n[28] G. Kresse and D. Joubert, From ultrasoft pseudopoten-\ntials to the projector augmented-wave method, Phys.\nRev. B 59, 1758 (1999).\n[29] J. D. Pack and H. J. Monkhorst, Special points for\nBrillouin-zone integrations, Phys. Rev. B 16, 1748\n(1977).\n[30] E. Hristova, R. Janisch, R. Drautz, and A. Hartmaier,\nSolubility of carbon in α-iron under volumetric strain and\nclose to the Σ5(310)[001] grain boundary: Comparison of\nDFT and empirical potential methods, Comput. Mater.\nSci.50, 1088 (2011).\n[31] T. Ochs, O. Beck, C. Els¨ asser, and B. Meyer, Symmetri-\ncal tilt grain boundaries in body-centred cubic transition\nmetals: An ab initio local-density-functional study, Phi-\nlos. Mag. A 80, 351 (2000).\n[32] A. M. Tahir, R. Janisch, and A. Hartmaier, Ab initio\ncalculation of traction separation laws for a grain bound-\nary in molybdenum with segregated C impurites, Model.\nSimul. Mat. Sci. Eng. 21, 075005 (2013).\n[33] R. A. Enrique and A. Van der Ven, Decohesion models\ninformed by first-principles calculations: The ab initio\ntensile test, J. Mech. Phys. Solids 107, 494 (2017).\n[34] J. H. Rose, J. R. Smith, and J. Ferrante, Universal fea-\ntures of bonding in metals, Phys. Rev. B 28, 1835 (1983).\n[35] O. Nguyen and M. Ortiz, Coarse-graining and renor-\nmalization of atomistic binding relations and universal\nmacroscopic cohesive behavior, J. Mech. Phys. Solids 50,\n1727 (2002).\n[36] R. L. Hayes, M. Ortiz, and E. A. Carter, Universal\nbinding-energy relation for crystals that accounts for sur-\nface relaxation, Phys. Rev. B 69, 172104 (2004).[37] A. Van der Ven and G. Ceder, The thermodynamics of\ndecohesion, Acta Mater. 52, 1223 (2004).\n[38] J. M¨ oller, E. Bitzek, R. Janisch, H. ul Hassan, and\nA. Hartmaier, Fracture ab initio: A forcebased scal-\ning law for atomistically informed continuum models, J.\nMater. Res. 33, 3750 (2018).\n[39] A. D. Banadaki and S. Patala, A three-dimensional poly-\nhedral unit model for grain boundary structure in fcc\nmetals, npj Comput. Mater. 3, 13 (2017).\n[40] C. H. Rycroft, VORO++: A three-dimensional Voronoi\ncell library in C++, Chaos 19, 041111 (2009).\n[41] S. Menon, G. D. Leines, and J. Rogal, pyscal: A python\nmodule for structural analysis of atomic environments, J.\nOpen Source Softw. 4, 1824 (2019).\n[42] A. Guzm´ an, Void analysis repository,\nhttps://gitlab.ruhr-uni-bochum.de/\nmechanical-properties-of-interfaces/\ngb-structure-and-segregation/void-analysis\n(2024).\n[43] S. Korte-Kerzel, T. Hickel, L. Huber, D. Raabe,\nS. Sandl¨ obes-Haut, M. Todorova, and J. Neugebauer, De-\nfect phases – thermodynamics and impact on material\nproperties, Int. Mater. Rev. 67, 89 (2022).\n[44] J. Wang, R. Janisch, G. K. Madsen, and R. Drautz,\nFirst-principles study of carbon segregation in bcc iron\nsymmetrical tilt grain boundaries, Acta Mater. 115, 259\n(2016).\n[45] H. L. Mai, X.-Y. Cui, D. Scheiber, L. Romaner, and S. P.\nRinger, An understanding of hydrogen embrittlement in\nnickel grain boundaries from first principles, Mater. Des.\n212, 110283 (2021).\n[46] H. Khanchandani and B. Gault, Atomic scale under-\nstanding of the role of hydrogen and oxygen segregation\nin the embrittlement of grain boundaries in a twinning\ninduced plasticity steel, Scr. Mater. 234, 115593 (2023)."    },    {        "title": "1512.07870v2.Polaritons_dispersion_in_a_composite_ferrite_semiconductor_structure_near_gyrotropic_nihility_state.pdf",        "content": "arXiv:1512.07870v2  [physics.optics]  25 Jun 2016Polaritons dispersion in a composite\nferrite-semiconductor structure near gyrotropic-nihili ty\nstate\nVladimir R. Tuza,∗\naInstitute of Radio Astronomy of National Academy of Science s of Ukraine,\nKharkiv, Ukraine\nAbstract\nIn the context of polaritons in a ferrite-semiconductor structur e which is in-\nfluenced by an external static magnetic field, the gyrotropic-nihilit y can be\nidentified from the dispersion equation related to bulk polaritons as a partic-\nularextreme state, atwhich thelongitudinalcomponent ofthecor responding\nconstitutive tensor and bulk constant simultaneously acquire zero . Near the\nfrequency of the gyrotropic-nihility state, the conditions of bran ches merging\nof bulk polaritons, as well as an anomalous dispersion of bulk and surf ace\npolaritons are found and discussed.\nKeywords: electromagnetic theory, polaritons, magneto-optical materials,\neffective medium theory, metamaterials\nPACS:42.25.Bs, 71.36.+c, 75.70.Cn, 78.20.Ci, 78.20.Ls, 78.67.Pt\n1. Introduction\nThe polaritons are modes of the electromagnetic field coupled to nor mal\nmodes (eigenwaves) which are inherent to a material and able to inte ract in\na linear manner with the electromagnetic field by virtue of their electr ical\nor magnetic character [1]. According to the quantum description, p olaritons\nare related to some ‘quasi-particle’ excitations consisting a photon coupled\nto an elementary excitation like plasmon, phonon, exciton, etc., whic h bring\n∗Institute of Radio Astronomy of National Academy of Sciences of U kraine, 4, Mystet-\nstv St., Kharkiv 61002, Ukraine\nEmail address: tvr@rian.kharkov.ua (Vladimir R. Tuz)\nPreprint submitted to Journal of Magnetism and Magnetic Mat erials June 7, 2021some polarizability into media. Nevertheless, since polaritons are mod es of\nthe electromagnetic field, their description is possible to fulfill on the basis of\nmacroscopic Maxwell’s equations, where polaritons are considered as modes\nexisting in a bulk material (bulk polaritons) as well as on a medium surfa ce\n(surface polaritons). In the latter case corresponding boundar y conditions\nmust be imposed in order to match the components of the field vecto rs on\nboth sides of the interface. Therefore, electromagnetic featur es of these bulk\nand surface modes in matter turn out to be closely related to the ma te-\nrial properties of a medium, and, in particular, to the resonant sta tes in\nthe frequency dependence of its macroscopic dielectric function [ 2]. In such\napproach, the polaritons are completely determined by the charac teristic fre-\nquencies of the relative permittivity of the medium.\nFurthermore, in the case of magneto-optically active media the pro blem\nof polaritons is mostly related to two distinct considerations of gyro elec-\ntric media with the (surface) magnetoplasmon and gyromagnetic me dia with\nthe (surface) magnon which involve the media characterization with either\npermittivity or permeability tensor having antisymmetric off-diagona l parts\n[3, 4, 5, 6, 7, 8]1. This distinction is convenient due to the physical mecha-\nnisms that cause corresponding resonant states (e.g. vibration o f molecules\nin dielectrics or magnetization in ferrites). Thus, characteristic fr equencies of\npermittivity are confined to the optical range (sometimes, in ion cry stals, to\nthe infrared one), whereas those of permeability are in the microwa ve range\n(occasionally, in antiferromagnets, in the submillimeter range).\nAlthough characteristic frequencies of permittivity and permeabilit y nor-\nmally lie far from each other, it is possible to find exceptions to this rule .\nIn particular, bigyrotropic media can be implemented artificially by pro p-\nerly combining together gyroelectric and gyromagnetic materials in a certain\nproportion or admixing inclusions of a special kind into a host medium.\nAs relevant examples layered magnetic-semiconductor heterostr uctures [10,\n11, 12, 13] and the magnetized electron-ion plasma consisting micro n ferrite\ngrains [14] can be mentioned. Such gyroelectromagnetic composites are now\nusually considered within the theory of metamaterials, in the framew ork of\nwhich they are widely discussed from the viewpoint of achieving negat ive\n1For the first reading on classification of polaritons in magnetic media w e refer to a\ncomprehensive review [9].\n2refraction and backward wave propagation2.\nFurther, the role of bigyrotropy inherent to gyroelectromagnet ic media in\nthespectralfeaturesofpolaritonsiselucidatedin[16,17,18],whe renecessary\nconditions for negative refraction and anomalous dispersion are fo und out\nin the (anti)ferromagnet-semiconductor superlattices (e.g., in Mn F2-CdTe\nnanostructures) being under an action of an external static mag netic field.\nIt is shown that the applied magnetic field essentially changes the spe c-\ntrum of polaritons in such composite media, increases the number of spectral\nbranches, while the characteristic frequencies become to be stro ngly depen-\ndent on the magnetic field. As a result, the dispersion features of p olaritons\nin different ranges of the external magnetic field are quite diverse, and not\nonly the number but also the limits of the frequency ranges with anom alous\ndispersion appear to be very sensitive to the strength of the magn etic field.\nAs a gradual development of this theory, in the present paper we s tudy\nparticular spectral features of polaritons that appear in a gyroe lectromag-\nnetic medium in the frequency band near a certain extreme state in t he ma-\nterial dispersion, when relative permittivity and relative permeability of the\nmedium simultaneously turn into zero. Infact, such a peculiarity is dis cussed\nwithintheconceptions of‘nihility’ [19,20,21]and‘epsilon-and-mu-ne ar-zero’\nmedia [22, 23]3, and is defined in [24, 25, 26, 27] as a ‘gyrotropic-nihility’\nstate. Thus, in the Faraday geometry the gyrotropic-nihility state is found\ncan be achieved in a composite ferrite-semiconductor superlattice in the mi-\ncrowave part of spectrum near the frequencies of ferromagnet ic and plasma\nresonances. Inthis case real partsof diagonal elements of both complex effec-\ntive permittivity and complex effective permeability tensors of such a rtificial\nmedium simultaneously acquire zero, while the off-diagonal elements a ppear\nto be non-zero quantities. Here we focus on the search of conditio ns for exis-\ntence of the gyrotropic-nihility state inthe gyroelectromagnetic s ystem being\nin theVoigt geometry from the viewpoint of the polaritons problem. For the\nbulk polaritons we revisit the results of [28], where the particular ext reme\nstate when permittivity and permeability of media simultaneously turn into\n2We consider a backward wave as a wave in which the direction of the Po ynting vector\nis opposite to that of its phase velocity [15].\n3We believe that these two terms ‘nihility’ and ‘epsilon-and-mu-near-z ero’ define the\nsame physical essence and the difference between them is only in the ir names. Therefore,\nfurther we use the term ‘nihility’ by virtue of personal preference s.\n3zero is referred to ‘resonant polaritons’4. Besides, spectral properties of the\nsurface polaritons are also studied.\n2. Dispersion relations for bulk and surface polaritons\nThereby, further in this paper we study polaritons dispersion feat ures\nin asemi-infinite stack of identical double-layer slabs (unit cells) periodi-\ncally arranged along the y-axis (figure 1). Each unit cell is constructed by\njuxtaposition together of ferrite (with constitutive parameters εf, ˆµf) and\nsemiconductor (with constitutive parameters ˆ εs,µs) layers with thicknesses\ndfandds, respectively. The stack possesses a periodic structure (with pe riod\nL=df+ds) that fills half-space y <0 andadjoins an isotropic medium (with\nconstitutive parameters ε1,µ1) occupying half-space y >0. We consider that\nthe structure is a finely-stratified one, i.e. its characteristic dimensions df,ds\nandLare all much smaller than the wavelength in the corresponding layer\ndf≪λ,ds≪λ, and period L≪λ(the long-wavelength limit). An external\nstatic magnetic field /vectorMis directed along the z-axis. It is supposed that the\nstrength of this field is high enough to form a homogeneous saturat ed state\nof ferrite as well as semiconductor subsystems.\nFigure 1: A composite finely-stratified ferrite-semiconductorstr ucture, which is influenced\nby an external static magnetic field in the Voigt geometry.\n4Here again a question about the terminology arises. The term ‘reson ant polaritons’\nis also introduced in [29] for the resonant state of the Breit-Wigner type in the scattering\namplitude of the electromagnetic waves in quantum wells.\n4Since all characteristic dimensions df,dsandLof the structure under\ninvestigation satisfy the long-wavelength limit, the standard homog enization\nprocedurefromtheeffective mediumtheory(see, [30,31], andApp endix A)5\nis applied in order to derive averaged expressions for effective cons titutive\nparameters of the structure. In this way, the finely-stratified m ultilayered\nsystem is approximately represented as a biaxialanisotropic (gyroelectro-\nmagnetic) uniform medium, whose first optical axis is directed along t he\nstructure periodicity, while the second one coincides with the direct ion of\nthe external static magnetic field /vectorM. Therefore, the resulting composite\nmedium is characterized with the tensors of relative effective permit tivity\nˆεeffand relative effective permeability ˆ µeff, whose expressions derived via\nunderlying constitutive parameters of ferrite ( εf, ˆµf) and semiconductor (ˆ εs,\nµs) subsystems one can find in Appendix B.\nLet us further consider a surface wave which propagates along th e in-\nterface of an isotropic dielectric and a composite structure (we dis tinguish\nthese media with the index j= 1,2). According to figure 1 the y-axis is\nperpendicular to the interface between the media, and the wave pr opagates\nalong the x-axis with a wavenumber kx. The attenuation of the wave in both\npositive and negative directions along the y-axis is defined by quantities κj.\nThe static magnetic field /vectorMis directed along the z-axis, so the system is\nconsidered to be in the Voigt geometry.\nIn ageneralform, the electric and magnetic field vectors /vectorEand/vectorHused\nhere are represented as [34]\n/vectorP(j)=/vector p(j)exp(ikxx)exp(∓κjy), (1)\nwhere a time factor exp( −iωt) is also supposed and omitted, and sign ‘ −’\nis related to the fields in the upper medium ( y >0,j= 1) and sign ‘+’ is\nrelated to the fields in the composite medium ( y <0,j= 2), respectively,\nwhich provide required wave attenuation along the y-axis.\n5As an alternative to [30, 31] a powerful approach based on 4 ×4-transfer matrix\nformalism [32, 33, 34] should be mentioned. It enables to perform th e homogenization\nprocedure and obtain a solution of the boundary-value problem with respect to polaritons\nin the most general case of linear bianisotropic materials. Neverthe less, in this paper we\nconsciously made a choice in favor of the method [30], since it makes po ssible to obtain an\nexplicit expressions for all components of effective permeability and effective permittivity\ntensors, which are further needed for solving an optimization prob lem and identification\nof asymptotes of polariton branches.\n5Involving a pair of the divergent Maxwell’s equations ∇ ·/vectorD= 0 and\n∇·/vectorB= 0 in the form\n∇·/vectorQ(j)=∇·/parenleftBig\nˆg(j)/vectorP(j)/parenrightBig\n= 0, (2)\nwhere ˆg(1)is related to the upper medium as a tensor quantity with ε1or\nµ1on its main diagonal and zeros elsewhere (i.e., ˆ g(1)=g1ˆI, whereˆIis the\nidentity tensor), and ˆ g(2)= ˆgeffis related to the composite medium, one\ncan immediately arrive to the relations between the field components in the\nupper (y >0) and composite ( y <0) medium as follows\nP(1)\ny=ikx\nκ1P(1)\nx, P(2)\ny=iκ2gxy−ikxgxx\niκ2gxx−kxgxyP(2)\nx, (3)\nfrom which the field polarization at an arbitrary fixed point of both me dia\ncan be determined.\nTaking into consideration continuity of components P(j)\nxandQ(j)\nyat the\ninterface y= 0 between the media\ng1P(1)\ny\nP(1)\nx=gyyP(2)\ny\nP(2)\nx−gxy, (4)\nand relations (3), the dispersion equation for the surfacepolaritons at the\ninterface between isotropic dielectric and bigyrotropic (gyroelect romagnetic)\nsemi-infinite media is obtained as\nκ2g1+κ1/parenleftbigg\ngxx+g2\nxy\ngyy/parenrightbigg\n+ikxg1gxy\ngyy= 0. (5)\nFrom a pair of the curl Maxwell’s equations ∇×/vectorE=ik0/vectorBand∇×/vectorH=\n−ik0/vectorD, wherek0=ω/cis the free space wavenumber, in a standard way the\nwave equation can be obtained in the form:\n∇×∇× /vectorP(j)+k2\n0ˆς(j)/vectorP(j)= 0, (6)\nwhere ˆς(j)isintroducedastheproductof ˆ µ(j)and ˆε(j)madeintheappropriate\norder.\nSubstituting field components (1) into the wave equation (6) allows u s to\nderive a relation between the field components in boththe isotropic d ielectric\nand composite media:\n/parenleftBigg\nk2\n0ς(j)\nxx+κ2\njk2\n0ς(j)\nxy−ikxκ2\nj\nk2\n0ς(j)\nyx−ikxκ2\njk2\n0ς(j)\nyy−k2\nx/parenrightBigg/parenleftBigg\nP(j)\nx\nP(j)\ny/parenrightBigg\n= 0, (7)\n6/parenleftbig\nk2\n0ς(j)\nzz−k2\nx+κ2\nj/parenrightbig\nP(j)\nz= 0. (8)\nFrom (7) and (8) it follows that in the considered system the TE mode\n{Hx, Hy, Ez}is not coupled to the TM mode {Ex, Ey, Hz}.\nDirect substitution of corresponding values into (7) for upper ( ς(1)\nxx=\nς(1)\nyy=ς(1)\nzz=ς1,ς(1)\nxy=ς(1)\nyx= 0) and composite ( ς(2)\nmn=ςmn) media, and\nexpanding the determinant, expressions related to the attenuat ion functions\nκjare obtained in the form:\nk2\nx−κ2\n1−k2\n0ς1= 0. (9)\nk2\nxςxx−κ2\n2ςyy−k2\n0εyyµyyεvµv−ikxκ2(ςxy+ςyx) = 0, (10)\nwhereµv=µxx+µ2\nxy/µyyandεv=εxx+ε2\nxy/εyyare the Voigt relative\npermeability and relative permittivity, which can be considered as the bulk\nmagnetic and dielectric constants.\nFromthecurl Maxwell’s equationsinvolving (1) andabove introduced the\nVoigt relative permeability µvand relative permittivity εvthe dispersion law\nfor thebulkpolaritons in the composite medium follows as solutions of two\nseparate equations related to the TE mode and the TM mode, respe ctively,\nk2\nxµxx−µyy(k2\n0εzzµv+κ2\n2) = 0, k2\nxεxx−εyy(k2\n0µzzεv+κ2\n2) = 0,(11)\nhandled in the form of functions of wavenumber kxversusk0, sinceµmn,εmn,\nµvandεvare all functions of frequency ωand thus they are functions of k0.\nCombining together relations (9), (10) and dispersion equation (5) with\nappropriate substitution of µ→gfor the TE mode, and ε→gfor the\nTM mode gives us the closed system of equations whose solutions for the\nwavenumber kxversusk0completely determine the spectral characteristics\nofthesurfacepolaritons. Consistentlygettingridoftheattenua tionfunctions\nκjfrom the dispersion equation (5), it can be expanded into the biquad ratic\nequation with respect to k2\nx:\nAk4\nx+Bk2\nx+C= 0, (12)\nwhereA=Y2+W2,B=−k2\n0(2VY+ς1W2),C=k4\n0V2,V=\nεyyµyyεvµv−ς1ςyy˜g2\nv,Y=ςxx+ (ςxy+ςyx)˜gxy+ (˜g2\nxy−˜g2\nv)ςyy,W=\n(ςxy+ςyx+ 2ςyy˜gxy)˜gv, and ˜gv=gv/g1, ˜gxy=gxy/gyy, whose solution is\ntrivial:\nk2\nx=−B±√\nB2−4AC\n2A. (13)\n7Fromfour roots of (13) those must be selected which satisfy the p hysical con-\nditions, namely, wave attenuation as it propagates, that imposes r estrictions\non the values of κjwhose real parts must be positive quantities.\n3. Analysis of polaritons dispersion conditions\nFrom the form of dispersion equations for bulk (11) and surface (1 2) po-\nlaritons it is obvious that their spectral features substantially dep end on the\ndispersion characteristics of components of both effective perme ability tensor\nand effective permittivity tensor of the resulting finely-stratified s tructure.\nMoreover, since the components of these tensors are all functio ns of the fre-\nquency, external magnetic field strength, layers’ thicknesses, and physical\nproperties of the materials forming the superlattice, the regions o f polaritons\nexistence are determined by the choice of the values of the corres ponding\nquantities. So we are dealing here with a multiparameter problem which\nrequires to be optimally solved in order to achieve the desired dispers ion\nfeatures of polaritons.\nImposing κ2= 0 into (11) we obtain the dispersion equations\nk2\nx=k2\n0εzzµvµyyµ−1\nxx, k2\nx=k2\n0µzzεvεyyε−1\nxx, (14)\nwhose solutions outline the regions of existence of bulk polaritons. A s it is\ndefined in [19], a ‘nihility’ state implies simultaneous equality to zero of re l-\native permittivity and relative permeability of a medium. Therefore, in the\nconsidered composite structure, in the context of the bulk polarit ons (14),\nsuch a state corresponds to a particular frequency, where εzz,µvandµzz,εv\nsimultaneously acquire zero for the TE modeand the TM mode, respe ctively.\nSince this peculiarity is obviously associated with the media gyrotropy we\ndistinguish it as the ‘gyrotropic-nihility’ state6. From the dispersion charac-\nteristics of the constitutive parameters one can conclude that int he structure\nunder study the gyrotropic-nihility state for the TM mode is not ach ievable\n6We should emphasize that in [28] the term ‘resonant polaritons’ is intr oduced for\nahypothetical isotropic medium in which characteristic frequencies (either resona nce or\nantiresonance) of permittivity and permeability coincide. In this pap er we demonstrate\nthat the discussed extreme state when both relative permittivity a nd relative permeability\nsimultaneously turn into zero can be achieved in a realstructure with a particular type\nof anisotropy (gyrotropy). So we use the term ‘gyrotropic-nihility ’ in order to distinguish\nexactly this state among other ones.\n8at all, since the longitudinal component µzzof the effective permeability ten-\nsor is a constant nonzero quantity in the whole frequency band of in terest.\nFrom the physical point of view, it is a consequence of the fact that the mag-\nnetic field vector in the TM mode is parallel to the external magnetic fi eld,\nwhich results in the absence of its interaction with the magnetic subs ystem.\nThus, the gyrotropic-nihility state can be achieved only for the TE m ode,\nand the search of conditions for its existence implies solving an optimiz a-\ntion problem, where εzzandµvare subjected to zero in the objective func-\ntion. During the solution of this problem both the magnetic field stren gth\n(and, accordingly, characteristic frequencies of the constitutiv e parameters)\nand structure period are fixed, and the search for the frequenc y where the\ngyrotropic-nihility state appears is proceeded via altering the layer s’ thick-\nnesseswithintheperiod. Thegraphicalsolutionofthediscussedop timization\nproblem is depicted in figure 2, where the resolved gyrotropic-nihility state\nis distinguished by arrows. In the structure under consideration t his state\nis found to be at a particular frequency fgn= 7.97 GHz which corresponds\nto the following geometric factors: δ1=df/L= 0.117;δ2=ds/L= 0.883;\nL/λ≈3×10−2.\nSince further our goal is to elucidate the dispersion laws of the bulk\npolaritons (which are in fact eigenwaves), we are interested in realsolutions\nof the first equation in (14) for the TE mode. In order to find the re al\nsolutions related to eigenwaves, absence of losses in constitutive p arameters\nof the underlying layers is supposed, i.e. we put b= 0 and ν= 0 in tensors\n(B.1) for ferrite and semiconductor subsystems, respectively. T hese solutions\nare depicted in figure 3(a) with the red dashed lines.\nIn the systems which stand out with two characteristic frequencie s, where\none resonance exists for permittivity and other one exists for per meability,\nthedispersionlawofthebulkpolaritonshasthreebranches[17], an dtypically\nthese branches are separated from one another by some forbidd en bands. In\nour case, the resonance of the relative permittivity εzzis at zero frequency,\ntherefore, there are only two branches in the dispersion law withou t any\nforbidden band between them. Remarkably, the branches merge e xactly at\nthe frequency of the gyrotropic-nihility state, which is marked out in figure\n3(a) with a circle. The upper branch is restricted by the light lines, wh erein\nthe bottom branch manifests an anomalous dispersion and is restric ted by\nthe line at which µxx= 0. It should be noted that although the dispersion\ncurves of the bulk polaritons are calculated for anidealized lossless s tructure,\nin a real system the losses are expected to be small near the frequ ency of the\n9zz \ngyrotropic nihility \nFigure 2: (a) Two surfaces depict behaviors of real parts of relat ive permeability (purple\nsurface) and relative permittivity (orange surface) versus freq uency and the ratio of the\nlayers’ thicknesses. The blue and red curves plotted on the surfa ces show the conditions\nRe(µv) = 0 and Re( εzz) = 0, respectively. Curves at the bottom are just projections\nand are given for an illustrative purpose. Dispersion curves of the t ensor components of\n(b) effective permeability and (c) effective permittivity at particular structure parameters\n(δ1= 0.117,δ2= 0.883,L= 1 mm) for which the gyrotropic-nihility state exists. For\nthe ferrite layers, under saturation magnetization of 2000 G, par ameters are: ω0/2π=\n4.2 GHz,ωm/2π= 8.2 GHz,b= 0.02,εf= 5.5. For the semiconductor layers, parameters\nare:ωp/2π= 10.5 GHz,ωc/2π= 9.5 GHz,ν/2π= 0.05 GHz, εl= 1.0,µs= 1.0.\n10Figure 3: (a) Dispersion characteristics of the bulk (red dash lines) and surface (blue\nthick solid lines) polaritons. Blue thin solid lines depict four solutions of t he dispersion\nequation for the surface polaritons. Green dash lines depict the as ymptotic conditions.\n(b) Frequency dependencies of the attenuation functions κjin the positive (upper panel)\nand negative (bottom panel) ranges of kx.δ1= 0.117,δ2= 0.883,L= 1 mm. Other\nparameters of the ferrite and semiconductor layers are the same as in figure 2.\n11gyrotropic-nihility state, since zero states of εzzandµvare both far from the\ncorresponding frequencies of the plasma and ferromagnetic reso nances.\nStill assuming that there are no losses in the constitutive layers, fo ur\nsolutionsofdispersionequation(12)withrespect tothepropagat ionconstant\nkxof the surface polaritons are calculated and presented in figure 3( a) with\nblue thin solid lines. Importantly, since the dispersion equation consis ts of a\nterm which is linearly depended on kx(see the last term in (10)), the spectral\ncharacteristics of the surface polaritons in the structure under study possess\nthe nonreciprocal nature, i.e. k0(kx)/ne}ationslash=k0(−kx). Therefore, the appropriate\nroot branches between these four solutions should be properly se lected in\norder to ensure that they are physically correct.\nAs was already mentioned, among these four solutions those must b e\nchosen which provide the wave attenuation as it propagates. It imp oses the\nrestriction that both attenuation functions κj(j= 1,2) simultaneously must\nbe real positive quantities. The corresponding curves of κjare presented in\nfigure3(b), andtakingintoaccount theirvaluesforeitherpositive ornegative\nrange ofkx, the physically correct root branches are highlighted in figure 3(a)\nwith blue thick solid lines. One can see that there is one root branch in\nthe range of positive kx, while there are two root branches in the range of\nnegative kx. From equation (13) it is evident that the asymptotic limits of\nall these root branches are defined by the condition A= 0 (i.e. Y2+W2= 0,\nimplying for the lossless system Yis a real number, while Wis an imaginary\nnumber, therefore, Ais always a real number, too). As a result, the surface\npolariton branches are restricted by two asymptotic conditions: Y−iW= 0\nandY+iW= 0 in positive and negative ranges of kx, respectively.\nFurthermore, in traditional systems the regions of existence of b ulk and\nsurface polaritons do not overlap, and the surface polaritons can propagate\nin the gaps between the regions where the bulk polaritons exist [1]. In the\nconsidered case, two bottom root branches confirm this rule. Nev ertheless,\nthe upper root branch in the range of negative kxmanifests a violation of this\nrule, demonstrating situation when the bulk and surface polaritons exist in\nthe same frequency range, but with different wavevectors, and t his particular\nroot branch of the surface polariton possesses an anomalous disp ersion.\n4. Conclusions\nTo conclude, in this paper the dispersion relations for both bulk and\nsurface polaritons in a finely-stratified ferrite-semiconductor st ructure which\n12is influenced by an external static magnetic field in the Voigt geometr y are\nderived. From the dispersion equation related to the bulk polaritons the\nconditions for existence of a particular extreme gyrotropic-nihility state are\nidentified through solving a multiparameter optimization problem.\nFrom analysis of the dispersion curves related to the bulk polaritons it is\nfound that in their spectral characteristics there are two branc hes without\nany forbidden bands between them, and one of these branches ma nifests an\nanomalous dispersion. Remarkably, these two branches merge exa ctly at the\nfrequency ofthegyrotropic-nihility state. The spectral featur esof thesurface\npolaritonsarealsoelucidated. Thesespectrapossessthenonrec iprocalnature\nwith different number of root branches in the positive and negative r anges of\nkx. Furthermore, one root branch in the negative range of kxmanifests an\nanomalous dispersion.\nIt isexpected thatthereal system should demonstrate alowlevel oflosses\nfor the bulk and surface polaritons near the frequency of the gyr otropic-\nnihility state, since zero states of both relative permittivity and rela tive\npermeability lie far from the corresponding frequencies of the plasm a and\nferromagnetic resonances. Verification of this statement requir es additional\nelaboration.\nNevertheless, from a theoretical viewpoint, the existence of the discussed\neffects in the polariton spectra is not in doubt, but the experimenta l verifi-\ncation is still a challenging task. It requires accurate choosing cons titutive\nmaterials, clear understanding their characteristic frequencies, solving an op-\ntimization problem for search magnetic filed strength, correspond ing thick-\nnesses and number of layers within the practical system, but neve rtheless,\nwe believe in its feasibility. Our confidence in success is confirmed by th e\nfacts that in semiconductors the density of the free charge carr iers strongly\ndepends on the temperature, as well as on the type of impurities an d the\ndoping level and thus can be varied in a wide interval, therefore, the neces-\nsary values of the effective plasma frequency can be achieved and a djusted\nto the properties of the magnetic subsystem.\n5. Acknowledgement\nThis work was supported by National Academy of Sciences of Ukrain e\nwith Program ‘Fundamental issues of creation of new nanomaterials and\nnanotechnologies’ for 2015-2019 years, Project no. 13/15-H.\n13Appendix A. Effective medium theory\nTaking into account the smallness of the layers’ as well as period’s th ick-\nnesses compared to the wavelength ( df≪λ,ds≪λ, andL≪λ), the\neffective medium theory is engaged in order to derive expressions fo r the av-\neraged constitutive parameters of the periodic structure under investigation.\nFollowing the method used earlier for deriving the components of the effec-\ntive permittivity tensor [30, 35] and the effective permeability tenso r [31, 36]\nfor multilayered systems (superlattices) consisted of anisotropic constituents\nwe can formulate the expressions of ˆ εeffand ˆµeffin ageneralform.\nIn this way, constitutive equations /vectorB= ˆµ/vectorHand/vectorD= ˆε/vectorEfor ferrite\n(0< z < d f) and semiconductor ( df< z < L ) layers, respectively, can be\nwritten as follow:\nQ(j)\nm=/summationdisplay\nng(j)\nmnP(j)\nn, (A.1)\nwhere/vectorQis substituted for the magnetic and electric flux densities /vectorBand/vectorD;\n/vectorPis substituted for the magnetic and electric field strengths /vectorHand/vectorE;gis\nsubstituted for permeability and permittivity µandε; the superscript ( j) is\nintroduced to distinguish between ferrite ( f→j) and semiconductor ( s→\nj) layers; subscripts mandnare substituted to iterate over corresponding\nindexes of the tensor quantities in Cartesian coordinates.\nIn the chosen problem geometry, the yaxis is perpendicular to the in-\nterfaces between the layers within the structure, and, therefo re, components\nP(j)\nx,P(j)\nz, andQ(j)\nyare continuous. Thus, the particular component P(j)\nycan\nbe expressed from equation (A.1) in terms of the continuous compo nents of\nthe field\nP(j)\ny=−g(j)\nyx\ng(j)\nyyP(j)\nx+1\ng(j)\nyyQ(j)\ny−g(j)\nyz\ng(j)\nyyP(j)\nz, (A.2)\nand substituted into equations for components Q(j)\nxandQ(j)\nz:\nQ(j)\nx=/parenleftBigg\ng(j)\nxx−g(j)\nxyg(j)\nyx\ng(j)\nyy/parenrightBigg\nP(j)\nx+g(j)\nxy\ng(j)\nyyQ(j)\ny+/parenleftBigg\ng(j)\nxz−g(j)\nxyg(j)\nyz\ng(j)\nyy/parenrightBigg\nP(j)\nz,\nQ(j)\nz=/parenleftBigg\ng(j)\nzx−g(j)\nzyg(j)\nyx\ng(j)\nyy/parenrightBigg\nP(j)\nx+g(j)\nzy\ng(j)\nyyQ(j)\ny+/parenleftBigg\ng(j)\nzz−g(j)\nzyg(j)\nyz\ng(j)\nyy/parenrightBigg\nP(j)\nz.(A.3)\nThentheseobtainedrelations(A.2)and(A.3)areusedforthefields averaging\n[30].\n14Since in thelong-wavelength limit thefields /vectorP(j)and/vectorQ(j)inside the layers\nare considered to be constant, the averaged (Maxwell) fields /an}b∇acketle{t/vectorQ/an}b∇acket∇i}htand/an}b∇acketle{t/vectorP/an}b∇acket∇i}htcan\nbe determined by the equalities\n/an}b∇acketle{t/vectorP/an}b∇acket∇i}ht=1\nL/summationdisplay\nj/vectorP(j)dj,/an}b∇acketle{t/vectorQ/an}b∇acket∇i}ht=1\nL/summationdisplay\nj/vectorQ(j)dj. (A.4)\nIn view of the above discussed continuity of components P(j)\nx,P(j)\nz, andQ(j)\ny,\nit follows that\n/an}b∇acketle{tPx/an}b∇acket∇i}ht=P(j)\nx,/an}b∇acketle{tPz/an}b∇acket∇i}ht=P(j)\nz,/an}b∇acketle{tQy/an}b∇acket∇i}ht=Q(j)\ny, (A.5)\nand on the basis of equations (A.2) and (A.3), the relations between the\naveraged fields components are obtained as:\n/an}b∇acketle{tQx/an}b∇acket∇i}ht=αxx/an}b∇acketle{tPx/an}b∇acket∇i}ht+γxy/an}b∇acketle{tQy/an}b∇acket∇i}ht+αxz/an}b∇acketle{tPz/an}b∇acket∇i}ht,\n/an}b∇acketle{tPy/an}b∇acket∇i}ht=βyx/an}b∇acketle{tPx/an}b∇acket∇i}ht+βyy/an}b∇acketle{tQy/an}b∇acket∇i}ht+βyz/an}b∇acketle{tPz/an}b∇acket∇i}ht,\n/an}b∇acketle{tQz/an}b∇acket∇i}ht=αzx/an}b∇acketle{tPx/an}b∇acket∇i}ht+γzy/an}b∇acketle{tQy/an}b∇acket∇i}ht+αzz/an}b∇acketle{tPz/an}b∇acket∇i}ht,(A.6)\nwhereαmn=/summationtext\nj(g(j)\nmn−g(j)\nmyg(j)\nyn/g(j)\nyy)δj,βyn=−/summationtext\nj(g(j)\nyn/g(j)\nyy)δj,βyy=/summationtext\nj(1/g(j)\nyy)δj,γmy=/summationtext\nj(g(j)\nmy/g(j)\nyy)δj,δj=dj/Lare geometric factors,\nandm,n=x,z.\nExpressing /an}b∇acketle{tQy/an}b∇acket∇i}htfrom the second equation in system (A.6) and substi-\ntuting it into the rest two equations, the constitutive equations fo r the flux\ndensities of the effective medium /an}b∇acketle{t/vectorQ/an}b∇acket∇i}ht= ˆgeff/an}b∇acketle{t/vectorP/an}b∇acket∇i}htcan be derived, where ˆ geff\nis a tensor\nˆgeff=\n˜αxx˜γxy˜αxz\n˜βyx˜βyy˜βyz\n˜αzx˜γzy˜αzz\n (A.7)\nwith components ˜ αmn=αmn−βynγmy/βyy,˜βyn=−βyn/βyy,˜βyy= 1/βyy,\nand ˜γmy=γmy/βyy.\nTaking into account nonzero components of relative permittivity an d rel-\native permeability tensors of underlying ferrite and semiconductor subsys-\ntems, both the effective permittivity tensor ˆ εeffand the effective permeabil-\nity tensor ˆ µeffof the composite finely-stratified ferrite-semiconductor struc-\nture can be obtained from (A.7) via the substitutions gxx=g(f)\nxxδf+g(s)\nxxδs+\n(g(f)\nxy−g(s)\nxy)2δfδsΓ,gxy=−gyx= (g(f)\nxyg(s)\nyyδf+g(s)\nxyg(f)\nyyδs)Γ,gyy=g(f)\nyyg(s)\nyyΓ,\ngzz=g(f)\nzzδf+g(s)\nzzδs,gxz=gzx=gyz=gzy= 0, and Γ = ( g(s)\nyyδf+g(f)\nyyδs)−1.\nIn general there is gxx/ne}ationslash=gzz, which means that the considered composite\nmedium is a biaxial bigyrotropic crystal.\n15Appendix B. Constitutive parameters of ferrite and\nsemiconductor subsystems\nThe expressions for tensors components of the underlying const itutive\nparameters of magnetic ˆ µf→ˆg(f)and semiconductor ˆ εs→ˆg(s)layers can be\nwritten in the form\nˆg(j)=\ng1ig20\n−ig2g10\n0 0 g3\n. (B.1)\nFor magnetic layers [37, 38] the components of tensor ˆ g(f)areg1= 1 +\nχ′+iχ′′,g2= Ω′+iΩ′′,g3= 1, and χ′=ω0ωm[ω2\n0−ω2(1−b2)]D−1,\nχ′′=ωωmb[ω2\n0+ω2(1 +b2)]D−1, Ω′=ωωm[ω2\n0−ω2(1 +b2)]D−1, Ω′′=\n2ω2ω0ωmbD−1,D= [ω2\n0−ω2(1+b2)]2+4ω2\n0ω2b2, whereω0is the Larmor\nfrequency and bis a dimensionless damping constant.\nFor semiconductor layers [39] the components of tensor ˆ g(s)areg1=\nεl/bracketleftbig\n1−ω2\np(ω+iν)[ω((ω+iν)2−ω2\nc)]−1/bracketrightbig\n,g2=εlω2\npωc[ω((ω+iν)2−ω2\nc)]−1,\ng3=εl/bracketleftbig\n1−ω2\np[ω(ω+iν)]−1/bracketrightbig\n, whereεlis the part of permittivity attributed\nto the lattice, ωpis the plasma frequency, ωcis the cyclotron frequency and\nνis the electron collision frequency in plasma.\nRelative permittivity εfof the ferrite layers as well as relative permeabil-\nityµsof the semiconductor layers are scalar quantities.\nReferences\n[1] D.E.Mills, E.Burstein, Polaritons: the electromagnetic modes of media,\nReports on Progress in Physics 37 (7) (1974) 817.\nURLhttp://stacks.iop.org/0034-4885/37/i=7/a=001\n[2] J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique,\nTheory of surface plasmons and surface-plasmon polaritons, Rep orts\non Progress in Physics 70 (1) (2007) 1.\nURLhttp://stacks.iop.org/0034-4885/70/i=1/a=R01\n[3] J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein,\nTheory of surface magnetoplasmons in semiconductors, Phys. Re v.\nLett. 28 (1972) 1455–1458. doi:10.1103/PhysRevLett.28.1455 .\nURLhttp://link.aps.org/doi/10.1103/PhysRevLett.28.1455\n16[4] A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, R. F. Wa l-\nlis, Surface polaritons on semi-infinite gyromagnetic media, Journal of\nPhysics C: Solid State Physics 6 (7) (1973) 1266.\nURLhttp://stacks.iop.org/0022-3719/6/i=7/a=016\n[5] R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein,\nTheory of surface polaritons in anisotropic dielectric media with applic ation to surface magnetoplasmons in semiconductors,\nPhys. Rev. B 9 (1974) 3424–3437. doi:10.1103/PhysRevB.9.3424 .\nURLhttp://link.aps.org/doi/10.1103/PhysRevB.9.3424\n[6] A. Boardman, N. King, Y. Rapoport, L. Velasco,\nGyrotropic impact upon negatively refracting surfaces, New Jour -\nnal of Physics 7 (1) (2005) 191.\nURLhttp://stacks.iop.org/1367-2630/7/i=1/a=191\n[7] R. Tagiyeva, M. Saglam, B. Boyacioglu,\nEffective-medium approach for surface-localized magnetic polarito ns in magnetic (ferromagnetic and antiferromagnetic) superlattic es,\nSuperlattices and Microstructures 41 (4) (2007) 237–247.\ndoi:10.1016/j.spmi.2007.01.001 .\nURLhttp://www.sciencedirect.com/science/article/pii/S0 74960360700002X\n[8] B.Hu,Y.Zhang,Q.Wang,Surface magneto plasmons and their a pplications in the infrared frequencies,\nNanophotonics 4 (2015) 383?–396. doi:10.1515/nanoph-2014-0026 .\nURLhttp://dx.doi.org/10.1515/nanoph-2014-0026\n[9] M. I. Kaganov, N. B. Pustyl’nik, T. I. Shalaeva,\nMagnons, magnetic polaritons, magnetostatic waves, Physics-Us pekhi\n40 (2) (1997) 181.\nURLhttp://stacks.iop.org/1063-7869/40/i=2/a=R04\n[10] A. Ivanov, O. Kotelnikova, V. Ivanov,\nGyrotropic left-handed media: Energy flux and circular dichroism,\nJournal of Magnetism and Magnetic Materials 300 (1) (2006) e67–e 69.\ndoi:10.1016/j.jmmm.2005.10.150 .\nURLhttp://www.sciencedirect.com/science/article/pii/S0 304885305008978\n[11] R.-X. Wu, T. Zhao, J. Q. Xiao,\nPeriodic ferrite-semiconductor layered composite with negative ind ex of refraction,\nJournal of Physics: Condensed Matter 19 (2) (2007) 026211.\nURLhttp://stacks.iop.org/0953-8984/19/i=2/a=026211\n17[12] R. H. Tarkhanyan, D. G. Niarchos,\nAnomalous refraction of backward waves in ferromagnet-semicon ductor superlattices in the presence of an external magnetic field ,\nPhysica Status Solidi (b) 245 (1) (2008) 154–158.\ndoi:10.1002/pssb.200743071 .\nURLhttp://dx.doi.org/10.1002/pssb.200743071\n[13] O.V.Shramkova, Transmission spectra in ferrite-semiconduc tor periodic structure,\nProgress in Electromagnetics Research M 7 (2009) 71–85.\ndoi:10.2528/PIERM09041305 .\nURLhttp://www.jpier.org/PIERM/pier.php?paper=09041305\n[14] B. Mesfin, V. N. Mal’nev, E. V. Martysh, Y. G. Rapoport,\nWaves and negative refraction in magnetized plasma with ferrite gra ins,\nPhysics of Plasmas 17 (11) (2010) 112109. doi:10.1063/1.3506818 .\nURLhttp://scitation.aip.org/content/aip/journal/pop/17 /11/10.1063/1.3506818\n[15] I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, S. Ilvonen,\nBw media – media with negative parameters, capable of supporting ba ckward waves,\nMicrowave and Optical Technology Letters 31 (2) (2001) 129–133 .\ndoi:10.1002/mop.1378 .\nURLhttp://dx.doi.org/10.1002/mop.1378\n[16] R.Tarkhanyan, D.Niarchos, Magnetic plasmon-polaritons in ne gative index gyromagnetic media,\nPhysica B: Condensed Matter 405 (14) (2010) 2964–2966, proce ed-\nings of the Eighth International Conference on Electrical Trans-\nport and Optical Properties of Inhomogeneous MediaETOPIM-8.\ndoi:10.1016/j.physb.2010.01.014 .\nURLhttp://www.sciencedirect.com/science/article/pii/S0 921452610000165\n[17] R. Tarkhanyan, D. Niarchos, M. Kafesaki,\nInfluence of external magnetic field on magnon-plasmon polaritons in negative-index antiferromagnet-semiconductor superlattices ,\nJournal of Magnetism and Magnetic Materials 322 (6) (2010) 603 –\n608.doi:10.1016/j.jmmm.2009.10.023 .\nURLhttp://www.sciencedirect.com/science/article/pii/S0 30488530901035X\n[18] I. Fedorin, V. Baibak, A. Bulgakov,\nInfluence of an external magnetic field on the dispersion propertie s of surface waves in the 1-d periodic biaxial metamaterial,\nEur. Phys. J. Appl. Phys. 66 (2) (2014) 20502.\ndoi:10.1051/epjap/2014140077 .\nURLhttp://dx.doi.org/10.1051/epjap/2014140077\n18[19] A. Lakhtakia, An electromagnetic trinity from ‘negative permitt ivity’\nand ‘negative permeability’, International Journal of Infrared an d Mil-\nlimeter Waves 23 (6) (2002) 813–818. doi:10.1023/A:1015726915359 .\n[20] S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, C. Simovsk i,\nWaves and energy in chiral nihility, Journal of Electromag-\nnetic Waves and Applications 17 (5) (2003) 695–706.\narXiv:http://dx.doi.org/10.1163/156939303322226356 ,\ndoi:10.1163/156939303322226356 .\nURLhttp://dx.doi.org/10.1163/156939303322226356\n[21] V.R.Tuz, C.-W.Qiu,Semi-infinite chiral nihility photonics: Parame tric dependence, wave tunelling and rejection,\nProgress in Electromagnetics Research 103 (2010) 139–152.\ndoi:10.2528/PIER10030706 .\nURLhttp://onlinewww.jpier.org/pier/pier.php?paper=1003 0706\n[22] A. Al` u, M. G. Silveirinha, A. Salandrino, N. Engheta,\nEpsilon-near-zero metamaterials and electromagnetic sources: T ailoring the radiation phase pattern,\nPhys. Rev. B 75 (2007) 155410. doi:10.1103/PhysRevB.75.155410 .\nURLhttp://link.aps.org/doi/10.1103/PhysRevB.75.155410\n[23] A.M.Mahmoud, N.Engheta, Wave-matter interactions in epsilo n-and-mu-near-zero structures,\nNature Communications 5 (2014) 5638. doi:10.1038/ncomms6638 .\nURLhttp://dx.doi.org/10.1038/ncomms6638\n[24] J.Q.Shen, Negative refractive index in gyrotropically magneto electric media,\nPhys. Rev. B 73 (2006) 045113. doi:10.1103/PhysRevB.73.045113 .\nURLhttp://link.aps.org/doi/10.1103/PhysRevB.73.045113\n[25] V. R. Tuz, O. D. Batrakov, Y. Zheng,\nGyrotropic-nihility in ferrite-semiconductor composite in Faraday g eometry,\nProgress in Electromagnetics Research B 41 (2012) 397–417.\ndoi:10.2528/PIERB12042603 .\nURLhttp://jpier.org/pierb/pier.php?paper=12042603\n[26] V.R.Tuz, Gyrotropic-nihility state in a composite ferrite-semic onductor structure,\nJournal of Optics 17 (3) (2015) 035611.\nURLhttp://stacks.iop.org/2040-8986/17/i=3/a=035611\n[27] V.R.Tuz, V.I.Fesenko, Gaussian beam tunneling through a gy rotropic-nihility finely-stratified structure,\nin: O. Shulika, I. Sukhoivanov (Eds.), Contemporary Optoelectron ics,\n19Vol. 199 of Springer Series in Optical Sciences, Springer Netherland s,\n2016, pp. 99–113. doi:10.1007/978-94-017-7315-7 .\nURLhttp://dx.doi.org/10.1007/978-94-017-7315-7\n[28] M. I. Kaganov, T. I. Shalaeva, Resonant polaritons, Physica S tatus So-\nlidi (b) 162 (2) (1990) 469–476. doi:10.1002/pssb.2221620218 .\n[29] F. Tassone, F. Bassani, L. Andreani,\nResonant and surface polaritons in quantum wells, Il Nuovo Ci-\nmento D 12 (12) (1990) 1673–1687. doi:10.1007/BF02451267 .\nURLhttp://dx.doi.org/10.1007/BF02451267\n[30] V.Agranovich, Dielectric permeability and influence of external fields on optical properties of superlattices,\nSolid State Communications 78 (8) (1991) 747–750.\ndoi:10.1016/0038-1098(91)90856-Q .\nURLhttp://dx.doi.org/10.1016/0038-1098(91)90856-Q\n[31] S. Eliseeva, D. Sementsov, M. Stepanov,\nDispersion of bulk and surface electromagnetic waves in bigyrotrop ic finely stratified ferrite-semiconductor medium,\nTechnical Physics 53 (10) (2008) 1319–1326.\ndoi:10.1134/S1063784208100101 .\nURLhttp://dx.doi.org/10.1134/S1063784208100101\n[32] P.S.Reese, A.Lakhtakia, Low-frequency electromagnetic p roperties of an alternating stack of thin uniaxial dielectric laminae an d uniaxial magnetic laminae,\nZ. Naturforsch. 46a (5) (1991) 384–388. doi:10.1515/zna-1991-0502 .\nURLhttp://www.degruyter.com/view/j/zna.1991.46.issue-5 /zna-1991-0502/zna-1991-0502.xml\n[33] A.Lakhtakia, Constraints on effective constitutive paramete rs of certain bianisotropic laminated composite materials,\nElectromagnetics 29 (6) (2009) 508–514.\ndoi:10.1080/02726340903098647 .\nURLhttp://dx.doi.org/10.1080/02726340903098647\n[34] J. A. Polo, T. G. Mackay, A. Lakhtakia,\nElectromagnetic Surface Waves: A Modern Perspective, Elsevier,\nOxford, 2013. doi:10.1016/B978-0-12-397024-4.00013-X .\nURLhttp://www.sciencedirect.com/science/article/pii/B9 78012397024400013X\n[35] A.Bulgakov, I.Fedorin,Surface electromagnetic waves in thin -layer biaxial structure in a magnetic field,\nPhysics of the Solid State 54 (8) (2012) 1566–1574.\ndoi:10.1134/S1063783412080070 .\nURLhttp://dx.doi.org/10.1134/S1063783412080070\n20[36] S. Eliseeva, D. Sannikov, D. Sementsov,\nAnisotropy, gyrotropy and dispersion properties of the periodica l thin-layer structure of magnetic-semiconductor,\nJournal of Magnetism and Magnetic Materials 322 (23) (2010) 3807 –\n3816.doi:10.1016/j.jmmm.2010.08.011 .\nURLhttp://www.sciencedirect.com/science/article/pii/S0 304885310005378\n[37] A. G. Gurevich, Ferrites at Microwave Frequencies, Heywood, London,\n1963.\n[38] R.E. Collin, FoundationforMicrowave Engineering, Wiley-Inters cience,\n1992.\n[39] F. G. Bass, A. A. Bulgakov, Kinetic and Electrodynamic Phenome na\nin Classical and Quantum Semiconductor Superlattices, Nova Scienc e,\nNew York, 1997.\n21"    },    {        "title": "0907.3127v1._Rectifying__reflection_from_a_magnetic_photonic_crystal.pdf",        "content": "arXiv:0907.3127v1  [cond-mat.other]  17 Jul 2009“Rectifying” reflection from a magnetic photonic crystal\nShiyang Liu1, Wanli Lu1, Zhifang Lin1, and S. T. Chui2\n1Surface Physics Laboratory, Department of Physics,Fudan U niversity, Shanghai 200433, China\n2Bartol Research Institute and Department of Physics and Ast ronomy,\nUniversity of Delaware, Newark, DE 19716, USA\nWhen an oscillating line source is placed in front of a specia l mirror consisting of an array of flat\nuniformly spaced ferrite rods, half of the image disappeare d at some frequency. We believe that this\ncomes from the coupling to photonic states of the magnetic su rface plasmon band. These states\nexhibit giant circulations that only go in one direction due to time reversal symmetry breaking.\nPossible applications of this “rectifying” reflection incl ude a robust one-way waveguide, a 90◦beam\nbender and a beam splitter, which are shown to work even in the deep subwavelength scale.\nPACS numbers: 78.20.Ls, 42.70.Qs, 41.20.Jb, 42.82.Et\nAnyonewhohaslookedathimselfin amirrorexpects a\nfaithful image from a localized source. As is illustrated in\nFig. 1(a – c), we find a very surprising result that when\nan oscillating line source is placed in front of a special\nmirror consisting of a uniformly spaced flat collection of\nferrite rods (indicated by the black circles), the left half\nof the image disappeared near some particular frequency.\nWe call this phenomenon “Yin-Yang” reflection (YYR),\nwith “Yin” denoting the darkenedregionand “Yang”the\nbrightened region. The physics behind this is related to\nthe quantized Hall effect (QHE) and one-way magnetic\nsurface plasmon band states.\nElectric currents that circulate around the edge of the\nsample are believed to be responsible for the QHE. Be-\ncauseofthebrokentimereversalsymmetry(TRS)caused\nby the external magnetic field, this current only goes in\none direction. There has recently been much interest\nin exploring if related phenomena can occur with pho-\ntons. Among others, a skew scattering effect involving\nelectromagnetic (EM) waves was discussed by Rikken\nand coworkers [1]; possible edge-like one-way waveguide\nfrom magnetic photonic crystal (MPC) bands with finite\nChern numbers was discussed by Haldane and Raghu [2]\nand Wang and coworkers [3].\nWe have also been searching for similar phenomena\ninvolving EM waves [4]. All QHE experiments deal with\ntransmission. Because of the continuity of the electric\nandmagneticfieldsattheboundary, photonicstateswith\ngiant circulations can be probed using reflection. States\nwith the largest one way circulation are derived from the\nmagnetic surface-plasmon (MSP) bands [5, 6].\nPlasmonic materials [7, 8, 9, 10, 11] are capturing in-\ncreasing interest due to their different promising applica-\ntions. Most attention until now has been focused on the\nelectric surface plasmons originating from the collective\nresonanceofelectronicdensitywaveandhostedbymetal-\nlic building blocks. The symmetry of Maxwell’s equa-\ntions with respect to the magnetic and electric degrees\nof freedom enables a symmetric type of phenomenon in\nmagnetic systems, which is known as a “magneticsurface\nplasmon” [12]. When a periodic array of such material\nFIG. 1: (color online). The profile of the electric field with\nthe sinusodial spatial dependence included (a), the amplit ude\nof the electric field (b), and the x-component of the Poynting\nvector (c) when a line source oscillating at a frequency clos e\nto the magnetic surface plasmon resonance is placed near the\nsurface [(0,1.5a)] of a special mirror made of a slab compose d\nof a square lattice of YIG ferrite rods, indicated by the blac k\ndots in the figure. Figure (d) displays the electric field when\nthe line source oscillates at a frequency corresponding to t he\none-way edge mode studied in [3].\nis assembled together, the photonic states that hop from\none MSP state to another form a MSP band[5, 6]. In\ncontrast to the electric surface plasmon band, the MSP\nband states only go in one direction (clockwise, for ex-\nample), resulting from the breakdown of time reversal\ninvariance caused by the finite magnetic field. The YYR\neffect comes from the coupling to states derived from\nthese bands.\nThe YYR effect has the potential to revolutionize mi-\ncrowave circuitry. The diffraction limit requires that the\nminimum size ofwaveguidesbe largerthan halfthe wave-\nlength of light. Surface plasmons have attracted much\nattention as a way of circumventing the diffraction limit.\nWe show below that the YYR can be exploited to build\ntunable subwavelength waveguides, beam benders and2\nbeam splitters. Furthermore, in these circuits, the EM\nwave exhibit a “superflow” behavior; the magnitude of\nthe Poynting vector does not decrease in the presence of\ndifferent kinds of defects. We next describe in detail our\nresults, which are obtained using the rigorous multiple\nscattering method [13, 16].\nFor definiteness, consider a MPC consisting of a\nsquare lattice of parallel single crystal yttrium-iron-\ngarnet (YIG) rods along zdirection in air separated by a\ndistance a. The radius of the YIG rod is r= 0.25a.\nFor single crystal YIG, the saturation magnetization\nM0= 1750 gauss. The damping coefficient α= 3×10−4,\nand the permittivity ǫs= 15+3 ×10−3i, corresponding\nto a gyromagnetic linewidth of 0 .3 Oe and a dielectric\nloss tangent of 2 ×10−4, respectively [15]. We focus on\nthe transversemagnetic(TM) wavewith the electric field\nparallel to the rod axis.\nTypical reflection behavior for a= 8 mm is shown in\nFigs. 1(a) and 1(b), where the line source oscillating at\na frequency of 5 GHz is located 1 .5aaway from a four-\nlayer MPC slab. The applied external static magnetic\nfield is such that the total field is 900 Oe, corresponding\nto a MSP resonance at fs= 4.97 GHz. The reflection\nis shaped such that the reflected wave is dramatically\ndifferent on the left hand side (LHS) and the right hand\nside (RHS) of the source. On the LHS, the scattered field\nlargely attenuates the incoming field near the interface.\nThe MPC slab seems to repel the wave away from its\nsurface, resulting in a shadowy region, called the “Yin”\nside. OntheRHS,the scatteredfieldinsteadsignificantly\nboosts the incoming field near the interface. The MPC\nslabseemstoattractthewavetoits surface,givingriseto\na brightened region, or a “Yang” side, with an enhanced\nwave field. We next discuss the physics of the YYR.\nBecause of the broken TRS, the scattered field consists\nof unequal amount of states with opposite angular mo-\nmentanand−n, resulting in a giant circulation. This\nunequal ratio is maintained as the sign of the wavevector\nis changed from ( kx,ky) to (−kx,ky), so that the helic-\nity of the circulation is unchanged. As a result, reflection\nfrom the LHS and the RHS ofthe sourcewill be different.\nThis difference is particularly dramatic only when the\nfrequency is near the MSP resonance, where the angu-\nlar momenta content is dominated by one sign, with the\nothersignalmostcompletelysuppressedleadingtoavery\nlarge circulation [4]. Consequently, only energy flow in\none direction is supported, while that in the other (oppo-\nsite) direction is substantially suppressed near the MPC\nsurface. Coupling to these states results in a brightened\nregionononesideandashadowyregionontheotherside.\nThis is manifested in Fig. 1(c), where the xcomponent\nof the Poynting vector is exhibited. The rightward en-\nergy flow is sustained and reinforced, while the leftward\nenergy flow is substantially suppressed, and eventually\nthe system ends up with a YYR phenomenon. With this\ntype of reflection, the EM wave is shaped to move mostlyrightward near the interface. Wang and coworkers [3] re-\ncently demonstrated one-way waveguide effects based on\nthe edge state of the MPC at a frequency regime away\nfrom the MSP. The asymmetry in the reflected field is\nnot as significant, as is shown in Fig. 1(d). Aside from\nthe variation due to the Bragg reflections, there is only\na slight asymmetry in the field pattern near the MPC\nsurface. This demonstrates the importance of the MSP\nresonance in enhancing the asymmetry of the reflection.\nWe suspect that the MSP band states can also enhance\nthe effect of possible edge state waveguides.\nNow we turn to explorethe possible applications of the\nYYR phenomenon. The first example is based on the re-\nmarkable asymmetry in the Poynting vector as shown in\nFig. 1(c). Because there are band gaps both above and\nbelow the MSP resonance, the EM wave can be confined\nbetween two MPC slabs, similar to the conventional pho-\ntonic crystal waveguide [18]. If the magnetization of the\ntwo MPC slabs are in opposite directions, then the EM\nwave reflected forward from one MPC slab will also be\nreflected forward from the other MPC slab, leading to a\ndifferent design of a one-way EM waveguide [2, 3, 19],\nas is illustrated in Fig. 2(a). In Fig. 2, a line source\nis placed at ( −5.5a,0) between two MPC slabs 2 aapart.\nThe parametersfor the MPC slabs as well as the oscillat-\ningfrequencyofthelinesourcearethesameasinFig. 1(a\n– c). It can be seen that the wave propagates rightward.\nFig. 2(b) shows the xcomponent Pxof the Poyntingvec-\ntorPin a logarithmic scale. To further demonstrate the\none-way transport characteristic, in Fig. 2(c) we display\nthe electric field along y= 0 and the rightward trans-\nmitted power, Tx=/integraltext3a\n−3aPxdy, as a function of x. In\naddition, the EM flux exhibits an extremely low decay\nrate, the propagation loss is less than 0 .002 dB/mm, us-\ning realistic material parameters for commercially avail-\nable YIG ferrite [15]. To illustrate the physics, in the\nfollowing, we shall neglect the damping.\nAn importantissueofcurrentinterestisthe robustness\nof the energy flow against defects and disorder. One-way\npropagation based on the YYR appears immune to scat-\ntering from defects and disorders. Typical behavior are\nshown in Fig. 3(b – d). In Fig. 3(b) we show the elec-\ntric field when a finite linear arrayof close-packedperfect\nelectrical conductor (PEC) rods of radii rp=1\n8aare in-\nserted into the channel from y=−2.5atoy= 2.5a,\nextending over 2 λ/3. The wave circumvents the PEC\ndefect, maintaining complete power transmission in the\nchannel, with TxstayingunchangedontheLHS andRHS\nof the defect, as shown in Fig. 3(e). The leftward propa-\ngating wavecaused by the backscatteringfrom the defect\nis completely suppressed, the wave gets around the de-\nfect and keeps moving rightward. By comparing with\nthe waveguide shown in Fig. 3(a), it is found that the\ndefect changes only the phase of the rightward propagat-\ning wave, partly owing to the delay incurred when it gets\naround the defect. In Fig. 3(c) and 3(d), we present the3\nFIG. 2: (color online). The electric field (a) and the x-\ncomponent of the Poynting vector (b) due to a line source\noff= 5 GHz located at ( −5.5a,0), between two MPC slabs\nwith opposite magnetization and 2 aapart. Here ais the lat-\ntice constant of MPC composed of YIG rods indicated by\nthe circles. Figure (c) displays the electric field E(blue solid\nline) aty= 0 and rightward transmitted power Tx(red dot-\nted line) versus x, referred to the left and right ordinate axes,\nrespectively. As can be seen, the wave moves only rightward.\nFIG. 3: (color online). (a) The electric field pattern when a\nline source oscillating at f= 5 GHz is placed between two\nMPC slabs of opposite magnetization and 2 aapart, showing\none-way transportation of EM wave. Introducing a finite lin-\near array of close-packed PEC rods (b), disorder in ferrite r od\npositions (b), or disorder in ferrite rod radii (c) does not o b-\nstruct or modify the one-way transportation characteristi cs,\nbut, instead, only causes the propagating wave to circumven t\ntheblockor changeitswavefront, while maintainingcomple te\ntransmission. The open circles (of different sizes) denote t he\nYIG rods while the solid circles in (b) indicate the PEC rods.\nFigure (e) shows normalized transmitted power versus xfor\n(a), (b), (c), and (d).profile of the electric field for the cases when disorder in\nthe positions and the radii of the YIG rods is introduced,\nrespectively, in the MPC slab. The change in position is\na random amount from zero to 25% of the lattice spacing\na; the random change in radius has a maximum of ±50%\noftheunperturbedradius0 .25a, smallenoughsothatthe\ndisordered rods do not overlap. As can be seen, the dis-\norder, either in position or in radius, only alters the wave\nform, but not the transmission power through the chan-\nnel, implying the robustness against disorder, consistent\nwith the fact that the MSP band states also exhibit fi-\nnite Chern numbers. For the edge state waveguide [2, 3],\nthe operating frequency lies in the Bragg band gap, so\nalthough their system is immune to scattering from the\ndefect, it may suffer from disorder in either the position\nor the radius of the building blocks in the photonic crys-\ntals, astheseeffectswilldestroythe“Bragg”bandgap[5].\nPhotonic circuits with no back-scattering based on the\nYYR can be achieved even in the deep subwavelength\nregime. Figure 4 shows such examples where the geome-\ntry is scaled down in size with a= 2 mm and r= 0.25a,\nbut the frequency f= 5 GHz is unchanged. The other\nparameters are the same as those in Figs. 3(a). A sub-\nwavelength guide is shown in 4(a), with the full lateral\nwidth at half maximum field amplitude wh∼0.08λ. In\nFig. 4(b), the configuration is similar to that in Figs. 2\nand 3 except that a cladding slab is added on top of the\nsystem. A line source is located at (0 ,−18a). The EM\nwaveis found tomakea 90◦turn with nearly100%power\ntransmission in the proximity of the MSP resonance fre-\nquency, as shown by the blue solid line in Fig. 4(d).\nIf one reverses the orientation of the magnetization for\nthose rods with coordinates x <0 in the cladding slab,\nThe propagation is seen to split at the bifurcation point,\nas shown in Fig. 4(c). The upward transmitted power,\nTy=/integraltext3a\n−3aPydx, is split with 50% power transmission to\nthe right and the other 50% to the left by symmetry, as\nshown by the red dashed line in Fig. 4(d). The wave\nexperiences an extremely low reflection at the corner ,\nas can be seen from the field distribution before bending\nand splitting in the vertical channel. Furthermore, as the\ndirectionofthemagnetizationcanbecontrolledbyanex-\nternal magnetic field, the function of the system can be\nswitched between the function of bending and splitting.\nIn summary, we have demonstrated a new phe-\nnomenon, named ”Ying-Yang” reflection when the EM\nwave is reflected from a MPC. The phenomenon is be-\nlieved to originate from the TRS breaking nature of the\nmagnetic surface plasmon band states. Possible applica-\ntions of this phenomenon include a one-way waveguide\nthat appears to be immune to defect and disorder, sharp\nwave bending and beam splitting with extremely low re-\nflection. These applications are expected to be realizable\neven in the deep subwavelength scale.\nThis work is supported by the China 973 program,\nNNSFC, PCSIRT, MOE of China (B08011), and Shang-4\nFIG. 4: (color online). The electric field patterns in subwav e-\nlength waveguides (a), 90◦beam bender(b) and splitter (c) at\nf= 5 GHz. The power transmitted horizontally Txnormal-\nized by the incoming vertical power, Tx/Ty, versus frequency\nis shown in (d). The lattice constant for the MPC is a= 2\nmm; the YIG rod radius, r= 0.25a. The full lateral width at\nhalf maximum field amplitude s wh<0.08λ.\nhai Science and Technology Commission. STC is partly\nsupported by the DOE.[1] G. L. J. A. Rikken and B. A. Van Tiggelen, Nature 381,\n54 (1996).\n[2] F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100,\n013904 (2008).\n[3] Z. Wang et al., Phys. Rev. Lett. 100, 013905 (2008).\n[4] S. T. Chui and Z. F. Lin, J. Phys. Condens. Matt. 19,\n406233 (2007).\n[5] S. Y. Liu et al., Phys. Rev. B 78, 155101 (2008).\n[6] S. T. Chui and Z. F. Lin, Phys. Rev E 78, 065601(R)\n(2008).\n[7] W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature\n424, 824 (2003).\n[8] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin,\nPhys. Rep. 408, 131 (2005).\n[9] V. N. Konopsky, and E. V. Alieva, Phys. Rev. Letts. 97,\n253904 (2006).\n[10] S. A. Maier, Plasmonics: Fundamentals and Applications\n(Springer, New York, 2007).\n[11] F. J. G. de Abajo, Rev. Mod. Phys. 79, 1267 (2007).\n[12] J. R. Gollub, et al.Phys. Rev. B 71, 195402 (2005).\n[13] D. Felbacq, G. Tayeb, and D. Maystre, J. Opt. Soc. Am.\nA11, 2526 (1994).\n[14] D. M. Pozar, Microwave Engineering 3rd Ed. (Wiley,\nNew York, 2005).\n[15] E. P. Wohfarth, in Ferromagnetic Materials (North-\nHolland, Amersterdam, 1986). Vol.2, p.293.\n[16] S. Y. Liu et al., Phys. Rev. Lett. 101, 157407 (2008).\n[17] H. C. van der Hulst, Light Scattering by Small Particles\n(Dover, New York, 1981).\n[18] A. Mekis et al., Phys. Rev. Lett. 77, 3787 (1996).\n[19] Z. Yu et al., Phys. Rev. Lett. 100, 023902 (2008)."    },    {        "title": "2310.13842v2.475_C_aging_embrittlement_of_partially_recrystallized_FeCrAl_ODS_ferritic_steels_after_simulated_tube_process.pdf",        "content": "475 °C aging embrittlement of partially recrystallized FeCrAl ODS ferritic\nsteels after simulated tube process\nZhexian Zhanga,1,∗, Daniel Morrallb,1, Kiyohiro Yabuuchia\naInstitute of Advanced Energy, Kyoto University, Gokasho, Uji, 611-0011, Kyoto, Japan\nbGraduate School of Energy Science, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Kyoto, Japan\nAbstract\nTube processing and aging effects in FeCrAl ODS steels are investigated in four mechanical alloyed ferritic\nODS steels, Fe15Cr (SP2), Fe15Cr5Al (SP4), Fe15Cr7Al (SP7) and Fe18Cr7Al (SP11). These steels were\nmade into 0.3mm thick plates by simulated tube processing (STP). Strengthening after partial recrystal-\nlization was achieved after the last cold rolling and heat treatment step. However, the ductility reduced\nabout one third of the as-extruded steels. The STPed steels were aged at 475 °C in sealed vacuum tubes up\nto 2000 hrs and 10000 hrs, respectively. The yield stress and elongation were investigated by tensile tests.\nThe results revealed that all the STPed steels fractured in a ductile manner irrespective of aging conditions.\nAging hardening and ductility reduction in STPed steels are similar to as-extruded ones. The STPed ODS\nsteels showed similar ageing embrittlement resistance as as-extruded steels, but much higher than the non-\nODS steels. The aging hardening based on cut-through and bow-pass mechanisms were discussed. The time\ndependent hardening of overaged steel ( β′only) was analyzed as well.\nKeywords:\nFeCrAl ODS steel, ATF cladding, simulated tube processing, aging embrittlement, aging hardening\n1. Introduction\nFeCrAl ferritic alloys are considered as promising\ncandidate materials for accident tolerant fuel (ATF)\ncladding in the designs for suppressing hydrogen\ngeneration reactions with hot water in light water\nreactors (LWR) at extreme high temperatures[1–\n3]. However, the neutron penalty caused by larger\nabsorption section of Fe atoms, which will reduce\nthe neutron efficiency in comparison to conven-\ntional zircaloy system, has to be relieved by re-\nducing the FeCrAl cladding wall thickness and/or\nenhancing the uranium enrichment of the nuclear\nfuel. For example, the thickness of iron-based alloy\ncladdings was calculated to be limited to 300 µm\n∗corresponding author\nEmail address: zzhan124@utk.edu (Zhexian Zhang)\n1This work was done by Zhexian Zhang, and Daniel Mor-\nrall when they were staff of Institute of Advanced Energy,\nKyoto University and student of Graduate School of En-\nergy Science, Kyoto University, respectively. Zhexian Zhang\nis now a visiting researcher in the University of Tennessee\nKnoxville.with 4.78% U235 fuel enrichment to match the same\ncycle length of Zircaloy without changing other fuel\npin geometries[4]. In general, reducing the cladding\ntube thickness is preferred than enhancing uranium\nenrichment upon the technical feasibility and econ-\nomy preference[5].\nNevertheless, the structural integrity of claddings\nrequires a minimum thickness to meet the strength\ndemand for safety consideration. To compen-\nsate for the strength loss by the thickness reduc-\ntion of cladding wall and to enhance the strength\nat elevated temperatures, the strategy of oxide\ndispersion strengthening (ODS) was adopted in\nthe development of FeCrAl ATF cladding mate-\nrials. Based on this strategy, several Japan na-\ntional programs of FeCrAl ODS ferritic steels R&\nD were conducted[6, 7]. These programs are on\nthe bases of the knowledges accumulated by the\nJapanese leading programs of R& D of ODS ferritic\nmartensitic steels with[8][9, 10] and without[11] Al-\naddition for the applications to core components\nof Gen IV fast reactors. After decades of inves-\ntigations, the FeCrAl ODS ferritic steels devel-\nPreprint submitted to arXiv November 6, 2023arXiv:2310.13842v2  [cond-mat.mtrl-sci]  3 Nov 2023oped in Japan have demonstrated excellent prop-\nerties, particularly the creep resistance[12–14], ox-\nidation/corrosion resistances[15–19] and radiation\ntolerance[20–23].\nHowever, the increased ultra-high strength of Fe-\nCrAl ODS steels also brought about difficulty in the\nfabrication processes such as cold rolling and pil-\nger milling[24, 25]. This concern was proposed to\nbe overcome by recrystallization treatment, which\nreduces the yield strength of ODS steels during\ntubing[26]. According to the previous study on\nFeCr(Al) ODS ferritic steels[27], the typical recrys-\ntallization temperatures after hot extrusion ranges\nfrom 1050 °C to 1400 °C, depending on the alloy\ncompositions and pre-mechanical processing (forge,\nrolling, etc). The on-set recrystallization tempera-\nture of FeCrAl ODS ferritic steels could be signifi-\ncantly reduced by the degree of cold work[26]. The\nreduction of yield stress could reach to 25% 50%\nafter fully recrystallization, while the property of\ntotal tensile elongation would barely change[28].\nIn the tubing process, a four-cycle cold-rolling\n(CR) and heat-treatment (HT) process was first de-\nsigned in the R& D of Fe9Cr ODS alloy[29, 30].\nLater, this processing route was applied to general\ntubing of FeCrAl ODS steels[7][31]. The thickness\nreduction was about 50% in each CR step. How-\never, the temperatures of the HT vary in interme-\ndiate and last steps. The intermediate HT temper-\natures were designed to be a little below the recrys-\ntallization temperature to induce only recovery to\navoid cracking in further rolling[32]. The recrystal-\nlization was only designed in the last step to pro-\nduce equiaxed grains (however, most of the grains\nstill elongated to the rolling direction, but generally\nthe anisotropy was greatly reduced) and reduce the\noverall yielding strength. Although recrystalliza-\ntion can effectively reduce the yielding strength, it\nhas been found that repeating recrystallization will\nbe retard by the previous recrystallization[32–34].\nThis is the reason that recrystallization was only\ndesigned in the last step in tubing processing.\nDuring the service of FeCrAl tube claddings in\nreactors, the steels may suffer aging embrittlement\nunder the operation temperatures. This aging ef-\nfect is owing to the formation of various fine pre-\ncipitates which cause the deterioration of mechan-\nical properties. According to the recent publica-\ntions based on atom probe tomography (APT), age-\nhardening could be brought about by both Cr-rich\nα′phases[35–40] andor (Al, Ti)-rich β′phases[41–\n44] depending on the concentration of Cr and Al inthe FeCrAl ODS steels. As for the effect of Al addi-\ntion on age-hardening, Kobayashi and Takasugi[45]\ninvestigated the age-hardening of diffused FeCrAl\nalloys with multiple concentrations and showed\nthat the addition of Al shifted the Fe-Cr miscibil-\nity boundary to a higher Cr concentration, conse-\nquently hinders the α-α′phase separation. Particu-\nlarly in the study by Dou et al, when Al is >7wt%,\nnoα′phase was formed in Fe15Cr-(7,9)Al ODS\nsteels[43], while the Al additions will enhance the\nformation of Ti-Al enriched β′precipitates caus-\ning age-hardening without the occurrence of α-α′\nphase separation[41]. Sang et al[42] reported that\ntheβ′could form in early stage during thermal ag-\ning in high Al ODS steels. The age-hardening of\nas-extruded FeCrAl ODS steels has been investi-\ngated at 475 °C up to 9000 hrs[46], while the aged\nFeCrAl ODS steels after tubing process have been\ninvestigated by Yano et al[31]. The aging of high-Al\nFeCrAl ODS steels were also investigated by Maji\net al[47] where again no α′but Al enriched precipi-\ntates (mainly FeAl and Fe 3Al) were formed in these\nsteels.\nThe solution to the aging embrittlement is to\noptimize the composition of FeCrAl steels. The\nconcentrations of Cr and Al are required to sat-\nisfy both the oxidation resistance at extreme high\ntemperature, and low aging rate at reactor oper-\nation temperatures. To this end, the “SP” series\nof FeCrAl ODS steels were designed and produced,\nwith the Cr between 12 and 18wt%, and the Al of\n0, 5 9wt%. In this range of Cr concentration, α′\nwill form through a special nucleation and growth\nway (where the Cr concentration in precipitates and\nsize increase simultaneously)[35], while Al will hin-\nder this process[48]. These researches focusing on\nthe SP-series FeCrAl steels have been intensively\ncarried out and summarized in a recent review[49].\nThis study belongs to the bunch of the research\nwork on the “SP” series FeCrAl ODS steels. The\nobjective is to investigate the aging behavior of the\nselected FeCrAl steels after simulated tube fabri-\ncation processing (STP). Different to conventional\ndesign with recrystallization only in the last HT\nof tubing process, we tentatively designed the full\nrecrystallization in the 3rd HT and partially recrys-\ntallization in the last HT of the STP. This design\naims to reduce the rolling difficulty in the 4th CR\nand increase the final strength of the steels than\nconventional fully recrystallized FeCrAl tube. The\nSTPed steels were thermal aged at 475 °C up to 2000\nhrs and 10000 hrs. The mechanical properties were\n2Figure 1: The workflow of experimental procedure includes\nsimulated tube processing and thermal ageing together with\neach measurement and observation.\ninvestigated by means of uniaxial tensile test. A\ncomparison of the aging hardening behavior was\nmade between the as-extruded and STPed FeCrAl\nODS steels. The hardening rates were analyzed by\ncombination of a precipitation kinetics model and\ntwo-fold hardening mechanism. The (Cr, Al) con-\ncentration dependence on hardening was discussed\nas well.\n2. Experiments\n2.1. Materials\nThe starting materials used in this study are Fe-\nCrAl ODS ferritic steels (SP series) produced by\nKOBELCO, Ltd. The chemical compositions are\nshown in Table 1. There are four steels with differ-\nent Al and Cr concentration, which are named as\nFe15Cr (SP2), Fe15Cr5Al (SP4), Fe15Cr7Al (SP7)\nand Fe18Cr7Al (SP11). The Fe15Cr (SP2) steel\ncontains no Al but 2wt% W. All the steels were\nproduced by mechanical alloying method starting\nwith Ar-gas-atomized alloy powders, element pow-\nders and Y 2O3powders. The mechanically alloyed\npowders were encapsuled into a can to degas at\n400 °C in a vacuum of 0.1 Pa for 2 hrs and extruded\nat 1150 °C into a rod with 25 mm diameter. Therod was finally annealed at 1150 °C for 1 hr and\nsubjected to air cooling.\nThe workflow of the STP and aging experiments\nare illustrated in Figure 1. The simulated tube fab-\nrication process was started with the as-received\nODS bars which were cut from the extruded rod.\nThe bars were subjected to cold rolling and ther-\nmally annealing followed by furnace cooling at a\nrate of ∽150 Khr in average to achieve a full ferrite\nphase. The CR-HT was repeated four times. The\nrolling process was illustrated in Figure 2a. The\nrolling was performed at room temperature, with\neach single rolling pass yielding ∽1 to 2% thickness\nreduction. The rolling direction (RD) was parallel\nto the extrusion direction without being reversed.\nAs the specimens were very hard, cracks were eas-\nily generated at the head of the specimen during\nthe rolling. In this case, we cut off these cracked\nparts to prevent it from growing deeper in follow-\ning rolling. The thickness of specimens was ap-\nproximately 50% reduced in each rolling cycle, with\nsubsequent annealing treatment at 950 °C, 850 °C,\n1150 °C and 1150 °C for 1 hr, respectively. The total\nthickness reduction ηand strain ϵare defined as:\nη= 1−h/h0,η=ln(h0/h). The initial sample\nthickness, h 0, was 4 mm. The parameters of h, η\nandϵin cold rolling and subsequent annealing tem-\nperatures were displayed in Table 2. Tensile speci-\nmens of dog-bone shape were produced from STPed\nplates of 0.3 mm thickness. Isothermal aging was\nperformed on the dog-bone tensile specimens sealed\nin vacuum capsules at 475 °C for 2000 hrs and 10000\nhrs followed by iced water quenching.\n2.2. Microstructural observations\nTransmission electron microscopy (TEM) was\nperformed on JEOL 2200 field emission TEM to\ninvestigate the microstructures of grain and oxide\nmorphology. The foils for TEM observation were\nthinned by focused ion beam (FIB, Hitachi FB2200)\nto 250 nm, followed by flash polishing in a mixture\nof 5% HClO 4and 95% CH 3OH at a voltage of 30\nV and temperatures between -30 °C and -65 °C.\nElectron Back Scatter Diffraction (EBSD) was\napplied to investigate the grain morphology via an\nEDAX detector equipped on Zeiss Ultra-55 field-\nemission scanning electron microscopy (FE-SEM)\nwith acceleration voltage of 10 to 15eV. The over-\nall grain morphology was scanned on an area of\n150µmx 150µmwith a step of 1 µmvia con-\nventional EBSD to identify recrystallization occur-\nrence. Since grains in ODS steels are generally sub-\n3Figure 2: a) Schematic view of the cold rolling in the simulated tube processing, b) IPF of the grain morphologies of four\nFeCrAl ODS ferritic steels rolling surface after each cold rolling and heat treatment (CR-HT) cycle, and c) the transmitted\nEBSD (TKD) image of cross-section of the fine subgrains of Fe15Cr after ageing for 2000 hr. The upward of conventional\nEBSD IPF is parallel to the rolling direction. The TKD specimen is normal to the rolling direction.\nTable 1: Chemical compositions of FeCrAl ODS ferritic steels (wt%, Bal. Fe)\nID Cr Al W Ti Y C O N Ar\nFe15Cr SP2 14.24 <0.01 1.85 0.23 0.18 0.028 0.12 0.005 0.006\nFe15Cr5Al SP4 14.39 4.65 - 0.32 0.39 0.032 0.22 0.005 0.006\nFe15Cr7Al SP7 14.13 6.42 - 0.51 0.38 0.032 0.22 0.005 0.006\nFe18Cr7Al SP11 16.83 6.31 - 0.49 0.38 0.032 0.22 0.004 0.006\nmicron size with small misorientations, the Trans-\nmission Kikuchi Diffraction (TKD)[50] was per-\nformed as well with a step size of 50 nm to show\nthe mixture of fine grains and recrystallized grains\nafter partially recrystallization.\n2.3. Mechanical tests\nMicro-Vickers hardness was tested by HMV-2T\n(Shimadzu Corp.) with 2 kg load and 10 sec hold-\ning time at room temperature. The hardness was\nmeasured on the rolling surface of the plates after\neach cycle of CR-HT.\nTensile tests were performed on INTESCO 205X\ntensile assembly with a load cell of 5 kN. The dog-\nborn miniaturized tensile specimens were sampled\nfrom the STPed plates with the loading direction\nparallel to the rolling direction. The gage geometry\nof the tensile specimen was 5 mm in length, 1.2 mm\nin width and 0.3 mm in thickness. The tests were\ncarried out at a displacement rate of 0.2 mm/min,resulting in an initial strain rate of 6.67 ×10-4/s.\nThe yield stress (YS) was defined as 0.2% off-set\nflow stress. Two or three specimens were tested\nat each aging condition. All the tensile tests were\nperformed at room temperature.\n3. Results\n3.1. Simulated tubing processing\nAccording to our previous research[28], the grain\nmorphology of the FeCrAl ODS steels after hot ex-\ntrusion have a strong α-fiber texture (RD <110>)\nstructure parallel to the extrusion direction, and\nhave fine and isotropic grain shape on the cross-\nsectional surface. It was also shown that the fibers\ncontained very fine sub-grains with small crystal\nmisorientations. The hardness of the as-extruded\nsteels are available in our previous publication[46].\nThe evolution of grain morphology after each\ncold rolling and heat treatment (CR-HT) is shown\n4Figure 3: The dispersion morphology of nano-particles in FeCrAl ODS ferritic steels at the conditions of as-extruded, simulated\ntubing processing (STP) and 475 °C 2000hrs aging. The wight arrows indicate oxide particles. The grain morphology of STPed\nFe15Cr was shown as well. There are both elongated and equiaxed grains, indicating partially recrystallization in this material.\nTable 2: The parameters of simulated tubing process\nThickness, h (mm) Total thickness reduction, ηTotal strain, εAnnealing temperature, T ( °C)\nInitial 4 0 0 -\nCR-HT1 2 0.5 0.69 950\nCR-HT2 1 0.75 1.39 850\nCR-HT3 0.6 0.85 1.90 1150\nCR-HT4 0.3 0.925 2.59 1150\n5Figure 4: The Vickers hardness of FeCrAl ODS ferritic steels\nduring simulated tubing processing after each cold rolling\nand heat treatment (CR-HT) cycle. All the hardness were\nmeasured on the rolling surface.\nin Fig. 2(b). After the first cycle (CR-HT1),\nFe15Cr7Al (SP7) and Fe18Cr7Al (SP11) were sub-\njected to recrystallization. It is obvious that\nFe15Cr5Al (SP4) recrystallized after the 2nd cy-\ncle of CR-HT. In Fe15Cr (SP2), which is an Al-free\nferritic steel, the recrystallization didn’t occur until\nthe 3rd cycle of CR-HT. After the fourth cycle of\nCR-HT, there were still fine grains remaining, in-\ndicating that the grains were only partially recrys-\ntallized. Fig.2(c) is a cross-section image (normal\nto RD) of Fe15Cr aged for 2000 hrs. As the grain\nboundaries are considered stable at 475 °C, they\ncan represent for the grain sizes after the STP. In\nFig.2(c), both fine grains and coarse grains coex-\nisted in the same specimen. The high thermal sta-\nbility during STP of the grain structure in Fe15Cr\n(SP2) was interpreted in terms of fine oxide parti-\ncle dispersion with a very high number density in\nAl-free ODS steel. These oxides could hinder the\nmovement of grain boundaries, so that elevate the\non-set recrystallization temperature. Fig.3 summa-\nrizes the typical morphology of oxides in Al-free\nand Al-added ferritic ODS steels. In Fe15Cr7Al\nand Fe18Cr7Al, the oxides are Y-Al-O type with\nlarger size but smaller density than Y-Ti-O oxides\nin Fe15Cr. These results correspond to the fact\nthat adding Al will coarsen the size of oxides in\nODS steels during fabrication[51]. The growth of\noxides during STP could be ignored due to short\nannealing time[52].\nThe hardness change by recrystallization reflects\nthe change in grain sizes, ignoring the influence oftextures. Cold rolling will induce subgrain bound-\naries and multiply dislocations, while thermal an-\nnealing will relieve the residual stress and trigger\nnucleation and grain growth if recrystallization oc-\ncurred. The Vickers hardness after each CR-HT\ncycle of each ODS steel is shown in Fig.4. The\nFe15Cr5Al and Fe15Cr7Al showed a similar behav-\nior in Vickers hardness change. Fe15Cr showed a\ndramatic decrease after the CR-HT3. Combined\nwith the grain morphology in Fig. 2(b), Fig.4 in-\ndicates that all the steels heated at 1150 °C will en-\ndure significant recrystallization in HT3. Although\nthe recrystallization was designed to soften material\nfor further thinning, all the specimens in this work\nwere finally hardened after the entire STP proce-\ndure compared to the as-extruded steels.\nThe final hardening in CR-HT4 is because of the\nrepeating recrystallization retarded by intermedi-\nate recrystallization in HT3. According to Leng\net al[34], repeating recrystallization requires higher\non-set temperature and has higher hardness than\nfirst recrystallization at the same annealing temper-\nature. Explanation was made by means of experi-\nments of EBSD orientation density function (ODF)\nanalysis[25, 32, 33, 49] and the theory built on nu-\ncleation driving force and grain boundary migra-\ntion rate[53]. First, recrystallization will produce\n{111}and{110}textures on the rolling plane. Cold\nrolling on the recrystallized {111}<112>crys-\ntals will produce strong {100}<110>texture,\nwhich contains extremely low strain energy that\nthe driving force for recrystallization is very low,\ntoo. Second, the grain boundary migration rate de-\npends on both the misorientation between the re-\ncrystallized nuclei and the matrix[54], and the pin-\nning force of fine oxides. For Al-free steels, the ox-\nides are extremely small so that the pinning force\ncontrols the migration rate. For Al-added steels,\nthe pinning force will be smaller. The nucleus of\n{111}<112>has a misorientation below 45 °on\nrolling surface{112}<110>and{111}<110>\n[25] that they may grow faster during HT4.\nIn practice, cracks easily occurred in the steels\nduring CR2 and CR3, particularly for Fe15Cr,\nwhich has extremely high hardness during CR3.\nThere are no cracks generated in CR4 as recrys-\ntallization in HT3 greatly reduced the yielding\nstrength. The final hardness after HT4 is slightly\nhigher than the as-extruded, which means the steels\nare only partially recrystallized. Through the de-\nsigned STP, the aim to increase the final strength\nthan conventional fully recrystallized steels were\n6Figure 5: The engineering stress-strain curves of STPed Fe15Cr, Fe15Cr5Al, Fe15Cr7Al, Fe18Cr7Al ODS steels before and\nafter ageing at 475 °C to 2000 hrs and 10000 hrs. Note that the elastic component includes the elongation of machine assembly.\nachieved.\n3.2. Tensile properties\nThe engineering stress-strain curves of the STPed\nODS steels were shown in Fig.5 with a presentative\ntest at each aging condition. The age-hardening\nshowed dependence on the content concentration.\nBefore aging, the tensile strength of FeCr ODS is\nreduced by Al-addition, which is due to the reduc-\ntion of density of oxide particles. The yield strength\nincreases with increasing Al and Cr concentration\nbecause of solid solution strengthening[55]. As for\nthe aging effects, age-hardening is much more sig-\nnificant in Al-added ODS steels (SP4, 7, 11) than\nthat in Al-free steel (SP2). This behavior is similar\nto the as-extruded ODS steels in which (Al, Ti)-\nrichβ′-phases (as well as α′-phases) were induced\nby the aging[42–44].\nFig.6 shows the yield stress (YS), ultimate tensile\nstress (UTS), uniform elongation (UE) and total\nelongation (TE) of all the tested specimens. Gen-\nerally, the scattering of YS is larger than that of\nUTS because the ill-defined proof stress could be\neasily affected by the stiffness of tensile machine\nand/or load cell especially for thin specimens. Thescattering of TE in Fig.6c was affected by the de-\nformation after necking. A notable variation in\nds(e)/deoccurred after the UTS, which means that\nthe area of cross section of the specimen shrank\nrapidly after the necking occurrence. There is an\ninconsistency occurred in the yield stress and Vick-\ners hardness of STPed SP2. In Fig.4, the Vick-\ners hardness of STPed SP2 was similar to the as-\nreceived (as-extruded), however, in Fig.6a, the yield\nstress of STPed SP2 is much lower ( 100MPa) than\nas-extruded steel. This might be owing to the\nanisotropy grain morphology in the steels after hot-\nextrusion and STP. As for the aging effect on the\ntensile strength and tensile elongation, all the 2000\nhrs aged FeCrAl ODS steels showed YS hardening\nand TE reduction. The 10000 hrs aging, however,\nresults in “recovery” effect with reduced hardening\nand increased elongation compared to the 2000 hrs\naged ones.\nThe true stress-strain ( σ-ϵ) curves were estimated\nfrom the plastic deformation using the following\nequations:ϵ=ln(eP\ns+ 1),σ(ϵ) =s·(eP\ns+ 1) where\neP\nsis the plastic component of engineering strain\nof specimen, sis the engineering stress, ϵandσ(ϵ)\nstands for the true strain and true stress respec-\ntively. The true stress-strain curve mainly devi-\n7Figure 6: The a) yield strength (YS), b) ultimate tensile strength (UTS), c) total elongation (TE), d) uniform elongation (UE)\nof ODS ferritic steels as-extruded (hollow) and after STP (solid), and after aging for both the specimens as extruded and after\nSTP.\n8Figure 7: Deformation energy ( J·m−3) of as-extruded and STPed steels before and after 475ř Caging.\nFigure 8: The morphology of fracture surface of STPed Fe15Cr, Fe15Cr5Al, Fe15Cr7Al and Fe18Cr7Al before and after 2000hrs\naging.\n9ates 1) after necking where the cross area reduced\ndramatically and the materials experienced three-\ndimensional stress state, and 2) around the initial\nplastic deformation regions where eP\ns/eE\ns≪1. The\nempirical Ludwik relationship was evaluated by the\ndata between 0.5% true strain to true uniform elon-\ngation:\nσ(ϵ) =σ0+Kϵn(1)\nwhereσ0is the true yield stress, Kis the strength\ncoefficient, nis the strain hardening exponent\nThe estimated Kandnvalues from true stress-\nstrain curves are listed in Table 3. Kis the ampli-\ntude of the strain hardening term and nis applied\non the strain ϵdirectly. Note that as the strain\nis smaller than 1, lower nwill lead to higher strain\nhardening ratio. From Table 3 we can conclude that\nthe 2000 hrs aged specimens have the lowest Kand\nncompared to other conditions.\nThe aging embrittlement can be described by the\nreduction of total deformation energy, u DE, in ten-\nsile test by:\nuDE=/integraldisplayUE\n0σdϵ+/integraldisplayTE\nUEσdϵ (2)\nThe first term in equation (2) represents the en-\nergy applied by uniform deformation (UDE) until\ntensile stress reaches the UTS. The second term is\ndefined as the fracture energy (FE) which is ac-\ncompanied by necking. In practice, the integration\nwas calculated by trapezoidal method. In Fig.7,\nthe STPed steels exhibited significant decreases in\nuDEcompared to extruded steels irrespective of Al\nconcentration in each ODS steel. This reduction\nshould be owing to the micro-crack generation dur-\ning cold rolling. The recrystallized layered grains\nmay accelerate the growth of cracks due to weak\ngrain boundary cohesion.\nAs for the effect of aging on the DE, three types of\ntrends were showed: 1) for the Fe15Cr, the STPed\nsteels showed reduction in DE after 2000hrs aging,\nbut recovered at 10000 hrs aging, which was even\nhigher than the non-aged one. This behavior is dif-\nferent to the as-extruded steels, whose DE at 9000\nhrs aging was still lower than non-aged. 2) for the\nFe15Cr7Al, the DE of both STPed and as-extruded\nsteels decreases as aging time increases. 3) for the\nFe15Cr5Al and Fe18Cr7Al, the DE of STPed steels\nreduced at 2000 hrs but increased at 10000 hrs\naging, which are similar to the as-extruded ones.\nThe three types of behavior of DE correspond to\nthe three different modes of precipitates inducedby aging: 1) only α′in Fe15Cr and 2) only β′in\nFe15Cr7Al were generated, but 3) both α′andβ′\nprecipitates formed in Fe15Cr5Al and Fe18Cr7Al,\nwhich will be discussed in Section 4.2.\n3.3. Fractography\nAll the specimens before and after aging frac-\ntured in a ductile manner with plastic shearing in-\nduced dimples on the rupture surfaces. This phe-\nnomenon indicates that the materials still behave\nas ductile after 10000 hrs aging in tensile test at\nambient temperature. This behavior is different\nto the recent research which showed a typical brit-\ntle fracture manner of Fe15Cr7Al ODS steel after\n15000 hrs aging with tensile loaded in the tube hoop\ndirection[31].\nFig.9 shows two characteristic features on the\nfracture surfaces. The first one is large precipi-\ntates located inside the dimples as shown in Fig.9a.\nThese precipitates are enriched in Al according to\nEDS spectrum analysis and can be deduced as alu-\nmina. These particles can function as the initial\nseparation sites because of dislocation pile-ups and\nthe weak adhesion of the interface between the par-\nticle and the matrix. The second one is the long sec-\nondary cracks as shown in Fig. 9b. These cracks are\nformed on the layered and elongated grain bound-\naries, which are parallel to the rolling surface. This\ndelamination is a typical phenomenon in laminated\nODS steels[56]. The bamboo-like grains in the\nSTPed steels will help the propagation of the sec-\nondary cracks[57]. The secondary cracks might be\nthe reason for the elongation reduction compared\nto the as-extruded ODS steels.\n4. Discussion\n4.1. The aging effect on total elongation\nThe fabrication of FeCrAl ODS cladding tubes\nrequires recovery and recrystallization as a stan-\ndard routine. Occurrence of recrystallization de-\npends on the cold rolling degree and annealing tem-\nperatures which determines stored energy, namely,\ndriving force of recrystallization. While Ha[27] re-\nported that a full recrystallization would not cause\nsever loss of elongation in extruded ODS steels, the\nresults from Yano et al[31] and Sakamoto et al[7]\nshowed a rather large ductility loss in pilger rolled\nrecrystallized FeCrAl ODS steels. There is approx-\nimately 30% reduction of total elongation in steels\nafter full tubing routine compared to as-extruded\n10Table 3: The strength coefficient Kand strain hardening opponent nin Ludwik relationship\n0 hr 2000 hrs 10000 hrs\nn K n K n K\nFe15Cr 0 .355±0.024 540.489±66.991 0.313±0.043 469.947±44.958 0.305±0.019 574.742±66.108\nFe15Cr5Al 0 .454±0.069 872.585±78.248 0.341±0.040 559.785±33.790 0.356±0.052 749.861±60.764\nFe15Cr7Al 0 .376±0.010 764.343±53.914 0.345±0.053 615.251±30.515 0.418±0.034 728.033±44.502\nFe18Cr7Al 0 .345±0.052 674.347±27.706 0.266±0.033 434.258±27.903 0.359±0.028 663.538±65.669\nones[31]. In this study, the STPed steels in Fig.6\nshowed a similar trend as those after full tubing\nroutine with a significant loss of elongation. Only\na small loss of elongation after the recrystallization\nin the work by Ha[27] is probably due to no tubing\nprocess put on, suggesting that the loss of elonga-\ntion is closely associated with cold rolling process.\nOne of the supreme behaviors in the plastic defor-\nmation of FeCrAl ODS steels is their smaller loss\nof elongation by thermal aging compared to non-\nODS steels[58]. To illustrate this phenomenon, the\naging-hardening in terms of the change in YS with\nrespect to the loss of elongation of all the steels were\nshown in Fig.10. The Fe15Cr-melt, Fe15CrC-melt\nand Fe15CrXs-melt are non-ODS steels produced\nby arc-melting method. The Fe15Cr and Fe12Cr\nare ODS steels produced by mechanical alloying\nmethod[59]. A commercial SUS430 which contains\n16% Cr without Al was compared as well. It should\nbe noted that the aging effect were quite stable af-\nter approximately 5000 hrs aging according to the\nprevious experiment results[60].\nFig. 10 shows that the loss of elongation by ag-\ning is rather smaller in ODS ferritic steels (red and\ngreen) than in arc-melted (non-ODS) alloys (hol-\nlow black) with respect to the same amount of age-\nhardening. This behavior is consistent with our\nprevious works[58, 60]. As for the comparison be-\ntween as-extruded (red) and STPed (green) condi-\ntions, the loss of elongation in these steels are quite\nsimilar (<0.03). This result indicates that the duc-\ntility loss by aging is less sensitive to the nature of\nODS steels (concentration, grain morphology, pre-\ncipitates, etc).\nThe rupture of ductile materials could be ex-\nplained by micro-voids forming along the center of\nthe necked region. The voids could form around\nprecipitates where dislocation pile up and stress\nconcentration occurs. Thus, non-deformable large\nparticles, such as core-shelled Y-Ti-O in Al-free\nODS steels, and β′and Y-Al-O in Al-added ODSsteels, could act as initial nucleation sites of micro-\nvoids. The theory to evaluate the ductile elongation\ndeveloped by McClintock[61]:\nϵf=(1−n)ln(l0/2b0)\nsinh/bracketleftbig\n(1−n) (σa+σb)//parenleftbig\n2σ/√\n3/parenrightbig/bracketrightbig (3)\nWhereϵfis the strain to fracture, nis the harden-\ning exponent in Ludwik relationship, l0is the mean\nspacing of micro-voids, b0is the initial radius of\nholes,σaandσbare stresses related to different di-\nrection of holes, σis the true flow stress.\nIt shows that the higher spacing of precipitates\n(micro-voids) and the higher strain-hardening ex-\nponent n in equation (1) will yield higher ductility.\nThe latter is true that the lowest n at 2000 hrs\naging in Table 3 also yields the lowest total elonga-\ntion. The former is related to the density of various\nprecipitates. As the total volume fraction of pre-\ncipitates is insensitive to aging period at over-aging\ncondition[48], density of precipitates will decrease\nas the radius increases, thus the fracture elongation\nwill increase after the peak aging hardening.\nThe excellent resistance to aging ductility loss in\nODS steels is owing to the smaller grain size in com-\nparison to the non-ODS steels. As recrystallization\noccurs, the density of grain boundaries and triple\njunctions will be greatly reduced. These defects\nare effective dislocation sources at which the stress\nconcentration will emit dislocations at initial plastic\nstrain. The deformation at vicinity of grain bound-\naries is easier than grain interior due to higher num-\nber of mobile dislocations which might avoid the\npile up at obstacles such as aging precipitates in\ncenter of grains. Therefore, the increased mobile\ndislocations emitted from triple junction and grain\nboundaries will contribute to the deformation of\nspecimen during tensile thus showing enhanced re-\nsistance in elongation reduction by aging.\nHowever, it should be also noted that grain\nboundaries could play a negative role in creep re-\nsistance at elevated temperatures. Under low stress\n11Figure 9: The SEM images of fracture surfaces: a) Al-containing particles in dimples and b) secondary cracks penetrating\nalong elongated grains.\nFigure 10: Relationships between age-hardening and loss of elongation at the conditions of as-extruded (red), after STP (green),\nand arc-melted (non-ODS) alloys (hollow). The ageing temperature was 475 °C for all the specimens and the ageing period\nwas 9000hrs and 10000hrs for as-extruded and STP, respectively.\n12that is less than the dislocation moving in center of\ngrains, the deformation was mainly based on grain\nboundary sliding[62]. Further, the emitted disloca-\ntions from triple junction could enhance the disloca-\ntion climb inside grains. It seems a trade-off existed\nin the grain size effect between aging resistance and\ncreep resistance.\n4.2. The time dependent aging hardening\nAs aforementioned, the aging embrittlement was\nmainly ascribed to the formation of α′andβ′pre-\ncipitates. Fig. ??illustrated the α′precipitation\ndomain in the Fe-Cr-Al ternary phase diagram.\nThe Fe15Cr (SP2) is in the inner region of α′\nsurrounded by the K-T curve. APT works have\ndemonstrated the α′precipitates formed since early\nstages of the aging[42]. The Fe15Cr5Al (SP4) and\nthe Fe18Cr7Al (SP11) are located close to the K-T\ncurve. The APT work showed the precipitates in\nFe15Cr5Al contain both α′andβ′and core-shell\nstructured oxides[43]. Currently there was no APT\nwork for Fe18Cr7Al, but it could be speculated\nthat the precipitates were similar to Fe15Cr5Al.\nThe Fe15Cr7Al (SP7) is located off-shore of the α′\nprecipitation region. The APT work also demon-\nstrated that no α′but a number of β′precipitation\nformed after aging in this steel[43, 44].\nDislocation interaction with precipitates are di-\nvided into two types 1) cutting-through and 2) bow-\npass[63, 64]. In the cutting-through mechanism, the\ncoherent precipitates are deformable. The harden-\ning of cutting-through could be expressed as:\n\n\n∆σchs=M/parenleftbig12\nπ/parenrightbig1\n2γ3\n2s/parenleftig\nf\nGb/parenrightig1\n21\nr\n∆σcohs=Mα(εG)3\n2/parenleftig\n2rf\nGb/parenrightig1\n2\n∆σms= 0.0055M(Gp−G)3\n2/parenleftig\n2f\nG/parenrightig1\n2/parenleftbigr\nb/parenrightbig0.275\n∆σcut−through = ∆σchs+ ∆σcohs+ ∆σms≈∆σms\n(4)\nWhere ∆σchsis the chemical strengthening re-\nlated to the surface energy of precipitates, ∆ σcohs\nis the coherency strengthening, ∆ σmsis the mod-\nulus strengthening, M= 3.06 is the Taylor factor,\nγsis the interfacial energy between precipitates and\nmatrix,G≈80 GPa is the shear modulus of typical\nFeCrAl ODS steels, Gp= 115 GPa is the modulus\nofα′,εis the misfit of the interfaces.\nThe non-deformable hardening mechanism can\nbe illustrated by the dispersoid barrier hardening\nmodel. A simplified Orowan type equation is used\nto describe this behavior:∆σbox−pass= 0.1Gbf1\n2\nrlnr\nb(5)\nWhereGis the shear modulus of matrix, bis\nthe Burgers vector of mobile dislocations, fis the\nvolume fraction of precipitates, ris the radius of\nprecipitates.\nA hypothesis was made in the following discus-\nsion that no supersaturation remained in the ma-\ntrix, which means the volume fraction fis close to a\nconstant. This hypothesis is considered valid when\naging over 2000 hrs.\nWhenfis constant and ris larger than 1 nm,\nthe derivative shows∂∆σcut−through\n∂r/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nf>0, which\nmeans the aging hardening is monotone increasing.\nSimilarly,∂∆σbow−pass\n∂r/vextendsingle/vextendsingle/vextendsingle/vextendsingle\nf<0, which means hard-\nening by non-deformable precipitates will decrease\nwith aging time (when r>1nm).\nThe critical radius of deformable α′precipitates\nis around 4 nm, calculated by equations 4 and 5.\nAbove this critical radius, the cutting-through force\nbecomes higher than bow-pass-by, that the α′will\nbecome non-deformable. The actual critical radius\nmay vary in different steels.\nThe hardening with precipitate radius and vol-\nume fraction by cut-through and bow-pass mecha-\nnism were shown in Fig.12. The hardening of cut-\nthrough mechanism is insensitive to particle radius.\nTherefore, the hardening in α′-only steels should be\nmainly induced by increasing of precipitates vol-\nume. This could explain the sever increase of hard-\nening in as-extruded Fe12Cr and Fe15Cr in the first\n2000 aging hours. After that, the radius of α′grad-\nually grew beyond the critical, the hardening mech-\nanism converted to bow-pass. As the volume frac-\ntion remained nearly constant, the hardening de-\ncreased after the mechanism converting point. This\ncould be supported by 5000 hrs aged as-extruded\nsteels[46] and the 10000hrs aged STPed Fe15Cr in\nthis study, whose hardening are lower than 2000hrs\naging, as shown in Fig.6a.\nThe hardening by bow-pass mechanism is sensi-\ntive to both precipitate radius and volume fraction.\nIn the early stage of aging ( 300hrs), β′started to\nappear with a rather large radius (2.58nm). The\naging hardening went to maximum around 700 hrs,\nthen started to decrease according to the Vickers\nhardness test[46]. This indicates the volume frac-\ntion reached saturation in the coarsening (overag-\n13Figure 11: The ternary diagram of Fe15Cr (SP2), Fe15Cr5Al (SP4), Fe15Cr7Al (SP7), Fe18Cr7Al (SP11). The Cr and Al\nconcentrations are normalized atom ratios (Fe% +Cr% +Al% =1). The superimposed green curve is the concentration boundary\nofα′precipitation developed by Kobayashi and Takasugi (K-T).\nFigure 12: The precipitate hardening by cut-through and bow-pass mechanism respectively.\n14Figure 13: The fitted aging hardening of Fe15Cr7Al (SP7).\ning) stage after 700hrs aging. The decreasing of\nhardening ascribes to the decreased number den-\nsity ofβ′in Al-added ODS steels.\nThe coarsening process of precipitation may sub-\nject to the following kinetic equation[65]:\n⟨R(t)⟩m−⟨R(0)⟩m=Krt (6)\nWhere⟨R(t)⟩is the mean size of precipitates at\ntimet,⟨R(0)⟩is the initial mean size, Kris the\nkinetic constant. In diffusion-limited coarsening, m\nequals 3, and in source/sink-limited coarsening, m\nequals 2[66].\nIn the analysis in PM2000[67], α′were found fol-\nlows the LSW theory[68, 69], where the radii of pre-\ncipitates,r, could be expressed by a simplified tem-\nporal power law:\nr=Krt1\n3 (7)\nHowever, the kinetic constant Krand the\nexponent of time showed recrystallization\ndependence[67]. Here we take the exponent\nof time as 1 /3 for both α′andβ′. For simplicity,\nthe change of oxides was ignored as well.\nWhen only non-deformable precipitate exists, the\ncombination of precipitation kinetics and hardening\nmechanism of equation 5 and 7 yields:\n∆σ= 0.1Gbf1\n2\nKrt−1\n3lnKrt1\n3\nb(8)\nHence the hardening is only dependent on aging\ntime. Rewrite equation 8 we get:\n∆σ·t1\n3=a+klnt (9)Wherea= 0.1Gbf1/2/Kr·ln(Krb) andk=\n(1/30)Gbf1/2/Kr. The constant Krcan be eval-\nuated byKr=b·exp(a/3k).\nThe fitting results from equation 9 were shown\nin Fig.13. The blue dash line is linear fitted by the\nVickers hardness tests on aged bulk extruded mate-\nrials, using the conversion equation YS= 2.76VH.\nThe STPed FeCrAl ODS steel has a higher harden-\ning than as-extruded. This may be owing to the re-\ncrystallization which eliminated grain boundaries,\nwhere Ti segregates. Thus, the volume fraction\nofβ′in STPed steel should be larger than in as-\nextruded, as predicted in Fig.12.\nThe derivate of equation 9 with respect to t\nyields:\n˙∆σ·t1\n3+ ∆σ·1\n3t−1\n3=k\nt(10)\nSet ˙∆σ= 0, combined with the equation 9, the\nrest terms in equation 10 can be written as:\ntmax=exp(3−a/k) (11)\nThis is the method to evaluate the over-aging\ntime where maximum age hardening occurred for\nthe non-deformable precipitates. The estimated ki-\nnetic constant Krand max hardening time tmax\nare listed in Table 4.\n5. Conclusion\nFour FeCrAl ferritic ODS steels, Fe15Cr (SP2),\nFe15Cr5Al (SP4), Fe15Cr7Al (SP7) and Fe18Cr7Al\n15Table 4: The parameters Krandtmaxof aged FeCrAl ODS\nsteels\nFe15Cr7Al Kr(×−3)tmax(hrs)\nSTPed 7.385 691\nAs-extruded 5.515 513\n(SP11), were fabricated by simulated tube process-\ning (STP) to plates with 0.3 mm thickness. The\nplates were aged at 475 °C for 2000 hrs and 10000\nhrs in vacuum. Uniaxial tensile tests were per-\nformed to investigate the aging embrittlement in\ndifferent steels. The obtained results are summa-\nrized as below:\n1. The four cycles of CR-HT STP with recrystal-\nlization in HT3 and repeating temperature in\nHT4 yielded partially recrystallization in the\nlast STP step.\n2. Tensile tests to the rolling direction showed\nthat yield stress returned similar to the as-\nextruded ones after STP, except SP2 whose YS\nreduced 100MPa. The TE reduction of STPed\nsteels is 1/3 of the extruded steels. All the\nSTPed steels showed reduction of deformation\nenergy in tensile tests compared to extruded\nsteels.\n3. The deformation energy change after aging\ncould be divided into three types, correspond-\ning to the precipitation types of α′andβ′pre-\ncipitates formation.\n4. For Al-free ODS steels after STP, the aging\nhardening is smaller than as-extruded ones.\nFor Al-added ODS steels after STP, the ag-\ning hardening haviour is similar to as-extruded.\nRecovered effect in hardening and elongation\nreduction appeared after 10000 hrs aging.\n5. All the specimens/materials after aging frac-\ntured in a ductile manner. There were two\ncharacteristic features on the tensile fracture\nsurface: 1) Al-containing particles were ob-\nserved in the dimples and 2) secondary crack-\ning along elongated layered grain.\n6. The loss of elongation by ageing is rather\nsmaller in ODS ferritic steels than in non-ODS\nalloys with respect to the same amount of age-\nhardening.\n7. Over-aging occurred before 10000 hrs anneal-\ning in all the STPed steels. The analysis com-\nbining Orowan hardening equation and LSW\ntheory showed that the STPed SP7 has a\nhigherβ′growth rate constant.6. Acknowledgement\nZXZ would like to thank Prof. Akihiko Kimura\nin Kyoto University for the supporting of the ex-\nperiment and the research communications.\nReferences\n[1] O. Ridge, O. Ridge, Accident Tolerant Fuel Concepts\nfor Light Water Reactors, IAEA Tecdoc Ser 1797 (2014)\n13–16.\n[2] K. Pasamehmetoglu, S. Massara, D. Costa, S. Bragg-\nSitton, M. Moatti, M. Kurata, D. Iracane, T. Ivanova,\nJ. Bischoff, C. Delafoy, State-of-the-Art Report on\nLight Water Reactor Accident-Tolerant Fuels, Techni-\ncal Report, Organisation for Economic Co-Operation\nand Development, 2018.\n[3] S. J. Zinkle, K. A. Terrani, J. C. Gehin, L. J. Ott, L. L.\nSnead, Accident tolerant fuels for LWRs: A perspective,\nJournal of Nuclear Materials 448 (2014) 374–379.\n[4] N. M. George, R. T. Sweet, J. J. Powers, A. Worrall,\nK. A. Terrani, B. D. Wirth, G. I. Maldonado, Full-core\nanalysis for FeCrAl enhanced accident tolerant fuel in\nboiling water reactors, Annals of Nuclear Energy 132\n(2019) 486–503.\n[5] K. A. Terrani, S. J. Zinkle, L. L. Snead, Ad-\nvanced oxidation-resistant iron-based alloys for LWR\nfuel cladding, Journal of Nuclear Materials 448 (2014)\n420–435.\n[6] S. Yamashita, F. Nagase, M. Kurata, T. Nozawa,\nS. Watanabe, K. Kirimura, K. Kakiuchi, T. Kondo,\nK. Sakamoto, K. Kusagaya, Technical basis of accident\ntolerant fuel updated under a Japanese R&D project,\nWater React. Fuel Perform. Meet., Jeju Island, Korea\n(2017).\n[7] K. Sakamoto, Y. Miura, S. Ukai, NH. Oono, A. Kimura,\nA. Yamaji, K. Kusagaya, S. Takano, T. Kondo,\nT. Ikegawa, Development of accident tolerant FeCrAl-\nODS fuel cladding for BWRs in Japan, Journal of Nu-\nclear Materials 557 (2021) 153276.\n[8] A. Kimura, S. Ukai, M. Fujiwara, Development of fuel\nclad materials for high burn-up operation of SCPR,\nProc. GENES4/ANP2003, Paper 1198 (2003).\n[9] A. Kimura, H.-S. Cho, N. Toda, R. Kasada, K. Yutani,\nH. Kishimoto, N. Iwata, S. Ukai, M. Fujiwara, High\nburnup fuel cladding materials R&D for advanced nu-\nclear systems: Nano-sized oxide dispersion strengthen-\ning steels, Journal of nuclear science and technology 44\n(2007) 323–328.\n[10] A. Kimura, R. Kasada, N. Iwata, H. Kishimoto,\nCH. Zhang, J. Isselin, P. Dou, JH. Lee, N. Muthuku-\nmar, T. Okuda, Super ODS steels R&D for fuel cladding\nof next generation nuclear systems 1) Introduction and\nalloy design, in: International Congress on Advances\nin Nuclear Power Plants 2009, ICAPP 2009, Atomic\nEnergy Society of Japan, 2009, pp. 2187–2194.\n[11] S. Ukai, M. Fujiwara, Perspective of ODS alloys ap-\nplication in nuclear environments, Journal of Nuclear\nMaterials 307 (2002) 749–757.\n[12] S. Ohtsuka, S. Ukai, M. Fujiwara, T. Kaito, T. Narita,\nImprovement of 9Cr-ODS martensitic steel properties\nby controlling excess oxygen and titanium contents,\njournal of nuclear materials 329 (2004) 372–376.\n16[13] A. Kimura, R. Kasada, N. Iwata, H. Kishimoto,\nCH. Zhang, J. Isselin, P. Dou, JH. Lee, N. Muthuku-\nmar, T. Okuda, Development of Al added high-Cr ODS\nsteels for fuel cladding of next generation nuclear sys-\ntems, Journal of Nuclear Materials 417 (2011) 176–179.\n[14] Y. Yano, T. Tanno, H. Oka, S. Ohtsuka, T. Inoue,\nS. Kato, T. Furukawa, T. Uwaba, T. Kaito, S. Ukai,\nUltra-high temperature tensile properties of ODS steel\ncladdings under severe accident conditions, Journal of\nNuclear Materials 487 (2017) 229–237.\n[15] HS. Cho, A. Kimura, Corrosion resistance of high-Cr\noxide dispersion strengthened ferritic steels in super-\ncritical pressurized water, Journal of Nuclear Materials\n367 (2007) 1180–1184.\n[16] J. Isselin, R. Kasada, A. Kimura, Corrosion behaviour\nof 16%Cr–4%Al and 16%Cr ODS ferritic steels under\ndifferent metallurgical conditions in a supercritical wa-\nter environment, Corrosion Science 52 (2010) 3266–\n3270. doi: 10.1016/j.corsci.2010.05.043 .\n[17] J. Lee, R. Kasada, A. Kimura, T. Okuda, M. Inoue,\nS. Ukai, S. Ohnuki, T. Fujisawa, F. Abe, Influence\nof alloy composition and temperature on corrosion be-\nhavior of ODS ferritic steels, Journal of Nuclear Ma-\nterials 417 (2011) 1225–1228. doi: 10.1016/j.jnucmat.\n2010.12.279 .\n[18] T. Liu, C. Wang, H. Shen, W. Chou, N. Y. Iwata,\nA. Kimura, The effects of Cr and Al concentrations on\nthe oxidation behavior of oxide dispersion strengthened\nferritic alloys, Corrosion Science 76 (2013) 310–316.\ndoi:10.1016/j.corsci.2013.07.004 .\n[19] H. Je, A. Kimura, Stress corrosion cracking suscepti-\nbility of oxide dispersion strengthened ferritic steel in\nsupercritical pressurized water dissolved with different\nhydrogen and oxygen contents, Corrosion Science 78\n(2014) 193–199. doi: 10.1016/j.corsci.2013.09.016 .\n[20] R. Kasada, H. Takahashi, H. Kishimoto, K. Yutani,\nA. Kimura, Superior Radiation Resistance of ODS\nFerritic Steels, Materials Science Forum 654–656\n(2010) 2791–2794. doi: 10.4028/www.scientific.net/\nMSF.654-656.2791 .\n[21] P. Song, Z. Zhang, K. Yabuuchi, A. Kimura, He-\nlium bubble formation behavior in ODS ferritic steels\nwith and without simultaneous addition of Al and Zr,\nFusion Engineering and Design 125 (2017) 396–401.\ndoi:10.1016/j.fusengdes.2017.03.139 .\n[22] P. Song, J. Gao, K. Yabuuchi, A. Kimura, Ion-\nirradiation hardening accompanied by irradiation-\ninduced dissolution of oxides in FeCr(Y, Ti)-ODS fer-\nritic steel, Journal of Nuclear Materials 511 (2018) 200–\n211. doi: 10.1016/j.jnucmat.2018.09.007 .\n[23] Y. Ha, A. Kimura, Effect of recrystallization on ion-\nirradiation hardening and microstructural changes in\n15Cr-ODS steel, Nuclear Instruments and Methods in\nPhysics Research Section B: Beam Interactions with\nMaterials and Atoms 365 (2015) 313–318. doi: 10.1016/\nj.nimb.2015.07.076 .\n[24] SA. Maloy, E. Aydogan, O. Anderoglu, C. Lavender,\nY. Yamamoto, Viability of thin wall tube forming\nof ATF FeCrAl.; Los Alamos National Lab.(LANL),\nLos Alamos, NM (United States), Pacific Northwest\nNational Lab.(PNNL), Richland, WA (United States)\n(2016).\n[25] S. Aghamiri, T. Sowa, S. Ukai, N. Oono, K. Sakamoto,\nS. Yamashita, Microstructure and texture evolution\nand ring-tensile properties of recrystallized FeCrAl ODScladding tubes, Materials Science and Engineering: A\n771 (2020) 138636. doi: 10.1016/j.msea.2019.138636 .\n[26] S. Ukai, S. Mizuta, T. Yoshitake, T. Okuda, M. Fu-\njiwara, S. Hagi, T. Kobayashi, Tube manufacturing\nand characterization of oxide dispersion strengthened\nferritic steels, Journal of Nuclear Materials 283–287\n(2000) 702–706. doi: 10.1016/S0022-3115(00)00114-8 .\n[27] Y. Ha, Recrystallization Behavior of Oxide Dispersion\nStrengthened Ferritic Steels (2014).\n[28] Y. Ha, A. Kimura, Effect of cold rolling on recrystalliza-\ntion behavior of Al-free and Al-added 15Cr-ODS ferritic\nsteels, Crystals 9 (2019) 145.\n[29] S. Ukai, S. Mizuta, M. Fujiwara, T. Okuda,\nT. Kobayashi, Development of 9Cr-ODS martensitic\nsteel claddings for fuel pins by means of ferrite to\naustenite phase transformation, Journal of Nuclear Sci-\nence and Technology 39 (2002) 778–788.\n[30] S. Ukai, S. Ohtsuka, Nano-mesoscopic structure control\nin 9Cr–ODS ferritic steels, Energy Materials 2 (2007)\n26–35.\n[31] Y. Yano, T. Tanno, S. Ohtsuka, T. Kaito, S. Ukai, Ef-\nfects of Thermal Aging on the Mechanical Properties of\nFeCrAl-ODS Alloy Claddings, Materials transactions\n62 (2021) 1239–1246.\n[32] T. Narita, S. Ukai, B. Leng, S. Ohtsuka, T. Kaito,\nCharacterization of recrystallization of 12Cr and 15Cr\nODS ferritic steels, Journal of Nuclear Science and\nTechnology 50 (2013) 314–320.\n[33] T. Narita, S. Ukai, T. Kaito, S. Ohtsuka, T. Kobayashi,\nDevelopment of two-step softening heat treatment for\nmanufacturing 12Cr-ODS ferritic steel tubes, Journal\nof nuclear science and technology 41 (2004) 1008–1012.\n[34] B. Leng, S. Ukai, T. Narita, Y. Sugino, Q. Tang,\nN. Oono, S. Hayashi, F. Wan, S. Ohtsuka, T. Kaito,\nEffects of two-step cold rolling on recrystallization be-\nhaviors in ODS ferritic steel, Materials Transactions 53\n(2012) 652–657.\n[35] C. Capdevila, M. Miller, K. Russell, J. Chao,\nJ. Gonz´ alez-Carrasco, Phase separation in PM 2000 ™\nFe-base ODS alloy: Experimental study at the atomic\nlevel, Materials Science and Engineering: A 490 (2008)\n277–288. doi: 10.1016/j.msea.2008.01.029 .\n[36] S. Novy, P. Pareige, C. Pareige, Atomic scale analysis\nand phase separation understanding in a thermally aged\nFe–20at.%Cr alloy, Journal of Nuclear Materials 384\n(2009) 96–102. doi: 10.1016/j.jnucmat.2008.10.008 .\n[37] C. Capdevila, M. Miller, G. Pimentel, J. Chao, In-\nfluence of recrystallization on phase separation kinet-\nics of oxide dispersion strengthened Fe–Cr–Al alloy,\nScripta Materialia 66 (2012) 254–257. doi: 10.1016/j.\nscriptamat.2011.11.003 .\n[38] S. A. Briggs, P. D. Edmondson, K. C. Littrell, Y. Ya-\nmamoto, R. H. Howard, C. R. Daily, K. A. Terrani,\nK. Sridharan, K. G. Field, A combined APT and SANS\ninvestigation of α′phase precipitation in neutron-\nirradiated model FeCrAl alloys, Acta Materialia 129\n(2017) 217–228. doi: 10.1016/j.actamat.2017.02.077 .\n[39] P. Edmondson, S. Briggs, Y.Yamamoto, R. Howard,\nK. Sridharan, K. Terrani, K. Field, Irradiation-\nenhancedα′precipitation in model FeCrAl alloys,\nScripta Materialia 116 (2016) 112–116. doi: 10.1016/j.\nscriptamat.2016.02.002 .\n[40] J. Ejenstam, M. Thuvander, P. Olsson, F. Rave, P. Sza-\nkalos, Microstructural stability of Fe–Cr–Al alloys at\n450–550 °C, Journal of Nuclear Materials 457 (2015)\n17291–297. doi: 10.1016/j.jnucmat.2014.11.101 .\n[41] C. Capdevila, M. Aranda, R. Rementeria, J. Chao,\nE. Urones-Garrote, J. Aldazabal, M. Miller,\nStrengthening by intermetallic nanoprecipitation\nin Fe–Cr–Al–Ti alloy, Acta Materialia 107 (2016)\n27–37. doi: 10.1016/j.actamat.2016.01.039 .\n[42] W. Sang, P. Dou, A. Kimura, Early-stage thermal age-\ning behavior of 12Cr, 12Cr–7Al and 18Cr–9Al ODS\nsteels, Journal of Nuclear Materials 535 (2020) 152164.\ndoi:10.1016/j.jnucmat.2020.152164 .\n[43] P. Dou, W. Sang, A. Kimura, Effects of the contents\nof Al, Ti, W and YO on long-term thermal ageing be-\nhavior of 15Cr ODS ferritic steels, Journal of Nuclear\nMaterials 534 (2020) 152129. doi: 10.1016/j.jnucmat.\n2020.152129 .\n[44] P. Dou, Z.-X. Xin, W. Sang, A. Kimura, Age-hardening\nmechanisms of 15Cr ODS ferritic steels with 5, 7 and\n9 wt.% Al at 475 °C for 9000 h, Journal of Nuclear\nMaterials 540 (2020) 152368. doi: 10.1016/j.jnucmat.\n2020.152368 .\n[45] S. Kobayashi, T. Takasugi, Mapping of 475 °C embrit-\ntlement in ferritic Fe–Cr–Al alloys, Scripta Materialia\n63 (2010) 1104–1107. doi: 10.1016/j.scriptamat.2010.\n08.015 .\n[46] W. Han, K. Yabuuchi, A. Kimura, S. Ukai, N. Oono,\nT. Kaito, T. Torimaru, S. Hayashi, Effect of Cr/Al\ncontents on the 475 ºC age-hardening in oxide disper-\nsion strengthened ferritic steels, Nuclear Materials and\nEnergy 9 (2016) 610–615. doi: 10.1016/j.nme.2016.05.\n015.\n[47] B. C. Maji, S. Ukai, N. Oono-Hori, Microstructural sta-\nbility and intermetallic embrittlement in high Al con-\ntaining FeCrAl-ODS alloys, Materials Science and En-\ngineering: A 807 (2021) 140858. doi: 10.1016/j.msea.\n2021.140858 .\n[48] A. Kimura, W. Sang, W. Han, K. Yabuuchi, Z. Xin,\nJ. Luan, P. Dou, Twofold age-hardening mechanism of\nAl-added high-Cr ODS ferritic steels, Journal of Nu-\nclear Materials 575 (2023) 154223.\n[49] S. Ukai, K. Sakamoto, S. Ohtsuka, S. Yamashita,\nA. Kimura, Alloy Design and Characterization of\na Recrystallized FeCrAl-ODS Cladding for Accident-\nTolerant BWR Fuels: An Overview of Research Ac-\ntivity in Japan, Journal of Nuclear Materials (2023)\n154508.\n[50] R. Keller, R. Geiss, K. Rice, Transmission Kikuchi\nDiffraction in the Scanning Electron Microscope, Na-\ntional Institute of Standards and Technology, Boulder\n(Colorado, USA) (2013).\n[51] N. H. Oono, S. Ukai, K. Tominaga, N. Ebisawa, K. To-\nmura, Precipitation of various oxides in ODS ferritic\nsteels, Journal of Materials Science 54 (2019) 8786–\n8799. doi: 10.1007/s10853-019-03516-6 .\n[52] N. Oono, S. Ukai, S. Hayashi, S. Ohtsuka, T. Kaito,\nA. Kimura, T. Torimaru, K. Sakamoto, Growth of oxide\nparticles in FeCrAl- oxide dispersion strengthened steels\nat high temperature, Journal of Nuclear Materials 493\n(2017) 180–188. doi: 10.1016/j.jnucmat.2017.06.018 .\n[53] F. J. Humphreys, M. Hatherly, Recrystallization and\nRelated Annealing Phenomena, elsevier, 2012.\n[54] Y. Hayakawa, JA. Szpunar, A new model of Goss tex-\nture development during secondary recrystallization of\nelectrical steel, Acta materialia 45 (1997) 4713–4720.\n[55] S. Ukai, Y. Yano, T. Inoue, T. Sowa, Solid-solution\nstrengthening by Al and Cr in FeCrAl oxide-dispersion-strengthened alloys, Materials Science and Engineer-\ning: A 812 (2021) 141076. doi: 10.1016/j.msea.2021.\n141076 .\n[56] Y. Kimura, T. Inoue, F. Yin, K. Tsuzaki, Delamination\ntoughening of ultrafine grain structure steels processed\nthrough tempforming at elevated temperatures, ISIJ\ninternational 50 (2010) 152–161.\n[57] A. Das, H.-W. Viehrig, E. Altstadt, F. Bergner, J. Hoff-\nmann, Why do secondary cracks preferentially form in\nhot-rolled ODS steels in comparison with hot-extruded\nODS steels?, Crystals 8 (2018) 306.\n[58] DONGSHENG. CHEN, Iron/Chromium Phase Decom-\nposition Behavior in Oxide Dispersion Strengthened\nFerritic Steels (2015).\n[59] D. Chen, A. Kimura, W. Han, Correlation of Fe/Cr\nphase decomposition process and age-hardening in\nFe–15Cr ferritic alloys, Journal of Nuclear Materials 455\n(2014) 436–439. doi: 10.1016/j.jnucmat.2014.07.069 .\n[60] D. Chen, A. Kimura, W. Han, H. Je, Age-hardening\nsusceptibility of high-Cr ODS ferritic steels and SUS430\nferritic steel, Fusion Engineering and Design 98–99\n(2015) 1945–1949. doi: 10.1016/j.fusengdes.2015.05.\n078.\n[61] F. A. McClintock, A Criterion for Ductile Fracture by\nthe Growth of Holes, Journal of Applied Mechanics 35\n(1968) 363–371. doi: 10.1115/1.3601204 .\n[62] S. Ukai, S. Kato, T. Furukawa, S. Ohtsuka, High-\ntemperature creep deformation in FeCrAl-oxide disper-\nsion strengthened alloy cladding, Materials Science\nand Engineering: A 794 (2020) 139863. doi: 10.1016/\nj.msea.2020.139863 .\n[63] A. J. Ardell, Precipitation hardening, Metallurgical\nTransactions A 16 (1985) 2131–2165.\n[64] J. W. Martin, Precipitation Hardening: Theory and\nApplications, Elsevier Science, 1998.\n[65] R. O’Hayre, Materials Kinetics Fundamentals, John\nWiley & Sons, 2014.\n[66] R. W. Balluffi, S. M. Allen, W. C. Carter, Kinetics of\nMaterials, John Wiley & Sons, 2005.\n[67] C. Capdevila, M. K. Miller, J. Chao, Phase separation\nkinetics in a Fe–Cr–Al alloy, Acta materialia 60 (2012)\n4673–4684.\n[68] I. M. Lifshitz, V. V. Slyozov, The kinetics of precipi-\ntation from supersaturated solid solutions, Journal of\nphysics and chemistry of solids 19 (1961) 35–50.\n[69] C. Wagner, Theorie der alterung von niederschl¨ agen\ndurch uml¨ osen (Ostwald-reifung), Zeitschrift f¨ ur\nElektrochemie, Berichte der Bunsengesellschaft f¨ ur\nphysikalische Chemie 65 (1961) 581–591.\n18"    },    {        "title": "1807.03127v1.Photocatalytic_activity_enhancement_by_addition_of_lanthanum_into_the_BiFeO3_structure_and_the_effect_of_synthesis_method.pdf",        "content": "1 Photocatalytic activity  enhancement by addition of \nlanthanum into the BiFeO 3 structure  and the effect \nof synthesi s method  \nHamed Maleki* \nFaculty of Physics , Sha hid Bahonar University  of Kerman , Kerman , Iran  \ne-mail address: hamed.maleki@ uk.ac.ir  \nKeywords : Photocatalytic properties ; Multiferroics ; optical bandgap, sol-gel; Lanthanum  \ndoped; hydrothermal.   \nAbstract : In this paper , the photocatalytic activity of multiferroic s BiFeO 3 (BFO) and \nBi0.8La0.2FeO 3 (BLFO) nanocrystals with two different morphologies which were synthesized \nby two different sol-gel (SG) and hydrothermal (HT) method s have  been studied . All the \nobtained samples  were characterized using X -ray diffractometer, Fourier transform infrared \nspectroscopy, transmission electron microscopy, UV -vis spectroscopy and vibrating sample \nmagnetometer.  Differential thermal analysis (DTA) measurements were pro bed ferroelectric - \nparaelectric first-order phase transition (T C) for all samples.  Addition of lanthanum decreases \nthe electric phase transition.  For photocatalyst application of bismuth ferrite, a dsorption \npotential of nanoparticles for methylene blue (MB) organic dye was evaluated.  The doping of \nLa in the BFO structure enhanced the photocatalytic activity and about 71% degradation of \nMB dye was obtained under visible irradiation. The magnetic and ferroelectric properties of \nBLFO nanoparticles improve compared to the undope d BiFeO 3 nanoparticles.  The non -\nsaturation at high applied magnetic field for as -prepared samples by HT is related to the size \nand shape of products.  This work not only presents an effect of lanthanum substitution into the \nbismuth ferrite structure on the physical properties of BFO, but also compares the synthesis \nmethod and its influence on the photocatalytic activity and multiferroics  properties  of all \nnanopowders.  \n1. Introduction  \nIn order to generate hydrogen, an environmentally friendly process has been offered to \nmodern society through p hotocatalytic degradation of pollutants and photocatalytic water 2 splitting using solar energy [1–3]. Multiferroic materials have recently drawn scientist’s \nattention  due to their vast  applications as a result of their  photocatalysis and photovoltaics \nproperties. The narrow energy band gap  and ferroelectric properties lead to  high absorption  of \nlight in the visible region  [4–7]. Bismuth ferrite, which simultaneously shows ferroelectric and \nferromagnetic behavior at and above room temperature (RT), has drawn attention for  two \ndecade s. This  increasing interest  in bismuth ferrite as a noble material is due to  its potential \napplication in multifunctional devices,  data st orage , sensors and photovoltaic technologies  [8–\n18]. This matter has the anti(ferro) -magnetic to paramagnetic transition at Neel temperature \nTN~370oC and ferroelectric -paraelectic first order phase transition at Curie temperature \nTC~830oC [19–23].  \nLiterature survey indicates that, w ith periodicity of 62 nm spin structure in BFO gives a \nspiral modulation and is a cause of G-type antiferromagnetic ordering of bulk bismuth ferrite  \n[24–26]. Moreover, due to the formation of secondary ph ase and impurities during synthesis \nprocess, BFO has large leakage current density  (because of various oxidation states of Fe ion  \nand the existence of oxygen vacancies)  [8,27 –29]. Many theoretical and experimental studies \nof bismuth ferrite have been carried out  to expand the applications and solve the problems \nhindering practical usage of BFO  [30–32]. To overcome these  obstacles , parallel to synthesis \nof BFO nanoparticles  with different methods [11,33 –35], it has been reported that A-site or B -\nsite substitution in to the structure of bismuth ferrite , is the most effective strategy to reduce the \nimpurity phases  and enhanced multifferoic properties  [36–44]. \nApart from these  multiferroic  properties of BiFeO 3, according to the narrow band -gap of \nBFO (~2.2 eV), bismuth ferrite has been also known as a magnetic photocatalyst at visible light \nirradiation  for water splitting and degradation of organic pollutants  [5,7,45] .  The weak \nferromagnetic nature of BiFeO 3 nanoparticles is also used for recovering the catalyst from \nsolution.  However, the photocatalytic efficiency of bismuth ferrite is also limited as a result of  \nits low conduction band (compared to H 2 or O 2) and small surface areas for catalytic reactions  \n[1,46] . In order to enhance photocatalytic ability on the degradation of pollutants, BFO has \nbeen synthesized by varyin g its synthesis method and  by varying its compositional parameters \nsuch as  substitution.  \nTo understand the origin of the influence of synthesis method , as well as the effect of \naddition of lanthanum into the structure of bismuth ferrite , we have synthesized  BiFeO 3 and \nBi0.8La0.2FeO 3 nanoceramics t hrough the sol -gel and hydrothermal methods . The synthesis was 3 done  to find a deep understanding about their effects on the  multiferroic properties and \nphotocatalytic activities of BiFeO 3 nanoparticles.  \n2. Experimental method  \n2.1 Sol-gel preparation of pure and La-doped BiFeO 3 \nBiFeO 3 and Bi 0.8La0.2FeO 3 nanoceramics were synthesize d via sol-gel (SG) process by \nusing Bi(NO 3)3.5H 2O, Fe(NO 3)3.9H 2O and La (NO 3)3.6H 2O (for the case of BLFO) as a starting \nmaterials , and  deionized  water  and 2-methoxyethanole  as a solvent  [47,48] . Stoichiometric \namount of bismuth, iron and lanthanum nitrate were completely dissolved in the solvent. Acetic \nacid w as added to the above solution dropwise (pH~1.5)  one hour later . A brownish and \ntransparent sol is obtained after 1.5 h of constant stirrin g. Then the temperature was increased \nto 90oC and  the solution was slowly evaporated and  after 3h heating and stirring, the gel is \nobtained. The precursor powders were dried for 2h at 110oC and were calcined at 650oC for \n3h. The as -prepared products synthesized through the sol -gel process were indexed SGBFO \nand SGBLFO for pure and La -doped bismuth ferrite respectively.  \n2.2 Hydrothermal synthesis of BFO and B LFO \nIn this method, for synthesis of BiFeO 3 (HTBFO) and Bi 0.8La0.2FeO 3 (HTBLFO) samples, \na stoichio metric amount of bismuth (III) nitrate pentahydrate (99%, Sigma), ferric (III) nitrate \nnonahydrate (99%, Merck) and lanthanum nitrate hexahydrate (99% Merck for HTBLFO) were  \ndissolved in 10 ml of deionized water. Then 30 ml KOH (4M) was added to the solution \ndropwise under constant stirring. After 30 min stirring, the solution was transferred into a \nstainless Teflon -lined autoclave and heated at 220oC for 12h. Then the solution cooled naturally \nto the RT.  The products were  separated from the solution by centrifugation, then washed \nseveral times w ith distilled water and ethanol,  and finally dried for 2 hours at 110 oC, in order \nto obtain brown  nano powder s. \n2.3 Characterization  \nFirst, the physical properties of pure and La -doped bismuth ferrite is studied. The \ncrystallinity and structural properties of products were investigated by X -ray diffractometer \n(XRD) on a Philips X’pert,  with Cu -Kα radiation (λ=1. 54056 Å) and Furrier transform \ninferared (FTI R) TENSOR27 spectro photo meter . The morphology and distribution of \nnanocrystals were  observed by using transmission electron microscopy (TEM, Leo -912-AB). \nThe thermal treatment and weight loss of the nanoparticles were recorded  by differential \nthermal and thermal gravimetric  analysis (TG -DTA, NETZSCH - PC Luxx 409)  at a heating 4 rate of 10oC/min from RT up to 1000oC in air . The magnetic properties were measured by a \nLake Shore (7410, SAIF) vibrating sample magnetometer (VSM) up to a maximum fi eld of 20 \nkG. The optical properties of products were examined by UV -vis absorption spectra using \nLambda900 spectrophotometer.  \nIn the second part, the photocatalytic activity of all samples were ev aluated by the \ndegradation of methylene blue in aqueous solution using 300  W Xenon lamp und er visible light \nirradiation. The starting  concentration of MB was chosen  4 mgl-1 with dispersing 0. 2g BFO or \nBLFO in  aqueous solution of 200 ml . For achieving an adsorption equilibrium of MB on \nproducts surface , the aqueous suspension was  stirred  magnetically  for a period of 75 min in the \ndark prior to irradiation.  Then by turning on the lamp the changes of MB concentration were \nmeasured . Concentration variations were studied  by measuring the absorbance of the solution \nat 664 nm using a UV -vis spectrophotometer. C/C 0  is known as the photocatalytic degradation \nratio of MB, which has been investigated in this study.  C0 was the starting concentration of MB \nand C was the concentration of M B at time t . \n3. Results and discussion  \n3.1 X-ray diffraction investigation  \nFig. 1 shows the XRD patterns of BFO and BLFO nanoparticles prepared by sol -gel (Fig. \n1 (a) and (b)) and hydrothermal (Fig. 1 (c) and (d)) methods. The recorded diffracted planes \nmatch well with the standard card of bismuth ferrite ( JCPDS car d No. 86 -1518 ) and XRD \npatterns confirm the single perovskite phase of BiFeO 3 with distorted rhombohedral structure \n(R3C). All patterns show strong and sharp diffraction peaks which indicate well crystallinity of \nall as -prepared particles. For pure BFO samples a few weak diffraction peaks related to the \nimpurity phases like Bi 2Fe4O9 and Bi 25FeO 40 are observed. By adding La into the structure of \nBFO, these peaks are remained for HTBLFO sample, however for SGBLFO nanopa rticles the \nimpurity phases  disappear ed. For nanoparticles prepared by SG, dopant lanthanum changes the \nposition of peaks a little to the smaller value and addition of La into the structure of bismuth \nferrite, leads  to a phase transformation from rhomboh edral to monoclinic structure which is \nobserved in the merging of two major peaks of BFO at 30<2θ<35 into the one peak (Figs.2 (b) \nand (d)) [47]. On the other hand, for HTBFO and HTBLFO nanoparti cles, at a larger angle, the \nmajor peaks exhibit  no phase transformation. The average crystallite size, has been obtained \nfrom the Scherrer formula D=Kλ\nβ Cos θ , where K is the shape factor that normally measures to \nbe about 0.89, λ is the wavelength of Cu -Kα radiation of the XRD, β is the width of the observed 5 diffraction peak at its half intensity maximum, and θ is the Bragg angle of each peak . The \ncalculated average  size for SGBFO  and SGBLFO  grains are 48 nm and 34 nm  respectively .  \n \n \nFig. 1  (a) XRD patterns of BiFeO 3 and Bi 0.8La0.2FeO 3 nanoparticles prepared by SG method , (b) \nsame plot in the range of 30<2θ<3 5, (c) XRD patterns of HTBFO and HTBLFO nanoparticles , (d) \nsame graphs  in the range of 30<2θ<3 5. \n3.2 Furrier transform infrared spectroscopy  \n      To get further insight  into the formation mechanism of BFO  nanoparticles , the FTIR spectra \nof all samples were recorded. Fig. 2 illustrate the FTIR spectra of all as -synthesized \nnanoceramics in the wavenumber range of 400 -4000 cm-1. Two major peaks between 400 -600 \ncm-1 correspond to the Fe -O stretching and O -Fe-O bending vibrations of perovskite FeO 6 \ngroups , which confirms t he formation of BFO nanoparticles  [11,49,50] . Between 1400 -1650 \ncm-1 two peaks are observed which are related to the symmetry bending vibration of C -H or C -\n6 H2 [51]. The broad band at 3300 -3700 cm-1 is due to the symm etric and a nti-symmetric \nstretching of H 2O and OH- bond.  \n \nFig. 2  FTIR spectra of BiFeO 3 and Bi 0.8La0.2FeO 3 nanoparticles prepared by both SG and HT \nmethod s \n3.3 Transmission electron microscope  \nTEM images of un -doped and La -doped BFO nanoparticles synthesized by SG and HT \nmethods are presented  in Fig. 3. The sol -gel as -prepared nanoparticles which  are shown in Fig. \n3 (a) and (b), have polyhedral morphology with the average size of 4 8 nm and 3 4 nm for \nSGBFO and SGBLFO nanoparticles respectively . TEM images of HTBFO and HTBLFO \nnanoceramics are illustrate in Fig. (c) and (d). The morphology of hydrothermal products are \nrod-like with diameters of ~ 52 nm (~ 43 nm) and length of less than 1µm for HTBFO \n(HTBLFO) nano particles.  This morpho logical change  via hydrothermal  method , was  strongly \ndependent on the synthesis process.  It could be due  to the nucleation rate of grains which is \nrelated to the condition of syn thesis process. In both synthesis methods, The La concentra tion \n7 had only a slight effect on the morphology and only reduced the size of grains , which is i n \nagreement with the results from Scherrer f ormula.   \n \nFig. 3.  TEM images of BiFeO 3 and Bi0.8La0.2FeO 3 synthesized by SG and HT method s, (a) image of \nSGBFO  sample , (b) SGBLFO, (c) HTBFO and (d) HTBLFO  \n3.4 Thermal behavior  \nFig. 4 shows the thermal gravitometric and differential thermal analysis (TG/DTA) curves \nof all products. In DTA curves, exothermic peaks  are related to the crystallization and \noxidation. On the other hand, phase transition and dehydration show endothermic peaks. TG \ncurves of SGBFO and SGBLFO samples reveal the decomposition of the organic part of \nsamples up to 400oC, with a wide exothermic  peak on the DTA curves and ~1. 3% of mass loss . \n8 For the HTBFO (HTBLFO) samples ( inset in Fig. 4 (b)), the total weight loss was 2.3% (1.5%) \nwhich is divided to three stages for HTBFO  nanoparticles . First loss of 0.5% up to 300oC and \nthen quick loss of 1% up to 390oC and finally 0.8% weight loss up to 700oC which is related \nto the complete decomposition of nanoparticles.  When the lanthanum is added into the BFO \nstructure , Curie temperature decreases from 830oC (827oC) for SGBFO (HTBFO) to 824oC \n(818oC) for SGB LFO (HTBLFO). The reason could be explain ed by lower polarizability of \nlanthanum ions in the structure of bismuth ferrite, compar ed to  bismuth , as a result, the Curie \ntemperature decreases  [52]. \n3.5 M-H hysteresis loops analysis of BFO and BN LFO nanoceramics  \nThe magnetic hysteresis loops of as-prepared  sample s were measured using VSM at RT  \nwith a maximum applied field of 20 KG  (Fig.5 ). For all products a weak ferromagnetic \nbehavior is observed. However HTBFO and HTBLFO nanoparticles didn’t show a completed \nsaturation magnetization.  A significant enhancement in the value of saturation  magnetization  \n(Ms) on SG synthesis method  is observed  due to the smaller particle size and morphology. The \nM-H hysteresis loops data (Table 1), indicate d that the remnant  magnetization (M r) and M s \ndecre ases with addition of lanthanum . However the coercive  forces increase. Dopant La and \nchanges in the distribution of the bismuth and consequently iron ions in the A -site and B -site \nof BFO structure, changes the magnetic moments and anisotropy [16,26]   9  \nFig. 4 (a) DTA curves of pure and 20%La -doped bismuth ferrite nanoparticles prepared by SG \nmethod . The inset shows the TG  curves of products , (b) DTA and TGA (as inset) curves of HTBFO \nand HTBLFO nanorods.  \n10  \nFig. 5  M-H hysteresis loops of all as -prepared samples through SG and HT methods at RT. Inset \nshows hysteresis loops of BiFeO 3 and Bi 0.8La0.2FeO 3 nanoparticles prepared by HT method  separately  \n \nTable 1. The saturation and remanent magnetization, as well as coercively  of BFO and BLFO \npowders synthesized by SG and HT methods.  \nHydrothermal Sol gel Sample \nHc(G) Mr(emu /g) Ms(emu /g) Hc(G) Mr(emu /g) Ms(emu /g) \n383.65 3  3-×10 7.077 0.109 39.034  15.596 ×10-3 0.797  BiFeO 3 \n426.832  3-×10.6812 0.094 90.788  10.452 ×10-3 0.696  Bi0.8La0.2FeO 3 \n \n3.6 Uv-vis spectroscopy analysis  \nThe optical  spectra of as-prepared products as shown in Fig. 6 reveals a high absorption in \nthe range of 500 -600 nm for all samples.  The direct optical band -gap energy of all nanoparticles \nwas ca lculated using Tauc’s equation (αhν)2=K(h ν-Eg), where K is a constant, α is the \nabsorption coefficient and hν is the photon energy  [53]. Eg is determined by plotting ( αhν)2 vs \n11 hν and extrapolati on of the straight line portion of the curves. The band gap decreases by La-\nsubstitution  into the BFO structure. The optical band -gap was calculated  2.12eV (2.13 eV) for \nSGBLFO (HTBLFO) nanoparticles which was lower than pure BFO samples  (2.16 eV for \nSGBFO and 2.1 7 eV for HTBFO ).  \n \nFig. 6 UV-vis adsorption of of BiFeO 3 and Bi 0.8La0.2FeO 3 nanoparticles prepared by both SG and HT \nmethod s \n3.7 Photocatalytic activity of BFO and BNFO  \nThe photocatalytic activity of BFO sand BLFO nanoparticles is evaluated by the \ndegradation of methylene blue (MB) under visible light irradiation. Herein, 0.2g sample was \nmixed by 4 mg/L of MB solution at RT.  The photocatalytic degradation is measured from \nrelation  C/C0, where  C and C0 are concentration at time  t and zero  respectively  considering the \ntime unit minutes . Fig. 7  (a) shows the photo -gradation coefficients of all products vs. time.  \nFor SGBFO and HTBFO grains, 26% and 21% of degradation take place in 300 min. However \n71% and 58% o f degradation take place with SGBLFO and SGBFO nanocatalysts in 5h \nrespectively. In principle , the efficiency of the photocatalysts depends on the factors like \ncrystallite size, morphology, surface area, and band gap and photoinduced electron -hole \nseparation effic iency of the catalyst.  Fig. 7 (b) shows the rate constant of ln(C 0/C) vs. time. The \nrate constant k is calculate d from the slopes of the fitted kinetics (ln(C/C o) = −kt) [54]. \n12  \n \nFig. 7 (a) Degradation of MB solution in the presence of sol -gel and hydrothermal prepared BiFeO 3 \nand Bi 0.8La0.2FeO 3 nanoparticles , (b) first order kinetics data for degradation of MB on SGBFO, \nSGBLFO, HTBFO and HTBLFO.  \n4. Conclusions  \n In summary, pure and La -doped BiFeO 3 nanoparticles were synthesized by  two \ndifferent sol -gel and hydrothermal methods. The effect of synthesis method, as well as, the \nenhancement of photocatalytic activity of bismuth ferrite nanoparticles by addition of \nlanthanum  is investigated. XRD a nalysis confirms the rhombohedrally -distorted  (R3C) \nperovskite structure for all products. The TEM studies reveal that as -prepared nanoparticles \nsynthesized by SG are semi -spherical powders. On the other hand, as -prepared samples \n13 synthesized by HT have rod -like shape.  DTA study indicated that addition of lanthanum in the \nBi-site in the structure of BFO decreases the Curie temperature (T C). Magnetic hysteresis loops \nshowed  the influence of synthesis method on the magnetic properties of samples. SGBFO and \nSGBLFO samples have much higher  saturated magnetization which could be related to \ndestruction of the spin cycloid magnetic ordering structure compare d to rod -like HTBFO and \nBLFO nanoparticles.  The photocatalytic reactivity of all sample s was evaluated in terms of the \ndegradation of MB in aqueous BFO and BLFO suspensions under visible light irradiation . The \nresults indicated that the photocatalytic activity of products depends not only on the synthesis \nmethod but also on the addition lanthanum into the structure of bismuth ferrite.  \nAcknowledgments  \n This work was supported by the research council of Shahid Bahonar University of \nKerman  (SBUK -RC). Partial financial support by Iranian nanotechnology initiative council \n(INIC) are acknowledged.  \n5.  References  \n[1] M. Humayun, A. Zada, Z. Li, M. Xie, X. Zhang, Y. Qu, F. Raziq, L. Jing, Applied \nCatalysis B: Environmental 180 (2016) 219.  \n[2] Y. Wu, W. Han, S.X. Zhou, M.V. Lototsky, J.K. Solberg, V.A. Yartys, Journal of \nAlloys and Compounds 466(1 –2) (2008) 176.  \n[3] S. Wang, D. Chen, F. Niu, N. Zhang, L. Qin, Y. Huang, Journal of Alloys and \nCompounds 688 (2016) 399.  \n[4] C.M. Cho, J.H. Noh, I. -S. Cho, J. -S. An, K.S. Hong, J.Y. Kim, Journal of the \nAmerican Ceramic Society 91(11) (2008) 3753. \n[5] F. Gao, X.Y. Chen, K.B. Yin, S. Dong, Z.F. Ren, F. Yuan, T. Yu, Z.G. Zou, J. -M. \nLiu, Advanced Materials 19(19) (2007) 288 9.  \n[6] Y.-L. Pei, C. Zhang, Journal of Alloys and Compounds 570 (2013) 57. \n[7] H. Maleki, Journal of Magnetism and Magnetic Materials 458 (2018) 277. \n[8] J. Wang, J.B. Neaton, H. Zheng, V. Nagarajan, S.B. Ogale, B. Liu, D. Viehland, V. \nVaithyanathan, D.G. Schlom, U. V Waghmare, N.A. Spaldin, K.M. Rabe, M. Wuttig, \nR. Ramesh, Science (New York, N.Y.) 299(5613) (2003) 1719. 14 [9] W. Eerenstein, N.D. Mathur, J.F. Scott, Nature 442(7104) (2006) 759. \n[10] J. Ma, J. Hu, Z. Li, C. -W. Nan, Advanced Materials 23(9) (20 11) 1062.  \n[11] H. Maleki, M. Haselpour, R. Fathi, Journal of Materials Science: Materials in \nElectronics 29(5) (2018) 4320. \n[12] A. Sarkar, G.G. Khan, A. Chaudhuri, A. Das, K. Mandal, Applied Physics Letters \n108(3) (2016) 33112. \n[13] S.K. Mandal, T. Rakshi t, S.K. Ray, S.K. Mishra, P.S.R. Krishna, A. Chandra, Journal \nof Physics: Condensed Matter 25(5) (2013) 55303. \n[14] Y. Bai, T. Siponkoski, J. Peräntie, H. Jantunen, J. Juuti, Applied Physics Letters \n110(6) (2017) 63903. \n[15] P.P. Biswas, T. Chinthakuntla, D. Duraisamy, G. Nambi Venkatesan, S. \nVenkatachalam, P. Murugavel, Applied Physics Letters 110(19) (2017) 192906. \n[16] G. Catalan, J.F. Scott, Advanced Materials 21(24) (2009) 2463. \n[17] D. Wang, M. Wang, F. Liu, Y. Cui, Q. Zhao, H. Sun, H. Jin, M. Cao, Ce ramics \nInternational 41(7) (2015) 8768. \n[18] H. Fki, M. Koubaa, L. Sicard, W. Cheikhrouhou -Koubaa, A. Cheikhrouhou, S. \nAmmar -Merah, Ceramics International 43(5) (2017) 4139.  \n[19] G.A. Smolenskii, V.A. Bokov, Journal of Applied Physics 35(3) (1964) 915. \n[20] P. Fischer, M. Polomska, I. Sosnowska, M. Szymanski, Journal of Physics C: Solid \nState Physics 13(10) (1980) 1931. \n[21] I. Sosnowska, T.P. Neumaier, E. Steichele, Journal of Physics C: Solid State Physics \n15(23) (1982) 4835. \n[22] J.M. Moreau, C. Miche l, R. Gerson, W.J. James, Journal of Physics and Chemistry of \nSolids 32(6) (1971) 1315. \n[23] R.T. Smith, G.D. Achenbach, R. Gerson, W.J. James, Journal of Applied Physics \n39(1) (1968) 70. \n[24] C. Ederer, N.A. Spaldin, Physical Review B 71(6) (2005) 60401. 15 [25] D. Sando, A. Barthélémy, M. Bibes, Journal of Physics: Condensed Matter 26(47) \n(2014) 473201. \n[26] J.T. Heron, D.G. Schlom, R. Ramesh, Applied Physics Reviews 1(2) (2014) 21303. \n[27] F. Huang, X. Lu, W. Lin, X. Wu, Y. Kan, J. Zhu, Applied Physics Lett ers 89(24) \n(2006) 242914. \n[28] Y.P. Wang, L. Zhou, M.F. Zhang, X.Y. Chen, J. -M. Liu, Z.G. Liu, Applied Physics \nLetters 84(10) (2004) 1731. \n[29] J.-H. Xu, H. Ke, D. -C. Jia, W. Wang, Y. Zhou, Journal of Alloys and Compounds \n472(1 –2) (2009) 473.  \n[30] J.B. Nea ton, C. Ederer, U. V. Waghmare, N.A. Spaldin, K.M. Rabe, Physical Review \nB 71(1) (2005) 14113. \n[31] T. Zhao, A. Scholl, F. Zavaliche, K. Lee, M. Barry, A. Doran, M.P. Cruz, Y.H. Chu, \nC. Ederer, N.A. Spaldin, R.R. Das, D.M. Kim, S.H. Baek, C.B. Eom, R. Rame sh, \nNature Materials 5(10) (2006) 823. \n[32] D. Lebeugle, D. Colson, A. Forget, M. Viret, P. Bonville, J.F. Marucco, S. Fusil, \nPhysical Review B 76(2) (2007) 24116. \n[33] R. Safi, H. Shokrollahi, Progress in Solid State Chemistry 40(1 –2) (2012) 6.  \n[34] J. Silva, A. Reyes, H. Esparza, H. Camacho, L. Fuentes, Integrated Ferroelectrics \n126(1) (2011) 47. \n[35] D. Varshney, A. Kumar, K. Verma, Journal of Alloys and Compounds 509(33) (2011) \n8421. \n[36] H. Singh, K.L. Yadav, Journal of Physics: Condensed Matter 23(38)  (2011) 385901.  \n[37] Y.-H. Lee, J. -M. Wu, C. -H. Lai, Applied Physics Letters 88(4) (2006) 42903.  \n[38] F.Z. Li, H.W. Zheng, M.S. Zhu, X.A. Zhang, G.L. Yuan, Z.S. Xie, X.H. Li, G.T. Yue, \nW.F. Zhang, J. Mater. Chem. C 5(40) (2017) 10615. \n[39] T. Durga Rao, S.  Asthana, Journal of Applied Physics 116(16) (2014) 164102.  \n[40] X. Qi, J. Dho, R. Tomov, M.G. Blamire, J.L. MacManus -Driscoll, Applied Physics \nLetters 86(6) (2005) 62903. 16 [41] X. Zhang, Y. Sui, X. Wang, Y. Wang, Z. Wang, Journal of Alloys and Compounds \n507(1) (2010) 157. \n[42] Q.R. Yao, Y.H. Shen, P.C. Yang, H.Y. Zhou, G.H. Rao, Z.M. Wang, J.Q. Deng, \nCeramics International 42(5) (2016) 6100. \n[43] B. Yotburut, P. Thongbai, T. Yamwong, S. Maensiri, Ceramics International 43(7) \n(2017) 5616. \n[44] M. Rangi, S.  Sanghi, S. Jangra, K. Kaswan, S. Khasa, A. Agarwal, Ceramics \nInternational 43(15) (2017) 12095. \n[45] R. Guo, L. Fang, W. Dong, F. Zheng, M. Shen, The Journal of Physical Chemistry C \n114(49) (2010) 21390. \n[46] Y. Zhang, A.M. Schultz, P.A. Salvador, G.S. Rohrer, Journal of Materials Chemistry \n21(12) (2011) 4168. \n[47] H. Maleki, S. Zare, R. Fathi, Journal of Superconductivity and Novel Magnetism \n(2017) 1. \n[48] H. Maleki, S. Falahatnezhad, M. Taraz, Journal of Superconductivity and Novel \nMagnetism (2018) 1. \n[49] A. Brisdon, Applied Organometallic Chemistry 24(6) (2010) n/a. \n[50] T. Gholam, A. Ablat, M. Mamat, R. Wu, A. Aimidula, M.A. Bake, L. Zheng, J. \nWang, H. Qian, R. Wu, K. Ibrahim, Journal of Alloys and Compounds 710 (2017) 843. \n[51] X. Yang, G. Xu, Z. Re n, X. Wei, C. Chao, S. Gong, G. Shen, G. Han, CrystEngComm \n16(20) (2014) 4176. \n[52] S. Karimi, I.M. Reaney, I. Levin, I. Sterianou, Applied Physics Letters 94(11) (2009) \n112903. \n[53] J. Tauc, Materials Research Bulletin 5(8) (1970) 721. \n[54] † X. H. Wang, † J.-G. Li, †,‡ H. Kamiyama, ‡ and Y. Moriyoshi, † T. Ishigaki*, \n(2006). \n "    },    {        "title": "1205.0906v1.First_principles_calculation_of_magnetoelastic_coefficients_and_magnetostriction_in_the_spinel_ferrites_CoFe2O4_and_NiFe2O4.pdf",        "content": "arXiv:1205.0906v1  [cond-mat.mtrl-sci]  4 May 2012First-principles calculation of magnetoelastic coefficien ts and magnetostriction\nin the spinel ferrites CoFe 2O4and NiFe 2O4\nDaniel Fritsch∗\nH. H. Wills Physics Laboratory, University of Bristol,\nTyndall Avenue, Bristol BS8 1TL, United Kingdom†\nClaude Ederer‡\nMaterials Theory, ETH Z¨ urich, Wolfgang-Pauli-Strasse 27 , 8093 Z¨ urich, Switzerland†\n(Dated: May 7, 2012)\nWe present calculations of magnetostriction constants for the spinel ferrites CoFe 2O4and NiFe 2O4\nusing density functional theory within the GGA+ Uapproach. Special emphasis is devoted to the\ninfluence of different possible cation distributions on the Bsite sublattice of the inverse spinel struc-\nture on the calculated elastic and magnetoelastic constant s. We show that the resulting symmetry-\nlowering has only a negligible effect on the elastic constant s of both systems as well as on the mag-\nnetoelastic response of NiFe 2O4, whereas the magnetoelastic response of CoFe 2O4depends more\nstrongly on the specific cation arrangement. In all cases our calculated magnetostriction constants\nare in good agreement with available experimental data. Our work thus paves the way for more\ndetailed first-principles studies regarding the effect of st oichiometry and cation inversion on the\nmagnetostrictive properties of spinel ferrites.\nPACS numbers: 75.80.+q, 71.15.Mb, 75.47.Lx\nI. INTRODUCTION\nMagnetostriction describes the deformation of a\nferro- or ferrimagnetic material during a magnetization\nprocess.1–7Thereby, one can distinguish between the\nspontaneous volume magnetostriction , which is indepen-\ndent of the magnetic field direction, and the so-called\nlinear magnetostriction which characterizes the change\nof length along a certain direction that depends on the\norientation of the applied magnetic field. The same mag-\nnetoelastic interaction that causes magnetostriction also\nleads to changes in the magnetic anisotropy as function\nof an externally applied strain.\nMagnetostrictive materials are very important for\napplications as magnetic field sensors and magneto-\nmechanical actuators, where a large (and often also\npreferably linear) magnetic field response is essential.8\nOn the other hand magnetostriction also causes noise\nand frictional losses in magnetic transformer cores, so\nthat in this context a minimization of magnetostriction\nis desirable.\nCoFe2O4(CFO) is known to have one of the largest\nmagnetostriction among magnetic materials that do not\ncontain any resource-critical rare-earth elements.9It has\nthus recently come into focus for use in magnetostrictive-\npiezoelectriccomposites,10–12wherethe goalisto achieve\ncrosscouplingbetween magneticand dielectric degreesof\nfreedom. Due to its insulating character and high mag-\nnetic ordering temperature, CFO together with NiFe 2O4\n(NFO) and other spinel ferrites is also a very attractive\ncandidate for spintronics applications, in particular for\nspin-filtering tunnel barriers.13,14For many of these ap-\nplications, thin films of CFO and NFO are epitaxially\ngrown on substrates with different lattice constants. The\nresulting substrate-induced strain can then lead to dis-tinctly different properties of the thin films compared to\nthe corresponding bulk materials.\nIn view of this, a good quantitative understanding of\nmagnetoelastic properties of spinel ferrites, that provides\na solid basisfor the interpretation ofexperimental results\nand allows for further optimization of magnetostrictive\nproperties, is highly desirable. In particular, the ability\nto accurately predict effects of cation off-stoichiometry\nor surface and interface effects can provide valuable in-\nsights into the fundamental mechanisms determining the\nobserved properties.\nIn previous work we have shown that first-principles\ncalculations based on density-functional theory (DFT)\nprovideasuitabledescriptionofthemagnetoelasticprop-\nerties of spinel ferrites,15,16thus demonstrating the feasi-\nbility of more detailed studies into strain-induced effects\nin thin film structures composed of CFO and NFO. Here\nwe extend our previous study, in order to provide a more\ncomprehensive picture of the magnetoelastic response of\nCFO and NFO, in particular including first-principles\ncalculations of the complete set of cubic magnetoelastic\nand magnetostrictive coefficients. Most importantly, we\ninvestigate the influence of different possible cation dis-\ntributions on the spinel Bsite sublattice on the magne-\ntoelastic response of these materials. The purpose of the\npresentworkis toprovideafirst-principlesbaseddescrip-\ntion of magnetoelastic coupling in spinel ferrites that can\nbe used as basis for further studies of the effect of cation\nsubstitution or off-stoichiometry on the magnetostrictive\nproperties of this important class of materials.\nThis paper is organized as follows. In Sec. IIA the\nspinel crystal structure is discussed, with special empha-\nsis on cation inversion and different possible cation ar-\nrangements on the Bsite sublattice. A general overview\nof magnetoelastic theory in cubic and tetragonal crystals2\nFIG. 1: (Color online) The spinel structure consists of an fc c\nnetwork of oxygen anions (red) with cations occupying differ -\nentinterstitial sites ofthefcc lattice, resultingintetr ahedrally\ncoordinated Asites (purple) and octahedrally coordinated B\nsites (brown). Picture has been generated using VESTA.17\nis given in Sec. IIB. Sec. IIC describes how we determine\nall elastic and magneto-elastic coefficients from total en-\nergyelectronicstructurecalculations, while Sec.IID pro-\nvidessomemoretechnicaldetailsofourcalculations. Our\nresults for CFO and NFO are presented in Sec. III, and\nour main conclusions are summarized in Sec. IV.\nII. THEORETICAL BACKGROUND AND\nCOMPUTATIONAL METHOD\nA. Inverse spinel structure and different cation\ndistributions\nBoth CFO and NFO crystallize in the cubic spinel\nstructure (see Fig. 1), which belongs to space group\nFd¯3m(No. 227). The spinel structure contains two in-\nequivalent cationsites, atetrahedrallycoordinated Asite\nand an octahedrally coordinated Bsite. In the normal\nspinel structure each of these sites is occupied by a par-\nticular cation species (e.g. divalent Mn2+on theAsite\nand trivalent Fe3+on theBsite in the caseof MnFe 2O4).\nHowever, in the inversespinel structure, the more abun-\ndant cation species (here: Fe3+) occupies all Asites and\n50% of the Bsites, with the remaining 50% of Bsites\noccupied by the less abundant cation species (here: Co2+\nor Ni2+). In practice, intermediate cases can also occur,\ncharacterized by an inversion parameter λ, ranging from\nλ= 0 for the normalspinel structure to λ= 1 for com-\nplete inversion.\nBoth CFO and NFO are experimentally found to be\ninverse spinels, with λ≈1 for NFO but only incom-\nplete inversion for CFO (with λbetween 0 .76−0.93, de-\npending strongly on sample preparation conditions).9,18\nBoth materials are generally found to be perfectly cu-\nbic, with a random distribution of divalent and trivalent\ncations over the Bsite sublattice. However, indicationsfor short-range cation order on the Bsites have been re-\nported recently for the case of NFO, both in bulk single\ncrystals as well as in thin films.19,20\nIn the present work we represent the inverse spinel\nstructure within a tetragonal unit cell containing 4 for-\nmula units (see also Ref. 21) using lattice vectors /vector a1=\n(a/2,−a/2,0),/vector a2= (a/2,a/2,0), and/vector a3= (0,0,c), so\nthatc/a= 1 corresponds to the unstrained, nominally\ncubic case. By distributing equal amounts of Co (respec-\ntively Ni) and Fe on the 8 Bsites within this unit cell,\n70 cation arrangements belonging to 8 different space-\ngroups can be generated. In the following we consider\nonly the three high-symmetry arrangements shown in\nFig. 2 (a)-(c), plus one additional low-energy configu-\nration for CFO, corresponding to 75% inversion, shown\nin Fig. 2 (d). The specific cation arrangements shown in\nFig. 2 in combination with the periodic boundary con-\nditions corresponding to the tetragonal lattice vectors\nreduce the space group symmetries to P4122 (No. 91),\nImma(No. 74),and P¯4m2(No. 115)forthefullyinverse\nconfigurations, and to P1 (No. 1) for the case with 75 %\ninversion. As we have previously shown,21bothP4122\nandImmacorrespond to low energy configurations for\nthe fully inversecase, with P4122 slightly lowerin energy\nthanImmafor both CFO and NFO, whereas the P¯4m2\nconfiguration is energetically much less favorable. The\nP1structurerepresentsalowenergyconfigurationforthe\ncaseλ= 0.75.21We also note that the P4122 configura-\ntion corresponds to the local structure suggested for the\nexperimentally observed short-range order in NFO,19,20\nwhereas the Immaconfiguration is equivalent to the one\nused in our previous study of magneto-elastic effects in\nCFO and NFO.15,16\nB. Magnetoelastic theory\nWithin the phenomenological theory of magnetoelas-\nticity, the magnetoelastic energy density f=E/Vis\nexpressed in terms of the direction cosines of the magne-\ntization vector, αi(i=x,y,z), and the components of\nthe strain tensor εij, relative to a suitably chosen (non-\nmagnetic) reference state.1–7This energy density can be\ndivided into a purely elastic term, fel, and a magnetoe-\nlastic coupling term, fme, which is usually taken as linear\nin the strain components. For a cubic crystal these terms\nhave the following form:22\nfcubic\nel=1\n2C11(ε2\nxx+ε2\nyy+ε2\nzz)+2C44(ε2\nxy+ε2\nyz+ε2\nzx)\n+C12(εyyεzz+εxxεzz+εxxεyy),\n(1)\nand\nfcubic\nme=B0(εxx+εyy+εzz)\n+B1(α2\nxεxx+α2\nyεyy+α2\nzεzz)\n+2B2(αxαyεxy+αyαzεyz+αzαxεzx),(2)3\nFIG. 2: (Color online) Cation distribution of Fe (brown) and Co (Ni) (blue) on the Bsites of the spinel structure for the\ndifferent configurations used in our calculations. Note that only the Bsublattice is shown. From left to right the depicted\nstructures correspond to spacegroups (a) P4122 (No. 91), (b) Imma(No. 74), and (c) P¯4m2 (No. 115). Figure (d) on the\nright displays the CFO low-energy solution with incomplete degree of inversion, λ= 0.75 corresponding to spacegroup P1 (No.\n1).21Pictures have been generated using VESTA.17\nwhereC11,C12, andC44are elastic and B0,B1, andB2\nare magnetoelastic coupling constants.\nThe relative length changealongan arbitrary(measur-\ning) direction with direction cosines βiis given by:\n∆l\nl=/summationdisplay\ni,jεijβiβj, (3)\nwhere the strain components depend on the magnetiza-\ntion directions. These equilibrium strains as function of\nthe magnetization direction can be found by minimizing\nthe sum of the two energy expressions (1) and (2) with\nrespect to all strain components. This results in:\n∆l\nl/vextendsingle/vextendsingle/vextendsingle/vextendsingle\ncubic=λα+3\n2λ100/parenleftbig\nα2\nxβ2\nx+α2\nyβ2\ny+α2\nzβ2\nz−1/3/parenrightbig\n+3λ111(αxαyβxβy+αyαzβyβz+αxαzβxβz).\n(4)\nHere,λα=−(B0+B1/3)/(C11+2C12) describes a pure\nvolume magnetostriction that is independent of the mag-\nnetization direction(this termis sometimesomitted from\nthe above formula and is of no concern in the present\nwork). The widely used magnetostriction constants of a\ncubic crystal are given by:\nλ100=−2\n3B1\nC11−C12, (5)\nand\nλ111=−B2\n3C44. (6)\nThese two coefficients measure the fractional length\nchange along the [100] ( βx= 1,βy=βz= 0) and [111]\n(βi= 1/√\n3) directions, when the sample is magnetized\nto saturation along the [100] ( αx= 1,αy=αz= 0) and\n[111] (αi= 1/√\n3) directions, relative to an ideal demag-\nnetized reference state which is defined by/angbracketleftbig\nα2\ni/angbracketrightbig\n=1/3\nand/angbracketleftαiαj/angbracketright= 0. In a polycrystalline sample one can onlymeasureadirectionaverageoverboth λ100andλ111given\nby:2\nλS=2\n5λ100+3\n5λ111. (7)\nAs noticed in Sec. IIA, the cation arrangements used\nto describe the inverse spinel structure within our cal-\nculations lower the cubic symmetry of the ideal spinel\nstructure to tetragonal ( P4122 andP¯4m2), orthorhom-\nbic (Imma), or even triclinic ( P1). A full first-principles\ndescription of magnetoelastic effects within these lower\nsymmetries would require the calculation of 6 (9, 21)\ndifferent elastic and 7 (12, 36) magnetoelastic coupling\nconstants for the mentioned tetragonal (orthorhombic,\ntriclinic) spacegroups, respectively.4Due to the resulting\nlarge computational effort, and considering the fact that\nexperimentally both CFO and NFO are found to be cu-\nbic, we do not attempt such a full determination of all\nelastic and magnetoelastic coefficients within the lower\nsymmetries, and instead evaluate our results using the\nrelations for the cubic case described above (i.e., similar\nto our previous work in Refs. 15 and 16). To estimate\nthe degree to which the lower symmetry affects our cal-\nculated coefficients, we also compare some of our data\nto the correct formulas corresponding to the lower sym-\nmetry. For simplicity we hereby restrict ourselves to the\ntetragonal case. The required equations are presented in\nthe following.\nWithin the lower tetragonal symmetry there are six\nindependent elastic and seven different magnetoelastic\ncoupling constants, in contrast to the three elastic and\nthree magnetoelastic coefficients in the cubic case.4The\nresulting expressions for felandfmethen read:6\nftet\nel=1\n2c11/parenleftbig\nε2\nxx+ε2\nyy/parenrightbig\n+1\n2c33ε2\nzz\n+c12εxxεyy+c13(εxx+εyy)εzz\n+2c44/parenleftbig\nε2\nyz+ε2\nxz/parenrightbig\n+2c66ε2\nxy,(8)\nwithcijdenoting the six different tetragonal elastic con-4\nstants, and\nftet\nme=b11(εxx+εyy)+b12εzz\n+b21/parenleftbig\nα2\nz−1/3/parenrightbig\n(εxx+εyy)+b22/parenleftbig\nα2\nz−1/3/parenrightbig\nεzz\n+1\n2b3/parenleftbig\nα2\nx−α2\ny/parenrightbig\n(εxx−εyy)+b′\n3αxαyεxy\n+b4(αxαzεxz+αyαzεyz),\n(9)\nwith the various b’s denoting the seven different tetrago-\nnal magnetoelastic coupling constants. The correspond-\ning cubic expressions (1) and (2) can then be obtained\nfrom (8) and (9) with the additional symmetry con-\nstraints: c11=c33=C11,c12=c13=C12,c44=c66=\nC44,b11=b12=B0+1/3B1,b22=−2b21=b3=B1,\nandb′\n3=b4=B2.\nC. Determination of elastic and magnetoelastic\nconstants\nIn order to determine the (cubic) elastic constants\nfor CFO and NFO, we first perform a full structural\nrelaxation of both systems. Similar to our previous\ninvestigations,15,16,21we thereby constrain the lattice\nvectors to “cubic” symmetry ( c/a= 1) and fix the in-\nternal coordinates of the AandBcations to ideal values\ncorresponding to the cubic spinel structure, i.e., we only\nallow for an optimization of the total volume and the\noxygen positions. We then determine the three indepen-\ndent cubic elastic constants C11,C12, andC44, and the\ntwo cubic magnetoelastic coupling constants B1andB2\nby distorting the equilibrium crystal structure in three\ndifferent ways: i) isotropic volume expansion, ii) con-\nstraining two of the three lattice dimensions and relax-\ning the third (“epitaxial strain”), and iii) by applying a\nvolume-conserving shear strain.\ni)Isotropic volume expansion. The dependence of the\ntotal energy Etoton the unit cell volume Vprovides the\nbulk modulus B, which is defined as\nB=V0/parenleftbigg∂2Etot\n∂V2/parenrightbigg/vextendsingle/vextendsingle/vextendsingle/vextendsingle\n(V=V0), (10)\nwithV0being the equilibrium volume. According to\nEq. (1) the bulk modulus Bof a cubic crystal can be\nexpressed in terms of the elastic moduli C11andC12as\nfollows:\nB=1\n3(C11+2C12). (11)\nii)Epitaxial strain. We follow the approach of Ref. 15 to\nobtain a second independent elastic constant by applying\nepitaxial strain , i.e., we constrain the “in-plane” lattice\nconstant to values ranging from −4% to +4% relative to\nthe theoretical equilibrium lattice constant a0, and we\nrelax the “out-of-plane” lattice constant and all internalstructural parameters of the oxygen anions. The rela-\ntion between the relaxed out-of-plane strain ε⊥and the\nfixed in-plane strain ε||then defines the so-called two-\ndimensional Poisson ratio ν2D. It follows from Eq. (1)\nthat for a cubic system ν2Dis given as:\nν2D=−ε⊥\nε||= 2C12\nC11. (12)\nThe elastic moduli C11andC12can then be obtained\nfrom Eqs. (11) and (12) using the bulk modulus and two-\ndimensional Poisson ratio calculated from DFT.\nFor the cation arrangements with tetragonal, or-\nthorhombic, or triclinic symmetry depicted in Fig. 2 the\nratioε⊥/ε||can be different for different orientations of\n“out-of-plane” and “in-plane” directions relative to the\ncrystal axes. To quantify the resulting difference we per-\nform calculations for two symmetry-inequivalent orien-\ntations of the applied strain ε||. In particular we ap-\nply the epitaxial constraint first within the xyplane\n(ε||=εxx=εyyandε⊥=εzz) and then also within\ntheyzplane (ε||=εyy=εzzandε⊥=εxx). Using\nthe tetragonal energy expressions of Eqs. (8) and (9) to-\ngether with the definition of ν2Din Eq. (12) one obtains\nν(xy)\n2D= 2c13/c33andν(yz)\n2D= (c12+c13)/c11for these two\ncases. The difference between these two values for ν2D\nthus gives a measure for the difference between c11and\nc33as well as between c12andc13.\nTo obtain the magnetoelastic coupling coefficient B1\nwemonitorthetotalenergydifferencesfordifferentorien-\ntations of the magnetization as a function of the applied\nin-plane constraint ε||and relaxed out-of-plane strain\nε⊥=−ν2Dε||. Using the cubic expression(2) for fmeone\ncan see that the strain dependence of the energy density\nfor all in-plane orientations of the magnetization is given\nbyB1·ε||, whereasthe strain dependence for out-of-plane\norientation is given by −B1·ν2D·ε||. The strain depen-\ndence of the total energy difference between out-of-plane\nversus in-plane orientation of the magnetization is thus\ngiven by:23\n∆E/V=−(ν2D+1)B1ε/bardbl. (13)\nThe coefficient B1can therefore be obtained from the\ncalculatedstrain-dependentmagneticanisotropyenergies\n(MAEs) and the previously determined two-dimensional\nPoisson ratio ν2D. WhileB1is not directly accessible by\nexperimental investigations, it is related to the magne-\ntostriction constant λ100via Eq. (5).\nInthetetragonalcasethemonitoredstraindependence\nof the total energy difference between out-of-plane ver-\nsus in-plane directions of the magnetization will depend\non the orientationof“out-of-plane”and “in-plane”direc-\ntions with respect to the tetragonal crystal axes. For the\nepitaxialconstraintappliedwithinthe xyplane(i.e. ε/bardbl=\nεxx=εyy, leading to a Poisson ratio ν(xy)\n2D= 2c13/c33)\nand using the tetragonal energy density (Eqs. (8) and\n(9)), the following expression for the strain dependence5\nof the total energy difference between in-plane and out-\nof-plane magnetization can be obtained:\n(∆E)(xy)/V= (2b21−ν(xy)\n2Db22)ε/bardbl,(14)\nwhich is valid for all in-plane orientations of the mag-netization. In contrast, for the epitaxial constraint ap-\nplied within the yzplane (i.e. ε||=εyy=εzz, leading\nto a Poisson ratio ν(yz)\n2D= (c12+c13)/c11) the resulting\n(∆E)(yz)/Vdepends on the specific in-plane direction\nand is given by:\n(∆E)(yz)/V=\n\n/parenleftBig\n−1\n2b3(ν(yz)\n2D+1)−(b21+b22−ν(yz)\n2Db21)/parenrightBig\nε/bardblfor (∆E)(yz)=E100−E001/parenleftBig\n−b3(ν(yz)\n2D+1)/parenrightBig\nε/bardbl for (∆E)(yz)=E100−E010/parenleftBig\n−3\n4b3(ν(yz)\n2D+1)−1\n2(b21+b22−ν(yz)\n2Db21)/parenrightBig\nε/bardblfor (∆E)(yz)=E100−E011/01¯1.(15)\niii)Volume-conserving shear strain. The third cubic\nelastic modulus C44is calculated according to Mehl,24\nby applying a volume-conserving monoclinic shear strain\nin thexyplane (ε/bardbl=εxy,ε⊥=εzz=ε2\n/bardbl/(1−ε2\n/bardbl),\nεxx=εyy=εyz=εzx= 0). The resulting change in\ntotal energy can then be written as:\nE(±ε/bardbl) = 2VC44ε2\n/bardbl+O[ε4\n/bardbl], (16)\nwhich allows for a straight-forwarddetermination of C44.\nFor the cation arrangements with tetragonal, or-\nthorhombic, or triclinic symmetry depicted in Fig. 2\ndifferent shear planes ( εxy,εyz,εzx) are connected to\ndifferent elastic moduli cii. Using the tetragonal en-\nergy expressions of Eqs. (8) and (9) together with the\nvolume-conserving monoclinic strain in the xyplane de-\nscribed above, one notices the connection of εxyandc66.\nHowever,choosingavolume-conservingmonoclinicstrain\nin theyzplane (ε/bardbl=εyz,ε⊥=εxx=ε2\n/bardbl/(1−ε2\n/bardbl),\nεyy=εzz=εxy=εzx= 0) yields directly c44, allowing\nfor a comparison with c66.\nSimilar to the first magnetoelastic coupling constant\nB1, the second coefficient B2is determined by monitor-\ning the total energy differences between different orien-\ntations of the magnetization as a function of the applied\nstrainε/bardbl. Depending on whether the shear strain ε/bardblis\napplied within the xyoryzplane, we consider the fol-\nlowing energy differences:\n(∆E)(xy)=E110−E100/010=E100/010−E1¯10(17)\n(∆E)(yz)=E011−E010/001=E010/001−E01¯1.(18)\nIn all cases, the strain-dependence of these total energy\ndifferences can be written as:\n∆E/V=B2ε/bardbl. (19)\nThus, the strain dependence of these energy differences\nis governed by the magnetoelastic coupling constant B2,\nwhich can be determined from the calculated ∆ E/V(ǫ/bardbl).\nSimilarto B1, themagnetoelasticcouplingconstant B2\nis also not directly accessible by experiment, but it is re-\nlated to the magnetostriction constant λ111via Eq. (6).Once the magnetostriction constants λ100andλ111are\nobtained, theaveragemagnetostrictionconstant λS, suit-\nable for polycrystalline samples, can be calculated from\nEq. (7).\nD. Other computational details\nAll calculations presented in this work are performed\nusing the projector-augmented wave (PAW) method,25\nimplemented in the Vienna ab initio simulation package\n(VASP 4.6).26–29StandardPAWpotentialssupplied with\nVASPwereusedinthecalculations, contributingnineva-\nlence electrons per Co (4s23d7), 16 valence electrons per\nNi (3p64s23d8), 14 valence electrons per Fe (3p64s23d6),\nand 6 valence electrons per O (2s22p4).\nThe generalized gradient approximation according to\nPerdew, Burke, and Ernzerhof (PBE)30is used in com-\nbination with the Hubbard “+ U” correction,31where\nU=3 eV and J=0 eV is applied to the dstates on all\ntransition metal cations. We have shown in Refs. 15,\n16, and 21 that this gives a realistic description of the\nelectronic structure of CFO and NFO and leads to re-\nsults which are in good overall agreement with available\nexperimental data.\nAll structural relaxations are performed within a\nscalar-relativisticapproximation, whereasspin-orbitcou-\nplingisincludedforthecalculationoftheMAEs. Aplane\nwave energy cutoff of 500 eV is used, and the Brillouin\nzone is sampled using a Γ-centered5 ×5×3k-point grid\nboth for the structural optimization and for all total en-\nergy calculations. We have verified that all quantities of\ninterest, in particular the magnetic anisotropy energies,\nare well converged for this k-point grid and planewave\nenergy cutoff.6\nIII. RESULTS AND DISCUSSION\nA. Structural properties\nThe equilibrium lattice constants a0, bulk moduli B,\ntwo-dimensional Poisson ratios ν2D, the resulting elastic\nconstants C11andC12, aswellas C44obtainedforthedif-\nferent cation arrangements for both CFO and NFO are\ngiven in Tab. I. One notices that the calculated lattice\nconstants for the two low-energy configurations Imma\nandP4122 are very similar to each other, and that the\nones for the higher energy P¯4m2 configuration and for\nthe case with 75 % inversion for CFO are slightly larger\nthan that (by less than 0.2%). This increase in lattice\nconstant is mirrored by a corresponding decrease in the\nbulk modulus (by about 3%). Overall, the variation\nof both bulk modulus and equilibrium lattice constant\nbetween different cation distributions is much smaller\nthan the slight under- and overestimation of these quan-\ntities with respect to the experimental value, which is\nwithin the usual limits of the PBE+ Uapproach (see also\nRef. 15).\nIt can also be seen that the difference in the two-\ndimensional Poisson ratios obtained for two different ori-\nentations of ε⊥is rather small and of similar magnitude\nas the differences between the various cation arrange-\nments. This indicates that the symmetry-loweringdue to\nthe different cation arrangements has only a small effect\non the elastic properties, which can still to a good ap-\nproximation be described by cubic elastic constants C11\nandC12.\nApplying the volume-conserving monoclinic strain as\ndescribed in Sec. IIB yields the remaining elastic mod-\nulusC44which is in very good agreement with the ex-\nperimental values for both CFO and NFO. To evaluate\nthe influence of different orientations of ε⊥onC44we\nappliedε⊥=εxyandε⊥=εyzwith the respective ε/bardbl\nto the low energy orthorhombic Immasymmetry. The\ndifference in the obtained C44is slightly larger compared\nto the difference in the C11andC12, but still within the\ntypical uncertainties of first-principles methods.\nOverall it appears that while the agreement between\nthe calculated and experimental lattice constants and\nelastic moduli is quite good and within the typical un-\ncertainties of state-of-the-art first-principles methods,\nthe uncertainties resulting from the symmetry-lowering\ncation arrangements are significantly smaller than that.\nTherefore, the elastic properties of the various cation ar-\nrangements of lower symmetry can be well described by\ncubic elastic constants.-0.50.00.5∆E [meV / 2 f.u.]P4122\n-0.50.00.5\n∆E [meV / 2 f.u.]\n-0.50.00.51.0\n∆E [meV / 2 f.u.]\n-1.0-0.50.00.5∆E [meV / 2 f.u.]Imma\n-4 -2 0 2 4\nε||=εxx=εyy [%]-0.50.00.5∆E [meV / 2 f.u.]P4m2\n-4 -2 0 2 4\nε||=εyy=εzz [%]-0.50.00.5\n∆E [meV / 2 f.u.]\nFIG. 3: Total energy difference ∆ Eper two formula units\n(f.u.) of NFO as function of the epitaxial constraint ε/bardblfor\ndifferent cation arrangements. The left (right) panels corr e-\nspond to the case with ε⊥=εzz(ε⊥=εxx). The panels from\ntop to bottom refer to symmetries P4122,Imma, andP¯4m2,\nrespectively. In case of ε⊥=εzz(ε⊥=εxx) the depicted en-\nergy difference ∆ Eis taken with respect to the [001] ([100])\ndirection, with the symbols denoting /trianglesolid[100] ([010]), /triangledownsld[010]\n([001]),◭[1¯10] ([01¯1]), and ◮[110] ([011]), respectively.\nB. Magnetoelastic properties\n1. NFO\nNext we focus on the magnetoelastic coupling in NFO.\nThe calculated MAEs necessary to determine the mag-\nnetoelastic coupling constant B1are depicted in Fig. 3.\nAs described in Sec. IIC these MAEs are defined here\nas the energy differences for various orientations of the\nmagnetization with respect to the magnetization direc-\ntion perpendicular to the applied strain plane, i.e., [001]\nforε/bardbl=εxx=εyyand [100] for ε/bardbl=εyy=εzz. Accord-\ning to Eq. (13) the slope of the curves given in Fig. 3 is\ndirectly related to the magnetoelastic coupling constants\nB1. At first sight, the slopes of all curves in all panels\nare very similar and negative, thus leading to a positive\nB1(the range of the yaxes is the same in all panels to\nallow for a direct inspection of slope differences).\nIn the tetragonal symmetries ( P4122 andP¯4m2) all\ncurves fall on top of each other for ε⊥=εzz(left pan-7\nTABLE I: Optimized equilibrium lattice constant a0, bulk modulus B, two-dimensional Poisson ratio ν2D, and elastic moduli\nC11,C12, andC44for CFO and NFO, obtained for different cation arrangements a nd strain orientations ( ε⊥=εzz=z\nandε⊥=εxx=x) in comparison to experimental data. The experimental ν2Dhas been evaluated from Eq. (12) using\nthe experimental elastic constants. P1 in case of CFO refers to the low-energy solution with incomp lete degree of inversion,\nλ= 0.75.21\nCFOa0 Bε⊥ ν2DC11 C12 C44\n(˚A) (GPa) (GPa) (GPa) (GPa)\nImma 8.463 172.3z 1.132 242.5 137.3 94.9\nx 1.147 240.8 138.1 83.2\nP4122 8.464 170.8z 1.129 240.7 135.9 84.7\nx 1.147 238.7 136.9 −\nP¯4m2 8.473 168.0z 1.132 236.4 133.8 92.3\nx 1.128 236.8 133.6 −\nP1 8.477 167.8z 1.155 233.6 134.9 87.7\nx 1.146 234.6 134.4 −\nExp. (Ref. 32) 8.392 185.7 1.167 257.1 150.0 85.3\nNFOa0 Bε⊥ ν2DC11 C12 C44\n(˚A) (GPa) (GPa) (GPa) (GPa)\nImma 8.426 177.1z 1.106 252.2 139.5 93.2\nx 1.115 251.2 140.0 87.6\nP4122 8.428 175.4z 1.116 248.7 138.8 87.4\nx 1.116 248.7 138.8 −\nP¯4m2 8.435 173.3z 1.116 245.7 137.1 91.0\nx 1.102 247.3 136.3 −\nExp. (Ref. 32) 8.339 198.2 1.177 273.1 160.7 82.3\nTABLE II: Magnetoelastic coupling constants ( B1,B2) and\nmagnetostriction constants ( λ100,λ111,λS) for NFO using\ndifferent cation arrangements and strain planes according t o\nε⊥=εzz=z(ε⊥=εxx=x) in comparison with available\nexperimental data. The average magnetostriction constant\nλShas been obtained using Eq. (7).\nε⊥B1λ100 B2λ111λS\n(MPa) ( ×10−6) (MPa) ( ×10−6)\nP4122z 6.6 −40.1 2.5 −9.7−21.9\nx 6.4 −38.6 − − −\nImmaz 6.1 −35.9 0.9 −3.4−16.4\nx 6.7 −40.3 1.9 −7.3−20.5\nP¯4m2z 6.5 −40.0 1.4 −5.3−19.2\nx 6.9 −41.3 − − −\nExp.Ref. 33a−36.0 −4.0−16.8\nRef. 34b−50.9 −23.8−34.6\nRef. 35c−43.0 −20.1−29.3\naSingle crystals with Ni 0.8Fe2.2O4composition.\nbSingle crystals of NiFe 2O4.\ncSingle crystals of NiFe 2O4.\nels), whereas there is a small offset between the curves\nin all other cases, due to the lower symmetry. In the\neven lower Immasymmetry this offset is also present for\nε⊥=εzz. Nevertheless, the variation with strain is very\nsimilar in all cases, and the values for B1, obtained by\naveragingover all curves corresponding to the same sym-\nmetry and strain orientation, are given in Tab. II. These\nvalues range from 6.1 MPa to 6.9 MPa, depending on the\nspecific cation arrangement and strain orientation. Dueto these rathersmall variations, we can conclude that the\nmagnetostrictive response in NFO can to a good approx-\nimation be described as cubic.\nTogether with the respective elastic constants from\nTab. I the magnetostriction constants λ100can be ob-\ntained via Eq. (5), and are also listed in Table II. It\ncan be seen that there is only a weak influence of ei-\nther cation arrangement or different strain planes on the\nNFO magnetostriction constant λ100, which ranges from\n−35.9×10−6to−41.3×10−6. This agrees perfectly\nwith experimental data ranging from −36.0×10−6to\n−50.9×10−6.\nThe calculated strain-dependent MAEs necessary for\nthe determination of B2are shown in Fig. 4. The dif-\nferent curves are adjusted to match at ε/bardbl= 0 in order\nto remove the corresponding offset which is irrelevant for\nthe present work. The MAEs are chosen according to\nEqs. (17) and (18) as energy differences between different\nin-plane orientations of the magnetization with respect\nto the applied shear strain ε/bardbl. According to Eq. (19) the\nslope of the curves given in Fig. 4 is directly related to\nthe magnetoelastic coupling constant B2. From Fig. 4\nit can be seen that the slopes of these curves are pos-\nitive, corresponding to positive B2. There are slightly\nstronger nonlinearities in the curves in each of the panels\ncompared to Fig. 3, as well as a stronger influence of the\nexplicitcationarrangements. The resultingmagnetoelas-\ntic coupling constants B2are listed in Tab. II and range\nfrom 0.9 MPa to 2.5 MPa, leading to magnetostriction\nconstants λ111ranging from −3.4×10−6to−9.7×10−6.\nThese values are compatible with the lower experimen-8\n-2-1012\nεxy [%]-0.050.000.05∆E [meV / 2 f.u.]\n-2-1012\nεyz [%]-2-1012\nεxy [%]-2-1012\nεxy [%]-0.050.000.05\n∆E [meV / 2 f.u.]\nFIG. 4: Total energy difference ∆ Eper two formula units (f.u.) of NFO as function of shear strai n for different cation\narrangements. The panels from left to right refer to symmetr iesP4122 (ε/bardbl=εxy),Imma(ε/bardbl=εxy),Imma(ε/bardbl=εyz), and\nP¯4m2 (ε/bardbl=εxy), respectively. The depicted energy differences ∆ Ecorrespond to [110]-[100] ( /trianglesolid), [110]-[010] ( /triangledownsld), [100]-[1 ¯10]\n(◮), and [010]-[1 ¯10] (◭), respectively, for ε/bardbl=εxyand equivalent directions for ε/bardbl=εyz.\ntal values, which themselves range from −4.0×10−6to\n−23.8×10−6. The last column in Tab. II also lists the\naveraged λSsuitable for polycrystalline materials using\nEq. (7).\nOverall, the different cation arrangements and strain\nplaneshaveonlyaratherweakinfluenceonthecalculated\nmagnetostriction constants of NFO, which agree very\nwell with the range of reported experimental data. We\ncan therefore confirm our earlier finding,15that DFT+ U\nmethods are suitable for a quantitative description of\nmagnetoelastic properties in this material. Moreover,\nalthough the symmetries of the investigated cation ar-\nrangements are not cubic, the magnetostrictive proper-\nties of NFO are very well described within the cubic the-\nory.\n2. CFO\nNow we turn to our results for CFO. The calculated\nMAEs for the determination of the magnetoelastic cou-\npling constant B1are depicted in Fig. 5. At first sight,\none notices again that all slopes are negative, leading to\na positive magnetoelastic coupling constant B1. How-\never, in contrast to NFO, the values are now much larger\nand also depend more strongly on the specific cation ar-\nrangement and orientation of the strain plane. In all\ncases except for the case of P¯4m2 withε/bardbl=εxx, we\nagainobtain anoffset between the different curves, which\nis due to the lower symmetry of the specific cation dis-\ntribution. The differences in slopes observable between\nthe various curves in the left panel of P4122 symmetry\nare due to the fact that in this case the system adopts\nan orbitally-ordered ground state with symmetry lower\nthan that of the underlying crystal structure. Strongest\ndeviations from linearity are observed in the low-energy\nsolution with symmetry P1 belonging to incomplete in-\nversionλ= 0.75.\nThe determined magnetoelastic coupling constants B1\naregiveninTab.III,rangingfrom18.9MPato42.0MPa.\nThe largestinfluence ofthe strainplane orientationis ob-\nserved for P4122 symmetry. Overall, the specific cationTABLE III: Magnetoelastic coupling constants ( B1,B2) and\nmagnetostriction constants ( λ100,λ111,λS) for CFO using\ndifferent cation arrangements and strain planes according t o\nε⊥=εzz=z(ε⊥=εxx=x) in comparison with available\nexperimental data. The average magnetostriction constant\nλShas been obtained using Eq. (7).\nε⊥B1λ100 B2λ111λS\n(MPa) ( ×10−6) (MPa) ( ×10−6)\nP4122z 18.9 −120.1 −8.4 32.9 −28.3\nx 32.8 −215.0 − − −\nImmaz 39.7 −251.7−11.6 40.9 −76.1\nx 29.2 −189.7−12.2 48.8 −\nP¯4m2z 42.0 −272.7−14.6 52.7 −77.5\nx 30.9 −199.4 − − −\nP1z 29.1 −196.3 −7.6 28.8 −61.2\nx 24.2 −160.9 − − −\nExp.Ref. 36a−225.0\nRef. 33b−250.0\nRef. 33c−590.0 120.0 −164.0\naPolycrystalline CoFe 2O4.\nbSingle crystals with Co 1.1Fe1.9O4composition.\ncSingle crystals with Co 0.8Fe2.2O4composition.\narrangement has a much larger influence on the obtained\nmagnetoelastic coupling constants in CFO compared to\nNFO. However, we note that even though there are pro-\nnounced differences between the two different strain ori-\nentations (left and right panels in Fig. 5) for the same\ncation arrangements, the strain dependence of the vari-\nous calculated energy differences for the same strain ori-\nentation (different curves within each panel) are very\nsimilar in each case. From expression (15) for tetrago-\nnal symmetry, we can therefore empirically observe that\nthe followingapproximaterelationshipholds between the\nvarious magnetoelastic coefficients:\n1\n2b3(ν2D+1)≈b21+b22−ν2Db21.(20)\nHowever, since the slopes in the left and right panels of\nFig. 5 differ, the stronger condition b3=b22=−2b21,\nwhich would be valid within cubic symmetry, is not ful-\nfilledin CFO.Thedeviationfromcubicsymmetrycaused9\n-4.0-2.00.02.04.0∆E [meV / 2 f.u.]P4122\n-4.0-2.00.02.04.0\n∆E [meV / 2 f.u.]\n-6.0-4.0-2.00.02.0\n∆E [meV / 2 f.u.]\n0.02.04.06.08.0∆E [meV / 2 f.u.]Imma\n-2.00.02.04.06.0∆E [meV / 2 f.u.]P4m2\n-4.0-2.00.02.0\n∆E [meV / 2 f.u.]\n-4 -2 0 2 4\nε||=εyy=εzz [%]-4.0-2.00.02.04.0\n∆E [meV / 2 f.u.]\n-4 -2 0 2 4\nε||=εxx=εyy [%]-2.00.02.04.06.0∆E [meV / 2 f.u.]P1\nFIG. 5: Total energy difference ∆ Eper two formula units\n(f.u.) of CFO as function of the epitaxial constraint ε/bardblfor\ndifferent cation arrangements. The left (right) panels corr e-\nspond to the case with ε⊥=εzz(ε⊥=εxx). The panels from\ntop to bottom refer to symmetries P4122,Imma, andP¯4m2,\nandP1 (low-energy solution for cation inversion λ= 0.7521).\nIn case of ε⊥=εzz(ε⊥=εxx) the depicted energy difference\n∆Eis taken with respect to the [001] ([100]) direction, with\nthe symbols denoting /trianglesolid[100] ([010]), /triangledownsld[010] ([001]), ◭[1¯10]\n([01¯1]), and ◮[110] ([011]), respectively.\nby the specific cation arrangements, is therefore more\nstrongly manifested in the magnetoelastic response of\nCFO compared to NFO. Nevertheless, the approximate\nrelation Eq. (20) indicates that some residue of the ap-\nproximate structural cubic symmetry is still present also\nin the case of CFO.\nThe magnetostriction constants of CFO can now be\nobtained via Eq. (5) and using the elastic constants in\nTable I. The resulting values are listed in Table III and\nrange from −120.1×10−6to−272.7×10−6. This agrees\nwell with the lower range of available experimental data,\nwhich itself variesbetween −225×10−6and−590×10−6.Thestrain-dependentMAEsnecessaryforthedetermi-\nnation of B2are shown in Fig. 6, analogous to the NFO\ncase. Most strikingly, and in contrast to NFO, the corre-\nsponding slope is negative, thus leading to a negative B2\ninCFO.Thespreadinslopesineachofthepanelsiscom-\nparable to NFO. While we obtain quite similar values for\nImmaandP¯4m2 symmetry (middle three panels), and\nalso forP4122 andP1, the latter two symmetries lead to\nsomewhat smaller values for B2than the former.\nOverall, B2ranges from −8.4 MPa to −14.6 MPa for\nthe symmetries corresponding to complete cation inver-\nsion, and −7.6MPa for the case with λ= 0.75(P1). The\nresulting magnetostriction constants λ111of CFO range\nfrom 28.8×10−6to 52.7×10−6, respectively. These val-\nues are lower than the (to the best of our knowledge only\navailable) value of 120 ×10−6reported experimentally.\nIn view of the relatively strong dependence on the spe-\ncific cation arrangement, no particular trend is apparent\non how the magnetostriction constants change with re-\nduced cation inversion ( P1 structure compared to the\nother cases with full inversion). Taking a closer look at\nthe individual magnetostriction constants λ100for all in-\nvestigated cation arrangements and strain planes, one\ncan notice that the largest magnetostriction occurs for\ncases where the cation species are arranged in alter-\nnating planes parallel to the applied strain plane, e.g.,\nε⊥=εzz=zforImmaandP¯4m2symmetry(seeFig.2).\nFurthermore, if one comparesthe two different strain ori-\nentations for P4122 symmetry, the magnetostriction is\nlarger for ε⊥=εxx=x, where the strain plane contains\nchains of Bsite cations with two equal cations next to\neach other in each chain. The magnetostriction value\nfor the strain plane containing alternating cation chains\nwithinP4122 symmetry is the smallest observed here.\nHowever, at present it is unclear whether these correla-\ntions between cation arrangement and λ100are mostly\ncoincidental, or whether they indeed indicate a deeper\nrelationship between these two properties. In any case\nour results give clear evidence that a fully quantitative\nmodel of anisotropy and magnetostriction in CFO needs\nto include crystal- or ligand-field effects that go beyond\nthe immediate nearest neighbor shell of the Co2+cation.\nThe effect of different distributions of Co2+and Fe3+\ncations on the Bsites surrounding a specific Co Bsite\nhas been taken into account in the theory of magnetic\nanisotropy for CFO by Tachiki,37and is also discussed\nby Slonczewski.38It was shown that the correspond-\ning crystal-field component can have a strong effect on\nthe resulting cubic magnetic anisotropy constants. The\nnoticeable dependence of our calculated magnetoelastic\ncoupling constants on the specific cation arrangement in\nCFO indicates that this crystal-fieldcomponent is indeed\nquite strong and needs to be taken into account within\na quantitative theory of anisotropy and magnetostriction\nin spinel ferrites.10\n-2-1012\nεxy [%]-0.2-0.10.00.10.2∆E [meV / 2 f.u.]\n-2-1012\nεyz [%]-2-1012\nεxy [%]-2-1012\nεxy [%]-2-1012\nεxy [%]-0.2-0.10.00.10.2\n∆E [meV / 2 f.u.]\nFIG. 6: Total energy difference ∆ Eper two formula units (f.u.) of CFO as function of shear strai n for different cation\narrangements. The panels from left to right refer to symmetr iesP4122 (ε/bardbl=εxy),Imma(ε/bardbl=εxy),Imma(ε/bardbl=εyz),P¯4m2\n(ε/bardbl=εxy), andP1 (ε/bardbl=εxy, low-energy solution for cation inversion λ= 0.7521), respectively. The depicted energy differences\n∆Ecorrespond to [110]-[100] ( /trianglesolid), [110]-[010] ( /triangledownsld), [100]-[1 ¯10] (◮), and [010]-[1 ¯10] (◭), respectively, for ε/bardbl=εxyand equivalent\ndirections for ε/bardbl=εyz.\nIV. SUMMARY AND CONCLUSIONS\nIn summary, we have presented a detailed first-\nprinciples study of elastic and magnetoelastic properties\nof the inverse spinel ferrites NFO and CFO. We have\ncalculated all cubic elastic and magnetoelastic constants\nfrom a variety of distorted crystal structures. Thereby,\nwehaveconsidereddifferentpossiblecationarrangements\nto represent the inverse spinel structure, and in the case\nof CFO we also considered a cation distribution corre-\nsponding to incomplete inversion with λ= 0.75. The\nmagnetoelastic coefficients are obtained from the strain\ndependence of the MAEs for two different deformations\nof the crystal structure.\nEven though the symmetry of the considered cation\narrangements is lower than cubic, our results show that\nthe elastic response of both NFO and CFO can to a good\napproximationbedescribed usingcubicelasticconstants.\nSince the elastic constants are mainly determined by the\nstrength of the chemical bonding, this indicates that Co,\nNi, and Fe all form bonds of similar strength with the\nsurrounding atoms.\nSimilarly, the magnetoelasticresponseofNFO can also\nto a good approximationbe described using the cubic ex-\npression for the magnetoelastic energy density (Eq. (2)).\nThis is indicated by the relatively small quantitative dif-\nferences in the calculated magnetoelastic coefficients for\nthe various cation arrangements. On the other hand,\nthe magnetoelastic coefficients of CFO show a stronger\ndependence on the specific cation arrangement and the\norientation of the applied strain, so that the cubic ap-\nproximations is less justified in that case. In addition,\nthe overall magnetoelastic response is much stronger in\nCFO than in NFO.\nBoth of these observations can be understood from the\nd7electron configuration of the Co2+cation, which leads\nto stronger spin-orbit effects compared with the d8con-\nfiguration of Ni2+. In the latter, the orbital magnetic\nmoment is strongly quenched by the dominant octahe-\ndral component of the crystal-field, and the system is less\nsensitive to additional crystal field components of lowersymmetry. In contrast, the orbital moment is not fully\nquenched by the octahedral crystal field for the d7con-\nfiguration of Co2+, and additional splittings, which are\ncreated by the different arrangements of the surrounding\nBsite cations, canhavemuch strongereffects onthe elec-\ntronic ground state within the partially filled minority-\nspint2gorbital manifold.\nBoth sign and magnitude of the calculated magne-\ntostrictionconstantsagreewellwith availableexperimen-\ntal data. Even for CFO, where the calculated magne-\ntostriction depends more strongly on the specific cation\ndistribution than for NFO, the resulting uncertainty is\nwithin the spread of available experimental data.\nFurther experimental data for single crystals is there-\nfore required for a more accurate comparison. We note\nthatanumberofobstaclescanin principleaffectanaccu-\nrate comparison between theory and experiment. Apart\nfrom potential influences of varying sample stoichiome-\ntry, degree of inversion, and measuring temperature, the\npreparation of an ideal demagnetized state with an es-\nsentially random orientation of magnetic domains is rel-\natively hard to achieve. For example, a state with 50 %\nof domains oriented parallel and 50 % of domains ori-\nented antiparallel with respect to a certain axis would\nhave zero magnetization but the magnetostrictive strain\nwouldalreadybesaturatedalongthatdirection. Further-\nmore, for systems with very strong magnetic anisotropy,\nsuch as e.g. CFO, it can be very difficult to achieve full\nsaturation along the hard direction.39Other sources of\ndisagreement between theory and experiment could be\ndue to the neglect of higher order terms in the energy\nexpression (2),2or most likely due to deficiencies in the\nexchange correlation potential used in the DFT calcu-\nlations. However, based on the currently available ex-\nperimental data it can be concluded that the GGA+ U\nmethod used in the present work is sufficiently accurate\nfor further investigation on the effects of cation distribu-\ntion, degree of inversion, and stoichiometry on the mag-\nnetostrictive properties of spinel ferrites.\nOur work thus provides a sound basis for future in-\nvestigations of magnetostriction and anisotropy in spinel11\nferritesaswellasforfuturefirstprinciplesstudiesofmag-\nnetoelectriccouplinginartificialmultiferroicheterostruc-\ntures containing either CFO or NFO in combination with\nferroelectric and/or piezoelectric materials.\nAcknowledgments\nThis work was done mostly within the School of\nPhysics at Trinity College Dublin, supported by Sci-ence Foundation Ireland under Ref. SFI-07/YI2/I1051\nand made use of computational facilities provided by\nthe Trinity Centre for High Performance Computing\n(TCHPC) and the Irish Centre for High-End Comput-\ning (ICHEC).\n∗Electronic address: daniel.fritsch@bristol.ac.uk\n†Previous address: School of Physics, Trinity College,\nDublin 2, Ireland\n‡Electronic address: claude.ederer@mat.ethz.ch\n1C. Kittel, Rev. Mod. Phys. 21, 541 (1949).\n2E. W. Lee, Rep. Prog. Phys. 18, 184 (1955).\n3E. R. Callen and H. B. Callen, Phys. Rev. 129, 578 (1963).\n4E. Callen and H. B. Callen, Phys. Rev. 139, A455 (1965).\n5A. E. Clark (North-Holland, 1980), vol. 1 of Ferromagnetic\nMaterials , pp. 531 – 589.\n6J. R. Cullen, A. E. Clark, and K. B. Hathaway, in Materi-\nals, Science and Technology (VCH Publishings, 1994), pp.\n529 – 565.\n7´E. du Tr´ emolet de Lacheisserie, in Magnetism: Fundamen-\ntals, edited by ´E. du Tr´ emolet de Lacheisserie, D. Gignoux,\nand M. Schlenker (Springer, 2005), pp. 351 – 397.\n8´E. du Tr´ emolet de Lacheisserie, in Magnetism: Materials\nand Applications , editedby ´E. duTr´ emolet deLacheisserie,\nD. Gignoux, and M. Schlenker (Springer, 2005), pp. 213–\n234.\n9V. A. M. Brabers (Elsevier, 1995), vol. 8 of Handbook of\nMagnetic Materials , pp. 189 – 324.\n10H. Zheng, J. Wang, S. E. Loand, Z. Ma, L. Mohaddes-\nArdabili, T. Zhao, L. Salamanca-Riba, S. R. Shinde, S. B.\nOgale, F. Bai, et al., Science 303, 661 (2004).\n11F. Zavaliche, H. Zheng, L. Mohaddes-Ardabili, S. Y. Yang,\nQ. Zhan, P. Shafer, E. Reilly, R. Chopdekar, Y. Jia,\nP. Wright, et al., Nano Letters 5, 1793 (2005).\n12N. Dix, R. Muralidharan, J.-M. Rebled, S. Estrad´ e,\nF. Peir´ o, M. Varela, J. Fontcuberta, and F. S´ anchez, ACS\nNano8, 4955 (2010).\n13M. G. Chapline and S. X. Wang, Phys. Rev. B 74, 014418\n(2006).\n14U. L¨ uders, M. Bibes, K. Bouzehouane, E. Jacquet,\nJ.-P. Contour, S. Fusil, J.-F. Bobo, J. Fontcuberta,\nA. Barth´ el´ emy, and A. Fert, Appl. Phys. Lett. 88, 082505\n(2006).\n15D. Fritsch and C. Ederer, Phys. Rev. B 82, 104117 (2010).\n16D. Fritsch and C. Ederer, J. Phys.: Conf. Ser. 292, 012014\n(2011).\n17K. Momma and F. Izumi, J. Appl. Cryst. 41, 653 (2008).\n18J. A. Moyer, C. A. F. Vaz, E. Negusse, D. A. Arena, andV. E. Henrich, Phys. Rev. B 83, 035121 (2011).\n19V.G. Ivanov, M. V.Abrashev, M. N.Iliev, M. M. Gospodi-\nnov, J. Meen, and M. I. Aroyo, Phys. Rev. B 82, 024104\n(2010).\n20M. N. Iliev, D. Mazumdar, J. X. Ma, A. Gupta, F. Rigato,\nand J. Fontcuberta, Phys. Rev. B 83, 014108 (2011).\n21D. Fritsch and C. Ederer, Appl. Phys. Lett. 99, 081916\n(2011).\n22We note that these expressions are in principle only valid\nfor the cubic pointgroups m3m,¯43m, and 432.\n23Note that we are not considering any strain indendent con-\ntributions to the magnetic anisotropy energy, which would\nlead to (strain independent) differences between inequiva-\nlent in-plane directions.\n24M. J. Mehl, Phys. Rev. B 47, 2493 (1993).\n25P. E. Bl¨ ochl, Phys. Rev. B 50, 17953 (1994).\n26G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).\n27G. Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994).\n28G. Kresse and J. Furthm¨ uller, Comput. Mat. Sci. 6, 15\n(1996).\n29G. Kresse and J. Furthm¨ uller, Phys. Rev. B 54, 11169\n(1996).\n30J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.\nLett.77, 3865 (1996).\n31V. I. Anisimov, F. Aryasetiawan, and A. I. Liechtenstein,\nJ. Phys.: Condens. Matter 9, 767 (1997).\n32Z. Li, E. S. Fisher, J. Z. Liu, and M. V. Nevitt, J. Materials\nScience26, 2621 (1991).\n33R. M. Bozorth, E. F. Tilden, and A. J. Williams, Phys.\nRev.99, 1788 (1955).\n34A. B. Smith and R. V. Jones, J. Appl. Phys. 37, 1001\n(1966).\n35K. I. Arai and N. Tsuya, J. Phys. Chem. Sol. 36, 463\n(1975).\n36Y. Chen, J. E. Snyder, C. R. Schwichtenberg, K. W. Den-\nnis, R. W. McCallum, and D. C. Jiles, IEEE Trans. Magn.\n35, 3652 (1999).\n37M. Tachiki, Progr. Theoret. Phys. 23, 1055 (1960).\n38J. C. Slonczewski, J. Appl. Phys. 32, 253S (2010).\n39M. Kriegisch, W. Ren, R. Sato-Turtelli, H. M¨ uller, and\nR. Gr¨ ossinger, J. Appl. Phys. 111, 07E308 (2012)."    },    {        "title": "1105.5969v1.Dependence_of_microwave_absorption_properties_on_ferrite_volume_fraction_in_MnZn_ferrite_rubber_radar_absorbing_materials.pdf",        "content": "Dependence of microwave absorption pr operties on ferrite volume \nfraction in M nZn ferrite/rubbe r radar absorbing ma terials\nAdriana M. Gama, Mirabel C. Re zende and Chri stine C. D antas\nDivisão de  Materiais (AMR), Instituto de Aeronáut ica e Espaço (IAE),\nDepartamento de Ciência e Tecnologia Aeroespacial (DCTA), Brazil\nAbstract\nWe report the analysis of measurements of the complex magnetic permeability (µr) and dielectric \npermittivity (εr) spectra of a rubbe r radar absorbing material (RAM) with various MnZn ferrite \nvolume fractions. The transmission/reflection measurements were carried out in a vector network \nanalyzer. Optimum conditions for the maximum microwave absorption were determined by \nsubstituting the complex permeability and permittivity in the impedance matching equation. Both \nthe MnZn ferrite content and the RAM thickness effects on the microwave absorption prope rties, in \nthe frequency range of 2 to 18 GHz, were evaluated. The results show  that the complex \npermeability and permittivity spectra of the RAM increase directly with the ferrite volume fraction. \nReflection loss calculations by the impedance matching degree (reflection coefficient) show the \ndependence of this parameter on bot h thickness and composition of RA M.\nKeywords:\nPACS: 77.22.Ch, 75.50.-y , 84.40.x b\n________________________________________\nEmail addr ess: adrianaamg@iae.cta.br; mirabelmcr@iae.cta.br; christineccd@iae.cta.br;\n(Adriana M. Gama, Mirabel C. Re zende and Chri stine C. D antas )\nAccepted to Journal of Magne tism and M agne tic Materials                      M ay 26, 2011\n11. Introduction\nIt is well know n that the development of radar absorbing materials (RAM) is funda mental in \nstealth technology, as well as in other applications in the microwave range, where the reduction of \nelectromagnetic interference and the solution of electromagnetic compatibility probl ems are \nnecessary. In order to design an adequate RAM, the complex permeability (µr = µ’ - iµ’’) and \npermittivity (εr = ε’ - iε’’) are funda mental phys ical quantities for determining the reflection or \nattenuation prope rties of the material.\nIn the case of ferrite-polymer composites, several studies have been carried out to \ninvestigate the effects of ferrite materials and their volume fractions on the microwave absorbing \nprope rties [1, 2]. In a similar way, the influence of conduc ting materials addition has been \ninvestigated [3]. Some attempts were also made to verify the correlation between the material \nconstants (µr and εr) and the microwave absorption in the UHF/VHF frequencies [4, 5].\nCom posite materials are useful as microwave absorbers due to their advantages in respect to \nlighter weight, lower cost, design flexibility, and adjustable microwave prope rties over intrinsic \nferrites. Usually, ferrite and ferrite composites backed with a conduc ting plate are used to achieve \nabsorption [4, 6, 7] .\nIn the case of a metal-single layered absorber, the norm alized input impedance with respect \nto the impedance in free space, Z, and reflection loss (RL) with respect to the norm al incident plane \nwave in a rectangular waveguide are given by [ 4, 7]:\n)2tanh(rrrrti Z εµλπεµ−= (1)\nRL (dB) =  20 log10 11\n+−\nZZ(2)\nwhere: λ is the wavelength of the incident plane wave in free space, and t is the sample thickness. \nThe impedance matching condition representing the perfect absorbing prope rties is given by Z → 1. \nThe impedance matching condition is determined by combination of six parameters µ’, µ’’, ε’, ε’’, \nλ and t. Their relationships for zero reflection is not simple, and numerical techniques can provi de \nsupport  to simulate the matching conditions.\nIn the present paper, the complex magnetic permeability and dielectric permittivity for \nrubbe r radar absorbing materials with various MnZn ferrite volume fractions are reported. The \neffects of different MnZn ferrite content and the thickness values of RAM on the microwave \nabsorption prope rties in the frequency range of 2 - 18 G Hz are also discussed. \n2. Ex perimental\nThe composite samples evaluated in the present investigation were prepared by using a \nMnZn ferrite powder supplied by Sontag S.A. Com pany from  Brazil and a silicone rubbe r from \nBASF Ltd. as a polymeric matrix. The MnZn ferrite particles were prepared by usual ceramic \nsintering method from  the mixture of Fe2O3, MnCO3 and ZnO. The stoichiometry of the prepared \nMnZn ferrite is Mn0,66Zn0,34Fe2O4, which has the spinel structure with a lattice constant a = 8.483 Å .\nThe densities of the MnZn ferrite and the silicon matrix of the present work are 5.029  and \n1.28 g/cm3, respectively. The volume fraction of the ferrite in the silicon matrix varied in the range \nvf = 0, 0.10, 0.15, 0.20, 0.27 a nd 0.37.\nElastomeric specimens filled with the magnetic powder were prepared by conve ntional \nmechanical mixture of the raw materials. The homogeneous mixtures were molded in a coaxial die \nwith inner diameter of 3 mm, an outer diameter of 7 mm and a length of 5 mm. The polymer curing \n2was perform ed at room  temperature for about 24 hours . At the end, flexible cylindrical composite \nspecimens were produc ed.\nScanning electron microscopy (SEM) examinations were perform ed employing a DSM 950 \nZeiss, without special preparation of the samples, and X ray diffraction (XRD) spectra of powders \nwere obtained using Cu Kα radiation from  an PW 1830  Philips X-ray diffractometer, and the \ndiffraction poi nts were recorded from  100 to 800.\nThe scattering parameters (S parameters) were measured and used to calculate the complex \nmagnetic permeability and dielectric permittivity of the prepared RAM [8 - 11]. The measurements \nwere perform ed according to the transmission/reflection method using an HP 8510C  vector network \nanalyzer, adapted with an APC7 coaxial transmission line [10], in the frequency range of 2–18 \nGHz.\n3. Results and discussion\nFigs. 1 and 2 show the SEM image and the XRD patterns of the MnZn ferrite, respectively. \nFig. 1 presents the varieties of particle sizes (1 – 50 µm) and shapes (acicular or plate) of the MnZn \nferrite.\nFig.1. A  SEM phot ography of t he MnZn ferrite used.\nThe X-ray diffraction pattern for the system Mn0,66Zn0,34Fe2O4 powder (Fig. 2) shows the \nexistence of a single cubic phase. The contributions related to the crystal structure were found  to be \nin good a greement with those obtained by a  JCPDS card (74-2401) for t he MnZn ferrite.\n10203040506070802θ/( 0 )\nFig.2. X RD pattern of t he Mn0,66Zn0,34Fe2O4 ferrite.\nFigs. 3 and 4 show the measured values of the real and imaginary permeability (µ’ and µ’’) \nand permittivity (ε’ and ε’’) quantities, respectively, as a function of the frequency, for the MnZn \nferrite-rubbe r composites at ferrite volume fractions of  vf = 0, 0.10,  0.15,  0.20,  0.27 and 0.37.  The \nreal compone nts of µ and ε parameters of the pure silicone rubbe r (vf = 0) are nearly constant in the \nevaluated frequency range, with values of 1 and 3, respectively. The imaginary compone nts of µ \nand ε present lower values, that vary from  0 to 1.2 and 0 to 0.7, respectively. These behaviors mean \nthat the pure  silicon rubbe r presents low magnetic and di electric losses [3, 4].\n3246810121416180,60,81,01,21,41,61,8\n0.150.10vf = 0\nvf = 0.20\nvf = 0.27vf = 0.37Real Permeability (µ´)\nFrequency (GHz)\n(a)\n246810121416180,00,20,40,60,81,01,21,41,61,82,0\nvf = 00.100.150.200.27vf = 0.37Imaginary Permeability (µ´´)\nFrequency (GHz)\n(b)\nFig. 3. Real (a) and imaginary (b) permeability for MnZn ferrite-rubbe r composites at vf = 0, 0.10, \n0.15, 0.20, 0.27 a nd 0.37.\n42468101214161824681012\nvf = 0vf = 0.10vf = 0.15vf = 0.20vf = 0.27vf = 0.37Real Permittivity (ε´)\nFrequency (GHz)\n(a)\n246810121416180123456\nvf = 0vf = 0.10vf = 0.15 vf = 0.20vf = 0.27vf = 0.37Imaginary Permittivity (ε´´)\nFrequency (GHz)\n(b)\nFig. 4. Real (a) and imaginary (b) permittivity for MnZn ferrite-rubbe r composites at vf = 0, 0.10, \n0.15, 0.20, 0.27 a nd 0.37.\nThe complex permittivity spectra of the composites generally reach increasingly higher \nvalues as the ferrite volume fraction increases, with a few exceptions at higher frequency ranges \n(above  14 GHz, see Fig. 4). This trend is also followed by the complex permeability spectra, but \nonly for lower frequencies (≤ 5 GHz) in the case of µ’ (Fig. 3(a)) and up to ∼12 GHz for µ’’ (Fig. \n3(b)).  The µ’ and µ’’ values decrease with the frequency increase, with an expone ntial-like \nbehavior. The ε’ is nearly independent of the frequency, however, the ε’’ varies in a very \ncomplicated manner. In both, the complex permeability and complex permittivity of composite \nmaterials show an ove rall dependence with the volume fraction of t he filler.\nTo obtain the impedance matching condition of the single-layered absorber, the graphical \nmap method has been used [5, 12]. This method assumes that the tan δε = ε’’/ε’ is constant in the \nfrequency range, and provi des the matching condition for ferrite and ferrite-polymer composite \nmaterials. However, the tan δε is not constant in this study since the ε’ and ε’’ vary with both \nfrequency and filler volume fraction in MnZn ferrite-rubbe r composites as shown in Fig. 4. \n5Therefore, in the present paper, we calculated the minimum value of reflection loss with sample \nthickness and frequency to obtain the matching condition by substituting the measured complex \npermeability and pe rmittivity of M nZn ferrite-rubbe r composites into Equations (1) a nd (2).\nFig. 5 shows the variation of the measured reflection losses of the studied RAM with \nthickness of 3.0 m m and va rious MnZn ferrite volume loadings (vf = 0.10, 0.15, 0.20, 0.27 a nd \n0.37).\n-40-35-30-25-20-15-10-5024681012141618\n vf = 0.37\n vf = 0.27\n vf = 0.20 vf = 0.15 vf = 0.10 Frequency (GHz)Reflection loss (dB)\nFig. 5. E ffects of M nZn ferrite volume fraction on t he reflection loss of the RAM (t = 3.0 m m).\nThe RAM samples here considered, with different MnZn ferrite contents, have a single-\npeaked-minimum curve. The reflection loss at the peak is the maximum attenuation of the incident \nwave and indicates the frequency at which the material offers its optimum wave attenuation \nprope rties. The frequency of the minimum reflection loss (fm) is shifted to a lower frequency band \nwith the increase of the volume fraction of M nZn ferrite (vf = 0.10 → fm = 13.0 G Hz; vf = 0.15 → fm \n= 12.0 GHz; vf  = 0.20  → fm = 9.0 GHz). As the MnZn ferrite volume fraction increases, the \nminimum reflection loss decreases from  -5 dB for vf = 0.10 t o -35 dB for vf = 0.20.\nAccording to Feng et al. [13], desirable RAM prope rties should comply with wider \nfrequency bandwidths of RL < - 10 dB. Therefore, in the design of RAM with better absorption \nperform ance, the requirement of wider frequency bandwidths should be observed. Frequency \nbandwidths can be calculated by subtracting the higher frequency from  the lower one at a given RL. \nWe have perform ed this calculation for 3 arbitrary values of RL as an illustration of our analysis, by \nreferring to the vf = 0.20 case. The detailed data are shown in Table 1. According to our analysis \n(c.f. Fig. 5 and Table 1) the MnZn ferrite volume fraction in the RAM is not proport ional to the \nfrequency bandwidth. The present RAM, developed from  the MnZn ferrite of vf = 0.20,  has the \nlargest frequency bandwidth of 4.5 GHz at RL = -10 dB, whereas those containing MnZn ferrites of \nvf = 0.15 a nd vf = 027 a re 2.5 G Hz and 3.0 G Hz, respectively.\n6Table 1 – F requency bandwidth for t he RAM sample with vf = 0.20.\nRL\n(dB)Lower\nFrequency\n(GHz)Higher\nFrequency\n(GHz)Frequency\nBandwidth\n(GHz)\n- 108.513.04.5\n- 2010.012.02.0\n- 3010.511.51.0\nIn our present study, a trend between volume fraction and reflection loss is not clear. For \nexample, from  vf = 0.10 to 0.20,  the amplitude of the RL peak increases with vf, but then decreases \nfor vf = 0.27 a nd 0.37.\nIn order to investigate the attenuation behavior of radar absorbing materials as a function of \nthe thickness, samples with MnZn ferrite of vf = 0.10 and 0.20 and various thickness values (t = 1.0, \n2.0, 3.0, 4.0, 5.0, 6.0, 7.0 and 8.0 mm) were simulated. Their reflection losses were calculated and \nthe results are shown in Fig. 6(a-b). It is clear that the reflection loss of the RAM presents a regular \ntrend at given MnZn ferrite volume fraction in the frequency range of 2 – 12 GHz. Note that the \nabsorption peak of the RAM with MnZn ferrite of vf = 0.10 (t ≤ 3.0 mm) cannot be perceived in the \n2 - 12 GHz range, from  the curvilinear trend in Fig. 6(a). In this case, it is observed that the \nattenuation values increases as the frequency increases with a proba ble presence of a minimum \nreflection loss peak in frequencies above  12 GHz. For thickness values above  4,0 mm, the \nfrequency of the minimum reflection loss moves towards the low frequency range with the \nthickness increase.\nWhen the volume fraction of MnZn ferrite is 0.20,  the reflection loss of the radar absorbing \nmaterial shows the same tendency as that of vf = 0.10.  Note that the amplitude of the main RL peak \ndecreases for smaller thicknesses for vf = 0.10,  in the frequency range analyzed. For vf = 0.20,  this \ntrend seems to reverse for t  ≤ 4.0 m m, as can be seen \nfrom  a large absorption pe ak for t  = 3.0 m m (Fig. 6(b)).\n-25-20-15-10-5024681012 Frequency (GHz)\n8.07.06.05.04.03.02.01.0Reflection loss (dB)\n(a)\n7-30-25-20-15-10-5024681012 Frequency (GHz)\n8.07.06.05.04.03.02.01.0Reflection loss (dB)\n(b)\nFig. 6. Calculation of the RAM thickness effects on the microwave absorption prope rties for: (a) vf \n= 0.10 a nd (b) vf = 0.20.\nIn conclusion, our results are in overall agreement with the literature [11 - 13] in the sense \nthat, when estimating the reflection loss of the RAM by the impedance matching degree, in which \nthe form er is determined by the combination of the six parameters µ’, µ’’, ε’, ε’’, λ and t, it is found \nthat the reflection loss cannot be reduced by m erely changing onl y the µr and εr parameters.\n4. Conclusion\nThe results of our s tudy on t he electromagnetic and w ave attenuation prope rties of the MnZn \nferrite-rubbe r radar absorbing m aterials can be summarized as follows.\n1)The spectra of the complex magnetic permeability and dielectric permittivity of a MnZn ferrite-\nsilicone rubbe r radar absorbing material, in the frequency range of 2 - 18 GHz, are provi ded, in \norder to establish their qua ntitative microwave absorption characteristics.\n2)We found  that a higher MnZn ferrite volume fraction generally favors the increase of the \ncomplex relative permeability and re lative permittivity of t he proc essed RA M.\n3)A prediction of the minimum RL as a function of frequency, sample thickness range and MnZn \nferrite volume fraction is given. The results show a regular trend of t he RL.\n4)With respect to those parameters, such that higher thicknesses imply better absorption \nprope rties, with the optimum frequency band shifted systematically towards lower values of \nfrequency. However, for higher vf´s it is inferred that smaller thicknesses might offer better \nabsorption prope rties for hi gher frequency bands (≥ 10 G Hz).\n85. Acknowledgements\nThe authors acknow ledge the financial assistance of Financiadora de Estudos  e Projetos \n(FINEP) (Process number 1757-6) and the National Counc il for Research and Development (CNPq) \n(Process num ber 305478/ 09-5).\n6. References\n[1] L. J. Deng, J . L. Xie, D. F. Liang, B. J . Guo, J . Funct. Mater. 30 (2) (1999) 118.\n[2] A. M. Gama, M. C. Rezende, Journa l of Aerospace Technology and Management, 2 (1) (2010) \n59.\n[3] A. N. Yusoff, M. H. Abdullah, S. H. Ahmad, S. F. Jusoh, A. A. Mansor, S. A. A. Hamid, J. \nApplied Physics 92 (2) (2002) 876.\n[4] Y. Naito, K. Suetake, IEEE Trans. MTT 19 (1) (1971) 65.\n[5] H. M. Musal, Jr., H. T. Hahn, IE EE Trans. Mag. 25 (5) (1989) 3851.\n[6] J. Y. Shin, J. H. Oh, IE EE Trans. Magn. 29 (1993) 3437.\n[7] S. S. Kim, S. B. Jo, K. I. Gueon, K. K. Choi , J. M. Kim, K. S. Churn,  IEEE Trans. Magn. 27 \n(1991) 5642.\n[8] O. Acher, M. Ledieu, Journa l of M agnetism and M agnetic Materials 258-259 (2003) 144-150.\n[9] O. Acher, A. L. Adenot, U. S. Patent 6,677,762, (1974).\n[10]  P. Bartley, S. Begley, S. Materials measurement (2006)  78p.  In: \n<http://www.die.uniroma1.it/personale/frezza/biblioteca/dispense/MisureMateriali.pdf> .\n[11] J. Shenhui, D. Ding, J . Quanxing, IE EE, (2003) 590-595.\n[12] H. M. Musal, Jr., D. C. S mith, IE EE Trans. Mag. 26 (1990) 1462.\n[13] Y. B. F eng, T . Qiu, C. Y . Shen, X. Y. Li, IEEE Trans. Magn. 42 (3) (2006) 363.\n9"    },    {        "title": "1506.06280v2.Effect_of_Sintering_Temperature_on_Structural_and_Magnetic_Properties_of_Ni0_6Zn0_4Fe2O4_Ferrite__Synthesized_from_Nanocrystalline_Powders.pdf",        "content": "Effect of Sintering Temperature on Structural and Magnetic Properties of \nNi0.6Zn0.4Fe2O4 Ferrite: Synthesized from Nano crystalline  Powder s \nM. A. Ali1*, M. N. I. Khan2, F. -U. -Z. Chowdhury1, D. K. Saha2, S. M. Hoque2, S. I. Liba2, \nS. Akhter2, and M. M. Uddin1 \n1Department of Physics, Chittagong University of Engineering and Technology (CUET), Chittagong -4349, \nBangladesh.  \n2Materials Science Division, Atomic Energy Center, Dhaka -1000 , Bangladesh.  \n \n*Email : ashrafphy31@gmail.com  \nAbstract:   \nThe effect of sintering temperatures ( Ts) on the structural and magnetic properties of \nNi0.6Zn0.4Fe2O4 (NZFO) ferrites synthesized by conventional double sintering method has been \nreported. The samples are sintered at 1200, 1250  and 1300 °C. The X-ray diffraction (XRD) \nanalysis  reveals the formation of a single phase cubic spinel structure of the sample . The \nmagnetic parameters such as saturation magnetization, Ms; coercive field, Hc; rem anent \nmagnetization, Mr and Bohr mag neton, μB are determined and well compared  with reported \nvalue s. The obtain ed values are found to be 71.94 emu/gm and 1.2 Oe for Ms and Hc, respectively \nat Ts=1300 C. Curie temperature ( Tc) at various Ts has also been calculated.  It is noteworthy t o \nnote t hat the sample with a very low Hc could be used in  transformer core and inductor \napplications.  \nKeywords:  Ni0.6Zn0.4Fe2O4 ferrite, soft ferrite, saturation magnetization, Curie temperature . \n \n1. Introduction  \nNickel –Zinc ferrites have attracted huge attention in recent years owing to their potential \napplications in power transformers in electronics, antenna rods, loading coils, microwave devices \nand telecommunication , and are promising candidates for microwave device applications due to \ntheir remarkable magnetic properties , high resistivity and low eddy current lo ss [1-5]. The \nproperties of the ferrites sensitively depend on the method of preparation, dimension of raw \nmaterials (nano or bulk), composition, sintering conditions  [6, 7]. Several authors have reported \nthe structural, electrical and magnetic properties of the Ni-Zn ferrites  prepared from  bulk or nano \npowder [ 8-18]. It is expected that dimension of the raw materials (nano powder)  could be \nchanged the magnetic as well as electrical properties of the Ni-Zn ferrites . However, most cases, \nthe Ni -Zn ferrites have been prepared from bulk powders or claimed synthesized nanocrystalline \npowders where the crystallite size  are calculated  using Scher rer equation  by analyzing X -ray diffraction (XRD) peaks . It is noted that the d etermination of the crystallite size  by the Scherrer \nequation  has some limitation  for solid state synthesis. Therefore, it is great importance to study \nthe effect of sintering temperature ( Ts) on the properties of Ni -Zn ferrite synthesized by nano \npowders as raw materials.  \nIn this work, we have studied the effect  of Ts on the structural and magnetic properties of NZFO  \nprepared by conventional double sintering route .   \n2. Material and Methods   \nThe polycrystalline samples of NZFO were synthesized using conventional double sintering  \ntechniques  route by taking  reagent grade oxides of nickel, zinc and iron nano  powders of purity \ngreater than 99.5% (US Research Nanomateria ls, Inc.) . The particle sizes of Fe2O3, NiO, and \nZnO nano powders  are  20-40, 15 -35 and 35 -45 nm, respectively were weighed according to \nthe corresponding composition . The weighed powder was mixed and ground for 3 hrs using  an \nagate mortar  and pestle. The slurry was drie d and loosely pressed into cake  using a hydraulic \npress. The cake is pre-sintered in air for 3 h rs at 900°C . The pre -sintered cake removed from the \nfurnace was  crushed  and again ground for 1 h r. The obtained powders was then pressed using a \nsuitable die in the form of ring ( 11 mm diameter; 3.4 mm thickness)  with a hydraulic press at a \npressure of 15 kN using 5% PVA  solution as a binder and the samples were finally sintered at \n1200, 1250, and 1300 °C for 4 hrs  in air . The crystalline phases of the prepared samples were \nstudied by XRD  [Philips X’pert Pro X -ray diffractometer (PW3040)] with Cu -Kα radiation (λ \n=1.5405 Å). The magnetic properties  (M-H curve, saturation magnetization, M s; coercive  field, \nHc; remanent  magnetization,  Mr; and Bohr magneton, μB) were  determined b y the v ibrating \nsample magnetometer  (VSM)  (Micro Sence EV9) with a maximum applied field of 1 5 kOe.  \nFrequency and temperature dependent permeability were investigated by using Wayne Kerr \nprecision impedance analyzer  (Model 65 120B). \n3. Results and Discussion  \n \n3.1.Structural properties  \nFig. 1 shows the powder XRD pattern of the calcined  NZFO  at 900°C . Very sharp, broad and \nwell-defined peaks have been observed from the XRD pattern indicating the cubic spinel phase \nof NZFO.  The average crystallite size  has been calculated which is found to be 51 nm [ 19]. Single  phase  cubic spinel structure  with Fd3 m space group symmetry  of NZFO has also been \nconfirmed at different Ts by the XRD study  (data not shown here)  [20].The average grain size s \nare determined from the SEM micrograph by linear intercept technique  and ranging between 1.4 \n- 7.8 m, which are almost homogeneously distributed throughout the sample surface  [20]. The \nobtained average grain size are significantly smaller than that of ref. [ 18] (size ranging between \n8-17 μm) for NZFO ferrites synthesized from bulk powders sintered at 1200, 1250, and 1300°C. \nSmaller grains have a meaningful influence on the magnetic as well as electrical properties of \nNZFO ceramics . \n \n \n \n \n \n \n \n \n \nFig. 1. The XRD pattern of  Ni0.6Zn0.4Fe2O4 ferrites  calcined  at 900°C for 3 hrs in air . \n3.2. Magnetic properties  \nThe room temperature static applied magnetic field , H (up to 1 5 kOe)  magnetization \nhysteresis loops of the NZFO ceramics sintered at various temperature 1200, 1250,  and 1300 °C  \nis shown in Fig. 2. The value of magnetization increases  with increasing applied magnetic field  \nup to a certain field above which the sample beco mes saturated . It is seen that the values of \ncoercive field (H c) of the samples  are found to be quite low ˂ 3 Oe indicating the studied \nsamples are soft ferrites.  Moreover, our obtained values are also smaller than that obtained by \nHossain  et al. [ 18]. The saturation magnetization ( Ms), coercive field ( Hc), remanent \nmagnetization, Mr, and Bohr Magneton , μB, are calculated  from the measured magnetic \nhysteresis loop  and are presented in Table 1. It is depicted that the value of Ms increases with \nincreasing Ts (Fig. 2 (b)) while the value of Hc decreases. This typical behavior can be attributed \n20 30 40 50 60 700306090120150\n (440)\n(422)(511)\n(400)\n(222)(311)\n(220)\n  Intensity (a. u.)\n2 (deg.)(111)taking into account variation of grain size that is strongly depend ent on the Ts. It is observed a t \nlow Ts, the grain size is smaller than that of higher Ts. It is obvious  that a large grain contains \nnumerous domain walls. In addition, the number of domain walls also increases as the crystallite \nsizes increases  with the increasing Ts.  Thus, the domain wall  motion is  affected by the grain size \nand enhanced with the i ncreaseof grain size [ 21].  \n  \n \n \n \n \n \nFig. 2 . The M–H loops of Ni0.6Zn0.4Fe2O4 ferrite samples  sintered at 1200, 1250 and 1300°C.  \n \nTable 1.  The parameters of Curie temperature, Tc, saturation magnetization, Ms, coercive field, \nHc, remanent magnetization, Mr and Bohr magneton, nB in compar ison with reported value for \ndifferent Ts. \nSintering Temperature , \nTs (°C) Curie \nTemperature, \nTc (°C) Ms \n(emu/gm)  Hc \n(Oe) Mr \n(emu/gm)  μB \n(Bohr \nmagnetron)  \n1200  190 \n 69.4272  \n72.9 [16] 2.6720  \n 0.33 \n 2.94 \n \n1250  215 \n350 [18]  70.9906  \n 2.3460  \n 0.28 \n 3.01 \n \n1300  240 \n 71.9468  \n79 [18] \n72.2 [16] 1.2590  \n 0.16 \n 3.05 \n \n-15 -10 -5 0 5 10 15-60-3003060\n  Magnetization (emu/gm)\nApplied field (kOe) Ts = 1200  C\n Ts = 1250  C\n Ts = 1300  C(a)\n0 4 8 12626466687072\n  Magnetization (emu/gm)\nApplied field (kOe) Ts = 1200  C\n Ts = 1250  C\n Ts = 1300  C(b)Domain wall needs low energy than that of domain rotation to produce magnetization. Therefore, \nthe contribution of domain wall movement in the magnetization is greater than that of domain \nrotation . It is also seen that the Ms increases while the Hc decreases with increasing Ts which can \nbe elucidated by the Brown’s relation :, Hc= 2K1/0Ms, where K1 is the anisotropy constant and µ0 \nis the permeability of free space.  Furthermore, the Mr decrease s while the  μB increases with \nincreasing Ts, as expected for ferromagnetic materials.  \n  \nFrequency dependent real part of the initial  permeability ( μ′) at various Ts is shown in Fig. 3 \n(a). It is noticed that the µ is fairly constant up to certain low frequencies with  maximum (214 at \n4 MHz for Ts=1300C and then falls rather rapidly to  a very low value at high frequency  (100 \nMHz). The fairly constant µvalues with a wide range frequency region is known as the zone of  \nutility of the ferrite  that demonstrate the compositional stability and quality of ferrites prepared \nby conventional double sintering  route . This characteristic is anticipated for various applications \nsuch as broadband pulse transformer and wide band read -write heads for video reco rding [ 22]. \nAt higher Ts, the permeability value is higher and the frequency of the onset of  ferrimagnetic  \n \n  \n \n \n \n \n \n \n \n \n \nFig. 3.  The frequency dependence of permeability  (a) real part (b) imaginary part  of \nNi0.6Zn0.4Fe2O4 samples sintered at 1200, 1250, 1300  °C for 4 hrs in air.  \n \nresonance  is lower that is good agreement with Snoek’s limit 𝑓𝑟𝜇𝑖′=constant  [23], where fr is \nthe resonance frequency of domain wall  motion, above which 𝜇𝑖′decreases. The ferrite materials \n1031041051061071080.51.01.52.02.53.0\n   (102)\nFrequency, f (Hz) Ts = 1200  C\n Ts = 1250  C\n Ts = 1300  C(a)\n1031041051061071080.00.51.01.52.02.5\n  '' (103)\nFrequency f (Hz) Ts = 1200  C\n Ts = 1250  C\n Ts = 1300  C(b)exhibit higher p ermeability but due to Snoek’s limit, have to be used according to the frequency \nrange in use. It is also seen that the value of μ′ increases with increasing Ts (grain size and Ms \nincreases with increasing Ts as discussed in previous section and table 1), and follows the Globus \nrelation 𝜇𝑖∝𝑀𝑠2 𝐷\n 𝐾1 where Ms is the saturation magnetization, D is the average grain size and K1 is \nthe magneto -crystalline anisotropy constant , as we expect for ferrite materials.  The stability \nregion of NZFO is found to be ~ 1kHz to 1.5 MHz, which is greater than that of NZFO \nsynthesized from bulk raw materials [ 18]. It is also observed  that the pe rmeability  increases with \nincreasing Ts while the utility zone decreases , larger grain growth at higher Ts could be attributed  \nthis trend. Moreover, a t high er Ts, the density is higher and larger grain size, near and accelerates  \ngrain to grain continuity in magnetic flux leading to higher permeability [22].  \nThe loss component is the imaginary part of initial permeability (μ′′) (magnetization is 90° \nout of phase with the  alternating magnetic field ) and represents ultimate operatin g frequency of \nmagnetic devices. Fig. 3 (b)  depicts  the loss component of the NZFO as a function of frequency . \nThe value of μ is much  higher  at lower  frequencies.  It decreases  rapidly at lower  frequencies but \nat high frequencies  its value  becomes  so small  that it becomes  independent  of frequency . It is \nalso noticed  that the loss component increases with increasing  Ts. The grain size increases with \nthe increase of Ts, as a  result the number and size of magnetic domains rises which are \ncontributing to loss  due to delay in domain wall motion.  \n \nFrequency dependent relative quality factor or quality factor (Q= /tan, µ is the real part of \ninitial permeability and tanδ is the loss factor of the samples ) of the samples sintered at 1200, \n1250, and 1300 °C  is shown in Fig. 4 . The high value of Q and  is expected for high frequency \nmagnetic applications. The Q -factor increases with an increase of frequency showing a peak and \ndecreases with further increase of frequency. It is seen that the Q -factor deteriorates beyond 10 \nMHz, i.e., the loss  tangent is minimum up to 10 MHz and then it rises rapidly. The loss is due to \nthe lag of domain wall motion with respect to the applied alternating magnetic field and is \nattributed to the various domain e ffects [24] such as non -uniform and non -repetitive domain wall motion, domain wall bowing, localized variation of flux density , nucleation and annihilation of \ndomain walls. This happens at the frequency where the permeability begins to drop with \nfrequency. This phenom enon is associated with the ferrimagnetic resonance within the domains \nand at the resonance maximum energy is transferred from the applied magnetic field to the lattice \nresulting in the rapid decrease in Q -factor. It is also seen that the Q value increases with \ndecreasing Ts and t he maximum value found to be 6534  at f = 2×106 MHz for the sample sintered \nat 1200 °C. The imperfection  and defects in 1200 °C  sintered sample  are lower than that of \nsamples  sintered at higher Ts, which enhance the operating frequency range of hopping  electrons \nbetween Fe2+ and Fe3+. Smaller grain size is  competent for larger Q values , due to this reason, \nsome  grades of Ni –Zn ferrites are deliberately sintered at lowtemperature . \n \n \n \n \n \n \n \n \n \n \n \nFig. 4.  The variation of Q factor with frequency of Ni0.6Zn0.4Fe2O4 samples sintered at 1200, \n1250  and 1300 °C for 4 hrs in air.  \n \nCurie temperature ( Tc) is the transition temperature above which the ferrite material loses its \nmagnetic properties. Temperature dependence of initial permeability, µi of the toroid shaped of \nNZFO  at constant frequency 1MHz of an AC signal is shown in Fig. 5.  With the increase of \n1031041051061071080246\n  Quality factor, Q ( 103)\nFrequency, f (Hz) Ts = 1200  C\n Ts = 1250  C\n Ts = 1300  Ctemperature, the initial permeability increases rapidly and then drops o ff sharply near the \ntransition temperature  known as Tc  showing the Hopkinson effect  [25]. The value of K1 becomes \nalmost negligible near the Tc results the peak is obtained.  At Tc, complete spin disorder take s \nplace, i.e. , a ferromagnetic  material  converts to a ferromagnetic  material . Moreover, t he \nsharpness of the permeability drop during phase transition indicates the  compositional \nhomogeneity and the verification of single phase cubic spinel of the studied samples, which has \nalso been confirmed by X - ray diffraction (Fig.1).  \n \n \n \n \n \n \n \n \n \n \nFig. 5.  The temperature dependence of the initial permeability (i) of Ni0.6Zn0.4Fe2O4 ferrite \nsamples sintered 1200, 1250 and 1300 ° C for 4 hrs in air.  \n \n4. Conclusions  \nThe effect  of sintering temperature on the  structural  and magnetic  properties of  Ni0.6Zn0.4Fe2O4 \nhas been  investigated.  The parameters such as grain size, saturation magnetization and coercive \nfield have been measured and well compared with the available data. The grain size of \nNi0.6Zn0.4Fe2O4 synthesized from nano powders as raw materials are smaller than that of \nsynthesized from bulk powders.  Wide range of operating frequency or stability region of the \nNi0.6Zn0.4Fe2O4 1 kHz to 10 MHz has been determined which is an advantage of that material. A \nvery low Hc (˂3 Oe) implies that this material  is a promising candidate for transformer core and \n0 1 2 3 43456\n  i(102)\nTs ( 102C) Ts = 1200  C\n Ts = 1250  C\n Ts = 1300  Cinductor applications. The magnetic properties of the Ni0.6Zn0.4Fe2O4 synthesized from nano \npowders are also better than that of the Ni -Zn ferrite synthesized from bulk materials.  It is \nexpected that our study would stimulate the scientist to synthesis  the materials/ compounds with \nnano powders as raw materials.  \n \nAcknowledgements  \nWe are gr ateful to the authority of CUET for the financial support of this work.  \nReferences  \n1. Anil Kumar  P S, Shrotri  J J, Kulkarni  S D, Deshpande  C E and Date S K 1996  Mater. \nLett. 27 293. \n2. Tsay  C Y, Liu K S, Lin T F and Lin I N 2000  J. Magn. Magn. Mater.  209 189. \n3. Bhise  B V, Dongare  M B, Patil  S A and Sawant  S R 1991 J. Mater. Sci. Lett.  10 922. \n4. Slick  P I, 1980 in Ferromagnetic Materials , North -Holland, Amsterdam, Wohlfarth  E P \n(Ed.)  2 196. \n5. Abraham  T 1994 Am. Ceram. Soc. Bull . 73 62. \n6. Verma  A, Goel  T C, Mendiratta  R G and Alam  M I 1999 Mater. Sci. Eng. B 60 156. \n7. Rao B P, Rao  P S V S and Rao K H 1997  IEEE Trans. Magn.  33 4454.  \n8. Costa A C F M, Tortella  E, Morelli M R and Kiminami  R H G A  2003 J. Magn . Magn . \nMate r. 256 174. \n9. Sorescu  M, Diamandescu  L, Peelamedu  R, Roy  R and  Yadoji  P 2004 J. Magn.  Magn. \nMater  279 195. \n10. Gawas  U B, Verenkar  V M S  and Mojumdar  S C2011 J. Therm . Anal .Calorim .104 879. \n11. Abdeen  A M J. Magn.  Magn. Mater  192 121. \n12. Kwon  Y M, Lee  M Y, Mustaqima  M, Liu  C and Lee  B W2014 J. Magn etics.1964. \n13. Yadoji  P, Peelamedu  R, Agrawal  D and  Roy R 2003 Mat. Sci. Engg. B 98269. \n14. Krishna K R, Kumar K V and Ravinder D 2012 Advances Mater. Phys. Chem. 2 185. \n15. Krishna  K R, Kumar  K V, Ravinder nathgupta  C and Ravinder  D 2012 Advances Mater . \nPhys . Chem .2 149. 16. Kothawale  M M , Tangsali  R B, Naik  G k, Budkuley  J S, Meena  S S and Bhatt  P 2012 \nSolid State Physics (India)  57. \n17. Rao B P  and Rao K H  1997 J. Mater. Sci. 32 6049 . \n18. Akther Hossain A K M, Mahmud S T , Seki  M, Kawai  T and Tabat a H. 2007  J. Magn. \nMagn. Mater. 312 210. \n19. Scherrer  P, 1918  Nachr. Ges. Wiss. Göttingen  26 98-100. \n20. Ali M  A, Khan  M N I , Chowdhury  F-U-Z, Akhter  S and Uddin  M M 2015  J. Sci. Res.  7 \n65. \n21. Jalaly  M, Enayati  M H , Kameli  P and Karimzadeh  F 2010 Physica B: Condensed Matter  \n405 507. \n22. Verma, A and Chatterjee  R 2006, J. Magn. Magn. Mater. 306313. \n23. Snoek  J L 1948  Physica  14 207. \n24. Valenzuela  R 1980 J. Mater. Sci. Lett. 15 175. \n25. Overshott  K J 1981 , IEEE Trans. Magn.  17 2698 . \n \n \n "    },    {        "title": "1805.04204v1.Maximizing_Specific_Loss_Power_for_Magnetic_Hyperthermia_by_Hard_Soft_Mixed_Ferrites.pdf",        "content": " \n1 \n Maximizing  Specific  Loss Power for Magnetic Hyperthermia  by Hard -Soft \nMixed Ferrites  \nShuli He1,2,4, Hongwang Zhang2, Yihao Liu1,3, Fan Sun2, Xiang Yu1, Xueyan L i1, Li \nZhang1, Lichen Wang1, Keya Mao3, Gangshi W ang3, Yinjuan Lin3, Zhenchuan Han3, \nRenat Sabirianov5, and Hao Z eng2* \n1 Department of  Physic s, Capital  Normal University , Beijing 100 48, China  \n2Department of Physics, University at Buffalo, SUNY , Buffalo , New York 14260, U SA \n3Chinese PLA General Hospital, Beijing 10048, China  \n4Beijing Advanced Innovation Center for Imaging Technology, Beijing 10048, China  \n5Department of Physics, University of Nebraska -Omaha, Omaha, NE  68182 , USA  \n \nAbstract  \nWe report maximized specific loss power  and intrinsic loss power approaching \ntheoretical limit s for AC magnetic field heating of nanoparticles . This is achieved by \nengineering the effective magnetic anisotropy  barrier of nanoparticles via alloying of \nhard and soft ferrites . 22 nm Co0.03Mn 0.28Fe2.7O4/SiO 2 NPs reached  a specific loss \npower  value of 3417  W/g metal at a field of 33 kA/m and 380 kHz.  Biocompatib le \nZn0.3Fe2.7O4/SiO 2 nanoparticle s achieved specific loss power  of 500 W/g metal and \nintrinsic loss power of 26.8 nHm2/kg at field parameters of 7 kA/m and 380 kHz , below \nthe clinical safety limit . Magnetic bone cement achieved heating adequate for bone \ntumor hyperthermia , incorporating ultralow dosage of just 1 wt% of nanoparticles . In \ncellular hyperthermia experiments, these nanop article s demonstrated high cell death \nrate at low field parameters . Zn0.3Fe2.7O4/SiO 2 nanoparticles show cell viabilities above \n97% at concentrations up to  500 µg/ml within 48 hrs, suggesting  toxicity lower  than \nthat of magnetite . \nKeywords:  magnetic nanoparticles, magnetic  hyperthermia , specific loss power, \nintrinsic loss power, magnetic anisotropy    \n2 \n Magnetic nanoparticles ( NPs) have received  great  attention over the past several \ndecades due to  their potential biomedical applications  in targeted drug delivery, \nbiological separation, magnetoresistive bio -sensing, magnetic resonance imaging , and \nas heat dissipation agents in  gene transcription, neural  stimulation and cancer \ntreatment .[1-12] Magnetic hyperthermia, first proposed by Gilchris t in 1957 ,[13] employs  \nheat dissipat ion by magnetic NPs in an alternating current ( AC) magnetic field  to kill \ntumor  cells. The design and synthesis of magnetic NPs should take into consideration \nthe following constraints : first of all, they should have the highest possible specific loss \npower ( SLP) within the field and frequency range deemed safe for human body to avoid \npotential side effects  and to be useful for treatment of small tumors ;[11] second, they \nshould be close  to superparamagnetic (SPM) with low magnetostatic interactions to \navoid agg lomeration ;[14,15] and third, they should be biocompatible  with low \ncytotoxicity .[16-19]  \nIron oxide  NPs are the most commonly used material s in magnetic hyperthermia \nbecause of their low toxicity .[20-23] Other ferrite NPs such as manganese ferrite , and \nmore recently, zinc ferrite  have also been explored due to their high magnetization \namong the ferrite family and stability against oxidation .[24,25] Relatively high SLP \nvalues  have been achieved by these NPs .[26] However, further increasing the SLP by \nincreasing  the saturation magnetization (MS) would be f utile. Although a high MS is \nbeneficial for increasing SLP, high MS materials are typically metall ic and face stability \nand toxicity issues in physiological environment.[21] An alternative approach  to \nmaximiz ing the SLP is to tune the effective anisotropy of the NPs.  For example, shape \nanisotropy can be used to increase SLP of iron oxide nanocubes .[20] Very large SLP has \nbeen obtained by tun ing the anisotropy of NPs through  hard-soft exchange -coupled \ncore/shell NP approach .[27] However, they were achieved at high field amplitude and \nfrequenc y values  unsuitable for clinical applications.[27]   \nIn this work, we report the design and synthesis of monodisperse  SPM NP s with \nmaximized SLP and intrinsic loss power ( ILP) at different field parameters . ILP is  \n3 \n defined as SLP/ H2f under linear response theory to compare the performance of NPs \nmeasured unde r different field parameters.[28] We first show that SLP can be maximized \nat H = 33 kA/m and f = 380 kHz , by alloying of hard cobalt ferrite  and soft manganese \nferrite to make CoxMn (0.3-x)Fe2.7O4, and tuning the size and composition of the mixed \nferrite NPs. Unlike  the core/shell approach, alloy ing allows convenient  control of the \neffective anisotropy  independent of NP size . A thin silica shell coating render s water -\nsolubility and bio -functionality .[22] 22 nm Co0.03Mn 0.28Fe2.7O4/SiO 2 NPs reach  a SLP \nvalue of 3417  W/g metal. We further optimize the composition of biocompatible  ZnxFe3-\nxO4 NPs for enhanced  SLP under clinical ly safe field parameters  (the product of field \namplitude and frequency Hf < 5109 A/(ms)). The Zn0.3Fe2.7O4 NPs achieved SLP and \nILP values of 1010 W/g metal and 15.7 nHm2/kg at H = 13 kA/m , 500 W/g metal and 26.8 \nnHm2/kg at 7 kA/m,  and 282 W/ gmetal and 59.9 nHm2/kg at 3 kA/m , respectively ( f = \n380 kHz ). Zn0.3Fe2.7O4/SiO 2 NPs show  no cytotoxicity after 48 hrs at concentration s up \nto 500 µg/ml. Using the optimized biocompatible NPs, we achieved comparable  \ntemperature rise with significant  decrease in dosage in a model mimicking  bone tumor \nhyperthermia .[29,30] Cellular hyperthermia using 300 µg/ml Zn0.3Fe2.7O4/SiO 2 NPs \nresulted in >89% cell death  upon 10 min exposure to AC field of H= 13 kA/m and f = \n380 kHz.  Our designed biocompatible NP with maximiz ed SLP and ILP provide a \npathway towards targeted magnetic hyperthermia treatment of small  tumors and \nmetastases[11], and rapid remot e neural stimulation .[4]  \nThe mechanism of heat loss in magnetic hyperthermia is the energy dissipated \nduring the magnetization reversal, and is therefore proportional to the product of the \narea of the AC magnetic hysteresis loop and the frequency .[31] An estimate of the upper \nlimit of achievable SLP  for ferrite NPs  can be done as follows: 𝑆𝐿𝑃 =4𝜇0𝑀𝑆𝐻𝑚𝑎𝑥\n𝑓, \nwhere 𝑀𝑆 is the saturation magnetization , 𝐻𝑚𝑎𝑥 the amplitude of the magnetic field,  \n the mass density of the NPs  and 𝑓 the frequency .  is a dimensionless factor \ndescribing the deviation from a square hysteresis, which is related to the degree of \nalignment, and should also dependent on the type s of effective anisotropy (uniaxial vs  \n4 \n cubic)  and inter -particle interactions . Using  =1 for aligned Stoner -Wohlfarth particles \nwith uniaxial anisotropy , 𝑀𝑆 ~ 480 kA/m , 𝐻𝑚𝑎𝑥  = 33 kA/m ,  ~ 5 g/cm3 and f =380 \nkHz, SLP is estimated to be ~ 5000 W/ gNP or ~ 7000 W/g metal. Any value higher than \nthat is likely non -physical. For complete ly random ensembles,  is reduced to 0. 39.[31] \nNote here the optimal AC coercivity  (𝐻𝑐) should be ~ 0.8𝐻𝑚𝑎𝑥. The AC hysteresis \narea is maximized this way despite the fact that a fraction of the NPs cannot be \nswitched[31].  as high as 0.46 has been report ed for magnetosomes aligned in an \nexternal field .[32] Thus the limit of SLP for any ferrite NPs at a field of 33 kA/m and \n380 kHz is about ½*7000 ~ 3500 W/g metal.  \nHow can we then tune the properties of NPs to approach the theoretical  limit s? The \nkey is to engineer the anisotropy  energy barrier for magnetization reversal to match a \nspecific field amplitude and frequency for a particular application .[4,15-18] According to \nthe Stoner -Wohlfarth  model ,[33] the anisotropy barrier is proportional to K uV , where K u \nis the uniaxial anisotropy constant and V is the volume of the magnetic grain , two \ncritical parameters  that can be tuned to maximize SLP . Ku and V together determine the \ntemperature and frequency depen dent coercivity  (𝐻𝑐), and the shape of the AC \nhysteresis loop.  Generally,  at optimized effective anisotropy, a large NP size is \npreferred since MS increases slightly with increasing size , as long as it is not too large \nto accommodate multi -domain state s which reduce 𝐻𝑐. Practi cally, the NPs should be \nkept nearly SPM to avoid dipole interaction induced agglomeration.  We therefore adopt \nthe follow ing strategy to maximize SLP at clinically relevant field parameters : 1. Use \nsoft ferrite Mn 0.3Fe2.7O4 as a starting material to find the largest size for high SLP \nwithout agglomeration , as magnetostatic interactions are dependent on 𝑀𝑆V ; 2. With \nsize optimized, tune the effective anisotropy  to control the barrier of magnetization \nreversal, by alloy ing of magnetically hard cobalt ferrite  with soft manganese ferrite to \nmaximize SLP. Since MnFe 2O4 has a magnetocrystalline  anisot ropy constant of 3.0×\n103 J/m3, while that of CoFe 2O4 is 2.0×105 J/m3, the anisotropy of the mixed ferrite \nwill be very sensitive to the amount of cobalt alloying. At a field of 33 kA/m and 380  \n5 \n kHz, t he SLP is maximized by tuning the  alloy composition of CoxMn 0.3-xFe2.7O4. One \nshould aim for a room temperature anisotropy field slightly higher than the field \namplitude to achieve the highest SLP.[31] The metal composition is limited to \n(Co+Mn):Fe = 1:9 to minimize potential toxicity; 3. Maximize SLP and ILP at field \nparameters below the clinical safety limit  (f = 380 kHz , H  13 kA/m and Hf < 5109 \nA/(ms)). As the anisotropy field  of magnetite is  larger than the field amplitude, alloying \nwith a soft ferrite such as Mn xFe3-xO4 is needed. For future  in vivo applications, however, \nwe choose zinc ferrite due to its bio -compatibility . Stoichiometric ZnFe 2O4 is \nantiferromagnetic  with low magnetization , while  non-stoichiometric Zn xFe3-xO4 is a \nsoft ferrite with MS moderately higher than that of Fe 3O4 at low  Zn content.[25] We thus \ntune its composition to maximize SLP and ILP at field amplitudes smaller than 13 kA/m.   \n \nAll types of magnetic cores were synthesized by a modified one -pot thermal \ndecomposition method .[12,34 ] These  NPs are monodisperse with narrow size distribution, \nas observed from transmission electron microscopy ( TEM ) images . Fig. 1(a) is the TEM \nimage of 22 nm Mn 0.3Fe2.7O4 NPs. NPs show well -defined facets, with polyhedr al shape . \nIn our experiments, NPs from 7 nm up to 22 nm were investigated  (Fig. S1) , below \nwhich the NPs show SPM behavior. When the sizes are larger than 22 nm, Mn 0.3Fe2.7O4 \nNPs become ferromagnetic and tend to agg lomer ate in the solution due to strong \nmagnetostatic interactions. Therefore, they are excluded from further investigations. A \nsilica shell was coated by reverse microemulsion  method .[35] The TEM image of the 22-\nnm Mn 0.3Fe2.7O4/SiO 2 NPs is shown in Fig.  1 (b). The silica shells were kept thin with \na thickness  of 4-5 nm  to minimize possible temperature gradient in AC field heating .[22] \nThe silica coating makes the NPs hydrophilic, leading to  aqueous dispersions stable for \nyears without agglomeration (Fig. S2 (a)). As shown in Fig S2(b), the zeta -potential of \nthe NPs is about -30 mV . Negative charges on NP surface produces sufficient repulsive \nforce to balance the magnetically induced attractiv e force to keep them from \naggregation .  \n6 \n Within the core size rang e of 7 nm to 2 2 nm, the SLP of an aqueous dispersion of 1 \nmg/ml Mn 0.3Fe2.7O4/SiO 2 NPs increases monotonically with increasing NP size, under \nan AC  field of 33 kA/m and 380 kHz. The temperature  change T vs time curves  \n(heating curves) are plotted  in Fig . 1 (c), where TT(t)-T0; T(t) is the temperature at \ntime t and T0 is ambient temperature. From the heating curves,  SLP vs size can be \nextracted using the Box-Lucas fitting known to give reliable SLP values,[36-39] and \nplotted in Fig. 1( d). The contribution from pure water under identical  conditions  was \nalso measured  and subtracted  as the background.  As can be seen from Fig. 1(c), the \nheating curve shows a negligibly small slope  for 7 nm N Ps, suggesting that 7 nm NPs \ncan hardly heat in such a field ; while 10  nm NPs start to heat with a low SLP of 164 \nW/g metal. Towards the other end of the size range, the S LP values for 18 -nm NPs are \nmuch higher, reaching 1140 W/g metal while 2 2-nm NPs have the highest value of  2278 \nW/g metal. This can be understood since larger NPs have higher energy barrier s for \nmagnetization reversal, thus the area of the AC hysteresis loop will be  larger . In Fig. \n1(d), the red line is a cubic fitting of SLP as  a function of NP diameter d. A reasonable \nagreement between the fitting and experimental data is found , suggesting that SLP is \nproportional to the NP volume .  \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n7 \n Figure 1 . Typical TEM images of  (a) 22  nm Mn 0.3Fe2.7O4 NPs, (b) 22 -nm \nMn 0.3Fe2.7O4/SiO 2 NPs, (c) Heating curves of aqueous solution s of Mn 0.3Fe2.7O4/SiO 2 \nNPs (1 mg NPs/ml) with core size s from 7 nm to 22 nm ; and(d) Size dependence of SLP  \nunder the AC field of 380 kHz, 33 kA/m . \nSince  there is an  upper size limit due to agglomeration, as discussed earlier, an \nalternative approach to enhanc ing SLP is to increase the effective magnetic anisotropy, \nwhile fixing the NP size to 22 nm . We realize  anisotropy tuning by cobalt alloying to \nproduce  mixed ferrites  CoxMn (0.3-x)Fe2.7O4. Compared to earlier reported core/shell \napproach,[27] cation alloying possesses  distinct  advantages : one pot synthesis with high \nreproducibility, and the ability to tune  anisotropy parameters independent of size.  \nIt is found that a  small percentage of Co alloying (i.e. a moderate ly larger  anisotropy) \nis optimum for maximizing SLP. The alloy composition (x~0 -0.08) was controlled  by \nvarying the ratio of Co to Mn precursors . For example, Co0.01Mn 0.29Fe2.7O4 NPs were \nsynthesized by mixing Co , Mn and Fe precursors with the molar ratio  of 0.01:0.29:2.7 . \nThe atomic ratio of Co:Mn:Fe measured by i nductively coupled plasma atomic \nemission spectroscopy (ICP -AES)  is 0.27:8.2:91, indicating that the composition of the \nfinal product replicates the precursor ratio . The magnetic hysteresis loops of CoxMn (0.3-\nx)Fe2.7O4 NPs (x~0 -0.03) measured at 300 K and 10 K are shown  in Figure 2  (a) to (c) . \nAll NPs are  SPM  at 300 K, while exhibiting hysteresis  at 10 K. The 10 K coercivit y \nincrease s rapidly with increasing Co content , from 27.9 kA/m  at x=  0.01 to 46.6 kA/m  \nat x=  0.03. With Co alloying (x~0 -0.03), the MS barely changes. The MS of Mn 0.3Fe2.7O4 \nNPs is 410 kA/m  at 300 K , comparable to  the bulk value of 446 kA/m , suggest ing \nexcellent crystallinity of the NPs . As shown in Fig. 2(d), the anisotropy  constant  Ku, \nestimated from low temperature coercivity HC and MS, increases monotonically with \nincreasing Co concentration. With just 1 at%  of Mn substituted by Co ( x = 0.03),  Ku \nincreases by 30 0% from 9×103 J/m3 to 2.8×104 J/m3. The SLP (Fig. 2(f)), extracted \nfrom the heating curves (Fig. 2(e)) measured at H = 33 kA/m and f = 380 kHz, first \nincrease s with increasing Co concentration, showing a peak at  x=0.03 , then decreases \nwith further increasing the Co amount. This is understood since  increasing effective \nanisotropy increases the energy barrier for magnetization reversal, and thus the area of  \n8 \n the AC hysteresis loop initially increases . However, with further increasing anisotrop y, \nthe field amplitude is insufficient to saturate  the mag netization at the operating \nfrequency, resulting in minor hysteresis loops with decreas ed area.  The maximum SLP \nis measur ed to be 3417 W/g metal for x= 0.03, which is more than 50% higher than that \nfor the same sized Mn 0.3Fe2.7O4. This value is close to the theoretical limit of SLP for \nferrite NPs , with an  value of 0.49 . This is higher than  = 0.39 for a random ensemble. \nWe suggest that the higher  not only reflects a certain de gree of alignment due to dipole \ninteractions, but also results from an effective anisotropy type close to cubic instead of \nuniaxial ( 𝑀𝑟/𝑀𝑆= 0.62 and 0. 7, for x = 0.02 and 0.03, respectively , as extract ed from \nFig. 2 ).  We further note that for the sample with maximized SLP, the estimated room \ntemperature anisotropy  field HK is ~ 36 kA/m (see Table 1 of Supporting Information, \nSI), slightly higher than the applied field of 33 kA/m .  \n \n \n \n \n \n \n \n \n \nFigure 2 . The magnetic hysteresis  loops of as-synthesized 22 nm CoxMn (0.3-x)Fe2.7O4 \nNPs with (a) x=0.00, (b) x=0.02, (c) x=0.03, measured at 10 K and 300 K,  respectively.  \n(d) Anisotropy constant Ku at 10 K for CoxMn (0.3-x)Fe2.7O4 NPs as a function of x; (e) \nHeating curves of aqueous solutions of CoxMn (0.3-x)Fe2.7O4/SiO 2 NPs (1 mg NPs/ml); and \n(f) Composition dependence of SLP  under the AC field of 380 kHz , 33 kA/m . \n \nIn general , SLP values increase with increasing frequency and amplitude of AC \nfields. However, for clinical hyperthermia application s, there is a safety limit on the \nproduct of field frequency and amplitude typically taken to be  Hf =5109 A/(ms).[40-42] \n \n9 \n Anisotropy optimized to achieve maxim um SLP at high field s will not be  optim al for \nclinically relevant low fields. Fig. S5(a) shows the heating curves of 22-nm \nCo0.03Mn 0.27Fe2.7O4/SiO 2 NP aqueous dispersion  (1 mg NPs/ml) under the AC field of \n380 kHz with different field amplitudes . As calculated  from the heating curve shown in \nFig. S5(a) (see SI) , the SLP at H =13 kA/m decrease s to just 266 W/g, and further \ndecreases to 40 W/g at 7 kA/m . To achieve large SLP and ILP at fields smaller than  13 \nkA/m ( Hf < 5109 A/(ms)), a softer material with a n anisotropy field comparable to the \nfield amplitude is needed . For clinical applications , we resort to non-stoichiometric zinc \nferrite NPs for their  biocompatibility and low anisotropy.[24] It is known that the M S of \nzinc ferrite is highly sensitive to Zn content , with  ZnFe 2O4 being  antiferromagnetic if \nZn2+ ions occupy the A -site of the spinel lattice  only.[43] One can tune the MS and \nanisotropy by varying the Zn: Fe ratio. Fig. 3(a) shows the composition dependence of \nroom temperature MS in Zn xFe3-xO4 NPs.  It can be seen that MS increases first \nmonotonically with increasing x, and reaches a maximum of 458 kA/m  at x =0.3, \ncomparable to  zinc ferrit e synthesized by other methods .[44-46] Fig. 3(b) shows the \ncomposition dependence of anisotropy Ku measured at 10 K , being nearly constant \nbelow x=0.3 and decreases with further increasing x . The room temperature HK is \nestimated to be 1 8.5 kA/m  (see SI) , suggesting an AC HC of 9.2 kA/m, which is close \nto the optimal value for the applied field H= 13 kA/m, leading to nearly  maximize d AC \nhysteresis area and thus SLP. The heating performance of 22 nm Zn0.3Fe2.7O4/SiO 2 NPs \nat varying field amplitudes were studied in detail. Fig. S 5(b) shows  heating curves of \nZn0.3F2.7O4/SiO 2 in the AC field of 380 kHz with varying amplitude s, and SLP as a  \nfunction of field is plotted in Fig. 3 (c). Comparing to Co0.03Mn 0.27Fe2.7O4/SiO 2, \nZn0.3Fe2.7O4/SiO 2 NPs exhibit much higher SLP at fields lower than 13 kA/m (Hf \n=4.9109 A/(ms), within the clinical  safety limit ). SLP is 1010 W/g metal at H = 13 kA/m. \nAchieving SLP > 1000 W/g at clinically safe field parameters is significant, since it \nwould allow sufficient heating for targeted treatment of  small tumors and metastases, \nat low NP concentration achievable through antibody targeting .[47] To co mpare with  \n10 \n other NPs, ILP is calculated and plotted in Fig. 3 (d). ILP is 15.7 nHm2/kg at H = 13 \nkA/m , a value significantly higher than that of NPs synthesized previously .[48] As can \nbe seen from fig. 3(d) , ILP of  Zn0.3Fe2.7O4 NPs reach es 26.8 nHm2/kg at 7 kA/m (SLP \n= 500 W/g metal). The  values are 0.37 and 0.34 for H = 13 and 7 kA/m, respectively, \nclose to the theoretical value of 0.39 for a completely random ensemble.  It is clear that \nSLP does not scale with H2 as predicted by the linear response th eory or ILP would be \na constant . As a comparison, bacteria magnetosomes are reported to have a SLP of 960 \nW/g NPs and ILP of 23.4 nHm2/kg at 410  kHz and  10 kA/m.[32] However, one should \nnote that these values were obtained by aligning the NPs in an external  field. Without \nfield alignment, the obtained SLP is expected  to be lower  by a factor of three .[32] While \nthe SLP increases monotonically with increasing field  for both samples as seen in Fig. \n3(c), the field dependence shows different behavior . Co 0.03Mn 0.27Fe2.7O4 NPs have  very \nlow initial SLP which increases slowly with field at H < 13 kA/m . This is because the \nfield amplitude of 13 kA/m is insufficient to saturate the magnetization of  \nCo0.03Mn 0.27Fe2.7O4 NPs due to their relatively  large anisotropy field. The AC hysteresis \nis expected to be nearly linear in field with very small opening. On the other hand, SLP \nincreases initially rapidly below 1 8 kA/m then slowly for Zn0.3Fe2.7O4, as its anisotropy \nfield is found to be 18.5 kA/m .   \n \n \n \n \n \n \n \n \n \n \n \n11 \n Figure  3. Composition dependence of (a) saturation magnetization MS, measured at 10 \nand 300 K; and (b) anisotropy constant Ku at 10 K, for ZnxFe3-xO4 NPs. (c) Field \ndependence of S LP for Z n0.3Fe2.7O4/SiO 2 and Co0.03Mn 0.27Fe2.7O4/SiO 2 NPs, (d) Field \ndependence of ILP for Zn 0.3Fe2.7O4/SiO 2 and Co0.03Mn 0.27Fe2.7O4/SiO 2 NPs. \nIn clinical hyperthermia applications, the contribution to heating due to physical \nrotation of NPs (Brownian relaxation) may be hindered in biological environment, e.g. \nin NPs embedded in bone cement. To investigate the realistic heating performance, we \nstudied AC field heating of NP  dispersions  in water/glycerol mixture with different \nglycerol concentration up to 80 vol%. As can be seen in Fig. S10, SLP decreases with \nincreasing glycerol concen tration at all field values studied. At 80 vol% glycerol, the \nSLP ranges from 50% (at 3 kA/m) to 70% (at 18 kA/m) of the values  for aqueous \nsolutions.  The reduction is primarily due to the high viscosity of glycerol , which is 60 \ntimes that of water  at room  temperature.[49] The high viscosity of the glycerol solution \nhinders the rotation of the NPs, mak ing Brownian motion ineffective in contributing to \nAC field heating. However, it is clear that the dominating contribution to hysteresis loss \nis the N éel rela xation , as more than 50% of the heating performance is retained for the \nmost viscos sample. This enables high heating of NP bone cement as discussed in the \nfollowing section.       \nSurgical resection combined with chemo - and radiotherapy has been a clinica l gold \nstandard for the treatment of  bone tumors . However, the patients are more likely to \nexperience a tumor recurrence due to the bone microenvironment -associated tumor \nresistance to chemo - and radiotherapy, or inadequate surgical margins. Targeted thermal \ntherapy of bone tumors become attractive because of its high selective damage of tumor \ntissue and repeatability .[50] We use  bone cement containing 1 wt% Zn0.3Fe2.7O4 NPs for \nlocal hyperthermia experiments. A  piece of pig rib with a hole 6.0 mm in diameter and \n6.0 mm in length were filled with the magnetic cement , and  exposed to an AC  field of \n380 kHz and 1 3 kA/m , as shown in Fig. 4 (a). The surrounding of the bone was water -\ncooled at 37 C to mimic cooling by blood vessels. The temperature rise of the pig rib \nwas recorded  by both a high-resolution infrared (IR) camera  and a fiber optic probe . It \ncan be seen that the temperature of the magnetic cement  rises rapidly to the therapeutic  \n12 \n threshold required for cancer hyperthermia (T >42 °C). The center of cement reach es \n50 °C within 1 minute ; and the temperature of entire  cement rises to above 50 °C within \n3 min . When the heating time is up to 30 min, the cement is heated to 70 °C, while the \nregion 25 mm away from the center is abo ve 46 °C. In Fig. 4 (a), t he red dots represent \nthe region with the temperature at the therapeutic threshold of 42 °C. With increasing \nexposure time, the region with temperature > 42 °C expands. After 25 min, the \ntemperature of the entire bone is over 42 °C. As a comparison, in a previous study ,[51] \nbone cement containing 60 wt% of magnetic materials was used to reach similar \ntemperature change at a  maximum  AC field of 100 kHz and 23.9 kA/m. A significant  \nreduction in dosage afforded by the high SLP of our optimized bio -compatible  NPs can \nnot only minimize any potential toxicity, but also preserve the mechanical integrity of \nthe bone cement.  \n \nTwo types of NPs, 22-nm Co0.03Mn 0.27Fe2.7O4/SiO 2 and Zn0.3Fe2.7O4/SiO 2, were \ntested for hyperthermia killing of Osteosarcoma MG -63 cells . Cell apoptosis was \nexamined by a flow -cytometry -based annexin -V fluorescein isothiocyanate  (see SI ), as \nshown in Fig. 4 ( b) to (e), respectively. Cells without NPs and with NPs but no AC field \nexposure were used as control . 1×104 MG-63 cells and Co0.03Mn 0.27Fe2.7O4/SiO 2 NP \nsolution  with a concentration of 25 g/ml were exposed to an AC magnetic field of 380  \nkHz, 33 kA/m for 3 min.  The percentage of the early and late apoptotic cells (i.e. cell \ndeath) is 81% in total, similar to values  reported previously  using a dosage of 50  \ngNPs/ml at 37.4 kA/m and 500 kHz (Hf  value 1.5 times higher) .[16] To test the \nperformance of Zn0.3Fe2.7O4/SiO 2 NPs,  a concentration of 300  gNPs/ml were used.   \nExposure to an  AC field of H = 13 kA/m  for 10 min resulted in 89% cell death, where \nthe early apoptotic cells was 79.35% and late apoptotic cells 9.83%.  It should be  \nemphasized  that all hyperthermia treatments in our studies were performed on adherent \ncells. Hyperthermia on  suspended cells  may overestimate cell death , as cells would be \ninevitably injured during the digestive proc ess.[18,39 ,52] Since  adherent cells more closely  \n13 \n simulate cells in vivo than suspended cells , our reported value s should be more relevant \nin guiding clinical applic ations .  \n \n \n \n \n \n \n \n \n \n \nFigure  4. (a) Infrared Photos of the bone heated under the field of 380 kHz, 13 kA/m ; \nApoptosis assay fluorescence from  Annexin V  and PI uptake by the MG -63 cells were \nmonitored by flow cytometry.  (b) MG-63 cells without NPs used as Control group.  (c) \nMG-63 cells with NPs but not heated used as the second  Control group.  (d) MG-63 \ncells incubated with 25 gNPs/ml Co0.03Mn 0.27Fe2.7O4 /SiO 2 NPs heated under the AC \nfield of  380 kHz, 33 kA/m (e) MG -63 cells incubated with 300  gNPs/ml Zn0.3Fe2.7O4 \n/SiO 2NPs heated under the AC field of 380  kHz, 13 kA/m.  \nCytotoxicity of different types of NPs to cells was also measured and compared .  \nThe viability of the MEF and MG -63 cells was determined by CCK -8 assay after \nincubation with various concentrations  of NPs  (Zn0.3Fe2.7O4/SiO 2, Fe3O4/SiO 2, and \nMn 0.3Fe2.7O4/SiO 2) for 24 and 48h.  Cells without NPs were used as control groups.  As \nshown in Fig. 5, the cytotoxicity is the lowest for Zn0.3Fe2.7O4/SiO 2 and highest for \nCo0.03Mn 0.27Fe2.7O4/SiO 2, with Fe 3O4/SiO 2 in between.  In the case of  Zn0.3Fe2.7O4/SiO 2, \n \n14 \n up to the  concentration  of 1000 µ g/ml , the cell viability show s no significant difference  \n(P > 0.05) from the  control groups after incubation for 24h. Though at 700 and 1000 \ng/ml after incubation  for 48  h, viability of cells with Zn0.3Fe2.7O4/SiO 2 is lower than \nthat of control groups,  it is still above 75% for ME F and abo ve 73% for MG -63 cells . \nFor MEF Incubat ed with Fe3O4/SiO 2 NPs at concentration  higher than 500 g/ml at \nboth incubation time  of 24 and 48  h, cell viability is lower than that of the control \nsample,  while Fe3O4/SiO 2 show s cytotoxicity in MG -63 starting at 300 g/ml upon \nincubation for 48 h . As for Co0.03Mn 0.27Fe2.7O4/SiO 2, cytotoxicity is observed at \nconcentration above  100 g/ml, regardless  of cell lines and incubation time.  At the \nhighest concentration  of 1000  g/ml and 48  h, cell viability is even as low as 9.48%.  \n \n \n \n \n \n \n \n \nFigure 5. The viability of the MEF  and MG-63 cells determined by CCK -8 assay \nafter incubation  in NP solutions with various concentrations for 24 h (a,b) and 48h  (c,d) . \n \nIn summary, we have designed and synthesized two types  of magnetic /silica \ncore/shell NPs . CoxMn 0.3-xFe2.7O4/SiO 2 with Co  concentration of x=0.03  result s in \nmaximized specific loss power of 3417  W/g at an AC field of 33 kA/m and 380 kHz; \nand biocompatible Zn0.3Fe2.7O4/SiO 2 achieved SLP of 1 010 W/g at a field of 13 kA/m \n \n15 \n and 380 kHz . The intrinsic loss power ranges from 15.7 to 59.9  nHm2/kg as the field \ndecreases from 13 to 3 kA/m  for the latter . We further demonstrate efficient \nhyperthermia using Zn 0.3Fe2.7O4 NPs in magnetic cement for bone tumor, incorpo rating \nultralow dosage of just 1 wt% of nanoparticles . Zn0.3Fe2.7O4 NPs also demonstrate good \nhyperthermia performance to kill cancer cells . Zn 0.3Fe2.7O4 NPs show excellent  \nbiocompatibility, exhibiting no cell cyto toxic ity at concentrations up to  500 µg/ml \nwithin 48 hrs. Our work provides a guidance for design of NPs with appropriate \nmagnetic p ropertie s for maximized heating power at any field parameters, and \nconversely , given a particular NP type, choice of field parameters leading to maximized \nheating  power. Furthermore, o ur biocompatible NP platform with greatly enhanced AC \nfield heating at low field  amplitude s are promising for targeted hyperthermia of small \ntumors and metastases . Further in vivo studies are needed to show the therapeutic effect \nof these optimized nanoparticles.   \n \n   \n16 \n Methods  \n1. Experimental Methods  \nSynthesis of Co xMn (1-x)Fe2O4 nanoparticles  \nA series  of CoxMn (0.3-x)Fe2.7O4 mixed ferrite NPs of different sizes and \ncomposition  were synthesized  by a one-pot solution  method through thermal \ndecomposition of a mixture of metal acetylacetonates with surfactants in a high -boiling \npoint organic solvent.  Iron(III) acetylacetonate  (2 mmol), manganese(II) \nacetylacetonate  and cobalt(II) acetylacetonate  (total 1 mmol), 1,2-hexad ecanediol , oleic \nacid (3 mmol), oleylamine (3 mmol), and 20 mL benzyl ether w ere mixed and \nmagnetically stirred under  a flow of nitrogen. The mixture was first heated to 393 K for \n30 minutes to remove the low boiling point solvent, then to 473 K and kept at that \ntemperature for 1 hour. At a ramping rate of 10 K min-1 the solution was further heated \nto reflux (~ 573 K) and kept at 573 K for 1 hour. The solution was cooled down to room \ntemperature by removing the heat source. The solution was treated  with ethanol  in the \nair atmosphere. Co xMn (1-x)Fe2O4 NPs were precipitated from the solution, centrifuged \nto remove the solvent, and redispersed in hexane.  The size of nanoparticles was tuned \nby the ratio of oleic acid to metal precursors.[12]  \nSynthesis o f Zn 0.3Fe2.7O4 nanoparticles  \nUnder a gentle flow of Ar, Iron(III) acetylacetonate  (2.7 mmol), zinc(II) \nacetylacetonate  (0.3 mmol), sodium oleate (2  mmol) and oleic acid (4 ml) were mixed \nwith benzyl ether (20 ml). The mixture was magnetically stirred under a flow of Ar and \nthen heated to 393 K for 1 h. Under an Ar blanket, the solution was further heated to \nreflux (~573 K) and kept at this temperature for 1h. The mixture was then cooled down \nto room temperature b y removing the heating mantle.  The size of nanoparticles were  \ntuned by controlling the heating rate during heating from 393 K to 573 K.  \nSilica coating of magnetic NPs \nThe silica shell s were coated on the h ydrophobic NPs via a reverse microemulsion \nmethod .[22,32 ] For 4-5 nm silica coating, 20 ml cyclohexane and 1.15 ml Igepal  CO-520  \n17 \n were mixed and 20 mg magnetic NPs in 2 ml cyclohexane  were added while stirring. \n0.15 ml ammonium hydroxide  (28-30%) was  then added , followed by 0. 1 ml TEOS. \nThe solution was  stirred at room temperature for 24 h and the resulting magnetic  \nNPs/SiO 2 core/shell NPs were precipitated by adding  ethanol and centrifugation. The \ncollected particles were  washed in ethanol and water twice and precipitated by \ncentrifugation  and finally redispersed in water.  \nCharacterizations  \nA Hitachi  H7650 (120kV) transmission electron microscope  was used to characterize \nthe size and morphology of the NPs. Energy dispersive X -ray spectroscopy and \ninductively coupled plasma atomic emission spectroscopy were employed to determine \nthe composition . The magnetic hysteresis loops were measured using a Quantum \nDesign Physical Property Measurement System  model 6000. Hyperthermia \nperformance of the NPs was investigated by a HYPER5 machine fabricated by MSI \nCompan y under a n AC magnetic field with frequency of 380 kHz. The temperature \nchange of the NP solution was monitored by a fiber optic probe.  \nIn vitro experiments  \nHuman osteogenic sarcoma MG -63 cells and mouse fibroblast cells  (MEF) were \npurchased from the American Type Culture Collection. MG-63 cells were plated in 35 -\nmm culture dishes at 80% confluence  (1× 106 cells) with 2ml of DMEM/HIGH \nGLUCOSE medium containing 10% fetal bovine serum.  The NP dispersion was added \nto culture d ishes, and the samples were  exposed to the AC magnetic field . Apopto tic \ncell was de tected by a flow cytometer (Beckman coulter Ltd., USA).  MEF cells were \nseeded in 96 -well plates at a density of 5 ,000 cells per well.  After incubation for 24 h r \nand 48 hr, the cell viabilities were determined by the standard Cell  Counting Kit -8 \n(CCK -8, Dojindo,  Japan) assay.  \n \n \n   \n18 \n References  \n[1] J. T. Dias, M. Moros, P. del Pino, S. Rivera, V. Grazu, J. M. de la Fuente, Angew. Chem. Int. \nEd. 2013 , 52, 11526.  \n[2] H. Huang, S. Delikanli, H. Zeng, D. M. Ferkey, A. Pralle, Nat. Nanotechnol. 2010 , 5, 602.  \n[3] S. A. Stanley, J. E. Gagner, S. Damanpour , M. Yoshida, J. S. Dordick, J. M. Friedman, \nScience 2012 , 336, 604.  \n[4] R. Chen, G. Romero, M. G. Christiansen, A. Mohr, P. Anikeeva, Science 2015 , 347, 1477.  \n[5] N. A. Frey, S. Peng, K. Cheng, S. H. Sun, Chem. Soc. Rev. 2009 , 38, 2532.  \n[6] S. G. Grancharov, H. Zeng,  S. H. Sun, S. X. Wang, S. O'Brien, C. B. Murray, J. R. Kirtley, G. \nA. Held, J. Phys. Chem. B 2005 , 109, 13030.  \n[7] A. H. Lu, E. L. Salabas, F. Schuth, Angew. Chem. Int. Ed. 2007 , 46, 1222.  \n[8] H. B. Na, I. C. Song, T. Hyeon, Adv. Mater. 2009 , 21, 2133.  \n[9] Q. A. Pank hurst, J. Connolly, S. K. Jones, J. Dobson, J. Phys. D: Appl. Phys. 2003 , 36, R167.  \n[10] C. J. Xu, S. H. Sun, Adv. Drug Deliver Rev. 2013 , 65, 732.  \n[11] S. Dutz, R. Hergt, Nanotechnology 2014 , 25, 452001.  \n[12] H. Zeng, P. M. Rice, S. X. Wang, S. H. Sun, J. Am. Chem. Soc.  2004 , 126, 11458.  \n[13] R. K. Gilchrist, R. Medal, W. D. Shorey, R. C. Hanselman, J. C. Parrott, C. B. Taylor, Ann. \nSurg. 1957 , 146, 596.  \n[14] C. L. Dennis, R. Ivkov, Int. J. Hyperther. 2013 , 29, 715.  \n[15] R. E. Rosensweig, J. Magn. Magn. Mater. 2002 , 252, 370.  \n[16] B. Mehdao ui, A. Meffre, J. Carrey, S. Lachaize, L. M. Lacroix, M. Gougeon, B. Chaudret, M. \nRespaud, Adv. Funct. Mater. 2011 , 21, 4573.  \n[17] R. Chen, M. G. Christiansen, P. Anikeeva, Acs Nano 2013 , 7, 8990.  \n[18] S. H. Noh, W. Na, J. T. Jang, J. H. Lee, E. J. Lee, S. H. Moon, Y. Lim, J. S. Shin, J. Cheon, \nNano Lett. 2012 , 12, 3716.  \n[19] J. P. Fortin, C. Wilhelm, J. Servais, C. Menager, J. C. Bacri, F. Gazeau, J. Am. Chem. Soc. \n2007 , 129, 2628.  \n[20] P. Guardia, R. Di Corato, L. Lartigue, C. Wilhelm, A. Espinosa, M. Garcia -Hernandez, F. \nGazeau, L. Manna, T. Pellegrino, Acs Nano 2012 , 6, 3080.  \n[21] R. Hergt, S. Dutz, R. Muller, M. Zeisberger, J. Phys -Condens Mat. 2006 , 18, S2919.  \n[22] H. Zhang, H. Huang, S. He, H. Zeng, A. Pralle, Nanosca le 2014 , 6, 13463.  \n[23] K. Maier -Hauff, F. Ulrich, D. Nestler, H. Niehoff, P. Wust, B. Thiesen, H. Orawa, V.  Budach, \nA. Jordan, J. Neuro -Oncol . 2011 , 103, 317.  \n[24] T. Zargar, A. Kermanpur, Ceram. Int. 2017 , 43, 5794.  \n[25] B. Behdadfar, A. Kermanpur, H. Sadeghi -Aliabadi,  M. D. Morales, M. Mozaffari, J. Magn. \nMagn. Mater. 2012 , 324, 2211.  \n[26] F. H. L. Starsich, G. A. Sotiriou, M. C. Wurnig, C. Eberhardt, A. M. Hirt, A. Boss, S. E. \nPratsinis, Adv. Healthc. Mater. 2016 , 5, 2698.  \n[27] J. H. Lee, J. T. Jang, J. S. Choi, S. H. Moon, S. H. Noh, J. W. Kim, J. G. Kim, I. S. Kim, K. I. \nPark, J. Cheon, Nat. Nanotechnol. 2011 , 6, 418.  \n[28] M. Kallumadil, M. Tada, T. Nakagawa, M. Abe, P. Southern, Q. A. Pankhurst, J. Magn.  \n19 \n Magn. Mater. 2009 , 321, 1509.  \n[29] M. Kawashita, K. Kawamura, Z. Li, Acta Biomater. 2010 , 6, 3187.  \n[30] C. Y. Xu, Y. Y. Zheng, W. Gao, J. S. Xu, G. Q. Zuo, Y. Chen, M. Z. Zhao, J. B. Li, J. L. \nSong, N. Zhang, Z. G. Wang, H. Y. Zhao, Z. C. Mei, Acs Appl. Mater. Inter. 2015 , 7, 13866.  \n[31] J. Car rey, B. Mehdaoui, M. Respaud, J. Appl. Phys. 2011 , 109, 083921.  \n[32] R. Hergt, R. Hiergeist, M. Zeisberger, D. Schuler, U. Heyen, I. Hilger, W. A. Kaiser, J. Magn. \nMagn. Mater. 2005 , 293, 80. \n[33] E. C. Stoner, E. P. Wohlfarth, Philos Tr. R. Soc. S -A 1948 , 240, 599.  \n[34] S. H. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, G. X. Li, J. Am. \nChem. Soc. 2004 , 126, 273.  \n[35] H. L. Ding, Y. X. Zhang, S. Wang, J. M. Xu, S. C. Xu, G. H. Li, Chem. Mater. 2012 , 24, \n4572.  \n[36] G. E. P. Box, H. L. Lucas, Biometrika 1959 , 46, 77. \n[37] K. Murase, H. Takata, Y. Takeuchi, S. Saito, Phys. Medica. 2013 , 29, 624.  \n[38] D. E. Bordelon, C. Cornejo, C. Gruttner, F. Westphal, T. L. DeWeese, R. Ivkov, J. Appl. \nPhys. 2011 , 109, 124904.  \n[39] R. R. Wildeboer, P. Southern, Q. A. Pankhurst, J. Phys. D: Appl. Phys. 2014 , 47. \n[40] R. Hergt, S. Dutz, J. Magn. Magn. Mater. 2007 , 311, 187.  \n[41] R. Chen, M. G. Christiansen, A. Sourakov, A. Mohr, Y. Matsumoto, S. Okada, A. Jasanoff, P. \nAnikeeva, Nano Lett. 2016 , 16, 1345.  \n[42] S. Dutz, R. Hergt, Int. J. Hyperther. 2013 , 29, 790.  \n[43] J. T. Jang, H. Nah, J. H. Lee, S. H. Moon, M. G. Kim, J. Cheon, Angew. Chem. Int. Ed. 2009 , \n48, 1234.  \n[44] Z. L. Lu, L. Y. Lv, J. M. Zhu, S. D. Li, X. C. Liu, W. Q. Zou, F. M. Zhang, Y. W. Du, Solid \nState Commun. 2006 , 137, 528.  \n[45] E. Petrova, D. Kotsikau, V. Pank ov, J. Magn. Magn. Mater. 2015 , 378, 429.  \n[46] M. L. Wen, Q. Li, Y. T. Li, J. Electron Spectrosc. 2006 , 153, 65. \n[47] A. Ito, M. Shinkai, H. Honda, T. Kobayashi, J. Biosci. Bioeng. 2005 , 100, 1. \n[48] S. Dutz, J. H. Clement, D. Eberbeck, T. Gelbrich, R. Hergt, R. Muller, J. Wotschadlo, M. \nZeisberger, J. Magn. Magn. Mater. 2009 , 321, 1501.  \n[49] J. B. Segur, H. E. Oberstar, Ind. Eng. Chem . 1951 , 43, 2117.  \n[50] K. Takegami, T. Sano, H. Wakabayashi, J. Sonoda, T. Yamazaki, S. Morita, T. Shibuya, A. \nUchida, J. Biomed. Mater. Res. 1998 , 43, 210.  \n[51] A. Matsumine, K. Takegami, K. Asanuma, T. Matsubara, T. Nakamura, A. Uchida, A. Sudo, \nInt. J. Clin. Oncol. 2011 , 16, 101.  \n[52] T. Sadhukha, L. Niu, T. S. Wiedmann, J. Panyam, Mol. Pharmaceut. 2013 , 10, 1432.  \n \nAcknowledgements  \nThis work was supported by  National Science Foundation of China  (Grant No. 51571146, 51471186, \n51372276 ). \n \n  \n20 \n Supporting Information  \n \nMaximizing Specific Loss Power for Magnetic Hyperthermia  by Hard -Soft Mixed \nFerrites  \nShuli H e1,2,4, Hongwang Z hang2, Yihao L iu1,3, Fan Sun2, Xiang Yu1, Xueyan L i1, Li \nZhang1, Lichen Wang1, Keya Mao3, Gangshi Wang3, Yunjuan Lin3, Zhenchuan Han3, \nRenat Sabirianov5, and Hao Z eng2* \n1 Department of  Physic s, Capital  Normal University, Beijing 100 048, China  \n2Department of Physics, University at Buffalo, SUNY , Buffalo , New York 14260, U SA \n3 Chinese PLA General Hospital, Beijing 1008 53, China  \n4Beijing Advanced Innovation Center for Imaging Technology, Beijing 100 048, China  \n5Department of Physics, University of Nebraska -Omaha, Omaha, NE  68182 , USA  \n \n*corresponding author: haozeng@buffalo.edu  \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n21 \n 1. Experimental Methods  \nSynthesis of Co xMn (0.3-x)Fe2O4 nanoparticles  \nA series of CoxMn (0.3-x)Fe2O4 mixed ferrite NPs of different sizes and composition \nwere synthesized by a one -pot solution method through thermal decomposition of a \nmixture of metal acetylacetonates with surfactants in a high -boiling point organic \nsolvent. Iron(III) acetylacetonate (2 mmol), manganese(II) acetylacetonate and \ncobalt(II) acetylacetonate (total 1 mmol), 1,2 -hexadecanediol, oleic acid (3 mmol), \noleylamine (3 mmol), and 20 mL benzyl ether were mixed and magnetically stirred \nunder a flow of nitrogen. The mixture was first hea ted to 393 K for 30 minutes to \nremove the low boiling point solvent, then to 473 K and kept at that temperature for 1 \nhour. At a ramping rate of 10 K min-1 the solution was further heated to reflux (~573 K) \nand kept at 573 K for 1 hour. The solution was cooled down to room temperature by \nremoving the heat source. The solution was treated with ethanol in the air atmosphere. \nCoxMn (0.3-x)Fe2O4 NPs were precipit ated from the solution, centrifuged to remove the \nsolvent, and redispersed in hexane. The size of nanoparticles was tuned by the ratio of \noleic acid to metal precursors.  \n \nSynthesis of Zn 0.3Fe2.7O4 nanoparticles  \nUnder a gentle flow of Ar, Iron(III) acetyla cetonate (2.7 mmol), zinc(II) \nacetylacetonate (0.3 mmol), sodium oleate (2 mmol) and oleic acid (4 ml) were mixed \nwith benzyl ether (20 ml). The mixture was magnetically stirred under a flow of Ar and \nthen heated to 393 K for 1 h. Under an Ar blanket, the solution was further heated to \nreflux (~573 K) and kept at this temperature for 1h. The mixture was then cooled down \nto room temperature by removing the heating mantle. The size of nanoparticles were \ntuned by controlling the heating rate during heating fro m 393 K to 573 K.  \n \nSilica coating of magnetic NPs  \nThe silica shells were coated on the hydrophobic NPs via a reverse microemulsion  \n22 \n method. For 4 -5 nm silica coating, 20 ml cyclohexane and 1.15 ml Igepal CO -520 were \nmixed and 20 mg magnetic NPs in 2 ml cycl ohexane were added while stirring. 0.15 \nml ammonium hydroxide (28 -30%) was then added, followed by 0.1 ml TEOS. The \nsolution was stirred at room temperature for 24 h and the resulting magnetic NPs/SiO2 \ncore/shell NPs were precipitated by adding ethanol and  centrifugation. The collected \nparticles were washed in ethanol and water twice and precipitated by centrifugation and \nfinally redispersed in water.  \n \nCharacterizations  \nA Hitachi H7650 (120kV) transmission electron microscope was used to characterize \nthe si ze and morphology of the NPs. Energy dispersive X -ray spectroscopy and \ninductively coupled plasma atomic emission spectroscopy were employed to determine \nthe composition. The magnetic hysteresis loops were measured using a Quantum \nDesign Physical Property Measurement System model 6000. Hyperthermia \nperformance of the NPs was investigated by a HYPER5 machine fabricated by MSI \nCompany under an AC magnetic field with frequency of 380 kHz. The temperature \nchange of the NP solution was monitored by a fiber optic  probe.  \n \nIn vitro experiments  \nHuman osteogenic sarcoma MG -63 cells and mouse fibroblast cells (MEF) were \npurchased from the American Type Culture Collection. MG -63 cells were plated in 35 -\nmm culture dishes at 80% confluence (1× 106 cells) with 2ml of DMEM/H IGH \nGLUCOSE medium containing 10% fetal bovine serum. The NP dispersion was added \nto culture dishes, and the samples were exposed to the AC magnetic field. Apoptotic \ncell was detected by a flow cytometer (Beckman coulter Ltd., USA). MEF cells were \nseeded in  96-well plates at a density of 5,000 cells per well. After incubation for 24 hr \nand 48 hr, the cell viabilities were determined by the standard Cell Counting Kit -8 \n(CCK -8, Dojindo, Japan) assay.   \n23 \n 2. TEM Images of Mn 0.3Fe2.7O4 and Mn 0.3Fe2.7O4/SiO 2 NPs with different sizes  \n \n \n \n \n \n \n \n \n \n \n \nFigure S1. TEM images of Mn 0.3Fe2.7O4 nanoparticles  of (a) 7 nm (b) 10nm, ( c) 16 nm, \n(d) 22 nm, (e) 16 -nm Mn 0.3Fe2.7O4/5-nm SiO 2 NPs, (f) 22 -nm Mn 0.3Fe2.7O4/5-nm SiO 2 \nNPs \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n24 \n \n3. Long term stability of the NP dispersion  \na \n \n \n \n \n \n \n \n \nb     \n \n    \n \n \n \nFigure S2. (a) A photograph of CoxMn 0.3-xFe2.7O4/SiO 2 aqueous dispersion s (10 \nmg NPs 𝑚𝑙−1), from left to right: x=0.00, x=0.01, x=0.02, x=0.03 . The samples are \nstable for > 24  months with no precipitation , (b) z -potential curve of  \nCo0.03Mn 0.27Fe2.7O4/SiO 2 nanoparticles.  \nAs shown in Fig S2(b), z eta potential of CoxMn 0.3-xFe2.7O4/SiO 2 NPs is about -30 \nmV . Negative charges on NP surface produces sufficient repulsive force to balance the \nmagnetically induced attractive force in water.  \n \n \n \n \n \n \n25 \n 4. Synthesis of Zn0.3Fe2.7O4 NPs -Tuning  of NP size s by heating rate  \nThe size s of Zn0.3Fe2.7O4 nanoparticles can be tuned by controlling the heating rate \nduring the synthesis from 393 K to 573 K.  The heating rate of 10 K /min leads to 22 -nm \nZFO NPs, and 6 K/min results  in 18 -nm ZFO NPs.  \n \n \n \n \n \n \n \n \n \n \n \n \nFigure S 3. TEM images of (a) Zn0.3Fe2.7O4 NPs, (b) Zn0.3Fe2.7O4@SiO 2 NPs \nsynthesized with the heating rate of 6 K/min, (c) Zn0.3Fe2.7O4 NPs, (d) \nZn0.3Fe2.7O4@SiO 2 NPs synthesized with the heating rate of 10K/min . \n \n \n \n \n \n \n \n \n \n \n26 \n 5. Measurement of magnetic anisotropy   \nSaturation magnetization MS of NPs was measured by an EV-9 vibrating sample \nmagnetometer. NPs w ere embedded in non -magnetic cement (purchased from Q uantum \nDesign  company) . The mass of organic coating on NPs was measured by \nthermogravimetric analysis. The net mass of NPs was used to determine the saturation \nmagnetization . The effective magnetic anisotropy  Ku was estimated from MS and HC at \n10 K, using 𝐾𝑢~𝑀𝑠𝐻𝑐. \n \nTable 1. Saturat ion magnetization MS measured at 10 and 300 K, coercitivity HC \nmeasured at 10 K, anisotropy Ku at 10 K, and estimated anisotropy field HK at 300 K of \nCoxMn 0.3-xFe2.7O4 NPs.  Ku increases with increasing Co alloying concentration x.   \n \nCoxMn 0.3-xFe2.7O4  x =0.00 x =0.01 x =0.02 x =0.03 \nMS (kA/m ) at 10 K  468.4 466.9  465.8  465.3  \nMS (kA/m ) at 300 K  410.5  409.5  408.9  408.4  \nHC (kA/m ) at 10 K  15.0 27.9 37.2 46.6 \nKu  (104 J/m3) at 10 K  0.9 1.66 2.2 2.8 \nHK (kA/m ) at 300 K  11.5 21.5 28.7 35.9 \n     \nTable 2. Saturation magnetization MS measured at 10 and 300 K, coercitivity HC \nmeasured at 10 K, anisotropy Ku at 10 K, and estimated anisotropy field HK at 300 K of \nZnxFe3-xO4 NPs.  \n \nZnxFe3-xO4 x =0.0 x =0.2 x =0.3 x =0.4 x =0.5 x =0.8 x =1.0 \nMS (kA/m)  at 10 K  461.7 506.8  526.8  511 505.3  316.1  171.7  \nMS (kA/m ) at 300 K  401.5 440.7 458.1 444.3  439.4  274.9  149.3  \nHC (kA/m ) at 10 K  28.2 25.3 24.6 23.1 20.8 18.7 18.1 \nKu  (104 J/m3) at 10 K  1.61 1.57 1.6 1.45 1.29 0.73 0.38 \nHK (kA/m ) at 300 K  21.3 19.1 18.5 17.4 15.7 14.1 13.7 \n  \n27 \n HK at 300 K i s estimated using the formula below to consider the thermal \nfluctuation of magnetic moment ;  is taken to be 3 [S1] \n \n𝐾𝑢(𝑇=0)\n𝐾𝑢(𝑇=300  𝐾)=[𝑀𝑆(𝑇=0)\n𝑀𝑆(𝑇=300  𝐾)]𝛾\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n28 \n 6. Measurement of solution temperature for SLP determination   \nThe temperature of the solution was measured by a fiber optic thermometer at \ndifferent locations of the vial. A schematic drawing of the measurement setup is shown \nin Fig. S4  (a). The heating curves for these locations ar e plotted in Fig. S 4 (b). \n \n \n \n \n \n \nFig. S4 . (a) Schematic drawing  of the measurement setup  used in  this work ; (b) The \nheating curve s measured at different locations (including outside the vial).  \n \nAs can be seen from Fig. S4 (b), the temperature inside the vial is uniform, with \nnegligible temperature difference for the probe located at the top, middle and bottom of \nthe solution in the vial. All SLP reported were measured with the probe located  at \nmiddle of the solution in the vial . Furthermore , the vial temperature , measured at the \nouter surface of the vial,  is considerably higher than the ambient temperature, \nsuggesting that the energy absorption by the container cannot be neglected. As can be \nseen from the heating curves for the probe located at the outer surface of the vial , the \nsurface temperature change of the vial can reach 2/3 of the solution temperature  change . \nFor example, a s the solution temperature increases by  60 C, the vial temperature can \nincrease by  40 C. Therefore, we stress that m easurements ignoring the energy \nabsorption of the container tends to underestimate the SLP values. However, since most \nprevious papers published SLP values without considering container absorption, in this \npaper all SLP values were calculated ignoring the vial absorption, for a fair comparison \nwith published results.  \n \n \n \n29 \n 7. AC filed heating curves for two type of NPs at different field amplitudes  \n \n \n \n \n \n \n \n \nFigure S 5. AC field heating of NPs measured by t emperature vs time curves  for (a) \nCo0.03Mn 0.27Fe2.7O4/SiO 2 NP and (b) Zn0.3Fe2.7O4/SiO 2 NP aqueous dispersion s (1 \nmg NPs/ml) under an AC field of 380 kHz with different field amplitudes.  \n \n \n \n \n \n \n \n \n \n \nFigure S 6. AC field heating curve  for Zn0.3Fe2.7O4/SiO 2 NP aqueous dispersion s (5 \nmg NPs/ml) under an AC field of 3 kA/m and 380 kHz. The temperature change reaches \n40 C in 25 min, demonstrating the remarkable heating capability of this material at \nultralow field.  \n \n \n \n30 \n \n0 20 40 60 80 100 120 1400102030405060\nmeasured\n Box-Lucas fittingT (K)\nt (Sec)a8. Extraction of SLP  \nFor reliable extraction of SLP, all heating curves are fitted by the Box -Lucas \nform ula ∆T=𝑆𝑚\n𝑘(1−𝑒−𝑘(𝑡−𝑡0))[S2] with 𝑆𝑚 and k as the fitting parameters. 𝑆𝑚 is \nthe initial slope of the heating curve, and  k is a constant describing the cooling rate. SLP \nis then calculated as 𝑆𝐿𝑃 =𝐶𝑣𝑆𝑚\n𝜌𝑖, where 𝐶𝑣 is the specific heat capacity of the solution \ntaken to be 4.184 J/(g C), and 𝜌𝑖 is the mass concentration of the metal in the NP \nsolution (e.g. for Fe 3O4, 1 mg NPs/ml = 0.724 mg Fe/ml).  \nThe reliability of the fitting is further verified by measuring the cooling curve \ndirectl y (shown  in Fig. S 7(b)), from which k can be extracted independently using \n∆T=𝑇0+(𝑇−𝑇0)𝑒−𝑘(𝑡−𝑡0). The difference is found to be smaller than 0.1%.   \n \n \n \n \n \n \n \n \nFigure S7. (a) Experimental h eating curve (black) and Box -Luca s fitting (red)  of \nCo0.03Mn 0.27Fe2.7O4/SiO 2 NP solution exposed in the ac field of  380 kHz  and 33 \nkA/m,  (b)  Experimental c ooling curve of NPs solution  (black) and fitting curve \nusing 𝑇(𝑡)=𝑇0+(𝑇−𝑇0)𝑒−𝑘(𝑡−𝑡0) (red) .  \n \n \n \n \n \n \n \n \n0 100 200 300 400253035404550556065\n measured\n fittingT (K)\nt (sec)b\nk=0.00195 s-1∆𝑇=𝑆𝑚\n𝑘(1−𝑒−𝑘(𝑡−𝑡0))  \n31 \n  \n \n \n \n \n \n \n \n \n \n \nFigure S8. Examples of h eating curve  (black) and Box -Luca s fitting curve (red) of \nCo0.03Mn 0.27Fe2.7O4/SiO 2 NP solution  exposed in the AC field of  380 kHz  under \ndifferent field  amplitudes.  \n \n \n \n \n \n \n \n \n \n \n \nFigure S9. Examples of h eating curve  (black) and Box -Luca s fitting curve (red) of \nZn0.3Fe2.7O4/SiO 2 NP solution  exposed in the AC field of  380 kHz  under different field  \namplitudes.  \n \n32 \n 9. SLP and ILP of NPs in recent studies  \n \nSample  SLP \n(W/g metal) ILP \n(nHm2/kg) AC field  Reference  \nMulticore -Fe2O3 2000  4.6 700 kHz, 25 kA/m  Ref. S3 \nZn0.4Co0.6Fe2O4/ \nZn0.4Mn 0.6Fe2O4 3886  5.6 500 kHz,  37.3 kA/m  Ref. S4 \nFe3O4 2452  5.6 520 kHz,  29 kA/m  Ref. S5 \nFe3O4 1000  6.3 100 kHz,  40 kA/m  Ref. S6 \nFe3O4 332 8.3 400 kHz,  10 kA/m  Ref. S7 \nmagnetosomes  960 23.4 410 kHz,  10 kA/m  Ref. S8 \nCo0.03Mn 0.27Fe2.7O4 3417  8.3 380 kHz,  33 kA/m  This work  \nZn0.3Fe2.7O4 1010  15.7 380 kHz,  13 kA/m  This work  \nZn0.3Fe2.7O4 500 26.7 380 kHz,  7 kA/m  This work  \nZn0.3Fe2.7O4 282 59.9 380 kHz,  3 kA/m  This work  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n33 \n 10. Measurements of the SLP at different percentage of glycerol  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure S 10. AC field heating of NPs measured by t emperature vs time curves for  \nZn0.3Fe2.7O4/SiO 2 NP water/ glycerol mixture dispersions (1 mg NPs/ml) (a) containing \n40% glycerol, (b) containing 80% glycerol, under an AC  field of 380 kHz with different \nfield amplitudes ; (c) Field dependence of SLP for Zn 0.3Fe2.7O4/SiO 2 aqueous and \nwater/ glycerol mixture dispersions.  \n \n \n \n \n \n \n \n \n34 \n 11. AC field induced cell apoptosis  (cell death) with  different exposure time  \nThe cell apoptosis for MG -63 cells incubated with ZFO NPs and exposed to an ac \nmagnetic field with different exposure time , as shown in Fig .S11. In Fig S 11 (c) to (f), \nthe third quadrant demonstrates the early apoptosis of cell, and the fourth quadrant \nrepresents late apopto sis. The total cell apoptosis is the sum of early apoptosis and late \napoptosis.  The efficiency  of cell apoptosis  increases with increasing exposure time in \nAC magnetic field . In particular , the p ercent age of late apoptotic cell s increase s more \nprominently with increasing  exposure time. Magnetic hyperthermia at ac field of 380 \nkHz and 13 kA/m f or 30 min leads to about 89%  cell apoptosis.   \n \n \n \n \n \n \n \n \nFigure S 11. Apoptosis assay  fluorescence from  Annexin V  and PI uptake by the MG -\n63 cells were monitored by flow cytometry.  (a)MG -63 cells without NPs used as a \ncontrol group.( b) MG -63 cells with NPs but not exposed to ac field  used as another \ncontrol group ; MG-63 cells incubated with 300 g/ml NPs heated under  the ac field of  \n380 kHz, 13 kA m-1 for (c) 5 min (d) 10 min (e) 20 min (f) 30 min.  \n \n \n \n \n \n \n \n35 \n References  \n[S1] C. Zener, Phys. Rev. 1954 , 96, 1335.  \n[S2] F. J. Teran, C. Casado, N. Mikuszeit, G. Salas, A. Bollero, M. P. Morales, J. Camarero, \nR. Miranda, Appl. Phys. Lett. 2012 , 101, 062413.  \n[S3] L. Lartigue, P. Hugounenq, D. Alloyeau, S. P. Clarke, M. Levy, J. C. Bacri, R. Bazzi, \nD. F. Brougham, C. Wilhelm, F. Gazeau, Acs Nano 2012 , 6, 10935.  \n[S4] J. H. Lee, J. T. Jang, J. S. Choi, S. H. Moon, S. H. Noh, J. W. Kim, J. G. Kim, I. S. \nKim, K. I. Park, J. Cheon, Nat. Nanotechnol. 2011 , 6, 418.  \n[S5] P. Guardia, R. Di Corato, L. Lartigue, C. Wilhelm, A. Espinosa, M. Garcia -Hernandez, \nF. Gazeau, L. Manna, T. Pellegrino, Acs Nano 2012 , 6, 3080.  \n[S6] R. Chen, M. G. Christiansen, A. Sourakov, A. Mohr, Y.  Matsumoto, S. Okada, A. \nJasanoff, P. Anikeeva, Nano Lett. 2016 , 16, 1345.  \n[S7] S. Dutz, J. H. Clement, D. Eberbeck, T. Gelbrich, R. Hergt, R. Muller, J. Wotschadlo, \nM. Zeisberger, J. Magn. Magn. Mater. 2009 , 321, 1501.  \n[S8] R. Hergt, R. Hiergeist, M. Zeisberger, D.  Schuler, U. Heyen, I. Hilger, W. A. Kaiser, \nJ. Magn. Magn. Mater. 2005 , 293, 80. \n \n "    },    {        "title": "2309.14639v1.Duality_of_switching_mechanisms_and_transient_negative_capacitance_in_improper_ferroelectrics.pdf",        "content": "1  Duality of switching mechanisms and transient negative capacitance in improper ferroelectrics  Xin Li,1‡ Yu Yun,1‡*, Pratyush Buragohain1, Arashdeep Singh Thind2,3, Donald A. Walko4  Detian Yang,1 Rohan Mishra,2,3 Alexei Gruverman1,5, Xiaoshan Xu1,5*  1Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588, USA 2Institute of Materials Science & Engineering, Washington University in St. Louis, St. Louis MO, USA 3Department of Mechanical Engineering & Materials Science, Washington University in St. Louis, St. Louis MO, USA 4Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA 5Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588, USA  ‡These authors contributed equally to this work.  *Corresponding author: Xiaoshan Xu (X.X.), Yu Yun (Y.Y.)       Abstract:            The recent discovery of transient negative capacitance has sparked an intense debate on the role of homogeneous and inhomogeneous mechanisms in polarizations switching. In this work, we report observation of transient negative capacitance in improper ferroelectric h-YbFeO3 films in a resistor-capacitor circuit, and a concaved shape of anomaly in the voltage wave form, in the early and late stage of the polarizations switching respectively. Using a phenomenological model, we show that the early-stage negative capacitance is likely due to the inhomogeneous switching involving nucleation and domain wall motion, while the anomaly at the late stage, which appears to be a reminiscent negative capacitance is the manifestation of the thermodynamically unstable part of the free-energy landscape in the homogeneous switching. The complex free-energy landscape in hexagonal ferrites may be the key to cause the abrupt change in polarization switching speed and the corresponding anomaly. These results reconcile the two seemingly conflicting mechanisms in the polarization switching and highlight their different roles at different stages. The unique energy-landscape in hexagonal ferrites that reveals the dual switching mechanism suggests the promising application potential in terms of negative capacitance.     2  Introduction               Ferroelectricity (FE), originating from broken inversion symmetry of crystal structures, are often described using the polarization-dependent free energy in the phenomenological Landau theory. In particular, for proper ferroelectrics, such as PbTiO3 and BiFeO3, it successfully explains the ferroelectric phase transition using polarization as the order parameter1-4. Understanding the effect of the free-energy landscape on the polarization switching process has been a crucial task that has attracted tremendous efforts5-8, since the latter is the foundation for the ferroelectric-based electronics.   According to the Landau-Khalatnikov (L-K) model9,10, homogeneous polarization switching in a proper FE system requires overcoming an energy barrier between the double potential wells followed by accelerated change of polarization. The non-monotonic polarization switching speed leads to negative capacitance (NC)11,12, as illustrated in Fig. 1a, where P and G are polarization and Gibbs free energy. Indeed, transient NC has been observed in ferroelectric capacitors in a resistor-capacitor (RC) circuit and was proposed as the signature of the double-well free-energy landscape11,12. This direct manifestation of the free-energy landscape in polarization switching as NC, if confirmed, suggests huge application potential, for example, in reduced-voltage switching of field-effect transistors for reducing energy cost. On the other hand, inhomogeneous switching based on nucleation of reversed domains and domain-wall propagation13-15 is also expected to result in transient NC, because overcoming the nucleation barrier also results in the non-monotonic switching speed, as sketched in Fig. 1b. In addition, if the polarization switching is dominated by the domain-wall motion, the effect of energy landscape in NC can be greatly reduced. Hence, there is an intense debate on the origin of transient NC, i.e., whether it can reveal the free-energy landscape, especially the thermodynamically unstable region.12,16 Moreover, there lacks a model that can reproduce the full-range wave form in which transient NC is observed.   In this regard, improper ferroelectric hexagonal ferrites (h-RFeO3, R: rare earth) and manganites (h-RMnO3) offer great opportunities, in that their multi-variable free-energy allows complex switching path and more abrupt changes with respect to the polarization. Hexagonal ferrites are formed by the triangular lattice of FeO5 bipyramids sandwiched by rare earth layers, as shown in the atomic structure in Fig. 1c. The spontaneous polarization (along c axis) originates from the coupling between the non-polar K3 mode which features buckling of the rare earth layer and collective rotation of FeO5 bipyramids (see Fig. 1c), and the polar Γ!\" mode with imbalanced atomic displacements along the c axis17-22. The K3 structural distortion can be described by the in-plane displacement of apical oxygen using the magnitude Q and angle (or phase) \", as shown in Fig. 1c, which serve as the primary order parameters. With three variables #, \", and P, a complex free-energy landscape is expected for hexagonal ferrites. A two-dimensional (# and \") version after minimization with respect to P is displayed in Fig. 1d, where three minima at \"=2&#$ and three at \"=(2&+1)#$ corresponds to P > 0 and P < 0, respectively, n is an integer 23. Intriguingly, the system remains in the local minimum of constant \" for initial polarization changes, as shown in Fig. 1e; an abrupt change is then expected when the local minimum disappears, which may lead to a more salient NC signature.  3  In this work, we studied polarization switching of improper ferroelectric h-YbFeO3 epitaxial thin films in an RC circuit for the first time. Driven by square waves, transient NC was observed at the early stage (~ 1 µs) of switching which is consistent with the time scale of the nucleation stage in the inhomogeneous switching. More intriguingly, we observe at a later stage (~ 10 µs) a non-monotonic dynamic capacitance, which can be understood as a signature of free-energy landscape. These results reconcile the controversy for the two physical origins of transient NC, i.e., both homogeneous and inhomogeneous switching mechanisms may have an impact on the dynamic capacitance, but at different stages of the switching. The role of the complex free-energy landscape of improper ferroelectric h-RFeO3 suggests their promising application in terms of the NC effects. Improper ferroelectricity of epitaxial h-YbFeO3 films   Epitaxial heterostructures h-YbFeO3/CoFe2O4 (CFO)/La0.7Sr0.33MnO3 (LSMO) were grown on SrTiO3 (STO) (111) substrate by pulsed laser deposition (see details in methods). The CFO layer serves as a buffer layer to mitigate the lattice mismatch between h-YbFeO3 and bottom electrode layer (LSMO). The out-of-plane X-ray diffraction (XRD) +−2+ scan in Fig. 2a indicates that h-YbFeO3 film is (00l)-oriented with no visible impurities. The RHEED images of h-YbFeO3 in the inset of Fig. 2a indicate characteristic diffraction streaks, corresponding to the tripling of in-plane unit cell in the ferroelectric phase (P63cm). The high-angle annular dark field (HADDF) STEM images in Fig.1 b, along h-YbFeO3 [100] direction, indicates the buckling of Yb layer within a single ferroelectric domain area. The amplitude and phase images of piezoresponse force microscopy (PFM) in Fig 2.c and d indicate the robust ferroelectricity of h-YbFeO3 films under the external electric field.  To investigate the polarization switching of the h-YbFeO3 thin films, we first measure the polarization (P)-voltage (V) hysteresis using the PUND (positive up and negative down) method, as shown in Fig. 2e. The thickness of h-YbFeO3 and CFO layer are 31 nm and 10 nm, respectively. The applied waveform with respect to double triangular pulse is depicted in the inset of Fig. 2e. The peak of switching current coincides with the coercive voltage (VC) of the P-V loop. Moreover, the switching dynamics are examined using the square pulses and fitted by the inhomogeneous switching models, including Kolmogorov-Avrami-Ishibashi (KAI) model corresponding to a constant nucleation rate 24-26, and the nucleation-limited switching (NLS) model 27-29 corresponding to a distribution of nucleation time t0; the results are shown in Fig. 2f. Clearly, the switching process can be well described by the NLS model 20. The voltage dependence of characteristic switching time -./0% and the width of distribution functions w were given in the inset of Fig. 2f, which may be attributed to the nanoscale grain size due to the antiphase boundaries in h-YbFeO3 films 28.  Transient NC effect            To probe the transient NC effects, we applied voltage pulse across an RC circuit using a function generator. Schematic diagram of the experimental set-up and the sample structures are shown in Fig. 3a. Channel 1 and channel 2 of oscilloscope are employed to simultaneously record the source voltage (VS) and the voltage on the resistor (VR) respectively; the voltage on the thin film (VFE) is obtained as VFE = VS -VR. Representative waveforms are shown in Fig. 3b. As VS is 4  switched from -5 V to +5 V, the voltage on the ferroelectric layer (VFE) increases from -5 V to ~ 1 V (Vpeak) at the beginning, then VFE quickly decreases to a negative value about -0.4 V (Vdip) at ≈ 2 µs. Afterwards, VFE increases before it saturates at VS, suggesting the ferroelectric polarization is close to fully switched at the end of the voltage pulse (see inset of Fig. 3b). As VS is switched from +5 V to -5 V, a similar behavior is observed (see Fig. S3 in supplementary material). In Fig. 3b, since the current I = VR/R = (VS - VFE )/R >0, surface charge density σ is always increasing. Hence, the voltage drop corresponds to the dynamic NC Adσ/dVFE < 0, where A is the area of the capacitor. We note that this is the first-time observation of transient NC in the thin film of improper ferroelectric hexagonal ferrites.    This transient NC is likely caused by the inhomogeneous switching. Consider a normal RC circuit with a standard capacitor, following a long period of constant VS, if the sign of VS is reversed, one expects a large initial current which decays monotonically with time. In other words, the voltage on the capacitor VS-IR also changes monotonically. For an FE capacitor with inhomogeneous switching, |dP/dt| ≈ |dσ/dt| (see supplementary materials) increases after the nucleation process, before it decreases when the polarization approaches saturation, as illustrated in Fig. 1b and demonstrated in Fig. 2f. This non-monotonic |dP/dt| ≈ |dσ/dt| leads to non-monotonic current I and non-monotonic 1&' because of the relation I=Adσ/dt and VFE = VS – IR. The part of decreasing VFE corresponds to the dynamic NC.   According to the inhomogeneous-switching mechanism, at the early stage, the maximum |dP/dt| occurs. Correspondingly, one expects a maximum current and a minimum VFE. Indeed, the maximum |dP/dt| in Fig. 2f and the minimum VFE (indicated as Vdip) in Fig. 3b, both occur at a time scale ~ 1 µs, which is in the early stage of the switching. In addition, the drop of voltage Vdrop ≡ Vpeak - Vdip can be modulated by the load resistance R: essentially Vdrop is directly related to ImaxR, where Imax is the maximum current. We have measured the VFE wave form with different R values (see Fig. 3c) and extracted Vdip as a function of R. As shown in Fig. 3d, Vdrop increases monotonically with R; the smaller Vdrop/R ratio at larger R values may have to do with the incomplete switching (see Fig. 3c). In addition, the switching current is limited by the load resistance, which explains why tdrop, the time between Vpeak and Vdip increases when R increases.  The influence of source voltage VS is displayed in Fig. 3e, where higher VS results in fast appearance of Vdip, or smaller tdrop, which is consistent with shorter nucleation time t0 with larger applied field shown in Fig. 2f. Larger VS also increases Imax, which increase Vdrop, consistent with the observation in Fig. 3f.   Despite the consistency of the NC effect in Fig. 3b with the inhomogeneous switching mechanism, more details of the VFE wave form can only be explained by invoking the homogeneous switching. First, Vdip drops below 0 in Fig. 3b, while the polarization keeps changing in the same direction, as indicated by the current I = (VS - VFE)/R >0\tfor the entire period displayed. This can be explained using the L-K model, in which the polarization switching is proportional to the sum of the external field EFE = -VFE/tFE and an internal field ELK = −()(*|'!\"+% exerted by the free-energy landscape:           \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t4\t,*,-=5&'+5./                                    (1) 5   where tFE is the thickness of the FE layer, 4 is the viscosity coefficient. Second, in addition to the NC effect at the early stage of the switching, a concave shape is observed in the VFE wave force at a later stage (≈ 40 µs), as shown in Fig. 3b inset. Therefore, the effect of free-energy landscape is still distinguishable, although it may not be large enough to cause NC. Next, we investigate the free-energy landscape of hexagonal ferrites whose complex switching path may manifest in the anomaly of the polarization switching (see supplementary materials).  Free-energy landscape and switching path   The multivariable Gibbs free energy G(Q, ϕ, P) of hexagonal ferrites suggest a complex switching path with continuous polarization. As shown in Fig. 1d and e, the energy landscape has a 6-fold rotational symmetry which reduces to 3-fold in an electric field. On the other hand, # is approximately constant during the polarization switching process, since the structural distortion has a larger energy scale than the electrostatic interactions, which allows simplification of the Gibbs free energy:  \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t6(ϕ,P)\t=6%−(:cos3ϕ+5&)?+0!?!−1#!5&!  (2)  where  6%, a>0 and b>0 are coefficients that only depend on Q, @% is the vacuum permittivity. G(Q, ϕ) is displayed in Fig. 4a near two neighboring potential wells at ϕ =0  and ϕ = π/3, where ?%=23 is the spontaneous polarization at zero field.   Assuming an initial state of energy minimum with ϕ = 0, corresponding to P = P0 >0, a constant 5&'< 0 is expected to reduce P from P0, as indicated in Fig. 4a and b as Step 1. Meanwhile, because P < P0, ELK = a – bP > 0 resists EFE. In addition, ϕ = 0 remains a local minimum because ∂2G/∂ϕ2 =9aPcos(3ϕ)>0. When P becomes negative, ∂2G/∂ϕ2 <0. ϕ = 0 becomes a maximum, which triggers a sudden change of ϕ, as indicated in Fig. 4a and b as Step 2. Minimizing G with respect to ϕ results in G = G0 -1/2 bP2 –1/2 ε0EFE2, corresponding to ELK = bP < 0 (see supplementary materials). Here ELK is in the same direction as EFE which accelerates polarization switching. With P < 0, ϕ = π/3 becomes the global minimum. When the system reaches ϕ = π/3, polarization switching adopt a constant ϕ, as indicated in Fig. 4a and b as the Step 3. Here ELK = a – bP becomes positive again, which resists the polarization switching. Combining Steps 1-3, |dP/dt| is expected to be non-monotonic. In particular, in Step 2 where the polarization switching accelerates, an increasing current is expected, which results in a decreasing VFE = VS – IR and potentially the NC effect. Note that the NC region in Fig. 4b ends at -P0, which is in the late stage of the polarization switching.  A schematic of the ELK(P) for proper ferroelectric is displayed in Fig. 4c. Although the overall trend, i.e., the “S” shape, in Fig. 4b and c are similar, the more abrupt change of ELK in Fig. 4b may make its effect more distinguishable in the polarization switching.  Fitting the VFE wave form considering dual mechanisms  6  Since both the homogeneous and the inhomogeneous switching appear to manifest in the polarization switching in Fig. 3b, we adopt a hybrid model. The distinction between the timing of the potential NC effects, i.e., the effect from inhomogeneous switching in the early stage and the effect from homogeneous switching in the late stage, suggests that the two effects can be resolved both experimentally and theoretically.  Given that the main abnormal feature of the VFE wave form is the NC at the early stage, the hybrid model is based on the NLS framework, assuming a distribution of nucleation rate. To account for the effect of the free-energy landscape, we replace the external field with the sum of external field 5&' and the internal field from the free-energy landscape. Since the “S” shapes of ELK(P) in Fig. 4b and c are similar, to facilitate the numerical simulation, we borrow the polynomial form of ELK(P) from the proper FE and assume                                                   5455(?)=−2B?−4D?$                                                         (3)  where B and D are fitting parameters, similar to the Landau coefficients.     As shown in Fig. 5a, the theoretical fitting replicates the VFE wave form, achieving much higher consistency than previous reports11,16,30,31. Within region (1), the electric field on ferroelectric layer Vtotal is always positive considering Eeff, as shown in Fig. 5b. Fig. S5 suggests that |P|≈|σ| is a good approximation, while the subtle difference reveals the NC. The transient NC occurs when P has only a small change from the initial state, indicating that this region was dominated by the nucleation process. Correspondingly, dσ/dt and dP/dt in Fig. 5c show two cross points (marked by green dashed circles), where they equal. Again, at the time when |dP/dt| and |dσ/dt| reach maximum, VFE reaches minimum, which is the end of the NC period. As shown in Fig. 5d, in the region (2), as the polarization reverses between B and C, Veff = -Eeff tFE crosses zero three times. Correspondingly, in Fig. 5e, |dP/dt| and |dσ/dt|, although still decrease monotonically, appear to flatten between B and C. As a result, VFE(t) exhibits a concave shape, which is reminiscent of NC. This anomaly occurs in a much later stage where P has changed significantly from the initial state, suggesting that it manifest the free-energy landscape, especially the thermodynamically unstable region. The comparison between experimental and theoretical Q-V hysteresis within the whole range is also given in Fig. 5f. In the NLS model, nucleation, which can be treated as the local “homogeneous” switching,  still contributes to the polarization switching at the late stage due to the distribution of the nucleation time. Essentially, during each nucleation, polarization switching undergoes a “slow-fast” procedure due to the energy barrier to overcome. The “fast” part contributes to the NC. On the other hand, domain-wall motion becomes increasingly more important, which is why the “S” shape Veff is smeared into a concave shape of VFE(t).   Conclusions           The long-overlooked hybrid-type switching dynamics, reflecting the duality of homogeneous and inhomogeneous ferroelectric switching of transient polarization, was revealed in improper ferroelectric based on transient NC effects for the first time. Essentially, the signature of inhomogeneous and homogeneous mechanisms can be distinguished due to their different 7  characteristic time. While the former occurs at the early stage as transient NC, the latter appears in the late stage as nonmonotonic dynamic capacitances. The complex free-energy landscape of improper ferroelectric hexagonal ferrites that leads to abrupt change of internal field is one key for the discernable manifestation of the homogeneous switching. These results may settle the long-standing debate on the origin of transient NC and suggest the promising application potential for hexagonal ferrites using NC.   Acknowledgment:           This work is primarily supported by the National Science Foundation (NSF), Division of Materials Research (DMR) under Grant No. DMR-1454618. The research is performed in part in the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience, which are supported by the NSF under Grant No. ECCS- 1542182, and the Nebraska Research Initiative. Work at Washington University is supported by NSF Grant No. DMR-1806147. STEM experiments are conducted at the Center for Nanophase Materials Sciences at Oak Ridge National Laboratory, which is a Department of Energy (DOE) Office of Science User Facility, through a user project. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science user facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.      Methods:  Sample preparation. h-YbFeO3 (YFO)/ CoFe2O4 (CFO) bilayer heterostructure were grown on the La0.67Sr0.33MnO3 (LSMO)/SrTiO3 (STO) (111) substrates by pulsed laser deposition (PLD) system with KrF excimer laser (248 nm wavelength) and a repetition rate of 2 Hz. The base pressure of the PLD system is 3×10-7 mTorr. Before the deposition, the substrates were pre-annealed at 700°C for 1 hour in vacuum. The oxygen partial pressure and substrate temperature during the growth of LSMO thin films were 70 mTorr and 650°C. The CFO layer was grown at a substrate temperature of 600°C under an oxygen pressure of 10 mTorr. The growth temperature of 680°C - 860°C and an oxygen pressure of 10 mTorr were employed to grow the h-YbFeO3 films. The typical thicknesses for h-YbFeO3, CFO, LSMO layers are 20-80 nm, ~10 nm and ~30 nm, respectively. After the deposition, the samples were cooled down to room temperature with a cooling rate of 10 °C/min under an oxygen pressure of 10 mTorr. Then the samples were post-annealed at 600°C in furnace for 3 hours under an atmosphere oxygen pressure to reduce the oxygen vacancies. The platinum top electrodes were ex-situ deposited using shadow mask by PLD system. The typical diameters of top electrodes are from 75 μm to 400 μm.  Structural characterization. The structural phase of the epitaxial films was determined using X-ray diffraction (XRD) (Rigaku SmartLab). Scanning transmission electron microscopy (STEM) imaging was carried out using the aberration corrected Nion UltraSTEMTM 200 microscope 8  (operating at 200 kV) at Oak Ridge National Laboratory. An electron transparent thin foil for STEM characterization was prepared using a Hitachi NB5000 focused ion and electron beam system. To protect against the ion beam damage, a 1-μm-thick carbon layer was deposited on top of the h-YbFeO3 film surface. A 20 kV beam with a current of 0.7 nA was used to cut the lift-out. Rough and fine milling were performed at 10 kV and 5 kV with beam currents of 0.07 nA and 0.01 nA respectively. The resulting foil was mounted on a Cu grid, which was baked at 160 ℃ under vacuum prior to the STEM experiments to remove surface contamination.  Electrical measurements. For the ferroelectric hysteresis loops and switching dynamic with NLS switching, the voltage pulses were applied using a Keysight 33621A arbitrary waveform generator while the transient switching currents were recorded by a Tektronix TDS 3014B oscilloscope. The PUND (positive-up-negative-down) method with double triangular pulse was carried out to measure ferroelectric hysteresis loops. The transient NC effects and dynamics of the ferroelectric polarization of heterostructure were measured by the function generator (HP 33120A) and oscilloscope (Tektronix TBS 1052B) using a Sawyer-Tower circuit shown in Fig. 2c. The source voltage VS was measured by the channel 1 of oscilloscope and the voltage on the load resistance VR was measured by the channel 2 of oscilloscope. The current across the sample is IF = VR/R, and the voltage on the sample is VF = VS - VR.   Simulation method. The self-developed python codes were used for simulating transient NC numerically. The spontaneous polarization, electrode size, resistance and magnitude of voltage source were set close to the experiments during simulation. The hybrid-type switching dynamics, combining NLS model and effective field from L-K model is written in the code, mimicking the procedure of recurrent neural network. Key parameters, including the electric field-dependent  logt0 and w for the NLS model, and Landau coefficients were optimized iteratively to make the time dependent VFE matches the experimental results within the whole range of voltage pulse. Meanwhile, the time-dependent polarization as well as free charge at the interface can be inferred simultaneously. The simulation for frequency-dependent transient NC is got after calculating VFE of sequent voltage pulses, and the final polarization state of previous pulse is used as the initial polarization state of next pulse. The absolute value of\t?676-628 would tend to stabilize after applying enough number of voltage pulse.     References   1. Landau, L. D. & Lifshitz, E. M. Electrodynamics of Continuous Media.  (Oxford, 1960).  2. Ong, L.-H., Osman, J. & Tilley, D. R. Landau theory of second-order phase transitions in ferroelectric films. Phys. Rev. B 63,144109 (2001).  3. Daraktchiev, M., Catalan, G. & Scott, J. F. Landau Theory of Ferroelectric Domain Walls in Magnetoelectrics. Ferroelectrics 375, 122-131 (2008). 9   4. Kumar, A. & Waghmare, U. V. First-principles free energies and Ginzburg-Landau theory of domains and ferroelectric phase transitions in BaTiO3. Phys. Rev. B 82,054117(2010).  5.        Gruverman. A., Rodriguez. B. J., Dehoff. C. Direct studies of domain switching dynamics in thin film ferroelectric capacitors. Appl. Phys. Lett. 87, 082902 (2005). 6.        D. J. Jung , M. Dawber , J. F. Scott. et al. Switching Dynamics in Ferroelectric Thin Films: An Experimental Survey. Integrated Ferroelectrics, 48:1, 59-68 (2002). 7.        J. F. Scott. A review of ferroelectric switching. Ferroelectrics, 503:1, 117-132(2016). 8.        Gruverman. A, Kholkin. A . Nanoscale ferroelectrics: processing, characterization and future trends. Rep. Prog. Phys. 69, 2443(2006). 9.        Vizdrik. G., Ducharme. S., Fridkin. V. M. et al. Kinetics of ferroelectric switching in ultrathin films. Phys. Rev. B 68, 094113(2003). 10.        Fridkin. V., Levlev. A., Verkhovskaya. K. Switching in One Monolayer of the Ferroelectric Polymer, Ferroelectrics, 314:1, 37-40(2005). 11.         Khan. A., Chatterjee. K., Wang. B. et al. Negative capacitance in a ferroelectric capacitor.Nature Mater 14, 182–186 (2015). 12.         Hoffmann, M., Fengler, F.P.G., Herzig, M. et al. Unveiling the double-well energy landscape in a ferroelectric layer. Nature 565, 464–467 (2019). 13.        Yang. T. J., Gopalan. V., Swart. P. J. et al. Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall. Phys. Rev. Lett. 82, 4106 (1999). 14.        Shin, YH., Grinberg, I., Chen, IW. et al. Nucleation and growth mechanism of ferroelectric domain-wall motion. Nature 449, 881–884 (2007). 15.         Grigoriev. A., Do. D.H, Kim. D. M. et al. Nanosecond Domain Wall Dynamics in Ferroelectric Pb(Zr,Ti)O3 Thin Films. Phys. Rev. Lett. 96, 187601 (2006). 16.         Chang. S-C., Avci.U. E., Nikonov. D. E. Physical Origin of Transient Negative Capacitance in a Ferroelectric Capacitor. Phys. Rev. Applied 9, 014010 (2018). 17. Wang, W. et al. Room-temperature multiferroic hexagonal LuFeO3 films. Phys. Rev. Lett. 110, 237601 (2013).  18. Xu, X. & Wang, W. Multiferroic hexagonal ferrites (h-RFeO3, R = Y, Dy-Lu): a brief experimental review. Mod. Phys. Lett. B 28, 1430008 (2014).  10  19. Sinha, K. et al. Tuning the Neel Temperature of Hexagonal Ferrites by Structural Distortion. Phys. Rev. Lett. 121, 237203 (2018).  20. Yun, Y. et al. Spontaneous Polarization in an Ultrathin Improper-Ferroelectric/Dielectric Bilayer in a Capacitor Structure at Cryogenic Temperatures. Phys. Rev. Appl. 18 (2022).  21.         Li, X., Yun, Y., Thind, A.S. et al. Domain-wall magnetoelectric coupling in multiferroic hexagonal YbFeO3 films. Sci Rep 13, 1755 (2023).  22.         Li, X., Yun, Y., Xu, X. S. Improper ferroelectricity in ultrathin hexagonal ferrites films. Appl. Phys. Lett. 122, 182901 (2023)  23. Zhang. C. X., Yang. K. L., Jia. P. et al. Effects of temperature and electric field on order parameters in ferroelectric hexagonal manganites. J. Appl. Phys. 123, 094102 (2018). 24.        Ishibashi. Y., Takagi. Y.  Note on Ferroelectric Domain Switching. J. Phys. Soc. Jpn. 31, 506-510 (1971).  25.        Jo. J. Y., Yang. S. M., Kim. T. H. Nonlinear Dynamics of Domain-Wall Propagation in Epitaxial Ferroelectric Thin Films. Phys. Rev. Lett. 102, 045701 ( 2009).  26.        Song. T., Sánchez. F., Fina. I. Impact of non-ferroelectric phases on switching dynamics in epitaxial ferroelectric Hf0.5Zr0.5O2 films. APL Mater. 10, 031108 (2022). 27.        Tagantsev, A. K., Stolichnov, I., Setter, N., Cross, J. S. & Tsukada, M. Non-Kolmogorov-Avrami switching kinetics in ferroelectric thin films. Phys. Rev. B 66, 214109 (2002). 28.        Jo. J. Y., Han. H. S., Yoon. J.-G. Domain Switching Kinetics in Disordered Ferroelectric Thin Films. Phys. Rev. Lett. 99, 267602 (2007). 29.        Gruverman. A., Wu. D., and J. F. Scott. Piezoresponse Force Microscopy Studies of Switching Behavior of Ferroelectric Capacitors on a 100-ns Time Scale. Phys. Rev. Lett. 100, 097601(2008). 30. Kim. Y. J., Park. H. W., Hyun. S. D. et al. Voltage Drop in a Ferroelectric Single Layer Capacitor by Retarded Domain Nucleation. Nano Lett 17, 7796-7802(2017).  31. Hao. Y., Li. T., Yun. Y. et al. Tuning Negative Capacitance in PbZr0.2Ti0.8O 3/SrTiO3 Heterostructures via Layer Thickness Ratio. Phys. Rev. Applied 16, 034004(2021).      11    Fig. 1 (a) Schematics of double well potential and NC effect for homogeneous switching. (b). Time-dependent polarization and the region of transient NC for inhomogeneous switching. (c) Atomic structure of h-YbFeO3. The arrows indicate the displacement pattern of the K3 distortion mode. (d) The energy landscape of h-RFeO3 with (d) zero and (e) positive external field.   \n12    Fig. 2 (a) Theta-2theta XRD scan for h-YbFeO3/CFO/LSMO/STO (111) thin films, inset is a room-temperature RHEED pattern. (b) HADDF-STEM image of the h-YbFeO3 layer, viewed along the [100] zone axis.  (c) Amplitude and (d) phase of PFM measurements after applying +4.5 V and -10 V, with size 3.5 × 3.5 FG. (e) P-V and I-V hysteresis measured by the PUND method. (f) The time-dependent polarization switching and related fitting by the NLS and the KAI model, with data from Ref 20. Inset is the dependence of nucleation time t0 on the applied voltage.   \n13   Fig. 3 (a) Schematic diagram of experimental set up. (b) The time-dependent changes of voltage under the positive pulse and (c) with different load resistance values. (d) The Vpeak, Vdip, Vdrop and tdrop for the transient NC effect measured using different load resistance values. (e) The time-dependent changes of voltage under different magnitude of source voltage and (f) related Vpeak, Vdip, Vdrop and tdrop for the transient NC effect.   \n Fig. 4 (a) Schematic of the polarization switching path from -P to +P for improper ferroelectric h-RFeO3. Schematics of polarization-dependent ELK and related regions of NC effect for h-RFeO3  (b) and proper ferroelectrics (c).  \n14    Fig. 5 (a) Experimental and simulated time dependent of VFE during the whole source voltage pulse. (b) The time-dependent VS,VFE, Veff, and Vtotal near the time of transient NC. (c) The mismatch between the speed of charging and polarization switching at the interface. (d) The time-dependent voltages change and (e) speed mismatch of charging and polarization switching in region 2. (f) The comparison between experimental and theoretical calculated Q-V loops.     \n"    },    {        "title": "2402.14168v1.Discrete_slip_plane_analysis_of_ferrite_microtensile_tests__On_the_influence_of_dislocation_source_distribution_and_non_Schmid_effects_on_slip_system_activity.pdf",        "content": "Discrete slip plane analysis of ferrite microtensile tests: On the influence of\ndislocation source distribution and non-Schmid effects on slip system\nactivity.\nJ. Wijnen, J.P.M. Hoefnagels, M.G.D. Geers, R.H.J. Peerlings∗\nDepartment of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands\nAbstract\nThe slip system activity in microtensile tests of ferrite single crystals is compared with predic-\ntions made by the discrete slip plane model proposed by Wijnen et al. (International Journal of\nSolids and Structures 228, 111094, 2021). This is an extension of conventional crystal plasticity\nin which the stochastics and physics of dislocation sources are taken into account in a discrete\nslip band. This results in discrete slip traces and non-deterministic mechanical behavior, similar\nto what is observed in experiments. A detailed analysis of which slip systems are presumed to\nbe active in experiments is performed. In small-scale mechanical tests on BCC metals and alloys,\nnon-Schmid effects are often needed to explain the observed response. Therefore, these effects are\nincorporated into the model by extending a non-Schmid framework commonly used to model {110}\nslip to {112}planes. The slip activity in the simulations is compared to the slip activity in single\ncrystal ferrite microtensile tests. This is done for the discrete slip plane model with and without\nnon-Schmid effects, as well as for a conventional crystal plasticity model. The conventional crystal\nplasticity model fails to predict the diversity in active slip systems that is observed experimentally.\nThe slip activity obtained with the discrete slip plane model is in convincingly better agreement\nwith the experiments. Including non-Schmid effects only entails minor differences. This suggests\nthat stochastic effects dominate the behavior of ferrite crystals with dimensions in the order of a\nfew micrometers and that non-Schmid effects may not play a large role.\nKeywords: Crystal plasticity, Ferrite, Non-Schmid effects, Slip system activity\n1. Introduction\nFerrite ( α-Fe) is a common phase in many advanced high-strength steels. Improving these steel\ngrades requires accurate modeling of the underlying polycrystalline microstructure, for which a\ndetailed understanding of the plastic behavior of ferrite at the microscale is essential. Small-scale\nmechanical tests on single crystals, such as micropillar compression tests or microtensile tests, play\nan important role in unraveling the plastic behavior of metals and alloys and have been extensively\nused to study both Face-Centered-Cubic (FCC) and Body-Centered-Cubic (BCC) crystals [1, 2, 3],\nincluding ferrite. The BCC structure of ferrite does, however, lead to more intricate behavior\n∗Corresponding author\nEmail address: r.h.j.peerlings@tue.nl (R.H.J. Peerlings)\nPreprint submitted to Journal February 23, 2024arXiv:2402.14168v1  [cond-mat.mtrl-sci]  21 Feb 2024compared to FCC phases, such as austenite. Plasticity of BCC metals is governed by the glide of\nscrew dislocations, which have some remarkable properties due to their compact and non-planar\ncore [4, 5]. Plastic slip can occur on multiple slip plane families. While at low temperatures slip is\nmainly observed on {110}planes, slip on {112}planes is commonly observed at room temperature\n[6, 7, 8, 9]. Occasionally, even slip on {123}planes is observed [10]. Furthermore, BCC metals\ndisplay non-Schmid effects, which means that stress components other than the resolved shear\nstress on a particular slip system affect the activation of dislocation glide [11, 12]. Non-Schmid\neffects give rise to an orientation-dependent mechanical response in small-scale mechanical tests of\nsingle ferrite crystals [8, 13, 14]. Additionally, they can cause the activation of slip systems that\nare not among the most favorably oriented systems in the considered test [15].\nDifferent CP frameworks that are used to study the ferrite response in small-scale mechanical\ntests incorporate non-Schmid effects [16, 17, 18]. However, large variations in slip system activity\nand stress-strain curves are often observed in small-scale mechanical tests of ferrite single crystals\n[10, 19], which can be attributed to the scarcity of dislocation sources in such small volumes\n[20, 21, 22]. This makes it difficult to determine whether slip on a secondary slip system is due to\nnon-Schmid effects or due to the absence of an easily activated dislocation source on the primary\nslip system. Conventional CP models do not account for these stochastic effects of the dislocation\nsources. Furthermore, CP simulations result in strain fields that are much more homogeneous and\nsmooth than the heterogeneous plasticity and localized slip traces observed in experiments.\nIn this study, the discrete slip plane (DSP) model, introduced by Wijnen et al. [23], is adopted\nto analyze the slip system activity in microtensile tests on ferrite single crystals, performed by Du\net al. [19]. This model accounts for the heterogeneity in plastic deformation due to variations in slip\nresistances between atomic planes. To determine the slip resistance of atomic planes, dislocation\nsources are randomly distributed throughout the sample. The strength of these dislocation sources\nis sampled from a statistical distribution that is based on the physics of dislocation sources in\nsamples with confined dimensions. Since both the spatial and strength distribution of dislocation\nsources are taken into account, this results in non-deterministic heterogeneous plastic flow within a\nsingle crystal. By making some assumptions, the model can be formulated as an enriched continuum\ncrystal plasticity model, which significantly reduces the computational cost and makes it suitable\nfor full-scale simulations of micron-sized mechanical tests.\nAs part of this work, additional analyses on the slip system activity in the experiments of Du\net al. [19] have been carried out. The qualitative characterization of visible slip traces is extended\nto quantify the amount of slip on the various active slip systems. This allows for a quantitative\ncomparison between the slip system activity in the experiments and the CP model calibrated as\nidentified [19]. Additionally, the results are here compared to the slip system activity in the DSP\nsimulations. Three different parameter sets are used for the DSP simulations. One parameter\nset only includes Schmid-based glide, while the other two parameter sets include non-Schmid\neffects through parameters that are identified from experiments [24] or atomistic simulations [25].\nFollowing this approach, the influences of both the stochastic effects and the non-Schmid effects,\nand their relative importance, are studied.\nNon-Schmid effects can be taken into account in crystal plasticity (CP) simulations through\nextra stress projection tensors. A physically based formulation for {110}⟨111⟩slip systems, in-\nspired by atomistic simulations, was introduced by Groger and Vitek [26]. This formulation makes\nuse of a secondary projection plane, similar to the works of Qin and Bassani [27, 28], and contains\nthree non-Schmid projection terms. A benefit of the three-term formulation is that it is relatively\n2straightforward to characterize from atomistic simulations [26, 29, 25]. Additionally, it was re-\ncently shown that the three-term formulation maybe recovered from ab-initio calculations, which\nallows for a physical interpretation of the parameters [30, 31]. The 5-term non-Schmid formulation,\nintroduced by Asaro and coworkers [32, 33, 34], is also adopted in several studies [35, 36, 37]. This\nformulation is often referred to as purely phenomenological and more general. However, Gr¨ oger and\nVitek [38] recently showed that the extra terms in this formulation arise because of the unfortunate\nchoice of the auxiliary projection plane and that both formulations are actually equivalent. There-\nfore, the three-term formulation will be incorporated into the DSP model. However, the original\nthree-term formulation is only defined for {110}⟨111⟩slip systems, while slip on {112}⟨111⟩slip\nsystems is frequently observed in the analyzed experiments. Therefore, the three-term formulation\nis extended to {112}⟨111⟩slip systems. This is done based on the assumption of composite slip\n[39].\nThe structure of this paper is as follows. In Section 2 the experiments done by Du et al. [19]\nare briefly summarized, as is the procedure for accurately analyzing the slip system activity. The\nnumerical model is presented in Section 3. This includes a review of the most important aspects\nof the DSP model presented in Wijnen et al. [23] and the extension of the three-term non-Schmid\nformulation to {112}⟨111⟩slip systems. Additionally, the distribution used for the stochastics of\ndislocation sources and the adopted simulation parameters are discussed. In Section 4 the results\nof the experimental and numerical analysis are presented and discussed. Finally, the conclusions\nare summarized in Section 5.\nNomenclature\na scalar\n⃗ a vector\nA second-order tensor\nA fourth-order tensor\nC=⃗ a⊗⃗b dyadic product\nC=A·B single tensor contraction\nc=A:B=AijBji double tensor contraction\n⃗ c=⃗ a×⃗b cross product\n2. Analysis of the experimental data\n2.1. Sample characterization\nThe uniaxial microtensile tests on interstitial free ferrite performed by Du et al. [19] are analyzed\nin more detail here, to facilitate an in-depth comparison with predictions made by the modeling.\nThe length of the gauge section of these specimens is 9 µm. The cross section is rectangular\nwith dimensions 3 ×2µm. The dislocation density of the specimen has been measured to be\napproximately 7 ·1011m−2.\nA total of thirteen specimens were cut from three different grains with different crystal orien-\ntations. The Euler angles of the three grains are given in Table A.2 in Appendix A. In Figure 1\nthe slip directions together with the {110}and{112}plane normals of the grains are plotted in a\npole figure, where the projection plane normal is equal to the loading direction ( x-axis). The four\nslip directions (marked by circles) are denoted by the characters A,B,C, and D. A slip direction\n3Figure 1: Polar plots of the ⟨111⟩slip directions, {110}plane normals and {112}plane normals of all three grains.\nThe projection plane normal is parallel to the loading direction ( x-axis). The slip directions (circles) are denoted\nby characters Athrough D, based on their deviation from the circle that makes a 45◦angle with the loading axis,\nmarked with a green line in the polar plots. Additionally, the deviation from the 45◦circle for the slip directions is\ngiven in degrees. All slip plane normals belonging to the same slip direction are marked with the same color.\nthat makes an angle of 45◦with the loading axis would be ideal for slip, since a slip system with\nthis slip direction may have a Schmid factor of 0.5. Therefore, the slip directions are ordered\nbased on how close their orientation is to 45◦(marked with a green circle in the polar plots). In\nall three grains, the primary slip system has a slip direction A. For Grain 1, all five microtensile\ntests were analyzed, while all four tests are analyzed for both Grains 2 and 3. A more detailed\ndescription of the experiments, e.g. regarding sample preparation, nanoforce tensile testing, and\nscanning electron microscopy (SEM) imaging, can be found in Du et al. [40, 19].\n2.2. Analysis of slip system activity\nA detailed slip system analysis was performed on the samples. Secondary electron images of\nfour different viewpoints were used to identify slip traces as well as the underlying slip systems.\nThese images show the front/right, front/left, back/right, and back/left surfaces of the samples.\nAn example is shown in Figure 2, where the front/right (Figure 2a) and back/left (Figure 2b)\nimages of a sample taken from Grain 1 are shown. Images of other samples show similar slip\n4(a)\n (b)Figure 2: Two SEM images of a sample from Grain 1. (a) shows the front and right side of the sample while (b)\nshows the back and left side of the sample. The identified traces are marked with colors, with a separate color for\neach slip system.\npatterns.\nThe orientations of the slip traces were measured and compared to the theoretical traces of the\navailable slip systems. Note that most slip traces are visible on all faces of the sample. However,\na single trace cannot always be assigned to a single slip system. Even on one side of the sample, a\ntrace sometimes has two parts that differ in orientation, for example, the ( ¯110)[ ¯1¯11]-(¯21¯1)[¯1¯11] slip\ntrace in Figure 2 (respectively the blue and brown dotted lines). This is an indication of cross slip.\nNevertheless, a complete slip trace can always be assigned to a specific slip direction, since screw\ndislocations only change their slip plane when cross slipping while their slip direction is maintained.\nThis means that all parts of a complete slip trace are assigned to slip systems with a common slip\ndirection. In this way, the slip direction of a trace was determined with high certainty. However,\noccasionally the orientation of part of a slip trace was still close to the theoretical slip trace of two\ncandidate slip systems.\nConsider again the ( ¯110)[ ¯1¯11]-(¯21¯1)[¯1¯11] slip trace in Figure 2 (respectively the blue and brown\ndotted lines). Different segments of this trace were assigned to either the ( ¯110) plane or the ( ¯21¯1)\nplane, but all parts have a common [ ¯1¯11] slip direction, i.e. slip direction A. Furthermore, a slip trace\nof which segments were assigned to the (31 ¯2) plane is visible (yellow dotted line). Occasionally,\na{123}⟨111⟩slip system was required to identify a complete trace with the same slip direction.\nHowever, {123}slip appeared to be significantly less frequent than {110}and{112}slip. For this\nreason, and due to the lack of knowledge on non-Schmid effects for {123}slip, only the {110}⟨111⟩\nand{112}⟨111⟩slip systems were taken into account in the simulations.\nThe identified slip traces in the SEM images and the fractional assignment of the slip steps to\n5Figure 3: SEM image of a slip step on the back side of a sample. The horizontal length of the slip step in the image\nis determined to be 0.14 µm.\nthe active slip systems are presented in the supplementary material for all 13 specimens (5 of grain\n1, 4 of grain 2, 4 of grain 3).\nThe amount of slip that has occurred on a particular slip system was determined by using\nimages of the front and/or back of the sample. In Figure 3 the slip step created by the trace of\nslip direction Cin Figure 2, as observed on the back side of the sample, is shown. The horizontal\nlength of this slip step was measured to be 0.14 µm. By projecting the horizontal slip step onto\nthe slip direction of this trace, the total slip step was calculated to be 0.17 µm. This was done for\nall clearly visible slip traces in a sample. The normalized slip magnitude in a certain slip direction\nwas then calculated by adding up the measured slip steps of traces with a common slip direction\nand dividing it by the total slip of all traces measured in this way. For example, the normalized\nslip magnitudes of the sample shown in Figure 2 are A= 0.51,B= 0.18, and C= 0.31. These\nnormalized slip magnitudes can be calculated either per sample or per grain.\nTo quantitatively determine the slip activity on specific slip systems, the measured slip steps for\ndifferent slip directions were subdivided. This was done based on the length of the visible traces.\nThe slip trace of slip direction Cin Figure 2 is considered as an example. Two full sides of this\nslip trace were assigned to the (21 ¯1)[1¯11] and the (31 ¯2)[1¯11] slip systems. Therefore, the amount\nof slip assigned to these slip systems was half of the total measured slip step of slip trace C, i.e.\n0.085 µm.\nThe analysis and data of all samples is provided in the supplementary material.\n3. Discrete slip plane model\n3.1. Model equations\nThe most relevant equations of the discrete slip plane model are explained below. For a more\ndetailed treatment of the model, the reader is referred to [23].\nIn its basic form, the model considers all atomic slip planes of a specific slip system. The initial\nslip resistance, s0, of a plane is given by\ns0=snuc+sfric+ 0.5Gb√ρdis, (1)\nwhere snucis the nucleation stress, sfricis the lattice friction, Gis the shear modulus, bis the length\nof the Burgers vector and ρdisis the initial dislocation density. The nucleation stress is assumed\nto vary significantly per atomic slip plane due to the presence, or absence, of dislocation sources\n6or obstacles. Therefore, its value for each plane is sampled from a probability density function\np(snuc). This results in a heterogeneous flow stress in a single crystal. The probability density\nfunction for the nucleation stress is based on the physics of single-arm dislocation sources, as the\nplasticity in small specimens is mainly governed by single-arm dislocation sources, as motivated\nand elaborated in Section 3.5.\nResolving each individual atomic slip plane in simulations is computationally prohibitive.\nTherefore, in the finite element implementation, the discrete planes are grouped into parallel bands\nof thickness l, which typically is much larger than the atomic spacing. This is done for all slip\nsystems. The slip resistance of a band is then taken equal to the slip resistance of the weakest\natomic plane contained in that band, i.e. the atomic plane with the lowest slip resistance. This\nessentially results in a crystal plasticity model in which some of the heterogeneity of the (dislo-\ncated) crystal, and its response, is preserved. The numerical solution procedure is consistent with\na standard crystal plasticity finite element (CPFE) framework and requires finite elements which\nare sufficiently small to resolve the slip system bands - typically l/2.\nThe plastic deformation is accounted for through the multiplicative split of the deformation\ngradient tensor into an elastic part, Fe, and a plastic part, Fp:\nF=Fe·Fp. (2)\nThe elastic response of the material is modeled with a Saint Venant-Kirchhoff type of model:\nSe=1\n2C: (FT\ne·Fe−I), (3)\nwhere Cis the fourth-order elasticity tensor.\nThe kinetics of a certain slip system αis described by a rate-dependent viscoplastic formulation:\n˙γα=˙v0\nl\u0012|τα|\nsα−τα\nNS\u00131\nr\nsign(τα), (4)\nwhere ˙ γαis the average shear strain rate in the band resulting from the slip system activity, ˙ v0\nis a reference slip velocity, ris a rate sensitivity parameter and lis the thickness of a band. The\nresolved shear stress, τα, in the stress-free intermediate configuration can be calculated by\nτα=\u0000\nSe·FT\ne·Fe\u0001\n:Pα\n0, (5)\nwhere Seis the second Piola-Kirchhoff stress tensor defined in the stress-free intermediate config-\nuration. The Schmid tensor, Pα\n0, is given by\nPα\n0=⃗ sα\n0⊗⃗ nα\n0, (6)\nwhere ⃗ s0and⃗ n0are the slip direction and slip plane normal in the undeformed (or intermediate)\nconfiguration, respectively. Additionally, a non-Schmid stress τNSis introduced in Equation (4)\nwhich is not present in the original formulation of the model. This non-Schmid stress is elaborated\nin Section 3.2.\nThe crystallographic decomposition defines the plastic velocity gradient tensor as the following\nsummation over all slip systems:\nLp=˙Fp·F−1\np=NX\nα=1˙γα⃗ sα\n0⊗⃗ nα\n0, (7)\n7where Nis the number of slip systems taken into account. Finally, the evolution of the slip\nresistance of a slip system is given by\n˙sα=k0l\u0012\n1−sα\ns∞\u0013aNX\nβ=1qαβ|˙γβ|, (8)\nwhere k0is the initial hardening rate, s∞is the saturation slip resistance, ais the hardening\nexponent and qis the cross-hardening matrix, where αandβare used to denote a particular slip\nsystem.\n3.2. Modeling Non-Schmid effects on {110}⟨111⟩slip systems\nNon-Schmid effects can be taken into account in a continuum setting by introducing extra stress\nprojection tensors [33, 27, 41]. By collecting multiple non-Schmid projection tensors in a single\ntensor Pα\nNS, the contribution of non-Schmid effects to plastic slip on a slip system can be written\nas\nτα\nNS=\u0000\nSe·FT\ne·Fe\u0001\n:Pα\nNS (9)\nThe non-Schmid stress, τα\nNS, affects the resistance to plastic slip, i.e. the glide stress that is required\nto initiate the motion of dislocations. It is hence introduced in the denominator of Equation (4)\nsuch that it reduces the effective slip resistance, following the approach of Mapar et al. [17].\nThe formulation with three non-Schmid projection terms by G¨ oger et al. [26] is adopted here.\nThe non-Schmid projection tensor of a {110}[111] slip system in this formulation is given by\nPα\nNS=a1⃗ sα\n0⊗⃗ n′α\n0+a2(⃗ nα\n0×⃗ sα\n0)⊗⃗ nα\n0+a3\u0000\n⃗ n′α\n0×⃗ sα\n0\u0001\n⊗⃗ n′α\n0, (10)\nwhere a1,a2anda3are material parameters, ⃗ sα\n0is the slip direction, ⃗ nα\n0is the slip plane normal\nand⃗ n′α\n0is the normal of a secondary projection plane which is obtained by rotating the slip plane\nnormal over an angle of −60◦around the slip direction.\nThe first term in Equation (10), multiplied by material parameter a1, is modeling the twinning/anti-\ntwinning (T/AT) behavior. Initially, T/AT effects were believed to arise due to the asymmetry of\nthe generalized stacking fault energy surface of {112}planes along the ⟨111⟩directions [11, 5]. This\nmakes shearing along the positive (twinning) [111] direction of a {112}plane easier than shear-\ning along the negative (anti-twinning) [111] direction. However, more recent ab-initio calculations\nlink the T/AT behavior to the deviation of the screw dislocation trajectory from a straight path\nbetween equilibrium positions on {110}planes [42]. In this case, parameter a1gets a physical\ninterpretation and can be connected to the angle of deviation from the straight path.\nThe other two non-Schmid coefficients, a2anda3, are modeling the effect of non-glide stresses\non the screw dislocation core. These stresses do not contribute to the Peach-Koehler force on\nthe dislocation but do affect the stress required to activate dislocation glide. An extension of\nthe ab-initio modeling methodology used to investigate the T/AT effects shows that the effect of\nnon-glide stresses can be explained by the anisotropic variation of the dilatation of a gliding screw\ndislocation and its elastic coupling to the applied stress [30]. The stresses related to parameters\na2anda3are resolved shear stresses on a plane that contains the slip direction but in a direction\nperpendicular to the slip direction. The vectors ⃗ s0,⃗ n0and⃗ n′0of the {110}[111] slip systems are\ngiven in Table A.3 in Appendix A. Note that a different secondary projection plane should be\nused for positive slip than for negative slip on a slip system, i.e. ⃗ n′0depends on the sign of τα.\nAdditionally, note that the use of Equation (10) is limited to {110}⟨111⟩slip systems since the\nsecondary projection planes with normals ⃗ n′0are only defined for {110}planes.\n8Figure 4: Sketch of composite zig-zag slip on a {112}slip plane. Alternating slip steps of a screw dislocation on the\n(01¯1) and ( ¯101) planes result in an apparent slip on the ( ¯1¯12) plane. The direction of the Burgers vector of the screw\ndislocation is [111], which is pointing out of the plane of the sketch.\n3.3. Modeling Non-Schmid effects on {112}⟨111⟩slip systems\nThe framework described in the previous section has been used to model non-Schmid effects\non{110}⟨111⟩slip systems in various BCC metals. Slip systems of the {112}⟨111⟩family are\nusually not considered. One of the primary reasons for this is that molecular dynamics simulations\n(with interatomic potentials that result in non-degenerate or compact screw dislocation cores,\nwhich is assumed to be the correct core structure based on more accurate ab-initio calculations\n[5, 43, 31]) only display slip on {110}planes. However, slip on {112}planes is frequently observed\nin experiments, especially for ferrite.\nThe precise mechanism behind slip on the {112}⟨111⟩family is poorly understood. Interest-\ningly, in early molecular dynamics (MD) simulations with potentials resulting in degenerate screw\ndislocation cores, slip was observed on {112}planes only [44, 45, 46]. This degenerate core has\ntwo variants due to asymmetry, entailing zig-zag slip. One variant only propagates on a specific\n{110}plane by kink pair nucleation. After an elementary step, the core structure switches to the\nother variant. This variant only propagates on another {110}plane with the same Burgers vector.\nThe resulting composed slip plane of these alternating elementary steps is a {112}plane with that\nsame Burgers vector. This is schematically shown in Figure 4, where a screw dislocation with a\n⟨111⟩Burgers vector, pointing out of the plane of the sketch, is depicted. By alternating slip steps\nof the same size on the (01 ¯1) and ( ¯101) planes, the apparent slip plane becomes ( ¯1¯12).\nThe hypothesis that slip on {112}⟨111⟩slip systems consists of zig-zag slip on two {110}⟨111⟩\nslip systems is also made in earlier literature [47, 48, 4]. More recently, Marichal et al. [39]\ninvestigated slip planes in Tungsten single crystal compression tests with in-situ Laue diffraction\nand confirmed that slip on apparent {112}planes can be described as composed zig-zag slip of\nelementary steps on {110}planes, as long as both {110}planes are equally stressed.\nThe hypothesis of composite slip is adopted here. In that case, every slip plane of the {112}⟨111⟩\nfamily can be written as a combination of two slip planes of the {110}⟨111⟩family. For example:\n(¯1¯12) = ( ¯101)−(01¯1). (11)\nInstead of calculating the Schmid tensor of, for instance, the ( ¯1¯12) [111] system through Equa-\ntion (6), it is now written as a combination of the Schmid tensors of the (01 ¯1) [111] and ( ¯101) [111]\nslip systems:\nP(¯1¯12)\n0=c\u0010\nP(¯101)\n0−P(01¯1)\n0\u0011\n, (12)\n9where cis the composite slip factor. When a value of 1 /√\n3 is adopted for c, the obtained Schmid\ntensor is equal to the one obtained by Equation (6), which means that slip due to pure glide\nstresses will occur just as easily on {112}planes as on {110}planes if both slip plane families have\nthe same slip resistance. Slip on {112}planes becomes more difficult for a lower value of cand\nless difficult for a higher value of c. Here, the value of 1 /√\n3 is adopted since this corresponds\nwith the conventional way of modeling slip on {112}⟨111⟩slip systems through Equation (6).\nThe combinations of {110}⟨111⟩slip systems which result in {112}⟨111⟩slip systems are given in\nTable A.4 in Appendix A.\nAdopting a similar approach allows for the calculation of the non-Schmid projection tensors of\nthe{112}⟨111⟩slip systems. For the ( ¯1¯12)⟨111⟩slip system the non-Schmid tensor becomes\nP(¯1¯12)\nNS=c\u0010\nP(¯101)\nNS−P(01¯1)\nNS\u0011\n. (13)\n3.4. The effect of non-Schmid stresses on dislocation glide\nTo demonstrate the effect of non-Schmid stresses on screw dislocation mobility, the straight\n[111] screw dislocation depicted in Figure 5a is considered. The Burgers vector points out of the\nplane of the sketch. A shear stress τ∗is applied on a plane containing the dislocation in a direction\nparallel to the dislocation line. This plane is termed the maximum resolved shear stress plane\n(MRSSP) in the remainder of this section. The direction of this shear stress is parallel to the\nBurgers vector, i.e. also pointing out of the figure. The MRSSP is rotated with an angle χwith\nrespect to the (101) plane. The ratio τ∗/sat yield is plotted for all {110}⟨111⟩and{112}⟨111⟩slip\nsystems as a function of χin Figure 5b, i.e. the lines indicate the values where τ∗/(s−τNS) = 1,\nwhich marks the activation of slip systems. The lower envelope of these curves may be regarded\nas a yield surface for this particular applied shear stress and the lowest curve for a given angle χ\nindicates which system is activated first at that angle - and at which level of stress. The dotted\nlines represent the case where only Schmid stresses are considered ( a1=a2=a3= 0). Here, the\nminimum value of τ∗/sis equal to 1 for each slip system. Moreover, the location of this minimum\nalways corresponds to the angle, χ, for which the MRSPP coincides with the slip plane of that\nparticular slip system.\nThe solid lines represent the {110}⟨111⟩slip systems where T/AT effects are taken into account\nbut omitting the effects of non-glide stresses ( a1= 0.2,a2=a3= 0). Here, the minimum value of\nτ∗/sis no longer located at the value of χat which the MRSSP is coinciding with the slip plane.\nInstead, the minimum shifts towards a {112}twinning plane.\nThe dashed lines represent the {112}⟨111⟩slip systems with only T/AT effects taken into\naccount. Here, the location of the minimum of τ∗/sis still located at the value of χwhere\nthe MRSSP is coinciding with the slip plane. However, there is a significant difference between\nthe minimum value of {112}twinning directions and anti-twinning directions, i.e. slip occurs much\neasier in twinning directions. Furthermore, a rotation of 180◦of the MRSSP, equivalent to changing\nthe sign of τ∗, changes {112}twinning directions to anti-twinning directions and vice versa. This\nT/AT behavior of {112}⟨111⟩slip systems corresponds to what usually is observed in experiments,\nwhich justifies the extension of the three-term non-Schmid formulation to {112}⟨111⟩slip systems\nthrough Equation (13) for T/AT effects.\nThe effect of the non-glide stresses cannot be demonstrated by only applying the shear stress,\nτ∗, to the MRSSP. Instead, an additional shear stress perpendicular to τ∗should be applied to\nthe MRSSP. When a constant value is taken for this perpendicular shear stress and one of the\nnon-glide stresses is taken into account, the result is similar to that of Figure 5b: slip on half of\n10(0̄1̄1)\n(101)\n(̄110)\n(1̄2̄1) T(112) T\n(̄21̄1) ATχ\nMRSSP(a)\n−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180\nχ  [∘]0.60.70.80.91.01.11.21.31.4τ*/ s  [-]\nT AT T AT T AT(0̄1̄1)\n(112)(101)\n(̄21̄1)(̄110)\n(1̄2̄1) (b)Figure 5: (a) Schematic of a [111] screw dislocation with {110}and{112}slip planes. A shear stress is applied\nover the MRSSP, which is defined by its angle, χ, with respect to the (101) plane. (b) The ratio between the shear\nstress applied to the MRSSP, τ∗, and the slip resistance, s, for the case where τ∗/(s−τNS) = 1, as a function of the\nMRSSP angle χ. The dislocation considered is a [111] screw dislocation. Twinning effects are taken into account by\nsetting a1= 0.2. The dotted lines represent the case where only Schmid glide is considered ( a1= 0).\nthe{112}planes becomes easier and the minima of the {110}planes shift towards the easier {112}\nplanes.\n3.5. Nucleation stress stochastics\nThe stress required to nucleate new dislocations, snuc, varies significantly between atomic planes.\nOn planes containing a dislocation source, the nucleation stress is relatively low. Contrarily, on\nplanes that do not contain a source, dislocations have to be nucleated from the free surface, which\nresults in a much higher nucleation stress. Therefore, the probability density function from which\nthe nucleation stresses of the planes are sampled consists of two contributions, as explained in\ndetail in [23]:\np(snuc) =fsrcg+(snuc) + (1 −fsrc)g−(snuc), (14)\nwhere g+(snuc) is the probability density function associated with planes that contain a dislocation\nsource, and g−(snuc) for those without a source, fsrcis the probability that a plane contains a\ndislocation source, which can be estimated by\nfsrc=ρsrcAd, (15)\nwith Athe area of a lattice plane in the sample, dthe lattice spacing and ρsrcthe dislocation source\ndensity.\nBecause the mechanical behavior of the samples considered in our study is dominated by a few\ndislocation sources, the choice of g−(snuc) generally has a negligible effect. Therefore, a narrow\nnormal distribution around the theoretical strength is adopted (see [23]). On the contrary, the\nchoice for g+(snuc) in Equation (14) is important. It has been shown that the single-arm (SA)\ndislocation source model introduced by Parthasarathy et al. [20] is capable of predicting the size-\ndependent strength of micropillars of both FCC [21, 49, 50, 23] and BCC [51, 52, 53] metals and\n11alloys. The model assumes that dislocation sources in such small samples are dislocations that are\npinned at one end, while the other end is connected to the free surface. When a stress is applied,\nthis dislocation spins around its pinning point, resulting in plastic slip on its slip plane. The stress\nrequired to operate a SA source is inversely related to the shortest distance to the free surface,\nλ, since this configuration results in the largest curvature and, consequently, line tension of the\ndislocation [54].\nIn the single-arm source model, every dislocation segment can act as a possible dislocation\nsource. Therefore, following Parthasarathy et al. [20] and later studies [21, 52], the source density,\nρsrc, in Equation (15) can be estimated from the initial dislocation density, ρdis, by\nρsrc=ρdis\nNLseg, (16)\nwhere Nis the number of slip systems and Lsegis the average length of dislocation segments in\nthe specimen, taken as the sample radius.\nThe probability density function of the shortest distance to the free surface, λfor a pinning\npoint with uniform position distribution, has previously been formulated for ellipsoidal-shaped\nplanes in cylindrical specimens [20]. However, this study considers samples with a cuboid-shaped\ngauge section. A slip plane in these cuboid specimens has the shape of a parallelogram. Examples\nof such parallelograms in a cuboid geometry with dimensions Ly= 3 µm and Lz= 2 µm are\ndepicted in Figure 6a. Four different slip planes with different normal vectors are shown. Using\ngeometrical considerations, the probability density function of λfor uniformly distributed pinning\npoints for these planes is derived as\ng+(λ) =2CA\nCB−8λ\nCBCC, (17)\nwith\nCA=Lys\u0012ny\nnx\u00132\n+ 1 + Lzs\u0012nz\nnx\u00132\n+ 1, (18)\nCB=LyLzs\u0012ny\nnx\u00132\n+\u0012nz\nnx\u00132\n+ 1 (19)\nand\nCC=s\n1−n2yn2z\u0000\nn2x+n2y\u0001\n(n2x+n2z), (20)\nwhere LyandLzare the edge lengths of the specimen in the y−andz−direction, i.e. Ly= 3µm\nandLz= 2µm in the tested samples, and nx,nyandnzare the components of the slip plane\nnormal ⃗ n0with unit length. Note that the above formulation assumes that the x-axis is aligned\nwith the central axis of the specimen.\nIn Figure 6b, the distributions for snucbased on Equation (17) are plotted for slip planes with\nnormal vectors (110), (101) and (√\n211). All three normal vectors represent an area at an angle of\n45◦with respect to the central x-axis (i.e. the [100]-loading direction). However, the angle over\nwhich they are rotated around the x-axis is different. This results in differently shaped slip planes\n(Figure 6a), and hence in different distributions, as can be seen in Figure 6b.\n12(a)\n0 5 10 15 20 25 30 35 40\nsnuc [MPa]0.000.010.020.030.040.050.06g+(snuc) [-]cuboid (110)\ncuboid (101)\ncuboid (√211) (b)Figure 6: (a) Parallelogram-shaped slip planes in a cuboid sample. The black solid shape has a normal vector equal\nto (100), i.e. it is aligned with the loading direction. The normal vectors of the other three planes shown are all at an\nangle of 45◦with the loading axis. (b) Probability density functions of the nucleation stress for the three differently\noriented slip planes in (a).\n4. Simulation results\nIn this section, the numerical and experimental results are compared. To make a complete\ncomparison, results obtained with a conventional CP FE model are also included. This model and\nits parameters are adopted from the original study by Du et al. [19].\nIn the DSP model, a bandwidth of l= 0.8µm is adopted, which is determined through a\nrefinement study similar to that proposed in Wijnen et al. [23]. The gauge section of the sample is\ndiscretized by 3456 quadratic hexahedral elements with 20 nodes and a reduced Gaussian quadra-\nture scheme with 8 quadrature points. A constant displacement is applied to both ends of the\nsample. Furthermore, the lateral displacement ( y/z-directions) is constrained at both ends, since\nin the experiment the deformation of the specimen ends is constrained due to the specimen shape\n[19]. This means that all three degrees of freedom are fully prescribed on the top and bottom\nfaces. In earlier studies, these lateral boundary conditions were found to influence the slip activity\n[19, 23].\nThe initial slip resistances in the DSP model are determined by Equation (1), where sfric,\nG, and bare known material parameters which are adopted from literature, while the initial\ndislocation density, ρdis, of the samples has been measured to be 7 ·1011m−2[19]. The nucleation\nstress, snucis sampled from the distribution p(snuc). All the identified simulation parameters are\ngiven in Table A.5. The hardening parameters in Equation (8) are identified from the stress-\nstrain curves of the ferrite microtensile tests, such that the median curves of the experiments and\nsimulations adequately match. In Figure 7 the experimental stress-strain curves are plotted for\nGrain 1 (Figure 7a) and Grain 2 (Figure 7b) as solid orange lines. The median curve of 100\nstress-strain curves obtained with the DSP model is shown as the solid blue line in Figure 7, while\nthe 25%-75% and 2%-98% percentiles are depicted as, respectively, the dark-blue and bright-blue\n130.00 0.02 0.04 0.06 0.08 0.10\nEng. Strain [-]050100150200250Eng. Stress [MPa]Experiments\nSim. median\nSim. P25%−P75%\nSim. P2%−P98%(a)\n0.00 0.02 0.04 0.06 0.08\nEng. Strain [-]050100150200250Eng. Stress [MPa]Experiments\nSim. median\nSim. P25%−P75%\nSim. P2%−P98% (b)Figure 7: Experimental and numerical stress and strain curves for (a) grain 1 and (b) grain 2. The numerical stress-\nstrain curves are represented by their median, 25%-75% percentile, and 2%-98% percentile.\nshaded areas. In the hardening regime, all experimental curves are distributed around the numerical\nmedian, and mostly in between the 2%-98% percentiles. Only one curve of Grain 2 has a part that\ndeviates significantly from the numerical stress-strain curves due to a large plateau. The degree\nof scatter between numerical stress-strain curves is mainly determined by fsrc(Equation (15)),\nwhich depends only on physical parameters such as the dislocation density. Adopting a dislocation\ndensity one order higher or lower than the measured value would give, respectively, too little or\ntoo much scatter.\nThe deformation and total accumulated slip contours obtained with the conventional CP model\nfor Grain 1 are shown in Figure 8a. The deformation is smeared out over most of the gauge section,\ncontrary to what is experimentally observed (e.g. Figure 2). Close to the boundaries at the top\nand bottom, passive regions are observed. These regions are the result of the applied boundary\nconditions, which prohibit deformation of top and bottom surfaces.\nDue to the non-deterministic nature of the DSP model, directly comparing a single simulation\nwith a single experiment is not meaningful. Therefore, 100 simulations were done for each grain.\nThis enables a statistical analysis of the simulation data. The deformation of five random real-\nizations simulated with the DSP model is depicted in Figures 8b to 8f. Multiple localizations of\ndifferent slip systems can be noticed, making the deformation of the samples qualitatively similar\nto the experimental sample of Figure 2, in the sense that localized discrete slip events are captured.\nRealizations 3, 4, and 5 (Figures 8d to 8f, respectively) reveal a single dominant localization band.\nHowever, these bands are the result of slip on three different slip systems, which are the ( ¯2¯1¯1)[¯111],\n(¯110)[ ¯1¯11] and (110)[ ¯111] systems for realizations 3, 4, and 5, respectively. In contrast, realizations\n1 and 2 (Figures 8b and 8c, respectively) reveal multiple localization bands of similar magnitude.\nTo study the influence of non-Schmid effects on the slip activity in the microtensile tests of\n14Figure 8: Deformed specimens and total accumulated slip contours for (a) the CP model and (b-f) five random\nrealizations of the DSP model for Grain 1.\n15ferrite, simulations with three different sets of non-Schmid parameters have been performed. In the\nfirst parameter set, non-Schmid effects are not taken into account ( a1=a2=a3= 0). In this way,\nslip is only dependent on the resolved shear stress on the slip plane, in the slip direction, similar\nto conventional CP models. The second parameter set, which does contain (non-zero) non-Schmid\nparameters, is adopted from Patra et al. [24], who studied the temperature dependence of the\nnon-Schmid parameters for ferrite, based on experiments performed by Spitzeg & Keh [8]. Their\nparameters obtained at room temperature are adopted here: a1= 0.0363, a2= 0.1601, a3= 0.3243.\nNote that these parameters are nearly equal to those found by Mapar et al. [17] in experiments\non ferrite samples extracted from dual-phase steel. Furthermore, parameter a1, responsible for\nthe T/AT effect, is approximately zero. This is in agreement with the ab-initio calculations of\nDezerald et al. [42], who found that the T/AT effect in ferrite is negligible. The third parameter\nset is adopted from Chen et al. [25] ( a1= 0.4577, a2= 0.1454, a3= 0.5645). These parameters\nwere identified from atomistic simulations with a magnetic bond-order potential. Contrary to the\nsecond set of parameters, the T/AT effect is prominent here.\n4.1. Quantitative slip analysis in different slip directions\nAt a more quantitative level, first, the slip activity in the different slip directions is considered,\nwithout distinguishing the individual slip systems, because the slip activity in the slip directions\ncan be determined with relatively high certainty, as explained in Section 2.2. The normalized slip\nmagnitudes in the slip direction are determined per grain and the results of the experiments and\nthe simulations are compared.\nFirst, the results obtained with the conventional CP model are considered, which are shown\nin Figure 9a. Here, the calculated normalized slip magnitudes calculated in the simulations are\nplotted against the normalized slip magnitudes in the experiments. A perfect match between the\nexperimental and numerical slip magnitudes implies that all data points would lie on the dashed\nline with slope 1. Clearly, the normalized slip magnitudes obtained with the conventional CP model\ndo not agree well with the experimental observations. The mean squared error (MSE) of the data\npoints with respect to the slope 1 line is 0.139. In the CP simulations slip direction Ais dominant\nin all grains (i.e. slip fraction close to unity), while the experimental slip magnitudes for this slip\ndirection are much lower. This already shows that the conventional CP model is not capable\nof predicting the global slip system activity in these small scale specimens. The conventional\nCP model predicts that almost all slip takes place on the primary slip system. Some activity\non secondary slip systems is observed due to boundary constraints, which was also demonstrated\nby Du et al. [19]. However, the amount of slip on the secondary slip systems observed in the\nexperiments is significantly higher.\nThe results for the DSP model using parameter set 1 are compared with the experimental results\nin Figure 9b. The experimental and numerical normalized slip magnitudes of Grain 1 (blue data\npoints) and Grain 2 (orange data points) match almost perfectly. However, a large discrepancy\nbetween the slip magnitudes of Grain 3 (green data points) is observed. The slip magnitude in\ndirection Ais significantly higher in the simulations compared to the experiments, while the slip\nmagnitude in direction Bis significantly lower in the simulations. Nevertheless, the DSP results\nmatch the experiments substantially better than for the conventional CP model, revealing an MSE\nof 0.022. With the discrete slip plane model, more slip takes place on the secondary slip systems\nwith slip direction Band even on slip systems with slip direction C, because there are not always\nenough weak dislocation sources present on the primary slip system. This shows the importance\nof taking the stochastics of dislocation sources into account.\n16Figure 9: Normalized slip magnitudes in the four BCC slip directions in the simulations versus the normalized\nslip magnitudes in all experiments for (a) the CP model and (b) the DSP model with parameter set 1 (Schmid\nbased glide), (c) parameter set 2 and (d) parameter set 3. Slip directions A and D are the slip directions that are,\nrespectively, closest to and furthest away from the 45◦orientation relative to the loading direction. The dashed line\nindicates a perfect match between experimental and numerical results.\nThe results of parameter sets 2 and 3, which both consider non-Schmid effects, are shown\nin, respectively, Figures 9c and 9d. Minor differences with respect to the results obtained with\nparameter set 1, with only Schmid glide, are observed. The obtained MSEs of parameter sets 2\nand 3 are 0.024 and 0.025, respectively. The match for slip directions AandBfor Grains 1 and 2\nare slightly worse than with parameter set 1, especially for parameter set 3. The large discrepancy\nbetween the experimental and numerical normalized slip magnitudes for Grain 3 is present for all\nthree parameter sets. A possible explanation is the small experimental batch size, which consists\nof only four samples.\n174.2. Quantitative analysis of slip system activity\nWe proceed to study the activity of individual slip systems. Recall that these activities, as\ndetermined from the experiments, have more uncertainty than those aggregated by slip direction\n(Section 4.1). It is nevertheless instructive to compare the numerically predicted and experimen-\ntally determined amount of slip in detail. We do this here for Grain 2. This grain is considered\nbecause it is oriented in single slip, meaning that it has one distinct primary slip system. However,\nsignificant slip on secondary slip systems is observed in the experiments, thus revealing the largest\ndiscrepancy with the CP simulations. Similar trends can be observed in Grain 1 and Grain 3, the\ndata of which are available in the supplementary material and are not discussed in detail here.\nIn the simulations, 12 {110}⟨111⟩and 12 {112}⟨111⟩slip systems are taken into account. In\nthe experiments, a trace of a {123}⟨111⟩slip system is occasionally observed, e.g. the (31 ¯2)[1¯11]\ntrace in Figure 2. To be able to compare the results, the amount of slip measured on {123}⟨111⟩\nslip systems is projected onto the adjacent {110}⟨111⟩and{112}⟨111⟩slip systems such that the\ntotal slip stays constant. For example, the unit normal of the (31 ¯2)[1¯11] slip system projected\nonto the unit normals of the ( ¯1¯10)[1 ¯11] and (21 ¯1)[1¯11] slip systems yields, respectively, 0.9449 and\n0.9820. Hence, fractions of 0.9449/(0.9449+0.9820)=0.4904 and 0.9820/(0.9449+0.9820)=0.5096\nof the amount of slip measured on the (31 ¯2)[1¯11] slip system are assigned to the ( ¯1¯10)[1 ¯11] and\n(21¯1)[1¯11] slip systems, respectively.\nThe relative slip system activity for individual slip systems as predicted by the CP model is\nshown by yellow-green bars in Figure 10a. The normalized slip magnitudes in the experiment are\nplotted as separate data points (black symbols) for each of the five samples, along with the mean\nof the data points (blue cross). The slip systems are numbered based on their slip direction and\norientation. Note that the slip system numbering differs from Tables A.3 and A.4, where the {110}\nand{112}slip families are grouped. Almost all slip in the simulation takes place on slip system 3,\nwhich is the primary slip system. However, in the experiments, a significant amount of slip on slip\nsystems 9, 10, and 15 was also observed. Hence, the CP model is not able to predict the activity of\nslip systems in the experiments. The MSE between the numerical and experimental mean values\nis 0.016.\nIn Figure 10b the slip system activity predicted by the DSP model with only Schmid effects,\ni.e. parameter set 1, is shown. Here, a box plot is used to represent the 100 realizations of the slip\nresistance distribution. The 2%, 25%, 75%, and 98% percentiles are used to construct the box plot.\nFurthermore, the mean of all the realizations is denoted with a red cross. A much more diverse\nactivity of slip systems compared to the CP model is observed. The three slip systems with the\nhighest mean and median, i.e. slip systems 3, 9, and 10, are also frequently observed to be active\nin the experiments. Furthermore, occasional activity on slip systems 2 and 15 is found in both\nthe simulations and the experiments. In the simulations, significant slip activity on slip system 4\nis also observed. No slip trace of this slip system is visible in the experiments. To summarize, all\nslip systems that are observed in the experiments are also active in the DSP simulations, however,\none additional slip system is active in the simulations. Nevertheless, a much better agreement\nwith experiments is obtained compared to the CP model. The MSE between the numerical and\nexperimental mean values is equal to 0.0048.\nThe simulation results for parameter sets 2 and 3, i.e. with non-Schmid effects, for Grain 2 are\nsummarized in Figures 10c and 10d, respectively. Parameter set 2 (Figure 10c) does not account\nfor the T/AT effect and has only moderate values for the other two non-Schmid parameters. No\nsignificant differences are observed between the slip activity obtained with parameter sets 1 and 2.\n18  (101)[̄1̄11]  (̄21̄1)[̄1̄11]  (̄110)[̄1̄11]  (1̄2̄1)[̄1̄11]  (0̄1̄1)[̄1̄11]  (112)[̄1̄11]  (0̄11)[̄111]  (12̄1)[̄111]  (110)[̄111]  (̄2̄1̄1)[̄111]  (̄10̄1)[̄111]  (1̄12)[̄111]  (011)[1̄11]  (̄112)[1̄11]  (10̄1)[1̄11]  (21̄1)[1̄11]  (̄1̄10)[1̄11]  (̄1̄2̄1)[1̄11]  (̄12̄1)[111]  (1̄10)[111]  (2̄1̄1)[111]  (̄101)[111]  (̄1̄12)[111]  (01̄1)[111]0.00.20.40.60.81.0Normalized slip magnitude [-]\n123456789101112131415161718192021222324Experimental data\nExperimental mean\nSimulation fraction(a) CP\n  (101)[̄1̄11]  (̄21̄1)[̄1̄11]  (̄110)[̄1̄11]  (1̄2̄1)[̄1̄11]  (0̄1̄1)[̄1̄11]  (112)[̄1̄11]  (0̄11)[̄111]  (12̄1)[̄111]  (110)[̄111]  (̄2̄1̄1)[̄111]  (̄10̄1)[̄111]  (1̄12)[̄111]  (011)[1̄11]  (̄112)[1̄11]  (10̄1)[1̄11]  (21̄1)[1̄11]  (̄1̄10)[1̄11]  (̄1̄2̄1)[1̄11]  (̄12̄1)[111]  (1̄10)[111]  (2̄1̄1)[111]  (̄101)[111]  (̄1̄12)[111]  (01̄1)[111]0.00.20.40.60.81.0Normalized slip magnitude [-]\n123456789101112131415161718192021222324Experimental data\nExperimental mean\nSimulation mean\nSimulation median\nSimulation P25%−P75%\nSimulation P2%−P98% (b) DSP parameter set 1\n  (101)[̄1̄11]  (̄21̄1)[̄1̄11]  (̄110)[̄1̄11]  (1̄2̄1)[̄1̄11]  (0̄1̄1)[̄1̄11]  (112)[̄1̄11]  (0̄11)[̄111]  (12̄1)[̄111]  (110)[̄111]  (̄2̄1̄1)[̄111]  (̄10̄1)[̄111]  (1̄12)[̄111]  (011)[1̄11]  (̄112)[1̄11]  (10̄1)[1̄11]  (21̄1)[1̄11]  (̄1̄10)[1̄11]  (̄1̄2̄1)[1̄11]  (̄12̄1)[111]  (1̄10)[111]  (2̄1̄1)[111]  (̄101)[111]  (̄1̄12)[111]  (01̄1)[111]0.00.20.40.60.81.0Normalized slip magnitude [-]\n123456789101112131415161718192021222324Experimental data\nExperimental mean\nSimulation mean\nSimulation median\nSimulation P25%−P75%\nSimulation P2%−P98%\n(c) DSP parameter set 2\n  (101)[̄1̄11]  (̄21̄1)[̄1̄11]  (̄110)[̄1̄11]  (1̄2̄1)[̄1̄11]  (0̄1̄1)[̄1̄11]  (112)[̄1̄11]  (0̄11)[̄111]  (12̄1)[̄111]  (110)[̄111]  (̄2̄1̄1)[̄111]  (̄10̄1)[̄111]  (1̄12)[̄111]  (011)[1̄11]  (̄112)[1̄11]  (10̄1)[1̄11]  (21̄1)[1̄11]  (̄1̄10)[1̄11]  (̄1̄2̄1)[1̄11]  (̄12̄1)[111]  (1̄10)[111]  (2̄1̄1)[111]  (̄101)[111]  (̄1̄12)[111]  (01̄1)[111]0.00.20.40.60.81.0Normalized slip magnitude [-]\n123456789101112131415161718192021222324Experimental data\nExperimental mean\nSimulation mean\nSimulation median\nSimulation P25%−P75%\nSimulation P2%−P98% (d) DSP parameter set 3Figure 10: Normalized slip magnitudes per slip system for Grain 2 for (a) the CP model and the DSP model with (b)\nparameter set 1 (Schmid based glide) (c) parameter set 2 and (d) parameter set 3.. All experiments are plotted as\nindividual data points, together with their mean and median. The DSP simulations are represented by their mean,\nmedian, 25%-75% percentile and 2%-98% percentile.\nHowever, the numerical means of most slip systems are shifted slightly towards the experimental\nmean, leading to an MSE of 0.0036. This is a small improvement compared to parameter set 1. A\nmore significant difference in slip activity is observed for parameter set 3 (Figure 10d). Here, the\nactivity of slip system 4 is almost fully suppressed. This is a result of the A/AT effect, which is\nprominent in parameter set 3 since slip system 4 is a {112}slip system that is loaded in its AT\ndirection. All slip systems which are active in simulations for parameter set 3 are active in the\nexperiments and vice versa. However, the MSE of the means is 0.0048, which is equal to the value\nfor parameter set 1 and higher than the value for parameter set 2.\nThe observations made for Grains 1 and 3 are similar to those for Grain 2. The MSE between\nthe CP model and the experiments is 0.015 for Grain 1 and 0.024 for Grain 3. Note that there is no\nmean value for the CP simulation since it is a single deterministic result. The MSEs obtained with\nthe mean values of the DSP model without non-Schmid effects (parameter set 1) of both Grains\nare significantly lower, namely, 0.0042 and 0.0064. No substantial changes in MSEs are observed\nwhen non-Schmid effects are taken into account. For parameter set 2, the MSE is 0.0035 for Grain\n1 and 0.0060 for Grain 3, which is slightly better compared to parameter set 1. For parameter\nset 3 the MSE of Grain 1 is 0.0052, which is worse than for the other parameter sets, whereas the\nMSE of Grain 3 is 0.044, which is slightly better than for the other two parameter sets. The MSEs\n19Table 1: Mean square errors between the means of the normalized slip magnitudes in the experiments and the\nsimulations. The numbering of the DSP models denotes the parameter set used in the simulations, i.e. non-Schmid\neffects are taken into account in DSP models 2 and 3, but not in DSP model 1.\nGrain CP model DSP model 1 DSP model 2 DSP model 3\n1 0.015 0.0042 0.0035 0.0052\n2 0.016 0.0048 0.0036 0.0047\n3 0.025 0.0064 0.0060 0.0044\nof all cases discussed above are summarized in Table 1.\n4.3. Discussion\nThe extensive comparison between experiments and simulations shows that the stochastics\nof dislocation sources has a major effect on the slip system activity in ferrite at the microscale.\nThe DSP model shows a diversity of active slip systems that is in adequate agreement with the\nexperimental observations, as opposed to the conventional CP model, which mainly shows slip\nactivity on the primary slip system.\nNon-Schmid effects seem to only play a minor role in the plastic behavior of ferrite at micrometer\nscales. Parameter set 2 is considered the most realistic since these experimentally obtained values\nare reported by two independent studies [24, 17] and comply with the negligible T/AT effect\nas observed in ab-initio calculations [42]. However, no qualitative differences in slip activity are\nobserved with this parameter set compared to the simulations without non-Schmid effects, i.e. the\nsame slip systems are active in basically the same proportions. Only a minor improvement in\nthe quantitative slip system activity is obtained by taking this set of non-Schmid parameters into\naccount. When the T/AT effect is fully taken into account, in parameter set 3, the activity of\nthe slip system that is not observed in the experiments, but which is occasionally active in the\nsimulations with the other two parameter sets, is suppressed. In this case, a complete qualitative\nmatch of the active slip systems between experiments and simulations is obtained. However, the\nquantitative match for this parameter set reveals a slightly larger difference than that of parameter\nset 2.\nThe above findings suggest that the distribution of dislocation sources, leading to heterogeneous\nplastic flow, plays a dominant role in the slip system activity of ferrite ingrains. This implies that\nincluding the stochastics of dislocation sources in simulations is not only important for capturing\nthe non-smooth strain field but also for accurately predicting the activation of slip systems. Non-\nSchmid effects, reveal only a minor effect. However, it should be noted that the presented analyses\nonly focus on the slip activity and not on the tension-compression asymmetry of the mechanical\nresponse which is often also attributed to non-Schmid effects. Moreover, in specimens of increasing\nsize, the stochastic effects may average out more quickly than the non-Schmid effects, especially\nin the case of a strong texture. Still, even for larger specimens, stochastic effects deserve attention\nwhen the focus lies on predicting localized events, such as the formation of plastic localization bands,\nthe initiation of damage, void nucleation, coalescence, and growth, or even fracture initiation and\npropagation, for which the DSP model simulations are expected to be valuable.\n205. Conclusions\nIn this paper, the slip activity in nanotensile tests of interstitial-free ferrite is studied with the\ndiscrete slip plane (DSP) model. To take non-Schmid effects into account, a commonly adopted\nframework for {110}⟨111⟩slip systems is extended to {112}⟨111⟩slip systems. It is shown that\nthe twinning/anti-twinning (T/AT) directions of the {112}⟨111⟩slip systems are captured by this\nextension.\nAn extensive analysis of the active slip systems in the experiments is performed. The results\ncompared the slip activities between the CP model and the DSP model, with and without non-\nSchmid effects. The main conclusions that are drawn for the behavior of ferrite at the microscale\nare:\n•The slip system activity in the experiments critically depends on the heterogeneity of plastic\ndeformation due to the presence of dislocation sources and obstacles.\n•Non-Schmid effects do not significantly contribute to the slip system activity of ferrite at the\nmicroscale.\nThis has the following implications for modeling:\n•Continuum crystal plasticity models with uniform properties are not suitable for analyzing\nsmall-scale mechanical tests since they fail to predict both the discrete character of the\ndisplacement field and the diversity of activated slip systems.\n•Modeling frameworks that do account for the stochastics of the dislocation network, such as\nthe DSP model, should be used to analyze small-scale experiments. Not only the average\nmechanical behavior of specimens is affected, but also the outliers which might be more critical\nfor localized events, such as the formation of plastic localization bands, damage initiation,\nvoid nucleation, and fracture.\nAuthor Contributions (CRediT)\nJob Wijnen: Conceptualization, Methodology, Investigation, Formal Analysis, Software, Writing\n- Original Draft, Visualization\nJohan Hoefnagels: Conceptualization, Methodology, Resources, Writing - Review & Editing,\nSupervision, Funding Acquisition\nMarc Geers: Methodology, Resources, Writing - Review & Editing, Supervision, Funding Acqui-\nsition\nRon Peerlings: Conceptualization, Methodology, Writing - Review & Editing, Supervision, Fund-\ning Acquisition\nDeclaration of Competing Interest\nThe authors declare that they have no known competing financial interests or personal rela-\ntionships that could have appeared to influence the work reported in this paper.\n21Acknowledgments\nThis research was carried out under project number S17012a in the framework of the Part-\nnership Program of the Materials innovation institute M2i (www.m2i.nl) and the Netherlands\nOrganization for Scientific Research NWO (www.nwo.nl; project number 16348).\nChaowei Du is gratefully acknowledged for providing the experimental data used in this study.\nData availability\nDetails of the experimental analysis are available in the supplementary material to this paper.\nThe raw and/or processed data required to reproduce these findings will be made available upon\nrequest.\nReferences\n[1] M. Uchic, P. Shade, D. Dimiduk, Plasticity of micrometer-scale single crystals in compression, Annual Review\nof Materials Research 39 (1) (2009) 361–386. doi:10.1146/annurev-matsci-082908-145422 .\n[2] J. Greer, J. D. Hosson, Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect, Progress\nin Materials Science 56 (6) (2011) 654 – 724. doi:https://doi.org/10.1016/j.pmatsci.2011.01.005 .\n[3] S. Shahbeyk, G. Z. Voyiadjis, V. Habibi, S. H. Astaneh, M. Yaghoobi, Review of size effects during micropillar\ncompression test: Experiments and atomistic simulations, Crystals 9 (11) (2019). doi:10.3390/cryst9110591 .\n[4] J. Christian, Some surprising features of the plastic deformation of body-centered cubic metals and alloys,\nMetallurgical Transactions A 14 (7) (1983) 1237 – 1256. doi:10.1007/BF02664806 .\n[5] S. L. Frederiksen, K. W. Jacobsen, Density functional theory studies of screw dislocation core structures in bcc\nmetals, Philosophical Magazine 83 (3) (2003) 365–375. doi:10.1080/0141861021000034568 .\n[6] P. Franciosi, L. T. Le, G. Monnet, C. Kahloun, M. H. Chavanne, Investigation of slip system activity in iron at\nroom temperature by SEM and AFM in-situ tensile and compression tests of iron single crystals, International\nJournal of Plasticity 65 (2015) 226–249. doi:10.1016/j.ijplas.2014.09.008 .\n[7] A. B. Hagen, C. Thaulow, Low temperature in-situ micro-compression testing of iron pillars, Materials Science\nand Engineering A 678 (2016) 355–364. doi:10.1016/j.msea.2016.09.110 .\n[8] W. A. Spitzig, A. S. Keh, Orientation and temperature dependence of slip in iron single crystals, Metallurgical\nTransactions 1 (10) (1970) 2751. doi:10.1007/BF03037811 .\n[9] C. R. Weinberger, B. L. Boyce, C. C. Battaile, Slip planes in bcc transition metals, International Materials\nReviews 58 (5) (2013) 296–314. doi:10.1179/1743280412Y.0000000015 .\n[10] C. Tian, D. Ponge, Leonsen, C. Kirchlechner, On the mechanical heterogeneity in dual phase steel grades:\nActivation of slip systems and deformation of martensite in DP800, Acta Materialia 183 (2020) 274–284. doi:\nhttps://doi.org/10.1016/j.actamat.2019.11.002 .\n[11] M. Duesbery, V. Vitek, Plastic anisotropy in b.c.c. transition metals, Acta Materialia 46 (5) (1998) 1481–1492.\ndoi:https://doi.org/10.1016/S1359-6454(97)00367-4 .\n[12] V. Vitek, M. Mrovec, J. L. Bassani, Influence of non-glide stresses on plastic flow: From atomistic to continuum\nmodeling, Materials Science and Engineering A 365 (1-2) (2004) 31–37. doi:10.1016/j.msea.2003.09.004 .\n[13] B. R. S. Rogne, C. Thaulow, Effect of crystal orientation on the strengthening of iron micro pillars, Materials\nScience and Engineering: A 621 (2015) 133–142. doi:https://doi.org/10.1016/j.msea.2014.10.067 .\n[14] A. Hagen, B. Snartland, C. Thaulow, Temperature and orientation effects on the deformation mechanisms of α-\nFe micropillars, Acta Materialia 129 (2017) 398–407. doi:https://doi.org/10.1016/j.actamat.2017.03.006 .\n[15] N. Kheradmand, B. R. Rogne, S. Dumoulin, Y. Deng, R. Johnsen, A. Barnoush, Small scale testing approach\nto reveal specific features of slip behavior in BCC metals, Acta Materialia 174 (2019) 142–152. doi:https:\n//doi.org/10.1016/j.actamat.2019.05.031 .\n[16] H. Lim, L. Hale, J. Zimmerman, C. Battaile, C. Weinberger, A multi-scale model of dislocation plasticity in\nα-Fe: Incorporating temperature, strain rate and non-Schmid effects, International Journal of Plasticity 73\n(2015) 100–118. doi:https://doi.org/10.1016/j.ijplas.2014.12.005 .\n[17] A. Mapar, H. Ghassemi-Armaki, F. Pourboghrat, K. S. Kumar, A differential-exponential hardening law for\nnon-Schmid crystal plasticity finite element modeling of ferrite single crystals, International Journal of Plasticity\n91 (2017) 268–299. doi:10.1016/j.ijplas.2016.11.009 .\n22[18] M. H. Joudivand S, E. Demir, A physically based model for bcc materials including non-Schmid effects and its\napplication to single crystals of α-iron at different model scales, Modelling and Simulation in Materials Science\nand Engineering 29 (5) (2021) 055016. doi:10.1088/1361-651x/abffe3 .\n[19] C. Du, F. Maresca, M. Geers, J. Hoefnagels, Ferrite slip system activation investigated by uniaxial micro-tensile\ntests and simulations, Acta Materialia 146 (2018) 314 – 327. doi:https://doi.org/10.1016/j.actamat.2017.\n12.054 .\n[20] T. Parthasarathy, S. Rao, D. Dimiduk, M. Uchic, D. Trinkle, Contribution to size effect of yield strength\nfrom the stochastics of dislocation source lengths in finite samples, Scripta Materialia 56 (4) (2007) 313 – 316.\ndoi:https://doi.org/10.1016/j.scriptamat.2006.09.016 .\n[21] K. Ng, A. Ngan, Breakdown of Schmid’s law in micropillars, Scripta Materialia 59 (7) (2008) 796 – 799.\ndoi:https://doi.org/10.1016/j.scriptamat.2008.06.019 .\n[22] J. El-Awady, M. Wen, N. Ghoniem, The role of the weakest-link mechanism in controlling the plasticity of\nmicropillars, Journal of the Mechanics and Physics of Solids 57 (1) (2009) 32 – 50. doi:https://doi.org/10.\n1016/j.jmps.2008.10.004 .\n[23] J. Wijnen, R. Peerlings, J. Hoefnagels, M. Geers, A discrete slip plane model for simulating heterogeneous\nplastic deformation in single crystals, International Journal of Solids and Structures 228 (2021) 111094. doi:\nhttps://doi.org/10.1016/j.ijsolstr.2021.111094 .\n[24] A. Patra, T. Zhu, D. L. McDowell, Constitutive equations for modeling non-Schmid effects in single crystal\nbcc-Fe at low and ambient temperatures, International Journal of Plasticity 59 (2014) 1–14. doi:https://doi.\norg/10.1016/j.ijplas.2014.03.016 .\n[25] Z. M. Chen, M. Mrovec, P. Gumbsch, Atomistic aspects of ⟨111⟩screw dislocation behavior in α-iron and the\nderivation of microscopic yield criterion, Modelling and Simulation in Materials Science and Engineering 21 (5)\n(2013) 055023. doi:10.1088/0965-0393/21/5/055023 .\n[26] R. Gr¨ oger, V. Racherla, J. L. Bassani, V. Vitek, Multiscale modeling of plastic deformation of Molybdenum and\nTungsten: II. Yield criterion for single crystals based on atomistic studies of glide of 1/2 ⟨111⟩screw dislocations,\nActa Materialia 56 (19) (2008) 5412–5425. doi:10.1016/j.actamat.2008.07.037 .\n[27] Q. Qin, L. Bassani, Non-Schmid yield behavior in single crystals, Journal of the Mechanics and Physics of Solids\n40 (4) (1992) 813–833.\n[28] Q. Qin, L. Bassani, Non-associated plastic flow in single crystals, Journal of the Mechanics and Physics of Solids\n40 (4) (1992) 835–862.\n[29] A. Koester, A. Ma, A. Hartmaier, Atomistically informed crystal plasticity model for body-centered cubic iron,\nActa Materialia 60 (9) (2012) 3894–3901. doi:https://doi.org/10.1016/j.actamat.2012.03.053 .\n[30] A. Kraych, E. Clouet, L. Dezerald, L. Ventelon, F. Willaime, D. Rodney, Non-glide effects and dislocation core\nfields in BCC metals, npj Computational Materials 5 (1) (2019) 109. doi:10.1038/s41524-019-0247-3 .\n[31] E. Clouet, B. Bienvenu, L. Dezerald, D. Rodney, Screw dislocations in BCC transition metals: from ab initio\nmodeling to yield criterion, Comptes Rendus. Physique (2021). doi:10.5802/crphys.75 .\n[32] R. J. Asaro, J. R. Rice, Strain localization in ductile single crystals, Journal of the Mechanics and Physics of\nSolids 25 (5) (1977) 309–338. doi:10.1016/0022-5096(77)90001-1 .\n[33] M. Dao, R. J. Asaro, Non-Schmid effects and localized plastic flow in intermetallic alloys, Materials Science and\nEngineering A 170 (1-2) (1993) 143–160. doi:10.1016/0921-5093(93)90376-P .\n[34] M. Dao, B. J. Lee, R. J. Asaro, Non-Schmid effects on the behavior of polycrystals-with applications to Ni 3Al,\nMetallurgical and Materials Transactions A 27 (1) (1996) 81–99. doi:10.1007/BF02647749 .\n[35] T. Yalcinkaya, W. Brekelmans, M. Geers, BCC single crystal plasticity modeling and its experimental identifi-\ncation, Modelling and Simulation in Materials Science and Engineering 16 (8) (2008). doi:10.1088/0965-0393/\n16/8/085007 .\n[36] H. Lim, C. R. Weinberger, C. C. Battaile, T. E. Buchheit, Application of generalized non-Schmid yield law\nto low-temperature plasticity in bcc transition metals, Modelling and Simulation in Materials Science and\nEngineering 21 (4) (2013) 045015. doi:10.1088/0965-0393/21/4/045015 .\n[37] M. Knezevic, I. J. Beyerlein, M. L. Lovato, C. N. Tom´ e, A. W. Richards, R. J. McCabe, A strain-rate and\ntemperature dependent constitutive model for BCC metals incorporating non-Schmid effects: Application to\ntantalum–tungsten alloys, International Journal of Plasticity 62 (2014) 93–104. doi:https://doi.org/10.1016/\nj.ijplas.2014.07.007 .\n[38] R. Gr¨ oger, V. Vitek, Impact of non-Schmid stress components present in the yield criterion for bcc metals\non the activity of 110 ⟨111⟩slip systems, Computational Materials Science 159 (2019) 297–305. doi:https:\n//doi.org/10.1016/j.commatsci.2018.12.021 .\n[39] C. Marichal, H. Van Swygenhoven, S. Van Petegem, C. Borca, {110}Slip with {112}slip traces in bcc Tungsten,\n23Scientific Reports 3 (1) (2013) 2547. doi:10.1038/srep02547 .\n[40] C. Du, J. P. M. Hoefnagels, L. I. J. C. Bergers, M. G. D. Geers, A uni-axial nano-displacement micro-tensile\ntest of individual constituents from bulk material, Experimental Mechanics 57 (8) (2017) 1249–1263. doi:\n10.1007/s11340-017-0299-6 .\n[41] J. Bassani, K. Ito, V. Vitek, Complex macroscopic plastic flow arising from non-planar dislocation core\nstructures, Materials Science and Engineering: A 319-321 (2001) 97–101. doi:https://doi.org/10.1016/\nS0921-5093(00)02008-6 .\n[42] L. Dezerald, D. Rodney, E. Clouet, L. Ventelon, F. Willaime, Plastic anisotropy and dislocation trajectory in\nBCC metals, Nature Communications 7 (1) (2016) 11695. doi:10.1038/ncomms11695 .\n[43] L. Ventelon, F. Willaime, Generalized stacking-faults and screw-dislocation core-structure in bcc iron: A compar-\nison between ab initio calculations and empirical potentials, Philosophical Magazine 90 (7-8) (2010) 1063–1074.\narXiv:https://doi.org/10.1080/14786431003668793 ,doi:10.1080/14786431003668793 .\n[44] J. Chaussidon, M. Fivel, D. Rodney, The glide of screw dislocations in bcc Fe: Atomistic static and dynamic\nsimulations, Acta Materialia 54 (13) (2006) 3407–3416. doi:https://doi.org/10.1016/j.actamat.2006.03.\n044.\n[45] M. Wen, A. Ngan, Atomistic simulation of kink-pairs of screw dislocations in body-centred cubic iron, Acta\nMaterialia 48 (17) (2000) 4255–4265. doi:https://doi.org/10.1016/S1359-6454(00)00288-3 .\n[46] J. Marian, W. Cai, V. V. Bulatov, Dynamic transitions from smooth to rough to twinning in dislocation motion,\nNature Materials 3 (3) (2004) 158–163. doi:10.1038/nmat1072 .\n[47] F. W. Noble, D. Hull, Deformation of single crystals of iron 3% silicon, The Philosophical Magazine: A Journal\nof Theoretical Experimental and Applied Physics 12 (118) (1965) 777–796. arXiv:https://doi.org/10.1080/\n14786436508218916 ,doi:10.1080/14786436508218916 .\n[48] B. ˇSest´ ak, N. Z´ arubov´ a, Asymmetry of slip in Fe-Si alloy single crystals, Physica Status Solidi (B) 10 (1)\n(1965) 239–250. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssb.19650100124 ,doi:https:\n//doi.org/10.1002/pssb.19650100124 .\n[49] B. Pan, Y. Shibutani, X. Zhang, F. Shang, Effect of dislocation pile-up on size-dependent yield strength in finite\nsingle-crystal micro-samples, Journal of Applied Physics 118 (1) (2015) 014305. arXiv:https://doi.org/10.\n1063/1.4926376 ,doi:10.1063/1.4926376 .\n[50] S. Takeuchi, K. Edagawa, Y. Kamimura, Theoretical justification of single-ended dislocation-source-controlled\ndeformation of micropillar fcc crystals, Phys. Rev. Lett. 126 (2021) 155501. doi:10.1103/PhysRevLett.126.\n155501 .\n[51] S.-W. Lee, W. D. Nix, Size dependence of the yield strength of fcc and bcc metallic micropillars with diameters\nof a few micrometers, Philosophical Magazine 92 (10) (2012) 1238–1260. arXiv:https://doi.org/10.1080/\n14786435.2011.643250 ,doi:10.1080/14786435.2011.643250 .\n[52] R. Soler, J. M. Wheeler, H.-J. Chang, J. Segurado, J. Michler, J. Llorca, J. M. Molina-Aldareguia, Understanding\nsize effects on the strength of single crystals through high-temperature micropillar compression, Acta Materialia\n81 (2014) 50–57. doi:https://doi.org/10.1016/j.actamat.2014.08.007 .\n[53] H. Yilmaz, C. J. Williams, J. Risan, B. Derby, The size dependent strength of Fe, Nb and V micropillars at\nroom and low temperature, Materialia 7 (2019) 100424. doi:https://doi.org/10.1016/j.mtla.2019.100424 .\n[54] S. I. Rao, D. M. Dimiduk, M. Tang, T. A. Parthasarathy, M. D. Uchic, C. Woodward, Estimating the strength\nof single-ended dislocation sources in micron-sized single crystals, Philosophical Magazine 87 (2007) 4777–4794.\ndoi:10.1080/14786430701591513 .\n24Appendix A. Slip systems and simulation parameters\nTable A.2: Orientations of all three grains in Proper Euler angles ( Z1X2Z3convention).\nGrain ϕ1[◦]ϕ2[◦]ϕ3[◦]\n1 333.6 37.9 25.7\n2 320.1 41.2 42.9\n3 258.7 142.6 258.3\nTable A.3: Slip plane normals, slip directions and auxiliary projection plane normals for {110}⟨111⟩slip systems.\nα ⃗ n 0 ⃗ s0 ⃗ n′+\n0 ⃗ n′−\n0 α ⃗ n 0 ⃗ s0 ⃗ n′+\n0 ⃗ n′−\n0\n1 (01 ¯1)⟨111⟩(¯110) (10 ¯1) 7 (0 ¯1¯1)⟨¯1¯11⟩(1¯10) ( ¯10¯1)\n2 ( ¯101) ⟨111⟩(0¯11) ( ¯110) 8 (101) ⟨¯1¯11⟩(011) (1 ¯10)\n3 (1 ¯10)⟨111⟩(10¯1) (0 ¯11) 9 ( ¯110) ⟨¯1¯11⟩(¯10¯1) (011)\n4 ( ¯10¯1)⟨¯111⟩(¯1¯10) (01 ¯1) 10 (10 ¯1)⟨1¯11⟩(110) (0 ¯1¯1)\n5 (0 ¯11)⟨¯111⟩(101) ( ¯1¯10) 11 (011) ⟨1¯11⟩(¯101) (110)\n6 (110) ⟨¯111⟩(01¯1) (101) 12 ( ¯1¯10)⟨1¯11⟩(0¯1¯1) ( ¯101)\nTable A.4: Slip plane normals and slip directions of {112}⟨111⟩slip systems. Furthermore, the pairs of {110}⟨111⟩\nslip systems that together constitute the apparent {112}⟨111⟩slip system are given.\nα ⃗ n 0 ⃗ s0 α1−α2\n13 ( ¯12¯1)⟨111⟩ 1−3\n14 ( ¯1¯12)⟨111⟩ 2−1\n15 (2 ¯1¯1)⟨111⟩ 3−2\n16 ( ¯2¯1¯1)⟨¯111⟩ 4−6\n17 (1 ¯12)⟨¯111⟩ 5−4\n18 (12 ¯1)⟨¯111⟩ 6−5\n19 (1 ¯2¯1)⟨¯1¯11⟩ 7−9\n20 (112) ⟨¯1¯11⟩ 8−7\n21 ( ¯21¯1)⟨¯1¯11⟩ 9−8\n22 (21 ¯1)⟨1¯11⟩ 10−12\n23 ( ¯112) ⟨1¯11⟩ 11−10\n24 ( ¯1¯2¯1)⟨1¯11⟩ 12−11\n25Table A.5: Parameters adopted in the simulations\nModel parameter Symbol Value\nLattice constant a 2.856 ˚A\nLattice friction sfric 10 MPa\nSaturation CRSS s∞ 4s\nHardening rate k0 30 GPa/ µm\nHardening exponent a 5\nLatent hardening coefficient qn 1.4\nInitial dislocation density ρ0 7·1011m−2\nRate sensitivity parameter m 0.05\nReference velocity ˙ v0 9·10−2µm/s\nElastic constants C11 233.5 MPa\nC12 135.5 MPa\nC44 118.0 MPa\nNon-Schmid parameter set 1 a1 0\na2 0\na3 0\nNon-Schmid parameter set 2 a1 0.0363\na2 0.1601\na3 0.3243\nNon-Schmid parameter set 3 a1 0.4577\na2 0.1454\na3 0.5645\n26"    },    {        "title": "1607.02323v1.Third_Order_Perturbed_Energy_of_Cobalt_Ferrite_Thick_Films.pdf",        "content": " \n1 \n  \nThird Order Perturbed Energy of Cobalt Ferrite Thic k Films \nP. Samarasekara \n          Department of Physics, University of Pera deniya, Peradeniya, Sri Lanka. \n \nAbstract \nMagnetic properties and easy axis orientation of co balt ferrite films with applied magnetic field \nand number of layers were studied. According to our  theoretical studies explained in this \nmanuscript, the magnetically easy and hard directio ns of cobalt ferrite films solely depend on in \nplane and out of plane magnetic fields. According t o 3-D and 2-D plots, there are many easy \nand hard directions at one particular value of in p lane or out of plane magnetic field. The \nmagnetic properties were investigated for cobalt fe rrite films with thickness up to 10,000 unit \ncells. The total magnetic energy was calculated for  a unit spin of cobalt. \n \n1.  Introduction \nCobalt ferrite with inverse spinel cubic structure is a soft non-uniaxial ferrimagnetic material. In \nthe applications of magnetic memory devices and mic rowave applications, where a small \nmagnetic anisotropy is required, cobalt ferrite is used. Easy axis of cobalt ferrite is along the \none of the edge of the cubic cell. Because almost a ll of the ferrites are oxides, they are corrosion \nresistive and mechanically hard. Films of cobalt fe rrite have been experimentally synthesized \nby rf sputtering [1, 2], evaporation method [3] and  pulsed laser deposition [4, 5]. However, it is \ndifficult to find any theoretical studies of cobalt  ferrite films. The magnetic properties of cobalt \nferrite films depend on film thickness [4]. \nPreviously, the magnetic properties of thin nickel ferrite and ferromagnetic films have been \nexplained by us using non-perturbed [6], 2 nd  order perturbed [7, 8, 11] and 3 rd  order perturbed \n[9, 10, 13] Heisenberg Hamiltonian modified by incl uding 4th  order magnetic anisotropy and \nstress induced anisotropy. The variation of magneti c properties and easy axis orientation with \nnumber of layers and stress induced anisotropy of N ickel ferrite films have been described in \nthose manuscripts. According to our previous studie s, many magnetically easy and hard \ndirections could be found with variations of stress  induced anisotropy and number of layers. In \nthis manuscript, the thick films of cobalt ferrite with thicknesses up to 10,000 unit cells have  \n2 \n been considered, as the number of unit cells determ ines the thickness of the film. The spins of \nFe 3+  and Co 2+  in the cell of cobalt ferrite have been taken into  account for the simulations \ndescribed in this manuscript. MATLAB computer softw are package was used for all the \nsimulations. Stress induced anisotropy plays a majo r role in ferrite films. According to our \nprevious experimental data, stress induced anisotro py plays a vital role in magnetic thin films \n[12, 14]. \n \n2.  Model \nFollowing modified Hamiltonian was used as the mode l. \n∑ ∑ ∑∑ − − − + −=\n≠ n m m mz\nmz\nm\nn m mn n mn mn m\nmn n m\nn m S D S D\nrSr rS\nrSSSSJ H\nm m\n,4 ) 4 ( 2 ) 2 (\n5 3) ( ) ( )).)( .( 3 .( .λ λ ωrrrrrrrr\n  \n        ∑∑− −\nm mm s m Sin K SH θ2 .rr\n                                                                                                                      (1) \nHere J is spin exchange interaction,  ω is the strength of long range dipole interaction , θ is \nazimuthal angle of spin , ) 2 (\nmD  and ) 4 (\nmD  are second and fourth order anisotropy constants, in H \nand out H are in plane and out of plane applied magnetic fie lds, sK is stress induced anisotropy \nconstant, n and m are spin plane indices and N is t otal number of layers in film. When the stress \napplies normal to the film plane, the angle between  m th  spin and the stress is  θm.  \n            The spinel cubic cell can be divided into 8 spin la yers with alternative A and Fe spins \nlayers 6. The spins in one layer and adjacent layers point in one direction and opposite \ndirections, respectively. The spins of A and Fe wil l be taken as 1 and p, respectively. A cubic \nunit cell with length a will be considered. Due to the super exchange interaction between spins, \nthe spins are parallel or antiparallel to each othe r within the cell. Therefore the results proven \nfor oriented case in one of our early report 6 will be used for following equations. But the angl e  \nθ will vary from  θm to  θm+1  at the interface between two cells.   \n                 \nFor a thin film with thickness Na, \nSpin interaction energy=E exchange = N(-10J+72Jp-22Jp 2)+8Jp ∑−\n=+−1\n11 ) cos( N\nmm m θ θ  \nDipole interaction energy=E dipole   \n3 \n ∑ ∑\n=−\n=+ + + + − + + −=N\nmN\nmm m m m m dipole p E\n11\n11 1 )] cos( 3) [cos( 41 . 20 )2cos 31 ( 415 . 48 θ θ θ θ ω θ ω  \nHere the first and second term in each above equati on represent the variation of energy within \nthe cell and the interface of the cell, respectivel y. Then total energy is given by \nE(θ) = N(-10J+72Jp-22Jp 2)+8Jp ∑−\n=+−1\n11 ) cos( N\nmm m θ θ  \n      ∑ ∑\n=−\n=+ + + + − + + −N\nmN\nmm m m m m p\n11\n11 1 )] cos( 3) [cos( 41 . 20 )2cos 31 ( 415 . 48 θ θ θ θ ω θ ω  \n       ∑\n=+ −N\nmm m m m D D\n14 ) 4 ( 2 ) 2 (] cos cos [ θ θ  \n     ∑\n=+ + − −N\nmm s m out m in K H H p\n1]2sin cos sin [) 1 ( 4 θ θ θ                                                                           (2)  \nHere the anisotropy energy term and the last term h ave been explained in our previous report \nfor oriented spinel ferrite 6. If the angle is given by  θm=θ+εm with perturbation  εm, after taking \nthe terms up to third order perturbation of  ε, \nThe total energy can be given as E( θ)=E 0+E( ε)+E( ε2)+E(ε3) \n \nHere \nE0= -10JN+72pNJ-22Jp 2N+8Jp(N-1)-48.415 ωΝ-145. 245ωΝ cos( 2θ) \n      +20.41 ωp[(N-1)+3(N-1)cos( 2θ) ] \n     )2sin cos sin () 1 ( 4 cos cos ) 4 (\n1 14 ) 2 ( 2θ θ θ θ θs out in mN\nmN\nmm K H HNp D D + + − − − −∑ ∑\n= =               (3)   \n∑ ∑−\n= =+ − =1\n1 1) ()2sin( 23 . 61 )2sin( 5 .290 ) (N\nmn mN\nmm p E ε ε θ ω ε θ ω ε  \n         ∑ ∑\n= =+ +N\nmN\nmm m m m D D\n1 1) 4 ( 2 ) 2 (2sin cos 2 2sin ε θ θ ε θ  \n         ∑ ∑ ∑\n= = =− + − − +N\nmN\nmN\nmm s m out m in K H Hp\n1 1 1] 2cos 2 sin cos )[ 1 ( 4 εθ εθ εθ                                     (4)  \n \n  \n4 \n ∑ ∑ ∑−\n= =−\n=− − + − −=1\n1 121\n12 2 2) ( 2 . 10 )2cos( 5 .290 ) ( 4 )(N\nmN\nmmN\nmn m m n p Jp E ε ε ω ε θ ω ε ε ε  \n           ∑−\n=+ −1\n12) ()2cos( 6 . 30 N\nmm n p ε ε θ ω      \n           ∑ ∑\n= =− + +N\nmN\nmm m m m D D\n1 12 ) 4 ( 2 2 2 2 ) 2 () sin 3 (cos cos 2 2 cos ε θ θ θ ε θ  \n          ∑ ∑\n= =+ − +N\nmN\nmmout \nmin H Hp\n1 12 2cos 2sin 2)[ 1 ( 4 εθ εθ ] 2sin 2\n12∑\n=+N\nmm sK εθ                                  (5) \n \n∑ ∑ ∑\n= = =− − + =N\nn mN\nmm mN\nmm n m D p E\n1 , 13 ) 2 (\n13 3 3sin cos 342sin 66 .193 ) ( 2sin 2 . 10 )( ε θ θ εθ ω ε ε θ ω ε  \n                ∑\n=− −N\nmm mD\n13 ) 4 ( 2 2) sin cos 35( sin cos 4 ε θ θ θ θ  \n                 ∑\n=− +N\nmmin Hp\n13cos 6)[ 1 ( 4 εθ ] 2cos 34sin 6 1 13 3∑ ∑\n= =+ −N\nmN\nmms\nmout K Hεθ εθ  \n \nThe sin and cosine terms in equation number 2 have been expanded to obtain above equations. \nHere n=m+1. \nUnder the constraint ∑\n==N\nmm\n10 ε , first and last three terms of equation 4 are zero.  \nTherefore, E( ε)= εαrr. \nHere θ θ εα 2sin ) ( ) (Brr=  are the terms of matrices with  \nθ ω θλ λ λ2 ) 4 ( ) 2 (cos 2 46 .122 ) ( D Dp B + + −=                                                                                              (6)  \nAlso εε εrr. .21)(2C E = , and matrix C is assumed to be symmetric (C mn =C nm ). \nHere the elements of matrix C can be given as follo wing, \nCm, m+1 =8Jp+20.4 ωp-61.2p ωcos(2 θ) \nFor m=1 and N,  \nCmm = -8Jp-20.4 ωp-61.2p ωcos(2 θ)+581 ωcos(2 θ) θ2 cos 2+) 2 (\nmD  \n      ) sin 3 (cos cos 42 2 2θ θ θ − +) 4 (\nmD )] 2sin( 4 cos sin )[ 1 ( 4 θ θ θs out in K H Hp + + − +                 (7)   \n5 \n For m=2, 3, ----, N-1 \nCmm = -16Jp-40.8 ωp-122.4p ωcos(2 θ)+581 ωcos(2 θ) θ2 cos 2+) 2 (\nmD  \n      ) sin 3 (cos cos 42 2 2θ θ θ − +) 4 (\nmD )] 2sin( 4 cos sin )[ 1 ( 4 θ θ θs out in K H Hp + + − +    \nOtherwise, C mn =0 \nAlso  ε βε εr. )(2 3= E  \nHere matrix elements of matrix  β can be given as following. \nWhen m=1 and N, \n) 2 (sin cos 342sin 2 . 10 2sin 66 .193 m mm D p θ θ θ ω θ ω β − + −=                               \n               θ θ θ θ θ θ sin 6cos 6)[ 1 ( 4 ) sin cos 35( sin cos 4) 4 ( 2 2 out in \nmH Hp D − − + − − ]2cos 34θsK+  \n                                                                            \nWhen m=2, 3, ------, N-1 \n) 2 (sin cos 342sin 4 . 20 2sin 66 .193 m mm D p θ θ θ ω θ ω β − + −=  \n            θ θ θ θ θ θ sin 6cos 6)[ 1 ( 4 ) sin cos 35( sin cos 4) 4 ( 2 2 out in \nmH Hp D − − + − − ]2cos 34θsK+  \nθ ω β 2sin 6 . 30 1 , pm m=+                                                                                                                                       (8)  \n \nOtherwise  βnm =0. Also  matrix  β is symmetric such that βnm =βmn . \n                                          \nFinally, the total magnetic energy given in equatio n 2 can be deduced to  \nE( θ)=E 0+εαrr.+ ε βεεεrrr. . .212+C                                                                                                                       (9)     \nOnly the second order terms of  ε will be considered for following derivation, since the \nderivation with the third order terms of  ε in above equation is tedious. \nThen E( θ)=E 0+εαrr.+ εεrr. .21C  \nUsing a suitable constraint in above equation, it i s possible to show that  α εrr.+−=C  \nHere C + is the pseudo-inverse given by  \n6 \n NECC −=+1 . .                                                                                                                                                 (10)  \nEach element in matrix E is 1.  \nAfter using εr  in equation 9, E( θ)=E 0 α αrr..21+− C - ) () (2α βα+ +C Cr\n                                            (11)  \n3.  Results and Discussion \nC+ given in equation 10 will be deduced to the standa rd inverse matrix of C, when N is really \nlarge. When the difference between m and n is one, C m, m+1 =8Jp+20.4 ωp-61.2p ωcos(2 θ).  If  Hin , \nHout  and K s are very large, then  C11 >>C 12 . If this  Cm, m+1 =0, then the matrix C becomes diagonal, \nand the elements of inverse matrix  C+ is given by  \nmm mm CC1=+. Therefore all the derivation \nwill be done under above assumption to avoid tediou s derivations. Value of p for cobalt ferrite \nis 1.67. \n \nFrom equation 3, \nE0= -10JN+120.24NJ-61.36JN+13.36J(N-1)-48.415 ωΝ-145. 245 ωΝcos(2 θ) \n      +34.1 ω[(N-1)+3(N-1)cos(2 θ)] \n \nFrom equation 7, \nC11 =CNN = -13.36J-34.07 ω+478.8 ωcos(2 θ) θ2 cos 2+) 2 (\nmD  \n                       ) sin 3 (cos cos 42 2 2θ θ θ − +) 4 (\nmD )] 2sin( 4 cos sin [ 68 . 2 θ θ θs out in K H H + + −    \nFor m=2, 3, ----, N-1 \nC22 =C 33 =----=C N-1,N-1 = -26.72J-68.14 ω+376.59 ωcos(2 θ) θ2 cos 2+) 2 (\nmD  \n      ) sin 3 (cos cos 42 2 2θ θ θ − +) 4 (\nmD )] 2sin( 4 cos sin [ 68 . 2 θ θ θs out in K H H + + −    \nFrom equation 6, \n)2sin( ] cos 2 15 .306 [2 ) 4 ( ) 2 (\n1 θ θ ω αλ λ D D + + −=  \n) 2 (\n11 sin cos 342sin 16 .168 m NN Dθ θ θ ω β β − −= =                               \n               θ θ θ θ θ θ sin 6cos 6[ 6 ) sin cos 35( sin cos 4) 4 ( 2 2 out in \nmH HD − − − − ]2cos 34θsK+   \n7 \n ) 2 (\n22 sin cos 342sin 66 .142 mDθ θ θ ω β − −=  \n            θ θ θ θ θ θ sin 6cos 6[ 6 ) sin cos 35( sin cos 4) 4 ( 2 2 out in \nmH HD − − − − ]2cos 34θsK+  \nθ ω β 2sin 5 . 76 1 ,=+m m     \n(C +α)2β(C +α)=  (C 11 +α1)2(β11 C11 +α1+β12 C22 +α2+-------+ β1N CNN +αN)  \n                          +(C 22 +α2)2(β21 C11 +α1+β22 C22 +α2+-------+ β2N CNN +αN) \n                          +(C 33 +α3)2(β31 C11 +α1+β32 C22 +α2+-------+ β3N CNN +αN)+--------       \n                            ------+(C NN +αN)2(βN1 C11 +α1+βN2 C22 +α2+-------+ βNNCNN +αN) \n)] 2 (4) (2) (2[ ) () (22 12 3\n22 22 12 22 \n11 12 \n2\n22 22 12 \n11 11 \n2\n11 3 2β ββ β β β βα α βα +−+++ + + =+ +\nCN\nC C C C C CC C  \nThe total magnetic energy can be found by putting a ll these terms in equation 11. \nFigure 1 is the 3-D plot of energy versus in plane magnetic field and angle for \n10 ) 2 (\n= = = =ω ω ω ωs out m K H D J and  5) 4 (\n=ωmD. The number of layers was taken as 10,000 in this \ncase. Energy minimums can be observed at , 69 , 56 , 28 , 13 , 10 =ωin H---etc, indicting that the film \ncan be easily oriented along easy direction of magn etization at these values of in plane magnetic \nfield. Also the graph has maximum values at 61 , 55 , 50 , 36 , 30 , 5 =ωin H,----etc. This means that it \nis difficult to align the film in hard directions a t these values of ωin H. However, there are \nseveral easy and hard directions at one of these va lues of in plane magnetic fields.  \n \n \n \n  \n8 \n 020 40 60 80 100 \n050 100 -3 -2 -1 012x 10 19 \nHin /ωangle θ(radians) E( θ)/ ω\n \nFig 1:  Graph of energy versus angle and in plane magnetic  field. \n \n2-D plot in figure 2 shows the variation of total m agnetic energy with angle at 28 =ωin H. Here, \nthe other parameters were kept at 10 ) 2 (\n= = = =ω ω ω ωs out m K H D J and  5) 4 (\n=ωmD. Number of \nlayers was kept at 10,000.  Easy axis can be observed at 3.4243 and 5.8434 radi ans for this \nparticular value of in plane magnetic field.  \n  \n9 \n 0 1 2 3 4 5 6 7-6 -5 -4 -3 -2 -1 01x 10 11 \nangle θ(radians) E( θ)/ ω\n \nFig 2:  Graph of energy versus angle at 28 =ωin H. \nThe total magnetic energy versus out of plane magne tic field and angle was plotted in figure \n3.In this case, the other parameters were kept at 10 ) 2 (\n= = = =ω ω ω ωs in m K H D J and  5) 4 (\n=ωmD. \nNumber of layers was kept at 10,000. There are ener gy minimums in the graph at \n, 72 , 49 , 37 , 23 , 15 =ωout H--- etc. This means that the film can be easily ori ented along \nmagnetically easy direction at these values of out of plane magnetic fields. Energy maximums \ncan be observed at 64 , 42 , 20 , 16 , 10 =ωout H, ---- etc . It is difficult to align the film in hard \ndirections at these values of ωout H.  \n \n  \n10 \n 020 40 60 80 100 \n050 100 -3 -2 -1 0123x 10 19 \nHout /ωangle θ(radians) E( θ)/ ω\n \n \nFig 3:  Graph of energy versus angle and out of plane magn etic field. \n \nIn figure 4, the graph of energy versus angle has b een plotted for  37 =ωout H.  Other parameters \nwere kept at the values given for figure 3.  Easy directions make 0.4084 and 6.15 radians with a  \nnormal line drawn to film plane at this specific va lue of out of magnetic plane.    \n11 \n 0 1 2 3 4 5 6 7-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 00.5 x 10 11 \nangle θ(radians) E( θ)/ ω\n \nFig 4:  Graph of energy versus angle at 37 =ωout H. \n  \n4.  Conclusion \nEasy and hard directions of cobalt ferrite films at  different values of in plane and out of plane \nmagnetic fields have been investigated. Easy direct ion as measured with normal line drawn to \nfilm plane is 196.2 and 334.8 degrees at N=10,000, 28 =ωin H, 10 ) 2 (\n= = = =ω ω ω ωs out m K H D J \nand  5) 4 (\n=ωmD.  Also easy directions were found to be 23.4 and 352. 4 degrees for N=10,000, \n37 =ωout H, 10 ) 2 (\n= = = =ω ω ω ωs in m K H D J and  5) 4 (\n=ωmD.  As given in 3-D plots, easy and hard \ndirections are determined by spin exchange interact ion, dipole interaction, second & fourth \norder anisotropy, in plane & out of plane magnetic fields, stress induced anisotropy and the \nthickness of the film. Therefore easy and hard dire ctions of thick cobalt ferrite films can be \ntuned by varying these energy parameters. \n  \n12 \n  \nREFERENCES \n1.  L. Stichauer et al., 1996.  Optical and magneto-optical properties of nanocryst alline cobalt   \n ferrite films.  Journal of Applied Physics 79, 3645. \n2.  ZhiYong Zhong et al., 2011.  Microstructure and magnetic properties of CoFe 2O4 thin films  \n deposited on Si substrates with an Fe 3O4 under layer.   Science China: Physics, Mechanics \nand Astronomy 54 (7), 1235-1238.  \n3.  N. Hiratsuka and M. Sugimoto, 1987. Preparation of amorphous cobalt ferrite films with  \n perpendicular anisotropy and their magneto optical  properties. IEEE Transaction on \nMagnetism  MAG. 23(5), 3326-3328. \n4.  Subasa C. Sahoo et al., 2012. Thickness dependent anomalous magnetic behavi or in pulsed  \nlaser deposited cobalt ferrite thin films.  Applied Physics A 106(4), 931-935. \n5.  G. Dascalu et al, 2013.  Magnetic measurements of RE doped cobalt ferrite th in films.  IEEE  \n Transaction on Magnetism 49 (1), 46-49. \n6. P. Samarasekara, 2007. Classical Heisenberg Hami ltonian Solution of Oriented Spinel    \n    Ferrimagnetic Thin Films. Electronic Journal of  Theoretical Physics 4(15), 187-200.   \n7. P. Samarasekara, M.K. Abeyratne and S. Dehipawal age, 2009. Heisenberg Hamiltonian with \nSecond Order Perturbation for Spinel Ferrite Thin F ilms. Electronic Journal of Theoretical \nPhysics 6(20), 345-356. \n8. P. Samarasekara, 2010. Determination of energy o f thick spinel ferrite films using    \n    Heisenberg Hamiltonian with second order pertur bation. Georgian electronic scientific   \n    journals: Physics 1(3), 46-49. \n9. P. Samarasekara and William A. Mendoza, 2011. Th ird Order Perturbed Heisenberg   \n      Hamiltonian of Spinel Ferrite Ultra-thin film s.  Georgian Electronic Scientific Journals:    \n      Physics 1(5), 15-24. \n10. P. Samarasekara, 2011. Investigation of Third O rder Perturbed Heisenberg Hamiltonian of   \n      Thick Spinel Ferrite Films. Inventi Rapid: Al gorithm Journal 2(1), 1-3. \n11. P. Samarasekara and S.N.P. De Silva, 2007. Heis enberg Hamiltonian solution of   \n       thick ferromagnetic films with second order   perturbation. Chinese Journal of  \n       Physics 45(2-I),  142-150. \n  \n13 \n 12. P. Samarasekara, 2003. A pulsed rf sputtering m ethod for obtaining higher deposition   \n      rates. Chinese Journal of Physics 41(1), 70-7 4. \n 13. P. Samarasekara and William A. Mendoza, 2010. Effect of third order perturbation on   \n       Heisenberg Hamiltonian for non-oriented ultr a-thin ferromagnetic films.   \n       Electronic Journal of Theoretical Physics 7( 24), 197-210.  \n14. P. Samarasekara and Udara Saparamadu, 2013. Eas y axis orientation of Barium hexa-  \n      ferrite films as explained by spin reorientat ion. Georgian electronic scientific   \n      journals: Physics 1(9), 10-15. \n \n \n \n \n \n \n \n \n  \n  "    },    {        "title": "1910.10120v1.Comment_on_Crystallite_size_dependent_exchange_bias_in_MgFe2O4_thin_films_on_Si__100___Journal_of_Applied_Physics__volume_124__page_053901__2018.pdf",        "content": "1 \n Comment  on “Crystallite size dependent exchange bias in MgFe 2O4 thin \nfilms on Si  (100)”,  [J. Appl. Phys.  124, 053901 (2018) ] \n \nHimadri Roy Dakua  \nDepartment of physics, Indian Institute of Technology Bombay, Mumbai, India – 400076  \n \nAbstract  \nK. Malli ck and P. S. A . Kumar1 had reported exchange bias effect in Mg -ferrite thin films, \ndeposited on Si substrate (with a buffer layer o f MgO) using Pulsed Laser Deposition (PLD) \ntechnique. The authors had presented the temperature dependence exchange bias effect, field \ndependence exchange bias effect and training effect of a selected Magnesium ferrite thin film \nof thickness 132 nm. Th ese studies were  followed by the film thickness dependence of \nexchange bias effect. However, the data pres ented for the 132 nm thick film shows mutually \ncontradicting values in each and every figures. Here, I point out these highly self-contradicting  \ndata in t his comment . \n \nComment  \nExchange B ias (EB)  effect is a well -known phenomenon within the society, working in \nmagnetism and magnetic materials. The EB effect is generally characterized by a horizontal \nshift (along the field axis) in the magnetic hysteresis  loop of a Field C ooled  (FC)  system.2, 3 \nFig. 1 shows schematic diagram of Zero Field Cooled ( ZFC) and FC M -H loops of a typical \nexchange bias system. The exchange bias field (H E) and the coercivity (H C) is calculat ed as \n- HE = (H1+H 2)/2 and H C = (H 1 – H2)/2, where  H1 and H 2 are two  coercive  fields shown in Fig. \n1. Malli ck and Kumar also used similar formulae to calculate the magnitude of H E and the \ncoercivity (H C) of their films.1 Since the FC M -H loop shifted along the negative field axis, it \nmust follow the simple relation |H 2| > |H 1| and |H 2| > H C.4 In training effect, the magnitude of \nHE gradually decreases as the |H 2| and |H 1| tend to be equal with increasing M -H loop \niterations.5 \n \n 2 \n \n-500 -250 0 250 500-100-50050100\n  M (arb. unit)\nH (arb. unit) ZFC\n FC\nH1H2 \nFig. 1. Schematic diagram of ZFC and FC M -H loops of a typical exchange bias system  \n \nMalli ck and Kumar  had presented the coercivity  (HC) data of a 132 nm thick Mg-ferrite film  \nin different figures of their paper .1 However, the coercivity value s of the film are found to be \ndifferent in different figures  for an identical measurement . Here I have pointed out the se \ndifferences one by one . \n1. The inset of FIG 1 (c) of the said paper shows the  expanded view of  + 6 kOe and - 6 kOe \nFC M -H loops of the 132 nm thick film measured at 10 K. Here, t he values of |H1| and \nǀH2ǀ of the + 6 kOe FC M -H loop are ~ 400  Oe and ~750  Oe respectively. Therefore, \nthe coercivity (H C) of + 6 kOe FC M -H loop of the film should  be H C = ~ 575 Oe at \n10 K. \n2. In FIG. 2 (a), t he authors had presented the cooling field dependence of H C (at 10 K) of \nthe same 132 nm thick film . Here the estimated value of H C of 6 kOe FC M -H loop is \nwithin the range 400  < HC < 460 Oe, w hich is very small than the estimated value \nreported in FIG. 1 (c).  \n3. While in FIG. 2 (b), the HC at 10 K  of the 6 kOe FC M -H loop  of same 132 nm thick \nfilm is  reported as ~ 360 Oe ! \n4. Mallik and kumar had also presented the  training effect of the same film at  5 K after \nfield cooling in 20  kOe magnetic field . They presented the negative descending \nbranches of the M -H loops in FIG 4 (a).  The value of |H 2| of the first M -H loop it eration \nis ~ 205  Oe. Since the  20 kOe FC M-H loop shifted along negative field axis , so one 3 \n must find |H 2| > |H 1| and |H 2| > HC. However , the authors reported (in FIG. 4 (b)) \nHC = ~ 325 Oe for the first iteration which is much higher than the |H 2| (~205  Oe)! \nSuch huge discrepancies in the coercivity values of the same film in different figures clearly \ntell that the exchange bias field might  be also alte red from the real values and  true nature. \nTherefore the discussion and conclus ion based on these results  could not be reliable . \n \n \nReferences  \n1. K. Mallick and P. Anil Kumar, Journal of Applied Physics 124 (5), 053901 (2018).  \n2. W. H. Meiklejohn and C. P. Bean, Physical Review 105 (3), 904 (195 7). \n3. J. Nogués and I. K. Schuller, Journal of Magnetism and Magnetic Materials 192 (2), 203 -232 \n(1999).  \n4. M. Kiwi, Journal of Magnetism and Magnetic Materials 234 (3), 584 -595 (2001).  \n5. A. Hochstrat, C. Binek and W. Kleemann, Physical Review B 66 (9), 092409 (2002).  \n "    },    {        "title": "1110.2024v1.Coaxial_Wire_Measurements_of_Ferrite_Kicker_Magnets.pdf",        "content": "arXiv:1110.2024v1  [physics.acc-ph]  10 Oct 2011COAXIAL WIREMEASUREMENTS OF FERRITEKICKERMAGNETS\nH.Day∗, CERN, Switzerland, UniversityofManchester, UK andCockc roft Institute,UK\nM.J.Barnes, F. Caspers, E. Metral,B. Salvant,C. Zannini,C ERN, Geneva,Switzerland\nR.M. Jones,UniversityofManchester,UK and Cockcroft Inst itute,UK\nAbstract\nFast kicker magnets are used to inject beam into and\neject beam out of the CERN accelerator rings. These\nkickers are generally transmission line type magnets with\na rectangular shaped aperture through which the beam\npasses. Unlessspecialprecautionsaretakentheimpedance\nof the yoke can provokesignificant beam inducedheating,\nespecially for high intensities. In addition the impedance\nmaycontributetobeaminstabilities. Theresultsoflongit u-\ndinal and transverseimpedancemeasurements,for various\nkicker magnets, are presented and compared with analyti-\ncal calculations: in addition predictions from a numerical\nanalysisarediscussed.\nINTRODUCTION\nFerrite kicker magnets are used extensively within the\nCERN accelerator complex to inject and extract beams\nfrom the various machines for transfer to experimental ar-\neas, other particle accelerators or to dump beams. They\nhave been known to be a significant source of beam cou-\npling impedance in the accelerator complex at CERN for\nsome time [1]. This is due to the proximity of very lossy\nmaterials to the beam. To counteract this a number of\nimpedancereductiontechniqueshavebeenappliedtothese\nmagnets,bothretroactivelytoexistingpiecesofequipmen t\n[2]andduringthedesignstages[3].\nDue to the difficulty of simulating ferrite kickers with\ntheimpedancereductionmeasuresinplace,itisoftenmore\nconvenienttomeasuretheirbeamimpedanceusingacoax-\nial wire setup as opposed to using simulations. Further\nworkcansubsequentlybedonetounderstandthemeasure-\nmentsandgiveguidancetosimulationstudies.\nCOAXIALWIREMEASUREMENT\nMETHODS\nThe coaxial wire method has been used for a number\nof decades as a bench-top method of measuring the beam\ncouplingimpedanceofacceleratorstructures. Itisbasedo n\ntheconceptthattheelectromagneticfieldprofilearoundan\nultrarelativistic charged particle is similar in nature to that\nofa shortelectricalpulsepropagatingalonga coaxialline .\nFor the measurements of the LHC-MKI (Large Hadron\nCollider Injection Kicker Magnets) the resonant coaxial\nwire method has been used. For the other measurements\npresented here the classical transmission method has been\nused. Bothofthese aredescribedinmoredetail in[2, 4].\n∗hugo.day@hep.manchester.ac.ukLHC-MKI INJECTIONKICKER\nMAGNETS\nThe LHC-MKIs are a set of transmission line ferrite\nkickermagnets. Unlikemostexistingkickermagnets,they\nwere designed with impedance reduction mechanisms in\nplace, in the form of a ceramic tube within which a series\nof longitudinal (from the beam point of view) conducting\nstrips are inserted to provide a low resistivity path for the\nimage currents. This was done to reduce both beam in-\nduced heating [5] and the likelihood of impedance based\ninstabilitiesinthe circulatingbeam.\nLongitudinalImpedance\nThe longitudinalimpedanceof the LHC-MKI was mea-\nsured using the resonator method. For reference measure-\nments, the beampipe of the counter-rotating beam in the\nkicker assembly was used. This is a copper tube of equal\nlength to the main magnet aperture. Values without the\nbeam screen are given by the Tsutsui formalism for two\nparallelplates[6,7,8].\nAscanbeseeninFig.1,theinclusionofthebeamscreen\nis highly effective in reducing the real impedance of the\nmagnet. The imaginary impedance is also greatly reduced\nacross the majority of the measured frequency spectrum,\nhowever two large peaks occur at ∼800 MHz and ∼1200\nMHz. A series of measurements were also done on an\nLHC-MKI magnet at different stages of preparationto see\nhow operationmay conditionthe impedanceofthe device.\nFig. 2demonstratesthatalthoughthebeamscreenremains\neffective in suppressing the real impedance, the prepara-\ntions for insertionin the LHC and operationwith the LHC\ncan cause significant changes in the impedance of devices\nbuilt to the same specification, particularly at frequencie s\ngreater than 1 GHz. Simulations to understand the source\nofthese peaksare currentlyunderinvestigation.\nTransverseImpedance\nIn common with the longitudinal impedance, the trans-\nverse (both dipolar and quadrupolar) impedances are\ngreatly reduced when compared to that expected for un-\nscreened ferrite. The large peak observed in the horizon-\ntal dipolar impedance at 1800 MHz (see Fig. 3) is thought\nto be a Higher Order Mode (HOM) present in the mea-\nsuring setup and thus does not represent a real impedance.\nThequadrupolarimpedanceisdrasticallyreducedatallfre -\nquencies by the beam screen. The behaviour of the trans-\nverse impedances with respect to the state of the beam\nscreen is similarly under investigation using simulationFigure1: Thelongitudinalimpedanceperunitlengthofthe\nLHC-MKIwith andwithoutthebeamscreen.\nFigure 2: The real longitudinal impedance per unit length\nof theLHC-MKI comparedat differentstages. T7(Tank7)\nis separatemagnetfromtheothermeasurements.\nFigure 3: The dipolar impedance per unit length of the\nLHC-MKI with and vertical dipolar without the beam\nscreen.\nFigure 4: The real horizontal quadrupolar impedance per\nunit length of the LHC-MKI with and without the beam\nscreen.\nmodels.\nSPS-MKEEXTRACTION KICKER\nMAGNETS\nTheSPS-MKEs(extractionkickermagnet)aretransmis-\nsion line ferrite kicker magnets to allow the extraction of\nbeam from the SPS to the LHC. Two families of MKEs\nexists; the L-type and the S-type, differing in the dimen-\nsions of the kicker aperture. Originally designed without\nimpedancereductiontechniquesinplace,recentdesiresfo r\nincreased beam performances were the cause for a con-\ncerted effort to devise effective retroactive impedance re -\nductions techniques to be applied to these magnets [2].\nComparisons between the measured impedances of two\nmagnets with and without the reduction, as well as an an-\nalytical calculation with the Tsutsui model can be seen in\nFig. 5. Theimpedanceofthe SPS-MKE wasmeasuredus-\ning the classical transmission method. For the reference\nmeasurementananalyticalcalculationwasmade.\nThe longitudinal impedance of the SPS-MKE is greatly\nsuppressed by the inclusion of serigraphy on the surface\nof the magnet (Fig. 5). Furthermorea comparisonof mea-\nsurements of the magnets without serigraphy to the Tsut-\nsui modelindicate a verygood agreementup to 600 MHz,\nwith divergence beyond this frequency due to differences\nbetweentheinternalstructureofthemagnetandtheTsutsui\nmodel. Again the large peak at ∼1700 MHz is postulated\nto beanartifactofthemeasurement.\nSPS-MKP INJECTIONKICKER\nMAGNETS\nThe SPS-MKP (injection kicker magnet) are a set of\ntransmissionlinemagnetsusedtoinjectbeamintotheSPS.\nOne of their features is that they are composed of a many\nsegments of ferrite separated by high voltage plates as can\nbeseeninFig.6. Measurementsandsimulationshavebeen\ncarried out to determine how the inclusion of the segmen-\ntation causes the measurements to differ from the analyticFigure5: Thelongitudinalimpedanceperunitlengthofthe\nSPS-MKEwithserigraphy(measured)andwithoutserigra-\nphy(measuredandcalculatedusingthe Tsutsuimodel).\nFigure6: AcutawayoftheSPS-MKPmodel. Notethethin\nlayers of segmentation between ferrite blocks. The model\nis simulatedwith ameshcountof1.3million.\nmodels.TheimpedanceoftheSPS-MKPwasmeasuredus-\ning the classical transmission method. Simulations were\ncarriedusingCST ParticleStudio[9].\nAs can be seen from the simulations (see Fig. 7), the\naddition of segmentation and the C-core shape cause an\nincrease in the peak value of the real impedance at ∼600\nMHz and also the generation of a lower frequencypeak at\n30-40MHz.\nCONCLUSIONAND OUTLOOK\nWe have demonstrated the effectiveness of the imple-\nmented impedance reduction techniques in lowering the\nbeam coupling impedance of a number of ferrite kicker\nmagnets at the CERN accelerator complex. In particular\nwehaveasignificantreductionintherealimpedancecom-\npared to their unshielded cases thereby reducing the prob-\nlem of beam-inducedheating. Furthermorewe can see the\ntheoreticalmodelscurrentlyinusearenotsufficienttoful ly\nexplain the measured impedance profiles due to not truly\nrepresentingthe internalmagnetstructure. Furtherwork i s\nunderwaytodevelopmodelsthatmoreaccuratelyrepresent\nthe magnetsinternalstructure.\nFigure 7: The real longitudinal impedance of the SPS-\nMKP.Comparisonbetweenmeasurementsandsimulations\nwith and without the segmentation. Seg indicates simula-\ntions with segmentation. Horizontal/vertical measure re-\nfer to measurementsmade duringdisplaced with measure-\nmentsin thehorizontalandverticalplanerespectively.\nACKNOWLEDGEMENTS\nThanks to Yves Sillanoli and Salim Bouleghlimat for\nhelpinthe mechanicalsetupofthe measurementsystem.\nREFERENCES\n[1] B.Salvant,“ImpedanceModeloftheCERNSPSandAspects\nof the LHCSingle-Bunch Stability”,EPFLThesis,2010\n[2] T. Kroyer. F. Caspers, E. Gaxiola, “Longitudinal and Tra ns-\nverse Wire Measurements for the Evaluation of Impedance\nReduction Measures on the MKE ExtractionKickers”, 2007,\nCERN-AB-Note-2007-028\n[3] M.J.Barnes,F.Caspers,L.Ducimetiere,N.Garrel,T.Kr oyer,\n“An Improved Beam Screen for the LHC Injection Kickers”,\nProc.PAC’07, Albuquerque, USA,June 2006, pp1574\n[4] H. Day, F. Caspers, R.M. Jones, E. Metral, ”Simulations o f\nCoaxial Wire Measurements of the Impedance of Asymmet-\nric Structures”,These proceedings\n[5] M.J. Barnes et al, “Measurement and analysis of SPS kicke r\nmagnet heating and outgassing with Different Bunch Spac-\ning”, PAC’09,Vancouver, Canada, May2009, FR2RAC02\n[6] H.Tsutsui,“Longitudinalimpedancesofsomesimplified fer-\nrite kicker magnet models”, EPAC’00, Vienna, Austria, June\n2000, pp1444\n[7] H. Tsutsui, “Transverse Coupling Impedance of a Simpli-\nfied Ferrite Kicker Magnet Model”, 2000, LHC-PROJECT-\nNOTE-219\n[8] B. Salvant, N. Mounet, C. Zannini, E. Metral, G. Rumolo,\n“Quadrupolar Transverse Impedance of Simple Models of\nKickers”, IPAC’10,Kyoto, Japan, May 2010, TUPD055\n[9]http://www.cst.com"    },    {        "title": "1804.08719v1.Unidirectional_Loop_Metamaterials__ULM__as_Magnetless_Artificial_Ferrimagnetic_Materials__Principles_and_Applications.pdf",        "content": "1\nUnidirectional Loop Metamaterials (ULM)\nas Magnetless Artificial Ferrimagnetic Materials:\nPrinciples and Applications\nToshiro Kodera, Senior Member, IEEE, and Christophe Caloz, Fellow, IEEE\nAbstract —This paper presents an overview of Unidirectional\nLoop Metamaterial (ULM) structures and applications. Mimick-\ning electron spin precession in ferrites using loops with unidi-\nrectional loads (typically transistors), the ULM exhibits all the\nfundamental properties of ferrite materials, and represents the\nonly existing magnetless ferrimagnetic medium . We present here\nan extended explanation of ULM physics and unified description\nof its component and system applications.\nIndex Terms —Unidirectional Loop Metamaterials (ULM),\nnonreciprocity, ferrimagnetic materials and ferrites, gyrotropy,\nFaraday rotation, metamaterials and metasurfaces, transistors,\nisolators, circulators, leaky-wave antennas.\nI. I NTRODUCTION\nOver the past decades, nonreciprocal components (isola-\ntors, circulators, nonreciprocal phase shifters, etc.) have been\nhave been almost exclusively implemented in ferrite tech-\nnology [1]–[8]. This has been the case in both microwaves\nand optics, despite distinct underlying physics, namely the\npurely magnetic effect (electron spin precession) in the former\ncase [3], [9], [10] and the magneto-optic effect (electron\ncyclotron orbiting) [11]–[13] in the latter case. However,\nferrite components suffer from the well-known issues high-\ncost, high-weight and incompatibility with integrated circuit\ntechnology, and magnetless nonreciprocity has therefore long\nbeen consider a holy grail in this area [14], [15].\nThere have been several attempts to develop magnetless\nnonreciprocal components, specifically 1) active circuits [16]–\n[21], and space-time [15] 2) modulated structures [22]–[27]\nand 3) switched structures [28] (both based on 1950ies para-\nmetric (e.g. [29], [30]) or commutated (e.g. [31]) microwave\nsystems). All have their specific features, as indicated in Tab. I.\nTABLE I\nCOMPARISON (TYPICAL AND RELATIVE TERMS )BETWEEN DIFFERENT\nMAGNETLESS NONRECIPROCITY TECHNOLOGIES PLUS FERRITE .\nmaterialPconsum. bias cost noise\nferrite yes zero magnet high N/A\nact. circ. no low DC low low\nswitched no med. RF high high\nmodulated no med. RF med. med.\nULM YES low DC low med\nWe introduced in 2011 [32] in a Unidirectional Loop\nMetamaterial (ULM) mimicking ferrites at microwaves and\nrepresenting the only artificial ferrite material, or metamaterial,\nexisting to date. This paper presents an overview of the ULM\nand its applications reported to date.\nT. Kodera is with the Department of Electrical Engineering, Meisei Univer-\nsity, Tokyo Japan (e-mail: toshiro.kodera@meisei-u.ac.jp). C. Caloz is with the\nDepartment of Electrical and Engineering, ´Ecole Polytechnique de Montr ´eal,\nMontr ´eal, QC, H2T 1J3 Canada.II. O PERATION PRINCIPLE\nA Unidirectional Loop Metamaterial (ULM) may be seen\nas a physicomimetic1artificial implementation of a ferrite in\nthe microwave regime . Its operation principle is thus based\nonmicroscopic unidirectionality , from which the macroscopic\ndescription is inferred upon averaging.\nA. Microscopic Description\nMicrowave magnetism in a ferrite is based on the precession\nof the magnetic dipole moments arising from unpaired electron\nspins about the axis of an externally applied static magnetic\nbias field, B0, as illustrated in Fig. 1(a), where B0k^ z. This is\na quantum-mechanical phenomenon, that is described by the\nLandau-Lifshitz-Gilbert equation [3], [10], [33]\ndm\ndt=\u0000\rm\u0002B0+\u000b\nMsm\u0002dm\ndt; (1)\nwhere mdenotes the magnetic dipole moment, \rthe gyromag-\nnetic ratio,Msthe saturation magnetization, and \u000bthe Gilbert\ndamping term. Equation (1) states that the time-variation rate\nofmdue to a transverse2RF magnetic field signal, HRF\nt\n(k^t;^t?^ z), is equal to the sum of the torque exerted by B0\nonm(directed along +^\u001e,^\u001e: azimuth angle), and a damping\nterm (directed along\u0000^\u0012,^\u0012: elevation angle) that reduces\nthe precession angle,  , to zero along a circular-spherical\ntrajectory (conserved jmj) when the RF signal is suppressed\n(relaxation).\nClassically, magnetic dipole moments can be associated\nwith current loop sources , according to Amp `ere law. Decom-\nposing a ferrite magnetic moment, m, into its longitudinal\ncomponent, mz, and transverse component, m\u001a, as shown in\nFig. 1(a), one may thus invoke the effective current loops Imz\neff\nandim\u001a\neffassource models for the corresponding moments.\nAmong these currents, only im\u001a\neffmatters in terms of mag-\nnetism, since Imz\neff, as the source associated with HRF\nz, does\nnot induce any precession (Footnote 2). im\u001a\neffis thus the current\none has to mimic to devise an “artificial ferrite.” This current,\nas seen Fig. 1, has the form of a loop tangentially rotating on\nan imaginary cylinder of axis z.\n1The adjective “physicomimetic” is meant here, from etymology, as “mim-\nicking physics.”\n2The longitudinal ( z) component does not contribute to precession, and\nhence to magnetism. Indeed, since B0k^ z, thez-component of mproduced by\nHRF\nzwould lead to mRF\nz\u0002(B0+\u00160HRF^ z) = [mRF\nz(B0+\u00160HRF)](^ z\u0002^ z) =\n0, the only torque being produced by the transverse component ( HRF\nt,^t2xy-\nplane), mRF\nt\u0002(B0+\u00160HRF^t) = (mRF\ntB0)(^t\u0002^ z)6= 0. In the rest of the\ntext, we shall drop the superscript “RF,” without risk of ambiguity since mt,\nis exclusively produced by the RF signal.arXiv:1804.08719v1  [physics.app-ph]  16 Apr 20182\nFig. 1. “Physicomimetic” construction of the Unidirectional Loop Metama-\nterial (ULM) “meta-molecule” or particle. (a) Magnetic dipole precession,\narising from electron spinning in a ferrite material about the axis (here z) of an\nexternally applied static magnetic bias field, B0, with effective unidirectional\ncurrent loops Imz\neffandim\u001a\neff, and transverse radial rotating magnetic dipole\nmoment m\u001aassociated with im\u001a\neff. (b) ULM particle [32], typically (but not\nexclusively [34]) consisting of a pair of broadside-coupled transistor-loaded\nrings supporting antisymmetric current and unidirectional current wave (shown\nhere with exaggeratedly small wavelength for the sake of visibility), with\nresulting radial rotating magnetic dipole moment emulating that in (a).\nGiven its complexity, the current im\u001a\neffmay a priori seem\nimpossible to emulate. However, what fundamentally matters\nfor magnetism is not this current itself, but the moment m\u001a,\nfrom which magnetization will arise at the macroscopic level\n(Sec. II-B). This moment may be fortunately also produced\nby a pair of antisymmetric \u001e-oriented currents, rotating on the\nsame cylinder, which can be produced by a pair of conducting\nrings operating in their odd mode [35], as shown in Fig. 1(b).\nIf this ring-pair structure is loaded by a transistor [32], as\ndepicted in the figure, or includes another unidirectionality\nmechanism such as the injection of an azimuthal modula-\ntion [34], m\u001awillunidirectionally rotate about zwhen excited\nby an RF signal, and hence mimic the magnetic behavior of the\nelectron in Fig. 1(b). The structure in Fig. 1 constitutes thus\ntheunit-cell particle of the ULM at the microscopic level .\nOne may argue there there is a fundamental difference\nbetween the physical system in Fig. 1(a) and its presumed\nartificial emulation in Fig. 1(b): the ferrite material also\nsupports the longitudinal moment mzwhereas the ULM does\nnot include anything alike. However, as we have just seen\nabove, particularly in Footnote 2, mzdoes not contribute to\nthe magnetic response. It is therefore inessential and does thus\nnot need to be emulated. So, the particle in Fig. 1(b), with its\nmoment m\u001ais all that is needed for artificial magnetism !\nDoes this mean that the ULM particle includes no counter-\npart to the static alignment of the dipoles due to B0(and\nproducing mz) in the ferrite medium? In fact, there isa\ncounterpart, although mz= 0 in the ULM. The fundamental\noutcome of the static alignment of the dipoles along zin\nthe ferrite is the alignment of the relevant magnetic dipoles\nm\u001ain the plane perpendicular to ^ z(or within the xy-plane)\nacross the medium, for otherwise the m\u001a’s of the different\ndomains [3], [10] would macroscopically cancel out. Such an\norientation of the m\u001a’s perpendicularly to ^ zis essential to\nemulate magnetism. How is this provided in the ULM? Simply\nbyfixing the rings in a mechanical support , such as a substrate,\nas will be seen later. So, the counterpart of the ferrite static\nalignment of dipoles is simply mechanical orientation in the\nULM.B. Macroscopic Description\nSince it mimics the relevant magnetic operation of a ferrite\nat the microscopic level, the unit-cell particle in Fig. 1(b) must\nlead to the same response as bulk ferrite at the macroscopic\nlevel when repeated according to a subwavelength 3D lattice\nstructure so as to form a metamaterial as shown in Fig. 2(a).\nThe ULM in Fig. 2(a), just as a ferrite3, forms a 3D\narray of magnetic dipole moments, mi, whose average over a\nsubwavelength volume V,\nM=1\nVX\ni=1mi= \n1\nVX\ni=1m\u001a;i!\n^\u001a=M\u001a^\u001a (2)\ncorresponds to the density of magnetic dipole moments, or\nmagnetization , as the fundamental macroscopic quantity de-\nscribing the metamaterial4.\n(a) (b)\nFig. 2. ULM structures obtained by periodically repeating the unit cell with\nthe particle in Fig. 1. (a) Metamaterial (3D), described by the Polder volume\npermeability (3a). (b) Metasurface (2D metamaterial), described by a surface\npermeability [36].\nFrom this point, one may follow the same procedure as in\nferrites [8], [37] to obtain the Polder ULM permeability tensor\n\u0016=2\n4\u0016 j\u0014 0\n\u0000j\u0014 \u0016 0\n0 0\u00160;3\n5; (3a)\nwith\u0016=\u00160\u0012\n1 +!0!m\n!2\n0\u0000!2\u0013\nand\u0014=\u00160!!m\n!2\n0\u0000!2;(3b)\nwhere!0and!mare the ULM resonance frequency (or\nLarmor frequency) and effective saturation magnetization fre-\nquency , respectively5, that will be derived in the next section.\nAs in ferrites, the effect of loss can be accounted for by\nthe substitution !0 !0+j\u000b!, where\u000ba damping factor\nin (1) [8].\nSo, a ULM may really be seen as a an artificial ferrite\nmaterial producing magnet-less artificial magnetism . However,\nitsnonreciprocity is achieved from breaking time-reversal\n(TR) symmetry by a TR-odd current bias , originating in the\ntransistor (DC) biasing, instead of a TR-odd external magnetic\nfield [14].\nULMs have been implemented only in a 2D format so far.\nThe corresponding structure is shown in Fig. 2(b), and may\n3The difference is essentially quantitative : while in the ferrite p=\u0015< 10\u00006\n(p: molecular lattice constant), in the ULM p=\u0015\u00191=10\u00001=5(p:\nmetamaterial lattice constant or period), but homogeneization works in both\ncases.\n4Whereas in a ferrite, we have M=Ms+MRF= (Ms+MRF\nz)^ z+MRF\nt\u0019\nMs^ z+MRF\n\u001a^\u001a, whereMsis the saturation magnetization of material, in the\nULMMs= 0. We shall subsequently drop the superscript “RF” also in M\u001a.\n5In a ferrite,!0=\rB0and!m=\r\u00160Ms.3\nbe referred to as a Unilateral Loop Metasurface (ULMS) .\nSection IV will present ULMS Faraday rotation and Sec. V-A\nwill discuss related applications.\nIII. ULM P ARTICLE AND DESIGN\nULMs may be implemented in different manners. Figure 3\nshows a ULM particle implemented in the form of a microstrip\ntransistor-loaded single ring placed on PEC plane. Assuming\na distance much smaller than the wavelength between the\nring and the PEC plane, the structure is equivalent, by the\nimage principle, to the antisymmetric double-ring structure in\nFig. 1(b) [35].\nFig. 3. ULM particle microstrip implementation in the form of a transistor-\nloaded single ring on a PEC plane, supporting the odd effective current\ndistribution and unidirectional current wave as in Fig. 1(b). The transistor\nbiasing circuit is not shown here.\nThe transistor-loaded ULM particle in Fig. 3, or Fig. 1(b),\nis essentially a ring resonator , whose total electrical size is\ngiven by [38]\n\fmsa(2\u0019\u0000\u000bTR) +'TR= 2\u0019; \f ms=k0p\u000fe=!\ncp\u000fe;(4)\nwhere\fmsis the microstrip line wavenumber ( \u000fe: effective\nrelative permittivity), ais the average radius of the ring, \u000bTR\nis the geometrical angle subtending the transistor chip, and\n'TRis the phase shift across it. Solving Eq. (4) for !provides\nthe resonance frequency of the resonator, and hence the ULM\nresonance frequency ,\n!0=\f\f\f\f(2\u0019\u0000'TR)c\nap\u000fe(2\u0019\u0000\u000bTR)\f\f\f\f; (5)\nin (3). The parameter !min the same relations follows from\nthe mechanical orientation of the moments, as explained in\nSec. II-B: although we do not have here a saturation magne-\ntizationMsleading to the frequency parameter !m=\r\u00160Mm\nin the ferrite, we have have an equivalent phenomenological\nparameter!massociated with the orientation of the rings,\nwhich may be found by extraction, as will be seen in Sec. IV.\nNote that ULMs may be designed for multi-band operation\nand enhanced-bandwidth operation. The former, in contrast\nto ferrites that are restricted to a single ferromagnetic reso-\nnance!0=\rB06, can in principle accommodate multiple\nresonances by simply incorporating rings of different sizes,\nas illustrated in Fig. 4. The latter, in contrast to ferrite whose\nbandwidth is inversely proportional to loss due to causality, can\nbe achieved by leveraging overlapping coupled resonances [2].\n6This restriction can be somewhat overcome in a structured ferromagnetic\nstructure, such as a ferromagnetic nanowire membrane supporting a remanent\nbistable population of up and down magnetic dipole moments with corre-\nsponding resonances !\"\n0=\r\u00160H\"\n0and!#\n0=\r\u00160H#\n0[39], [40].\n(a) (b)Fig. 4. Unique magnetic properties of the ULM attainable by using multiple\nrings of resonance frequencies !0n, here two rings with resonance frequencies\n!01and!02. (a) Multiband operation using independent rings with separate\nresonance frequencies. (b) Enhanced bandwidth using coupled-resonant rings\nwith overlapping resonance frequencies.\nThe single-ring-PEC ULM implementation of Fig. 3 is\nideal for microstrip components [38] and reflective metasur-\nfaces [32]. However, for 3D ULM [Fig. 2(a)] structures and\ntransmissive metasurfaces (Sec. IV), a transparent version of\nthat ULM is required. This could theoretically be realized with\na pair of rings, as in Fig. 1(b), but may be more conveniently\nimplemented in the form of circular slots in a Coplanar Wave-\nGuide (CPW) type technology, as reported in [41].\nIV. F ARADAY ROTATION\nFaraday rotation is one of the most fundamental and useful\nproperties of magnetic materials. Given their artificial ferrite\nnature (Sec. III), ULMs can readily support this effect. The\nFaraday angle is given by [3], [8]\n\u0012F(z) =\u0000\u0012\f+\u0000\f\u0000\n2z\u0013\n;with\f\u0006=!p\n\u000f(\u0016\u0006\u0014);(6)\nwhere\u0016and\u0014are the Polder tensor components in (3b),\nwith the resonance ( !0) given by (5) and the saturation\nmagnetization frequency ( !m) discussed in Sec. III. Inter-\nesting, the ULM allows the option to reverse the direction\nof Faraday rotation by simple voltage control (instead of\nmagnet mechanical flipping in a conventional ferrite) using\nan antiparallel transistor pair load, as demonstrated in [42].\nFigure 5 shows a reflective Faraday ULM metasurface\n(ULMS) structure, based on the particle in Fig. 3, and re-\nsponse, initially reported in [32]. The results confirm that the\nULM works exactly as a ferrite, whose equivalent parameters\nare given in the caption.\nFig. 5. Reflective Faraday rotating ULMS based on the particle in Fig. 3 [32].\n(a) Perspective representation of the metasurface with rotated plane of polar-\nization. (b) Theoretical [Eq. (6)] and experimental polarization rotation angle\nversus frequency. Here, \u000fr= 2:6,!0=2\u0019= 7:42GHz (Bequiv.\n0= 0:265 T),\n!m=2\u0019= 28 MHz (\u00160Mequiv.\ns = 1 mT) and\u000b= 1:9\u000210\u00003Np\n(\u0001H=\u000b!0=\r\u0016 0= 0:4mT.)\nULM Faraday rotation has also been reported in transmis-\nsion, using the circular-slot ULM structure mentioned at the4\nend of Sec. III. Using slots, and hence equivalent magnetic\ncurrents, instead of rings supporting electric currents, that\nstructure really operates as an artificial magneto-optic material,\nwith a permittivity tensor replacing the magnetic tensor in (3a).\nA similar Faraday rotation effect may also be achieved using\narrays of twisted dipoles loaded by transistors [43].\nV. A PPLICATIONS\nA. Metasurface Isolators\nThe transmissive ULMS in [41] can be straightforwardly\napplied to build a Faraday isolator [3], [4], [44], [45], as shown\nin Fig. 6. As the wave propagates from the left to the right, its\npolarization is rotated 45\u000eby the left ULMS in the rotation\ndirection imposed by the transistors (here, clock-wise). It thus\nreaches the polarizer with its electric field perpendicular to\nthe conducting strips and therefore unimpededly crosses it. It\nis finally rotated back to its initial (vertical) direction by the\nright ULMS, whose rotation direction is opposite to the left\none (here, counter-clockwise). In the opposite direction, the\nright ULMS rotates the wave polarization in such a manner\nthat its electric field is parallel to the conducting strips of the\npolarizer, so that the wave is completely reflected. It is then\nrotated again by the right polarizer and gets back to the right\ninput orthogonal to the original wave7.\nFig. 6. Isolator using two transmissive Faraday rotation ULMSs [41] and a\n45\u000epolarizer. The bottom-left inset shows the transmissive “magneto-optic”\nslot-ULM demonstrated in [41], that may be used for this application.\nFaraday rotation is not the only approach to realize spatial\nisolation , as in Fig. 6. Such isolation may be simply achieved,\nwithout any gyrotropy but still magnetlessly, with a metasur-\nface consisting of back-to-back antenna arrays interconnected\nby transistors [47]; this nonreciprocal metasurface may exhibit\nan ultra wideband response and provide transmission gain.\nB. Nonreciprocal Antenna Systems\nThe ULM structure may be used in various nonreciprocal\nradiating (antenna, reflector and metasurface) applications.\nFigure 7 shows a nonreciprocal antenna system and its re-\nsponse [48]. The structure [Fig. 7(a)] is a ULM magnet-\nless version of the nonreciprocal ferrite-loaded Composite\nRight/Left-Handed (CRLH) open-waveguide leaky-wave an-\ntenna introduced in [49], [50], with the ferrite material re-\nplaced by a 1D ULM structure. This structure may be used\nas a nonreciprocal full-space scanning antenna [Figs. 7(b)\nand (c)], whose unidirectionality provides protection against\ninterfering signals, or as an antenna diplexer system , where\nnonreciprocity effectively plays the role of a circulator with\nhighly isolated uplink ( 3!1) and downlink ( 2!3) paths.\n7Lossy polarizers can be added, if necessary (The final wave could be\nreflected back), for dissipative (rather than reflective) isolation [46].\nFig. 7. ULM CRLH leaky-wave isolated-antenna or antenna-duplexer sys-\ntem [48]. (a) Prototype with port definitions. (b) Measured radiation patterns.\n(c) Measured scattering parameters.\nC. Isolators and Circulators\nULM technology also enables various kinds of nonre-\nciprocal components. Figure 8(a) shows a ULM microstrip\nisolator [38]. The ULM structure below the microstrip line is\ncomposed of two rows of transistor-loaded rings with opposite\nbiasing, and hence opposite allowed wave rotation directions.\nAs the wave from the microstrip line reaches a ring pair,\nits mode is coupled into a stripline mode with strip pair\nconstituted by the longitudinal sections of the overlapping\nrings, and usual antisymmetric currents. In the propagation\ndirection where these currents are co-directional, with allowed\nrotation direction of the ULM, the stripline mode is allowed\nto propagate, whereas in the opposite propagation direction, it\nis inhibited and dissipates in matching resistors on the rings.\nFigure 8(b) shows a ULM microstrip circulator [38], which is\nbased on mode-split counter-rotating modes as all circulators.\nFig. 8. ULM components [38]. (a) Isolator [51]. (b) Circulator [38].\nVI. C ONCLUSION\nWe have presented an overview of ULM structures and\napplications. The ULM physics has been described in great\ndetails, revealing that the ULM really represents an artificial\nferrite medium. It is in fact the only existing medium of\nthe kind. It has been pointed out that the ULM may offer\nunique extra benefits compared to ferrites, such a multiband\noperation, ultra broadband and electronic Faraday rotation\ndirection switching.5\nREFERENCES\n[1] A. G. Fox, S. E. Miller, and M. T. Weiss, “Behavior and applications\nof ferrites in the microwave region,” The Bell System Technical Journal ,\nvol. 34, no. 1, pp. 5–103, Jan 1955.\n[2] G. L. Matthaei, E. M. T. Jones, and S. B. Cohn, “A nonreciprocal,\nTEM-mode structure for wide-band gyrator and isolator applications,”\nIRE Transactions on Microwave Theory and Techniques , vol. 7, no. 4,\npp. 453–460, October 1959.\n[3] B. Lax and K. J. Button, Microwave ferrites and ferrimagnetics .\nMcGraw-Hill, 1962.\n[4] L. J. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Applied\nOptics , vol. 3, no. 4, Apr. 1964.\n[5] S. Wang, J. Crow, and M. Shah, “Studies of magnetooptic effects\nfor thin-film optical-waveguide applications,” IEEE Transactions on\nMagnetics , vol. 7, no. 3, pp. 385–387, September 1971.\n[6] G. P. Rodrigue, “A generation of microwave ferrite devices,” Proc. IEEE ,\nvol. 76, no. 2, pp. 121–137, Feb. 1988.\n[7] T. Aoyama, T. Hibiya, and Y . Ohta, “A new Faraday rotator using a thick\nGd:YIG film grown by liquid-phase epitaxy and its applications to an\noptical isolator and optical switch,” Journal of Lightwave Technology ,\nvol. 1, no. 1, pp. 280–285, March 1983.\n[8] D. M. Pozar, Microwave Engineering , 4th ed. Wiley, 2011.\n[9] M. Faraday, Faraday’s Diary , T. Martin, Ed. George Bell and Sons,\n1933, vol. IV , Nov. 12, 1839 - June 26, 1847.\n[10] A. G. Gurevich and G. A. Melkov, Magnetization Oscillations and\nWaves . CRC Press, 1996.\n[11] L. Rayleigh, “On the magnetic rotation of light and the second law of\nthermo-dynamics,” Nature , vol. 64, pp. 577–578, Oct 1901.\n[12] L. D. Landau and L. P. Pitaevskii, Electrodynamics of Continuous Media ,\n2nd ed., ser. Course of theoretical physics. Butterworth-Heinemann,\n1984, vol. 8, Chap. XII.\n[13] A. K. Zvezdin and V . A. Kotov, Modern Magnetooptics and Magne-\ntooptical Materials . CRC Press, 1997.\n[14] C. Caloz, A. Al `u, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L.\nDeck-L ´eger, “What is nonreciprocity? – Part I,” IEEE Antennas Wireless\nPropag. , vol. 17, 2018, this issue.\n[15] ——, “What is nonreciprocity? – Part II,” IEEE Antennas Wireless\nPropag. , vol. 17, 2018, this issue.\n[16] S. Tanaka, N. Shimomura, and K. Ohtake, “Active circulators amp, the\nrealization of circulators using transistors,” Proc. IEEE , vol. 53, no. 3,\npp. 260–267, March 1965.\n[17] Y . Ayasli, “Field effect transistor circulators,” IEEE Transactions on\nMagnetics , vol. 25, no. 5, pp. 3242–3247, Sep 1989.\n[18] I. J. Bahl, “The design of a 6-port active circulator,” in 1988., IEEE MTT-\nS International Microwave Symposium Digest , May 1988, pp. 1011–\n1014 vol.2.\n[19] S. Tang, C. Lin, S. Hung, K. Cheng, and Y . Wang, “Ultra-wideband\nquasi-circulator implemented by cascading distributed balun with phase\ncancelation technique,” IEEE Transactions on Microwave Theory and\nTechniques , vol. 64, no. 7, pp. 2104–2112, July 2016.\n[20] S. A. Ayati, D. Mandal, B. Bakkaloglu, and S. Kiaei, “Integrated\nquasi-circulator with RF leakage cancellation for full-duplex wireless\ntransceivers,” IEEE Transactions on Microwave Theory and Techniques ,\nvol. PP, no. 99, pp. 1–10, 2017.\n[21] K. Fang and J. F. Buckwalter, “A tunable 5–7 GHz distributed active\nquasi-circulator with 18-dBm output power in CMOS SOI,” IEEE\nMicrowave and Wireless Components Letters , vol. 27, no. 11, pp. 998–\n1000, Nov 2017.\n[22] S. Qin, Q. Xu, and Y . E. Wang, “Nonreciprocal components with\ndistributedly modulated capacitors,” IEEE Transactions on Microwave\nTheory and Techniques , vol. 62, no. 10, pp. 2260–2272, Oct 2014.\n[23] N. Estep, D. Sounas, and A. Al `u, “Magnetless microwave circulators\nbased on spatiotemporally modulated rings of coupled resonators,”\nTrans. Microw. Theory Tech. , vol. 64(2), pp. 502–518, 2016.\n[24] A. Kord, D. L. Sounas, and A. Al `u, “Magnet-less circulators based on\nspatiotemporal modulation of bandstop filters in a delta topology,” IEEE\nTransactions on Microwave Theory and Techniques , vol. 66, no. 2, pp.\n911–926, Feb 2018.\n[25] S. Taravati, N. Chamanara, and C. Caloz, “Nonreciprocal electromag-\nnetic scattering from a periodically space-time modulated slab and\napplication to a quasisonic isolator,” Phys. Rev. B , vol. 96, no. 16, pp.\n165 144:1–11, October 2017.\n[26] S. Taravati and C. Caloz, “Mixer-duplexer-antenna leaky-wave system\nbased on periodic space-time modulation,” IEEE Transactions on An-\ntennas and Propagation , vol. 65, no. 2, pp. 442–452, Feb 2017.[27] N. A. Estep, D. L. Sounas, J. Soric, and A. Al `u, “Magnetic-free non-\nreciprocity and isolation based on parametrically modulated coupled-\nresonator loops,” Nat. Phys , p. 923, Nov. 2014.\n[28] R. Negar and K. Harish, “Magnetic-free non-reciprocity based on\nstaggered commutation,” Nature Communications , vol. 7, p. 7:11217,\n2016.\n[29] A. L. Cullen, “A travelling-wave parametric amplifier,” Nature , vol. 181,\nno. 4605, p. 332, Feb. 1958.\n[30] R. Landauer, “Parametric amplification along nonlinear transmission\nlines,” J. Appl. Phys. , vol. 31, no. 3, pp. 479–484, Mar. 1960.\n[31] L. E. Franks and I. W. Sandberg, “An alternative approach to the\nrealization of network transfer functions: The N-path filter,” The Bell\nSystem Technical Journal , vol. 39, no. 5, pp. 1321–1350, Sept 1960.\n[32] T. Kodera, D. L. Sounas, and C. Caloz, “Artificial Faraday rotation using\na ring metamaterial structure without static magnetic field,” Appl. Phys.\nLett., vol. 99, no. 3, pp. 031 114:1–3, July 2011.\n[33] L. Landau and E. Lifshits, “On the theory of the dispersion of magnetic\npermeability in ferromagnetic bodies,” Physikalische Zeitschrift der\nSowjetunion. , vol. 8, pp. 153–169, 1935.\n[34] D. Sounas and A. Al `u, “Angular-momentum-biased nanorings to realize\nmagnetic-free integrated optical isolation,” ACS Photonics , vol. 1(3), pp.\n198–204, 2014.\n[35] D. L. Sounas, T. Kodera, and C. Caloz, “Electromagnetic modeling\nof a magnet-less non-reciprocal gyrotropic metasurface,” IEEE Trans.\nAntennas Propag. , vol. 61, no. 1, pp. 221–231, January 2013.\n[36] K. Achouri and C. Caloz, “Design, concepts and applications of elec-\ntromagnetic metasurfaces,” arXiv , vol. 1712.00618v1, Dec. 2017, in\npreparation.\n[37] D. Polder, “On the theory of ferromagnetic resonance,” Physica , vol. 15,\nno. 1, pp. 253–255, 1949.\n[38] T. Kodera, D. L. Sounas, and C. Caloz, “Magnetless non-reciprocal\nmetamaterial (MNM) technology: application to microwave compo-\nnents,” IEEE Trans. Microw. Theory Tech. , vol. 61, no. 3, pp. 1030–1042,\nMarch 2013.\n[39] L.-P. Carignan, V . Boucher, T. Kodera, C. Caloz, A. Yelon, and\nD. M ´enard, “Double ferromagnetic resonance in nanowire arrays,” Appl.\nPhys. Lett. , vol. 45, no. 6, pp. 062 504–1:3, Aug. 2009.\n[40] V . Boucher, L.-P. Carignan, T. Kodera, C. Caloz, A. Yelon, and\nD. M ´enard, “Effective permeability tensor and double resonance of\ninteracting bistable ferromagnetic nanowires,” Phys. Rev. B , vol. 80, pp.\n224 402:1–11, Dec. 2009.\n[41] T. Kodera, D. L. Sounas, and C. Caloz, “Faraday rotation by artificial\nelectric gyrotropy in a transparent slot-ring metamaterial structure,” in\nProceedings of the 2012 IEEE International Symposium on Antennas\nand Propagation , July 2012, pp. 1–2.\n[42] ——, “Switchable magnet-less non-reciprocal metamaterial (MNM) and\nits application to a switchable Faraday rotation metasurface,” IEEE\nAntenn. Wireless Propag. Lett. , vol. 11, pp. 1454–1457, December 2012.\n[43] Y . Shen, D. Kim, Ye, L. Wang, I. Celanovic, L. Ran, J. D. Joannopoulos,\nand M. Solja ˇci´c, “Metamaterial broadband angular selectivity,” Physical\nReview B , vol. 90, p. 125422, September 2014.\n[44] C. L. Hogan, “The ferromagnetic Faraday effect at microwave frequen-\ncies and its applications: The microwave gyrator,” The Bell System\nTechnical Journal , vol. 31, no. 1, pp. 1–31, Jan 1952.\n[45] R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical\nFaraday rotator,” Appl. Opt. , vol. 3, no. 9, pp. 1079–1083, Sep 1964.\n[46] A. Parsa, T. Kodera, and C. Caloz, “Ferrite based non-reciprocal radome,\ngeneralized scattering matrix analysis and experimental demonstration,”\nIEEE Trans. Antennas Propag. , vol. 59, no. 3, pp. 810–817, Mar. 2011.\n[47] S. Taravati, B. S. Khan, S. Gupta, K. Achouri, and C. Caloz, “Nonre-\nciprocal nongyrotropic magnetless metasurface,” IEEE Trans. Antennas\nPropag. , vol. 65, no. 7, pp. 3589–3597, June 2017.\n[48] T. Kodera, D. L. Sounas, and C. Caloz, “Non-reciprocal magnet-less\nCRLH leaky-wave antenna based on a ring metamaterial structure,”\nIEEE Antenn. Wireless Propag. Lett. , vol. 10, pp. 1551–1554, January\n2012.\n[49] T. Kodera and C. Caloz, “Uniform ferrite-loaded open waveguide\nstructure with CRLH response and its application to a novel backfire-to-\nendfire leaky-wave antenna,” IEEE Transactions on Microwave Theory\nand Techniques , vol. 57, no. 4, pp. 784–795, April 2009.\n[50] ——, “Low-profile leaky-wave electric monopole loop antenna using\nthe\f= 0 regime of a ferrite-loaded open waveguide,” IEEE Trans.\nAntennas Propag. , vol. 58, no. 10, pp. 3165–3174, Oct. 2010.\n[51] T. Kodera, D. L. Sounas, and C. Caloz, “Isolator utilizing artificial\nmagnetic gyrotropy,” in 2012 IEEE/MTT-S International Microwave\nSymposium Digest , June 2012, pp. 1–3."    },    {        "title": "2209.09302v1.Resolving_diverse_oxygen_transport_pathways_across_Sr_doped_lanthanum_ferrite_and_metal_perovskite_heterostructures.pdf",        "content": "Resolving diverse oxygen transport pathways across Sr-doped lanthanum ferrite and metal-perovskite heterostructures  S.D. Taylor,1,+,* K.H. Yano,2,+ M. Sassi1, B.E. Matthews,2 E.J. Kautz,2 S.V. Lambeets,1 S. Neumann,2 D.K. Schreiber,2 L. Wang,1 Y. Du,1 S.R. Spurgeon2,3,* 1. Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99352 USA 2. Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA 99352 USA 3. Department of Physics, University of Washington, Seattle, WA 98195 USA  +First coauthors.  *Corresponding authors: sandra.taylor@pnnl.gov; steven.spurgeon@pnnl.gov     2  Abstract Perovskite structured transition metal oxides are important technological materials for catalysis and solid oxide fuel cell applications. Their functionality often depends on oxygen diffusivity and mobility through complex oxide heterostructures, which can be significantly impacted by structural and chemical modifications, such as doping. Further, when utilized within electrochemical cells, interfacial reactions with other components (e.g., Ni- and Cr-based alloy electrodes and interconnects) can influence the perovskite’s reactivity and ion transport, leading to complex dependencies that are difficult to control in real-world environments. Here we use isotopic tracers and atom probe tomography to directly visualize oxygen diffusion and transport pathways across perovskite and metal-perovskite heterostructures, i.e., (Ni-Cr coated) Sr-doped lanthanum ferrite (LSFO). Annealing in 18O2(g) results in elemental and isotopic redistributions through oxygen exchange (OE) in the LSFO while Ni-Cr undergoes oxidation via multiple mechanisms and transport pathways. Complementary density functional theory (DFT) calculations at experimental conditions provide rationale for OE reaction mechanisms and reveal a complex interplay of different thermodynamic and kinetic drivers. Our results shed light on the fundamental coupling of defects and oxygen transport in an important class of catalytic materials.   3  Introduction Perovskite structured transition metal oxides (general chemical formula of ABO3) are widely studied in chemistry and condensed matter physics, owing to their strong coupling among lattice, spin, and orbital degrees of freedom.1 These crystals can accommodate a variety of property-defining cation species, giving rise to diverse electronic, magnetic, and optical behavior.2 For instance, their catalytic activity and properties can be significantly influenced by substitution or partial substitution of the A- and/or B-site cations.3–6 Among the many perovskites being pursued for catalytic applications, Sr-doped lanthanum ferrites (La1-xSrxFeO3; LSFO) have attracted particular attention for photocatalytic water splitting,7–10 with Fe as the B-site transition metal cation driving selective oxidation. The La3+ cations are substituted by cations in a lower oxidation state (i.e., Sr2+), leading to the partial oxidation of the B cations to a higher oxidation state and/or to the formation of oxygen vacancies, which results in better catalytic activity.10 The perovskite’s ability to accommodate a range of substituents and dopants provides significant flexibility in its composition and associated oxidation state. This tunability in turn enables tailoring of the perovskite’s physicochemical properties for various applications such as cathode materials in solid oxide fuel cells (SOFCs), catalysts and oxygen carriers in heterogeneous catalysis, oxygen separation membranes, and solid-state gas sensors.11 The mobility of oxygen ions is a key parameter affecting a perovskite’s reactivity and functionality across these applications.12 Diffusion through the oxide bulk follows a vacancy-mediated mechanism, where transport occurs by discrete hops of oxygen anions to neighboring vacancies.10 Diffusion rates can be further manipulated by modifying vacancy or other defect populations via cation doping.13–15 Further, as mixed ionic-electronic conductors, oxygen from the environment can reversibly adsorb/desorb into the lattice and exchange by continuous changes in oxidation state, without changes to the bulk crystal structure.10,16,17 However, the oxygen exchange (OE) reaction itself consists of numerous elementary steps and reaction sequences, such as oxygen adsorption, reduction and dissociation, diffusion of the 4  disassociated species, and subsequent incorporation into the host (cathode/electrolyte) lattice,18 which have yet to be fully understood. Within designed electrochemical cells, ion transport is also influenced by synergistic reactions with the various components of the electrode and interconnects. For instance, in the design of intermediate temperature (600-800°C) SOFCs, chromia-forming stainless steel interconnects are desirable due to the higher electronic and thermal conductivity, lower cost, and easier fabrication than traditional ceramic parts.19–21 However, a significant challenge in their application is the severe degradation of the cathode performance resulting from poisoning via Cr-species evaporated from the interconnect alloy oxide scale. Deposition of Cr-species blocks active sites on the electrode surface, negatively affecting charge transfer and oxygen diffusion,19 although the specific controlling mechanisms are convoluted and poorly understood.22 Knowledge of oxygen reactivity and transport pathways in the oxide catalyst and relative to components of the electrochemical cell can provide fundamental insight into degradation mechanisms, guiding cell design to optimize performance. In this study, we directly resolve oxygen transport pathways across (metal-)perovskite heterostructures at the nanoscale for insight into diffusivity and surface exchange reactions. To do so, oxygen diffusion was studied within a model LSFO system (La0.5Sr0.5FeO3 grown on (001) [LaAlO3]0.3[Sr2AlTaO6]0.7, [LSAT]) and across a heterogeneous metal-LSFO system (Ni- and Cr-metal). We employed recently developed isotopic tracer techniques with atom probe tomography (APT), a powerful technique used to resolve elemental and isotopic distributions in three dimensions (3D) with sub-nanometer resolution.23–26 LSFO serves as a model system to study vacancy-mediated oxygen transport in the bulk, as rapid diffusion was previously measured although this has not been directly resolved at the nanoscale.13,27 Thin films of Ni and Cr were also deposited on top of the LSFO as surrogate interfaces for metallic anodes and interconnects in electrochemical cells.28 APT specimens were prepared and annealed in gaseous 18O2 using the in situ atom probe (ISAP) method.29 After annealing, local changes in the elemental and isotopic distributions were readily observed by APT, informing unique transport pathways across the stack. These 5  observations are key to understanding mass transport phenomena controlling the degradation, rejuvenation, and stability of complex perovskite catalysts and oxide heterostructures.  Methods Materials synthesis La1-xSrxFeO3 (x = 0.5) films nominally ~9 nm thick (~22 unit cells) were epitaxially grown on (001)-oriented LSAT substrates using pulsed laser deposition; the growth details have been described elsewhere.9 In brief, the laser pulse (248nm) energy density was ~2J/cm2 and the repetition rate is 1Hz. During the deposition, the substrate was kept at 700 °C under an oxygen partial pressure of 10 mTorr. After deposition, the samples were cooled to room temperature in 10 mTorr oxygen. Cr- and Ni-layers (~15 nm and ~30 nm, respectively) were then deposited on the LSFO surface via ion beam sputtering deposition (IBSD) at room temperature.  Annealing experiments To probe oxygen transport across this system, an isotopic tracer was used during material processing to couple with APT analysis. APT specimens were annealed in 18O-enriched oxygen gas (400°C, 4h, 3 mbar 18O2; 99 atomic % (at.%) purity, Sigma Aldrich) using the in ISAP method, detailed elsewhere.29 This method allows for the direct observation of sub-nanometer scale element redistributions at the specimen surface.30–32 Briefly, this approach involves the direct exposure of APT specimens to a controlled gaseous environment at select pressures, temperatures, and times in a chemical reactor chamber attached directly to a commercial local electrode atom probe (LEAP) system. Following annealing the specimens were transferred directly into the APT analysis chamber under ultrahigh vacuum and analyzed. The conditions were chosen such that oxygen transport across the thin film (~10 nm) could be resolved by APT, based on extrapolations from previous studies; i.e., oxygen diffusion at 400°C is estimated to be ~10-18 m2 s-1 or 1 nm2 s-1 when extrapolating diffusion measurements in La0.6Sr0.4FeO3 from 900 – 1100°C.13  6  APT analyses Samples were prepared for scanning transmission electron microscopy (STEM) and APT using conventional focused-ion beam scanning electron microscopy techniques (FIB-SEM; FEI Quanta 3D-FEG or Helios NanoLab dual-beam microscopes).33,34 In particular, the APT specimens were prepared such that the final tip geometry consisted of Ni at the tip apex, underlain by Cr, LSFO, and LSAT, in sequence (see APT specimen preparation protocol in Supplementary Information (SI); Figure S1). Microstructural and compositional characterizations of the thin film by both STEM and APT were done to get baseline measurements of the as-grown specimens.  APT samples were analyzed in a CAMECA LEAP 4000XHR at a base temperature of 40 K in laser-assisted field evaporation (λ = 355 nm) at pulse rates of 125 and 200 kHz. The laser pulse energy was set between 80 and 150 pJ and the detection rate was maintained at 0.002 detected ions per pulse by varying the applied volage. The 3D APT reconstructions were done using the Integrated Visualization and Analysis Software (IVAS 3.8.5a45) with the shank angle approximation. APT reconstructions were scaled using STEM measurements of the film thicknesses and the interplanar spacing of the LSFO atomic bilayers that were also resolvable using spatial distribution maps (SDMs). The oxygen bilayer spacing of LSFO as calculated by density functional theory (DFT) is, on average, 1.945Å in the [001] direction, and APT field evaporation and thus reconstruction captures every other of these bilayers (3.89Å). Using this scaling the films’ thicknesses were consistent with that measured by STEM. Elemental and isotopic analyses were achieved through the careful assignment of ionic species best representative of the different phases (see SI for more detail).  Two APT specimens were analyzed for each condition (i.e., as-grown, annealed perovskite, and annealed metal-perovskite). Elemental concentrations were used to monitor potential phase transformations in the specimens after annealing in O2. Isotopically-resolved measurements were used to follow the provenance of oxygen from the reactor chamber (18O) across the specimen as the as-grown oxides were 16O-dominant (natural abundance (NA) for O = 99.8% 16O, 0.2% 18O) and interpret oxygen ingress and mobility from 7  the reactor environment. Elemental and isotopic compositions were shown to be consistent between duplicate APT specimens in the same condition (Table S1). One specimen from each experiment is shown in the main text as the representative sample; elemental and isotopic analyses of the remaining specimens are provided in the SI (Figure S2).  STEM analyses STEM high-angle annular dark field (STEM-HAADF) images were acquired on a probe-corrected JEOL GrandARM-300F microscope operating at 300 kV, with a convergence semi-angle of 29.7 mrad and a collection angle range of 75 – 515 mrad.  Theory calculations The VASP package35 was used to perform density functional theory (DFT) simulations of defective and Sr-doped LSFO materials. All the simulations used the generalized gradient approximation (GGA) as parametrized in the PBEsol functional36 in combination with the Hubbard correction37 (Ueff = U – J = 4 eV) to better describe the Coulomb repulsion of the 3d electrons of the Fe atoms.38 All the simulations used a cutoff energy of 550 eV and a 2×2×2 Monkhorst-Pack k-points mesh to sample the Brillouin zone. The total energy was converged to 10-6 eV/cell, the force components were relaxed to 10-5 eV/Å, and all the simulations used spin-polarization. The generation of a 50% Sr-doped LSFO (i.e., La0.5Sr0.5FeO3) unit cell used as a starting structure a 2×2×2 supercell (160 atoms) of pure LaFeO3 (LFO) compound. The relaxation of the orthorhombic (space group Pbnm #62) LFO as a G-type anti-ferromagnetic materials yielded lattice parameters a = 5.537 Å (-0.72%), b = 5.537 Å (-0.60%), and c = 7.793 Å (-0.72%), in good agreement with the experimental lattice parameters a = 5.55 Å, b = 5.57 Å, and c = 7.85 Å.39 The structure of a 50% La/Sr mixed compound was generated using the Special Quasirandom Structure (SQS) code available from the Alloy Theoretic Automated Toolkit (ATAT).40 Once the lattice parameters and coordinates of the 50% Sr-doped structure 8  were optimized, one oxygen vacancy was introduced into the structure and only the coordinates were relaxed while the lattice parameters were kept fixed at their optimized values. The temperature and O2 partial pressure (𝑝O2) dependence of the Gibbs free energy, ∆𝐺!$𝑇,𝑝O2', of oxygen vacancy was determined by ab initio thermodynamics simulations, following the equation: ∆𝐺!$𝑇,𝑝O2'=$𝐸\"O#+𝐸\"O$%&+∆𝜇(𝑇)\"O'−$𝐸perf#+𝐸perf$%&+∆𝜇(𝑇)perf'+'((𝐸O2#+𝐸O2$%&+∆𝜇O2(𝑇,𝑝O2))      (1) where 𝐸\"O# and 𝐸perf# are the DFT total energies of the La0.5Sr0.5FeO3 solid systems with and without oxygen vacancy, 𝐸\"O$%& and 𝐸perf$%& are the zero-point-energy of the defective and defect-free system. 𝐸O2#, 𝐸O2$%&, and ∆𝜇O2(𝑇,𝑝O2) are respectively the total DFT energy, the zero-point-energy, and the temperature and O2 partial pressure dependent chemical potential of oxygen. The DFT total energy of molecular O2 was corrected to the experimental atomization energy of the gaseous species41 leading to an energy correction of 1.482 eV. In order to account for temperature effect in La0.5Sr0.5FeO3, ∆𝜇(𝑇)\"O and ∆𝜇(𝑇)perf are the temperature-dependent chemical potentials of the system with and without an oxygen vacancy. All the temperature-dependent chemical potentials were calculated using the following relation: ∆𝜇(𝑇)=(𝐻(𝑇)−𝐻°(298.15))−𝑇𝑆     (2) where 𝐻(𝑇) and 𝐻°(298.15) are the system enthalpy at a temperature 𝑇 and at 𝑇=298.15 K, and 𝑆 is the entropy. In the simulations, the phonon frequencies were calculated using the Phonopy code.42 The simulations of O vacancy migration pathways used the climbing image nudged elastic band method (CINEB) as implemented in the Transition State Tools for VASP (VTST).43 9  Results and Discussion Baseline characterization of as-grown sample The baseline microstructure of the heterostructure was established by high-resolution STEM-HAADF imaging, as shown in Figure 1. Atomic resolution imaging confirms the epitaxial and single crystal nature of the LSFO thin films on the highly crystalline-LSAT substrate. The sputtered Ni and Cr metal layers are nanocrystalline, as expected. The LSFO film structure is largely uniform with few to no microscopic defects (with the exception of some steps near the LSFO-LSAT interface) (Figure 1b), though oxygen vacancy concentrations are expected to be significant at this level of Sr-doping.14  \n  Figure 1: Cross-sectional STEM-HAADF imaging of a) the Ni-Cr-LSFO-LSAT heterostructure taken along the LSAT [010] zone, and b) the LSFO and LSAT structure with black arrows indicating steps in the substrate. The elemental and isotopic composition of the metal-perovskite stack was characterized by APT (see SI for more details on elemental analyses, Figure S2 and Table S1). 3D chemical reconstructions clearly show the unique stack geometry and chemistry of the metal-perovskite system (Figure 2a). The baseline compositions of the phases in the as-grown specimens are in reasonable agreement with that expected (Figure 2b, Table S1,). That is, the Ni and Cr coatings are largely metallic (77.7 ± 2.5 at.% Ni and 70.6 ± 1.5 at.% Cr, respectively, based on the average composition and standard deviation across the two APT \n10  tips measured). Oxygen is present in both layers (13.3 ± 1.5 at.% and 21.6 ± 1.2 at.% in both Ni and Cr layers, respectively), which is present in the IBSD chamber during deposition.23 Aluminum, an impurity introduced by Al components in the sputter system, is also present at low concentrations (6.8 ± 1.5 at.% and 6.6 ± 0.25 at.% in Ni and Cr layers, respectively).  Quantification of the as-grown LSFO composition shows that Fe is the primary cation (27.2 ± 0.1 at.% Fe) followed by Sr and then La (18.5 ± 0.4 at.% and 10.7 ± 0.5 at.%, respectively). The measured O concentration is only 43.3 ± 0.9 at.% versus the expected concentration of 60 at.% O of the ABO3 stoichiometry. While some of this O deficiency could reflect oxygen vacancies due to the Sr-doping, it is important to note that oxygen quantification is inherently challenging in APT44,45, especially in Fe-base oxides.23,44,46–48 We can nonetheless follow changes in concentrations before and after annealing to determine relative composition changes. The APT-measured as-grown LSAT composition (7.6 at.% La, 14.1 at.% Sr, 10.0 at.% Al, 8.5 at.% Ta, and 58.7 at.% O, based on the composition from one APT specimen) is in reasonable agreement with expectations (3.6 at.% La, 16.4 at.% Sr, 11.8 at.% Al, 8.2 at.% Ta, and 60 at.% O). APT analyses along the defined [001] direction of the LSFO film show a homogeneous composition along the depth of each phase, with little to no elemental intermixing as demarcated by the sharp interfaces between phases (Figure 2a-b). The oxygen isotopic composition of each phase and across the heterostructure was determined using a single, consistent species, i.e. O1+ species (16 – 18 Da). This avoided potential interferences given the multi-isotopic and elemental nature of this system (see Methods and SI for details on 18O analytical protocols), The oxygen composition is expressed as the fraction of 18O relative to 16O and 18O (f18O).23 The average f18O measurements for the bulk Ni, Cr, LSFO, and LSAT was 0.05 ± 0.02, 0.04 ± 0.00(1), 0.01 ± 0.00(4), and 0.01 respectively (Figure 2c, Table S1). These f18O measurements within each phase of the as-grown specimen are within reason of that expected, i.e., near NA (0.002); the presence of hydrogen in the APT analysis chamber leads to the slight deviations.49 Nonetheless, these measurements show the oxygen isotopic composition within the as-grown specimen is effectively at NA. As shown 11  shortly, following annealing, changes in f18O are significant and thereby can be used to reliably infer oxygen diffusivity and reactions across the stack.  \n Figure 2: APT reconstructions, elemental profiles, and f18O for the (a-c) as-grown vs. (d-f) annealed perovskite vs. (g-i) annealed metal-perovskite specimens. Shading is used to highlight the uncertainty associated with the counting statistics (1σ, see Methods). To compare the behavior and mobility of oxygen in isolated perovskites to those in the presence of the metallic overlayers, APT was used to further prepare specimens prior to reaction. For some APT specimens, the Ni-Cr overlayers were field evaporated, leaving tips with only LSFO-LSAT remaining. The remaining specimens, APT specimens with Ni-Cr-LSFO-LSAT configuration, remained intact. These two specimen geometries are referred to as annealed perovskite and annealed metal-perovskite, respectively. The annealed LSFO-LSAT specimen enables us to isolate and infer oxygen mobility based on properties inherent to perovskites, which are further guided by complementary ab initio simulations \n12  performed here and observations from previous studies. In turn, these analyses also provide insight into unique oxygen transport mechanisms for the annealed metal-perovskite specimens.  Oxygen mobility in the annealed-perovskite system Following annealing of the perovskite tips in 18O2, the elemental and isotopic compositions were assessed to determine whether the phase was altered. The elemental compositions of the annealed LSFO and LSAT layers are consistent with their as-grown counterparts (Figure 2d-f, Table S1). Notably, the O concentration in the annealed LSFO is within variability of the as-grown measurements (43.8 ± 0.3 at.% vs. 43.3 ± 0.9 at.%, respectively), indicating there is no net addition or removal of oxygen during reaction.  Though elemental analyses indicate phase alteration does not occur, the oxygen isotopic composition demonstrates that lattice natural isotopic abundance oxygen in the LSFO nearly completely exchanges with the 18O-enriched environmental O2 (Figure 2f, Table S1). Quantitatively, the LSFO f18O increases from 0.01 ± 0.0(04) in the as-grown specimen to 0.84 ± 0.01 after annealing. In comparison LSAT does not experience OE, remaining near NA (f18O = 0.04). Additionally, isotopic measurements along [001] indicate OE is homogeneous along the depth of the LSFO film. Elemental composition analyses also show that the LSFO and LSAT exhibit no evidence of phase transformations. While OE in perovskites has not been measured previously at these modest temperatures, the extent of exchange seems reasonable based on rough predictions for oxygen diffusivity in LSFO and surface exchange to occur. Arrhenius extrapolations of La0.6Sr0.4FeO3 estimate oxygen diffusivity at 400°C to be ~10-18 m2 s-1 or 1 nm2 s-1.13 Using that estimate, the characteristic diffusion distance for the 4h anneal would be around 240 nm, significantly longer than our film thickness of 10 nm, consistent with the total OE we observe. Additionally, the needle-shaped APT specimen geometry and large surface area exposed could facilitate OE via surface exchange. For example, LFO annealed in 18O2 (g) at > 900°C showed the most OE occurs near the surface and decreases into the bulk, based on limited observations from lower-13  resolution isotopic exchange depth profile measurements with secondary ion mass spectrometry (i.e., > 100 nm).27  Oxygen exchange mechanisms Oxygen transport and exchange in LSFO is ultimately controlled by the behavior and concentration of oxygen vacancies.18 Our experimental observations are consistent with this (e.g., the highly-crystalline LSAT is unreactive while extensive oxygen diffusion and exchange in LSFO reflects inherently high defect concentrations). To support the experimental observations, atomistic modeling was used to further probe the vacancy-mediated transport mechanisms and driving forces at play. Specifically, the thermodynamic stability and migration energy barriers of oxygen vacancies in LSFO were simulated and quantified using DFT. The thermodynamic stability was first probed using ab initio thermodynamics calculations that can incorporate the effects of various experimental conditions (e.g., oxygen partial pressure, temperature, chemical potential differences between oxygen isotopes, and Sr concentrations). Subsequently the energetic drivers and migration barriers for vacancy-mediated transport, thought to influence the incorporation/removal of lattice oxygen and diffusion, were further evaluated.  The calculation of the Gibbs free energy of formation of an oxygen vacancy in LSFO indicates that heating increases the instability of vacancies, which may be a potential driver for oxygen incorporation into the lattice (Figure 3a). The degree of instability introduced by heating is also affected by the oxygen partial pressure, such that an increase in pO2 further increases the instability of O vacancies. At the oxygen partial pressure used in this study (pO2 = 3 mbar), O vacancies are found to be 1.31 eV less stable at 670 K than at ambient temperature. This thermodynamically favors oxygen ingress from the environment to occupy O vacancies. Countering this tendency, the vacancy concentration in the material is also restrained and maintained by the perovskite composition (i.e., Sr doping); our experimental observations are nominally consistent with this notion, as the oxygen concentration (an indirect indication of vacancy content) does not change during reaction. Thus, while annealing makes O vacancies less 14  energetically favorable thermodynamically, a steady-state vacancy concentration is maintained throughout the reaction.  To understand oxygen diffusion via vacancy-hopping mechanisms, the energetics for O vacancy migration in the perovskite lattice were calculated using the climbing image nudged elastic band (CINEB) method. To quantify the impact of Sr doping on the O vacancy migration energy barrier as a function of the Sr/O-vacancy separation distance (Figure 3b), we used a supercell where one La atom was substituted by a Sr atom and compared it to O vacancy migration in pure LFO. In the case of pure LFO, the highest calculated energy barrier is 0.73 eV, in good agreement with previously reported experimental and theoretical values of ~0.70 – 0.80 eV.12,13,50 However, when Sr is present in the lattice, the migration of a 1st neighbor O vacancy away from Sr must overcome a first energy barrier of 0.80 eV, compared to 0.62 eV for pure LFO. While subsequent energy barriers along the pathway are smaller, ranging from 0.56 eV to 0.69 eV, this indicates that O vacancies are more strongly associated with Sr. The trend obtained is in good agreement with the literature, suggesting that the energy barrier for the migration of the O vacancy increases with the Sr fraction.50–52 However, these high energetic barriers seemingly contradict observations from diffusion studies, as oxygen diffusion increases with Sr doping (e.g., bulk diffusion in La1-xSrxFeO3 [x = 0.4, 1000°C] was measured to be 4 – 5 orders of magnitude faster than that in pure LFO).1350–52This suggests that the impact of Sr doping on the concentration of O vacancies is a more important factor driving oxygen migration than its associated cost to the energy barrier. Therefore, high vacancy concentrations predominantly control oxygen diffusivity in LSFO, irrespective of the energetic barriers for vacancy migration, and enable long-range oxygen diffusion and migration.  In order to provide a rationale for the significant OE observed, bulk thermodynamic calculations for LSFO composed of either 16O and 18O were performed as function of temperature to evaluate the impact of isotope substitution on the chemical potential of LSFO. At 400°C, a difference of 20 meV/formula unit (1 formula unit = La0.5Sr0.5FeO3 or 6.67 meV/O atom) in favor of the 18O-LSFO compound is obtained (Figure 3c). Based on this difference, the calculation of the Boltzmann factor to approximate the fraction 15  of 18O yields to 70% if we consider the energy gain per formula unit or 89% if we use the energy gain per O atom. On average, this approximation suggests that LSFO would favor the near complete replacement (~80%) of lattice 16O by 18O, which is consistent with our experimental observations. The influence of isotopic mass in combination with the thermodynamic instability of vacancies at 400°C and pO2 = 3 mbar highlights some of the potential driving forces for OE.  \n Figure 3: a) Gibbs free energy of O vacancy formation in LSFO (x=0.5) as function of pO2 for temperatures of 25°C (298K) and 400°C (670K). The vertical dashed line indicates the experimental pO2 (3 mbar). b) Impact of a single Sr substitution on the migration energy barrier of O vacancy. The O vacancy pathway investigated is indicated by blue squares. When Sr is introduced, the initial image configuration (position 0) corresponds to a O vacancy being 1st neighbor with the Sr species. The energy barriers have been calculated relative to the local minima just prior to the transition state. c) Comparison of the chemical potential (per formula unit) of LSFO for a compound made of two different O isotopes, either 16O or 18O. The chemical potential difference is shown by the green curve and right y-axis in meV/f.u. The vertical dashed line indicates the temperature at which experiments have been performed.  \n16  Oxygen mobility in annealed metal-perovskite  Knowing the mobility and reactivity of oxygen in the pure perovskite system, the annealed metal-perovskite specimens were analyzed to determine how the metallic overlayers influence transport mechanisms. Elemental analyses of the LSFO and LSAT show the phases effectively remain the same as that in the annealed-perovskite case (Figure 2g, h; Table S1). LSAT has not undergone any chemical change or isotopic exchange, again demonstrating it is effectively inert. The bulk LSFO elemental composition remains similar to the annealed-perovskite (and as-grown) specimens, and there is no net oxygen concentration change during reaction (42.3 ± 0.0(3) at.% O). Oxygen isotopic analysis also shows near complete OE in LSFO, similar to that in the perovskite-annealed specimens (f18O 0.82 ± 0.07 vs. 0.84 ± 0.01, respectively). The elemental and oxygen isotopic composition of the Ni and Cr layers overlying LSFO have changed significantly following annealing, indicative of metal oxidation and phase transformation (Figure 2g, h; Table S1). That is, Ni has clearly oxidized, as the oxygen concentration in the Ni layer has increased from 13.3 ± 1.5 at.% in the as-grown to 44.0 ± 0.4 at.% after annealing, suggestive of a NiO-like phase. The Cr-layer is also partially oxidized following annealing, primarily at its interfaces with other layers; i.e.  Cr-rich oxides, similar to Cr2O3,53 formed near the Ni/Cr (~45 at.% Cr, 50 at.% O) and Cr/LSFO interfaces (~40 at.% Cr, ~60 at.% O) (see Figure 2). The Cr bulk experiences less oxidation relative to the interfaces and is largely metallic (e.g. only ~25 at.% O), similar to the as-grown material. It is important to note that the specimen outer surface is not included in the APT reconstruction as this was outside the field of view, although we would expect the exposed Cr surfaces to have also oxidized. Some elemental mixing between the Ni and Cr regions has also occurred, as a thin mixed Ni-Cr oxide layer is now present between the Cr-rich oxide (near the Ni-Cr interface) and the Cr-bulk. In comparison, no cation intermixing (i.e. mixed oxides) is found at the Cr-LSFO interface. Prior work on the oxidation behavior of a Ni-Cr alloys indicated the initial stage of oxidation involved the formation of an outward growing mixed Ni-Cr oxide due to the rapid movement of cations, like Ni.54–56 Later stages indicate a Cr-17  rich inward growing oxide layer formed via migration of O from the environment moving towards the metal interfaces and along grain boundaries. This suggests that, at the Ni-Cr interface, a Ni-Cr mixed oxide is initially formed (likely from oxygen originally present in the metal layers; Table S1) followed by a Cr-rich inner oxide.  In addition to cation transport phenomena inferred from elemental analyses, isotopic analyses suggest oxidation occurs by different pathways for each metallic phase (Ni/NiO and Cr/Cr2O3). That is, f18O in the Ni layer has increased from 0.05 ± 0.02 in the as-grown specimen to 0.78 ± 0.07 after annealing (Figure 2c, i), indicating that oxidation occurs from gaseous 18O from the environment. Measurements and visualization of the oxygen isotopic distribution also show 18O homogeneously distributed over the Ni phase (Figure 2i, Figure 4).  This is not the case for Cr oxidation. That is, the oxygen isotopic content in the bulk is largely 16O (f18O = 0.15 ± 0.10) (Figure 2i, Figure 4). More so, the Cr-oxides formed at the interfaces display a gradient in 18O, where f18O is highest near the LSFO phases and decreases approaching the Cr bulk (from 0.70 ± 0.05 to 0.10 ± 0.10). Similar observations are made for the Cr-oxide at the Ni-Cr interface (f18O decreases from 0.38 ± 0.08 at the interface to 0.08 ± 0.04 towards the Cr-bulk). The 18O distribution across the interfaces are also noticeably diffuse. Thus, in contrast to Ni oxidation, these observations suggest that Cr within the central volume of the APT specimen, within our field of view, is not simply oxidized by gaseous oxygen from the environment.  \nFigure 4: 2D heat map showing the oxygen isotopic composition across the annealed metal-perovskite specimen.  18  Several parameters can contribute to the ability to form a protective, Cr-rich oxide film including thermodynamics of oxide formation, kinetics (i.e., ion mobility), and environmental parameters (oxygen partial pressure, presence of water vapor, temperature, etc.). At the temperature used in this study (400°C), Cr2O3 is thermodynamically more stable (lower free energy of formation) in comparison to other transition metal oxides such as NiO.57 Hence, we hypothesize that oxygen anions are mobile and are consumed in the formation of a Cr oxide at the Ni/Cr and Cr/LSFO interface, whereas NiO is formed due to exposure in the in situ reactor chamber, where oxygen partial pressure is higher and there is sufficient driving force for Ni oxidation.58,59 Within the field of view, through the center of the APT specimen, we expect that a Cr oxide is formed from the reaction of Cr with nearby oxygen anions from the neighboring phases (e.g., from migration of oxygen anions from adjacent LSFO and the Ni(-oxide) layer), whereas Ni oxide is formed after exposure to elevated temperature 18O2 gas. This is consistent with experimental measurements for the f18O gradient at the Cr-LSFO interface of the annealed specimen. We would expect that outside the field of view, Cr along the surface of the APT specimen oxidizes by the gaseous environment. The passivating Cr-oxide film could prevent 18O ingress from the sides of the APT specimen, whereas the Ni (NiO) and LSFO are relatively O permeable. This would make the NiO and LSFO the predominant O sources for Cr oxidation within our field of view.   Conclusions Our combined elemental and isotopic observations across the as-grown, annealed perovskite, and annealed metal-perovskite specimens reveal diverse oxygen transport pathways across the system, controlled by the unique reactivity and relationships between phases. This includes (1) exchange between oxygen in LSFO lattice and the gaseous environment, (2) Ni oxidation by gaseous 18O2 from the environment, and (3) Cr oxidation by pulling oxygen from the neighboring NiO and LSFO phases (Figure 5).  19   \n  Figure 5: Conceptual schematic of the diverse oxygen transport pathways and reactions, highlighting OE between lattice oxygen in LSFO and 18O2(g) coupled with oxidation of the metallic layers. Vertical dashed lines denote the conceptual field of view captured by APT; we hypothesize that the oxidation and passivation of the Cr could have also occurred over the exposed tip surfaces outside the field of view (i.e., more translucent regions at the shanks). Extensive OE in LSFO is consistent with vacancy-mediated mechanisms, where transport and exchange occurs by discrete hops of oxygen ions to neighboring vacant sites and, in this case, leads to the near complete replacement of lattice 16O with 18O from the environment. The consistent O concentrations in the LSFO for the perovskite-annealed and metal-perovskite annealed specimens relative to the as-grown specimen suggest that steady-state composition is reached, as there is no net addition or removal of oxygen in the LSFO layer (Figure 2). The theoretical simulations performed provide a rationale for OE reaction mechanisms and highlight a complex interplay of different factors. The thermal instability of vacancies, further enhanced by high O2 partial pressure, provides a thermodynamic driver for oxygen atoms from the environment to occupy them. However, the composition (i.e., Sr doping) of the material forces the system to maintain a steady-state vacancy concentration throughout the reaction. While the concentration of O vacancy is dictated by the degree of Sr doping, we propose that defect concentration is the main driver for lattice diffusion and that the increase of the migration energy barrier with Sr doping has a small impact on diffusion and exchange. In addition to thermodynamic of defects and diffusion \n20  mechanisms, simulations showed that the isotopic substitution of 16O in the LSFO lattice by 18O lowers the chemical potential of the material, thereby favoring replacement. Measurements and visualization of the oxygen isotope distribution at high-spatial and chemical resolution reveal different oxidation mechanisms and pathways for Ni versus Cr. While Cr-species will affect electrode performance by blocking active sites on the surface,19 we show here that Cr can also potentially scavenge O from neighboring oxides. It also appears the reaction at least partially passivates, as the Cr metal layer did not fully oxidize, although this will depend on the cell’s environmental conditions (e.g. temperature, oxygen pressure, etc.).  More broadly, this study demonstrates how the unique coupling of isotopic tracers with APT can provide insight into local, nanoscale reactions as well as potential reaction sequences. While this study was designed to investigate model heterostructures, this approach could be adapted to investigate engineering conditions and materials of interests to SOFCs and beyond. For instance, this approach can be applied to probe oxygen diffusion and exchange systematically, such as across LSFO heterostructures with varying dopants and doping concentrations. This can provide much-needed mechanistic insight into oxygen reactions with perovskites, which are of great significance as electrocatalysts with applications to oxygen reduction reactions. Our approach presents new opportunities to resolve oxygen reaction pathways across complex oxide heterostructures, which can inform fields from  catalysis to corrosion science.  References (1)  Davies, P. K.; Wu, H.; Borisevich, A. Y.; Molodetsky, I. E.; Farber, L. Crystal Chemistry of Complex Perovskites: New Cation-Ordered Dielectric Oxides. Annu. Rev. Mater. Res. 2008, 38, 369–401. https://doi.org/10.1146/annurev.matsci.37.052506.084356. (2)  Dawber, M.; Rabe, K. M.; Scott, J. F. Physics of Thin-Film Ferroelectric Oxides. Rev. Mod. Phys. 2005, 77 (October), 1083–1130. 21  (3)  Wang, L.; Stoerzinger, K. A.; Chang, L.; Zhao, J.; Li, Y.; Tang, C. S.; Yin, X.; Bowden, M. E.; Yang, Z.; Guo, H.; You, L.; Guo, R.; Wang, J.; Ibrahim, K.; Chen, J.; Rusydi, A.; Wang, J.; Chambers, S. A.; Du, Y. Tuning Bifunctional Oxygen Electrocatalysts by Changing the A-Site Rare-Earth Element in Perovskite Nickelates. Adv. Funct. Mater. 2018, 28 (39), 1–8. https://doi.org/10.1002/adfm.201803712. (4)  Liu, J.; Jia, E.; Wang, L.; Stoerzinger, K. A.; Zhou, H.; Tang, C. S.; Yin, X.; He, X.; Bousquet, E.; Bowden, M. E.; Wee, A. T. S.; Chambers, S. A.; Du, Y. Tuning the Electronic Structure of LaNiO3 through Alloying with Strontium to Enhance Oxygen Evolution Activity. Adv. Sci. 2019, 6 (19). https://doi.org/10.1002/advs.201901073. (5)  Wang, L.; Adiga, P.; Zhao, J.; Samarakoon, W. S.; Stoerzinger, K. A.; Spurgeon, S. R.; Matthews, B. E.; Bowden, M. E.; Sushko, P. V.; Kaspar, T. C.; Sterbinsky, G. E.; Heald, S. M.; Wang, H.; Wangoh, L. W.; Wu, J.; Guo, E. J.; Qian, H.; Wang, J.; Varga, T.; Thevuthasan, S.; Feng, Z.; Yang, W. Understanding the Electronic Structure Evolution of Epitaxial LaNi1- XFexO3Thin Films for Water Oxidation. Nano Lett. 2021, 21 (19), 8324–8331. https://doi.org/10.1021/acs.nanolett.1c02901. (6)  Zhou, Y.; Guan, X.; Zhou, H.; Ramadoss, K.; Adam, S.; Liu, H.; Lee, S.; Shi, J.; Tsuchiya, M.; Fong, D. D.; Ramanathan, S. Strongly Correlated Perovskite Fuel Cells. Nature 2016, 534 (7606), 231–234. https://doi.org/10.1038/nature17653. (7)  Comes, R.; Chambers, S. Interface Structure, Band Alignment, and Built-In Potentials at LaFeO3/n-SrTiO3 Heterojunctions. Phys. Rev. Lett. 2016, 117 (22), 1–5. https://doi.org/10.1103/PhysRevLett.117.226802. (8)  Shen, H.; Xue, T.; Wang, Y.; Cao, G.; Lu, Y.; Fang, G. Photocatalytic Property of Perovskite LaFeO3 Synthesized by Sol-Gel Process and Vacuum Microwave Calcination. Mater. Res. Bull. 2016, 84, 15–24. https://doi.org/10.1016/j.materresbull.2016.07.024. 22  (9)  Stoerzinger, K. A.; Wang, L.; Ye, Y.; Bowden, M.; Crumlin, E. J.; Du, Y.; Chambers, S. A. Linking Surface Chemistry to Photovoltage in Sr-Substituted LaFeO3 for Water Oxidation. J. Mater. Chem. A 2018, 6 (44), 22170–22178. https://doi.org/10.1039/c8ta05741a. (10)  Chang, H.; Bjørgum, E.; Mihai, O.; Yang, J.; Lein, H. L.; Grande, T.; Raaen, S.; Zhu, Y. A.; Holmen, A.; Chen, D. Effects of Oxygen Mobility in La-Fe-Based Perovskites on the Catalytic Activity and Selectivity of Methane Oxidation. ACS Catal. 2020, 10 (6), 3707–3719. https://doi.org/10.1021/acscatal.9b05154. (11)  Hwang, J.; Rao, R. R.; Giordano, L.; Katayama, Y.; Yu, Y.; Shao-Horn, Y. Perovskites in Catalysis and Electrocatalysis. Science (80-. ). 2017, 358 (6364), 751–756. https://doi.org/10.1126/science.aam7092. (12)  Zheng, Y. S.; Zhang, M.; Li, Q.; Zhu, Y. A.; Sui, Z. J.; Chen, D.; Zhou, X. G. Electronic Origin of Oxygen Transport Behavior in La-Based Perovskites: A Density Functional Theory Study. J. Phys. Chem. C 2019, 123 (1), 275–290. https://doi.org/10.1021/acs.jpcc.8b11249. (13)  Ishigaki, T.; Yamauchi, S.; Kishio, K.; Mizusaki, J.; Fueki, K. Diffusion of Oxide Ion Vacancies in Perovskite-Type Oxides. J. Solid State Chem. 1988, 73 (1), 179–187. https://doi.org/10.1016/0022-4596(88)90067-9. (14)  ten Elshof, J. E.; Lankhorst, M. H. R.; Bouwmeester, H. J. M. Oxygen Exchange and Diffusion Coefficients of Strontium‐Doped Lanthanum Ferrites by Electrical Conductivity Relaxation. J. Electrochem. Soc. 1997, 144 (3), 1060–1067. https://doi.org/10.1149/1.1837531. (15)  Li, M.; Wang, Y.; Wang, Y.; Chen, F.; Xia, C. Bismuth Doped Lanthanum Ferrite Perovskites as Novel Cathodes for Intermediate-Temperature Solid Oxide Fuel Cells. ACS Appl. Mater. Interfaces 2014, 6 (14), 11286–11294. https://doi.org/10.1021/am5017045. (16)  Liu, J.; Jia, E.; Stoerzinger, K. A.; Wang, L.; Wang, Y.; Yang, Z.; Shen, D.; Engelhard, M. H.; 23  Bowden, M. E.; Zhu, Z.; Chambers, S. A.; Du, Y. Dynamic Lattice Oxygen Participation on Perovskite LaNiO3during Oxygen Evolution Reaction. J. Phys. Chem. C 2020, 124 (28), 15386–15390. https://doi.org/10.1021/acs.jpcc.0c04808. (17)  Adler, S. B.; Chen, X. Y.; Wilson, J. R. Mechanisms and Rate Laws for Oxygen Exchange on Mixed-Conducting Oxide Surfaces. J. Catal. 2007, 245 (1), 91–109. https://doi.org/10.1016/j.jcat.2006.09.019. (18)  Ascolani-Yael, J.; Montenegro-Hernández, A.; Garcés, D.; Liu, Q.; Wang, H.; Yakal-Kremski, K.; Barnett, S.; Mogni, L. The Oxygen Reduction Reaction in Solid Oxide Fuel Cells: From Kinetic Parameters Measurements to Electrode Design. JPhys Energy 2020, 2 (4). https://doi.org/10.1088/2515-7655/abb4ec. (19)  Zhou, L.; Mason, J. H.; Li, W.; Liu, X. Comprehensive Review of Chromium Deposition and Poisoning of Solid Oxide Fuel Cells (SOFCs) Cathode Materials. Renew. Sustain. Energy Rev. 2020, 134 (August), 110320. https://doi.org/10.1016/j.rser.2020.110320. (20)  Horita, T.; Xiong, Y.; Kishimoto, H.; Yamaji, K.; Brito, M. E.; Yokokawa, H. Chromium Poisoning and Degradation at (La,Sr)MnO[Sub 3] and (La,Sr)FeO[Sub 3] Cathodes for Solid Oxide Fuel Cells. J. Electrochem. Soc. 2010, 157 (5), B614. https://doi.org/10.1149/1.3322103. (21)  Kim, J. Y.; Canfield, N. L.; Chick, L. A.; Meinhardt, K. D.; Sprenkle, V. L. Chromium Poisoning Effects on Various Cathodes. In Advances in Solid Oxide Fuel Cells: Ceramic Engineering and Science Proceedings; 2005; p Ch. 15. (22)  Wang, R.; Sun, Z.; Lu, Y.; Gopalan, S.; Basu, S. N.; Pal, U. B. Comparison of Chromium Poisoning between Lanthanum Strontium Manganite and Lanthanum Strontium Ferrite Composite Cathodes in Solid Oxide Fuel Cells. J. Power Sources 2020, 476 (July), 228743. https://doi.org/10.1016/j.jpowsour.2020.228743. 24  (23)  Yano, K. H.; Kohnert, A. A.; Banerjee, A.; Edwards, D. J.; Holby, E. F.; Kaspar, T. C.; Kim, H.; Lach, T. G.; Taylor, S. D.; Wang, Y.; Uberuaga, B. P.; Schreiber, D. K. Radiation-Enhanced Anion Transport in Hematite. Chem. Mater. 2021, 33 (4), 2307–2318. https://doi.org/doi.org/10.1021/acs.chemmater.0c04235. (24)  Taylor, S. D.; Liu, J.; Zhang, X.; Arey, B. W.; Kovarik, L.; Schreiber, D. K.; Perea, D. E.; Rosso, K. M. Visualizing the Iron Atom Exchange Front in the Fe(II)-Catalyzed Recrystallization of Goethite by Atom Probe Tomography. Proc. Natl. Acad. Sci. U. S. A. 2019, 116 (8), 2866–2874. https://doi.org/10.1073/pnas.1816620116. (25)  Baiutti, F.; Chiabrera, F.; Diercks, D.; Cavallaro, A.; Yedra, L.; López-Conesa, L.; Estradé, S.; Peiró, F.; Morata, A.; Aguadero, A.; Tarancón, A. Direct Measurement of Oxygen Mass Transport at the Nanoscale. Adv. Mater. 2021, 33 (48). https://doi.org/10.1002/adma.202105622. (26)  Schweinar, K.; Gault, B.; Mouton, I.; Kasian, O. Lattice Oxygen Exchange in Rutile IrO2during the Oxygen Evolution Reaction. J. Phys. Chem. Lett. 2020, 11 (13), 5008–5014. https://doi.org/10.1021/acs.jpclett.0c01258. (27)  Ishigaki, T.; Yamauchi, S.; Fueki, K.; Naitoh, H.; Adachi, T. Tracer Diffusion Coefficient of Oxide Ions in LaFeO3 by SIMS Measurement. 1984, 441–444. https://doi.org/10.1007/978-3-642-82256-8_114. (28)  Mahato, N.; Banerjee, A.; Gupta, A.; Omar, S.; Balani, K. Progress in Material Selection for Solid Oxide Fuel Cell Technology: A Review. Prog. Mater. Sci. 2015, 72, 141–337. https://doi.org/10.1016/j.pmatsci.2015.01.001. (29)  Lambeets, S. V.; Kautz, E. J.; Wirth, M. G.; Orren, G. J.; Devaraj, A.; Perea, D. E. Nanoscale Perspectives of Metal Degradation via In Situ Atom Probe Tomography. Top. Catal. 2020, 63 (15–18), 1606–1622. https://doi.org/10.1007/s11244-020-01367-z. 25  (30)  Kautz, E. J.; Gwalani, B.; Lambeets, S. V. M.; Kovarik, L.; Schreiber, D. K.; Perea, D. E.; Senor, D.; Liu, Y. S.; Battu, A. K.; Tseng, K. P.; Thevuthasan, S.; Devaraj, A. Rapid Assessment of Structural and Compositional Changes during Early Stages of Zirconium Alloy Oxidation. npj Mater. Degrad. 2020, 4 (1), 1–9. https://doi.org/10.1038/s41529-020-00133-6. (31)  Devaraj, A.; Barton, D. J.; Li, C.; Lambeets, S. V.; Liu, T.; Battu, A.; Vaithiyalingam, S.; Thevuthasan, S.; Yang, F.; Guo, J.; Li, T.; Ren, Y.; Kovarik, L.; Perea, D. E.; Sushko, M. L. Visualizing the Nanoscale Oxygen and Cation Transport Mechanisms during the Early Stages of Oxidation of Fe–Cr–Ni Alloy Using In Situ Atom Probe Tomography. Adv. Mater. Interfaces 2022, 2200134, 2200134. https://doi.org/10.1002/admi.202200134. (32)  Kautz, E. J.; Lambeets, S. V.; Royer, J.; Perea, D. E.; Harilal, S. S.; Devaraj, A. Compositional Partitioning during Early Stages of Oxidation of a Uranium-Molybdenum Alloy. Scr. Mater. 2022, 212, 114528. https://doi.org/10.1016/j.scriptamat.2022.114528. (33)  Thompson, K.; Lawrence, D.; Larson, D. J.; Olson, J. D.; Kelly, T. F.; Gorman, B. In Situ Site-Specific Specimen Preparation for Atom Probe Tomography. Ultramicroscopy 2007, 107 (2–3), 131–139. https://doi.org/10.1016/j.ultramic.2006.06.008. (34)  Giannuzzi, L. A.; Drown, J. L.; Brown, S. R.; Irwin, R. B.; Stevie, F. A. Applications of the FIB Lift-out Technique for TEM Specimen Preparation. Microsc. Res. Tech. 1998, 41 (4), 285–290. https://doi.org/10.1002/(SICI)1097-0029(19980515)41:4<285::AID-JEMT1>3.0.CO;2-Q. (35)  Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B - Condens. Matter Mater. Phys. 1996, 54 (16), 11169–11186. https://doi.org/10.1103/PhysRevB.54.11169. (36)  Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100 (13), 1–4. https://doi.org/10.1103/PhysRevLett.100.136406. 26  (37)  Dudarev, S.; Botton, G. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B - Condens. Matter Mater. Phys. 1998, 57 (3), 1505. https://doi.org/10.1103/PhysRevB.57.1505. (38)  Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. First-Principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: The LDA + U Method. J. Phys. Condens. Matter 1997, 9 (4), 767–808. https://doi.org/10.1088/0953-8984/9/4/002. (39)  Selbach, S. M.; Tolchard, J. R.; Fossdal, A.; Grande, T. Non-Linear Thermal Evolution of the Crystal Structure and Phase Transitions of LaFeO 3 Investigated by High Temperature X-Ray Diffraction. J. Solid State Chem. 2012, 196 (March 2020), 249–254. https://doi.org/10.1016/j.jssc.2012.06.023. (40)  Van De Walle, A.; Tiwary, P.; De Jong, M.; Olmsted, D. L.; Asta, M.; Dick, A.; Shin, D.; Wang, Y.; Chen, L. Q.; Liu, Z. K. Efficient Stochastic Generation of Special Quasirandom Structures. Calphad Comput. Coupling Phase Diagrams Thermochem. 2013, 42, 13–18. https://doi.org/10.1016/j.calphad.2013.06.006. (41)  Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1997, 78 (7), 1396. https://doi.org/10.1103/physrevlett.78.1396. (42)  Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science. Scr. Mater. 2015, 108, 1–5. https://doi.org/10.1016/j.scriptamat.2015.07.021. (43)  Henkelman, G.; Uberuaga, B. P.; Jónsson, H. Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113 (22), 9901–9904. https://doi.org/10.1063/1.1329672. (44)  Gault, B.; Saxey, D. W.; Ashton, M. W.; Sinnott, S. B.; Chiaramonti, A. N.; Moody, M. P.; Schreiber, D. K. Behavior of Molecules and Molecular Ions near a Field Emitter. New J. Phys. 27  2016, 18 (3). https://doi.org/10.1088/1367-2630/18/3/033031. (45)  Devaraj, A.; Colby, R.; Hess, W. P.; Perea, D. E.; Thevuthasan, S. Role of Photoexcitation and Field Ionization in the Measurement of Accurate Oxide Stoichiometry by Laser-Assisted Atom Probe Tomography. J. Phys. Chem. Lett. 2013, 4 (6), 993–998. https://doi.org/10.1021/jz400015h. (46)  Bachhav, M.; Danoix, F.; Hannoyer, B.; Bassat, J. M.; Danoix, R. Investigation of O-18 Enriched Hematite (α-Fe 2 O 3 ) by Laser Assisted Atom Probe Tomography. Int. J. Mass Spectrom. 2013, 335, 57–60. https://doi.org/10.1016/j.ijms.2012.10.012. (47)  Bachhav, M.; Danoix, R.; Danoix, F.; Hannoyer, B.; Ogale, S.; Vurpillot, F. Investigation of Wustite (Fe1-XO) by Femtosecond Laser Assisted Atom Probe Tomography. Ultramicroscopy 2011, 111 (6), 584–588. https://doi.org/10.1016/j.ultramic.2010.11.023. (48)  Taylor, S. D.; Liu, J.; Arey, B. W.; Schreiber, D. K.; Perea, D. E.; Rosso, K. M. Resolving Iron(II) Sorption and Oxidative Growth on Hematite (001) Using Atom Probe Tomography. J. Phys. Chem. C 2018, 122 (7), 3903–3914. https://doi.org/10.1021/acs.jpcc.7b11989. (49)  Kaspar, T. C.; Taylor, S. D.; Yano, K. H.; Lach, T. G.; Zhou, Y.; Zhu, Z.; Still, E. K.; Hosemann, P.; Spurgeon, S. R.; Schreiber, D. K. Bulk and Short-Circuit Anion Diffusion in Epitaxial Fe2O3 Films Quantified Using Buried Isotopic Tracer Layers. Adv. Mater. Interfaces 2021, 2001768. (50)  Ritzmann, A. M.; Muñoz-García, A. B.; Pavone, M.; Keith, J. A.; Carter, E. A. Ab Initio DFT+U Analysis of Oxygen Vacancy Formation and Migration in La1-XSrxFeO3-δ (x = 0, 0.25, 0.50). Chem. Mater. 2013, 25 (15), 3011–3019. https://doi.org/10.1021/cm401052w. (51)  Orikasa, Y.; Nakao, T.; Oishi, M.; Ina, T.; Mineshige, A.; Amezawa, K.; Arai, H.; Ogumi, Z.; Uchimoto, Y. Local Structural Analysis for Oxide Ion Transport in La 0.6Sr0.4FeO3-δ Cathodes. J. Mater. Chem. 2011, 21 (36), 14013–14019. https://doi.org/10.1039/c1jm11358e. (52)  Søgaard, M.; Vang Hendriksen, P.; Mogensen, M. Oxygen Nonstoichiometry and Transport 28  Properties of Strontium Substituted Lanthanum Ferrite. J. Solid State Chem. 2007, 180 (4), 1489–1503. https://doi.org/10.1016/j.jssc.2007.02.012. (53)  Yano, K. H.; Kohnert, A. A.; Kaspar, T. C.; Taylor, S. D.; Spurgeon, S. R.; Kim, H.; Wang, Y.; Uberuaga, B. P.; Schreiber, D. K. Radiation Enhanced Anion Diffusion in Chromia. J. Phys. Chem. C 2021, 125 (50), 27820–27827. https://doi.org/10.1021/acs.jpcc.1c08705. (54)  Blades, W. H.; Reinke, P. From Alloy to Oxide: Capturing the Early Stages of Oxidation on Ni-Cr(100) Alloys. ACS Appl. Mater. Interfaces 2018, 10 (49), 43219–43229. https://doi.org/10.1021/acsami.8b15210. (55)  Wang, C. M.; Genc, A.; Cheng, H.; Pullan, L.; Baer, D. R.; Bruemmer, S. M. In-Situ TEM Visualization of Vacancy Injection and Chemical Partition during Oxidation of Ni-Cr Nanoparticles. Sci. Rep. 2015, 4, 1–6. https://doi.org/10.1038/srep03683. (56)  Luo, L.; Zou, L.; Schreiber, D. K.; Baer, D. R.; Bruemmer, S. M.; Zhou, G.; Wang, C. M. In-Situ Transmission Electron Microscopy Study of Surface Oxidation for Ni-10Cr and Ni-20Cr Alloys. Scr. Mater. 2016, 114, 129–132. https://doi.org/10.1016/j.scriptamat.2015.11.031. (57)  Ellingham, H. J. T. No Title. J. Soc. Chem. Ind. 1944, 63 (125). (58)  Douglass, D. L. The Oxidation Mechanism of Dilute Ni-Cr Alloys. Corros. Sci. 1968, 8 (9), 665–678. https://doi.org/10.1016/S0010-938X(68)80101-5. (59)  Wood, G. C.; Wright, I. G.; Ferguson, J. M. The Oxidation of Ni and Co and of Ni/Co Alloys at High Temperatures. Corros. Sci. 1965, 5 (9), 645–661. https://doi.org/10.1016/S0010-938X(65)90203-9. (60)  Kilburn, M. R.; Wacey, D. Nanoscale Secondary Ion Mass Spectrometry (NanoSIMS) as an Analytical Tool in the Geosciences; 2015; Vol. 2015-January. https://doi.org/10.1039/9781782625025-00001. 29   Acknowledgments This research was supported by the Chemical Dynamics Initiative/Investment, under the Laboratory Directed Research and Development (LDRD) Program at Pacific Northwest National Laboratory (PNNL). DKS acknowledges support from the US Department of Energy (DOE) Office of Science, Basic Energy Sciences, Materials Science and Engineering Division for supporting APT data analysis and interpretation. PNNL is a multi-program national laboratory operated for the U.S. Department of Energy (DOE) by Battelle Memorial Institute under Contract No. DE-AC05-76RL01830. The growth of thin film samples was supported by DOE Office of Science, Basic Energy Sciences under award #10122. Experimental sample preparation and APT analysis was performed at the Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at PNNL. STEM data was collected in the Radiological Microscopy Suite (RMS), located in the Radiochemical Processing Laboratory (RPL) at PNNL. We would also like to thank Dr. Blas Uberuaga (Los Alamos National Laboratory) for helpful discussions on the simulations. Data Availability Statement All relevant data are presented in the main text or supplementary information. STEM, APT, and DFT data can be made available upon request by contacting the authors.   Author Contributions S.D.T., K.H.Y., and S.R.S. conceived and developed the project plan. L.W. and Y.D. prepared the thin film samples. S.D.T., K.H.Y., E.J.K., S.N., and D.K.S. conducted APT analysis. B.M. conducted STEM sample preparation and imaging. M.S. conducted theory calculations. All authors contributed to the writing and editing of the manuscript. 30  Competing Interests Statement The authors declare no competing interests.    31  ToC graphic \n   \n32  Supplementary Information for “Resolving diverse oxygen transport pathways across Sr-doped lanthanum ferrite and metal-perovskite heterostructures”  S.D. Taylor,1,+,* K.H. Yano,2,+ M. Sassi1, B.E. Matthews,2 E.J. Kautz,2 S.V. Lambeets,1 S. Neumann,2 D.K. Schreiber,2 L. Wang,1 Y. Du,1 S.R. Spurgeon2,3,* 1. Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99352 USA 2. Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA 99352 USA 3. Department of Physics, University of Washington, Seattle, WA 98195 USA  +First coauthors.  *Corresponding authors: sandra.taylor@pnnl.gov; steven.spurgeon@pnnl.gov   Includes: • Figure S1: APT specimen preparation • Figure S2: Ion assignment in mass spectra • Table S1: Elemental compositions of the tips measured • Oxygen isotopic analyses and f18O quantification o Figure S3: Analyses of key O ionic and isotopic species  o Figure S4: f18O quantification  • Figure S5: Analysis of remaining tips  33  APT specimen preparation While samples were prepared in a typical FIB-SEM fashion, additional SEM images are provided here as context for the Ni/Cr-metal capping scheme. SEM images (Figure S1a-b) before sharpening show Pt cap as well as the metal cap, the LSFO, and the LSAT substrate. After sharpening (Figure S1c) the Ni/Cr protective cap remains. For the Annealed specimens, the tip was run through the Ni and Cr layers in the LEAP 4000XHR before annealing. In these cases, the tip would start with the LSFO and have no protective cap remaining. \n Figure S1: FIB-SEM preparation of APT tip from the Ni-Cr-LSFO-LSAT stack. Sample preparation is typical for an APT specimen; however, these SEM images are provided for additional context of capping scheme (a) before and (b) after tip sharpening.   Elemental analyses Compositional analyses were enabled through assignment of ionic species to the peaks in the mass spectra consistent with the known elemental and/or isotopic compositions (see description of elemental analysis in SI, Figure S2 and Table S1). Given the multi-elemental nature of this system and resulting complicated mass spectra, the ionic assignment was better enabled by analyzing bulk sections and then deducing major ions appropriate to each phase. In turn, the compositional profiles were calculated by breaking the tip into manageable sections and then stitching them together (Figure S2).  \n34  Elemental concentrations were determined by decomposing all ionic species. The error in the concentrations was estimated by standard counting statistics and is represented by the standard deviation σ (Eqn. 1): 𝜎=8*!(',,\t.\t*!)0   Eqn. 1 where Ci is the measured atomic concentration of element i and N is the total number of atoms detected. Atomic concentrations of each tip condition where bulk concentrations are averaged over two samples with the standard deviation are provided in Table S1. In some cases, LSAT was not captured during the run.   35   Fig S2: Mass spectra from as-grown specimen highlighting multi-elemental and isotopic nature of the heterostructure. Ion species were determined through analyses isolating the bulk in each layer. Dominant, general ionic species are labelled. Intensity is log-scale.    \n36   Table S1: Average elemental and oxygen isotopic compositions of each layer in each set of experiment. Measurements are based off two APT specimens for each experiment, considering the standard deviation (i.e. ± value). LSAT compositions are based off one tip per experiment.   At. %  As-Grown Annealed perovskite Annealed metal-perovskite Ni Cr LSFO LSAT LSFO LSAT Ni Cr LSFO LSAT Ni  77.29 ± 2.47 1.23 ± 0.05     43.43 ± 2.60 8.22 ± 1.40   Cr  2.56 ± 0.  02 70.58 ± 1.53     7.87 ± 0.78 50.24 ± 1.43   O  13.33 ± 1.46 21.59 ± 1.23 43.26 ± 0.91 58.65 43.79 ± 0.26 57.13 44.01 ± 0.35 34.09 ± 3.44 42.31 ± 0.03 58.1 La    10.71 ± 0.50 7.61 10.89 ± 0.02 7.15   11.30 ± 0.22 7.2 Fe    27.20 ± 0.11  27.24 ± 0.12    27.85 ± 0.02  Sr    18.49 ± 0.42 14.13 17.76 ± 0.01 13.63   18.25 ± 0.24 13.02 Ta     8.45  8.04    7.47 Al  6.82 ± 1.46 6.59 ± 0.25  10.02  13.19 4.70 ± 2.18 7.45 ± 0.61  13.13 f18O  0.05 ± 0.02 0.04 ± 0.00(1) 0.01 ± 0.00(4) 0.01 0.84 ± 0.01 0.04 0.78 ± 0.07 0.19 ± 0.07 0.82 ± 0.07 0.06    37  18O analyses and f18O quantification  The oxygen isotopic composition was analyzed across the specimen to follow oxygen transport in the solid between the different sources, i.e., 18O2 (g) and the 16O-solid phases, using the O1+ ionic species at 16-18Da. While it was typically a minor oxide-species in all the layers (i.e., ~7 ion% in NiO, ~3 ion% in Cr, ~2 ion% in LSFO, ~9 ion% LSAT), it was consistently observed across the heterostructure – thereby enabling measurements across the interfaces and the different layers. It also led to minimal isobaric and polyatomic interferences, as shown by the f18O profile of the as-grown specimen which reproduces concentrations effectively at NA (Figure 2c).  We also assessed the oxygen isotopic composition of all the other major oxide ionic species present in the system for comparison (Fig. S4). We find that most of the major ionic species are isolated to a single phase within the heterostructure (e.g., FeO1+ at 70-74 Da is only within LSFO) and thus would not be able to reproduce measurements at interfaces/across the different phases as needed for our study. However, their isotopic compositions are consistent with that of O1+ and thus support observations for oxygen exchange or oxidation occurring; for instance, in the LSFO layer, the LaO1+ species at 155-157 Da is 16O-dominant in the as-grown state vs. 18O-dominant in the annealed (metal-)perovskite specimens, similar to that observed using O1+. In some cases, significant interferences were present and complicate isotopic analysis; for instance, f18O analyses using the NiO1+ species in the Ni layer (74 – 78 Da) would suffer due unavoidable overlaps between 58Ni18O1+ with 60Ni16O1+ at 76Da. In turn, these analyses further confirm that oxygen isotopic compositions across the heterostructure are best achieved using the O1+ specie. The oxygen isotopic fraction was calculated from  16O1+ and 18O1+ ion counts (at 16 and 18 Da, respectively) (Eqn. 2). The error or uncertainty in the measured counts was calculated (Eqn. 3), and the uncertainty in the ratios was propagated (Eqn. 4).60 A bin size of 1 nm was used for the concentration profiles as this led to reasonable measurements in uncertainty while being able to clearly resolve oxygen compositions across the interfaces. 38  𝑓𝑂'1= 0\"#$0\"%$2\t0\"#$= 0\"#$0$  Eqn. 2 𝜎3=\t<𝑁3    Eqn. 3 𝜎!'14=\t8>5\"#$0\"#$?(+>5&0$?(∙\t𝑓𝑂'1     Eqn. 4  \n Figure S3: Isotopic analyses of key O ionic and isotopic species in a) Ni, b) Cr, (c) LSFO, and (d) LSAT phases. Peaks are labelled with their relevant ionic species that are present. Each range is normalized to the dominant 16O isotope, to effectively measure changes in 18O concentrations from the as-grown to perovskite and metal-perovskite annealed specimens. Potential PMI are identified in some cases, as denoted by multiple ionic species associated with a single peak. \n39  Analysis of Remaining Tips Two tips of each condition were run and the analysis for the second set is provided in Figure S5. Like the data provided in the text (Figure 2), panels (a-c) are of the as-grown, (d-f) the annealed perovskite, and (g-I) the annealed metal-perovskite samples. Atom map reconstructions, elemental concentration profiles, and f18O profiles are all included. These samples are consistent with those presented in the text.   \n Figure S5. Analyses from additional APT tips with APT reconstructions, elemental profiles, and f18O for the as-grown vs. annealed perovskite vs. annealed metal-perovskite specimens. Shading is used to highlight the uncertainty associated with the counting statistics.  \n"    },    {        "title": "1907.06758v1.Study_of_CoFe2O4_CoFe2_nanostructured_powder.pdf",        "content": "Study of CoFe\n2\nO\n4\n/CoFe\n2\n \nnanostructured \npowder\n \nE. S\n. \nFerreira\n1\n, E. F. Chagas\n1\n, A. P. Albuquerque\n1\n, R. J. Prado\n1\n \nand E. Baggio\n-\nSaitovitch\n2\n \n1\nInstituto de Física, Universidade Federal de Mato Grosso, 78060\n-\n900 Cuiabá\n-\nMT, Brazil.\n \n2\nCentro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud, 150 Urca Rio de Janeiro, Brazil\n \n \nAbstract\n \n \nW\ne report a\nn experimental\n \nstudy \nof the\n \nCoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposite\n, \na \nnanostructured material formed by \nhard\n \n(CoFe\n2\nO\n4\n) and \nsoft\n \n(CoFe\n2\n)\n \nmagnetic \nmateria\nls\n. The \nprecursor material, \ncobalt ferrite\n \n(CoFe\n2\nO\n4\n),\n \nwas prepared \nusing \nthe\n \nconventional s\ntoichiometric \ngel\n-\ncombustion method.\n \nT\nhe nanocomposite \nmaterial was obtained\n \nby\n \nreducing part\nially the precursor material using activated \ncharcoal as reducing agent \nin\n \nair and argon atmospheres, at 800 and 900\no\nC \nrespectively\n.\n \nThe magnetic hysteresis loops \ndemonstrate\n \nthat\n, in general, \np\nrepared nanocomposite samples \ndisplay \nsingle magnetic behavior\n,\n \nindicating \nexchange coupling between the \nsoft and hard \nmagnetic phases\n. \nHowever, for \nnanocomposite samples prepared at higher temperatures\n,\n \nthe hysteresis \nmeasurements \nshow\n \nsteps \ntypical of \ntwo\n-\nphase\n \nmagnetic behavior\n, suggesting \nthe existence of two non\n-\ncoupled magnetic phases. \nThe \nstudied \nnanocomposite\ns\n \npresent\ned\n \ncoercivity\n \n(H\nC\n)\n \nof \nabout 0.7 kOe\n,\n \nwhich is \nconsiderably \nlower than the \nexpected value for\n \ncobalt ferrite. \nA\n \nhuge increase \nin\n \nH\nC\n \n(\n>4\n4\n0%\n) \nand maximum \nenergy product (about 240%) \nwas obtained for \nthe nanocomposite \nafter \nhigh \nenergy milling \nprocessing\n.\n \n \n \nIntroduction\n \n \nThe \nmagnetic ferrites like \nM\n2+\nFe\n2\n3+\nO\n4\n \n(M = Ni; Co, Fe, Li, Mn, Zn, etc.) \nhave been\n \nused \nfor\n \nseveral \napplication\ns\n \nsuch as \nhigh\n-\ndensity\n \nmagnetic storage [1], electronic devices, biomedical applications [2\n-\n4], \npermanent magnets [5] and hydrogen production [6]. Among the hard ferrite\ns\n \nthe \nCoFe\n2\nO\n4\n \n(cobalt ferrite) \nplays an important role\n, \npresent\ning\n \npromising \ncharacteristic\ns\n \nsuch as high mag\nnet\n-\nelastic effect [7], \nchemical stability, electrical insulation, moderate saturation magnetization (M\nS\n), tunable coercivity (H\nC\n) \n[8\n-\n11] and thermal chemical reduction [6, 12, 13]. \nHowever,\n \nfor\n \npermanent magnet application\ns\n \nthe \nparameters M\nS\n \nand H\nC\n \nare \nof\n \nfundamental\n \nimportance\n, defining \nthe quantity called as\n \nthe figure of merit \nfor permanent magnets, the\n \nenergy product\n \n(BH)\nmax\n.\n \nThis quantity tends to increase with increasing of both quantities\n. The (BH)\nmax\n \nis an energy density (independent of the mass) \nthat can be simplified as a \nmeasure of the maximum amount of magnetic energy stored in a magnet.\n \nThe tunable \nbehavior of \ncoercivity \nin\n \ncobalt ferrite allows \nthe\n \nincrease\n \nin\n \nH\nC\n \n[8,\n \n11]\n, and \nn\numerous\n \nmethods\n \nas\n \nthermal annealing [\n9\n], capping [\n10\n] and \nmechanical milling treatment [\n8, 11\n]\n \nhave been used \nto this purpose. \nFor powdered cobalt ferrite materials, the highest coercivity achieved so far is \n9.5 kOe\n,\n \nreported by Limaye\n \net al.\n \n[\n10\n] \nthrough \ncapping the nanoparticles with oleic acid\n. \nH\nowever, \nin tha\nt work, \nsaturation magnetization decreased to 7.1 emu/g\n, a \nvalue about 10 times less than that expected \nfor\n \nuncapped nanoparticles. \nOn the other hand\n, Liu \net al.\n \n[\n11\n]\n \nP\nonce\n \net al.\n \n[\n8\n] \nand \nGalizia\n \net al.\n \n[\n14\n] \nobtained \nhigh \ncoercivity \nCoFe\n2\nO\n4\n \n(5.\n1,\n \n4.2 and \n3.7\n \nkOe respectively) with \nrelatively \nsmall decrease \nin\n \nM\nS\n \nusing \nhigh energy \nmechanical milling.\n \nFurthermore,\n \nthe thermal chemical reduction \nenable\ns\n \nus \nto \nincrease the M\nS \nthrough the partial \nconversion of hard ferrimagnetic\n \ncompound \nCoFe\n2\nO\n4\n \nin\nto\n \nthe soft \nferromagnetic intermetallic alloy \niron \ncobalt (CoFe\n2\n), producing the \nCoFe\n2\nO\n4\n/CoFe\n2\n \nexchange coupled \nnanocomposite \n[1\n5\n-\n1\n7\n].\n \nThe hysteresis \ncurve for \na\n \nnanocomposite with effective\n \nmagnetic \ncoupl\ning\n \nshould have\n \na \nsingle material \nmagnetic \nbehavior \n(called by \nZeng \net al.\n \n[18] \nas single\n-\nphase\n-\nlike behavior)\n \nwith M\nS\n \nand H\nC\n \nbetween the values \nexpected to CoFe\n2\nO\n4\n \n(\nM\nS\n \nand H\nC\n \nabout 70 emu/g and 1.0 kOe) and CoFe\n2\n \n(M\nS\n \nabout 230 emu/g, though \nvery small H\nC\n).\n \nTh\nis interesting\n \ncombination\n,\n \nof \na\n \nhard magnetic\n \nmaterial (\nCoFe\n2\nO\n4\n)\n \nwith \na soft one \n(\nCoFe\n2\n)\n \nin\nto\n \nan exchange coupled nanocomposite\n,\n \npresent\ns\n \nenormous potential to hard magnetic \napplications.\n \nIn a previous work\n \n[13]\n,\n \nof our \ngroup\n, hard/soft CoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposites were obtained by\n \nthermal treatment of \na \ncobalt\n \nferrite\n/\ncarbon (activated charcoal)\n \nmixture \nin argon atmosphere, as indicated \nby equation below\n:\n \n \n\u0000\u0000\n\u0000\u0000\n\u0000\n\u0000\n\u0000\n+\n2\n\u0000\n∆\n→\n\u0000\u0000\n\u0000\u0000\n\u0000\n+\n2\n\u0000\n\u0000\n\u0000\n      \n \n(1)\n \n \nThe symbol Δ indicates that thermal energy is necessary in the process.\n \nAccording \nto \nthe reduction\n \nprocess indic\nated\n \nin\n \neq. (1)\n,\n \ntwo moles of carbon \nare\n \nenough to convert \nall CoFe\n2\nO\n4\n \nin CoFe\n2\n \nbut, in practice, this \ndoes \nnot happen.\n \nIn\n \nthis previous\n \nwork\n \n[13]\n, \nt\nhe reduction \nprocess was \ndone\n \nusing \na \npowder of the mixture\n \n(cobalt ferrite plus carbon)\n \nin air and\n/or\n \ncontroll\ned\n \ninert \natmosphere (argon)\n. I\nn all case\ns\n \nthe\n \nmaster\ning of\n \nthe process\n \nwas difficult\n \nand, i\nn\n \na sample treatment in \nargon atmosphere with 2 molar of C\n,\n \nonly about 40%\n \nof CoFe\n2\nO\n4\n \nwas converted in\n \nCoFe\n2\n. The main \nreason \nmaking\n \ndifficult \nthe\n \ncontrol \no\nf \nthe reduction process was attributed to the reaction of carbon with \noxygen \nin\n \nair or \nwith \nresi\ndual oxygen in \nthe “\ninert\n”\n \natmosphere\n \n[13]\n.\n \nTrying to solve these problems, i\nn this w\no\nrk, we use\nd\n \na \nslightly different\n \nprocedure \nto obtain the \nCoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposites. Here, t\nhe mixture of cobalt ferrite with activated charcoal\n \nwas pressed\n \nto prepare a disk\n, aiming \nto avoid the contact \nbetween\n \ninternal mixture (inside the disk) with the \natmosphere of the furnace during the thermal treatment. \nT\nhis method \nc\nould \nfacilitate the control of CoFe\n2 \ncontent in the nanocomposite CoFe\n2\nO\n4\n/CoFe\n2\n. \nMoreover\n, \nthe same \nmilling \nprocedure \nused \npreviously \nto \npure nanostructured \ncobalt ferrite [8]\n \nwas performed\n \nin this work \nto increase the \nH\nC\n \nof the \nCoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposite, with\n \nexcellent\n \nresults.\n  \nExperimental\n \n \nThe \nnanostructured cobalt ferrite \nprecursor material was prepared using a conventional \ngel\n-\ncombustion method as \ndescribed \nin \nreference [\n19\n]\n. \nHigh\n-\npurity (99.9%) raw compounds were used. \nCobalt nitrate and iron nitrate (VETEC, Brazil) were dissolved in 450 ml of distilled water in a ratio \ncorresponding to the selected final composition. Glycine (VETEC, Brazil) was added in a proportion of \none an\nd half moles per mole of metal atoms, and the pH of the solution was adjusted with ammonium \nhydroxide (25%, Merck, Germany). The pH was tuned as closely as possible to 7, taking care to avoid \nprecipitation. The resulting solution was concentrated by evapor\nation using a hot \nplate at 300\n \n°\nC until a \nviscous gel was obtained. This hot gel finally burnt out as a result of a vigorous \nexothermic reaction. The \nsystem remained homogeneous throughout the entire process and no \nprecipitation was observed. Finally, \nthe \nas\n-\nreacted material was calcined in air at 700\n \n°\nC for 2 h in order \nto remove the organic residues.\n \nThe nanocomposite was obtained mixing cobalt ferrite with activated charcoal for three different \nratios \n1:1; 1:2 and 1:5 (molar mass of CoFe\n2\nO\n4\n:C).\n \nThe mixtu\nres were\n \npressed to form small disk\ns of 10 \nmm diameter and about 1 mm \nthickness\n, thermally treated at 800 °C in air and at 900\n \n°\nC in argon \natmosphere. \nAiming to obtain a total\nly\n \nreduc\ned\n \nsample (transforming all \nCoFe\n2\nO\n4\n \ninto \nCoFe\n2\n) a mixture \npowder with \nexcessive quantity of carbon (1:\n24\n)\n \nwas also prepared and thermally \ntreated in a \ntubular \nfurnace at \n900\n \n°\nC\n \nin argon atmo\ns\nphere\n.\n \nFor elucidation, the sample naming used in this work follow a \nsimple labelling rule, for example, the name CFO\n-\n5C\n-\n800 indicate \nthat 5 moles of charcoal was used \nduring thermal reduction process of the sample and that it was thermally treated at 800 °C.\n \nA\n \nSpex 8000 high\n-\nenergy mechanical ball miller\n,\n \nwith 6 mm diameter zirconia balls, was employed \nfor \nthe \nmilling processing of all \nsamples\n, aiming\n \nexclusively\n \nto increase the\nir\n \nH\nC\n. The processing time \nwas 1.5 h for all samples\n, using \nball/sample mass ratio of about 1/7. Detailed milling conditions are \ndescribed in Ponce \net al.\n \n[8].\n \nThe crystalline phases of the nano\ncomposite\n \nwere identi\nfied by X\n-\nray diffraction (XRD)\n, using a \nShimadzu XRD\n-\n6000 diffractometer installed at\n \nthe\n \nLaboratório Mult\niusuário de Técnicas Analíticas\n \n(\nL\na\nM\nu\nTA\n/ UFMT\n–\nCuiabá\n-\nMT\n–\n \nBrazil). It \nis\n \nequipped with graphite monochromator and conventional \nCu tube (0.1541\n84\n \nnm), and work\ns\n \nat 1.2 kW (40 kV, 30 mA), using the Bragg\n-\nBrentano geometry.\n \nMagnetic measurements (hysteresis loops at 300 and 50 K) were carried out using a vibrating sample \nmagnetom\neter (VSM) model VersaLab Quantum Design, insta\nlled at CBPF, Rio de Janeiro, \nBrazil. \n \n \nResults and discussion\n \n \nIt is well known that the magnetic behavior of CoFe\n2\nO\n4\n \nis quite different from that found for CoFe\n2\n. \nThe former is a hard ferrimagnetic material \nwith maximum M\nS\n \nof about 70 emu/g while the second is \nknown to be a soft ferromagnet with M\nS\n \nof about 230 emu/g [\n20\n]. Consequently, in the case of \nnanocomposite formation presenting \nmagnetic\n \ncoupling, one can assume an intermediate magnetic behavior that\n \ndepends of the relative amount of CoFe\n2\n \nformed during the reduction process and, also, of \nthe microstructure of the material.\n \nThe hysteresis curves obtained for samples CFO\n-\n5C\n-\n800; CFO\n-\n2C\n-\n800; CFO\n-\n1C\n-\n800; CFO\n-\n5C\n-\n900; CFO\n-\n2C\n-\n900; CFO\n-\n1C\n-\n900 are shown in th\ne figure 1. Measurements reveal clear differences \nbetween M\nS\n \nof the samples prepared at 800 \n°\nC, as seen in figure 1(A). However, coercivity values \nobtained are very close and the shape of the hysteresis loop is quite similar. Samples prepared at 900 °C \nals\no present similar H\nC\n \nbut different M\nS\n \nvalues. On the other hand, the shape of the hysteresis loop \nobtained for sample CFO\n-\n5C\n-\n900 is different from those obtained for the two other samples prepared at \n900 °C, as shown in figure 1(B).\n \n \nFig\nure\n \n1 \n–\n \nHysteresis\n \ncurves at room temperature for samples treated at (A) 800\n \n°C and (B) 900 °C.\n \n \nThere are only two reasonable possibilities to explain the different M\nS\n \nvalues obtained for the \nsamples presented in figure 1: (i) an intense cationic redistribution caused by t\nhe thermal process used \nto \nprepare the \nsample or (ii) the formation of CoFe\n2\nO\n4\n/CoFe\n2\n \ncomposite. \n \nTo understand how the cationic redistribution could affect the M\nS\n \nis\n \nnecessary to know the cobalt \nferrite crystalline structure \nand its \ndistribution of \nmagnetic ions\n.\n \nThe \nCoFe\n2\nO\n4\n \nis a ferrimagnetic material \nthat has an inverse spinel structure with three magnetic sites per \nformula unit. The CoFe\n2\nO\n4\n \nstructure can \nbe summarized by [\n21\n]:\n \n(\n\u0000\u0000\n\u0000\n\u0000\n\u0000\n\u0000\n\u0000\n\u0000\u0000\n\u0000\n\u0000\n\u0000\n)\n[\n\u0000\u0000\n\u0000\n\u0000\n\u0000\n\u0000\u0000\n\u0000\n\u0000\n\u0000\n\u0000\n\u0000\n]\n\u0000\n\u0000\n\u0000\n\u0000\n \n(2)\n \nIn this representation, \nthe round and the square brackets indicate A \n(tetrahedral coordination of four \nO\n2\n-\n \nanions site) \nand B sites\n \n(two octahedral coordination of six O\n2\n-\n \nanions sites)\n, respectively,\n \nand\n \ni \n(the \ndegree of inversion) describes the fraction \nof the tetrahedral sites occupied by Fe\n3+\n \ncations. The ideal \ninverse spinel structure has \ni \n= 1\n \nand\n \nthe normal spinel has\n \ni \n= 0\n. A\n \nmixed spinel structure present \ni\n \nvalues \nbetween 0 and 1. \n \nIn an ideal inverse spinel cobalt ferrite, half of the Fe\n3+\n \ncations\n \n(magnetic moment of 5μ\nB\n) occupy \nthe A\n-\nsites and the other half the B\n-\nsites, together with Co\n2+\n \ncations (see that there are two B sites per \nformula unit). Since the magnetic moments of the ions in the A and B sites are aligned in an anti\n-\nparallel \nway, ther\ne is no magnetic contribution of the Fe\n3+\n \ncations in this case. Therefore, the net magnetic \nmoment of the ideal inverse spinel cobalt ferrite is due exclusively to the Co\n2+\n \ncations (magnetic moment \nof 3μ\nB\n). However, normally, the cobalt ferrite presents a \nmixed spinel structure and, consequently, there \nare Co\n2+\n \nand Fe\n3+\n \ncations in both tetrahedral and octahedral sites, \ni.e. \n, when \ni \ndecreases toward 0 (normal \nspinel), it means swap of Fe\n3+\n \ncations from site A with Co\n2+\n \ncations from site B, increasing the net \nmagnetic moment of the material and, consequently, promoting an increase of the \nM\nS\n. \nTherefore, the \nmagnetic behavior\n \nof the CoFe\n2\nO\n4\n, as \nsaturation magnetization\n, is strongly affected by structural changes \nand/or che\nmical disorder/substitution.\n \nAs an example, to an ideal inverse spinel (\ni = \n1) a magnetic moment of 3.0 μ\nB\n \nper formula unit \n(equivalent to M\nS\n \n=71.4 emu/g) is expected. For sample \nCFO\n-\n5C\n-\n800 we obtained \nM\nS \n= 90 emu/g, that is \nequivalent to a magnetic moment\n \nof\n \n3.8 μ\nB\n \nper formula unit and \ni = \n0.8, which means a swap of 20% of \nthe Co cations in the material. This value to \ni\n \nsounds reasonable, however highest values of M\nS\n \nfound in \nthe literature were 83.1 and 83.12 emu/g by Sato Turtelli \net al.\n \n[2\n1\n] and \nKumar \net al\n. [\n22\n], respectively. \nThese literature values are equivalent \nto \nμ = 3.5 μ\nB\n \nper\n \nformula unit and \ni = \n0.88 (12% of Co cations were \nswapped by Fe). For this reason we do not consider the cationic redistribution \nis \nresponsible for the \nincrease in M\nS\n. \nThus\n,\n \nafter thermal chemical reduction, \nfor the samples studied in this work\n, \nwe consider \nthe formation of CoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposite as responsible for \nthe increase in M\nS\n.\n \nUsing the extrapolation \nto zero \nof the M versus 1/H plot to estimate the M\nS\n \nvalues\n \nof each sample, \nand c\nonsidering the M\nS\n \nexpected to pure inverse spinel cobalt ferrite (71.4 emu/g) and pure CoFe\n2\n \n(230 \nemu/g) [2\n0\n], one can estimate the content of CoFe\n2\n \nin the composite (see table \n1\n). \nWe do not consider the \neffect of canted magnetic mome\nnt from surface cations.\n \n \nTable \n1\n \n–\n \nMagnetic parameters of the samples, obtained at room temperature.\n \nSample\n \nM\nS\n \n(emu/g)\n \nM\nR \n(emu/g)\n \nM\nR\n/\nM\nS\n \nH\nC\n \n(kOe)\n \nContent of \nCoFe\n2\n \n(%)\n \n(BH)\nmax\n \n(MGOe)\n \nCFO\n-\n5C\n-\n800\n \n90\n \n21\n \n0.23\n \n0.7\n \n13\n \n0.35\n \nCFO\n-\n2C\n-\n800\n \n84\n \n29\n \n0.35\n \n0.7\n \n9\n \n0.32\n \nCFO\n-\n1C\n-\n800\n \n75\n \n18\n \n0.24\n \n0.7\n \n3\n \n0.26\n \nCFO\n-\n5C\n-\n900\n \n79\n \n29\n \n0.37\n \n0.7\n \n6 \n \n0.27\n \nCFO\n-\n2C\n-\n900\n \n87\n \n21\n \n0.24\n \n0.6\n \n11 \n \n0.15\n \nCFO\n-\n1C\n-\n900\n \n72\n \n18\n \n0.25\n \n0.7\n \n2\n \n0.14\n \n \nThe CoFe\n2\n \ncontent in the nanocomposite was found to be small in all cases, indicating \nas false our\n \ninitial assumption that carbon of the mixture inside the disk reacts only with oxygen from CoFe\n2\nO\n4\n \n(generating CoFe\n2\n). Two reasons can cause this effect: (i) residual oxygen inside the mixture sample disk \nreacted with the carbon and (ii) certain content o\nf carbon do not reacts with cobalt ferrite during the \nthermal treatment. The second option probably occurs due to the morphology of the material, which \npermits the formation of a CoFe\n2\n \nshell around the CoFe\n2\nO\n4\n \ncore of the grain, shielding it and limiting t\nhe reduction power of the activated charcoal during thermal treatment. In any case, this \neffect makes difficult \nto control the quantity of CoFe\n2\n \nin the nanocomposite CoFe\n2\nO\n4\n/CoFe\n2\n. \n \nThe small amount of CoFe\n2\n \nformed in samples treated in both air and argon atmospheres, as \nindicated in table \n1\n, suggests that changes in the atmosphere of the furnace do not cause significant \ndifferences on the CoFe\n2\n \ncontent of the composite.\n \nThe coercivity observed for all sample\ns was very similar, and close to 0.7 kOe\n, a va\nlue smaller than \nthose obtained by Cabral \net al.\n \n[12] and Leite \net al.\n \n[13]. In other words, this value is lower than that \nexpected for a pure cobalt ferrite and higher than that expected for pure CoFe\n2\n \nand, co\nnsequently, in \nagreement with the formation of the composite CoFe\n2\nO\n4\n/CoFe\n2\n.\n \nTo perform a more detailed investigation about the differences between the shapes of the hysteresis \ncurves obtained from samples prepared at 900\n \n°\nC, the hysteresis loops were also \nmeasured at low \ntemperature (50 K). These measurements are shown in figure \n2\n. The low temperature hysteresis enhances \nthe visualization of \nthe behavior observed at room temperature (300 K). For example, the hysteresis \ncurves obtained for samples CFO\n-\n2C\n-\n900\n \nand CFO\n-\n1C\n-\n900 \npresent a typical\n \ntwo\n-\nphase magnetic \nbehavior, and the hysteresis curve obtained for sample CFO\n-\n5C\n-\n900 presents a \nsingle\n-\nphase\n \nmagnetic \nbehavior, suggesting the coupling between the different magnetic phases\n \npresent\n \ninto the \nsample\n. The \nderivative of the hysteresis curve (first quadrant decreasing field only) confirms our assumption (figure \n2\nC), because the two\n-\nphase \nmagnetic \nbehavior is characteristic of two magnetic phases coexisting without \nexchange \ncoupling\n \nbetween them\n. Similar\n \nbehavior was observed by Sun \net al.\n \n[\n23\n]. \n \nNanocomposites with \nexchange coupling or exchange spring present single magnetic phase behavior \n[15\n-\n17, \n24\n, 25\n]\n, h\nowever\n,\n \nthese effects \ndepend on\n \nthe \ncrystallite \nsize of the compounds. Zeng \net al.\n \n[18] \nshowed the single magnetic phase behavior can vanish\n,\n \nto the same nanocomposite\n,\n \ndepending of the \nrelative size \nof\n \nthe compounds\n,\n \nresulting in two\n-\nphase behavior.\n \nInterestingly, the two\n-\nphase magnetic behavior was not observed in samples prepared at 800\n \n°\nC\n, \neven in the low temperature hysteresis\n \ncurves\n, see figure \n2B\n. This result reinforces our assumption that \nnanoparticles coalescence is the driving force towards the two\n-\nphase \nmagnetic \nbehavior\n. \nMore \nvisible \neffects of coalescence \na\nre expected \nto samples t\nreated \nat\n \nhigher temperatures\n, \nwith consequent increase \nin\n \ncrystallite size.\n \nAn additional aspect observed in 50 K hysteresis loop is the huge increase \nin\n \ncoercivity. This effect \nwas \nalso \nobserved by other authors \n[\n13, \n26\n]. However, it\n \nis more significant \nin\n \nsamples with single \nmagnetic behavior presenting H\nC\n \nclose to\n \n5kOe (see figures \n2\nA and \n2\nB). In samples presenting two\n-\nphase \nbehavior the coercivities were considerably smaller, \ni.e.\n, 2.4 kOe \nfor\n \nCFO\n-\n2C\n-\n900 and H\nC\n \n= 1.8 kOe \nfor\n \nsample\n \nCFO\n-\n1C\n-\n900\n \n(figure 2A)\n. \nA work studying this effect is under development.\n \n  \n0\n5\n1 0\n1 5\n2 0\n2 5\n0\n2\n4\n6\n8\n C F O - 2 C - 9 0 0\n C F O - 5 C - 9 0 0\n C F O - 1 C - 9 0 0\nDerivative\n(\nx\n10\n-3\n)\nH ( k O e )\n( C )\n \nFig\nure\n \n2\n \n–\n \nHysteresis curves (A) at 50K for samples treated at 900 \n°\nC and (B) at 300 and 50K to sample \nCFO\n-\n5C\n-\n800\n. \n(C) Derivative of the first quadrant\n \n(only decreasing field) M versus H, at 50K, for samples \ntreated at \n900\n \n°\nC.\n   \n \n \nLiu and Ding [11] have shown that is possible to obtain a noteworthy increase \nin\n \ncoercivity of cobalt \nferrite powder via high\n-\nenergy mechanical milling. Moreover, Ponce \net al.\n \n[8] extended this method to \nnano\nstructured \npowder\ns\n \nusing specific milling parameters. Although, we could have had milled the cobalt \nferrite to obtain a high coercivity CoFe\n2\nO\n4\n, but the thermal treatment at 800 or 900\n \n°\nC used to obtain the \nnanocomposite CoFe\n2\nO\n4\n/CoFe\n2\n \nis known to decrease strain and structu\nral defects and, consequently, also \ndecreasing H\nC\n \n[19].\n \nAiming to obtain a similar effect \nfor\n \nthe nanocomposite CoFe\n2\nO\n4\n/CoFe\n2\n, the samples CFO\n-\n2C\n-\n800 \nand CFO\n-\n1C\n-\n800 were milled using the same milling conditions described in the reference [8]. The result \nof\n \nthe milling process to the sample CFO\n-\n2C\n-\n800 is shown in figure 4\n,\n \na huge increase in H\nC\n \nof samples \nCFO\n-\n1C\n-\n800 (not shown) and CFO\n-\n2C\n-\n800 was obtained\n, showing that \nthe effect obtained \nafter milling \nin pure CoFe\n2\nO\n4\n \n(a decrease of M\nS\n \nand an enormous increase of H\nC\n) can also be achieved in\n \nthe \nCoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposite. \nSpecifically, in the case of sample CFO\n-\n2C\n-\n800\n,\n \nthe coercivity \nat room \ntemperature increased from 0.7 to 3.8 kOe\n \nand, a\ns a consequence of the change in H\nC\n, (BH)\nmax\n \nin\ncreased \nfrom 0.32 to 1.1 MGOe at room temperature and to 2.6 MGOe at 50K\n. The magnetic parameters for the \nsample CFO\n-\n2C\n-\n800 before and after milling are presented in table \n2\n. This is a very interesting result, \nsince the high\n-\nenergy milling procedure used i\nn this work allows to obtain \nnanostructured powder\n \nwith \nhigh (BH)\nmax\n.\n \n \n \nTable 2 \n–\n \nMagnetic parameters \nobtained \nfor sample CFO\n-\n2C\n-\n800, \nat 300 K before milling and at 300 and \n50\n \nK \nafter milling process.\n \nSample\n \nT (K)\n \nM\nS\n \n(emu/g)\n \nM\nR \n(emu/g)\n \nM\nR\n/\nM\nS\n \nH\nC\n(kOe)\n \n(BH)\nmax\n \n(MGOe)\n \nCFO\n-\n2C\n-\n800\n \n300\n \n84\n \n32\n \n0.38\n \n0.7\n \n0.32\n \nCFO\n-\n2C\n-\n800\n(milled)\n \n300\n \n60\n \n34\n \n0.57\n \n3.8\n \n1.1\n \nCFO\n-\n2C\n-\n800\n(milled)\n \n50\n \n64\n \n48\n \n0.75\n \n11.1\n \n2.6\n \n \n \nFigure 3 presents a clear decrease of M\nS \nafter milling\n, t\nhis effect is associated to the decrease of the \nmean crystallite size due to the milling process [8, 11, 14]. \nThe reduction of the crystallite size increases \nthe number of surface magnetic ions and the cant\ning\n \neffect of these surface ions is \nresponsible fo\nr the\n \ndecrease in\n \nM\nS\n.\n \n \n \nFig\nure\n \n3\n \n–\n \nHysteresis curves for sample CFO\n-\n2C\n-\n800, obtained at 300 K before and after milling and at \n50 K after milling process.\n \n \nAn additional interesting property was observed in the hysteresis loop at 50K (see figure \n3\n). Milled\n \nCoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposites present H\nC\n \nmore than twice higher than those of non\n-\nmilled samples \n(coercivity changes from 5.0 to 11 kOe after milling). This enormous increase in H\nC\n \nwith the decrease of \ntemperature requires further investigation.\n \nXRD \nexperi\nments were also performed, in order to obtain \ndiffraction \npatterns\n \nfrom cobalt ferrite \nsamples before (pristine sample) and after thermal treatment at 800 \nand\n \n900\n \n°\nC \nin air and argon \natmosphere\n \nrespectively\n,\n \nas\n \nsho\nwn in figure \n4\n.\n \nThe \ninset of figure \n4\n \npresents\n \nthe \nx\n-\nray diffraction\n \npatter\nn\n \nof\n \nthe pristine sample and a refinement using \nMatch\n \nsoftware (solid line).\n \nThe only objective of this \nrefinement is to show that pristine cobalt ferrite is monophasic.\n \nThe \nc\nomparison between XRD patterns\n \nbefore and\n \na\nfter thermal treatment at 800\n \n°\nC\n \nshow\n \nno visible \nsignificant differences\n, except \nfor \nthe narrowing \nof \nthe peaks\n \nafter thermal treatment\n. Such n\narrowing is \nusually related\n \nto\n \nthe reduction in quantity of defects, \nimprovements\n \nin the crystal lattice distortion \naround defects \n(local strain) \nand/or\n, consequently,\n \nto the increase of the mean cry\nstallite size of the \nmaterial [\n27\n]\n.\n \n \nFig. \n4 \n-\n \nXRD patterns \nof several\n \nanalyzed\n \nsamples\n,\n \nas labeled\n.\n \n \nThe mean crystallite size of the cobalt ferrite phase (see table \n3\n) was estimated by the Scherrer \nmethod for the (311) diffraction peak, at 35.5 ° in 2\nθ\n. \nThe \nresults, as expected, indicate \nthat\n \ncrystallite size\n \nincreases\n \nwith the tempe\nrature of the thermal\n \ntreatment.\n \n \n \nTable \n3\n \n–\n \nMean \ncrystallite \nsize\n \nestimated \nfrom \nthe \nScherrer equation for\n \nthe cobalt ferrite\n \n(\n311\n)\n \nXRD \npeak\n \nof the samples\n.\n \n \n \nHowever,\n \nsamples \nthermally treated at 900 °C \npresented three \nnew\n \nsmall\n \ndiffraction\n \npeaks (indicated \nby arrow\ns\n \nin figure \n4\n). These peaks \ndo\n \nnot \nmatch\n \nwith \nthe XRD patterns expected \nfor\n \nCoFe\n2\n \n[13\n], \nbeing \nidentified as CoO\n \ncrystalline phase (ICSD Card # 9865). \nThe existence of these small peaks indicates \nphase separation due to a small lack in stoichiometry of the synthesized material. This small difference in \nSample\n \nD (nm)\n \nP\nristine\n \n12\n \nCFO\n-\n5C\n-\n800\n \n39\n \nCFO\n-\n2C\n-\n800\n \n34\n \nCFO\n-\n1C\n-\n800\n \n38\n \nCFO\n-\n5C\n-\n900\n \n57\n \nCFO\n-\n2C\n-\n900\n \n45\n \nCFO\n-\n1C\n-\n900\n \n49\n stoichiometry is common in a chemical process of synthesis, due \nto the hygroscopic nature of the reagents \nused in the process and, if necessary, can be eliminated changing in a few percent the cobalt and/or iron \nnitrate masses used in the synthesis. \nConsequently, these small peaks do not indicate partial reduction of \nt\nhe \nmaterial\n \n(formation of \nCoFe\n2\n)\n \nand, a\nlso, the CoO phase does not contribute to hysteresis curve \nbecause it is antiferromagnetic [\n28\n]. \n \nTherefore\n,\n \nwe associate the two\n-\nphase behavior to \nthe increase in \nthe mean crystallite size. This\n \nassumption \nagrees\n \nwith the \nbehavior of the m\nean crystallite \nsize \nin function of the thermal treatment \ntemperature \nobtained from Scherrer equation (\ntable \n3\n). \n \nThe absence of \nx\n-\nray diffraction\n \npeaks related with CoFe\n2\n \nphase in the patterns shown \nin figure 1 \nagrees with results obtained by Zhang\n \net al.\n \n[15]. These authors,\n \nusing a similar process, could not \nobserve the presence\n \nof CoFe\n2\n \nin the nanocomposite CoFe\n2\n/CoFe\n2\nO\n4\n,\n \nby XRD, \nuntil the content reached \nabout 30 %, relating the absence of CoFe\n2\n \nphase diffraction peaks to its poor crystallinity. Therefore, the \nabsence of C\noFe\n2\n \ndiffraction peaks in the diffractograms shown in figure \n4\n \ndoes not exclude the \nformation of this phase.\n \nFor information, the thickness of the CoFe\n2\n \nshell around the \nnanostructured \nCoFe\n2\nO\n4\n \ncore was \nestimated for sample \nCFO\n-\n5C\n-\n800\n, that with the higher \nCoFe\n2\n \ncontent, \nsupposing\n \nspherical \nCoFe\n2\nO\n4\n \nnanoparticles with diameter equal to the mean crystallite size obtained from XRD measurements (see \ntable \n3\n)\n \ncovered with a uniform CoFe\n2\n \nshell. M\nass density of both CoFe\n2\nO\n4 \nand CoFe\n2\n \ncrystalline \nphases\n \nwere used\n. \nThe result indicates that only a very thin CoFe\n2\n \nshell\n, having around 1nm, was formed\n.\n \nOne \nhas\n, also, to consider that (i) if disordered CoFe\n2\n \nshell and CoFe\n2\nO\n4\n \ncore can result in respectively larger \nand/\nor smaller values for the CoFe\n2\n \nshell thickness\n, \nreducing the importance of this consideration in a \nmore precise calculation\n, (ii) a nanostructured material (as that studied in this work) can present much \nmore relative surface/volume area than that of a perfect sphere, further reducing the estimated thic\nkness \nof the CoFe\n2\n \nshell. Therefore, the thickness of the CoFe\n2\n \nshell must be \nless than the estimated 1 nm. This \nestimative is fully consistent with the absence of diffraction peaks from a highly disordered CoFe\n2\n \nphase.\n \nAiming\n \nto maximize the reduction of \na CoFe\n2\nO\n4\n \nduring thermal treatment \n(transforming \nmore\n \nCoFe\n2\nO\n4\n \ninto CoFe\n2\n)\n,\n \na mixture powder with \nan extreme \nquantity of carbon (1:24) was also prepared and \nthermally treated in a tubular furnace at 900 °C in argon atmosphere. \nThe \nXRD pattern \nof\n \nsample \nCFO\n-\n24\n-\n900\n \nis\n \nshown in figure \n5\n \ntogether with the theoretical\n \ndiffractogram expected for a pure CoFe\n2\n \nsample\n. \nThe result \nsuggest\ns \nthat something between an almost total and a\n \ntotal conversion \nof\n \nCoFe\n2\nO\n4\n \ninto CoFe\n2\n \ntook place\n. \n \n \nFigure \n5\n \n-\n \nXRD pattern\n \nobtained\n \nfrom\n \nsample \nCFO\n-\n24\n-\n900\n \nand theoretical fit \nsupposing\n \nCoFe\n2\n \ncrystalline \nstructure\n.\n \n \nFinally, on the difficulty reported \nhere, and in previous work [13], \nin attempting to master the \nreduction \nproces\ns\n, this last result indicate that a greater amount of \ncarbon has to be used to achieve larger \nconversion efficiency, even in inert atmosphere.\n \nFuture investigations are needed to improve reduction \nprocess efficiency of CoFe\n2\nO\n4\n \nin CoFe\n2\n, in order to evaluate the magnetic behavior of the nanocomposite \nwith high\ner CoFe\n2\n \ncontent.\n \n \nConclusion\n \nWe use a new procedure to obtain the CoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposite\n. Despite the XRD patterns \nsuggesting that CoFe\n2\n \nis not formed, magnetic measurements indicate that nanocomposite \nare\n \nobtained, \nhowever with small \namount\n.\n \nThe pre\nparation method of the nanocomposite at 900\no\nC produces samples \nwith two magnetic phase behavior\n \nand a third phase was observed the antiferromagnetic cobalt oxide \nCoO\n. This behavior was not observed in samples prepared at 800\no\nC, indicating an\n \nexchange coupling \nbetween the magnetic phases.\n \n \nThe most important result of this work is to show that H\nC\n \nof the CoFe\n2\nO\n4\n/CoFe\n2\n \nnanocomposite \ncan \nbe \nincrease\nd\n \nusing the same \nmilling \nmethod \nemployed \npreviously\n \nto cobalt ferrite\n.\n \nAs a consequence,\n \nwe \nobtain\ne\nd\n \na sample that reached\n \nan increase in \n(BH)\nmax\n \nof \nabout 240%\n, but f\nuture investigations are needed \nto evaluate the magnetic behavior of the nanocomposite with higher CoFe\n2\n \ncontent.\n \n \nAcknowledgments\n \n \nThe authors would like to thank the\n \nCAPES Brazilian \nfunding agency\n \nto the master students grant.  \nIn addition, E. Baggio\n-\nSaitovitch acknowledges support from FAPERJ through several grants including \nEmeritus Professor fellow and CNPq for BPA and corresponding grants\n.\n \nR\neferences\n \n \n1.\n \nV. Pillai, D. O. Shah,\n \nSynth\nesis of High\n-\nCoercivity Cobalt F\nerrite Particles Using Water\n-\nin\n-\nOil \nMicroemulsions \nJ. Magn. Magn\n. Mater. 163 (1996) 243\n-\n248.\n \n2.\n \nM. Colombo, S. Carregal\n-\nRomero, M. F. Casula, L. Gutierrez, M. P. Morales, I. B. Bohm, J. T. \nHeverhagen, D. Prosperi, J. W. Parak, \nBiological applications of magnetic nanoparticles, Chem. Soc. \nRev. 41 (2012) 4306\n-\n4334.\n \n3.\n \nT.E. Torres, A.G. Roca, M.P. Morales, A. Ibarra, C. Marquina, M.R. Ibarra, G.F. Goya, Magnetic \nproperties and energy absorption of CoFe\n2\nO\n4\n \nnanoparticles for magnetic \nhyperthermia, J. Phys.: Conf. \nSer. 200 (2010) 072101.\n  \n4.\n \nJ.H. Lee, J.T. Jang, J.S. Choi, S.H. Moon, S.H. Noh, J.W. Kim, J.G. Kim, I.S. Kim, K. I. Park, J. \nCheon, Exchange\n-\ncoupled magnetic nanoparticles for efficient heat induction, \nNat. Nanotechnol.\n \n6 (2011)\n \n418\n-\n422.\n \n \n5.\n \nY.C. Wang, J. Ding, J.B. Yi, B. H. Liu, T. Yu, Z.X. Shen, High\n-\ncoercivity Co\n-\nferrite thin films \non\n \n(100)\n \nSiO\n2\n(100)\n-\nSiO2\n \nsubstrate, Appl. Phys. Lett. 84 (2004) 2596\n-\n2598.\n \n \n6.\n \nJ.R. Scheffe, M.D. Allendorf, E.N. Coker, B.W. Jacobs, A.H. McDaniel, A.W.\n \nWeimer, Hydrogen \nProduction via Chemical Looping Redox Cycles Using Atomic Layer Deposition\n-\nSynthesized Iron Oxide \nand Cobalt Ferrites, Chem. Mater. 23 (2011) 2030\n-\n2038.\n \n \n7.\n \nC. Nlebedim, J.E. Snyder, A.J. Moses, D.C. Jiles, \nDependence of the magnetic and \nmagnetoelastic \nproperties of cobalt ferrite on processing parameters\n, J. Magn. Magn. Mater. 322 (2010) 3938\n-\n3941.\n \n \n8.\n \nA.S. Ponce, E.F. Chagas, R.J. Prado, C.H.M. Fernades, A.J. Terezo, E. Baggio\n-\nSaitovitch, High \ncoercivity\n \ninduced by mechanical milling in cobalt ferrite cobalt powders, \nJ. Magn. Magn. Mater. 344 \n(2013) 182\n-\n187\n.\n \n \n9.\n \nW.S. Chiua, S. Radiman, R. Abd\n-\nShukor, M.H. Abdullah, P.S. Khiew, Tunable coercivity of \nCoFe2O4 nanoparticles via thermal annealing treatment, \nJ All\noys Compd\n \n459 (2008) 291\n–\n297.\n \n \n10.\n \nM.V. Limaye, S.B. Singh, S.K. Date, D. Kothari, V.R. Reddy, A. Gupta, V. Sathe, R. J. Choudhary, \nS.K. Kulkarni, High coercivity of oleic acid capped CoFe2O4 nanoparticles at room temperature, \nJ. Phys. \nChem. B\n \n113 (2009) 9070\n–\n9076.\n \n \n11.\n \nB. H. Liu and J. Ding, Strain\n-\ninduced high coercivity in CoFe2O4 powders, Appl. Phys. \nLett. 88 \n(2006) 042506. \n \n \n12.\n \nF.A.O. Cabral, F.L.A. Machado, J.H. Araujo, J.M. Soares, A.R. Rodrigues, A. Araujo, Preparation and \nmagnetic study of the CoFe2O4\n-\nCoFe2 n\nanocomposite powders, IEEE Trans. \nMagn. 44 (2008) 4235\n-\n4238.\n \n \n13.\n \nG.C.P. Leite, E.F. Chagas, R. Pereira, R.J. Prado, A.J. Terezo, E. Baggio\n-\nSaitovitch, Exchange \ncoupling behavior in bimagnetic \nCoFe2O4/CoFe2\n \nJ. Magn. \nMagn. Mater. \n324 (2012) 2711\n-\n2016.\n \n \n14.\n \nP\n. \nGalizia\n,\n \nM\n. \nCernea\n,\n \nV\n. \nMihalache\n, \nL\n.\n \nDiamandescu\n,\n \nG\n. \nMaizza\n,\n \nC\n.\n \nGalassi\n, \nEasy batch\n-\nscale \nproduction of cobalt ferrite nanopowders by two\n-\nstep milling: S\ntructural and magnetic characterization\n, \nMater. Design 130 (2017) 327\n-\n335.\n \n 15.\n \nY. Zhang, B. Yan, Jun O. Yang , B. Zhu, S. Chen, X. Yang, Y. Liu, R. Xiong, Magnetic properties of \ncore/shell\n-\nstructured CoFe2/CoFe2O4 composite nano\n-\npowders synthesized via oxidation reaction, \nCeram. Int.\n \n41 (2015) 11836\n–\n11843\n.\n \n \n16.\n \nJ.M. Soares, F.A.O. Cabral, J.H. de Araújo, F.L.A. Machado, Exchange\n-\nspring behavior in \nnanopowders of CoFe2O4\n–\nCoFe2, Appl. Phys. Lett. 98 (2011) 072502.\n \n \n17.\n \nJ.M. Soares, V.B. \nGaldino, O.L.A. Conceição, M. A. Morales, J.H. de Araújo, F.L.A. Machado, \nCritical dimension for magnetic exchange\n-\nspring coupled core/shell CoFe2O4/CoFe2 nanoparticles J. \nMagn. Magn. Mater.  326 (2013) 81\n–\n84.\n \n \n18.\n \nH. Zeng, J. Liu, J.P. Liu, Z.L. Wang, S. Sun,\n \nExchange\n-\ncoupled nanocomposite magnets by \nnanoparticle self\n-\nassembly, Nature 420 (2002) 395\n-\n398.\n \n \n19.\n \nE. F. Chagas A.S. Ponce, R.J. Prado, G.M. Silva, J. Bettini, E. Baggio\n-\nSaitovitch, \nThermal effect on \nmagnetic parameters of high\n-\ncoercivity cobalt ferrite, \nJ\n. Appl. \nPhys. 116 (2014) 033901.\n \n \n20.\n \nT.Ungar in \"Industrial Applications of X\n-\nray Diffraction\"; eds: Chung & Smith. Marcel Dekker, New \nYork, 2000. P. 847\n.\n \n \n21.\n \nM. Mohan, V. Chandra, S.S. Manoharan, A new nano CoFe2 alloy precursor for cobalt ferrite \nproduction vi\na sonoreduction process, \nCurr. Sci.\n \n94 (2008) 473\n–\n476.\n \n \n22.\n \nR.Sato Turtelli\n, \nM.Atif\n, \nN.Mehmood\n, \nF.Kubel\n, \nK.Biernacka\n, \nW.Linert\n, \nR.Grös\nsinger\n, \nCz.Kapusta\n, \nM.Sikora\n,\n \nInterplay between the cation distribution an\nd production methods in cobalt ferrite\n \nMater. \nChem. Phys. 132 (2012) 832\n-\n838.\n \n \n23.\n \nK. Kumar, A.Sharma, Md. A. Ahmed, S. S. Mali, C. K. Hong, P. M. Shirage Morphology\n-\ncontrolled \nsynthesis and enhanced energy product (BH)max of CoFe2O4 nanoparticles, New J. Chem\n. 42 (2018) \n15793\n-\n15802\n.\n \n \n24.\n \n \nX. Sun, Y.Q. Ma, Y.F. Xu, S.T. Xu, B.Q. Geng, Z.X. Dai, G.H. Zheng, Improved magnetic \nperformance at low and high temperatures in non\n-\nexchange\n-\ncoupling CoFe2O4/CoFe2 nanocomposites, \nJ \nAlloys Compd\n \n645 (2015) 51\n-\n56.\n \n \n25.\n \nN. J. O. Silva, A. Millan, F. Palacio, M Martins, T. Trindade, I Puente\n-\nOrench, J. Campos, Remanent \nmagnetization in CoO antiferromagnetic nanoparticles, \nPhys. Rev. B \n82\n \n(\n2010\n) \n094433\n–\n094440\n.\n \n \n26.\n \nE.F. Kneller, R. Hawig, The exchange\n-\nspring magnet: a new mater\nial principle for permanent \nmagnets, IEEE Trans. \nMagn. \n27 (1991) 3588\n–\n3600.\n \n 27.\n \nR. Skomski, J.M.D. Coey, Giant energy product in nanostructured two phase magnets, Phys. Rev. B \n48 (1993) 15812\n–\n15816.\n \n \n28.\n \nK.Gandha, K. Elkins, N. Poudyal, J. P. Liu, \nSynthesis and c\nharacterization of CoFe2O4 nanoparticles \nwith high coercivity, J\n. App. Phys. \n117\n \n(2015) 7A7361.\n \n "    },    {        "title": "2309.14377v1.Quantifying_Li_content_for_compositional_tailoring_of_lithium_ferrite_ceramics.pdf",        "content": "Journal of the European Ceramic Society 43 (2023) 3351–3359\nAvailable online 5 February 2023\n0955-2219/© 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-\nnc-nd/4.0/ ).Quantifying Li-content for compositional tailoring of lithium \nferrite ceramics \nC. Granados-Mirallesa,*, A. Serranoa, P. Prietob, J. Guzm ˘an-Míngueza, J.E. Prietoc, \nA.M. Friedeld,e, E. García-Martínb,c, J.F. Fern˘andeza, A. Quesadaa \naInstituto de Cer˘amica y Vidrio, CSIC, ES-28049 Madrid, Spain \nbDpto. de Física Aplicada, Universidad Aut˘onoma de Madrid, Madrid ES-28049, Spain \ncInstituto de Química Física ‘Rocasolano ’, CSIC, Madrid ES-28006, Spain \ndInstitut Jean Lamour, UMR CNRS 7198 and Universit ˘e de Lorraine, FR-54000 Nancy, France \neFachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit at Kaiserslautern, DE-67663 Kaiserslautern, Germany   \nARTICLE INFO  \nKeywords: \nSintered ceramics \nRietveld analysis \nConfocal Raman spectroscopy \nMagnetic properties \nLithium quantification ABSTRACT  \nOwing to their multiple applications, lithium ferrites are relevant materials for several emerging technologies. \nFor instance, LiFeO 2 has been spotted as an alternative cathode material in Li-ion batteries, while LiFe 5O8 is the \nlowest damping ferrite, holding promise in the field of spintronics. The Li-content in lithium ferrites has been \nshown to greatly affect the physical properties, and in turn, the performance of functional devices based on these \nmaterials. Despite this, lithium content is rarely accurately quantified, as a result of the low number of electrons \nin Li hindering its identification by means of routine materials characterization methods. In the present work, \nmagnetic lithium ferrite powders with Li:Fe ratios of 1:1, 1:3 and 1:5 have been synthesized, successfully \nobtaining phase-pure materials (LiFeO 2 and LiFe 5O8), as well as a controlled mixture of both phases. The \npowders have been compacted and subsequently sintered by thermal treatment (Tmax 1100 •C) to fabricate \ndense pellets which preserve the original Li:Fe ratios. Li-content on both powders and pellets has been deter -\nmined by two independent methods: (i) Rutherford backscattering spectroscopy combined with nuclear reaction \nanalysis and (ii) Rietveld analysis of powder X-ray diffraction data. With good agreement between both tech-\nniques, it has been confirmed that the Li:Fe ratios employed in the synthesis are maintained in the sintered \nceramics. The same conclusion is drawn from spatially-resolved confocal Raman microscopy experiments on \nregions of a few microns. Field emission scanning electron microscopy has evidenced the substantial grain \ngrowth taking place during the sintering process – mean particle sizes rise from ≪600 nm in the powders up to \n3.8(6) µm for dense LiFeO 2 and 10(2) µm for LiFe 5O8 ceramics. Additionally, microstructural analysis has \nrevealed trapped pores inside the grains of the sintered ceramics, suggesting that grain boundary mobility is \ngoverned by surface diffusion. Vibrating sample magnetometry on the ceramic samples has confirmed the ex-\npected soft ferrimagnetic behavior of LiFe 5O8 (with Ms 61.5(1) Am2/kg) and the paramagnetic character of \nLiFeO 2 at room temperature. A density of 92.7(6)% is measured for the ceramics, ensuring the mechanical \nintegrity required for both their direct utilization in bulk shape and their use as targets for thin-film deposition.   \n1.Introduction \nLithium ferrites (i.e, LiFeO 2, LiFe 5O8) are materials of great interest \ndue to their multiple and varied properties and applications. More \nspecifically, the rock-salt lithium ferrite, LiFeO 2, is an antiferromagnetic \n(AFM) material below ≪90 K and paramagnetic at room temperature \n(RT) [1,2] . LiFeO 2 has drawn great attention as an alternative to LiCoO 2, \nthe most widely used cathode material in commercial Li-ion batteries. With a very similar atomic structure, LiFeO 2 has been proposed as a \ncandidate for substituting the Co-based ferrite owing to the greater \nabundance, lower price and non-toxicity of Fe compared to that of Co. \n[1,3–5]. LiFeO 2 is also a good chemical sorbent for CO2, which is used as \na strategy to reduce the amount of CO2 released to the atmosphere [6,7] , \nand it has also been proposed as electrocatalyst material for a sustain -\nable NH3 production through reduction of N2 [8]. Additionally, the \nunusual optical transitions recently reported for LiFeO 2 open the door \n*Corresponding author. \nE-mail address: c.granados.miralles@icv.csic.es (C. Granados-Miralles).  \nContents lists available at ScienceDirect \nJournal of the European Ceramic Society \nu{�~zkw! s{yo|kro>! ÐÐÐ1ow�o�t o~1m{y2w{m k�o2uo�~mo~k y�{m!\nhttps://doi.org/10.1016/j.jeurceramsoc.2023.02.011 \nReceived 16 December 2022; Received in revised form 27 January 2023; Accepted 3 February 2023   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3352for using this material for various spintronic and photo-catalysis appli -\ncations [9]. \nThe spinel lithium ferrite, LiFe 5O8, is a soft ferrimagnetic (FiM) \nmaterial with great technological significance. Spinel ferrites in general \nare widely used in microwave devices (e.g. isolators, circulators, phase \nshifters, absorbers) [10,11] . Compared to other soft spinel ferrites, \nLiFe 5O8 stands out with the highest Curie temperature (TC ≪950 K) [10, \n12] and the lowest losses at high microwave frequencies [13,14] . Some \nyears ago, a Gilbert damping parameter of 2.1 ×10\u00003 was measured for \na LiFe 5O8 single-crystal [13], and a more recent study has reported a \nvalue as low as 1.3 ×10\u00003 for an epitaxial LiFe 5O8 thin film, drawing \nattention to this material as a promising candidate for spintronic ap-\nplications. Other applications of LiFe 5O8 include gas sensing or anode \nmaterial for Li-ion batteries [15,16] . \nA good number of studies on both lithium ferrite phases have been \ncited above, in which single-crystals, thin films or powder samples are \nstudied based on a plethora of characterization techniques, e.g. X-ray \nand neutron diffraction, Raman, infrared and Mossbauer spectroscopy, \nscanning and transmission electron microscopy, etc., as well as various \nphysical property measurement, e.g., charge-discharge voltage profiles, \nferromagnetic resonance, magnetic hysteresis, N ˘e el/Curie temperature \ndetermination, dielectric properties, etc. Generally speaking, an appro -\npriate and accurate quantification of the Li content is often lacking. The \nreduced number of electrons in lithium makes it difficult to quantify \nbased on the characterization techniques routinely employed to deter -\nmine the elemental composition of materials [17]. However, lithium \nquantification is rather critical given that the Li-content has been \ndemonstrated to have a great influence over some physical properties \n[18], therefore conditioning the performance of functional devices \nbased on lithium ferrites. Moreover, Li has been seen to have a tendency \nto escape through evaporation promoted by the elevated temperatures \ngenerally employed in the material preparation [14]. \nIn this work, lithium ferrite powders with different Li:Fe ratios have \nbeen synthesized. The powders have subsequently conformed into pel-\nlets and sintered following a traditional ceramic processing method. \nElemental composition of the samples has been extracted from Ruth-\nerford backscattering spectroscopy combined with nuclear reaction \nanalysis (RBS-NRA), Rietveld analysis of powder X-ray diffraction \n(PXRD) data has yielded quantitative phase and elemental compositions \nas well as unit cell dimensions for the different phases present in each \nsample, while the samples homogeneity has been investigated by \nconfocal Raman microscopy (CRM). All mentioned techniques demon -\nstrate with good agreement that the phase composition of the powders is \nessentially maintained on the sintered ceramics, which is crucial in \nterms of the material functionality. Microstructural analysis has shed \nlight on the processes that occur during sintering of the ceramics, \nevidencing the role of the Li-content of the starting powders. The mag-\nnetic properties of the ceramics have been investigated through \nvibrating sample magnetometry (VSM) measurements at RT. \n2.Experimental methods \n2.1. Sample preparation \nAppropriate amounts of Li2CO3 and α-Fe2O3 (≽99% and ≽96%, \nSigma-Aldrich) were mixed to attain Li:Fe ratios of 1:1, 1:3 and 1:5. The \ndry powders were mixed using a LabRAM resonant acoustic mixer from \nResodyn (80 g, 1 min at ≪61.5 Hz, max. acceleration 63 G’s). The \nmixture was thermally treated in air atmosphere (4 h at 900 •C) in a \nlaboratory furnace. Synthesis heating profiles may be found in Fig. S1a \nin the Supporting Information (SI). The synthesis treatment was opti-\nmized based on previous experiments (not shown here) so that a cubic \nphase with as low unit cell parameter as possible is obtained for the 1:5 \nLi:Fe ratio mixture (LiFe 5O8 a ≪8.33 Å) [13,19,20] , given that too low \ntemperature is reported to yield hematite (hexagonal/rhombohedral) \nand too high temperature have been seen to produce magnetite (cubic, a ≪8.39 Å) [21]. The expected reactions for each Li:Fe ratio are: [22,23] . \nLiBFe1B1⇒Li2CO 3Fe2O3→2LiFeO 2CO 2↑ (1)  \nLiBFe1B3⇒Li2CO 33Fe 2O3→LiFeO 2LiFe 5O8CO 2↑ (2)  \nLiBFe1B5⇒Li2CO 35Fe 2O3→2LiFe 5O8CO 2↑ (3) \nThe obtained powders were gently grinded in an agate mortar, \nyielding to three different powder samples, which will be subsequently \nreferred to as DLi-Fe 1–1 powdF, DLi-Fe 1–3 powdFand DLi-Fe 1–5 \npowdF. \nThe synthesized powders were pressed into cylindrical pellets \n(ø1cm, 0.75 g powders, 6wt% lubricant) using a stainless-steel die of \nappropriate dimensions and a manual press from Tonindustrie (5min, \n125MPa). The pellets were then heated in air atmosphere (4h at \n1100•C) in the same furnace used for the synthesis, now following a 3- \nstep thermal cycle previously reported to yield high-density LiFe 5O8 \npieces [24]. (see Fig. S1b for sintering heating profiles). The obtained \nceramic samples are given the following IDs: DLi-Fe 1–1 ceramF, \nDLi-Fe 1–3 ceramFand DLi-Fe 1–5 ceramF. \n2.2. Sample characterization \nThe elemental composition of the samples (Li, Fe, O) was evaluated \nby means of ion beam analysis techniques. RBS combined with NRA was \ncarried out at the 5MV tandem accelerator at CMAM using Hat \n3.0MeV [25]. A silicon barrier detector placed at a scattering angle of \n150•was used to measure the backscattering yield and the sample po-\nsition was controlled with a three-axis goniometer. For the measure -\nment, the pellets were grinded to powders using 800 grit dry SiC \nsandpaper and the obtained powders were fixed on a carbon adhesive \ntape. The powder samples were directly mounted on the carbon tape. \nThe experimental conditions for the RBS-NRA measurements were \nspecifically chosen to detect and quantify the Li present in the sample. In \nparticular, non-invasive characterization of the lithium content was \nperformed using the [7] Li(p, α)4He nuclear reaction, which \ncross-section has a broad maximum at a proton energy of 3MeV. This \nnuclear reaction is considered the most suitable for lithium quantifica -\ntion since the signal intensity is proportional to the amount of the \nnaturally occurring [7] Li isotope while yielding a high signal-to-noise \nratio [26]. The in-depth quantification and distribution of Li and all \nthe other elements in the samples were determined with the SIMNRA \nsimulation software package [27]. \nPXRD data were collected in the 2θ-range 14–78•using a Bruker D8 \nAdvance X-Ray diffractometer (ω-2θ diffraction scans) equipped with a \nLynx Eye detector and a Cu anode (Kα1(Cu)1.5406 Å) operated at \n40kV and 30mA. The powder samples were measured as-synthesized, \nwhile the ceramics were ground into powders prior to the PXRD mea-\nsurement. Rietveld analysis of the PXRD data was performed with the \nsoftware FullProf [28], using a Thompson-Cox-Hastings pseudo-Voigt \nfunction to describe the peak-profile [29]. The crystallographic phases \nincluded in the Rietveld models were α-LiFeO 2 (rock-salt structure, \nFm3m (225), a4.158(1) Å) [17] and α-LiFe 5O8 (spinel structure, P4332 \n(212), a8.3339(1) Å) [30]. Find a detailed description of the phases in \nTables S1 and S2, respectively. Notably, LiFe 5O8 crystallizes in the or-\ndered α-LiFe 5O8 phase rather than the high-symmetry β-LiFe 5O8 phase \n(Fd3m) (see Fig. S3). A NIST standard (LaB 6 SRM® 660b) [31] was \nmeasured in the same experimental conditions as the samples in order to \nestimate the instrumental-contribution to the peak-broadening and a \nLorentzian isotropic size parameter was refined to describe the \nsample-contribution to the broadening. Refinements of the Rietveld \nmodels yielded quantitative information on the samples (incl. phase \ncomposition, elemental analysis for the individual phases). \nPhases lacking long-range order are not discernible based on \ndiffraction data. Therefore, the samples were further characterized by \nRaman spectroscopy to reveal possible non-crystalline phases. In C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3353particular, the samples were investigated using a confocal Raman sys-\ntem (WITec ALPHA 300RA) in which the spectrometer is coupled with \nan optical microscope, allowing recording spatially-resolved Raman \ndata (2D-Raman maps). The measurements were performed at RT with a \nlinearly p-polarized Nd:YAG laser (532 nm) and a 100x objective lens \n(NA0.95). A low laser excitation power (0.5mW) was used to avoid \nsample damage and/or overheating. Representative Raman spectra were \nobtained from averaging single spectra recorded every 200nm (expo -\nsure time 2s) throughout an area of at least 5×5µm2. Several re-\ngions of powdered samples were measured in order to analyze their \nhomogeneity. Raman results were analyzed by using WITec Project Plus \nSoftware. In all cases, Raman spectra were normalized to the highest \nintensity vibration mode. A fraction of the pellets was ground into \npowders with an agate mortar, while the powder samples were \nmeasured as-synthesized. \nThe density of the ceramics was determined by the Archimedes ’ \nmethod in distilled water at 25•C. Theoretical densities were calculated \nfor all samples using the refined phase compositions and unit cell di-\nmensions extracted from Rietveld analysis of the PXRD data. Relative \ndensities were calculated dividing measured (Archimedes) by calculated \n(theoretical) density values. \nThe morphology and microstructure of the samples were investi -\ngated based on secondary electron images of FE-SEM using a Hitachi S- \n4700 microscope. Fresh fractured surfaces were imaged for the ceramic \nsamples. The powders were measured directly. Grain size distributions \nand average grain sizes for both powders and pellets were extracted \nfrom the FE-SEM images using the software ImageJ [32]. \nA hot-stage microscope (HSM) from Hesse Instruments with an EMI \nimage analysis and data processing software allowed extracting dilato -\nmetric curves for DLi-Fe 1–1 powdFand DLi-Fe 1–5 powdF, which \nserved to study the sintering kinetics of LiFeO 2 and LiFe 5O8, respec -\ntively. For HSM measurements, the sample was placed on an alumina \nsubstrate and heated up to 1500•C with a heating rate of 10•C/min. \nRT magnetic hysteresis of the dense ceramics was investigated using \na vibrating sample magnetometer (VSM) from Microsense (model EZ 7). \nThe cylindrical pellets were mounted on a quartz rod with a quartz disk \non one end onto which the samples were fixed with Teflon tape. VSM \nmeasurements were performed at RT in a field range of up to 2.1T. \nSaturation magnetization, Ms, and coercive field, Hc, values are extrac -\nted from the measured hysteresis loops; Ms being the magnetization \nvalue at the maximum applied field (i.e., Ms M(2.1T)) and Hc the H- \nfield value at M0. 3.Results and discussion \n3.1. Elemental and phase composition. Structural characterization \nThree compositions were prepared using Li:Fe ratios of 1:1, 1:3 and \n1:5 in the form of powders and ceramics. Fig. 1a shows the RBS-NRA \nspectra measured for the three powders. In the figure, the surface sig-\nnals from O, Fe and Li are marked by arrows and the Li signal has been \nmagnified on the inset. The measured RBS-NRA spectra show notable \ndifferences in terms of the metallic content for the various samples. For \ninstance, DLi-Fe 1–1 powdFseems to have significantly more Li than \nthe other two samples while the Fe signal appears diminished, as ex-\npected from the Li:Fe ratios used in the synthesis. Aiming at quantifying \nthese differences in elemental composition, and particularly in the Li:Fe \ncontent, relevant RBS-NRA spectra have been simulated using the \nSIMNRA commercial code [27]. Measured and simulated spectra for a \nrepresentative sample (DLi-Fe 1–5 powdF) are displayed on Fig. 1b in \nred and black color, respectively, illustrating the good agreement ach-\nieved between experiment and theory. \nIn Fig. 1b, the independent elemental contributions to the total \nsimulated spectrum are also represented. In addition to the Li, Fe and O \npresent in the sample itself, C was also included in the simulations in \norder to account for the contribution of the carbon tape on which the \npowders were fixed for the measurement. The cross-section input related \nto the lithium nuclear reaction [7] Li(p, α)4He was extracted from Paneta \net al. [26] For C and O, the 12C(p,p)12C and 16O(p,p)16O \nelastic-scattering cross-sections have been used [27]. The Rutherford \nscattering cross section was used to simulate the Fe intensity. \nAs a consequence of the samples morphology (powders fixed on \ncarbon tape), the elemental signals of the spectrum show a continuous \ndecrease as the ion beam penetrates deeper in the sample (tails towards \nlower energies), in contrast with the sharp peaks generally recorded for \nthin films. The elemental concentrations, determined by SIMRA simu-\nlations, were included to fit the spectra. The fit was carried out assuming \nthat the sample is composed by 10 different layers and a porosity of a \n40%. Additional fits (not shown here) of the RBS-NRA data have \ndemonstrated the porosity does not significantly affect the calculated \nelemental composition. \nSimilar measurements and simulations were carried out for the \nceramic samples, producing alike results, although as it appears from the \nspectra recorded for the pellets, these samples suffered a slight \ncontamination originating from the SiC sandpaper used to grind them to \npowders for the measurement. Thus, the accuracy of the quantification \nis lower for the ceramics, as an additional contribution from Si had to be \nincluded in the simulation. Table 1 includes the Fe/Li ratios resulting \nfrom the simulations for all powder and ceramic samples. The obtained \nFe/Li values seem to indicate that the Li:Fe ratios of the starting mixtures \nFig. 1.(a) RBS-NRA spectra of the three powder samples. Inset: magnification of the yield corresponding to the lithium signal. (b) Measured and simulated RBS-NRA \nspectra corresponding to sample DLi-Fe 1–5 powdFin red and black color, respectively, along with the individual elemental contributions to the total simulated \nspectrum. Inset: magnification of the Li signal. C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3354are essentially maintained after both the synthesis at 900•C and sin-\ntering at 1100•C, within the calculated errors. Preparation of Li ferrites \nthrough conventional ceramic methods has been traditionally avoided, \nas the high temperatures required for sintering have been seen to pro-\nmote the evaporation of Li. [14] However, this has not been the case for \nthe samples under study here, as the Li-content determined on the ce-\nramics is comparable to the Fe/Li ratios of 1, 3 and 5 employed for the \nsynthesis. A possible explanation for stoichiometry preservation in the \npresent samples is the optimization of the ceramic processing carried out \nhere, yielding powders with stoichiometric composition, good crystal -\nlinity and particle sizes which allow sintering at a relatively low \ntemperature. \nThe measured PXRD patterns were fitted to Rietveld models con-\ntaining two phases: α-LiFeO 2 (rock-salt structure) and α-LiFe 5O8 (spinel \nstructure). Fig. 2a shows the fit for a representative sample (see Fig. S2 \nfor remaining samples). Here, the experimental data is represented by \nthe grey symbols while Rietveld models for LiFeO 2 and LiFe 5O8 are \nrepresented by the red and green lines, respectively. The total Rietveld \nmodel is the sum of these two individual phases (not shown in the figure) \nand the discrepancy between the data and the total model is depicted by \nthe black line at the bottom. The bar graph in Fig. 2c illustrates the composition of each sample in mass percentage (wt%). Pure LiFeO 2 and \nLiFe 5O8 powders are obtained from Li:Fe ratios of 1:1 and 1:5, respec -\ntively. Subsequent sintering of the 1:5 powders do not seem to affect \nphase composition while a small fraction of LiFe 5O8 arises in the 1:1 \nsample. The 1:3 Li:Fe ratio leads to coexistence of the two phases in the \npowder sample: LiFe 5O8 as the main phase, with 83(1) wt%, and a 16.9 \n(8) wt% of LiFeO 2. After the sintering treatment applied to the 1:3 \npowders, the minority phase content increases up to 23.4(9) wt%. \nThe refined cell dimensions for the rock-salt phase are in good \nagreement with the reported for LiFeO 2 (see values in Table S3) [17]. \nRefined cell parameters for the spinel phase are plotted in Fig. 2b. While \nall values are within the expected range for LiFe 5O8, sample DLi-Fe 1–5 \nceramFpresents a greater value than all the other samples. This small \nshift towards larger unit cell dimensions may be understood based on \nthe greater Fe-content of this sample compared to the others (see Table 1 \nand Table S4), given that the isostructural iron oxide magnetite Fe3O4 is \n8.3985(5) Å, [33] although further characterization by means of e.g. \nMossbauer spectroscopy is needed to confirm this hypothesis. The large \nuncertainty on the cell dimensions reported for DLi-Fe 1–1 ceramFis \ndue to the low concentration of LiFe 5O8 present in this sample. \nAs a last stage of the data refinement, atomic occupancies were \nrefined for the metal cations, while the oxygen sites were assumed fully \noccupied, and from the refinements, the lithium content was calculated. \nThe lithium content on each phase is defined as x in Fig. 3a, x repre -\nsenting the chemical subscript corresponding to Li in the phases defined \nas LixFe1-xO2 and LixFe5-xO8 (check Table S4 for numerical values). In \nthe theoretical LiFeO 2 structure, Liand Fe3are equally distributed \nfilling the 4a Wyckoff position (see Table S1 for full phase description). \nIn this work, the occupancies of both atomic positions were refined, \nrevealing that the 4a position has a slight Li-deficiency in all the samples \nstudied (see red symbols in Fig. 3a). The x calculated for the rock-salt \nphase ranges from 0.84(2) to 0.942(9), slightly below the theoretical \nvalue of 1. One could say that the Li-content in LiFeO 2 tends to drop as Table 1 \nFe/Li ratios obtained from the simulated RBS-NRA spectra and from Rietveld \nrefinements of PXRD data for the different samples.  \nsample Fe/Li ratio \nfrom NRA Fe/Li ratio \nfrom PXRD \nDLi-Fe 1–1 powdF 1.0(1) 1.12(5) \nDLi-Fe 1–3 powdF 3.2(1) 4.3(2) \nDLi-Fe 1–5 powdF 5.2(1) 4.9(2) \nDLi-Fe 1–1 ceramF 0.9(2) 1.44(6) \nDLi-Fe 1–3 ceramF 2.6(2) 3.9(2) \nDLi-Fe 1–5 ceramF 5.1(2) 5.3(2)  \nFig. 2.(a) PXRD data and corresponding Rietveld model for sample DLi-Fe 1–3 powdF. (b) Unit cell parameter, a, of the spinel phase and (c) sample composition \nextracted from Rietveld analysis (left: powders, right: pellets). C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3355the amount of Fe used in the synthesis increases but the calculated un-\ncertainties do not really allow drawing a clear trend. \nFor the LiFe 5O8 phase, it has been previously reported that the Li\ncations have a tendency to lodge at the octahedral positions of the \nstructure [13,34,35] . Therefore, in the Rietveld models of the present \nwork, the tetrahedral sites (8c) were always fully occupied by Fe3. On \nthe other hand, the Liand Fe3content on the octahedral sites (with \nWyckoff symbols 4a and 12d, respectively) was refined so that the two \ncations could freely swap with one another as long as both sites \nremained fully occupied. The obtained trends for the Li-content in the \nspinel phase are displayed in green color in Fig. 3a. For all samples, the \nchemical subscript for Li, x, is fairly close to the theoretical value of 1 \n(within a ±0.05 uncertainty). For sample DLi-Fe 1–1 ceramF, the low \nsignificance of the LiFe 5O8 phase did not allow for refining atomic oc-\ncupancies. Similar to the rock-salt scenario, no clear trend is identified \nfor the Li content in the spinel phase, although the obtained results lay in \nall cases within ±5% of the theoretical value. \nAn overall Fe-to-Li content has been calculated considering the \nrefined coefficients and weight fractions for each phase, and they are \nplotted in Fig. 3b as a function of the Fe/Li ratios used in the synthesis. \nThe calculated ratios correlate well with the nominal compositions, \nalthough the calculated values for DLi-Fe 1–3 powdFand DLi-Fe 1–3 ceramF(i.e., 4.3(2) and 3.9(2), respectively) are above the expected \nvalue of 3. The Fe/Li values calculated from the RBS-NRA simulations \nare also plotted in Fig. 3b for comparative purposes. The results from \nboth techniques are in very good agreement for both end compositions, \nalthough a discrepancy in the Li-Fe 1–3 samples is noted. It is worth \nnoting that the discrepancy is observed for the samples that have a \nmixture of phases, while the agreement is better for samples in which \none phase predominates. \nAveraged Raman spectra of the powders and ceramics on represen -\ntative superficial regions are displayed in Fig. 4a. The Raman signal \ncorresponding to DLi-Fe 1–3 powdFand DLi-Fe 1–5 powdFare very \nsimilar to one another, showing Raman vibrational modes at 128, 202, \n237, 264, 301, 322, 259, 282, 403, 440, 493, 521, 553, 611, 666 and \n713cm\u00001. These modes can be associated with the LiFe 5O8 spinel phase, \nand more specifically, with the α polymorph, for which 6A114E20F2 \nphonon Raman modes are allowed [13,20,22] . In addition, some bands \nat larger wavenumbers are observed, at around 1161 and 1376 cm\u00001, \nwhich are attributed to second-order modes [22]. The spectrum \nmeasured for DLi-Fe 1–1 powdFis completely different from the other \ntwo powder samples. In this case, three broad vibrational modes are \nidentified at 180, 394 and 624cm\u00001. This spectrum can be attributed to \nthe LiFeO 2 rock-salt phase [1,36,37] . From the group factor analysis, \nFig. 3.(a) Lithium content on LiFeO 2 (red) and LiFe 5O8 (green). The theoretical coefficient of Li in both phases is 1. (b) Ratio between the Fe and Li content \ncalculated from Rietveld refinements of PXRD patterns (yellow) and RBS-NRA simulated spectra (blue). \nFig. 4.(a) Raman spectra averaged over \nF5×5µm2 regions for as-prepared powders \nand sintered pellets (ceramics). (b) (left) Opti-\ncal image taken on sample DLi-Fe 1–3 ceram -\nFand (right) in-plane Raman image on the \n15×15µm2 region delimited by the white \nsquare on the optical image, the colors identify \nregions of the Raman image with a similar \nRaman spectrum. (c) Main Raman spectra \nrecognized in the Raman mapping from figure \nb, corresponding to the rock-salt and spinel \nphases (in red and green color, respectively). In \nfigure c, the allowed Raman modes for the rock- \nsalt phase are indexed. For the spinel phase, A1 \nand F2 Raman modes are identified with the \ncorresponding tags while untagged bands \ncorrespond to E vibrational modes.   C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3356two phonon modes are active in Raman: A1Eg. The Raman band at \n394cm\u00001 (Egis attributed to the O–Fe–O bending while the vibrational \nmode at 624cm\u00001 (A1corresponds to the Fe–O stretching mode of FeO 6 \noctahedra. The vibrational band at around 180cm\u00001 can be assigned to \nthe Li-cage in an octahedral environment, as identified by C. Julien in \nRaman spectra for similar materials, i.e, LiMO 2 (MNi, Co, Cr) [37]. \nFinally, similar to the spinel structure, a band around 1276 cm\u00001 related \nto an overtone is also visible. \nWith respect to the sintered pellets fabricated from the powder \nsamples, vibrational modes for DLi-Fe 1–3 ceramFand DLi-Fe 1–5 \nceramFare corresponding to the LiFe 5O8 phase while DLi-Fe 1–1 \nceramFpresents a convolution of the two identified Raman spectra: \nLiFe 5O8 LiFeO 2. Subtle changes in the position, full width high \nmaximum (FWHM) and intensity of the Raman bands are noted when \ncomparing powder and ceramic samples. The fluctuations in the relative \nintensities of the bands can be attributed to different crystallographic \norientations of the grains, while the subtle differences in position and \nFWHM may be associated with slight changes on the grain sizes or small \nstrain that may be induced in the structure during the synthesis or sin-\ntering processes. No binary Li or Fe oxides are identified in any sample \n[38,39] . \nWith the aim of gaining semi-quantitative information on the con-\ncentration and distribution of each of the phases, spatially-resolved \nanalysis of the confocal Raman data has been carried out. Fig. 4b \nshows the corresponding analysis for sample DLi-Fe 1–3 ceramF. \nFig. 4b (right) shows the in-plane Raman image corresponding to the \nregion marked on the optical image from the left. In the 2D Raman \nimage, two distinct phases are discriminated, with regions colored in red \nand green corresponding to the rock-salt and spinel phases, respectively. \nFrom both the Raman and optical images, it is roughly estimated that the \nrock-salt phase accounts for about 1/3 of the total surface mapped, \nwhich is in rather good agreement with the 23.4(9) wt% extracted from \nRietveld analysis for that phase in sample DLi-Fe 1–3 ceramF. Raman \nmap analysis for the remaining the samples may be found in Fig. S4, \nyielding results compatible with those from Rietveld analysis. \nAverage Raman spectra corresponding to the two colored regions \nfrom Fig. 4b are plotted in Fig. 4c in matching colors. In Fig. 4c, the rock- \nsalt Raman spectrum (red) has been multiplied by a factor 5 to achieve an overall intensity comparable to that of the spinel one (green). The \nneed for this x5 factor highlights the great difference in Raman cross \nsection of these two phases. As a consequence of this imbalance between \nphases, the average Raman spectra for the samples in this work do not \ngive a good idea of the actual concentration of each phase. This explains \nwhy the average Raman spectrum for DLi-Fe 1–3 ceramF, plotted at the \nbottom of Fig. 4a, gives the impression of a nearly pure LiFe 5O8 sample, \ndespite being calculated from the superficial region shown in Fig. 4b, \nwith a clear contribution from LiFeO 2. The same happens for the cor-\nresponding powder sample Li-Fe 1–3 powdF. This is even more \nnoticeable for DLi-Fe 1–1 ceramF, which according to PXRD is nearly \nsingle-phase LiFeO 2 (96(2) wt%) while the averaged Raman spectra \nshown in Fig. 4a seems to be predominantly spinel phase. Spatially- \nresolved analysis of the data removes some of the uncertainties that \nmight derive from phase identification based on average Raman spectra \nexclusively, evidencing the need for Raman mapping experiments. \n3.2. Particle size distribution, morphology and densification \nFig. 5a-c show FE-SEM micrographs for the three powder samples. In \nall three cases, relatively loose particles with fairly isotropic morphology \nare observed. Particle sizes extracted from the micrographs were suc-\ncessfully fitted to a lognormal distribution, yielding similar mean values \nof ≪600nm for all three powders (within uncertainties, see Table 2). \nSize distributions differ to some extent, with DLi-Fe 1–1 powdFshow -\ning a wider distribution with somewhat more representation of large \nsizes than DLi-Fe 1–3 powdF, and the latter also more than DLi-Fe 1–5 \npowdF. \nThe microstructure of fresh fractured surfaces of the ceramics is \nshown in Fig. 5d-f. For DLi-Fe 1–1 ceramF(Fig. 5d), the former particle \nmorphology has evolved to grains with irregular morphology and \nfaceted grain boundaries which are interconnected through sintering \nnecks. The grains have experimented some growth, reaching a mean \nvalue of 3.8(6) µm, which proves insufficient to eliminate the inter-\nconnected porosity observed in the sample. The fracture is mainly \nintergranular, suggesting that mass transport during sintering is limited \nto coalescence of clusters of particles. All these evidences are indicative \nof an early sintering stage, which is also in agreement with the \nFig. 5.FE-SEM micrographs for (a) DLi-Fe 1–1 powdF, (b) DLi-Fe 1–3 powdF, (c) DLi-Fe 1–5 powdF, (d) DLi-Fe 1–1 ceramF, (e) DLi-Fe 1–3 ceramFand (f) DLi- \nFe 1–5 ceramF. Particle size distribution based on the relevant image, data fitted to a lognormal distribution. C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3357temperature behavior displayed by the powders employed to fabricate \nthis ceramic. As shown by the shrinkage curve for DLi-Fe 1–1 \npowdFextracted from hot-stage microscopy measurements (see \nFig. S5a), at the sintering temperature used (i.e., 1100•C), mass trans -\nport is rather limited and the compound has barely started shrinking, \nD8%. The sintering process has reached a more advanced stage for DLi- \nFe 1–3 ceramF(Fig. 5e), with appearance of grains with large sizes, \nalthough the lognormal mean value of 3.4(2) µm is, within uncertainties, \nequivalent to that for the 1–1 ceramic (see Table 2). The microstructure \nof DLi-Fe 1–3 ceramFis a combination of the observed for the 1–1 and \n1–5 ceramics –not surprising given the mixed composition of this in-\ntermediate sample – and a mixture of both intra- and intergranular \nfractured surfaces are found. DLi-Fe 1–5 ceramF(Fig. 5f) has come to a \nmuch further sintering stage than the other two ceramics. Characteristic \n3-point junctions with 120•angles appear for DLi-Fe 1–5 ceramF, \nindicating the sintering process approaches its final stage [40]. In the \n1–5 ceramic, the grains have grown substantially –finding particles over \n30µm in diameter – and size distribution expands considerably. A mean \ngrain size of 10(2) µm is extracted for the lognormal fit. The fractured \nsurface of DLi-Fe 1–5 ceramFis clearly intragranular, as expected when \ngrain growth occurs during sintering. All this is again understood based \non the shrinkage curve of DLi-Fe 1–5 powdF(see Fig. S5b), which ev-\nidences that for this composition, the greatest mass transport (and in \nturn, the maximum densification speed) takes place at a temperature \nnear the sintering point (i.e., 1100•C). \nA pronounced grain growth generally comes as a consequence of a \nfast grain boundary mobility. As grain boundary mobility is typically \nfaster than the processes required to remove the air between particles, it \nis common for pores to appear in these conditions. For DLi-Fe 1–5 \nceramF, a great number of trapped pores are visible and different stages \nof pore coalescence are found (see Fig. 5f). Similar pores have been \npreviously observed on sintered LiFe 5O8 samples [41–43]. Coalescence \nof intragranular pores and subsequent pore removal involves displace -\nment of the air trapped in the pores towards the surface, and conse -\nquently, it requires much more energy than grain boundary diffusion. \nHence, the rapid grain growth observed here suggests that, in this sys-\ntem, mass transport during sintering is assisted by grain boundary \ndiffusion, while pore coalescence may occur only to a small extent. Li \nhas a high vapor pressure at the selected sintering temperature and \ntherefore, one could expect vapor transport processes to be favored for \nthese materials [44]. However, the preservation of the Li-content after \nsintering denotes that vapor-phase assisted processes must not be \ndominant at the selected sintering temperature, although small contri -\nbutions from such processes to the mass transport cannot be completely \nruled out. \nWhile the presence of intragranular pores is especially relevant for \nDLi-Fe 1–5 ceramF, a few of these pores are also visible in DLi-Fe 1–3 \nceramFwhile no pores are found in DLi-Fe 1–1 ceramF. This together \nwith the grain growth observed for each sample, suggests that mass \ntransport diffusion must be much more favorable in LiFe 5O8 than in \nLiFeO 2, despite the fact that the latter has a higher proportion of Li. This \nis counterintuitive a priori, given that Li-cations are known for their high \nmobility, which would in principle be expected to favor mass transport. \nA possible explanation of this phenomenon could reside on the crystal \nstructures of these two materials. In both rock-salt and spinel structures, Lications occupy the octahedral sites defined by six O2- anions. The Li- \nO bond distances extracted from Rietveld analysis of PXRD data (see \nTable 2) are shorter for LiFeO 2 than for LiFe 5O8, meaning that Li-cations \nare less strongly bound to the oxygen anions in the spinel structure, \nwhich might be the reason why diffusion is greater in LiFe 5O8, in spite of \nits lower Li-content. \nThe relative densities measured for the ceramic samples (see Table 2) \nare in good agreement with the sintering stage attained for each. Thus, \nthe density is greater for DLi-Fe 1–5 ceramFthan for DLi-Fe 1–3 \nceramF, while the lowest value is measured for DLi-Fe 1–1 ceramF. In \nall three cases, the attained densities ensure a good mechanical integrity, \nwhich together with the Li:Fe stoichiometry preservation demonstrated, \nmakes them suitable for many applications, including their use as targets \nfor thin-film deposition by means of e.g. sputter or pulsed-laser depo-\nsition (PLD). This is of great use considering many of the applications of \nLi ferrites require a thin-film morphology. Density improvement is \ngenerally expected from increasing the sintering temperature, however, \na higher working temperature would increase the Li-cation partial \npressure, very likely altering the Li:Fe ratio of the produced ceramic. \nBased on the sintering mechanisms inferred from the FE-SEM micro -\nstructural analysis, it follows that density betterment should come from \nstrategies promoting mass transport through surface diffusion mecha -\nnisms while retaining the Li-cation partial pressure as low as possible. In \nparticular, the use of additives on the surface of the particles of alike \nsystems has been previously proposed as a suitable route to reduce the \nsintering temperature and allow an effective control of grain growth \n[41,45,46] . However, the present work demonstrates that that optimi -\nzation of the ceramic processing also allows producing dense ceramics \nwith stoichiometry preservation, which is key for their technological \napplication. \n3.3. Magnetic properties \nMagnetization, M, as a function of an externally applied magnetic \nfield, Happ, has been measured at RT on the ceramic samples and the \nrecorded hysteresis loops are plotted in Fig. 6. DLi-Fe 1–5 ceram -\nFexhibits a low-coercivity cycle, as expected for a soft ferrimagnet \n(FiM) such as LiFe 5O8. Both Raman microscopy and powder diffraction \nagree upon this sample being phase-pure LiFe 5O8, and the saturation \nmagnetization, Ms, of 61.5(1) Am2/kg measured here fits well into this \nscenario – the Ms values reported for dense LiFe 5O8 pieces span within \n57–63 Am2/kg [23,47,48] . From CRM and PXRD it follows that LiFeO 2 \nis the majority phase in DLi-Fe 1–1 ceramF. LiFeO 2 is an antiferro -\nmagnet (AFM) with an ordering temperature below RT, and therefore, \nno hysteretic behavior is to be expected for this material at RT. A small \nhysteresis loop is recorded for DLi-Fe 1–1 ceramF(see red curves in \nFig. 6), which can only arise from the little LiFe 5O8 present in the sample \n(4.4(3) wt% according to Rietveld analysis). In this case, the Ms value is \nalmost null, given the predominance of the paramagnetic (PM) phase \nand low concentration of FiM material. DLi-Fe 1–3 ceramFis a mixture \nof the two magnetic materials described above (77(1) wt% LiFe 5O8, 23.4 \n(9) wt% LiFeO 2 according to diffraction). It presents a hysteresis curve \nsimilar to that of DLi-Fe 1–5 ceramF, only the Ms decreases down to \n47.2(1) Am2/kg. Phase composition (wt% LiFe 5O8) for each sample can \nbe roughly estimated from the measured Ms with the formula Table 2 \nLognormal mean particle/grain sizes obtained from FE-SEM. Li-O bond distances obtained from Rietveld refinements of PXRD data. Absolute and relative densities \nmeasured for the pellets.  \nsample Particle (powders) or grain (ceramics) mean size (µm) Li-O on rocksalt (Å) Li-O on spinel (Å) Archimedes density (g/cm3) Relative density (%) \nDLi-Fe 1–1 powdF 0.64(6) 2.07909 - - - \nDLi-Fe 1–3 powdF 0.54(4) 2.07830 2.11292 - - \nDLi-Fe 1–5 powdF 0.53(2) - 2.11297 - - \nDLi-Fe 1–1 ceramF 3.8(6) 2.07847 2.11290 3.26 74.3(3) \nDLi-Fe 1–3 ceramF 3.4(2) 2.07822 2.11295 4.07 87.1(5) \nDLi-Fe 1–5 ceramF 10(2) - 2.11385 4.41 92.7(6)  C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3358MssampleMs⊑Li\u0000Fe1\u00005ceramF×wt%LiFe 5O8, assuming \nthat (i) DLi-Fe 1–5 ceramFis phase-pure LiFe 5O8 and (ii) Ms for the PM \nphase should be ≪0. The results from these calculations –collected in  \nTable 3, along with the Ms values – are in very good agreement with the \nwt% LiFe 5O8 obtained from Rietveld analysis of PXRD data (see Fig. 2c). \nUnfortunately, the coercivity, Hc, values extracted from the curves \nare near the resolution limit of the measurement. During the measure -\nment, the Happ was swept in steps of 2 mT, so this is considered as the \nmeasurement error. Therefore, we cannot rigorously determine any Hc \nD4 mT, although a clear difference between DLi-Fe 1–1 ceramFand \nDLi-Fe 1–5 ceramFis qualitatively observed. Note that even though the \nHc in DLi-Fe 1–1 ceramFis a consequence of the LiFe 5O8 present in the \nsample, the Hc measured here is much higher than that for the phase- \npure material. Such magnetic hardening (increase in Hc) can be \nexplained if picturing the sample as a set of small deposits of FiM ma-\nterial (LiFe 5O8) dispersed through a non-magnetic matrix (LiFeO 2). The \ndilution of ferri- or ferromagnetic (FiM, FM) particles reduces the \ndipolar interaction among them, causing an enhancement of Hc; this \neffect has been previously reported and is well understood [49,50] . On \nthe other hand, the coercivity value measured for DLi-Fe 1–5 ceramFis \nmuch lower (see Fig. 6 inset), which is believed to be closely related to \nthe severe grain growth this sample undergoes as a consequence of the \nsintering treatment at 1100•C, clearly yielding the FiM material in a \nmulti-domain magnetic configuration. Besides the pores mentioned \nearlier, the grains in DLi-Fe 1–5 ceramFseem fairly continuous and \nhomogeneous (see FE-SEM in Fig. 5f), as also demonstrated by the rather \nhigh density of the piece (relative density of 92.7(6)%). This micro -\nstructure heavily favors the motion of the magnetic domain walls \nthroughout the large grains, which is known to be the most probable \nmechanism for magnetization reversal in bulk samples [12,51] . \nLow-hampered domain wall motion implies a rapid propagation of any \ndisturbance caused by an external field, therefore diminishing the co-\nercive field of the material. Previously reported Hc values for dense \nLiFe 5O8 pellets are considerably scattered, ranging between 0.4 and 16 \nmT [23,24,35,48,52] , and similar values are found for powders [21,53, \n54]. \n4.Conclusions \nLithium ferrite samples have been prepared as loose powders and \nsintered ceramics, attaining a relative density of 92.7(6)% for a phase- \npure LiFe 5O8 pellet. The lithium content has been evaluated based on Rutherford backscattering spectroscopy combined with nuclear reaction \nanalysis and Rietveld analysis of powder X-ray diffraction data, in both \ncases confirming that the Li:Fe ratios remain relatively steady during the \nsynthesis at 900•C and sintering at 1100•C, yielding a final dense \nproduct with controlled lithium content. This is in contrast with previ -\nous works reporting that the high temperatures required by conven -\ntional ceramic methods promote lithium evaporation and yield Li- \ndeficient products. Preservation of the Li:Fe stoichiometry of the ce-\nramics prepared here is attributed to a combination of both good quality \nof the synthesized powders and the relatively low sintering temperature \nemployed. The controlled stoichiometry and mechanical integrity of the \nceramics prepared here allows their direct utilization in bulk shape, in \naddition to their use as targets for thin-films deposition. Field emission \nscanning electron microscopy has revealed the substantial grain growth \ntaking place during sintering, going from ≪600nm powders to LiFeO 2 \nand LiFe 5O8 ceramics with mean sizes of 3.8(6) and 10(2) µm, respec -\ntively. Large pores have been detected on the ceramics, especially on the \nphase-pure LiFe 5O8 material, which have been attributed to an \nincreased grain boundary mobility by surface diffusion, also compatible \nwith the intense grain growth observed. Additionally, the increased \nmobility and rapid growth has been seen to be more favored for LiFe 5O8 \nthan for LiFeO 2, despite the lower Li-content of the first. The phase-pure \nLiFe 5O8 ceramic shows a soft ferrimagnetic hysteretic behavior with a \nsaturation magnetization of 61.5(1) Am2/kg while the pellet with Li:Fe \n1:1 displays the antiferromagnetic behavior expected for LiFeO 2. \nPhase compositions estimated from the measured Ms are in good \nagreement with that obtained from Rietveld analysis of PXRD data. \nDeclaration of Competing Interest \nThe authors declare that they have no known competing financial \ninterests or personal relationships that could have appeared to influence \nthe work reported in this paper. \nAcknowledgements \nThis work has been supported by grants RTI2018-095303-B-C51 and \nRTI2018-095303-A-C52 funded by MCIN/AEI/ 10.13039/ \n501100011033 and by “ERDF A way of making Europe ” and grants \nPID20210124585NB-C31, PID2021 –124585NB-C32 and PID2021- \n124585NB-C33 funded by MCIN/AEI/ 10.13039/501100011033 and \nby the “European Union NextGenerationEU/PRTR ”. C.G.-M. acknowl -\nedges financial support from grant FJC2018 –035532-I funded by MCIN/ \nAEI/ 10.13039/501100011033 and grant RYC2021 –031181-I funded \nby MCIN/AEI/10.13039/501100011033 and by the “European Union \nNextGenerationEU/PRTR ”. A.S. acknowledges financial support from \nthe Comunidad de Madrid for an “Atracci ˘on de Talento Investigador ” \ncontract No. 2017-t2/IND5395 and grant RYC2021-031236-I funded by \nMCIN/AEI/10.13039/501100011033 and by the “European Union \nNextGenerationEU/PRTR ”. A.Q. acknowledges financial support from \ngrant RYC-2017023320 funded by MCIN/AEI/ 10.13039/ \n501100011033 and by “ESF Investing in your future ”. The authors \nacknowledge support from CMAM for beamtime proposals with codes \nSTD019/20, STD026/20 and STD033/20. \nFig. 6.RT magnetization (M) versus applied field (Happ) hysteresis loops for the \ndense ceramics. On the insets, the near H 0 region is magnified for DLi-Fe 1–1 \nceramF(red) and DLi-Fe 1–5 ceramF(green) to qualitatively demonstrate the \nbehavior of Hc. Table 3 \nSaturation magnetization, Ms, and coercivity, Hc, extracted from measured \nhysteresis loops and wt% LiFe 5O8 calculated from the Ms values, assuming DLi- \nFe 1–5 ceramFis phase-pure LiFe 5O8.  \nsample Ms (Am2/kg) Hc (mT) wt% \nDLi-Fe 1–1 ceramF 0.96(6) 8(2) 2% \nDLi-Fe 1–3 ceramF 47.2(1) D4 77% \nDLi-Fe 1–5 ceramF 61.5(1) D4 100%  C. Granados-Miralles et al.                                                                                                                                                                                                                   Journal of the European Ceramic Society 43 (2023) 3351–3359\n3359Appendix A.Supporting information \nSupplementary data associated with this article can be found in the \nonline version at doi:10.1016/j.jeurceramsoc.2023.02.011 . \nReferences \n[1]A.E. Abdel-Ghany, A. Mauger, H. Groult, K. Zaghib, C.M. Julien, Structural \nproperties and electrochemistry of α-LiFeO 2, J. Power Sources 197 (2012) \n285–291. \n[2]S. Layek, E. Greenberg, W. Xu, G.K. Rozenberg, M.P. Pasternak, J.-P. Iti˘e, D. \nG. Merkel, Pressure-induced spin crossover in disordered α-LiFeO 2, Phys. Rev. B 94 \n(2016), 125129 . \n[3]J. Li, J. Li, J. Luo, L. Wang, X. He, Recent advances in the LiFeO 2-Based materials \nfor Li-Ion batteries, Int. J. Electrochem. Sci. 6 (2011) 1550 –1561 . \n[4]A.R. Armstrong, D.W. Tee, F. La Mantia, P. Nov˘ak, P.G. Bruce, Synthesis of \ntetrahedral LiFeO 2 and its behavior as a cathode in rechargeable lithium batteries, \nJ. Am. Chem. Soc. 130 (2008) 3554 –3559 . \n[5]R. Kanno, T. Shirane, Y. Kawamoto, Y. Takeda, M. Takano, M. Ohashi, \nY. Yamaguchi, Synthesis, structure, and electrochemical properties of a new \nlithium iron oxide, LiFeO 2, with a corrugated layer structure, J. Electrochem. Soc. \n143 (1996) 2435 –2442 . \n[6]J.F. G˘omez-García, J.A. Mendoza-Nieto, A. Ya~nez-Aulestia, F. Plascencia- \nHern ˘andez, H. Pfeiffer, New evidences in CO Oxidation and selective \nchemisorption of carbon oxides on different alkaline ferrite crystal phases (NaFeO 2 \nand LiFeO 2), Fuel Process. Technol. 204 (2020), 106404 . \n[7]I. Yanase, A. Kameyama, H. Kobayashi, CO2 absorption and structural phase \ntransition of α-LiFeO 2, J. Ceram. Soc. Jpn. 118 (2010) 48–51. \n[8]W. Gu, Y. Guo, Q. Li, Y. Tian, K. Chu, Lithium iron oxide (LiFeO 2) for \nelectroreduction of dinitrogen to ammonia, ACS Appl. Mater. Interfaces 12 (2020) \n37258 –37264 . \n[9]V.K. Dien, N.T. Han, W.-P. Su, M.-F. Lin, Spin-Dependent optical excitations in \nLiFeO 2, ACS Omega 6 (2021) 25664 –25671 . \n[10] M. Pardavi-Horvath, Microwave applications of soft ferrites, J. Magn. Magn. Mater. \n215 (2000) 171–183. \n[11] V.G. Harris, A. Geiler, Y. Chen, S.D. Yoon, M. Wu, A. Yang, Z. Chen, P. He, P. \nV. Parimi, X. Zuo, C.E. Patton, M. Abe, O. Acher, C. Vittoria, Recent advances in \nprocessing and applications of microwave ferrites, J. Magn. Magn. Mater. 321 \n(2009) 2035 –2047 . \n[12] J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, New \nYork, NY, 2001 . \n[13] N. Pachauri, B. Khodadadi, M. Althammer, A.V. Singh, B. Loukya, R. Datta, \nM. Iliev, L. Bezmaternykh, I. Gudim, T. Mewes, A. Gupta, Study of structural and \nferromagnetic resonance properties of spinel lithium ferrite (LiFe 5O8) single \ncrystals, J. Appl. Phys. 117 (2015), 233907 . \n[14] P. Hern ˘andez-G ˘omez, M.A. Valente, M.P.F. Graça, J.M. Mu~noz, Synthesis, \nstructural characterization and broadband ferromagnetic resonance in Li Ferrite \nnanoparticles, J. Alloy. Compd. 765 (2018) 186–192. \n[15] R.P. Patil, B.V. Jadhav, M.R. Kadam, D.R. Patil, P.P. Hankare, LPG gas sensing \napplication of lithium ferrite, Mater. Focus 5 (2016) 46–50. \n[16] H. Zeng, T. Tao, Y. Wu, W. Qi, C. Kuang, S. Zhou, Y. Chen, Lithium Ferrite \n(Li0.5Fe2.5O4) nanoparticles as anodes for lithium ion batteries, RSC Adv. 4 (2014) \n23145 –23148 . \n[17] J.C. Anderson, M. Schieber, Order-Disorder transitions in heat-treated rock-salt \nlithium ferrite, J. Phys. Chem. Solids 25 (1964) 961–968. \n[18] A. Boufelfel, Electronic structure and magnetism in the layered LiFeO 2: DFTU \ncalculations, J. Magn. Magn. Mater. 343 (2013) 92–98. \n[19] P.B. Braun, A superstructure in spinels, Nature 170 (1952), 1123 –1123 . \n[20] M.N. Iliev, V.G. Ivanov, N.D. Todorov, V. Marinova, M.V. Abrashev, R. Petrova, Y. \nQ. Wang, A.P. Litvinchuk, Lattice dynamics of the α and β Phases of LiFe 5O8, Phys. \nRev. B - Condens. Matter Mater. Phys. 83 (2011) 1–7. \n[21] S. Soreto, M. Graça, M. Valente, L. Costa, Lithium Ferrite: Synthesis, Structural \nCharacterization and Electromagnetic Properties, in: M. Seehra (Ed.), In Magnetic \nSpinels - Synthesis, Properties and Applications, Vol. 395, InTech, 2017, pp. 31–50. \n[22] W. Cook, M. Manley, Raman characterization of α- and β-LiFe 5O8 prepared through \na solid-state reaction pathway, J. Solid State Chem. 183 (2010) 322–326. \n[23] M. Dasari, G.R. Gajula, D.H. Rao, A.K. Chintabathini, S. Kurimella, B. Somayajula, \nLithium ferrite: the study on magnetic and complex permittivity characteristics, \nProcess. Appl. Ceram. 11 (2017) 7–12. \n[24] P. Peshev, M. Pecheva, A study of sintering and magnetic parameters of spinel \nlithium ferrite; I. Pure lithium ferrite, Mater. Res. Bull. 15 (1980) 1055 –1061 . \n[25] A. Redondo-Cubero, M.J.G. Borge, N. Gordillo, P.C. Guti˘errez, J. Olivares, R. P˘erez \nCasero, M.D Ynsa, Current status and future developments of the ion beam facility \nat the centre of micro-analysis of materials in madrid, Eur. Phys. J. 136 (2021) 175. \n[26] V. Paneta, A. Kafkarkou, M. Kokkoris, A. Lagoyannis, Differential cross-section \nmeasurements for the 7Li(p,p 0) 7Li, 7Li(p,p 1) 7Li, 7Li(p, α0) 4He, 19F(p,p 0)19F, 19F(P, Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At. 288 (2012) \n53–59. \n[27] M. Mayer, SIMNRA, a simulation program for the analysis of NRA, RBS and ERDA. \nAIP Conf. Proc. 475 (1999) 541. \n[28] J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by \nneutron powder diffraction, Phys. B Condens. Matter 192 (1993) 55–69. \n[29] P. Thompson, D.E. Cox, J.B. Hastings, Rietveld refinement of debye –scherrer \nsynchrotron X-Ray data from Al2O3, J. Appl. Crystallogr. 20 (1987) 79–83. \n[30] A.I. Smolentsev, A.B. Meshalkin, N.V. Podberezskaya, A.B. Kaplun, Refinement of \nLiFe 5O8 crystal structure, J. Struct. Chem. 49 (2008) 953–956. \n[31] NIST. Standard Reference Material ® 660b: Line Position and Line Shape Standard \nfor Powder Diffraction ⊑https://www-s.nist.gov/srmors/certificates/660b.pdf ⊒\n(accessed Nov 13, 2022). \n[32] C.A. Schneider, W.S. Rasband, K.W. Eliceiri, NIH Image to ImageJ: 25 years of \nimage analysis, Nat. Methods 9 (2012) 671–675. \n[33] M.E. Fleet, The structure of magnetite: symmetry of cubic spinels, J. Solid State \nChem. 62 (1986) 75–82. \n[34] C. Boyraz, D. Mazumdar, M. Iliev, V. Marinova, J. Ma, G. Srinivasan, A. Gupta, \nStructural and magnetic properties of lithium ferrite (LiFe 5O8) thin films: influence \nof substrate on the octahedral site order, Appl. Phys. Lett. 98 (2011), 012507 . \n[35] S.E. Shirsath, R.H. Kadam, A.S. Gaikwad, A. Ghasemi, A. Morisako, Effect of \nsintering temperature and the particle size on the structural and magnetic \nproperties of nanocrystalline Li0.5Fe2.5O4, J. Magn. Magn. Mater. 323 (2011) \n3104 –3108 . \n[36] P. Rosaiah, O.M. Hussain, Microstructural and electrochemical properties of Rf- \nSputtered LiFeO 2 Thin Films, J. Nanosci. 2014 (2014) 1–6. \n[37] C. Julien, Local cationic environment in lithium nickel-cobalt oxides used as \ncathode materials for lithium batteries, Solid State Ion. 136–137 (2000) 887–896. \n[38] F.S. Gittleson, K.P.C. Yao, D.G. Kwabi, S.Y. Sayed, W.-H. Ryu, Y. Shao-Horn, A. \nD. Taylor, Raman spectroscopy in lithium-oxygen battery systems, \nChemElectroChem 2 (2015) 1446 –1457 . \n[39] M. Testa-Anta, M.A. Ramos-Docampo, M. Comesa ~na-Hermo, B. Rivas-Murias, \nV. Salgueiri ~no, Raman spectroscopy to unravel the magnetic properties of iron \noxide nanocrystals for bio-related applications, Nanoscale Adv. 1 (2019) \n2086 –2103 . \n[40] M.N. Rahaman. Ceramic Processing and Sintering, Secondnd ed., CRC Press, 2017 . \n[41] P. Peshev, M. Pecheva, A study of sintering and magnetic parameters of spinel \nlithium ferrite: II. Lithium ferrite containing Bi2O3, Mater. Res. Bull. 15 (1980) \n1199 –1205 . \n[42] N. Gupta, M.C. Dimri, S.C. Kashyap, D.C. Dube, Processing and properties of \ncobalt-substituted lithium ferrite in the GHz frequency range, Ceram. Int. 31 \n(2005) 171–176. \n[43] Y. Gao, H. Zhang, L. Jin, H. Su, Y. Liu, L. Jia, Y. Liao, Y. Li, Improving the magnetic \nproperties of Li-Zn-Ti Ferrite by doping with H3BO3-Bi2O3-SiO 2-ZnO Glass for LTCC \nTechnology, J. Electron. Mater. 43 (2014) 3653 –3658 . \n[44] R.E. Honig, Vapor Pressure Data for the More Common Elements; David Sarnoff \nResearch Center, Radio Corp. Am. RCA Lab. Div. (1957) . \n[45] J.F. Fern˘andez, A.C. Caballero, P. Dur˘an, C. Moure, Improving sintering behaviour \nof BaTiO 3 by small doping additions, J. Mater. Sci. 31 (1996) 975–981. \n[46] J.C. Guzm ˘an-Mínguez, L.M. Vicente-Arche, C. Granados-Miralles, J.F. Fern˘andez, \nA. Quesada, Improvement of the magnetic properties of SrFe 12O19 ceramics by \ntailored sintering with SiO2 addition, J. Alloy. Compd. 860 (2021), 157890 . \n[47] Y. Sharma, R. Agarwal, L. Collins, Q. Zheng, A.V. Ievlev, R.P. Hermann, V. \nR. Cooper, K.C. Santosh, I.N. Ivanov, R.S. Katiyar, S.V. Kalinin, H.N. Lee, S. Hong, \nT.Z. Ward, Self-Assembled room temperature multiferroic BiFeO3-LiFe5O8 \nnanocomposites, Adv. Funct. Mater. 30 (2020) 1–10. \n[48] R.P. Patil, S.B. Patil, B.V. Jadhav, S.D. Delekar, P.P. Hankare, Structural and \nmagnetic properties of Co substituted Li0.5Fe2.5O4, J. Magn. Magn. Mater. 401 \n(2016) 870–874. \n[49] J.R. Martínez, J.R. Alba, I.G. de; Blanco-Esqueda, A. Guerrero-Serrano, G. Ortega- \nZarzosa, Coercivity values enhancement by incorporation of magnetic powders in \ninorganic matrix hosts, N. J. Glas. Ceram. 3 (2013) 1–5. \n[50] Xavier Batlle, Amílcar Labarta, Finite-Size effects in fine particles: magnetic and \ntransport properties, J. Phys. D. Appl. Phys. 35 (2002) 201. \n[51] F. Jimenez-Villacorta, L.H. Lewis, Advanced Permanent Magnetic Materials, in: J. \nM.G. Estevez (Ed.), Nanomagnetism, One Central Press, Cheshire, UK, 2014, \npp. 161–189. \n[52] J. Li, D. Zhou, Influence of Ag doping on the dielectric and magnetic properties of \nLiFe 5O8 Ceramics, J. Alloy. Compd. 785 (2019) 13–18. \n[53] N. Thomas, T. Shimna, P.V. Jithin, V.D. Sudheesh, H.K. Choudhary, B. Sahoo, S. \nS. Nair, N. Lakshmi, V. Sebastian, Comparative study of the structural and \nmagnetic properties of alpha and beta phases of lithium ferrite nanoparticles \nsynthesized by solution combustion method, J. Magn. Magn. Mater. 462 (2018) \n136–143. \n[54] S. Singhal, K. Chandra, Cation distribution in lithium ferrite (LiFe 5O8) PRepared \nVia Aerosol Route, J. Electromagn. Anal. Appl. 02 (2010) 51–55. C. Granados-Miralles et al.                                                                                                                                                                                                                   "    },    {        "title": "0812.2343v2.Magnetoelectric_Effect_for_Novel_Microwave_Device_Applications.pdf",        "content": "MAGNETOELECTRIC EFFECT FOR NOVEL MICROWAVE DEVICE APPLICATIONS \n  \nE.O. Kamenetskii, M. Sigalov, and R. Shavit \n \nMicrowave Magnetic Laboratory \nDepartment of Electrical and Computer Engineering \nBen Gurion University of the Negev, Israel \ne-mail: kmntsk@ee.bgu.ac.il \n \n(December 12, 2008) \n \nABSTRACT \n \nIn a normally magnetized thin-film ferrite disk with \nmagnetic-dipolar modes, one can observe magnetoelectric \noscillations. Such magnetoelectric properties of an \nelectrically small sample can be considered as very attractive phenomena in microwaves. In this paper we \ndiscuss the question on novel microwave device \napplications based on ferrite magnetoelectric particles.  \nIndex Terms — Ferromagnetic resonance, \nMagnetoelectric effect, Microwave devices  \n1. INTRODUCTION \n \nAn idea to create microwave devices where the magnetic \ncharacteristics are controlled by an electric field and/or the electric characteristics are controlled by a magnetic field – \nthe magnetoelectric (ME) devices – looks as a very \nattractive subject for novel applications. Presently, ME interaction in ferrite-ferroelectric composites have \nfacilitated a new class of microwave signal processing \ndevices. When a ferrite in a ferrite-ferroelectric bilayer is driven to the ferromagnetic resonance (FMR) and an \nelectric field is applied across a ferroelectric, the ME effect \nresults in a frequency or field shift of FMR. Thus \nmicrowave devices based on FMR can be tuned with both \nelectric and magnetic fields. Several dual tunable microwave ferrite-ferroelectric-bilayer devices have been \ndemonstrated so far. There are microwave attenuators, \nresonators, filters, and phase shifters [1].     The ability to control magnetism with electric fields has \nan obvious technological appeal.  Together with the way of \ndevelopment and creation of ME devices based on ferrite-ferroelectric bilayers, unique microwave devices can be \nrealized based on so-called ferrite ME particles. The ME \nresponse requires simultaneous breaking of space inversion \nand time-reversal symmetries. The electric polarization is \nparity-odd and time-reversal-even. At the same time, the magnetization is parity-even and time-reversal-odd. One cannot consider (classical electrodynamically) a system of \ntwo coupled electric and magnetic dipoles as local sources \nof the ME field [2]. These symmetry relationships make \nquestionable an idea of a simple combination of two \n(electric and magnetic) small dipoles to realize local ME \nparticles for electromagnetics. In a presupposition that a particle with the near-field cross-polarization effect is really \ncreated, one has to show that inside this particle there are \ninternal dynamical motion processes with special symmetry properties. It has been found that while the ME properties \nare not allowed in classical point-like particles, small ferrite \ndisks with magnetic eigen oscillations, magnetic vortex and chiral structures may present a solution [3]. Recent studies, \nboth theoretical [4] and experimental [5], show unique ME \nproperties of a quasi-2D ferrite disk with magnetic-dipolar-\nmode oscillations. Small ferrite ME particles demonstrate \nstrong resonance responses to RF electric and magnetic fields in a local region – the region with sizes much less \nthan the free-space electromagnetic wavelength. The near \nfields of ferrite ME particles are characterized by special symmetry properties. This allows considering ferrite ME \nparticles among the most promising structures for novel \nmicrowave applications.    \n2. FERRITE ME PARTICLES \n \nIn a normally magnetized ferrite disk with magnetic-\ndipolar-mode (MDM) [or magnetostatic-wave (MSW)] oscillations, one can observe the ME properties in \nmicrowaves. For the first time, the MDM (or MSW) \noscillations were found in small ferrite spheres [6]. Further experiments with thin ferrite disks [7] showed very rich \nmultiresonance MDM spectra in such particles. In 1970s –\n1980s, the main stream in studies of microwave devices based on magnetostatic waves and oscillations was aimed to \nrealization of compact delay lines, filters, and planar \nresonators [8]. A strong interest in this kind of microwave \ndevices was caused by the fact that magnetostatic waves \nhave a very small wavelength (two-four orders of a magnitude less than the electromagnetic-wave wavelength  2at the same frequency). A return to studies of the MDM \nspectra in thin-film ferrite disks was made recently. It was shown that MDMs in a normally magnetized ferrite disk are \nenergy-eigenstate oscillations. Moreover it has been proven \nthat the MDM orthogonality relations can be satisfied when there are effective surface magnetic currents on a lateral \nsurface of a disk. Due to these currents one has eigen \nelectric fluxes and eigen electric (anapole) moments. For \nevery MDM, there exists also a vortex circulation of the \npower flow density inside a ferrite disk. Unique symmetry properties of MDMs in a ferrite disk result in appearance of \nmicrowave ME effects [4]. These effects were verified in \ndifferent microwave experiments [5].      Recently, it was shown [9] that ferrite ME particles can \nbe effectively studied based on the HFSS numerical \nsimulation program [10]. Fig. 1 shows a typical picture of the vortex circulation of the power flow density inside a \nferrite disk for the 1\nst MDM.  \n \n              \n  \n                                    ( a) \n \n           \n  \n                                    \n                                     ( b) \n \nFig. 1. The power flow density distribution for the 1st \nMDM in a quasi-2D ferrite disk. The frequency is f = 8.52 \nGHz and the bias magnetic field H 0 = 4900 Oe. The disk \ndiameter is D = 3 mm and the thickness is t = 0.05 mm. (a) \nNumerically modeled vortex; (b) analytically derived MDM vortex. A black arrow in Fig. 1 (a) clarifies the power-flow \ndirection inside a disk. \n     As an example of ME properties, Fig. 2 shows numerical \nresults of the electric field distributions at different time \nphases for the 1\nst oscillating mode in a ME particle composed as a thin ferrite disk with a wire surface \nmetallization. One has an in-plane non-rotating electric dipole. At the same time a magnetic dipole rotates in a disk \nplane. The concept of such a ferrite ME particle was \nproposed in [11].   \n     \n \n \nFig. 2. The electric field structure in a ferrite ME particle \ncomposed as a thin ferrite disk with a wire surface metallization. \n \n    It appears now that the MDM ME particles can be considered among the most promising structures for novel \nmicrowave applications. There could be: (a) high-resolution \nnear-field microwave sensors, (b) dense microwave ME metamaterials, (c) novel compact microwave radiating \nsystems, and (d) microwave electrostatic-control spin-based \nlogic devices and quantum-type computation. \n \n3. ME NEAR-FIELD MICROWAVE SENSORS\n \n \nMeasurement of the electromagnetic response of materials \nat microwave frequencies is important for both fundamental and practical reasons. During last years near-field sensors \nfor microwave microscopy have created the opportunity for \na new class of electrodynamics experiments of materials and integrated circuits [12]. One of the most sensitive forms of \ncontemporary near-field microwave microscopy is that the \nsample is put near the open end of a transmission-line \nresonator, and changes in the resonant frequency and \nquality factor are monitored as the sample is scanned. It becomes clear that new perfect lenses that can focus beyond \nthe diffraction limit could revolutionize near-field \nmicroscopy. We propose use of a small ferrite ME particle as an effective near-field sensor for novel microwave \nmicroscopes.  \n    Due to special symmetry properties of magnetic ordering in thin ferrite disks with MDM oscillations there exist eigen \nelectric fluxes. These fluxes should be very sensitive to the \npermittivity parameters of materials abutting to the ferrite x y \nz 0Hr\n  3disk. Dielectric samples above a ferrite disk with a higher \npermittivity than air confine the electric field closely outside the ferrite, thereby changing the loop magnetic currents in a \nferrite disk and thus transforming the MDM oscillating \nspectrum. This effect was verified experimentally and explained theoretically in Refs. [4, 5]. Fig. 3 shows the \nexperimental results of the frequency shift of the MDM \npeak positions for a ferrite disk with a dielectric loading due \nto the eigen electric fluxes. The first peaks in the spectra are \nmatched by proper correlations of bias magnetic fields.   \n \nFig. 3. Transformation of the MDM oscillating spectrum for \ndifferent dielectric loads. \n     Based on ferrite ME particles, effective near-field sensors \nfor novel microwave microscopes can be realized. The main \nprinciple of the near-field microscopy is the use of evanescent modes decaying expon entially. These modes are \nsuperoscillatory and thus provide a means to probe high \nspatial frequency structure of the sample. The scattered field is computed perturbatively. Since the wavelength of MDMs \nis three orders of magnitude less than the electromagnetic-\nwave wavelength, the ferrite-particle sensors should have \nvery high-resolution characteristics. \n \n4. DENSE MICROWAVE ME METAMATERIALS\n \n \nPresently, there is a strong interest in electromagnetic artificial materials with local ME properties. The properties \nof ferrite ME particles and ME fields originated from such \nparticles give very new insights into a problem of dense \nmicrowave ME composites. Such materials can be useful \nfor novel microwave waveguides and antenna systems.      In 1948 Tellegen suggested that an assembly of the lined \nup electric-magnetic dipole twins can construct a new type \nof an electromagnetic material [13]. Till now, however, the problem of creation of the Tellegen medium is a subject of \nstrong discussions. An elementary analysis makes \nquestionable an idea of a simple combination of two (electric and magnetic) dipoles to realize local materials \nwith the Tellegen particles as structural elements. A \nclassical multipole theory describes an effect of \"ME coupling\" when there is time retardation between the points \nof the finite-region charge and current distributions and this time retardation is comparable with time retardation \nbetween the origin and observation points. In such a case, \nan expression for the field contains combinations of both magnetic and electric multipole moments. One may obtain \nthe EM-wave phase shift between the points of the finite-\nregion charge and current distributions, \n1ϕ, comparable \nwith the EM-wave phase shift between the origin and \nobservation points, 0ϕ, even for a very small scatterer. To \nobtain such an effect of \"ME coupling\" one should make a \nscatterer in a form of a small LC delay-line section. In the \nfar zone of this scatterer we will observe \"ME coupling\". \nThis can be explained with help of Fig. 4. Let a \ncharacteristic size of a scatterer be r and R r<< , where R  \nis a distance between the origin point and the observation \npoint P. Let 1k be the wavenumber of the EM wave \npropagating in a LC delay line and 0k be the wavenumber \nof the EM wave in vacuum. In a case when 0 1 k k>> , one \nmay obtain Rk kr0 0 1     =≈=ϕ ϕ . All the proposed \n\"electromagnetic ME scatterers\" have a typical form of a \ndelay-line section with distinctive inductive and capacitive \nregions. In a series of experimental papers one can see that \nthe \"ME coupling\" effect in these particles was observed only in the propagation-wave behavior, without any near-\nfield characterizations. \n \n \n \nFig. 4. Effect of \"ME coupling“ in a small electromagnetic \nscatterer. A scatterer has a form of a LC delay-line section \nand the phase shifts are Rk kr0 0 1     =≈=ϕ ϕ  \n \n    To realize dense microwave ME materials, local ME structural elements should be used. While a local ME \nparticle cannot be realized as a classical scatterer with the \ninduced parameters, it can be created as a small magnetic \nsample with eigen magnetic oscillations having special \nsymmetry breaking properties [3]. A model for coupled ferrite ME particles underlies a theory of ME \"molecules\" \nand dense ME composites. The model is based on the \nspectral characteristics of MDM oscillations and an analysis of the overlap integrals for interacting eigen oscillating ME  4elements [14]. Fig. 5 gives the numerical results of the \nmagnetic-field distributions fo r even and odd modes in two \ncoupled ferrite particles. \n    The chiral-state resonances in a ferrite disk can be \ndescribed by helical MS-potential modes [15]. Because of the symmetry breaking effects, dense ferrite-particle ME \ncomposites will have the left-hand-resonance and the right-\nhand-resonance responses. Fig. 6 represents a dense \nmicrowave ME composite material with an illustration of \nhelical (chiral) states of the MDMs inside ferrite particles. \n \nFig. 5. The magnetic-field distributions for even and odd \nmodes in two coupled ferrite particles. \n \n \nFig. 6. A dense microwave ME composite material with an \nillustration of helical (chiral) states of the MDMs inside ferrite particles. \n \n5. NOVEL COMPACT MICROWAVE RADIATING \nSYSTEMS \n \nIn open resonant microwave structures with ferrite \ninclusions there exist the vortex-type fields and Poynting-\nvector phase singularities. A circularly polarized EM radiation obtained from a chiral-state vortex antenna with a \nsmall ferrite inclusion can be considered as being originated \nfrom a vortex topological defect in space. Recent studies of patch antennas with ferrite disk inclusions show unique \nmicrowave characteristics [16].      Fig. 7 shows the Poynting vector distributions above the \npatch antenna with a small ferrite-disk inclusion. At the same direction of a bias magnetic field, one has two chiral-\nstate resonances at different frequencies. \n \n                ( a)                                    ( b) \n Fig. 7. The Poynting vector distributions above the patch for \ntwo resonance frequencies and the same direction of a bias \nmagnetic field:  (a) left-hand chiral resonant state; (b) right-hand chiral resonant state.     \n     \n    Novel compact microwave radiating systems can be \nrealized when ferrite disks work at the MDM ME behavior.  \n \n6. MICROWAVE ME LOGIC DEVICES \n \nDevices based on magnetic ordering may provide an interesting alternative to co nventional semiconductor gates. \nMDM ME ferrite disks have well-spaced energy levels \nowing to there intrinsic spectral characteristics. They also have eigen electric moments. These properties make them \nfeasible for electrostatic-control logic devices operating at \nroom temperatures.  \n    Presently, there is a very strong interest in realization of \nlogic devices and computation systems working based on the quantum-type algorithms. Since MDMs are energetically \northogonal, there is no magnetic dipole-dipole interaction \nbetween the spins of different modes. This allows considering MDMs as Hilbert-space oscillations. Recent \npropositions [17], [18] show unique perspective in use of \nferrite ME particles for realization of novel room-temperature quantum-type computation devices. One of the \nschemes can be created with use of two coupled MDM ME \nparticles as a quantum-type gate. Another implementation is \nbased on the adiabatic transfer of ME-particle-state \ncoherence to the cavity mode. The initial eigenstates describe the ME-particle-cavity system. The final \neigenstates contains a contribution from the excited ME-\nparticle state.    \n    Let \n1f be a resonance frequency of cavity mode 101TE  \nand 2f be a resonance frequency of cavity mode 201TE . It \nis clear that a ME particle placed in a cavity center may \ninteract with the cavity electric field in a case of 101TE  \nmode and with the cavity magnetic field in a case of 201TE  \nmode. The high- Q microwave cavity with these two \nresonance frequencies can be viewed, respectively, as a \n(a)\n(b) 5two-state system: 0 and 1. The particle characteristic \ndimension is much less than the EM-wave wavelength (in \nFig. 8 we premeditatedly increased the particle sizes for \nclearer observation). The main absorption peak (the first-\norder ME mode) corresponds to the “ground” g state of a \nME particle and the second absorption peak (the second-\norder ME mode) is the “excited” e state. Suppose that we \nrealized a cavity with frequencies  1f and 2f \ncorresponding to frequencies of the ME-particle first two \npeaks at DC magnetic )(\n0IH . The initial state \n0,ginitial=ψ  describing the ME-particle-cavity system \ncorresponds to the case of the main ME mode at frequency \n 1f, bias magnetic field )(\n0IH  and cavity mode 101TE  (Fig. \n9 (a)). For a certain magnetic field )(\n0)(\n0I IIH H<  we can \nshift the oscillating spectrum of the particle to the position \nshown in Fig. 9 (b). In this case a RF electric field of cavity \nmode 101TE  excites the second-mode ME oscillation in a \nparticle. This is the 0,e state. Now we turn a DC magnetic \nfield back to quantity )(\n0IH  (Fig. 9 (c)). The final cavity \neigenstate (201TE  mode) contains a quantized contribution \nfrom the excited ME-particle state. As a result, we have a \n“shift” through the transformations 1, 0, 0, g e g →→ .  \n \n \nFig. 8. ME particle inside a high- Q cavity: The quantum-\ntype entanglement between the external (cavity mode) and the internal (MDM) states. \n \n \n \n  \n \n  \n \n  \n  \n  \nFig. 9. A scheme illustrating how coherence of the MDM  \nlevels is mapped directly onto a cavity field.  The above mechanism shows how the source (the control \nqubit – the ME particle) can “teach” the field to evolve \ntoward a desirable quantum state. \n \n7. CONCLUSION  \n \nWe showed that novel microwave devices with unique \ncharacteristics for both near-field and far-field manipulations can be realized based on ferrite ME particles. \n \n8. REFERENCES \n \n[1] A. S. Tatarenko, G. Srin ivasan, and D. A. Filippov, Electron. \nLett., 43, No. 12 (2007); A. B. Ustinov, G. Srinivasan, and Yu. K. \nFetisov, J. Appl. Phys. 103, 063901 ( 2008); A. S.  Tatarenko, G. \nSrinivasan, and M. I. Bichurin, Appl. Phys. Lett ., 88, 183507 \n(2006).    \n[2] J. D. Jackson, Classical Electrodynamics , 2nd ed. (Wiley, New \nYork, 1975). [3] E. O. Kamenetskii, M. Siga lov, and R. Shavit, e-print:  \narXiv:0807.4280 (2008), J. Appl. Phys . [in press]. \n[4] E. O. Kamenetskii, Physical Review E  63,  066612 (2001); E. \nO. Kamenetskii, M. Sigalov, and R. Shavit, J. Phys .: Condens. \nMatter  17, 2211 (2005); E. O. Kamenetskii, J. Phys. A: Math. \nTheor.  40, 6539 (2007). \n[5] A. K. Saha, E. O. Kamenetskii, and I. Awai, J. Phys. D: Appl. \nPhys. 35, 2484 (2002); E. O. Kamenetskii, A. K. Saha, and I. \nAwai, Physics Letters A  332, 303 (2004); M. Sigalov, E. O. \nKamenetskii, and R. Shavit , J. Appl. Phys . 104, 053901 (2008). \n[6] R. L. White, I. H. Solt, Phys. Rev . 104, 56 (1956). \n[7] J. F. Dillon, Jr., J. Appl. Phys . 31, 1605 (1960).  \n[8] W. S. Ishak, Proc. IEEE  76, 171 (1988), \n[9] M. Sigalov, E. O. Ka menetskii, and R. Shavit, J. Phys .: \nCondens. Matter  21, 016003 (2009).  \n[10] High Frequency Structure Simulator , www.hfss.com, Ansoft \nCorporation, Pittsburgh, PA 15219. \n[11] E. O. Kamenetskii, Microw. Opt. Technol. Lett . 11, 103 \n(1996). \n[12] B. T. Rosner and D. W. van der Weide, Rev. Sci. Instrum . 73, \n2505 (2002). \n[13] B. D. H. Tellegen, Philips. Res. Rep . 3\n, 81 (1948).  \n[14] E. O. Kamenetskii,  e-print: arXiv:0808.1198 (2008). \n[15] E. O. Kamenrtskii, J. Magn. Magn. Mater . 302, 137 (2006).  \n[16] M. Sigalov, E. O. Kamenetsk ii, and R. Shavit, In Proc. of the \nICEAA'07 (Torino, Ital y, Sept. 17 – 21, 2007), IEEE CNF, pp. \n834-837; J. Appl. Phys . 104, 113921 (2008). \n[17] E. O. Kamenetskii and O. Voskoboynikov, Int. J. Comput. \nResearch  15, 133 (2008). \n[18] M. Sigalov, E. O. Kamenetsk ii, and R. Shavit, In Proc. of the \nMETAMATERIALS 2008 (Pamplona, Spain, Sept. 23 - 26, 2008). \n \n"    },    {        "title": "1606.08118v1.Structural_and_electrical_properties_of_Sn_substituted_double_sintering_derived_Ni_Zn_ferrite.pdf",        "content": "Highlights  \n \n1. Dielectric u nusual behavior has been successfully explained by the Rezlescu \nmodel.  \n2. Long  (ns) is determined , can be utilized for memory and spintronics device s. \n3. ath is calculated and well compared with aexpt. \n4. Sn substituted Ni -Zn single phase inverse cubic spinel has been synthesized . \n Highlights (for review) \n Structural and electrical properties of Sn substituted double sintering derived \nNi-Zn ferrite  \n \nM.A. Alia, M.N. I. Khan  b, F.-U.-Z. Chowdhury  a, S.M. Haque  b, M.M. Uddin  a,* \n \na Department of Physics, Chittagong University of Engineering and Technology (CUET) , \nChittagong -4349, Bangladesh.  \nb Materials Science Division, Atomic Energy Center, Dhaka -1000, Bangladesh.  \nAbstract  \nThe Sn substituted Ni -Zn ferrites were synthesized by the standard double sintering technique  \nusing nano powders  of nickel oxide (NiO), zinc  oxide (ZnO), iron oxide (Fe 2O3) and tin oxide \n(SnO 2). The structural and electrical properties have been investigated by  the X -ray diffraction,  \nscanning electron microscopy, DC resistivity and dielectric  measurements.  Extra intermediate \nphase ha s been det ected along with the inverse cubic spinel phase  of Ni-Zn ferrite. Enhancement \nof grain size is observed in Sn substituted Ni -Zn ferrites. DC resistivity as a function of \ntemperature has been investigated by two probe method. The DC resistivity was found to  \ndecrease whereas the dielectric constants increase with increasing Sn content in Ni -Zn ferrites. \nThe dielectric constant of the as prepared sample s is high enough to  use these materials  in \nminiaturized memory devices based capacitive components or energy storage principles.  \n \nKeywords:  Ni-Zn ferrite, double sintering method, structural properties, electrical properties, DC \nresistivity, activation energy.  \n \n \n \n* Corresponding author.  \nE-mail address: mohi@cuet.ac.bd ( M. M. Uddin ) \n *Manuscript\nClick here to view linked References \n 1. Introduction   \nIn recent years , the spinel  ferrites  belong to AB 2O4 structure having tetrahedral A site and \noctahedral B site  have drawn huge attention due to their characteristic properties to meet the \nnecessities  in various applications.  Remarkable p rogresses have been observed  to inv ent and \ndevelopment of new ferrites.  The research and application of magnetic  materials have been \ndeveloped  considerably  in the few past decades . The Ni -Zn ferrites  have been found to be the \nmost  versatile ferrites system s from the viewpoint of their techn ological  application  because of \nits high electrical resistivity, high permeability, chemical stability and low eddy current losses  \n[1-5], especially ideal for high frequency applications.  The properties of Ni -Zn ferrites can be \naltered by changing chemical  composition, preparation methods, sintering temperature (T s) and \nimpurity element or levels. The improvement of t he basic properties of Ni -Zn ferrites  regarding \nvarious application s have been reported [6 -20] by altering chemical composition, doping ions  or \nlevels  having different valence states. The tetravalent ions such as Ti4+, Sn4+ and Si4+ substitution \nhave  greatly influenced the properties Ni-Zn ferrites [ 21].  \nDetails investigation onTi4+ doping in Ni -Zn ferrite system has been carried out [ 6-8, 12, 17] \nwhile introduction of Sn4+ has attracted less attention [ 7, 9]. Though some studies have mainly \nfocused on the magnetic properties of Sn substituted  Ni-Zn ferrites , the nonmagnetic properties \nsuch as electrical conductivity and  dielectric properties ar e not reported.  The materials with high -\ndielectric constants (≥ 103) have become immense interest for the miniaturized memory devices \nthat are based on the capacitive components or energy storage principles [22 , 23]. Moreover, \ninvestigations are limited in  substitution of non -magnetic ions of Fe3+ in Ni -Zn ferrite system.  \nSimultaneous change of Ni and Zn  by Sn substitution in the Ni -Zn ferrite system is essential to \nelucidate  basic understanding and mechanism.   \n In this study, we have report ed the structural and electrical properties  of pure and Sn substituted \nNi-Zn ferrite.  To the best of our knowledge;  this is the first detailed study on tin substituted Ni -\nZn ferrite  prepared by double sintering technique . \n2. Materials and methods   \n Solid state reaction route w as followed to synthesize Sn substituted Ni -Zn ferrite,  Ni0.6-\nx/2Zn0.4-x/2SnxFe2O4 (x = 0.00, 0.05, 0.10, 0.15, 0.20 and 0.30)  (NZSFO) . We have  used high \npurity (99.5%) (US Research Nanomaterials, Inc.)  oxide precursors . The nano powders are taken \nas raw materials . The particle size of nickel oxide (NiO), zinc oxide (ZnO), iron oxide (Fe 2O3) \nand tin oxide (SnO 2) are 20-40, 15 -35, 35 -45 and 35 -55 nm, respectively. The preparation \ntechnique is described  elsewhere [5]. The final sintering of the samples was carried out  at \n1300°C for 4 h in air and natural cooling was followed . Structural characterization of the \nsynthesized samples was carried out by X-ray diffraction (XRD) using Philips X’pert Pro X -ray \ndiffractometer (PW3040) with Cu -Kα radiation (λ = 1.5405 Å ) and s canning electron microscope \n(SEM) . DC resistivity was measured usin g Keithley -6514 DC measurement s ystem.  Dielectric \nmeasurements  were done  by a Wayne Kerr precision impedance analyzer (6500B) in the \nfrequency range of 10 Hz to 100 MHz with drive v oltage 0.5V  at room temperature .  \n3. Results and discussion  \n3.1 Structural properties  \nThe XRD  patterns of Sn substitut ed Ni -Zn ferrites with the chemical composition Ni 0.6-\nx/2Zn0.4-x/2SnxFe2O4 (NZSFO) are  shown  in Fig. 1.  It is seen that the observed peaks (1 11), (220), \n(311), (400), (422), (511), (440) and (533) confirmed the spinel structure of the  Ni0.6Zn0.4Fe2O4 \n(NZFO)  for x=0.0. The extra new intermediate phase  of NiSnO 3 and SnO 2 is observed at around \n2=33.3 for the Sn concentration higher than that of x > 0.1. Similar extra phase of  NiSnO 3 has  \n also been observed and reported in Sn substituted NiFe 2O4 ferrite system [ 24]. The intensity of \nextra phase increases with the increase of Sn concentration.  The corresponding positions of all \nthe sharp peaks were used to obtain the interplanar spacing. The lattice parameter for each peak \nof the samples was calculated using  the equation  \n .  \n \n \n \n \n \n \nFig. 1. The X-ray diffraction  pattern s of NZSFO (x = 0.0, 0.05, 0.1, 0.15, 0.2 and 0.3) ferrites \nsamples.  \n \nTo determine the exact lattice parameter, Nelson –Riley (N-R) extrapolation method was \nused. The N -R function is represented by the equation \n . The exact \nlattice parameter a 0 was determined using least square  fit method from the plot of lattice \nparameter ‘a’ of each peak versus  F() [figure not shown].  \nTheoretical calculation of lattice parameter can also be done  using the following equation  \n )] (3 ) (\n338\n0 0 Rr Rr aB A th  \n, where R 0 is the radius of the oxy gen ion (1.32 Å) [ 3] and r A \nand rB are the ionic radii of the tetrahedral (A -site) and octahedral (B -site) sites, respectively  \n[25]. The values of r A and r B can be calculated from the cation distribution of the system and be \nrepresented by \n20 30 40 50 60 70x=0.30\nx=0.20\nx=0.15\nx=0.10\nx=0.05\n  Intensity (a. u. )\n2 (deg.)x=0.00(111) (220)(311)\n(222) (400) (422) (511)(440) \n \n) ( ) ( ) (4 2 3      Snr C Cdr C Fer CrASn AZn AFe Aand\n ) ( ) ( ) (21 4 3 2      SnrC FerC NirC rBSn BFe BNi B\n [26, 27]. \nThe information  of cation distribution can be used to know  about the magnetic behavior of ferrite  \nsample . The materials with desired properties for practical application can be developed with the \nhelp of cation dis tribution [28]. The cation distribution is assumed  based on the hypothesis that \nSn has a tendency to occupy tetrahedral (A) site at lower concentration , whereas  it occup ies the \noctahedral site at higher concentration . The cation  distribution  of A and B si tes for each \nsubstitution  level (Sn content) is presented in Table 1. The ionic radii for Fe, Ni, Zn and Sn are \n0.65, 0.6 9, 0.75 and 0.69  Å, respectively.  \nThe effect  of Sn substitution  on the lattice constant , aexpt is shown  in Fig. 2  (a). It is found  \nthat the lattice constant initially decreases  up to x = 0.1 and  there after it increases at x = 0.15, \nagain it decreases up to x = 0.3 and finally increases for x > 0.3. It indicates  that the variation  of \na with x does not  obey the Vegard’s  law [ 29]. Our experi mental results follow nonlinear trend \nwith x which is consistent with the reported observation for Sn substituted NiFe 2O4 [24]. The \nvariation  of theoretical  lattice constant with Sn content is also shown in Fig. 2 (a). The similar \ntrend for both experiment al and calculated lattice constant is observed. The lattice constant of all \nthe doped composition is less than that of the parent one. A decreasing trend  in lattice constant \nwith an increase in the content of Sn can be attributed to the ionic size differen ces since the unit \ncell has to contract when substituted by ions with smaller size. The ionic radius of the Sn4+and \nZn2+is 0.69 and 0.75Å, respectively.  The partial replacement of Zn2+ by Sn4+ might  be expected \nto cause shrinkage of the unit cell. It can b e noted that the ionic radii of Sn and Ni is same \n(0.69Å), hence the substitution of Sn for Ni does not affect the lattice constant  value .  \n \n \n  \n     \n \n \n \n \n \n \n \n \nFig. 2 . (a) The experimental and theoretical lattice constant s; (b) the average grain size  as a \nfunction of Sn concentration  (x = 0.0, 0.05, 0.1 , 0.15, 0.2  and 0.3)  of NZSFO ferrites . \n \nThe X -ray density (ρx-ray), bulk density (ρb) and porosity (P) of the NZSFO ferrites are \npresented  in Table 1. Normally the ρb of the same composition is smaller than the  ρx-ray. This can \nbe explained by the existence of pores within the samples which are developing during the \nsintering process and depend on the sintering temperatures, conditions and time. The ρb of doped \nsample (NZSFO) is less than that of the parent (NZF O). The porosity of the NZSFO increases \nalmost linearly with Sn doping concentration and relatively higher values are observed. The \nporosity in the samples is strongly dependent on the amount of applied pressure during sample \npreparation . In the present ca se, the applied pressure is  10 kN/cm2 (1 ton/cm2).  \n \n3.2 Microstructure study   \nFig. 3  (a-g) shows the SEM micrographs o f Sn substituted Ni -Zn ferrite taken at room \ntemperature. Clear grains and grain boundaries are evident from the micrographs. SEM \nmicrog raphs reveal the polycrystalline nature of microstructures with grains of different shapes \nand size. The linear intercept technique  has been used to calculate the average grain size  \n0.0 0.1 0.2 0.3102030\n   \n Grain size (nm)\nSn concentration, x(b)\n0.0 0.1 0.2 0.38.368.408.44\n ath\n  Lattice Constant  (ﾅ)\nSn contcentration aexpt (a) \n Table 1   \nVariation s of lattice parameter, X -ray density, bulk density, average grain size, porosity and  activation energy of (NZSFO).  \nSn \ncontent, \nx Chemical formula  A site  B site  rA \n(Å) rB \n(Å) ath \n(Å) aexp \n(Å) ρx-ray \n(gm/cc)  ρb \ndB \n(gm/cc)  Dg \n(m) P \n(%) Ea \n(eV) \n0.0 Ni0.6Zn0.4Fe2O4 FeZn 0.4 FeNi 0.6 0.95 0.532  8.43341  8.39311  5.32 4.28 07.8 19.6 0.19 \n0.05 Ni.575Zn.375Sn.05Fe2O4 FeZn 0.375Sn0.025 [FeNi 0.575Sn0.025]O42- 0.948  0.532  8.4311  8.38996  5.41 3.73 10.1 31.0 0.119  \n0.1 Ni.55Zn.35Sn.1Fe2O4 FeZn 0.35Sn0.03 [FeNi 0.55Sn0.07]O42- 0.933  0.538  8.42595  8.37546  5.52 3.85 18.8 30.2 0.116  \n0.15 Ni.525Zn.325Sn.15Fe2O4 FeZn 0.325Sn0.035 [FeNi 0.525Sn0.0115]O42\n- 0.917  0.545  8.42079  8.38137  5.59 4.10 21.0 26.6 0.1023  \n0.2 Ni.5Zn.3Sn.2Fe2O4 FeZn 0.3Sn0.04 [FeNi 0.5Sn0.016]O42- 0.902  0.552  8.41563  8.37665  5.68 3.80 30.1 33.1 0.099  \n0.3 Ni.45Zn.25Sn.3Fe2O4 FeZn 0.25Sn0.05 [FeNi 0.45Sn0.25]O42- 0.872  0.566  8.40532  8.34531  5.91 3.87 34.8 34.5 0.11  \n  \n \n \n \n \n \n \n \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig. 3. SEM micrographs of  the NZSFO ferrite for (a) x = 0.0, (b) x = 0.05, (c) x = 0.1, (d)  x = \n0.15, (e) x = 0.2 , and (f) x = 0.3.  \n \n \n(g) (c) (d) \n(e) (f) \n \n(a)  \n \n(b)   \n (grain diameter) and values are given in Table 1 for different Sn concentration  [30]. Micrographs \nshow that the grains are almost homogenously distributed  throughout the sample surface.  \nIt is seen from the Fig. 2  (b) that the grain size increases with increasing Sn content.  Some \noxides , like SnO 2, could bring down the melting point. So for the same sintering temeprature , \nprese nce of Sn helps to sinter better or it is equivalent to raising the sintering temperature  for the \nferrite. As we know that the grain size is increased with increasing sintering temperature. As a \nresult  enhancement of grain  might be  expected.  \n \n3.3. Electric al properties  \n3.3.1 . DC resistivity  \nDC resistivity of the NZSFO samples was measured by two probe method and is plotted  \nas a function of temperature in Fig. 4  (a). It is observed that the resistivity decreases \nexponentially with increasing temperature indi cating semiconductor behavior of the prepared \nferrites. It is also found that the resistivity decreases with increasing Sn contents x which can be \nexplained as a consequence of microstructural and structural modification owing  to the change  in \ncomposition.  It is observed from the SEM micrographs that the grain size increases with \nincreasing Sn concentration . As a  result the number of grains and the grain boundaries \ndecreases.  The insulating behavior of grain boundaries may be attributed to the bulk of the \nresistivity in ferrite  [31]. The grain size increases faster than the porosity in NZSFO with the \nincrease of Sn contents.  The average grain size for x = 0.0 (NZFO) is found to be around 4.2 -7.8 \nμm, while for the NZSFO ferrite  the range is 10-34 μm. Though  the porosity cause s an increase \nin resistivity but the increase in grain size results in  a decrease in resistivity . The combine d effect \nof the two events might decrease the resisitivty of prepared ferrites.   In addition, another reason \nis that Sn simultan eously substituted Zn ions (prefer tetrahedral A  site) and Ni ions (prefer  \n octahedral B site ) [32], this will lead to the migration of Fe3+ and Fe2+ (which is responsible for \nelectric conduction  in ferrite) a nd the fluctuation of valence  states for tin as Sn2+ and Sn4+ \nincreases the electronic exchange resulting the resistivity decreases. The reduction of resistivity \nmight be a result of the combined effect.   \nThe DC electrical resistivity as a function temperature of the samples can be presented by \nthe Arr henius type equation: \n , where ρ and ρ 0 are resistivity of samples at \nany temperature and room temperature , respectively. The parameter Ea is the activation energy; k \nis the Boltzman n constant (= 8.62×10-5 eV) and T is the absolute temperature. The activation \nenergy in the ferro magnetic region of the sample was calculated f rom the plot of Fig. 4 (b)  using \nthe relation  \n  [33] and presented in Table 1.  \n \n \n \n \n \n \n \n \n \n \nFig. 4. (a) Variation of resistivity as a function of temperature and (b) log  vs. 1000/T graph for \ndiffer ent Sn concentration.    \nThe value of E a is found to be decreased with increasing Sn content which confirms the \nelectronic character of the conduction process.  The value of activation energy is higher for the \nsample with high electrical resistivity. Our cal culated values are consistent with this conclusion \n1.5 2.0 2.5 3.01234\n  log \n1000/T x=0.0 0\n x=0.05\n x=0.1 0\n x=0.15\n x=0.2 0\n x=0.3 0(b)\n1 2 3 405101520\n   (-cm)\n(C  102) x=0.0 0\n x=0.05\n x=0.1 0\n x=0.15\n x=0.2 0\n x=0.3 0(a) \n except for x = 0.3 [34]. The c onduction process due to electron exchange between Fe3+ and Fe2+ \nmay be accelerated with the increase of  Sn content.  \n \n3.3.2 . Dielectric relaxation properties   \nThe dielectric p ermittivity ( ) [ =CL/0A, where, C is the capacitance, L is the thickness, A is \nthe cross -sectional area of the flat surface of the pellet and ε 0 is the constant of permittivity for \nfree space]  and tan of the NZSFO ceramics for ( x = 0.0, 0.05, 0.1, 0.15, 0.2 and 0.3)  as a \nfunction of frequency  are illustrated in Fig. 5. At lower frequency t he value of  is much  higher \nwhile it shows very small value at high frequency.  It is also observed that the  shows fast \ndecreasing trend with increasing frequency at  lower  frequencies, whereas  it decreases slowly at \nhigher frequencies  even  becomes  almost zero and independent  of frequency. This can be \nelucidated  by the Koop’s phenomenological theory  based on the Maxwell -Wagner model [ 35-\n37] considering  inhomogeneous double layer dielectric structure. The Koop’s theory assumes \nthat the ferrites  are composed of well conducting grains separated by a thin layer of poorly \nconducting grain boundaries. The grains with high conductivity are form ed during the ferrite \npreparation.  These grains are separated by poorly conducting grain boundaries. These  grain \nboundaries could be formed during the sintering process due to the superficial  reduction or \noxidation of crystallites in the porous materials as a result of their direct  contact with the firing \natmosphere [ 38]. The poorly conducting grain boundaries ha ve been  found to be effective at \nlower frequencies while ferrite fairly conducting grains is effective at high frequencies [ 39]. \nTherefore, the values of ε ´ are found to be higher at lower frequencies and with increasing \nfrequency it decrease s.  \n It is found  that the dielectric constant of Sn substituted  NZSFO ferrite is higher than that \nof NZFO . The observed variation in the dielectric constant  with Sn concentration could be \nexplained  on the basis of local displacement of charge carriers  in presence of exter nal electric \nfield and octahedral  (B) site occupancy of Sn ions.  In NZSFO ferrite  system, two probable \nconduction mechanisms, viz. electron hopping between Fe3+ and Fe2+ and hole hopping between \nNi3+ and Ni2+ ions might be operative. Ferrite system contain ing Ni when sintered and cooled in \nair, a considerable amount of oxygen is absorbed, giving rise to the formation of Ni3+ ions. In \noxygen rich region, conduction takes place through Ni2+ ↔ Ni3+ and in  oxygen deficient \nregions, conduction takes place throu gh electron hopping between Fe3+ ↔ Fe2+. Tin cations (Sn2+ \nand Sn4+) have greater tendency to occupy the octahedral sites in comparison to tetrahedral sites \n[40].  Since  Sn is replacing nickel at B site (w ith the increase of Sn concentrations ), a large \nnumb er of Fe3+ ions are expected to present in B  site and there is a possibility of electron \nexchange between Fe2+ ↔ Fe3+ due to Zn volatilization.  This can also be attributed from the \nfluctuation of valence states of Sn2+ and Sn4+. Moreover, microstructure ha s great influence in \ndielectric constant. The dielectric constant of ferrite generally increases  with increasing grain \nsizes. Large grain size ha s noticeable difference  between grain and grain boundaries resistances \nwhich enhances polarization and hence di electric constant [4 1]. \nFrequency dependent loss factor (tan , is defined as /) for different Sn  concentration \nof NZSFO is shown in Fig. 5  (b). The curve s show the dielectric relaxation peaks at a particular \nfrequency [42]. The dielectric relaxation pe aks appear when the externally applied AC electric \nfield becomes equal to that of the jumping frequency of localized electric charge carrier [43]. \nThe unusual behavior of the dielectric in ferrites could be successfully explained by the Rezlescu \nmodel whic h states that the collective contribution of both types of electric charge carriers \n(electron and hole) to the dielectric polarization is the main source for that type of dielectric  \n relaxation  [44]. In ferrites, the electrical conduction arises due to the electron exchange between \nFe2+ and Fe3+ and hole transfer between Ni3+ and Ni2+ at the octahedral (B) sites which is similar \nto that of dielectric polarization in ferrites [44 , 45]. The ions of Fe and Ni are formed by the \nfollowing mechanism:  Ni2+ + Fe3+ ↔ Ni3+ + Fe2+ and Fe3+ ↔ Fe2+ + e−.   \n  \n \n  \n \n \n \n \n \n \n \nFig. 5. Frequency dependence of (a) dielectric constants and (b) dielectric loss tangent for \ndifferent Sn concentration. [Inset : formation of peaks ]. \n \n3.3.3 . Electric modulus  \nBy the study of complex diele ctric modulus t he information  about  the electrical response \nof the materials can be understood.  It also gives information  on the nature  of polycrystalline  \nsamples (homogenous or  inhomogeneous) . The electric modulus provides ideas  about the \nelectrical relax ation process  of a conducting  material  [46]. In order to reconfirm the relaxation \nprocess in the sample the real  and imaginary parts of the electric modulus are calculated using \nthe relations  \n \n \n1021031041051061071080123456\n  tan(102)\nFrequency, f (Hz) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30(b)\n104105106107048\n  tan\n f (Hz) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30\n102103104105106107108012345\n  (109)\nFrequency, f (Hz) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30(a) \n \n \nIt is observed that the value of M´(ω) is very low (approaching zero) in the low frequency region \nand continuously increasing with the rise in  frequency by showing a tendency to saturate at \nmaximum asymptotic value (i.e., M ∞ =1/e ∞) (Fig. 6), which indicates  the short range mobility of \nthe charge carrier  conduction process in the samples [ 47]. \nThe variation of M´´(ω) as a function of frequency for  different Sn concentration is \ncharacterized by  a clearly resolved peak  in the pattern. Significant asymmetry in the peak with \ntheir positions lyin g in the dispersion region of M´(ω) and M ´´(ω) versus frequency pattern  is \nobserved . The low frequency side of the M´´(ω) peak determines the range in which charge \ncarriers can move over long distances i.e., successful hopping of charge carriers is possibl e. The \nhigh frequency side of the M´´(ω) peak determines the range in which the charge carriers are \nspatially confined to their potential wells and being mobile over short distances.  Thus,  the peak \nfrequency is indicative  of transition from long range to s hort range mobility with increase in \nfrequency.  The peak frequency shifts towards higher value with increasing Sn contents. The \ncharacteristic frequency at which M´´(ω) is maximum ( M´´ max) corresponds to relaxation \nfrequency and is used for the evaluation of relaxation time, \n . The dielectric \nrelaxation time ( ) is found to be 8 ns and 159 ns for x= 0.0 and 0.05 and 80 ns for 0.05< x<0.3.  \n \n \n  \n \n \n \n \n \n10210310410510610710801234\n  (10-3)\nFrequency, f (Hz) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30(a)\n1021031041051061071080246\n10210310410510610706121824\n \n Frequency, f (Hz) M (10-5) x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30\nFrequency, f (Hz)M (10-3)\n   \n  x=0.00 (b) \n  Fig. 6.  Variation of (a) real and (b) imaginary part of electric modulus of NZSFO.  \n3.3.4. Impedance spectroscopy  \nA complete perception  of the electrical properties of the electro -ceramic materials such as \nimpedance of electrodes, grain and grain boundari es can be understood  by the complex \nimpedance spectrum technique  (Cole -Cole plot  or Nyquist plot). A Cole -Cole plot typically \nconsists  of two successive semicircles: first semicircle is due to the contribution of the grain \nboundary at low frequency and second is due to the grain or bulk properties at high frequency of \nthe materials.  \nFig. 7  (a) shows t he variation of real part of impedance as a function of  frequency for different \ndoping concentration of NZSFO . The pattern  of variation of Z´  shows dispersion in the low \nfrequency region followed  by a small plateau and, finally, all the curves c oalesce. This behavior \nindicates an increase in conduction with doping and frequency. At the higher frequencies, the \nimpedance (Z´) curves are merged for the samples ( x = 0.0 – 0.3) shows a possible  release of \nspace charge results the space charge polariza tion is reduced.  \nFig. 7 (b)  illustrates the frequency response of the imaginary  part of impedance for the \nNZSFO. It can be seen that the maxima value of Z  shifts towards higher frequency side for up \nto x= 0.1 while it shifts slightly lower frequency for  further increasing Sn up to x = 0.2.  \nFurthermore , at x= 0, two peaks are observed , which represent the combined contribution of the \ngrain and grain boundary.  \n \n \n \n \n \n \n1021031041051061071080246\n  Z (103)\nFrequency, f (Hz) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30(a)\n1021031041051061071080.00.51.01.52.0\n  \nFrequency, f (Hz)Z (103) \n  x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30(b) \n  \nFig. 7. Variation of (a) real and  (b) imaginary part of complex impedance of NZSFO.  \n \nThe complex impedance spectra ( Cole -Cole plot ) of the sample  measured for different Sn \nconcentration are shown in  Fig. 8(a). The Cole -Cole plot typically  show s two partially \noverlapping semicircular arcs at low temperatures  with center lying slightly below th e real axis \nsuggesting the  departure from ideal Debye type of relaxation process . Two very clear \nsemicircular arcs have been observed  for x = 0.0 for NZFO , whereas only one  semicircular arc is \nobserved for NZSFO (x = 0. 05, 0.1, 0.15, 0.2 and 0.3). The pres ence of one of the semicircular \narcs is diminished  with the introduction of Sn concentration. The observed two overlapping \nsemicircular arcs for pure NZFO are due to the contribution of the grain  (bulk) and grain \nboundary  to electrical properties of the ma terial [5].  The contribution of grains is dominant in the \nNZSFO samples leading to a single semicircular arc. It can be understood that grain size \n(diameter) increases with increasing Sn contents in the NZSFO [shown in Fig. 2 (b)]  which \nmeans grain boundar y decreases . The contribution of grain boundary is also dec reased  results \none semicircle in the NZSFO samples. Fig. 8 (b) represents the RC equivalent circuit for single \nsemicircle for the NZSFO samples.   \n \n \n \n \n \n(b) \n \nFig. 8. (a) Cole -Cole plot of the NZSFO (b) equivalent model circuit for single semicircle Cole -\nCole plot.  \n0 1 2 3 4 5 6 70.00.51.01.52.0 \n Z(103)\nZ(103) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.3 0(a)Rg \nCg  \n 4. Conclusions  \nThe NZSFO (x =  0.0, 0.05, 0.1, 0.15, 0.2  and 0.3) ferrites , sintered at 1300 °C , have been \nsynthesized and the structural and electrical properties  have been  studied . The prese nce of Sn \nions has a remarkable influence  on the properties of Ni -Zn ferrites. The lattice constant is found \nto be decrease d where as enhancement of grain size is found in Sn substituted Ni -Zn ferrites .  A \ndecrease in resistivity , i.e. enhancement of conduc tivity and dielectrics constant , is also notic ed \nfor NZSFO (x = 0 .05, 0.1, 0.15, 0.2  and 0.3).  The unusual behavior of the dielectric in ferrites \ncould be successfully explained by the Rezlescu model.  Irregular long range and non -Debye  type \ndielectric rela xation is observed in the NZSFO.  The complex impedance spectra show principal \ncontribution of grain resistance  for the NZSFO, confirmed by the classical Cole -Cole  complex \nimpedance spectra. Long spin dielectric relaxation times in several nano  second range s have \nbeen observed in the NZSFO . This long spin relaxation time makes NZSFO as one of the \npromising candidates for future memory materials and spintronics device applications.  \n \nAcknowledgment  \n \nThe authors are grateful to the Directorate of Research and  Extension, CUET for arranging the  \nfinancial  support for this work .  \n \n \n \n \n \n \n \n \n  \n References  \n[1] Q. Chen, P. Du, W. Huang, L. Jin, W. Weng, G. Han, Appl. Phys. Lett. 90 (2007) 132907.  \n[2] M. Sugimoto, Ceram. J. Am. Soc. 82 (2) (1999) 269.  \n[3] J. Smit, H.P.G. Wijn, Ferrites (1959) 136.  \n[4] W. Eerenstein, N.D. Mathur, J.F. Scott, Nature 442 (2006)759.  \nM.A. Ali, M.N.I. Khan, F. -U.-Z. Chowdhury, S. Akhter , M.M. Uddin , J. Sci. Res. 7 (2015)  \n65. \n[5] D.C. Khan, M. Misra, A.R. Das,  J. Appl. Phys. 53 (1982) 2722 . \n[6] A.R.  Das, V. S. Ananthan, D.C. Khan, J. Appl. Phys. 57 (1985) 4189 . \n[7] D.C. Khan, M. Misra, Bull. Mater. Sci.  7(1985) 253 . \n[8] D.C. Khan, R .C. Srivastava, A .R. Das, J. Phys. :Condens. Matter 4 (1992) 1379.  \n[9] P.K. Maskar, S.V. Kakatkar, R.S. Patil, V.A. Jadhav, N.D. Chaud hari, A.M. Sankpal, S.R. \nSawant, Mater. Chem. Phys. 41 (1995) 156157.  \n[10] M. Pal, P. Brahma, D. Chakravorty, J. Magn. Magn. Mater. 152 (1996) 370.  \n[11] O.G. Mundada, K.M. Jadhav, G.K. Bichile, J.  Mater. Sci. Lett. 16 (1997) 432.  \n[12] B.P. Rao, K. H. Rao, K. Trinadh , O.F. Caltun , J. Optoelectr. Adv. Mater. 6 (2004) 951.  \n[13] K. Sun, Z. Lan, Z. Yu, L. Li, J. Huang, Japanese J. Appl. Phys. 47 (2008) 7871.  \n[14] A. Kumar, Annveer, M. Arora, M.S. Yadav, R.P. Pant, Phys. Proc. 9 (2010) 20 . \n[15] S. Hua, Z.  Huai -wu, T. Xiao -li, J. Yu -lan, Trans . Nonferrous Met. Soc. China 21  (2011) \n109. \n[16] M. Kaiser, Physica B 407 (2012) 606.  \n[17] B. Kaur, M. Arora, A. Shankar, A.K. Srivastava R.P. Pant, Adv. Mat. Lett.,  3 (2012) 399.  \n[18] M. Hashim, Alimuddin, S.  Kumar, S. Ali, B.H. Koo, H. Chung, R . Kumar, J. Alloy. Comp. \n511 (2012) 107.  \n[19] A. Mandal,  D. Ghosh, A. Malas, P. Pal, C. K. Das , J. Engg. Art. ID 391083 (2013) 1.  \n[20] V.A. Bokav, G. V. Novikov, Y. G. Saksonov, V.T. Trukhtanov, S.T. Yuschchuk, Sov. Phys. \nSolid S tate 16 (1975) 2364.  \n[21] C.C. Homes, T. Vogt, S.M. Shapiro, S. Wakimo to, A.P. Ramirez, Science 293 (2001) 673.  \n[22] C.C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, M. A. Subramanian, A.P. Ramirez, \nPhys. Rev. B 67  (2003) 092106.  \n[23] S. Balaji, R. K. Selvan, L.J . Berchmans, S. Angappan, K. Subramanian, C.O. Augustin, \nMater. Sci. Eng. B  119 (2005) 119.  \n[24] S.A. Mazen, M.H. Abdallah, R. I. Nakhla, H. M. Zaki, F. Metaw, Mater. Chem. Phys., 34 \n(1993) 35.  \n[25] M. Panatage, S.E. Shirsath, B.G. Toksha, S. Jadhab, S.J. Sukla, K.M. Jadhab, Appl. Phys. \nA 95 (2009) 429.  \n[26] A. Globus, H. Pascard, V. Cagan, J. Phys. Colloques, 38 (1977) C1 -163-C1-168.  \n[27] M.A. Hakim, S.K. Nath, S.S. Sikder, K.H. Maria, J. Phys. Chem. Solids, 74 (2013) 1316.  \n[28] L. Vegard, Phys. Astro. 5 (1921) 17.  \n[29] A.K. M. Akther Hossain, “Investigation of colossal magnetoresistance in bulk and thick \nfilm magnetites,” Ph. D. Thesis, Imperial College, London, (1998).  \n[30] A. Verma, R. Chatterjee, J. Magn. Magn. Mater. 306 (2006) 313.  \n[31] M.E. McHenry, D.E. Laughlin, Acta Mater. 48 (2000) 223.  \n[32] S.P. Chaudhuri, S.K. Patra, A.K. Chakraborty, J . Euro . Ceram . Soc. 19 (1999) 2941.  \n[33] Z.Y. Li, B.G. Liu, K.C. Zhou, D. Zhang , L. Zhang, Mater. Res. Bull. 45 (2010) 1668.  \n[34] Z. Yue, J. Zhou, L. Li, X. Wang, Z. Gui, Mater. Sci. Engg. 86 (2001) 64.   \n [35] K.W. Wagner, Analen der. Physik., 345 (1913) 817.  \n[36] J.C. Maxwell,  A Treatise on Electrici ty and Magnetism. Clarendon Press, Oxford, (1982).  \n[37] P. Reddy, T. Rao, J. Less -Common Met. 86 (1982) 255.  \n[38] B. Kumar, G. Srivastava, J. Appl. Phys. 75 (1994) 6115.  \n[39] S. Baijal, C. Prakash, P. Kishan, K.K. Laroia, J Phys C 17 (19 84) 5993.  \n[40] A. Sutka, K. A. Gross, G.  Mezinskis, G. Bebris, M. Knite, Phys. Scr. 83 (2011) 025601.  \n[41] C.G. Koops, Phys. Rev. 83 (1951) 121.  \n[42] V.R. Murthy , J. Sobnandari, Phys. Stat. Sol. (a) 36 (1976) K133.  \n[43] N. Rezlescu , E. Rezlescu, Phys. Stat. Sol. (a) 23 (1974) 575.  \n[44] L.G.V. Uitert, J. Chem. Phys . 23 (1955)  1883.  \n[45] J.R. Macdonald, Impedance Spectroscopy: Emphasizing Sol id State Material and Systems, \nWiley, New  York, (1987).  \n[46] K.P. Padmasree, D.D. Kanchan, A.R. Kulkami, Solid State Ionics 177 (2006) 475.   \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n  \n Table Caption  \nTable 1  Variation s of lattice parameter, X -ray density, bulk density, average grain size, porosity \nand activation energy of (NZSFO).  \n \n \n \nFigure Captions  \nFig. 1. The  X-ray diffraction patterns of NZSFO (x = 0.0, 0.05, 0.1, 0.15, 0.2 and 0.3) ferrites \nsamples.  \n \nFig. 2.  (a) The experimental and theoretical lattice constant s; (b) the average grain size  as a \nfunction of Sn concentration  (x = 0.0, 0.05, 0.1, 0.15, 0.2 and 0.3)  of NZSFO ferrites . \n \nFig. 3.  SEM micrographs of the NZSFO ferrite for (a) x = 0.0, (b) x = 0.05, (c) x = 0.1, (d) x = \n0.15, (e) x = 0.2 , and (f) x = 0.3.  \n \n \nFig. 4.  (a) Variation of resistivity as a function of temperature and (b) log  vs. 1000/T graph for \ndifferent Sn concentration.    \n \nFig. 5. Frequency dependence of (a) dielectric constants and (b) d ielectric loss tangent for \ndifferent Sn concentration. [Inset: formation of peaks].  \n \nFig. 6. Variation of (a) real and (b) imaginary part of electric modulus of NZSFO.  \n \nFig. 7. Variation of (a) real and (b) imaginary part of complex impedance of NZSFO.  \n \nFig. 8. (a) Cole -Cole plot of the NZSFO (b) equivalent model circuit for single semicircle Cole -\nCole plot.  (g) \n(i) (g) \n(i) "    },    {        "title": "2001.09774v1.Non_exponential_magnetic_relaxation_in_magnetic_nanoparticles_for_hyperthermia.pdf",        "content": "arXiv:2001.09774v1  [physics.app-ph]  27 Jan 2020Non-exponential magnetic relaxation in magnetic nanopart icles for hyperthermia\nI. Gresits,1, 2Gy. Thur´ oczy,3O. S´ agi,2S. Kollarics,2G. Cs˝ osz,2B. G.\nM´ arkus,2N. M. Nemes,4, 5M. Garc´ ıa Hern´ andez,4,5and F. Simon2, 6\n1Department of Non-Ionizing Radiation, National Public Hea lth Center, Budapest, Hungary\n2Department of Physics, Budapest University of Technology a nd Economics and MTA-BME\nLend¨ ulet Spintronics Research Group (PROSPIN), Po. Box 91 , H-1521 Budapest, Hungary\n3Department of Non-Ionizing Radiation, National Public Hea lth Institute, Budapest, Hungary\n4GFMC, Unidad Asociada ICMM-CSIC ”Laboratorio de Heteroest ructuras con Aplicaci´ on en Espintronica”,\nDepartamento de Fisica de Materiales Universidad Complute nse de Madrid, 28040\n5Instituto de Ciencia de Materiales de Madrid, 28049 Madrid, Spain\n6Laboratory of Physics of Complex Matter, ´Ecole Polytechnique F´ ed´ erale de Lausanne, Lausanne CH-1 015, Switzerland\nMagnetic nanoparticle based hyperthermia emerged as a pote ntial tool for treating malignant tumours. The\nefficiency of the method relies on the knowledge of magnetic p roperties of the samples; in particular, knowledge\nof the frequency dependent complex magnetic susceptibilit y is vital to optimize the irradiation conditions and to\nprovide feedback for material science developments. We stu dy the frequency-dependent magnetic susceptibility\nof an aqueous ferrite suspension for the first time using non- resonant and resonant radiofrequency reflectometry.\nWe identify the optimal measurement conditions using a stan dard solenoid coil, which is capable of providing\nthe complex magnetic susceptibility up to 150 MHz. The resul t matches those obtained from a radiofrequency\nresonator for a few discrete frequencies. The agreement bet ween the two different methods validates our ap-\nproach. Surprisingly, the dynamic magnetic susceptibilit y cannot be explained by an exponential magnetic\nrelaxation behavior even when we consider a particle size-d ependent distribution of the relaxation parameter.\nPACS numbers:\nIntroduction\nNanomagnetic hyperthermia, NMH,1–13is intensively stud-\nied due to its potential in tumor treatment. The prospective\nmethod involves the delivery of ferrite nanoparticles to th e ma-\nlignant tissue and a localized heating by an external radiof re-\nquency (RF) magnetic field affects the surrounding tissue on ly.\nThe key medical factors in the success of NMH4–6,14include\nthe affinity of tumour tissue to heating and the specificity of\nthe targeted delivery.\nConcerning the physics and material science challenges, i)\nthe efficiency of the heat delivery, ii) its accurate control and\niii) its precise characterization are the most important on es.\nConcerning the latter, various solutions exists which incl udes\nmodeling the exciting RF magnetic field with some knowledge\nabout the magnetic properties of the ferrite15–19, measure-\nment of the delivered heat from calorimetry15,17,20–22, or deter-\nmining the dissipated power by monitoring the quality facto r\nchange of a resonator in which the tissue is embedded23,24.\nAll three challenges are related to the accurate knowledge\nof the frequency-dependent complex magnetic susceptibili ty,\n/tildewideχ=χ′−iχ′′, of the nanomagnetic ferrite material. The dis-\nsipated power per unit volume, Pis proportional to the value\nofχ′′at the working frequency, ω, as:P= 0.5µ0ωχ′′H2\nAC,\nwhereµ0is the vacuum permeability, HACis the AC mag-\nnetic field strength. Although measurement of /tildewideχ(ω)is a well\nadvanced field due to e.g. the extensive filter or transformer\napplications10,25–34, we are not aware of any such attempts for\nnanomagnetic particles which are candidates for hyperther -\nmia.\nKnowledge of /tildewideχ(ω)would allow to determine the optimal\nworking frequency, which is crucial to avoid interference d ue\nto undesired heating of nearby tissue e.g. by eddy currents1,3,9.\nIn addition, an accurate characterization of /tildewideχ(ω)can provide\nan important feedback to material science to improve the fer -\nrite properties. Last but not least, measurement of /tildewideχ(ω)wouldallow for a better theoretical description of the high frequ ency\nmagnetic behavior of ferrites. Most reports suggest1,3,9,35that\na single relaxation time, τ, governs the frequency dependence\nof/tildewideχ(ω). The magnetic relaxation time, τ, is given by to\nthe Brown and N´ eel processes; these two processes describe\nthe magnetic relaxation due to the motion of the nanomag-\nnetic particle and the magnetization of the nanoparticle it -\nself (while the particle is stationary). When the two pro-\ncesses are uncorrelated, the magnetic relaxation time is gi ven\nas1/τ= 1/τB+1/τN, whereτBandτNare the respective re-\nlaxation times. These two relaxation types have very differ ent\nparticle size and temperature dependence, which would allo w\nfor a control of the dissipation. Nevertheless, the major op en\nquestions remain, i) whether the single exponential descri p-\ntion is valid, and ii) what the accurate frequency dependenc e\nof the magnetic susceptibility is.\nMotivated by these open questions, we study the frequency\ndependence of /tildewideχon a commercial ferrite suspension up to\n150 MHz. We used two types of methods: a broadband non-\nresonant one with a single solenoid combined with a network\nanalyzer and a radiofrequency resonator based approach. Th e\nlatter method yields the ratio of χ′′andχ′for a few discrete\nfrequencies. The two methods give a good agreement for\nthe frequency-dependent ratio of χ′′/χ′which validates both\nmeasurement techniques. We find that the data cannot be ex-\nplained by assuming that each magnetic nanoparticle follow s\na magnetic relaxation with a single exponent even when the\nparticle size distribution is taken into account. Our work n ot\nonly presents a viable set of methods for the characterizati on\nof/tildewideχbut it provides input to the theories aimed at describing\nthe magnetic relaxation in nanomagnetic particles and also a\nfeedback for future material science developments.2\nI. THEORETICAL BACKGROUND AND METHODS\nThe physically relevant quantity in hyperthermia is the\nimaginary part of the complex magnetic susceptibility, /tildewideχ, i.e.\nχ′′as the absorbed power is proportional to it. Although,\nwe recently developed a method to directly determine the ab-\nsorbed power during hyperthermia23, a method is desired to\ndetermine the full frequency dependence of /tildewideχ. This would\nnot only lead to finding the optimal irradiation frequency du r-\ning hyperthermia but it could also provide an important feed -\nback to materials development and for the understanding of\nthe physical phenomena behind the complex susceptibility i n\nferrite suspensions.\nThe generic form of the complex magnetic susceptibility of\na material reads:\n/tildewideχ(ω) =χ′(ω)−iχ′′(ω). (1)\nLinear response theory dictates that these can be transform ed\nto one another by a Hilbert transform36,37as:\nχ′(ω) =1\nπP/integraldisplay∞\n−∞χ′′(ω′)\nω′−ωdω′, (2)\nχ′′(ω) =−1\nπP/integraldisplay∞\n−∞χ′(ω′)\nω′−ωdω′, (3)\nwherePdenotes the principal value integral.\nWe note that we use a dimensionless volume susceptibility\n(invoking SI units) throughout. If a single relaxation proc ess is\npresent (similar to dielectric relaxation or to the Drude mo del\nof conduction, which yield /tildewideǫ(ω)and/tildewideσ(ω), respectively), the\ncomplex magnetic susceptibility takes the form:\nχ′(ω) =χ01\n1+ω2τ2, (4)\nχ′′(ω) =χ0ωτ\n1+ω2τ2, (5)\nwhereχ0is the static susceptibility.\nThe corresponding χ′andχ′′pairs can be constructed\nwhen multiple relaxation times are present in the descrip-\ntion of their frequency dependence. There is a general\nconsensus1,4,8,14,17,19,38–42although experiments are yet lack-\ning, that the single relaxation time description approxima tes\nwell the frequency dependence of the magnetic nanoparticle s.\nThe frequency dependence of χ′′is though to be described by\nthe relaxation time of the nanoparticles: 1/τ= 1/τN+1/τB,\nwhere the N´ eel and Brown relaxation times are related to the\nmotion of the magnetization with respect to the particles an d\nthe motion of the particle itself, respectively.\nWe used a commercial sample (Ferrotec EMG 705, nominal\ndiameter 10 nm) which contains aqueous suspensions of sin-\ngle domain magnetite (Fe 3O4) nanoparticles. We verified the\nmagnetic properties of the sample using static SQUID mag-\nnetometry; it showed the absence of a sizable magnetic hys-\nteresis (data shown in the Supplementary Information), whi ch\nproves that the material indeed contains magnetic mono-\ndomains.A. Measurements with non-resonant circuit\nAt frequencies below ∼5−10MHz the conventional\nmethods of measuring the current-voltage characteristics can\nbe used for which several commercial solutions exist. This\nmethod could e.g. yield the inductivity change for an induct or\nin which a ferrite sample is placed. However, above these fre -\nquencies the typical circuit size starts to become comparab le\nto the electromagnetic radiation wavelength thus wave effe cts\ncannot be neglected. The arising complications can be con-\nveniently handled with measurement of the Sparameters, i.e.\nthe reflection or transmission for the device under test.\nObtaining /tildewideχ(ω)is possible by perturbing the circuit prop-\nerties of some broadband antennas or waveguides while mon-\nitoring the corresponding Sparameters43(the reflected am-\nplitude,S11, and the transmitted one, S21) with a vector net-\nwork analyzer (VNA). We used two approaches: i) a droplet\nof the ferrite suspension on a coplanar waveguide (CPW) was\nmeasured and ii) about a 100 µl suspension was placed in a\nsolenoid. It is crucial in both cases to properly obtain the n ull\nmeasurement, i.e. to obtain the perturbation of the circuit due\nto the ferrite only. For the solenoid, we found that a sam-\nple holder filled with water gives no perturbation to the cir-\ncuit parameters as expected. In contrast, the CPW parameter s\nare strongly influenced by a droplet of distilled water whose\nquantity can be hardly controlled therefore performing the null\nmeasurement was impossible and as a result, the use of the\nCPW turned out to be impractical. Additional details about\nthe VNA measurements, including details of the failure with\nthe CPW based approach, are provided in the Supplementary\nInformation.\nIn the second approach, we used a conventional solenoid\n(shown in Fig. 2) made from 1 mm thick enameled copper\nwire, its inner diameter is 6 mm and it has a length of 23 mm\nwith 23 turns. The coil is soldered onto a semi-rigid copper R F\ncable that has a male SMA connector. Fig. 2. shows the equiv-\nalent circuit which was found to well explain the reflection c o-\nefficient in the DC-150 MHz frequency range (more precisely\nfrom 100 kHz which is the lowest limit of our VNA model\nRohde & Schwarz ZNB-20). The frequency dependence of\nthe wire re ce due to the skin-effect was also taken into ac-\ncount in the analysis. The parallel capacitor arises from th e\nparasitic self capacitance of the inductor and from the smal l\ncoaxial cable section. Further details about the validatio n of\nthe equivalent circuit (i.e. our fitting procedure) are prov ided\nin the Supplementary Information.\nThe frequency dependent complex reflection coefficient, Γ\n(same asS11this case), and Zof the studied circuit are related\nby44:\nΓ =Z−Z0\nZ+Z0, (6)\nwhereZ0is the 50 Ωwave impedance of the cables and Z\nis the complex, frequency dependent impedance of the non-\nresonant circuit. It can be inverted to yield Zas:Z=Z01+Γ\n1−Γ.\nThe admittance for the empty solenoid reads:\n1\nZempty=1\nR(ω)+iωL+iωC, (7)\nThe analysis yields fixed parameters for R(ω)andC, whereas\nthe effect of the sample is a perturbation of the inductivity :3\nVNA \nC\nCR\nL\nFIG. 1: Upper panel: photograph of the solenoid used in the no n-\nresonant susceptibility measurements. Lower panel: the eq uivalent\ncircuit model including a parasitic capacitor, Cdue to the small coax-\nial cable section and the self capacitance of the inductor. Rhas a\nfrequency dependence due to the skin-effect.\nFIG. 2: Upper panel: photograph of the solenoid used in the no n-\nresonant susceptibility measurements. Lower panel: the eq uivalent\ncircuit model including a parasitic capacitor, Cdue to the small coax-\nial cable section and the self capacitance of the inductor. Rhas a\nfrequency dependence due to the skin-effect.\nL→L(1+η/tildewideχ(ω)). We introduced the dimensionless filling\nfactor parameter, η, which is proportional to the volume of the\nsample per the volume of the solenoid, albeit does not equal t o\nthis exactly due to the presence of stray magnetic fields near\nthe ends of the solenoid. This parameter, η, also describes\nthat the susceptibility can only be determined up to a linear\nscaling constant with this type of measurement. In principl e,\nthe absolute value of /tildewideχ(ω)could be determined by calibrating\nthe result by a static susceptibility measurement (e.g. wit h a\nSQUID magnetometer) and by extrapolating the dynamic sus-\nceptibility to DC. It is however not possible with our presen t\nsetup asχshows a strong frequency dependence down to our\nlowest measurement frequency of 100 kHz.\nA straightforward calculation using Eq. (7) yields that\nη/tildewideχ(ω)can be obtained from the measurement of the admit-\ntance in the presence of the sample, 1/Zsample as:\nη/tildewideχ=/parenleftBig\n1\nZsample−iωC/parenrightBig−1\n−/parenleftBig\n1\nZempty−iωC/parenrightBig−1\niωL(8)\nB. Measurements with resonant circuit\nFig. 3 shows the block diagram of the resonant circuit mea-\nsurements which is the same as in the previous studies23,24.\nThis type of measurement is based on detecting the changesSource\nLR\nCT50 ΩHybrid\njunctionDetectorCM\nResonator\nFIG. 3: Left: Block diagram of the resonant measurement meth od.\nRight: The schematics of the resonator circuit. It has 2 vari able ca-\npacitors, the tuning ( CT) is used for setting the resonant frequency\nand the matching ( CM) is for setting the impedance of the resonator\nto 50Ωat resonant frequency. Detailed description is in Ref. 23\nin the resonator parameters, resonance frequency ω0and qual-\nity factor, Q. The presence of a magnetic material induces a\nchange in these parameters43–45as:\n∆ω0\nω0+i∆/parenleftbigg1\n2Q/parenrightbigg\n=−η/tildewideχ (9)\nHerein,∆ω0and∆/parenleftBig\n1\n2Q/parenrightBig\nare changes in resonator eigenfre-\nquency and the quality factor. The signs in Eq. (9) express\nthat in the presence of a paramagnetic material, the resonan ce\nfrequency downshifts (i.e. ∆ω0<0) and that it broadens (i.e.\n∆/parenleftBig\n1\n2Q/parenrightBig\n>0) when both χ′andχ′′are positive.\nThe resonator measurement has a high sensitivity to minute\namounts of samples43however its disadvantage is that its re-\nsult is limited to the resonance frequency only. Eq. (9) is\nremarkable, as it shows that the ratio ofχ′′andχ′can be\ndirectly determined at a given ω0(we use throughout the ap-\nproximation that Qis larger than 10, thus any change to ω0\ncan be considered to the first order only). Namely:\nχ′′\nχ′=−ω0∆/parenleftBig\n1\n2Q/parenrightBig\n∆ω0=−∆HWHM\n∆ω0(10)\nwhere we used that the half width at half maximum, HWHM\nis: HWHM =ω0/2Q. The broadening of the resonator profile\nmeans that ∆HWHM is positive.\nThis expression provides additional microscopic informa-\ntion when the magnetic susceptibility can be described by a\nsingle relaxation time:\n−∆HWHM\n∆ω0=χ′′\nχ′=ω0τ (11)\nE.g. when a measurement at 50 MHz returns −∆HWHM\n∆ω0= 1,\nwe then obtain directly a relaxation time of τ= 3ns. The right\nhand side of Eq. (11) can be also rewritten as ω0τ=f0/fc,\nwhere we introduced a characteristic frequency of the parti cle\nabsorption process, i.e. where χ′′has its maximum.\nThis description has an interesting consequence: it makes\nlittle sense to use tiny nanoparticles, i.e. to push τto an exces-\nsively short value (or fcto a too high value). The net absorbed4\npower reads: P∝fχ′′and when the full expression is sub-\nstituted into it, we obtain P∝f2\nfc/parenleftbigg\n1+f2\nf2c/parenrightbigg. This function is\nroughly linear with fbelowfcand saturates above it to a con-\nstant value. This means that an optimal irradiation frequen cy\nshould be at least as large as fc.\nII. RESULTS AND DISCUSSION\n/s45/s48/s46/s48/s54/s45/s48/s46/s48/s51/s48/s46/s48/s48/s48/s46/s48/s51/s48/s46/s48/s54\n/s32/s82/s101/s97/s108\n/s32/s73/s109 /s104/s99 /s39/s40 /s119 /s41/s32/s44/s32 /s104/s99 /s39/s39/s40 /s119 /s41 /s71\n/s115/s97/s109/s112/s108/s101/s45/s71\n/s101/s109/s112/s116/s121\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48/s48/s46/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51\n/s32/s104/s99 /s39/s40 /s119 /s41\n/s32/s104/s99 /s39/s39/s40 /s119 /s41\n/s70/s114/s101/s113/s117/s101/s110/s99/s121 /s32/s40/s77/s72/s122/s41\nFIG. 4: The reflection coefficient for the solenoid with the sa mple\ninside, relative to the empty solenoid (upper panel). The re al and\nimaginary parts of the dynamic susceptibility as obtained f rom the\nreflection coefficients according to Eqs. (7) and (8). Note th at neither\ncomponent of /tildewideχfollows the expected Lorentzian forms.\nWe measured the reflection coefficient for the non-resonant\ncircuit,Γempty, i.e. for an empty solenoid in the 100 kHz-\n150 MHz range. The lower frequency limit value is set by\nvector network analyzer and values higher than 150 MHz are\nthought to be impractical due to water dielectric losses and\neddy current related losses in a physiological environment1–3.\nWe also measured the corresponding reflection coefficients\nwhen the ferrite suspension sample, Γsample and only distilled\nwater was inserted into it. The presence of the water refer-\nence does not give an appreciable change to Γ(data shown\nin the Supplementary Information) as expected. The differ-\nenceΓsample−Γempty is already sizeable and is shown in Fig.\n4. The dynamic susceptibility is obtained by first determini ng\nthe empty circuit parameters (details are given in the SM) an d\nthese fixed R,LandCare used together with Eqs. (7) and (8)\nto calculate /tildewideχ(ω). The result is shown in the lower panel of\nFig. 4.\nWe note that the use of Eq. (8) eliminates Rand we have\nalso checked that the result is little sensitive to about 10 %change in the value of LandC, therefore the result is robust\nand it does not depend much on the details of the measurement\ncircuit parameters. The ratio of the two components is parti c-\nularly insensitive to the parameters: Lcancels out formally\naccording to Eq. (8) but we also verified that a 20 % change\ninCleaves the ratio unaffected.\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48/s48/s46/s48/s48/s46/s49/s48/s46/s50/s48/s46/s51\n/s70/s114/s101/s113/s117/s101/s110/s99/s121 /s32/s40/s77/s72/s122/s41/s99 /s39/s39/s47 /s99 /s39/s32/s110/s111/s110/s45/s114/s101/s115/s111/s110/s97/s110/s116\n/s32/s114/s101/s115/s111/s110/s97/s110/s116\nFIG. 5: The comparison of the ratios of χusing the non-resonant\nbroadband and the resonator based (at some discrete frequen cies) ap-\nproaches.\nFig. 5 shows the ratio of the two terms of the dynamics\nmagnetic susceptibility, χ′′(ω)/χ′(ω), as determined by the\nbroadband method and using the resonator based approach.\nThe latter data is presented for a few discrete frequencies.\nThe two kinds of data are surprisingly close to each other,\ngiven the quite different methods as these were obtained. Th is\nin fact validates both approaches and is a strong proof that\nwe are indeed capable of determining the complex magnetic\nsusceptibility of the ferrofluid sample up to a high frequenc y.\nOne expects that the signal to noise performance of the res-\nonator based approach is superior to that obtained with the\nnon-resonant method by the quality factor of the resonator46,\nwhich is about 100. In fact, the data shows just the opposite o f\nthat and the resonator based data point show a larger scatter ing\nthan the broadband approach. This indicates that the accura cy\nof the resonator method is limited by a systematic error, whi ch\nis most probably related to the inevitable retuning of the re s-\nonator and the reproducibility of the sample placement into\nthe resonator.\nThe experimentally observed dynamic susceptibility has\nimportant consequences for the practical application of hy per-\nthermia. Given that the net absorbed power: P∝fχ′′, it\nsuggests that a reasonably high frequency, f, should be used\nfor the irradiation, until other types of absorption, e.g. d ue to\neddy currents1–3, limit the operation.\nWe finally argue that the experimental observation cannot\nbe explained by an exponential magnetic relaxation either d ue\nto the rotation of magnetization (the Ne´ el relaxation) or d ue5\nto the rotation of the particle itself (the Brown relaxation ). In\nprinciple, both relaxation processes are particle size dep en-\ndent; in the nanometer particle size domain the Brown proces s\nprevails and it was calculated in Ref. 3 that for a particle di -\nameter of d= 10 nm we get τ= 300 ns (fc= 21 MHz) for\nd= 11 nm,τ= 2µs (fc= 3 MHz), and for d= 9 nm,\nτ= 50 ns (fc= 125 MHz). These frequencies would in prin-\nciple explain a significant χ′′(ω)in the1−100MHz range,\nsuch as we observe.\nHowever, a simple consideration reveals from Eqs. (4) and\n(5) that for a single exponential magnetic relaxation for ea ch\nmagnetic nanoparticle, the ratio of χ′′/χ′is astraight line as\na function of the frequency, which starts from the origin wit h\na slope depending on the distribution of the different τparam-\neters and particle sizes. Similarly, a single exponential r elax-\nation would always give a monotonously decreasing χ′(ω),\nirrespective of the particle size and τdistribution. Clearly,\nour experimental result contradicts both expectations: χ′′/χ′\nis not a straight line intersecting the origin and χ′(ω)signif-\nicantly increases rather than decreases above 20 MHz. We\ndo not have a consistent explanation for this unexpected, no n-\nexponential magnetic relaxation, which should motivate fu r-\nther experimental and theoretical efforts on ferrofluids. W e\ncan only speculate that a subtle interplay between the Ne´ el\nand Brown processes could cause this effect, whose explana-\ntion would eventually require the full solution of the equat ion\nof motion of the magnetic moment and the nanoparticles, such\nas it was attempted in Ref. 35.\nSummary\nIn summary, we studied the frequency-dependent dynamic\nmagnetic susceptibility of a commercially available ferro fluid.\nKnowledge of this quantity is important for i) determining\nthe optimal irradiation frequency in hyperthermia, ii) pro vid-\ning feedback for the material synthesis. We compare the re-\nsult of two fully independent approaches, one which is based\non measuring the broadband radiofrequency reflection from\na solenoid and the other, which is based on using radiofre-\nquency resonators. The two approaches give remarkably sim-\nilar results for the ratio of the imaginary and real parts of t he\nsusceptibility, which validates the approach. We observe a sur-\nprisingly non-exponential magnetic relaxation for the ens em-\nble of nanoparticles, which cannot be explained by the distr i-\nbution of the magnetic relaxation time in the nanoparticles .\nAcknowledgements\nThe authors are grateful to G. F¨ ul¨ op, P. Makk, and Sz.\nCsonka for the possibility of the VNA measurements and for\nthe technical assistance. Jose L. Martinez is gratefully ac -\nknowledged for the contribution to the SQUID measurements.\nSupport by the National Research, Development and Innova-\ntion Office of Hungary (NKFIH) Grant Nrs. K119442, 2017-\n1.2.1-NKP-2017-00001, and VKSZ-14-1-2015-0151 and by\nthe BME Nanonotechnology FIKP grant of EMMI (BME\nFIKP-NAT) are acknowledged. The authors also acknowledge\nthe COST CA 17115 MyWA VE action.6\n1Q. Pankhurst, J. Connolly, S. Jones, and J. Dobson, Journal o f\nPhysics D-Applied Physics 36, R167 (2003).\n2M. Kallumadil, M. Tada, T. Nakagawa, M. Abe, P. Southern, and\nQ. A. Pankhurst, Journal of Magnetism and Magnetic Material s\n321, 1509 (2009).\n3D. Ortega and Q. A. Pankhurst, in Nanoscience: Volume 1: Nanos-\ntructures through Chemistry (The Royal Society of Chemistry,\n2013), vol. 1, pp. 60–88, ISBN 978-1-84973-435-6.\n4C. S. Kumar and F. Mohammad, Advanced Drug Delivery Re-\nviews 63, 789 (2011).\n5M. Angelakeris, Biochimica et Biophysica Acta (BBA) - Gener al\nSubjects 1861 , 1642 (2017).\n6A. J. Giustini, A. A. Petryk, S. M. Cassim, J. A. Tate, I. Baker , and\nP. J. Hoopes, Nano Life 01, 17 (2010).\n7K. M. Krishnan, IEEE transactions on magnetics 46, 2523 (2010).\n8J. Beik, Z. Abed, F. S. Ghoreishi, S. Hosseini-Nami, S. Mehrz adi,\nA. Shakeri-Zadeh, and S. K. Kamrava, Journal of Controlled R e-\nlease 235, 205 (2016).\n9S. Spirou, M. Basini, A. Lascialfari, C. Sangregorio, and C. Inno-\ncenti, Nanomaterials 8, 401 (2018).\n10P. de la Presa, Y . Luengo, M. Multigner, R. Costo, M. P. Morale s,\nG. Rivero, and A. Hernando, The Journal of Physical Chemistr y\nC116, 25602 (2012).\n11C. L. Dennis, A. J. Jackson, J. A. Borchers, R. Ivkov, A. R. For e-\nman, P. J. Hoopes, R. Strawbridge, Z. Pierce, E. Goerntiz, J. W.\nLau, et al., Journal of Physics D: Applied Physics 41, 134020\n(2008).\n12E. Kita, T. Oda, T. Kayano, S. Sato, M. Minagawa, H. Yanagihar a,\nM. Kishimoto, C. Mitsumata, S. Hashimoto, K. Yamada, et al.,\nJournal of Physics D: Applied Physics 43, 474011 (2010).\n13G. Vallejo-Fernandez, O. Whear, A. G. Roca, S. Hussain, J. Ti m-\nmis, V . Patel, and K. O’Grady, 46, 312001 (2013).\n14E. A. Perigo, G. Hemery, O. Sandre, D. Ortega, E. Garaio,\nF. Plazaola, and F. J. Teran, Applied Physics Reviews 2(2015).\n15E. Garaio, J. Collantes, J. Garcia, F. Plazaola, S. Mornet, F . Couil-\nlaud, and O. Sandre, Journal of Magnetism and Magnetic Mater i-\nals368, 432 (2014).\n16E. Garaio, J. M. Collantes, F. Plazaola, J. A. Garcia, and\nI. Castellanos-Rubio, Measurement Science and Technology 25,\n115702 (2014).\n17E. Garaio, O. Sandre, J.-M. Collantes, J. A. Garcia, S. Morne t, and\nF. Plazaola, Nanotechnology 26, 015704 (2015).\n18V . Connord, B. Mehdaoui, R. P. Tan, J. Carrey, and M. Respaud,\nReview of Scientific Instruments 85, 093904 (2014).\n19J. Carrey, B. Mehdaoui, and M. Respaud, Journal of Applied\nPhysics 109, 083921 (2011).\n20S. Y . Wang, S. Huang, and D. A. Borca-Tasciuc, IEEE Transac-\ntions on Magnetics 49, 255 (2013).\n21A. Espinosa, R. Di Corato, J. Kolosnjaj-Tabi, P. Flaud, T. Pe lle-\ngrino, and C. Wilhelm, ACS Nano 10, 2436 (2016).\n22K. H. Bae, M. Park, M. J. Do, N. Lee, J. H. Ryu, G. W. Kim,\nC. Kim, T. G. Park, and T. Hyeon, ACS Nano 6, 5266 (2012).\n23I. Gresits, G. Thur´ oczy, O. S´ agi, B. Gy¨ ure-Garami, B. G. M ´ arkus,\nand F. Simon, Scientific Reports 8, 12667 (2018).\n24I. Gresits, G. Thur´ oczy, O. S´ agi, I. Homolya, G. Bagam´ ery ,\nD. Gaj´ ari, M. Babos, P. Major, B. G. M´ arkus, and F. Simon, Jo ur-\nnal of Physics D: Applied Physics 52, 375401 (2019).\n25M. H. Ahmed, A. Hossain, and S. Choudhury, Turkish Journal of\nPhysics 42(2018).\n26M. K. Ghosh, Y . Gao, H. Dozono, K. Muramatsu, W. Guan,\nJ. Yuan, C. Tian, and B. Chen, Heliyon 5, e02229 (2019).\n27V . Radoni´ c, N. Blaˇ z, and L. ˇZivanov, Acta Physica Polonica A\n117, 820 (2010).\n28D. S. Akhter, D. Paul, M. Hakim, D. Saha, B. Anjuman, and F. Is-lam, The Bangladesh Journal of Scientific Research 4, 551 (2012).\n29K. M. Chowdary and S. A. Majetich, Journal of Physics D: Ap-\nplied Physics 47, 175001 (2014).\n30H. Meuche and M. Esguerra, Journal de Physique IV Colloque 07,\nC1 (1997).\n31N. Bowler, AIP Conference Proceedings 820, 1269 (2006).\n32R. Dosoudil, E. Uˇ sak, and V . Olah, Journal of Electrical Eng ineer-\ning61, 111 (2013).\n33B. W. M. Kuipers, I. A. Bakelaar, M. Klokkenburg, and B. H. Ern ,\nReview of Scientific Instruments 79, 013901 (2008).\n34S. Berkum, J. Dee, A. Philipse, and B. H. Ern´ e, Internationa l Jour-\nnal of Molecular Sciences 14, 10162 (2013).\n35P. Ilg, Physical Review E 100, 022608 (2019).\n36H. Alloul, Introduction to the Physics of Electrons in Solids, Grad-\nuate Texts in Physics (Springer-Verlag, Berlin Heidelberg, 2011),\nISBN 978-3-642-13564-4.\n37C. P. Slichter, Principles of Magnetic Resonance (Spinger-Verlag,\nNew York, 1989), 3rd ed.\n38D. Eberbeck, N. L¨ owa, U. Steinhoff, T. Viereck, M. Schillin g, and\nL. Trahms, Biomedizinische Technik/Biomedical Engineeri ng58,\n1 (2013).\n39S. Dutz and R. Hergt, Nanotechnology 25, 452001 (2014).\n40R. Rosensweig, Journal of Magnetism and Magnetic Materials\n252, 370 (2002), proceedings of the 9th International Conferen ce\non Magnetic Fluids.\n41C. N. Obeada and I. Malaescu, Physica B: Condensed Matter 424,\n69 (2013).\n42S. Dutz and R. Hergt, International Journal of Hyperthermia 29,\n790 (2013).\n43L. Chen, C. Ong, C. Neo, V . Varadan, and V . Varadan, Microwave\nElectronics: Measurement and Materials Characterization (Wi-\nley, 2004).\n44D. M. Pozar, Microwave Engineering (John Wiley & Sons, Inc.,\n2004).\n45C. P. Poole, Electron Spin Resonance (John Wiley & Sons, New\nYork, 1983), 1983rd ed.\n46B. Gy¨ ure-Garami, B. Blum, O. S´ agi, A. Bojtor, S. Kollarics ,\nG. Cs˝ osz, B. G. M´ arkus, J. V olk, and F. Simon, Journal of Ap-\nplied Physics 126, 235702 (2019).\n47I. S. Maksymov and M. Kostylev, Physica E Low-Dimensional\nSystems and Nanostructures 69, 253 (2015).7\nAppendix A: Magnetic properties of the sample\n/s45/s49/s46/s48 /s45/s48/s46/s53 /s48/s46/s48 /s48/s46/s53 /s49/s46/s48/s45/s48/s46/s52/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50/s48/s46/s52/s109/s97/s103/s110/s101/s116/s105/s99/s32/s109/s111/s109/s101/s110/s116/s32/s40/s101/s109/s117/s41\n/s45/s48/s46/s48/s53/s48 /s45/s48/s46/s48/s50/s53 /s48/s46/s48/s48/s48 /s48/s46/s48/s50/s53 /s48/s46/s48/s53/s48/s45/s48/s46/s52/s45/s48/s46/s50/s48/s46/s48/s48/s46/s50/s48/s46/s52/s109/s97/s103/s110/s101/s116/s105/s99/s32/s109/s111/s109/s101/s110/s116/s32/s40/s101/s109/s117/s41\n/s109\n/s48/s72 /s32/s40/s84/s41/s72/s121 /s115/s116/s101/s114/s101/s115/s105/s115/s61/s32/s50/s32/s109/s84\nFIG. 6: The magnetic moment of the sample, m, versus the mag-\nnetic field strength, µ0H, curve for the ferrite particle suspension.\nThe absence of a sizeable magnetic hysteresis indicates tha t this is a\nmonodomain sample. The estimate for the maximum hysteresis value\nis about 2 mT.\nThe magnetic moment versus the magnetic field strength,\nµ0H, is shown in Fig. 6 as measured with a SQUID magne-\ntometer. Notably, the sample magnetism shows a saturation\nabove 0.1 T, however it has a very small hysteresis of about\n2 mT. Common hard, multidomain ferromagnetic materials,\nwhich saturate is small magnetic fields, usually display a si g-\nnificant hysteresis. Our observation agrees with the expect ed\nbehavior of the sample, i.e. that it consists of mono-domain\nnanoparticle, which can easily align with the external mag-\nnetic field.\nAppendix B: Details of the non-resonant susceptibility\nmeasurement\nWe discuss herein how the solenoid based broadband sus-\nceptibility measurement can be performed. We first prove tha t\nthe equivalent circuit, presented in the main text, provide s an\naccurate description. The reflectivity data is shown in Fig. 7.\nWe obtain a perfect fit (i.e. the measured and fitted curves\noverlap) when we consider the equivalent circuit in the main/s45/s49/s48/s49/s82/s101/s40 /s71 /s41\n/s32/s77/s101/s97/s115/s117/s114/s101/s100\n/s32/s77/s111/s100/s101/s108/s105/s110/s103/s44/s32 /s82 /s40/s119 /s41/s44/s32 /s76 /s44/s32 /s67\n/s32/s77/s111/s100/s101/s108/s105/s110/s103/s44/s32 /s82 /s40/s119 /s41/s44/s32 /s76\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48/s45/s49/s48/s49\n/s70/s114/s101/s113/s117/s101/s110/s99/s121 /s32/s40/s77/s72/s122/s41/s73/s109/s32/s40 /s71 /s41\nFIG. 7: The reflection coefficient, Γ, and its modelling with vari-\nous equivalent circuit assumptions. The best fit is obtained when the\nequivalent circuit containing a frequency dependent wire r esistance\n(with a small DC value) was considered in addition to an induc tor\nand a capacitor. The absence of the capacitor does not give an appro-\npriate fit (dotted red curve). We note that a constant wire res istance,\nhowever with an unphysically large value, gives also an appr opriate\nfit.\ntext with parameters RDC= 15.5(2) mΩ,L= 0.62(1)µH,\nandC= 4.65(1) pF. This fit also considered the frequency\ndependency of the coil resistance due to the skin effect, who se\nDC value is RDC= 13 mΩ. We also performed the fit without\nconsidering the skin effect, which gave an unrealistically large\nRDC= 150 mΩwhile the fit being seemingly proper. A fit\nwithout considering a capacitor does not give a proper fit (do t-\nted curve in the figure): its major limitation is that it canno t\nreproduce the zero crossing of Γ, i.e. a resonant behavior in\nthe impedance of the circuit. As a result, we conclude that th e\nequivalent circuit in the main text provides a proper descri p-\ntion of the measurement circuit and that the fitted parameter s\ncan be used to obtain the complex susceptibility of the sampl e,\nas we described in the main text.\nFig. 8. demonstrates that the presence of the sample gives\nrise to a significant change in the reflection coefficient, Γ,\nwhereas the reflection is only slightly affected by the prese nce\nof the water (maximum Γchange is about 0.2 % below 150\nMHz) and its effect is limited to frequencies above 150 MHz.\nProbably, the inevitably present stray electric fields (due to the\nparasitic capacitance of the solenoid) interact with the wa ter\ndielectric, which results in this effect. The stray electri c fields\nand the parasitic capacitance become significant at higher f re-\nquencies: then there is a significant voltage drop across the\nsolenoid inductor coil, thus its windings are no longer equi -\npotential and an electric field emerges.\nAppendix C: Details of the susceptibility detection using a CPW\nThe coplanar waveguide or CPW is a planar RF and mi-\ncrowave transmission line whose impedance is 50 Ωat a wide\nfrequency range43,44. The CPW can be thought of as a halved\ncoaxial cable which makes the otherwise buried electric and8\n/s48 /s53/s48 /s49/s48/s48 /s49/s53/s48/s45/s48/s46/s48/s54/s45/s48/s46/s48/s51/s48/s46/s48/s48/s48/s46/s48/s51/s48/s46/s48/s54/s71\n/s119/s97/s116/s101/s114/s47/s115/s97/s109/s112/s108/s101/s45/s71\n/s101/s109/s112/s116/s121\n/s70/s114/s101/s113/s117/s101/s110/s99/s121/s32/s40/s77/s72/s122/s41/s71\n/s115/s97/s109/s112/s108/s101/s45/s71\n/s101/s109/s112/s116/s121 \n/s32/s82/s101/s97/s108\n/s32/s73/s109\n/s71\n/s119/s97/s116/s101/s114/s45/s71\n/s101/s109/s112/s116/s121 \n/s32/s82/s101/s97/s108\n/s32/s73/s109\nFIG. 8: Reflection coefficients, Γ, with respect to the empty circuit.\nΓwater denotes the reflection coefficient when the solenoid is filled\nwith water in a quartz tube. Note that the sample gives rise to a signif-\nicant change in the reflection below 100 MHz, whereas the pres ence\nof water (dashed lines) only slightly changes it above this f requency.\nmagnetic fields available to study material parameters, ess en-\ntially as a small piece of an irradiating antenna43,44. However\nas we show below, the inevitable simultaneous presence of th e\nelectric and magnetic field hinders a meaningful analysis.\nS11 S21R* RS R* L* LS L* \nC* CS C* G* GS G* CPW section CPW section Sample drop\nPort 2 Port 1 \nFIG. 9: Upper panel: The equivalent circuit of a CPW section w ith\na sample on the top. LS,RS,CS, andGSare effective inductance,\nseries resistance, capacitance, and shunt conductance of t he small\nCPW section which contains the sample, respectively. L∗,R∗,C∗,\nandG∗are corresponding distributed circuit parameters which ar e\nnormalized to unit length. In an ideal waveguide R∗= 0 andG∗=\n0, and also Z0=/radicalbig\nL∗/C∗. Lower panel: Photo of CPW with a\ndroplet of the sample. Port 1 is labeled with green and Port 2 i s with\nred tape.\nWe show the U shaped CPW section use in our experiments\nalong with the equivalent circuit of the CPW in Fig. 9. As\nthis device has two ports, one can measure the frequency de-\npendent complex reflection ( S11) and transmission ( S21) co-\nefficients simultaneously with a VNA. We placed the sample\ndroplet on the top of the gap section of the CPW between the\ncentral conductor and the grounding side plate, where the RF\nmagnetic field component is the strongest. The presence ofthe sample influences all parameters for the waveguide sec-\ntion where it is placed: the inductance Ls, capacitance Cs, the\nseries resistance Rs, and the shunt inductance Gs. All 4 pa-\nrameters are extensive, i.e. these depend on the quantity of the\nsample and one can express the inductivity as Ls=L0(1+η/tildewideχ)\nwhereL0is the inductivity of the CPW section which is af-\nfected by the sample, ηis the relevant filing factor that is di-\nmensionless and /tildewideχis the complex magnetic susceptibility.\nTheSparameters for such a device read47:\nS11,sample=Rs+iωL s+Z0\n1+Z0(Gs+iωC s)−Z0\nRs+iωL s+Z0\n1+Z0(Gs+iωC s)+Z0(C1)\nand\nS21,sample=2Z0\n1+Z0(Gs+iωC)\nRs+iωL s+Z0\n1+Z0(Gs+iωC s)+Z0(C2)\nWe calibrated the system that without sample (empty case)\nso that the VNA shows 0 for S11and real 1 to S21on the\nentire frequency range. During the calibration, port 1 of th e\nVNA was connected to the CPW and we assembled and disas-\nsembled the necessary calibrating elements (OPEN, SHORT,\nMATCH) onto port 2 and the second end of the CPW. There-\nfore the VNA reference plane was this end of the CPW. The\ncalibration could be achieved down to Γ<5·10−4(not\nshown).\nMagnetic field \nElectric fieldε0εr ceramic\nFIG. 10: Cross section of a coplanar waveguide showing the el ectric\nand magnetic field. Note that magnetic field is present around the\ncentral conductor and that there is a significant electric fie ld in the\ntwo gaps between the central conductor and the neighboring g round\nplates.\nWe first measured the reflection transmission coefficient\nchange under the influence of a small distilled water droplet\nwith approximately the same size as that of the sample. We\nobserve a Γchange up to about 5 % (maximum value at 150\nMHz, data not shown) for both coefficients, which is a size-\nable value. We note that the solenoid investigation, which w e\ndiscussed in the main paper, gave a change in Γfor the influ-\nence of water of about 0.2 %. Clearly, this larger sensitivit y of\nthe measurement for water is due to the electric field which is\nsignificant for the CPW and is much smaller for the solenoid.\nIt is even more intriguing that the effect of the sample is\nprimarily to shift the real parts of both S11andS21by the same\namount even at DC, while leaving the imaginary components\nunchanged (data not shown). For our typical droplet size, su ch9\nas this shown in Fig. 9, this amount is ∆Γ≈0.04. Rewriting\nEqs. (C1) and (C2) in the zero frequency limit, yields:\nS11,sample, DC=Rs+Z0\n1+Z0Gs−Z0\nRs+Z0\n1+Z0Gs+Z0, (C3)\nS21,sample, DC=2Z0\n1+Z0Gs\nR+Z0\n1+Z0Gs+Z0. (C4)\nWe find that in the reasonable limit of Rsample/lessorsimilarZ0, the\ninfluence of Gsdominates and that the experimental finding\nimplies the presence of a significant shunt conductance due t o\nthe sample. We speculate that this may be due to the presence\nof excess OH−ions in the ferrofluid (the Ferrotec EMG 705\nhas a pH of 8-9), which conduct the electric current. Again,\nthis effect is the result of the finite electric field across th e gap\nof the CPW, where we place the sample.\nThe two effects, the presence of a significant capacitance\ndue to water and a shunt inductance due to the conductivity\nof the ferrofluid, occur simultaneously when using a CPW for\nthe measurement. In fact, the effect of these factors domina te\nthe reflection/transmission. This means that determining t he\nmagnetic susceptibility for a case when a finite electric fiel d is\npresent, proves to be impractical.\nAppendix D: Additional details on the theory of resonators\nCoil+Sample Trimmer \ncapacitors \nFIG. 11: Photograph of the radiofrequency resonator. The sa mple,\nmeasurement coil and the two trimmer capacitors are indicat ed.\nFig. 11. shows a photograph of the radiofrequency res-\nonator circuit which was used in the studies. Note the presen ce\nof the two trimmer capacitors, which act as frequency tuning\nand impedance matching elements.\nThe following equation was used in the main text to deter-\nmine the relation between resonator parameters and the mate -\nrial properties:\n∆ω0\nω0+i∆/parenleftbigg1\n2Q/parenrightbigg\n=−η/tildewideχ (D1)We note that the - sign before the imaginary term on the left\nhand side varies depending on the definition of the sign in the\ncomplex response function /tildewideχ. We use the convention of Ref.\n43 where /tildewideχ=χ′−iχ′′which results in the + sign in Eq. (D1).\nThe factor 2 in Eq. (9) may seem disturbing but it is the di-\nrect consequence of the Qfactor definition: Q=FWHM/ω0,\nwhere FWHM is the full width at half maximum of the res-\nonance curve (in angular frequency units). Thus 1/2Q=\nHWHM/ω0, where HWHM is the half width at half maximum\nof the resonance curve. We also recognize that a Lorentzian\nshaped resonator profile can be expressed as1\n(ω−ω0)2+1/τ2,\nwhereτis the time constant of the resonator and τ= 2Q/ω0.\nThis also means that HWHM = 1/τ.\nThis allows to express the above equation in a more com-\npact way by introducing the complex angular frequency of the\nresonator:\n/tildewideω=ω0+iω0\n2Q=ω0+i1\nτ. (D2)\nIt is interesting to note that the complex Lorentzian linesh ape\nprofile is proportional to 1/i/tildewideω. It then follows from Eq. (D2)\nthat Eq. (D1) can be expressed as:\n∆/tildewideω\nω0=−η/tildewideχ (D3)\nwhere∆/tildewideωis the shift (or change) of (the complex) /tildewideω.\nFig. 12 shows the changes in the reflection curves at the\nresonant method.\nFrequency (MHz)60 60.5 61 61.5 62|Γ|2\n00.20.40.60.81\nEmpty\nSample\nFIG. 12: The reflection curves at the resonant method. The shi ft of\nthe resonance frequency due to the sample (red) is clearly vi sible."    },    {        "title": "1111.1866v1.Analysis_of_the_Collective_Behavior_of_a_10_by_10_Array_of_Fe3O4_Dots_in_a_Large_Micromagnetic_Simulation.pdf",        "content": "arXiv:1111.1866v1  [cond-mat.mes-hall]  8 Nov 2011Analysis of the Collective Behavior of a 10 by 10 Array\nof Fe3O4Dots in a Large Micromagnetic Simulation\nChristine C. Dantas\nDivis˜ ao de Materiais (AMR), Instituto de Aeron´ autica e Es pa¸ co (IAE), Departamento\nde Ciˆ encia e Tecnologia Aeroespacial (DCTA), Brazil, FAX/ Tel: 55 12 3941-2333\nAbstract\nWe report a full (3D) micromagnetic simulation of a set of 100ferrite (Fe3O4)\ncylindrical dots, arranged in a 10 by 10 square (planar) array of sid e 3.27µm,\nexcited by an external in-plane magnetic field. The resulting power s pectrum\nof magnetic excitations and the dynamical magnetization field at the result-\ning resonance modes were investigated. The absorption spectrum deviates\nconsiderably from that of a single particle reference simulation, pre senting a\nmode-shifting and splitting effect. We found an inversion symmetry t hrough\nthe center of the array, in the sense that each particle and its inve rsion\ncounterpart share approximately the same magnetization mode be havior.\nMagnonic designs aiming at synchronous or coherent tunings of spin -wave\nexcitations at given spatially separated points within a regular squar e array\nmay benefit from the new effects here described.\nKeywords: spin waves; micromagnetic simulations; thin films\nEmail address: christineccd@iae.cta.br (Christine C. Dantas)\nPreprint submittedtoPhysica E: Low-dimensional Systemsa nd NanostructuresSeptember5, 20181. Introduction\nFor several decades, there has been a great interest in the stud y of the\ncollective spin excitations in magnetically ordered media, and recently the-\noretical and experimental investigations have been thoroughly co nducted\n[1, 2, 3, 4, 5]. These investigations established the prospect of con trolling\nSWsinmagnoniccrystals(similarlytothecontroloflightinphotoniccr ystals\n[6]), motivating a whole new field, currently being referred to as magn onics\n(c.f. [7] and references therein).\nInmagnoniccrystals, dipolar(magnetostatic) interactionshave a nimpor-\ntant physical role, since they couple excitation modes of individual, c losely-\nspaced particles, affecting both the static and dynamic behavior of the mag-\nnetization [8, 9, 10]. This effect results in the formation of collective m odes\nin the form of Bloch waves [11, 12, 13, 14], leading to allowed and forbid den\nmagnonic states at given frequencies, or band gaps [15, 16]. These and other\nparticular characteristics stimulated new research directions in th e study of\n“spin-waves” [17] (hereon SWs), given the possibility of designing filt ers and\nwaveguides for microwave nanotechnology applications [18, 19].\nHowever, only recently experimental and numerical investigations on the\nmodification of normal modes of magnetic excitations in periodically ar -\nranged nanomagnets have been carried out in some detail [20, 21, 2 2, 23,\n24, 25, 26, 27], given the need for advanced experimental and com putational\ncapabilities. The general theoretical formulation of magnetic phen omena at\nscales of ∼10−6−10−9m is based on the Landau-Lifshitz-Gilbert (LLG)\nequation [28, 29, 30] for the magnetization dynamics. Note that th e LLG\nequation only be solved analytically for special cases [31], hence comp uta-\n2tional micromagnetics with increasingly detailed simulations have been an\nimportant aid at understanding micromagnetic phenomena [32, 33].\nInaseriesofpapersbyKruglyaketal. [23,24,25,26], particulara ttention\nwasgiven to theinvestigation ofthemagnetizationdynamics ofsqua re arrays\nof submicron elements of different sizes under a range of bias fields. These\ninvestigations involved the use of time-resolved scanning Kerr micro scopy\nto probe the magnetic response of nanoelements, along with microm agnetic\nsimulations to aid the analysis of the resulting spectra. These works have\ngenerally shown that the positionof the modefrequencies as a func tionof the\nelement size as well as their relative absorption amplitudes present a com-\nplex dependence and follows a nonmonotonic behavior. It was also ob served\nthat the position of mode frequencies did not follow the prediction of the\nmacrospin model for an isolated element. It was inferred that a non uniform\ndistribution of the demagnetizing field could be responsible for nonun iform\nprecession within the elements of the array, adding to the complex d epen-\ndence theroleofexchange interaction. Ithas alsobeen notedtha t, asthesize\nof the element in the array is decreased, the edge regions of a given element\npresent increasingly dominant modes confined by the demagnetizing field in\nrelation to uniform modes. In addition, in studies where the orientat ion of\nthe external magnetic field was rotated in the element plane of the a rray,\nthe effective magnetic field inside a given element also presented an “e xtrin-\nsic” anisotropic contribution due to the stray field from nearby elem ents,\nas contrasted to an “intrinsic” anisotropy occurring in an isolated e lement.\nFurthermore, a dynamical configurational anisotropy was necessary to quali-\ntativelyexplainthedata. Anadditionalimportantfeature, specially observed\n3in micromagnetic simulations of arrays of nanoelements, is the splittin g of\nprecessional modes, a feature experimentally verified recently as detectable\ncollective spin wave modes extended throughout the array [27].\nHere we report a 100-particles micromagnetic simulation – to our kno wl-\nedge, the largest detailed micromagnetic calculation ever performe d at the\ngivenscaleandnumberofparticles, withacarefulobservationoft heaccuracy\nrequirements (see accuracy details in Section 2.3 of Ref. [34], which were also\nadopted here). This work is part of an ongoing project [35, 34] mot ivated\nby the theoretical investigation and design of new nanostructure d magnetic\nconfigurations with interesting SWs or magnonic band gapbehavior, suitable\nfor different applications in the microwave frequency range. We sho w that\nthe collective magnetization behavior is constrained by an inversion s ym-\nmetry through the center of the array. In particular, this opens interesting\npossibilities for applications that require spatially coordinated patte rns.\n2. Methods\nThe simulations were performed by using the freely available integrat or\nOOMMF (Object Oriented Micromagnetic Framework)[36], which was in-\nstalled and executed on a 3 GHz Intel Pentium Desktop PC, running K uru-\nminLinux. The present 100-particlessimulation turned outto bea co mputa-\ntionally demanding one (taking about 4 months for completion, consid ering\ninterruptions), and no other variation of the parameters were at tempted at\nthis time. We applied the same methodology described in our previous w orks\n[35, 34], based in the procedure given by Jung et al. [37].\nAn incident in-plane magnetic field was applied uniformly to the ferrite\n4particles, composed by a static ( dc) magnetic field ( Bdc≡µ0Hdc) of 100\nmT in the ydirection, and a varying ( ac) magnetic field ( Bac≡µ0Hac)\nof small amplitude (1 mT) in the xdirection, with the functional form:\nBac= (1−e−λt)Bac,0cos(ωt). We varied the frequency ( f=ω/(2π)) from 2\nto 9.8 GHz, in steps of 0 .2 GHz, resulting in 40 different OOMMF frequency\nruns. The time domain of the applied Bacfield was discretized in intervals\nof 0.005 ns.\nOOMMF performed the numerical integration of the LLG equation lea d-\ning to the evolution of the magnetization field of 100 ferrite particles regu-\nlarly distributed in a square, 10 by 10 array of side 3 .27µm. The particles\nwere identical cylindrical dots (each with a diameter d= 0.3µm and thick-\nnessδ= 85 nm). We adopted a small interparticle (edge-to-edge) spacing\n(s= 0.03µm≪d). The simulation was stopped at 5 ns, giving 1000 out-\nputs for each frequency run. A reference simulation of a single-pa rticle with\na diameter d= 0.3µm was also conducted, with the same global parameters\nof the 100-particles simulation. Table 1 lists the parameters used to set up\nthe OOMMF integrator in both cases.\nThe power spectra of magnetic excitations were obtained by exclud ing\ndata from the first 2 ns of the averaged magnetization vector in th exdi-\nrection,/angbracketleft/vectorM/angbracketrightx(t≤2 ns), and taking the Fourier transform of the remaining\ntime domain data, /angbracketleft/vectorM/angbracketrightx(2< t≤5 ns). The maximum Fourier peak at\neach frequency provided the magnitude of absorption at the given frequency.\nA spline fit to the absorption data was performed in order to facilitat e the\ncomparison of the overall behavior of the curves, but individual da ta points\nwere maintained.\n53. Results\nThepowerspectraofmagneticexcitationsforthe100-particless imulation\nand single-particle simulation are shown in Fig. 1. The resonance peak in\nthe power spectrum of the single-particle simulation is clearly split into four\ndistinct peaks of lower amplitude in the 100-particles simulation, with t wo\npeaks at a lower and the other two at a higher frequency with respe ct to the\nreference fundamental mode, which is located at the gap between resonances\n2 and 3 of the 100-particles simulation.\nWe analysed the nature of the modes of interest by an inspection of the\ntime-dependent magnetization vector field configuration. Bitmaps or “snap-\nshots”ofthecorrespondingsimulationsweregenerated, selecte dattwopoints\nof theacfield cycle, namely, at the highest ( τ) and lowest ( τ+π) representa-\ntive amplitudes of the equilibrium magnetization oscillation. We subsamp led\nthex-component of themagnetization field in order to show 9 vectors pe r cell\nelement, and different pixel tonalities correspond to different value s ofMx.\nIn Fig. 1 (inset), the magnetization vector field of the one-particle simulation\naround its resonance peak is shown. This should be contrasted with those of\nFig. 2 (snapshots of the 100-particles simulation at the previously id entified\nfour peaks of interest).\nFig. 3(a) shows some zoom-out regions of the 100-particles simulat ion in\norder to allow for the identification of several types of magnetizat ion mode\nbehavior, which will be discussed in more detail in the next section. On the\nother hand, from a visual inspection of the 10 by 10 snapshots, it is possible\nto identify an inversion symmetry through the center of the array in such\na way that each particle and its inversion counterpart share appro ximately\n6the same mode behavior in the array. In other words, by setting a C artesian\ngrid on the array, where the origin of the coordinates is the center of the\narray, and where each element is centered at coordinates ( i,j), an inversion\ntransformation ( i,j)→(−i,−j) leaves the magnetization configuration of\nthe array approximately invariant. Some examples are shown in Fig. 3 (b).\nThis global symmetry should arise from dipolar couplings, but the exa ct for-\nmulation is yet not clearly understood. This effect has already been p ointed\nout in our previous work in the cases of 2 by 2 and 3 by 3 array simulatio ns\n(c.f. Fig 8 of Ref. [35] and discussions in Ref. [34]), but it was not pos sible\nat that time to extrapolate whether the effect would persist in a larg er array.\nIn order to address in a more quantitative way the magnetization dy -\nnamics distribution in the array, we computed two simple estimators, which\nnevertheless establish the relevance of the visually noted effect. T he first\nestimator is the modulus of the difference of average magnetization values\nat the points of the acfield cycle: m(i,j)≡| /angbracketleftMx/angbracketright(i,j)(τ)−/angbracketleftMx/angbracketright(i,j)(τ+π)|;\nwhere/angbracketleftMx/angbracketright(i,j)is the average magnetization of a given particle at grid coor-\ndinates (i,j). The second estimator, σ(i,j), is the modulus of the difference of\nstandard deviation values of particle magnetizations within the arra y, that\nis, the standard deviation is computed with reference to the avera ge magne-\ntization of the wholearray. Fig. 4 shows the resulting m(i,j)andσ(i,j)maps\ncomputed for the 4 modes of interest. Notice that each map pixel is labelled\nby the particle coordinate ( i,j). We discuss these maps in more detail in the\nnext section.\n74. Discussion and Conclusion\nIt is presently understood that particular features of the power spec-\ntra of magnetic excitations can be associated with the various type s of\nnodal behavior of the time-dependent magnetization field (see, e.g ., Refs.\n[21, 9, 20, 23, 24, 25, 26]). A general “spin-wave” behavior (SWB) for the\nexcitations indicates that the magnetization vectors present sma ll ampli-\ntude oscillations about a nonuniform static magnetization field. In ad dition,\nthe following subclasses of excitations can be identified [20, 34]: (i) “Quasi-\nuniform” behavior (QUB) : the movement of each magnetization vector is\nsimilar to that of its neighbors, except for the regions around the e dge of the\nparticle; and (ii) “Edge-like” behavior (EDB) : the magnetization field in the\ncentral region of the particle is almost entirely static and aligned with the\ndirection of the external dcfield; the nonuniformly distributed magnetization\nvectors present small amplitude oscillations near the edges of the p article. In\nparticular, these modes may be more affected by the dipolar coupling s from\nnearby particles.\nIn the present work, the nature of the reference absorption pe ak is basi-\ncally due to QUB, whereas the 100-particles simulation presents all t ypes of\nbehavior (as can be seen from an inspection of the zoom-out region s exem-\nplified in Fig. 3(a)). In particular, peak 1 at 3 .8 GHz is dominated by QUB,\nwith a few EDB cases specially for particles at the borders of the arr ay. Peak\n2 at 4.8 GHz shows a mixture of QUB and EDB, with a few SWB in some\nparticles at the top and bottom of the array. The number of SWB ca ses\nappears to increase in peak 3 at 6 .0 GHz and is the dominant absorption\nmechanism of peak 4 at 7 .2 GHz, specially for particles located towards the\n8center of the array. This effect is approximately the same as that o bserved\npreviously for 3 by 3 arrays (c.f. Fig. 9 of Ref. [34]).\nIn order to address in a more quantitative way the inversion symmet ry\nin the array (c.f. Fig. 2), as pointed out in the previous section, we r efer to\nthem(i,j)andσ(i,j)estimators shown in Fig. 4. It is clear that m(i,j)gives\nlarger values for larger amplitudes of the average particle magnetiz ation,\nbut also the original inversion symmetry through the center of the array of\nthe magnetization configuration should be translated approximate ly into a\nsymmetry around a central horizontal axis in a m(i,j)map. It is clear that if\nthe standard deviation distribution is similar at the two opposite amplit ude\npoints, thenamapof σ(i,j)shouldbeuniform. Thisestimatoralsogiveslarger\nvalues for particles whose behavior with respect to the whole array presents\na substantial difference at the two points of the cycle, thus furnis hing an\noverall measure of the degree of cycle “coherence”.\nThe expected central horizontal axis symmetry is indeed seen in Fig . 4\n(left column of panels), which corroborates our visual analysis. In peak 1,\nm(i,j)is larger for particles localized in the top and bottom rows of the arra y.\nIn peak 2, note the interesting regular, alternating magnetization excitations\nalong specific rows of the array (also inferred from a visual inspect ion of the\nsnapshots). Peaks 3 and 4 show higher values of m(i,j)in the central regions,\nin contrast to peak 1. The σ(i,j)estimator results (Fig. 4, right column of\npanels) show that, excluding the top and bottom rows of the array s in cases\n1, 3 and4, the array behavior is reasonably similar at the two extrem es of the\ncycle. However, case 2 shows again a pattern, where the second a nd ninth\nrows (related to particles with very low amplitudes of the average pa rticle\n9magnetization, c.f. left column of panels) have standard deviations that\nsignificantly differ at the two extremes of the cycle.\nQualitatively, the results reported in the present work, specially th e split-\nting of the resonance mode and its decreased relative amplitude, as well as\nthe spatially nonuniform behavior of the elements in the array, are c ompati-\nblewith thebehavior of thecollective excitations reportedinsimilar pr evious\nworks [23, 24, 25, 26, 27]. Particularly, in Ref. [27], for the first time the col-\nlective spin wave modes of the entire array has been experimentally d etected.\nWith the aid of a micromagnetic simulation of a 3 ×3 array, the authors ob-\nserved how the row/column elements behaved out of phase with the rest of\nthe elements of the array, qualitatively explaining the nature of the splitting\nof the precessional modes of the absorption spectrum. Our resu lts show that\nthis behavior is even more complex when considering a more extended array\nof 10×10 elements. Yet, as already mentioned, a symmetry pattern can b e\nidentified. Indeed, the inversion symmetry here noted is compatible with the\nexperimentally observed “tilt” of the modes in regions of higher amplit ude\n[27], relatively to the horizontal and vertical axes, reported in tha t work. We\nbelieve that such a “tilt” would be observed in a larger simulation for th at\nmaterial.\nIn summary, our present results and previous indications allow us to infer\nthat, for interparticle (edge-to-edge) separations at least of t he order of ∼10\nto 20% of the particle’s diameter, dipolar couplings in periodically arran ged\ncylindrical nanomagnets will cause aglobal, coherent magnetization behavior\nacross a square array distribution, with an inversion symmetry thr ough the\ncenter of the array (for in-plane magnetic excitations). The powe r spectrum\n10shows aclear four-foldresonance feature, wherein themagnetiz ationfielddis-\ntribution and dynamics show interesting patterns and trends. We h ope that\nthe effect here reported will stimulate the development of a theory that will\ngenerally describe and predict similar mode symmetries in periodic arra ys.\nOur results may be of interest for magnonic device architectures, specially\nfor applications dealing with pairwise SWs excitations of submicron fer rite\nparticles at spatially separated points in a periodic square array.\n5. Acknowledgments\nWe thank the anonymous referee for useful comments and corre ctions.\nWe acknowledge the support of Dr. Mirabel C. Rezende and FINEP/ Brazil.\n6. References\nReferences\n[1] K. Hillebrands, B. & Ounadjela, Spin Dynamics in Confined Magnetic\nStructures I, III, Berlin: Springer, 2002.\n[2] G. Gubbiotti, et al., Spin dynamics in thin nanometric elliptical Permal-\nloy dots: A Brillouin light scattering investigation as a function of dot\neccentricity, Phys. Rev. B 72 (18) (2005) 184419–184427.\n[3] R. Sellmyer, D. & Skomski, Advanced Magnetic Nanostructures, New\nYork: Springer, 2006.\n[4] S. Kronmuller, H. & Parkin, Handbook of Magnetism and Advanced\nMagnetic Materials vol 3, Chichester: Wiley, 2007.\n11[5] S. Neusser, et al., Anisotropic Propagation and Damping of Spin Wa ves\nin a Nanopatterned Antidot Lattice, Physical Review Letters 105 ( 6)\n(2010) 067208–067212.\n[6] J. D.Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Mold-\ning the Flow of Light, Princeton: Princeton Univ. Press, 1995.\n[7] V. V. Kruglyak, S. O. Demokritov, D. Grundler, Magnonics, Jour nal of\nPhysics D Applied Physics 43 (26) (2010) 264001–264015.\n[8] C. Mathieu, et al., Anisotropic magnetic coupling of permalloy micron\ndots forming a square lattice, Applied Physics Letters 70 (1997) 29 12–\n2914.\n[9] J. Jorzick, et al., Quantized spin wave modes in micron size magnetic\ndisks, Journal of Applied Physics 87 (2000) 5082–5084.\n[10] M. Bailleul, R. H¨ ollinger, C. Fermon, Microwave spectrum of squa re\nPermalloy dots: Quasisaturated state, Phys. Rev. B 73 (10) (200 6)\n104424–104438.\n[11] G. Gubbiotti, et al., Magnetostatic interaction in arrays of nano met-\nric permalloy wires: A magneto-optic kerr effect and a brillouin light\nscattering study, Phys. Rev. B 72 (22) (2005) 224413–224420.\n[12] L. Giovannini, F. Montoncello, F. Nizzoli, Effect of interdot couplin g\non spin-wave modes in nanoparticle arrays, Phys. Rev. B 75 (2) (20 07)\n024416–024423.\n12[13] Z. K. Wang, et al., Observation of frequency band gaps in a one-\ndimensional nanostructured magnonic crystal, Applied Physics Let ters\n94 (8) (2009) 083112–083115.\n[14] R. Zivieri, et al., Collective spin modes in chains of dipolarly interactin g\nrectangular magnetic dots, Phys. Rev. B 83 (5) (2011) 054431–0 54440.\n[15] S. L. Vysotskii, S. A. Nikitov, Y. A. Filimonov, Magnetostatic spin\nwaves in two-dimensional periodic structures (magnetophoton cr ystals),\nJournal of Experimental and Theoretical Physics 101 (2005) 547 –553.\n[16] G. Gubbiotti, et al., Brillouin light scattering studies of planar meta llic\nmagnonic crystals, Journal of Physics D Applied Physics 43 (26) (20 10)\n264003–264017.\n[17] G. A. Gurevich, A. G.& Melkov, Magnetization Oscillations andWav es,\nNew York: Chemical Rubber Corp., 1996.\n[18] K.Baberschke, Whyarespinwave excitationsallimportantinna noscale\nmagnetism?, Physica Status Solidi (b) 245 (2007) 174–181.\n[19] A. Khitun, M. Bao, K. L. Wang, Magnonic logic circuits, Journal o f\nPhysics D Applied Physics 43 (26) (2010) 264005–264016.\n[20] S.Jung, etal.,Ferromagneticresonanceinperiodicparticlearr ays, Phys.\nRev. B 66 (13) (2002) 132401–132405.\n[21] G.Gubbiotti, etal., Normalmodesplittingininteractingarraysof cylin-\ndrical permalloy dots, Journal of Applied Physics 99 (8) (2006) 080 000–\n080003.\n13[22] S. Tacchi, et al., Anisotropic dynamical coupling for propagating collec-\ntive modes in a two-dimensional magnonic crystal consisting of inter act-\ning squared nanodots, Phys. Rev. B 82 (2) (2010) 024401–02440 9.\n[23] V. V. Kruglyak, A. Barman, R. J. Hicken, J. R. Childress, J. A. K a-\ntine, Precessional dynamics in microarrays of nanomagnets, Jour nal of\nApplied Physics 97 (10) (2005) 10A706.\n[24] V. V. Kruglyak, A. Barman, R. J. Hicken, J. R. Childress, J. A. K a-\ntine, Picosecond magnetization dynamics in nanomagnets: Crossov er to\nnonuniform precession, Phys. Rev. B 71 (22) (2005) 220409(R).\n[25] V. V. Kruglyak, P. S. Keatley, R. J. Hicken, J. R. Childress, J. A .\nKatine, Dynamicconfigurationalanisotropyinnanomagnets, Phys . Rev.\nB 75 (2) (2007) 024407.\n[26] P. S. Keatley, V. V. Kruglyak, A. Neudert, E. A. Galaktionov, R . J.\nHicken, J. R. Childress, J. A. Katine, Time-resolved investigation of\nmagnetization dynamics of arrays of nonellipsoidal nanomagnets wit h\nnonuniform ground states, Phys. Rev. B 78 (21) (2008) 214412.\n[27] V. V. Kruglyak, P. S. Keatley, A. Neudert, R. J. Hicken, J. R. C hildress,\nJ. A. Katine, Imaging Collective Magnonic Modes in 2D Arrays of Mag-\nnetic Nanoelements, Physical Review Letters 104 (2) (2010) 0272 01.\n[28] E. Landau, L. & Lifshitz, On the theory of the dispersion of mag netic\npermeability in ferromagnetic bodies, Physik. Z. Sowjetunion 8 (193 5)\n153–160.\n14[29] T. L. Gilbert, A lagrangian formulation of the gyromagnetic equa tion\nof magnetization field, Phys. Rev. 100 (1955) 1243–1253.\n[30] W. F. Brown, Micromagnetics, Interscience Publishers, 1963.\n[31] M. d’Aquino, Nonlinear magnetization dynamics in thin-films and\nnanoparticles, Doctorate Thesis in Electrical Engineering, Univers it` a\nDegli Studi di Napoli, It´ alia, 2004.\n[32] J. Fidler, T. Schrefl, TOPICAL REVIEW: Micromagnetic modelling -\nthe current state of the art, Journal of Physics D Applied Physics 33\n(2000) 135–156.\n[33] A. Aharoni, Micromagnetics: past, present and future, Phys ica B 306\n(2001) 1–9.\n[34] C. C. Dantas, A. M. Gama, Micromagnetic simulations of spinel fe r-\nrite particles, Journal of Magnetism and Magnetic Materials 322 (20 10)\n2824–2833.\n[35] C. C. Dantas, L. A. de Andrade, Micromagnetic simulations of sm all ar-\nrays of submicron ferromagnetic particles, Physical Review B 78 (2 008)\n024441–024449.\n[36] M.Donahue, D.Porter, OMMF User’s Guide, Version 1.0, http://math.nist.gov/oommf/ ,\nInteragency Report NISTIR 6376, National Institute of Standa rds and\nTechnology, Gaithersburg, MD.\nURLhttp://math.nist.gov/oommf/\n15[37] S. Jung, J. B. Ketterson, V. Chandrasekhar, Micromagnetic calculations\nof ferromagnetic resonance in submicron ferromagnetic particles , Phys.\nRev. B 66 (13) (2002) 132405–132409.\n16Table 1: Main OOMMF parameters, fixed for all simulations.\nSimulation Parameter/Option Parameter\nSaturation magnetization [A/m] 5 .0×105\nExchange stiffness [J/m] 1 .2×10−11\nAnisotropy constant [J/m3] −1.10×104\nAnisotropy Type cubic\nFirst Anisotropy Direction (x,y,z) (1 1 1)\nSecond Anisotropy Direction (x,y,z) (1 0 0)\nDamping constant 0 .005\nGyromagnetic ratio [m/(A.s)] 2 .21×105\nParticle thickness [nm] 85 .0\nCell size [nm] 5 .0\nDemagnetization algorithm type const. in each cell\n17Fig. 1:Top panel: Power spectrum of magnetic excitations of the 100-\nparticles simulation. Bottom panel: Comparison of the former spectrum\n(diamond symbols) with that of the single-particle reference simulat ion (dot\nsymbols). Four distinct peaks in the spectrum of the 100-particles simulation\nare identified. “Snapshots” of the magnetization vector field of th e one-\nparticle simulation around the resonance peak are indicated by the a rrow.\nSnapshot to the left refers to the highest amplitude of the oscillatio n and the\nsnapshot to the right, to the lowest one.\nFig. 2: “Snapshots” of the magnetization vector field of the 100-partic les\n(10 by 10 particle array) simulation around the four peaks identified in the\nprevious figure. For each peak, the upper snapshot shows the ma gnetization\nstate of the array at the highest amplitude of the oscillation ( τ) whereas the\nsnapshot immediately below, at the lowest amplitude ( τ+π). Symmetry\naxes are shown schematically at the top left of the figure.\nFig. 3: (a) Amplified particular selections (3 by 4 sub-arrays given by\nthe solid rectangular shown inside the 10 by 10 array snapshots), a t the two\npoints of the cycle. (b) Illustration of the symmetric mode behavior : one\nexample of particle pairs is taken from each of the four peaks at τ. Grid\ncoordinates are indicated above the particles.\nFig. 4: Estimator maps ( m(i,j)andσ(i,j)distributions) for the arrays, as\nexplained in the main text. New symmetry axis is indicated.\n18Figure 1:\n19Figure 2:\n20(a)\n(b)\nFigure 3:\n21Figure 4:\n22"    },    {        "title": "1410.2068v1.Cellular_Uptake_and_Biocompatibility_of_Bismuth_Ferrite_Harmonic_Advanced_Nanoparticles.pdf",        "content": "Page 1 of 28 \n Cellular Uptake and Biocompatibility of Bismuth Ferrite Harmonic Advanced \nNanoparticles  \n \n \nDavide Staedler1, a; Solène Passemard1, a; Thibaud Magourouxb; Andrii Rogovb; Ciaran Manus \nMaguirec; Bashir M. Mohamedc; Sebastian Schwungd; Daniel Rytzd; Thomas Jüstele; \nStéphanie Hwub; Yannick Mugnierf; Ronan Le Dantecf; Yuri Volkovc,g; Sandrine Gerber -\nLemairea; Adriele Prina -Melloc,g; Luigi Bonacinab,* and Jean-Pierre Wolfb \n1These authors contributed equally to this work.  \naInstitute  of Chemical Sciences and Engineering, EPFL, Batochime, 1015, Lausanne, \nSwitzerland.  \nbGAP -Biophotonics, Université de G enève, 22 Chemin de Pinchat, 1211 Genève 4, \nSwitzerland.  \ncNanomedicine Laboratory and Molecular Imaging group, S chool of Medicine , Trinit y Centre \nfor Health Sciences, Trinity College, D8, Dublin, Ireland . \ndFEE Gmbh, Struthstrasse 2, 55743 Idar -Oberstein, Germany.  \neFachbereich Chemieingenieur wesen, Fachhochschule Münster, Stegerwaldstrasse 39, 48565 \nSteinfurt, Germany . \nfUniv. Savoie, SYMME, F-74000 Annecy, France . \ngCRANN Naughton Institute , Trinity College,  D2, Dublin, Ireland . \n* Corresponding author  \n Page 2 of 28 \n Funded by:  Partially funded by European Commission funded project NAMDIATREAM \nproject (FP7 LSP ref 246479) and CAN project (European Regional Development Fund \nthrough the Ireland Wales Programme 2007 -13 INTERREG 4A);  \nConflicts of interest:  the authors d eclare no conflict of interest.  \nAbstract  \nBismuth Ferrite (BFO) nanoparticle s (BFO -NP) display interesting optical (no nlinear \nresponse) and magnetic properties which make them amenable for bio -oriented applications  \nas intra - and extra membrane contrast  agents . Due to the relatively recent availability of this \nmaterial in well dispersed nanometric form, its biocompatibility was not known to date. In \nthis study, w e present a thorough assessment of the effects of  in vitro   exposure of human \nadenocarcinoma (A549) , lung squamous carcinoma (NCI -H520) , and acute monocytic \nleukemia (THP -1) cell lines to  uncoated and poly(ethylene glycol) -coated  BFO -NP in the \nform of cytotoxic ity, haemolytic response and biocompatibility . Our results support the \nattractiveness of the functional -BFO towards biomedical applications focused on advanced \ndiagnostic imaging .  \n \n \nKeywords  \nNanophotonic , non -linear imaging , bismuth ferrite, PEGylation,  biocompatibility.  Page 3 of 28 \n  \nBackground   \nMost of nano photonics  approaches  (quantum dots, plasmonic nanoparticles ( NP), up -\nconversion NP)  for health applications  present static  optical properties (absorption bands, \nsurface plasmon resonances) often in the UV -visible spectral region and do not fully allow for \nexploiting  the tuning capabilities of new laser sources and their latest extension s in the \ninfrared . To circumvent these limitations, a few research groups in the last years have \nintroduced a new nanotechnology approach based on inorganic nanocrystals with non -\ncentrosymmetric structures . Such  nanomaterials presen t a very efficient nonlinear response, \nand can be easily imaged by their second harmonic generation (SHG)  in multi -photon \nimaging platforms. 1-6 Such harmonic NP (HNP) do not suffer from conventional optical \nlimitations such as photob leaching and blinking  allowing long -term mon itoring of developing \ntissues 4, 7. Several HNP have been recently synthesized and tested for biological applications  \n3-5, 7. Particular care should be paid to assess the ability of these NP to reach intracellular \ntargets without causing major interferences to the  cell metabolism. In this context, this \nsubcellular targeting becomes increasingly important as key parameters for the understating of \ncomplex events in living cells 8, 9. In fact, the possibility to freely chang e detection \nwavelength can be exploited for subtle co -localization studies with organelle -specific dyes, as \nthe signal from NP can always be selectively told  adapt. However, one aspect that is not fully \nunderstood and remains uncertain is how nanomaterials interact with cellular interface s such \nas cytoskeletal membranes  since it is known that small alterations in their physicochemical \nproperties can drastically influence  the cells -NP interactions , especially the uptake \nmechanisms 9, 10. Therefore,  lead-NP-candidate identification  process based on high \nthroughput screening as decision -making process is a prerequisite for the validation of new \nSHG NP for bio-imaging applications. Here we present a study based on BiFeO 3 (bismuth Page 4 of 28 \n ferrite, abbreviated as BFO)  NP (BFO -NP), which were recently successfully introduced as \nphotodynamic tool s and imaging  probes  11. Nonetheless, such is the technological novelty of \nthis new group of materials that there is stil l a knowledge gap that requires the scientific \ncommunity attention towards the investigation of the interaction at the  cellular and subcellular \nlevel s. The opportunity of closing this gap is presented by providing the first thorough \ninvestigation  on the e ffects of BFO -NP in cell ular metabolism and uptake mechanism s. \nToxicity and biocompatibility were assessed by automated high content screening, recording \ncytotoxicity, lysosomal mass and cell permeability , in line with previously published works 12, \n13. Cellular uptake was investigated by co -localizing the NP with specific f luorophores for ce ll \nmembranes and  endosomes. Moreover, in  this paper we present  for the first time to our \nknowledge the most efficient protocol  for the coating of these H NP with poly( ethylene glycol ) \n(PEG)  derivatives to promote colloidal stability and biocompatibility in biological media, and \nto allow post -functionalization with bioactive molecules14, 15.  In this c ontext, the \nbiocompatibility, cellular uptake and intracellular localization  of free and PEG coated BFO -\nNP were compared.  \n \n \n \n \n Page 5 of 28 \n Methods  \nPreparation of a polydisperse suspension of BFO  \nThe starting  BFO suspension (lot BFO0018 , 62.5 wt % ) in ZrO 2 balls was provided by the \ncompany FEE (Germany) under a collaboration agreement . Two mL of the suspension were \ntaken off and diluted in 2 L of EtOH. The suspended nanoparticles were ultra -sonicated \novernight (O/N) and sedimented for 10 days. Fifty mL of the upper po lydisperse suspension \nwere transferr ed in a round bottom flask, 4 mL  of oleic acid was added and EtOH was \nremoved under  vacuum. The residue  was weigh ed and suspende d in EtOH to obtain  a stock \nsolution at 3.6 mg.mL-1. \nCoating of BFO -NP \nBFO -NP (solution in EtOH, 3.6 mg/mL, 583 µL) were diluted in 1 mL of a mixture of \nEtOH:toluene 1:1 and aqueous ammonia (25%, 320 µL ) was  added. The suspension was \nultra-sonicated for 30 min. Amino silane -PEG  (2) and azido silane -PEG  (1), synthetized as \ndescribed  in ref.13  (ratio 1:1, 43 µmol, 100 mg) were added and the suspension was ultra -\nsonicated at 40 °C for 16 hr.  The suspension was then concentrated under  vacuum to a small \nvolume and distributed  in plastic tubes . To each Eppendorf  was added a mixture of \ndichloromethane (DCM):EtOH:water (1:1:1 , 1 mL ) and the solutions were shake n until \nemulsion. The emulsion was broken by centrifugation (10 min, 13 000 rpm) and a DCM layer \nshowed the presence of a slight ly orange suspension, whic h corresponded to coated BFO -NP. \nThe aqueou s layer, containing t he excess of unreacted polymers , was removed. To each \nEppendorf  was added a mixture EtOH :water (1:1, 0.5 mL)  and the solutions were shaken  until \nemulsion , then centrifugated  (10 min, 13 000 rpm). The procedure  was repeated 5 times t o \nobtain pure suspension of BFO -NP in DCM. The organic solvent can be easily removed in \nvacuum  and replaced by EtOH. The BFO -NP concentration was calculated by measuring the Page 6 of 28 \n turbidity of the solutions by spectrometry at 600 nm (Synergy HT) and by comparing th e \nvalues with a standard -curve prepared using the stock solution at 3.6 mg/mL.  \nCharacteriza tion of uncoated and coated BFO -NP \nAdvanced  physic o-chemical characterization of BFO -NP was recently performed16. In this \nwork BFO -NP were characterized using a Zetasizer NanoZ (M alvern) for the measurement of \nthe dynamic light scattering (DLS) and the zeta potential.  Suspensions of uncoated or coated \nBFO -NP (20  µL) were  diluted in 1 mL of distilled water . Acetic acid ( 100 µL) was added and \nthe resulting suspension s were ultra-sonicated for 30 min and analysed . \nNanoparticles characterization in biological media  \nThe ph ysico -chemical characterization  of the NP was carried out by nanoparticle tracking \nanalysis ( NTA ). BFO -NP at 25 µg/ml were vortexed  for 5s to disperse the particles and then \ndiluted at 1 µg/mL in different solutions (0.22 µm filtered): diethylpyrocarbonate (DEPC) \nwater, Dulbecco's Modified Eagle Medium (DMEM), Ham's F -12K (Kaighn's) Medium \n(F12K) and Roswell Park Memorial Institute (R PMI) culture media, and their supplemented \nform with 10% fetal bovine serum (FBS). The dispersions were then analyzed via NTA  for \nthe physico -chemical characterization measurement of hydrodynamic radius and \npolydispersity index (PDI) at room tem perature (R T) of individual BFO -NP. NTA \nmeasurement was done using a Nanosight NS500 (Nanosight). The device consists of an \nEMCCD camera (ANDOR) mounted on a conventional optical microscope with a 20x \nobjective and LM14 viewing unit containing a 532 nm continuous wav e laser light source. \nIntroduction of each sample into the LM14 vi ewing unit was automated via an on board \nperistaltic pump with manual focus of nanoparticle following the manufacturer’s standard \noperating procedures. The NanoSight NS500 recorded six indep endent 90 second s videos \ncontaining fresh nanoparticle populations with each recording. Analysis was conducted in \nbatch mode and analysed with the NTA 2.3 software. All measurements were carried out Page 7 of 28 \n three times at physiologically relevant pH (pH = 7.4) and  means and standard deviations (SD) \nwere calculated. Quality assurance over the measurements carried out was guaranteed by the \nadoption of Quality Nano (QNano, FP7 project) standard operating procedures (SOPs), which \nhave been developed as part of large in ter laboratory comparative study focused on \nnanoparticle physico -chemical characterization17. \nCell model and culturing conditions  \nHuman lung -derived A549 and NCI -H520 cancer cell lines and human monocytic  THP -1 cell \nline are available from ATCC (American Tissue Culture Collection, Manassas, VA, USA). \nA549 were grown in DMEM medium containing 4.5 g/L glucose, 10% FBS and \npenicillin/streptomycin (PS) in a 37 ˚C incubator with 5 % CO 2 at 95 % humidity. NCI -H520 \nand THP -1 were grown in complete Roswell Park Memorial Institute (RPMI) 1640 medium \nsupplemented with 10% FCS and PS in a 37 ˚C incubator with 5 % CO 2 at 95 % humidity. \nFor differentiation into macrophages, THP -1 cells were plated at a density of 20'000  cells/cm2 \nin RPMI 1640 supplemented with 10% FBS and 100 ng/ml phorbol 12 -myristate 13 -acetate \n(PMA, Sigma -Aldrich) for 72h. Differentiated THP -1 cells adhered to the bottom of the wells.  \nFluorescent staining for cellular imaging  \nThe cells were grown for  48h or 72h for activated PMA THP -1 cells, in a 24 well plate \ncontaining one rod -shaped microscope slide (BD Falcon). After this tim e the cells were \nexposed to BFO -NP at 25 µg/mL or to vehicle (ethanol) at indicated time. For endosomes \nimaging the cell lay ers were exposed for 2h to 15 µg/mL of the fluorescent probe FM1 -43FX \n(Invitrogen). After incubation, the cells were fixed in 4% formaldehyde in PBS for 30 min, \nthen washed once in 0.1% Triton X -100 in PBS and twice in PBS, then maintained in \nformaldehyde.  For membrane staining, cells were fixed and then exposed to 0.1 µg/mL Nile \nRed (Invitrogen) in PBS for 5 min, then rinsed twice in PBS and maintained in formaldehyde. \nCell nuclei were stained with 4',6' -diamidino -2-phenylindole (DAPI).  Page 8 of 28 \n Multiphoton Laser Scanning Microscopy  \nThe cells were observed using a Nikon multiphoton inverted microscope (A1R -MP) coupled \nwith a Mai -Tai tunable Ti:sapphire oscillator from Spectra -Physics (100 fs, 80 MHz, 700 -\n1000 nm). A Plan APO 40× WI N.A. 1.25 objective was used to focus the excitation laser and \nto epi -collect the SHG signal and dye markers fluorescence. Nanoparticles and fluorescent \ndyes (FM1 -43FX and Nile Red) were excited at 790 nm and observed through tailored pairs \nof dichroic mirror s and interferometric  filters (Semrock, FF01 - 395/11 -25 for SH, FF01 -\n607/70 -25 for fluorescence). Statistics were calculated by averaging measured values from \nsamples between 40 and 170 cells per condition for cell labelling and between 8 and 100 cells \nper condition for co -localization measurements. Cell labelling was analysed by dividing the \nnumber of cells labelled by at least one nanoparticle to the total number of cells in a \nmicroscopy fi eld and expressed as % of total cells. Co -localization with endosomes was \nestimated by counting the number of nanoparticles co -localizing with the fluorescence signal \nfrom cell membrane dye FM1 -43FX using Nikon Imaging Software (NIS) and dividing it by \nthe total number of nanoparticles located inside each cell and expressed as % of all parti cles \ninternalized in each cell.  \nIn vitro dose and exposure endpoint determination  \nCytotoxicity on three -cell line models was investigated in vitro after 2 4 h and 72 h incubation \nwith BFO -NP. Following standardization of the BFO preparation protocols, all were injected \ninto 96 well plates to a final volume of 200 m L/well. A549, NCI -H520 and activated PMA \nTHP -1 cells were incubate d with 1.0, 2.5, 5.0, 7.5 or 10  µg/mL of uncoated and coated BFO -\nNP for 24 h and 72 h in a 37 ˚C incubator with 5 % CO 2 at 95 % hu midity. Experiments were \nrepeated three times, using triplicate wells each time for each formulation tested. Positive and \nnegative controls were also included into each experiment in order to quantify the extent of \ntoxicity response induced by each particl e. Three positive controls were Valinomycin (VAL, Page 9 of 28 \n Fisher Scientific) (final concentration 120 μM) to measure changes in mitochondrial \ntransmembrane potential, Tacrine (TAC, Sigma -Aldrich)  (final concentration 100 μM)  to \nmeasure changes in lysosomal mass/pH  and Quantum Dots (CdSe)  (final concentration at 1 \nμM) to measure nanoparticle -induce d uptake 12. After 24 h and 72 h incubation, cells were \nwashed in phosphate -buffered saline solution (PBS) at pH 7.4 and fixed in 3 % \nparaformaldehyde (PFA). A multiparametric cytotoxicit y assay was performed using the \nCellomics® HCS reagent HitKitTM as per manufacturer’s instructions (Thermo Fisher \nScientific Inc.). For each experiment, each plate well was scanned and acquired in a \nstereology configuration of 6 randomly selected fields. I n total, each endpoint data plot in the \nheatmaps represents the analysis of an average of 270,000 cells = 3 runs x 3 triplicates x 6 \nfields x 5000 cells (on average from t = 0 h). Images were acquired at 10 x magnification \nusing three detection channels wit h different excitation filters. These included a DAPI filter \n(channel 1), which detected blue fluorescence of the Cellomics® Hoechst 33342 probe \nindicating nuclear intensity at a wavelength of 461 nm; FITC filter (channel 2), which \ndetected green fluoresce nce of the Cellomics® cell permeability probe indicating cell \npermeability at a wavelength of 509 nm and a TRITC filter (channel 3), which detected the \nlysosomal mass and pH changes of the Cellomics® LysoTracker probe with red fluorescence \nat a wavelength of 599 nm.  \n \nStatistical analysis  \nResponse of each cell type to the coated and uncoated BFO -NP was analysed by 2 -way \nANOVA with Bonferroni post -test analysis. A p -value <0.05 was considered to be \nstatistically significant. In this work we are comparing 4 cell parameters associated with the \ncytotoxicity response of 3 cell lines exposed to uncoated or coated BFO, at 5 doses, with 3 \ncontrols; therefore, the statistical value assoc iated with our work carried out by High Content Page 10 of 28 \n Screening and data mining is of significance. To visualize the data, KNIME (http:// \nKNIME.org, 2.0.3) data exploration platform and the screening module HiTS \n(http://code.google.com/p/hits, 0.3.0) w ere used. Knime is a modular open -source data \nmanipulation and visualization programme, as previously reported12, 18-20. All measured \nparameters were normalized using the per cent of the positive controls. Z score was used for \nscoring the normalized values. These scores were summarized using the mean function as \nfollows Z score (x -mean)/SD, as from previous work12, 18-20. Heatmaps graphical illustration \nin a colorimetric gradient table format was adopted as the most suitable schematic \nrepresentation to report on any statistical significance and variation from normalized controls \nbased on their Z score value. Heatmap tables illustrate the range of variation of  each \nquantified parameter from the minimum (green) through the mean (yellow) to the maximum \n(red) according to the parameter under analysis.  \nHaemolysis assay  \nFresh human blood in lithium heparin -containing tubes was obtained from leftovers of \nanalytical blood with normal values. The plasma was removed by centrifugation for 10 min at \n2500 rpm and the blood cells were washed three times with sterile isotonic PBS solution, then \ndiluted 1:10 in PBS. Cell suspension s (300 µL) were added to 1200 µL of each solution \ncontaining NP or chemicals in human plasma or PBS at indicated concentrations . Nanopure \nwater  (1200 µL)  was used as a positive control and human plasma or PBS  (1200 µL) were \nused as negative control s. The mixtures were gently mixed then kept for 2h at RT, centrifuged \nfor 2 min at 4000 rpm and the absorbance of the upper layers was measured at 540 nm in an \nabsorbance multi -well plate reader (Synergy HT). The percentage of haemolysis of the \nsamples was calculated by dividing the difference in absorbance between the samples and the \nnegative control by the difference in absorbance betwe en the positive and negative controls. Page 11 of 28 \n Experiments were conducted in triplicate wells and repeated twice. Means + SD were \ncalculated.  \nResults   \nAs previously stated , this work present s for the first time several important aspect s relevant to \nthe translation of BFP -NP into a novel biomedical imaging probe for advanced diagnostic \nscreening . \nCoating and characterization of BFO -NP \nThe presence of reactive hydroxyl groups at the surface  of BFO -NP facilitates the surface \ncoating chemi stry. Modified poly (ethylene glycol ) (PEG) 2000 (molecular weight of 2000 \ng/mol, 45 units) containing silane anchoring groups  and reactive functionalities  were \nsynthetized as previously published15 and used to perform covalent coating via silane  (Si) \nligation  (Figure 1 ).  \nA previous ly published  study, by some of the authors, focused on the  surface coating and \npost-functionalization of  metal oxide NP such as iron oxide NP15. In this work, BFO -NP were \ntreated with an equimolar mixture of α - triethoxysilyl -ω-azido and α - triethoxysilyl -ω-amino \nPEG oligomers 1 and 2, prepared from linear PEG 2000, in the presence of aqueous \nammonia15. Ultra -sonication at 40°C for 16 hours, followed by repetitive cycles of \ndecantation/centrifugation into 1:1:1 DCM:EtOH: water  resulted in coated BFO -NP (PEG -\nBFO -NP), which  were suspended in EtOH for further characterization.  Efficient coating was \nproved by  FT-IR analysis (Supplementary Figure 1 ). Size and surface charge  characteristic s \nof uncoated BFO -NP (U-BFO -NP) and PEG -BFO -NP were measured  using DLS and zeta \npotential  techniques as previously described15. Upon coating, the zeta potential value shifted \nfrom -29.0 ± 1.3 mV to -9.8 ± 0.3 mV and the mean hydrodynamic diameter decreased  from \n128.8 ± 11.2 nm to 96.1 ± 8.3 nm. The decrease in the hydr odynamic diameter of coated Page 12 of 28 \n BFO -NP can be attributed to a better dispersion of the NP in the solvent  as a result of a \npossible colloidal stabilisation 21. \nBFO -NP stability and characterization  in biological media  \nFor both uncoated and coated BFO -NP, extended physico -chemical characterization was \ncarried out after ultracentrifugation and re-dispersion in ultrapure deionized water prior to \nincubation into relevant biological dispersing media. The two devised BFO -NP potential \nprobes  were also characterized by NTA , aiming at the identification of hydrodynamic radii, \nthe colloidal and the aggregation stabilities at physiologically relevant condit ions (Figure 2 ). \nInterestingly, U-BFO -NP form ed aggregates in biological relevant media, particularly when \nthe media were supplemented with serum. PEG -BFO -NP r esulted in a decrease  of aggregate \nformation, and thus a better stability of the suspension.  This finding was further confirmed \nafter 24h incubation (supple mentary Figure 2 ) \nInteraction between BFO -NP and human derived cells  \nThe interactions between U-BFO -NP and PEG -BFO -NP were then studied in three human -\nderived cell lines, one human adenocarcinoma cell line (A549) derived from alveolar \nepithelial type II cells, one lung squamous carcinoma cell line (NCI -H520)  5 and one human \nacute monocytic leukemia cell line (THP -1) as a model for macrophages 22. These \nexperiments were aimed  to observe the interaction  between particles and cell membranes in \nvitro  and to explore the uptake of particles in cells, particularly the endocytic pathways. \nIndeed, endocytosis represents one of the main internalization mechanisms of NP in cells  10, 14, \n23, particularly in macrophages  23, 24. For the quantification of particles associated with the \nplasma membranes and internalized into the cytoplasm, ce lls were exposed to BFO -NP, fixed \nand labelled wit h a fluorescent probe  used to stain membranes and lipids  25. HNP uptake by \nendocytosis was observed by co -localizing the SHG signal with a molecular probe \nspecifically internalized in the endosomes 26. It is worth pointing out that for the following Page 13 of 28 \n uptake quantification we purposel y adopted an extremely strong criterion (a cell is labelled if \nat least one particle is in contact with it). Even with this strict definition, we observed \nsignificant difference in uptake between 2  h and 24 h, with the notable exception of the \nmacrophages.  In fact,  a consistent uptake by these latter cells was observed after short \nexposur es (2 h and 24  h), whereas in human lung -derived NCI -H520 cancer cells the  uptake \nof the HNP was only observed after 72  h incubation ( Figure 3 ). HNP internalization in human \nlung-derived cancer cells is exposure -time dependent  (Figure 3 ). Indeed, H NP generally \nadhere to the cell membrane after  2 h and are then internalized when increasing exposure \ntime. After 72  h exposure, B FO-NP form ed aggregate s in intracellular organelles, such as \nlysosome or endosomes . We did not observe a statistically significant difference in labelling \nbetween  PEG -BFO -NP and U -BFO -NP after 2 h or 24  h exposure (Figure 3 ). Interestingly  the \ninteraction  HNP with immune THP -1 cells  was fairly rapid , as more than 80% of cells were \nfound to have internalized at least one particle already af ter 2  h exposure. Such finding is in \nline with previous observations , since it is known that  THP -1 phagocytic cells rapidly envelop \nand digest extraneous  objects as initial response to infection  or foreign body invasion  22, 27, 28. \nConversely , the labelling of A549 and NCI -H520 cells showed a clear exposure  dependent  \nbehaviour . After 72 h, the number of labelled cells was significantly higher in the presence of \nPEG -BFO -NP than with U-BFO -NP (Figure 3 ), suggesting the existence of an exocytosis \nmechanism  for the uncoated BFO -NP as already observed  and reported  for others metallic NP \n29, 30. In macrophages , the uptake of  uncoated particles  is mainly endocytic -dependent , \nwhereas the PEGylation of BFO -NP completely reduced the endocytic -mediated uptake \n(Figure 3 ). This mechanism of particle internalization was  confirmed by multiphoton  laser \nscanning microscopy z-stack analysis of differentiated THP -1, which showed clusters of \nBFO -NP into the cytoplasm of cells h aving internalized uncoated BFO -NP after 24 h \nexposure ( Figure 4 ) as opposed to the behaviour  observed with coated BFO -NP, which Page 14 of 28 \n showed a reduced uptake . In the lung -derived cancer cell lines only a weak fraction of H NP \nco-localized with the endosomes after 2  h and 24  h exposure, nonetheless this portion  \nincrease d for the  NCI-H520 cells after 72  h exposure to the particles.   \nMultiparametric cy totoxicity evaluation of BFO -NP \nThe c ytotoxicity of uncoated and coated BFO -NP was investigated in vitro  on the two human \nlung-derived  NCI-H520 and A549 cancer cell lines  and the macrophage -derived THP -1 cells , \nafter 24  h and 72  h exposure to increasing concentrations (1, 2.5, 5, 7.5 and 10 μg/ ml) of \nparticles . Experiments were repeated three times, using triplicate wells each time for e ach \nformulation tested, as shown in supplementary Table 1 . Three key parameters of toxicity -\nattributed phenomena were analysed during this assay: cell number, lysosomal  mass and  pH, \nand cell membrane permeability , as previously reported 12. Indeed , it is known that some \ntoxins can interfere with the cell’s functionality by affecting the pH of organelles such as \nlysosomes and endosomes, or by causing an increase in the number of lysosomes  present  12, 31. \nCell membrane permeabili ty changes can be measured as enhancement of cell membrane \ndamage and decreased cell viability as result of cell nuclear -staining counting reduction  12, 32. \nMoreover, three positive control s were introduced in this analysis: CdSe qua ntum dots (QD), \nwhich are established toxic NP 12, Valinomycin  (Vac) , an induc er of energy -dependent \nmitochondrial swelling causing  cell membrane perm eability  33 and Tacrine  (Tac) , a reversible \ncholinesterase inhibitor which cause s increase s in cellular lysosome content and lysosom al \nmass  34. The rate of cell viability and proliferation was assessed by automated quantitative \nanalysis of the nuclear count and cellular morphology; in parallel to  that the fluorescent \nstaining intensities reflecting cell permeability and lysosomal  mass/pH changes were also \nquantified for each individual cell measured within each imaged field  and then \ncolorimetrically normalised against the respective controls  (Figure 5 ). A multiparametric \nanalysis of the cellular responses allow ed the identificatio n of the different toxicity levels  Page 15 of 28 \n between the two BFO -NP. In general, BFO -NP in concentration range of 1 -10 μg/ml showed \nlow cytotoxicity on the cell models adopted. In agreement wit h the previous results, THP -1 \ncells are the most affected cells between the three cell lines  since these are the first line \nimmune response to any foreign objects such as nanoparticles . For b oth PEG -BFO -NP and U-\nBFO -NP a time -dependent and dose -dependent toxicity  was measured . However, these effects \nwere more pronounced when c ells were exposed to  uncoated particles . Among the parameters \nmeasured during the NP comparison, the c ell permeability parameter showed the most \npronounced difference , suggesting that BFO -NP, particularly uncoated particles, interfered \nmainly with the physiology of the plasma membrane, as also shown by the Vac response  as \npositive control  for cellular permeability. PEG -BFO -NP got stored in lysosomal \ncompartments as from lysosomal concentratio n response, which was also comparable to the \nresponse to Tac  used positive control for lysosomal response.  \nHaemolysis assay  \nAfter having assessed the colloi dal stability of PEG -coated BFO -NP in biological media, the \ninteractions with cell membranes were te sted by assessing their h aemolytic effect on human \nred blood cells (HRBc) according to established protocols 5, 35. Haemolysis is define d as the \ndestruction of red blood cells and it is regarded as a key parameter for the evaluation of NP \nbiocompatibility  5, 35, 36. NP can exert haemo lytic effect by electrostatic interactions with \nmembrane proteins or by other NP-specific mechanisms such as the generation of reactive \noxygen species (ROS), causing irreversible damage to cells. The assessment of the \nhaemolysis of uncoated B FO-NP showed a  weak ha emolytic potential ( Figure 6 ), comparable \nto that of metallic NP observed in other bio -assays 36, 37. Upon PEG coating, this potential was \nsignificantly reduced (p<0.001 , Figure 6 ). These statistically significant results proved that \nPEGylation of the m etal oxide core contributed to the reduction of the interaction between \ncell membranes and particles surface.  Page 16 of 28 \n Discussion  \nBFO -NP are a class of nano materials  with unique optical and physical properties attracting \nthe interest of researchers for several  technological applications , in particular  related to their \nmultiferroics nature . We have shown recently their potential in the context of advanced  non-\nlinear optical imaging16. Recently BFO -NP were employed in vitro  in a pilot study where they \nproved to be able to locally induc e DNA damages by deep UV generation  11. The cytotoxicity, \nhaemolytic response and internalization  mechanisms evidence here reported  for coated BFO -\nNP suggested good biocompatibility and a great potential for biomedical imaging in \ndiagnostic applications . Therefore, the  aim of this work was , for the first time,  to present the \nbehaviour  of these particles in their uncoated  or PEGylated form. Such assessment comes \ntimely after the first demonstrations of their interest for bio -imaging and selective \nphotointeraction , as, due to their novelty, there is still a knowledge gap that requires the \nscientific community attention towards the investigation of their biological effect. NP must be \ncoated with biocompatible  polymers in order to stabilize  the NP suspensions in biol ogical \nmedia and to increase their biocompatibility 38, 39. Coating with organic polymers also allows \nparticles conjugation and functionalization with biologically -active ligands, such as targeting -\nspecific ligands, therapeutic agents, peptides or antibodies15, 40. Here we present a method for \nthe successful PEGylation of BFO -NP based on heterobifunctional PEG olig omers , for which \na fast and convenient large scale synthesis protocol was recently published  15. PEG was \nselected as coating polymer due to its interesting properties for biomedical applications. \nIndeed, when comp ared to any other known polymer, PEG exhibits high hydrophilicity, low \nprotein adsorption, low uptake by immune cells, and no toxicity properties  14, 41, 42. Our \nfindings confirmed the important role of th is kind of coating in terms of biocompatibility. \nInterestingly as presented here,  PEG -BFO -NP are less toxic and their uptake in immune -\nresponsive THP -1 cells is reduced. As a result of the multiparametric cytotoxicity evaluation, Page 17 of 28 \n we hypothesize that BFO -NP toxicity is mainly mediated by electrostatic interactions with the \nsurface of the particles and the cell membranes. The reduction of cytotoxicity observed upon \ncoating is probably due to a steric barrier between the surface of the coated particles and the  \nlipid membrane of cells  14, 15, 41. PEG -BFO -NP were  internalized in intracellular organelles  \nand they remained located into the cells  sensibly longer than U-BFO -NP. This opens \ninteresting ways for biomedical applications , which require  stable incorporation of H NP in \ncells. In the future , more detailed stud ies about BFO -NP co-localization in cells are needed in \norder to better understand the pathways involved in the internalization of these particles. \nMoreover, more detailed assessment of the immune response associated with these pa rticles, \nsuch as a cytokine profile after exposure to the particles, could be interesting for the \nelucidation of their biological effects since they are immune -responding to foreign body  43-45. \nHowever, this work confirm ed the biocompatibility of BFO-NP and their utility as \nnano probe s for biological applications.   \n \n \n \n \n \n \n \n \n \n \n Page 18 of 28 \n Bibliography  \n1. L. Bonacina, Nonlinear nanomedecine: harmonic nanoparticles toward targeted \ndiagnosis and therapy . Mol Pharm . 2013;10:783 -92 \n2. J. Extermann, L. Bonacina, E. Cuna, C. Kasparian, Y. Mugnier, T. Feurer, et al., \nNanodoublers as deep imaging markers for multi -photon microscopy . Opt Express . \n2009;17:15342 -9 \n3. T. Magouroux, J. Extermann, P. Hoffmann, Y. Mugnier, R. Le Dantec, M. E. Jaconi, et al., \nHigh -speed tracking of murine cardiac stem cells by harmonic nanodoublers . Small . \n2012;8:2752 -6 \n4. P. Pantazis, J. Maloney, D. Wu and S. E. Fraser, Second harmonic generating (SHG) \nnanoprobes for in vivo imaging . Proc. Natl. A cad. Sci. U. S. A.  2010;107:14535 -40 \n5. D. Staedler, T. Magouroux, R. Hadji, C. Joulaud, J. Extermann, S. Schwung, et al., Harmonic \nnanocrystals for biolabeling: a survey of optical properties and biocompatibility . ACS Nano . \n2012;6:2542 -9 \n6. L. Bonacina, Y . Mugnier, F. Courvoisier, R. Le Dantec, J. Extermann, Y. Lambert, et al., \nPolar Fe(IO3)(3) nanocrystals as local probes for nonlinear microscopy . Appl Phys B -Lasers O . \n2007;87:399 -403 \n7. M. Zielinski, D. Oron, D. Chauvat and J. Zyss, Second -harmonic gener ation from a single \ncore/shell quantum dot . Small . 2009;5:2835 -40 \n8. L. Y. Chou, K. Ming and W. C. Chan, Strategies for the intracellular delivery of \nnanoparticles . Chemical Society Reviews . 2011;40:233 -45 \n9. T. H. Kim, W. A. El -Said, J. H. An and J. W. Choi, ITO/gold nanoparticle/RGD peptide \ncomposites to enhance electrochemical signals and proliferation of human neural stem cells . \nNanomedicine . 2013;9:336 -44 \n10. H. Herd, N. Daum, A. T. Jones, H. Huwer, H. Gha ndehari and C. M. Lehr, Nanoparticle \ngeometry and surface orientation influence mode of cellular uptake . ACS Nano . 2013;7:1961 -73 Page 19 of 28 \n 11. D. Staedler, T. Magouroux, S. Passemard, S. Schwung, M. Dubled, G. S. Schneiter, et al., \nDeep UV generation and direct DNA  photo -interaction by harmonic nanoparticles in labelled \nsamples . Nanoscale . 2014;6:2929 -36 \n12. A. Prina -Mello, K. Crosbie -Staunton, G. Salas, M. D. Morales and Y. Volkov, \nMultiparametric Toxicity Evaluation of SPIONs by High Content Screening Technique: \nIdentification of Biocompatible Multifunctional Nanoparticles for Nanomedicine . Ieee \nTransactions on Magnetics . 2013;49:377 -382 \n13. B. M. Mohamed, N. K. Verma, A. Prina -Mello, Y. Williams, A. M. Davies, G. Bakos, et al., \nActivation of stress -related signall ing pathway in human cells upon SiO2 nanoparticles exposure \nas an early indicator of cytotoxicity . J Nanobiotechnology . 2011;9:29  \n14. S. Hak, E. Helgesen, H. H. Hektoen, E. M. Huuse, P. A. Jarzyna, W. J. Mulder, et al., The \neffect of nanoparticle polyethyl ene glycol surface density on ligand -directed tumor targeting \nstudied in vivo by dual modality imaging . ACS Nano . 2012;6:5648 -58 \n15. S. Passemard, D. Staedler, L. Ucnova, G. S. Schneiter, P. Kong, L. Bonacina, et al., \nConvenient synthesis of heterobifuncti onal poly(ethylene glycol) suitable for the \nfunctionalization of iron oxide nanoparticles for biomedical applications . Bioorg. Med. Chem. \nLett. 2013;23:5006 -10 \n16. S. Schwung, A. Rogov, G. Clarke, C. Joulaud, T. Magouroux, D. Staedler, et al., Bismuth \nFerr ite Nanocrystals for Bio -Imaging based on Nonlinear Optical Harmonic  Generation . ArXiv . \n2014;1407.4271  \n17. P. Hole, K. Sillence, C. Hannell, C. M. Maguire, M. Roesslein, G. Suarez, et al., \nInterlaboratory comparison of size measurements on nanoparticles us ing nanoparticle tracking \nanalysis (NTA) . J Nanopart Res . 2013;15:2101  \n18. D. Movia, A. Prina -Mello, D. Bazou, Y. Volkov and S. Giordani, Screening the Cytotoxicity \nof Single -Walled Carbon Nanotubes Using Novel 3D Tissue -Mimetic Models . ACS Nano . \n2011;5:9278 -9290  Page 20 of 28 \n 19. D. Movia, A. Prina -Mello, Y. Volkov and S. Giordani, Determination of spiropyran \ncytotoxicity by high content screening and analysis for safe application in bionanosensing . Chem. \nRes. Toxicol.  2010;23:1459 -66 \n20. B. M. Mohamed, N. K. V erma, A. M. Davies, A. McGowan, K. Crosbie -Staunton, A. Prina -\nMello, et al., Citrullination of proteins: a common post -translational modification pathway \ninduced by different nanoparticles in vitro and in vivo . Nanomedicine (Lond) . 2012;7:1181 -95 \n21. A. K.  Gupta and S. Wells, Surface -modified superparamagnetic nanoparticles for drug \ndelivery: preparation, characterization, and cytotoxicity studies . IEEE Trans Nanobioscience . \n2004;3:66 -73 \n22. T. Kohro, T. Tanaka, T. Murakami, Y. Wada, H. Aburatani, T. Hamaku bo, et al., A \ncomparison of differences in the gene expression profiles of phorbol 12 -myristate 13 -acetate \ndifferentiated THP -1 cells and human monocyte -derived macrophage . J Atheroscler Thromb . \n2004;11:88 -97 \n23. R. Shukla, V. Bansal, M. Chaudhary, A. Basu , R. R. Bhonde and M. Sastry, Biocompatibility \nof gold nanoparticles and their endocytotic fate inside the cellular compartment: a microscopic \noverview . Langmuir . 2005;21:10644 -54 \n24. A. Lankoff, W. J. Sandberg, A. Wegierek -Ciuk, H. Lisowska, M. Refsnes, B . Sartowska, et \nal., The effect of agglomeration state of silver and titanium dioxide nanoparticles on cellular \nresponse of HepG2, A549 and THP -1 cells . Toxicol. Lett.  2012;208:197 -213 \n25. Y. Lee, I. Yang, J. E. Lee, S. Hwang, J. W. Lee, S. S. Um, et al., Enhanced Photocurrent \nGeneration by Forster Resonance Energy Transfer between Phospholipid -Assembled \nConjugated Oligoelectrolytes and Nile Red . Journal of Physical Chemistry C . 2013;117:3298 -3307  \n26. G. H. Hansen, K. Rasmussen, L. L. Niels -Christiansen and  E. M. Danielsen, Endocytic \ntrafficking from the small intestinal brush border probed with FM dye . Am J Physiol Gastrointest \nLiver Physiol . 2009;297:G708 -15 \n27. J. Auwerx, The Human Leukemia -Cell Line, Thp -1 - a Multifaceted Model for the Study \nof Monocyte -Macrophage Differentiation . Experientia . 1991;47:22 -31 Page 21 of 28 \n 28. S. Tsuchiya, M. Yamabe, Y. Yamaguchi, Y. Kobayashi, T. Konno and K. Tada, \nEstablishment and characterization of a human acute monocytic leukemia cell line (THP -1). Int. \nJ. Cancer . 1980;26: 171-6 \n29. B. D. Chithrani and W. C. Chan, Elucidating the mechanism of cellular uptake and \nremoval of protein -coated gold nanoparticles of different sizes and shapes . Nano Lett . \n2007;7:1542 -50 \n30. H. Jin, D. A. Heller, R. Sharma and M. S. Strano, Size-depe ndent cellular uptake and \nexpulsion of single -walled carbon nanotubes: single particle tracking and a generic uptake \nmodel for nanoparticles . ACS Nano . 2009;3:149 -58 \n31. B. J. Marquis, S. A. Love, K. L. Braun and C. L. Haynes, Analytical methods to assess \nnanoparticle toxicity . Analyst . 2009;134:425 -39 \n32. H. A. Jeng and J. Swanson, Toxicity of metal oxide nanoparticles in mammalian cells . J \nEnviron Sci Health A Tox Hazard Subst Environ Eng . 2006;41:2699 -711 \n33. D. D. Lofrumento, G. La Piana, D. I. Abbresci a, V. Palmitessa, V. La Pesa, D. Marzulli, et al., \nValinomycin induced energy -dependent mitochondrial swelling, cytochrome c release, cytosolic \nNADH/cytochrome c oxidation and apoptosis . Apoptosis . 2011;16:1004 -13 \n34. D. K. Monteith, J. C. Theiss, J. R. Ha skins and F. A. de la Iglesia, Functional and \nsubcellular organelle changes in isolated rat and human hepatocytes induced by \ntetrahydroaminoacridine . Arch. Toxicol.  1998;72:147 -56 \n35. Q. He, J. Zhang, J. Shi, Z. Zhu, L. Zhang, W. Bu, et al., The effect of PEGylation of \nmesoporous silica nanoparticles on nonspecific binding of serum proteins and cellular responses . \nBiomaterials . 2010;31:1085 -92 \n36. J. Choi, V. Reipa, V. M. Hitchins, P. L. Goering and R. A. Malinauskas, Physicochemical \nCharacterization and In  Vitro Hemolysis Evaluation of Silver Nanoparticles . Toxicol. Sci.  \n2011;123:133 -143 \n37. Y. N. Zhao, X. X. Sun, G. N. Zhang, B. G. Trewyn, I. I. Slowing and V. S. Y. Lin, \nInteraction of Mesoporous Silica Nanoparticles with Human Red Blood Cell Membranes: Si ze \nand Surface Effects . ACS Nano . 2011;5:1366 -1375  Page 22 of 28 \n 38. M. M. Lin, H. H. Kim, H. Kim, J. Dobson and K. Kim do, Surface activation and targeting \nstrategies of superparamagnetic iron oxide nanoparticles in cancer -oriented diagnosis and \ntherapy . Nanomedicine ( Lond) . 2010;5:109 -33 \n39. N. B. Shah, G. M. Vercellotti, J. G. White, A. Fegan, C. R. Wagner and J. C. Bischof, Blood -\nnanoparticle interactions and in vivo biodistribution: impact of surface PEG and ligand \nproperties . Mol Pharm . 2012;9:2146 -55 \n40. P. R. Gil  and W. J. Parak, Composite nanoparticles take aim at cancer . ACS Nano . \n2008;2:2200 -5 \n41. J. L. Perry, K. G. Reuter, M. P. Kai, K. P. Herlihy, S. W. Jones, J. C. Luft, et al., PEGylated \nPRINT nanoparticles: the impact of PEG density on protein binding, mac rophage association, \nbiodistribution, and pharmacokinetics . Nano Lett . 2012;12:5304 -10 \n42. A. Verma and F. Stellacci, Effect of surface properties on nanoparticle -cell interactions . \nSmall . 2010;6:12 -21 \n43. C. Hanley, A. Thurber, C. Hanna, A. Punnoose, J. Zhang and D. G. Wingett, The Influences \nof Cell Type and ZnO Nanoparticle Size on Immune Cell Cytotoxicity and Cytokine Induction . \nNanoscale Res Lett . 2009;4:1409 -20 \n44. C. M. Sayes, K. L. Reed and D. B. War heit, Assessing toxicity of fine and nanoparticles: \ncomparing in vitro measurements to in vivo pulmonary toxicity profiles . Toxicol. Sci.  \n2007;97:163 -80 \n45. I. Siglienti, M. Bendszus, C. Kleinschnitz and G. Stoll, Cytokine profile of iron -laden \nmacrophages : implications for cellular magnetic resonance imaging . J. Neuroimmunol.  \n2006;173:166 -73 \n \n \n \n Page 23 of 28 \n  \nFigure s \n \n \n \n \nFigure 1 : Synthesis of coated BFO -NP.  PEG oligomer (1) and PEG oligomer (2) were \nsynthetized from PEG 200 0 (MW 2000 Da) as published15, then used  for the coating of BFO -\nNP. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nPage 24 of 28 \n  \n \n \n \n \n \n \n \n \n \n \nFigure 2 : Nanoparticle Tracking Analysis of U -BFO -NP (light grey bars) and PEG -BFO -NP \n(dark grey bars) in biological media. Complete: media supplemented with 10% foetal bovine \nserum (FBS); DEPC: diethylpyrocarbonate; DMEM: Dulbecco's Modified Eagle Medium; \nF12k: Ham's F -12K (Kaighn's) Medium; RPMI -1640: Roswell Park Memorial Institute 1640.  \nSize distribution of BFO -NP after dispersion at 1 µg/mL in DEPC water solution (DEPC), \nDMEM medium (DMEM), D MEM medium supplemented with 10% FBS (complete \nDMEM), F12k medium (F12k), F12k medium supplemented with 10% FBS (complete F12k), \nRPMI 1640 medium (RPMI -1640) and RPMI 1640 medium supplemented with 10% FBS \n(complete RPMI -1640). All measurements were carried  out three times at pH 7.4, then means \nand standard deviations (SD) were calculated.  \n \n \n \n \nPage 25 of 28 \n  \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 3 : BFO -NP uptake in human -derived cell lines  \nFirst row: NCI -H520 cancer cells exposed to PEG -BFO -NP at 25 µg/mL for 2h, 24h and 72h . \nGreen: SHG signal of BFO -NP; yellow: co -localization between the probe for lipid \nmembranes and the particles; blue circles: highlight of HNP co -localizing with FM1 -43FX.  \nScale bar: 10 µm.  \nSecond row: % of labelled A549, NCI -H520 and THP -1 cells exposed  to U-BFO -NP (brown \nbars) or PEG -BFO -NP (blue bars) at 25 µg/mL for 2h, 24h or 72h (only NCI -H520). \nStatistical comparisons were done using a Student's t -test: *p<0.05, **p<0.01, ***p<0.001. †: \nno HNP co -localizing with endosomes were observed.  \n \n \n \nPage 26 of 28 \n  \n \n \n \n \n \n \n \n \nFigure 4 : uptake of uncoated BFO -NP by activated THP -1 cells.  \nTHP -1 cells were exposed for 24h at 25 μg/ml U -BFO -NP (green), then stained with a \nfluorescent probe for endosomes (red, FM1 -43FX). The picture was extracted from a z -stack \nand shows 2 slice v iews centered at the yellow cross along its y z axis (right panel) and x z \naxis. Inset: Image of a THP -1 cell after 24h exposure to to 25 μg/ml of PEG -BFO -NP. Scale \nbars: 10 μm.  \n \n \n \n \n \n \n \n \n \n \nPage 27 of 28 \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 5 : Heatmaps  tables illustrating toxicity indicated parameters of BFO -NP in human -\nderived cell lines. Heatmaps were generated from the analysis of n= 3 experiments, each with \ntriplicate wells for each of the parameters under investigation: cell count, lysosomal mass, cell \npermeability and nuclear area. Colorimetric gradient table spans from: Dark green: lower than \n15% of maximum value measured; Bright green = 30%; Yellow = 50%; Bright orange: 60%; \nDark orange = 75%; Red higher than 75% of maximum value. N/C untreated c ontrols \n(negative) and P/C as positive controls such as QD: quantum dots, TAC: Tacrine, VAL: \nValinomycin). Heatmap values are normalised using the per cent of the positive controls and, \nZ score was calculated as described in the statistical analysis sectio n. \nPage 28 of 28 \n  \n \n \n \n \n \n \n \n \nFigure 6 : Haemolytic effect of U -BFO -NP and PEG -BFO -NP. \nHBRc were exposed to NP (25 µg/mL) for 2h. Results were expressed as % of haemolysis of \nNP-exposed HRBc compared to unexposed cells. Results are the means + SD of triplicates of \ntwo indep endent experiments. Values of U -BFO -NP were compared to those of  PEG -BFO -\nNP by a Student's t -test (p<0.001). This picture was done using Servier Medical Art images.  \n"    },    {        "title": "1302.3983v2.Room_Temperature_Nanoscale_Ferroelectricity_in_Magnetoelectric_GaFeO3_Epitaxial_Thin_Films.pdf",        "content": " 1(Accepted in Physical Review Letters) \n \nRoom Temperature Nanoscale Ferroelect ricity in Magnetoelectric GaFeO 3 \nEpitaxial Thin Films \n \nSomdutta Mukherjee§1, Amritendu Roy§2, Sushil Auluck3, Rajendra Prasad1, Rajeev Gupta1,4 and \nAshish Garg2 \n \n1Department of Physics, Indian Inst itute of Technology Kanpur, Kanpur- 208016, India \n2Department of Materials Science and Engineer ing, Indian Institute of Technology Kanpur, Kanpur- \n208016, India \n3National Physical Laboratory, K.S Krishnan Marg, New Delhi 110012, India \n4Materials Science Programme, Indian Instit ute of Technology Kanpur, Kanpur- 208016, India \n  \nAbstract  \n \nWe demonstrate room temperature ferroelectricity in the epitaxial thin films of magnetoelectric \nGaFeO\n3. Piezo-force measurements show a 180o phase shift of piezoresponse upon switching the \nelectric field indicating nanoscale ferroelectricity in  epitaxial thin films of gallium ferrite. Further, \ntemperature dependent impedance analysis with a nd without the presence of an external magnetic \nfield clearly reveals a pronounced magneto-dielect ric effect across the magnetic transition \ntemperature. In addition, our first principles calculations show that Fe ions are not only responsible \nfor ferrimagnetism as observed earlier, but also gi ve rise to the observed ferroelectricity, making \nGFO an unique single phase multiferroic.   Keywords:  Gallium ferrite, ferroelectricity, magnetoelect ric effect, first-principles calculation. \n                                                \n \n§ SM and AR contributed equally to this work.  2Pursuit of multifunctionalities in single phase or composite materials has led to sustained research on \nmultiferroic materials. These materials, mostly artificially synthesized, can give rise to a variety of novel applications such as spintronic and da ta storage devices, se nsors and actuators. \n1, 2 Rare \noccurrence of natural multiferroic materials has led to extensive search for materials systems 3, 4 and \nover the last decade, a combination of advan ced synthesis and characterization techniques 5, 6 and \nstate-of-the-art firs t-principles studies 7, 8 have predicted numerous multiferroic materials. However, \nwith the exception of ferroelectric-antiferromagnetic BiFeO 3, most materials demonstrate \nmultiferroism at very low temperatures.5, 9 Thus, it is vital to explore new multiferroic materials \ndemonstrating multiferroic effect with significant magnetoelectric  (ME) coupling near or above \nroom temperature (RT) in order to realize their technological promise.  \nGallium ferrite (Ga 2-xFexO3 or GFO) is a room temperature piezoelectric10-14  and near room \ntemperature ferrimagnetic material with its ma gnetic transition temperature tunable to room \ntemperature and above by tailoring its composition.15 Though, the magnetic ch aracteristics of GFO \nare widely studied,10, 13, 16-18 intriguingly there is no evidence of its ferroelectric nature. While an \nearly report19 attributed asymmetrically placed Ga1 ions  within the unit cell responsible for observed \npiezoelectric response of GFO, recen t first-principles calculations20 showed that within the inherently \ndistorted structure of GFO, larg e ionic displacements with respec t to the centrosymmetric positions \nresult in a large spontaneous polarization in the ground state20 and even hint towards possible \nferroelectric switching.21 Thus, inability to observe saturated ferro electric hysteresis loops (if any) in \nGFO bulk and single crystal samples is likely to em anate from the measurement difficulties, possibly \ndue to substantial electr ical leakage above 200 K.22-24 On the other hand, epitaxial thin films of pure \nand doped GFO, grown on a variety of single crysta lline substrates show a large reduction in the \nleakage current24, 25 and are more likely to demonstrate ferro electric behavior if probed locally.  \nIn this work, we report  RT nanoscale ferroelectric switchin g in (010)-oriented epitaxial thin \nfilms of GFO, along with the presence of near RT  ferrimagnetism. Subsequent first-principles  3calculations reveal that Fe ions  are responsible for both ferroele ctricity and ferrimagnetism making \nGFO an unique multiferroic material.3 In the remaining paragraphs, we  first describe the structural \nanalysis of as grown thin film s followed by their electrical and magnetic characterization and first-\nprinciples calculations results substantiating ferro electricity as well as ma gnetoelectric coupling. \nGaFeO 3 (GFO) thin films were grown on commerc ially available single crystalline cubic \nyittria stabilized zirconia, YSZ (0 01) substrate (lattice parameter, aYSZ = 5.125 Å). For electrical \ncharacterization, transparent conduc ting indium tin oxide (ITO) was used as bottom electrode. Both \nGFO and ITO were grown using pulsed laser depos ition (PLD) technique with KrF excimer laser ( λ \n= 248 nm) operated at 3 Hz and 10  Hz, respectively. GFO films of 200 nm thickness were grown at \n800 C in an oxygen ambient (p O2 ~ 0.53 mbar) using a laser fluence of 2 J cm-2 from a \nstoichiometric target of gallium ferrite15 while ITO films of 40 nm thickness were grown using a \nlaser fluence of 1 J cm-2 at 600C at p O2 ~ 110-4 mbar using an ITO target. The films were \nsubsequently cooled at 1 C min-1 to 300 C  a t  t h e  s a m e  O 2 pressure used for GFO deposition \nfollowed by natural cooling to room temperature.  X-ray diffraction of the as grown film was \nperformed using PANalytical X’Pert Pro MRD diffractometer using CuK α radiation. Surface \ntopography and domain structure were  studied using scanning probe microscope (Asylum Research) \nequipped with Olympus AC240TS Ti/Ir tip operated  at resonance frequenc y. The same setup was \nused to carry out switching spectroscopy mappi ng (SSPFM) measurements with Rocky mountain \ncantilever equipped with 25Pt400B solid pt probe . For SSPFM measurement, we used Dual Ac \nResonance Tracking (DART) mode . For impedance measurement, Pt top electrode (~ 200 m \ndiameter) was deposited by sputtering, using sha dow mask technique. Impedance data was acquired \nusing Agilent Impedance analyzer 4294A connected to a commercial ARS He close cycle cryo-probe \nstation placed between two magnetic pole pieces.  \n First-principles calculations were performed using density functional theory within the \ngeneralized gradient approximation (GGA+U) with Perdew and Wang (PW91) functional26 as  4implemented in  Vienna ab-initio  simulation package (VASP) 27 and using rotationally invariant \napproach 28 with onsite Coulomb potential U eff = 5.5 eV to treat the localized d electrons of Fe ions. \nThis value of U eff has been found to yield r easonable agreement between calculated and experimental \nmagnetic moments of Fe ions in GFO. Furt her, small variation of the value of U eff was found not to \nalter the structural stability. We verified the consistency of our calculations by repeating the \ncalculations using GGA method with the optimized version of Perdew-Burke -Ernzerhof functional \nfor solids (PBEsol).29 The GGA functionals PW91 and PBEsol al so yielded similar results.  More \ninformation on calculation details can be found elsewhere.20  \nFigure. 1  (a) shows the -2 X-Ray diffraction (XRD) pattern of  phase pure and 200 nm thin \nGFO films deposited on (001)-oriente d yittria stabilized zirconia (YSZ ) substrates buffered with a 40 \nnm indium tin oxide (ITO) layer, also acting as  the bottom electrode. Th e figure shows only {010} \ntype of peaks of GFO (orthorhombic Pc2 1n symmetry) along with (001) peaks of ITO and YSZ \nindicating an out of plane ep itaxial relationship as (010) GFO || (001) ITO || (001) YSZ. Calculated out of \nplane lattice parameter, b ~ 9.4012 Å, is in excellent agreem ent (~ 0.02% difference) with b-axis \nlattice parameter of bulk single crystal10 indicating that the film is fully relaxed along film’s b-axis. A \nsmall lattice mismatch between ITO ( aITO ~ 1.016 nm) and diagonal [( aYSZ2\n+ cYSZ2)1/2] of in-plane \nlattice parameters of GFO of 0.4% 30 and  lattice mismatch between aITO and 2 aYSZ of 1.13% \nindicates that GFO film is coherently strained within the substrate plane, also demonstrated by the corresponding reciprocal space map (Figure 1(c)). Nature of in-plane orientat ion of the film was \ndetermined by performing a -scan corresponding to (221) peak  of GFO, (222) peak of ITO \nelectrode and (111) peak of the YSZ substrate. As shown in Figure. 1(b), the presence of four equally \nspaced peaks for ITO and YSZ indicates that ITO f ilms maintain similar crys tallographic orientation \nas of YSZ. However we observe 12 peaks in the -scan of GFO films indicating existence of \ndifferent growth variants. Different growth varian ts are commonly seen in epitaxial thin films of  5oxides 31, 32 which are largely due to te ndency of single crystal oxide substrates to cleave along \ncertain crystallographic planes leav ing facets on the substrate surface.  \nTopography of a 200 nm thick GFO film estim ates average grain size ~ 96 nm and RMS \nroughness ~ 9.5 nm. Converse piezoelectr ic effect with lock-in techni que was employed to study the \nlocal piezoelectric switching behavior and to estimate the d 33 coefficient. PFM was used in \nspectroscopic mode where measurement was done in a fixed tip position with a dc bias voltage swept \nin a cyclic manner. The dependence of local piezoelectric vibration on the corresponding voltage \nsweep is referred as local piezoelect ric hysteresis loop. On a macrosc opic scale, there will be weak \nfield dependence of piezoelectric coefficient, d 33, with continuously varying bias field. To verify the \npresence of ferroelectricity, we applied a sequence of  dc voltage in a triangular saw-tooth form in an \nattempt to switch the polarization with a 2 V ac volta ge simultaneously applied in order to record the \ncorresponding piezoresponse. To mi nimize the effect of electrosta tic interaction, piezoresponse was \nmeasured during “off” state at each step, and phase voltage hysteresis loop is evident. The d 33 \ndependence of the polarization can be obtai ned by local bias voltage switching.  \nWe investigated the piezo- and ferroelectric behavior of these films using piezoresponse force \nmicroscopy (PFM). Figure 2 (a) and (b) show PFM amplitude and phase images acquired over \n1.251.25 m2 area in PFM Dual AC Resonance Trackin g imaging mode, using a cantilever of \nstiffness 2 N m-1 and a Ti/Ir tip. Figure 2(a) shows the out -of-plane polarization as depicted by the \nbright yellow regions while Fi gure 2(b) shows the presence of  antiparallel na nodomains with \nconcurrently minor presence of domains with intermediate domain angle. For studying local \npiezoelectric and ferroelectric switching, we also plotted the phase and butterfly amplitude loops \nupon sweeping bias voltage. Figure 2 (c) and (d) s how the corresponding amplitude (A) and phase \n() loops as a function of dc bias voltage. The butterfly loop in Figure 2(c) reveals the first harmonic \nsignal under applied dc bias field and is signature of piezoelectric response of the thin films. The \npiezoresponse tends to saturate  at relatively high voltages suggesting that the response is  6piezoelectric instead of el ectrostatic. The phase ( ) corresponds to the phas e of piezoresponse and its \nreversal with voltage is shown in Figure 2(d). This  reversal occurs beyond a coercive voltage, ~ -2.9 \nV at negative side and ~ 3.6 V at positive side while the phase contrast is ~180  clearly suggesting \npolarization switching and thus , ferroelectric character of  our GFO thin films.  \nHaving shown RT ferroelectricity, it would be in teresting to explore possible magnetoelectric \ninteraction in GFO thin films sin ce such an effect would increase th e material’s acceptability as a \nclose to room temperature multiferroic memory ma terial. We then probed possible magnetoelectric \ncoupling by performing temperature dependent imped ance spectroscopic analysis, from 50 K to 325 \nK. Figure. 3 presents the plot of r eal part of dielectric constant ( ) at frequencies 1, 5, 10, 25, 50 and \n100 kHz. The Figure shows that the onset of increase in the dielectric constant is approximately at \n150 K at 1 kHz, shifting to higher temperatures at higher frequencie s. However, plots show a hump \nin the dielectric constant ( ) at ~235 K, in the vicinity of ferr i to paramagnetic tr ansition temperature \n(as shown in the bottom inset). Such deviation in th e dielectric constant from a typical temperature \ndependent dielectric behavior is considered as an indication of th e magnetoelectric coupling in GFO. \nThe temperature (T m) corresponding to peak position in  exhibits a weak frequency dependence and \nshifts towards higher temperature from 230 K at 1 kH z to 240 K at 100 kHz. Further, we measured \nthe dielectric constant at 10 kHz in pres ence of two different magnetic fields ( 0H = 0.25 and 0.5 T) \nacross T m. As shown in the top inset of Figure 3, with  increasing magnetic field, the dielectric \nanomaly across T m becomes suppressed, providing unambiguous evidence of magnetoelectric \ncoupling in GFO thin films. The calcul ated magnetodielectric coefficient ( (H)- (0)/ (0)) at 0.5 \nTesla is -0.154. Interestingly, this value is nearly one or der of magnitude highe r than those observed \nin polycrystalline GFO 22. This increase in the coupling strengt h of epitaxial GFO films could arise \ndue to several reasons: epitaxial strain, constrained 2-D film geom etry, or microstructure and it \nwould be of further interest to probe the exact cause such as by carrying out thickness dependent \nstudies.  7To understand the mechanism of nanoscale ferroele ctricity in epitaxial gallium ferrite thin \nfilms, we further performed firs t-principles calculations on the ground state structure of GFO using \nGGA+U technique. Initially, we identified orthorhombic Pnna  as the possible centrosymmetric \nstructure of GFO which transf orms to noncentrosymmetric Pc2 1n (Pna2 1, according to international \ntable of crystallography) stru cture, using the calculation approaches reported earlier20, 21. Using \noptimized structures of centrosymmetric Pnna  and noncentrosymmetric Pna2 1 phase of GFO (say \nP), we constructed a second Pna2 1 cell which is a mirror image of optimized Pna2 1 (P) structure \nacross the displacement coordinate with respect to the centrosymmetric Pnna  cell. The calculations \nshow that the two polarization st ates have identical ground stat e energies, a ke y signature of \nferroelectricity in a material. A comparison between  the centrosymmetric and polar structures, as \nshown in Figure. 4  (a), shows that there is a large displace ment of Fe atoms w ith respect to other \natoms with particularly large distortion se en for Fe2-O octahedra when GFO undergoes \ntransformation to a noncentrosymmetric structure. Ou r calculations estimate that both the Fe ions in \nthe Pna2 1 structure displace by a much larger distance  along the polar direction (|u| ~ 0.22Å) in \ncomparison to the Ga ions (|u| ~ 0.13Å) upon Pnna→Pna2 1 transformation. Such a large \ndisplacement of atoms is expected to cost  a large energy and could possibly hint why  a thermally \ninduced phase transition in GFO has been elusive. Based on these displacements, the calculated spontaneous polarization of th e polar structure is 0.28 C.m\n-2 using the nominal ionic charges of the \nconstituent ions and 0.33 C m-2 using Born effective charges which are in close agreement with other \nreports.21 Our calculations also show  that the polarization contri bution from the Fe ions is \nsignificantly larger than that by the Ga ions and therefore sugge st that ferroelectricity in GFO is \nbrought about predominantly via displacement of Fe ions. \nThe calculated energy difference between centrosymmetric and noncentrosymmertic \nstructures is  0.61 eV f.u-1 for GFO using GGA+U and is in agreement with literature.21  However, \nthe magnitude of the energy barrie r is quite large in comparison to common perovskite ferroelectric  8oxides such as PbTiO 3 and PbZrO 330. The abnormally large change in the energy upon ferroelectric \nphase transition cannot be explained by the large structural distortion al one and lack of any structural \nphase transition makes it even more puzzling. Se veral temperature dependent experimental studies 10, \n33, 34 do not show any phase transiti on from non-centrosymmetric to centrosymmetric structure at \nleast until 1368 K implying that its ferroelectric T c is even higher. As a consequence, the energy \ndifference between two structures of GFO and the accompanying distortion should only be \nconsidered qualitatively. In this co ntext, our observations of saturated loops in epitaxially strained \nGFO thin film samples are suggestive of a redu ced energy barrier between centrosymmetric and \nnoncentrosymmetric structures.35 An alternative explanation for the observed discrepancy between \nthe calculated energy barrier and observed ferroel ectric switching at room temperature in GFO films \ncould be the presence of domains in these samp les as domains in ferroelectrics are known to \nsignificantly reduce the energy barrier required for switching.36, 37 Further, for sustainable \nferroelectric polarization, in ad dition to showing a double poten tial well, GFO must remain \ninsulating all along during ferroel ecrric switching i.e. from P  to P. Spin-resolved total density of \nstates calculations at every point  on the switching path, as shown in the insets of Figure. 4(b), \ndemonstrate insulating nature of the system during polarization switching.  \nAs far as mechanism of multiferroism in GFO is concerned, we now combine the reasons of \nobserved ferroelectricity and magnetism together to evolve a collective picture. Previous theoretical \nand experimental studies10, 13, 38 have conclusively shown that th e observed ferrimagnetism in GFO is \ndue to cationic site disorder where some Fe ions  occupy Ga sites. In addition, as shown in the \npreceding paragraphs, ferroelectricity also emanates  from the displacement of Fe ions from the \ncentrosymmetric structure along c-axis of GFO ( b-axis for conventional Pc2 1n symmetry). These \nobservations together suggest that the multiferroism in GFO originates from the same ionic species i.e. Fe ions, making it a unique multiferroic. Such mech anism of multiferroism is in contrast to the  9conventional perception that ferroelectricity (empty cation d-shell) and magnetism (partially filled \ncation d-shell) exclude each other.3  \nHaving shown that the same ion is responsible for magnetism and ferroelectricity in in GFO, \nwe now explore the magnetoelectric coupling in GFO (experimental evidence s hown in Fig. 3)  by \ncalculating the energy difference between ferroelec tric and paraelectric phases upon changing the \nmagnetic spin configuration. We calculated the energy barrier ( ΔE) between ferroelectric and \nparaelectric phases of GFO coexisting with different spin structures, viz. antiferromagentic spin \nordering and unpolarized spins (non-magnetic). The calculations show that the energy barrier is \nlower by 60 meV for an antiferroma gentic spin configuration, also  bolstering the fact that the \nantiferromagentic spin structure of ferroelectric pha se of GFO is more stab le. This, in conjunction \nwith previous observations of pres ence of magneto-str uctural coupling33, 38 in GFO, shows that \nferroelectric GFO possesses both magnetoelectric and magnetostructural coupling. Overall, presence \nof ferroelectricity, ferrimagnetism,  magneto-electric-structural coupl ing in GFO thin films in the \nvicinity of room temperature make GFO an ex citing material from the perspective multi-mode \ndevices such as se nsors and memories. \nIn summary, we have shown a first conclusive  experimental evidence  of nanoscale room \ntemperature ferroelectricity in epitaxial thin films of gallium ferrite along with presence of \nmagnetoelectric coupling. Intere stingly, our first-principles calculatio ns suggest that it is the Fe ions \nwhich are responsible for both ferroelect ricity as well as ferrimagnetism.  This finding is crucial as it \nestablishes GFO as a near room temperature multife rroic and as a single phase  material showing both \nferroelectric and ferrimagnetic ordering, obviating th e need of exchange bias multilayer junctions. \nThe work was partially funded by Department  of Science and technology, Govt. of India \nthrough the project SR/S2/CMP-0098/2010. Authors thank Amir Moshar (Asylum Research) for \nPFM measurements, Anurag Gupta (NPL, New Delhi, India) for magnetic measurements and DST \nNanoscience unit for XRD studies. Authors thank Dr . D. Stoeffler (IPCMS, Strasbourg) and Prof.  10J.F. Scott (Cambridge University) for fruitful discussions and SA tha nks NPL, New Delhi for \nfinancial assistance.  11References \n 1. J. F. Scott, Nat Mater 6 (4), 256-257 (2007). \n2. M. Gajek, M. Bibes, S. Fus il, K. Bouzehouane, J. Fontcubert a, A. Barthelemy and A. Fert, \nNat Mater 6 (4), 296-302 (2007). \n3. N. A. Hill, The Journal of Physical Chemistry B 104 (29), 6694-6709 (2000). \n4. D. Khomskii, Physics 2, 20 (2009). \n5. J. H. Lee, L. Fang, E. Vlahos, X. Ke, Y. W. J ung, L. F. Kourkoutis, J.-W. Kim, P. J. Ryan, T. \nHeeg, M. Roeckerath, V. Goian, M. Bernhagen, R.  Uecker, P. C. Hammel, K. M. Rabe, S. \nKamba, J. Schubert, J. W. Freelan d, D. A. Muller, C. J. Fennie,  P. Schiffer, V. Gopalan, E. \nJohnston-Halperin and D. G. Schlom, Nature 466 (7309), 954-958 (2010). \n6. S. Lee, A. Pirogov, M. Kang, K.-H. Jang, M. Yonemura, T. Kamiyama, S. W. Cheong, F. \nGozzo, N. Shin, H. Kimura, Y. Noda and J. G. Park, Nature 451 (7180), 805-808 (2008). \n7. C. J. Fennie and K. M. Rabe, Physical Review Letters 97 (26), 267602 (2006). \n8. J. H. Lee and K. M. Rabe, Physical Review Letters 104 (20), 207204 (2010). \n9. B. Lorenz, Y. Q. Wang, Y. Y. S un and C. W. Chu, Physical Review B 70 (21), 212412 \n(2004). \n10. T. Arima, D. Higashiyama, Y. Kaneko, J. P.  He, T. Goto, S. Miyasaka, T. Kimura, K. \nOikawa, T. Kamiyama, R. Kumai a nd Y. Tokura, Physical Review B 70 (6), 064426 (2004). \n11. B. F. Levine, C. H. Nowlin and R. V. Jones, Physical Review 174 (2), 571 (1968). \n12. S. C. Abrahams, J. M. Reddy and J. L. Bernstein, The Journal of Chemical Physics 42 (11), \n3957-3968 (1965). \n13. R. B. Frankel, N. A. Blum, S. Foner, A. J. Freeman and M. Schieber, Physical Review Letters \n15 (25), 958 (1965). \n14. D. L. White, Bull. Am. Phys. Soc. 5, 189 (1960). \n15. S. Mukherjee, V. Ranjan, R. Gupta and A. Garg, Solid State Communications 152 (13), \n1181-1185 (2012). \n16. S. Mukherjee, A. Garg and R. Gupta, Applied Physics Letters 100 (11), 112904-112904 \n(2012). \n17. M. Kubota, T. Arima, Y. Kaneko, J. P. He, X. Z. Yu and Y. Tokura, P hysical Review Letters \n92 (13), 137401 (2004). \n18. D. C. Kundaliya, S. B. Ogale, S. Dhar, K.  F. McDonald, E. Knoesel, T. Osedach, S. E. \nLofland, S. R. Shinde and T. Venkatesan, Journal of Magnetism and Magnetic Materials 299 \n(2), 307-311 (2006). \n19. S. C. Abrahams and J. M. Reddy, Physical Review Letters 13 (23), 688 (1964). \n20. A. Roy, S. Mukherjee, R. Gupta, S. Auluck, R. Prasad and A. Garg, Journal of Physics: \nCondensed Matter 23 (32), 325902 (2011). \n21. D. Stoeffler, Journal of Physics: Condensed Matter 24 (18), 185502 (2012). \n22. V. B. Naik and R. Mahendiran, journal article 106, 123910 (2009). \n23. A. Shireen, R. Saha, P. Mandal, A. Sundare san and C. N. R. Rao, Journal of Materials \nChemistry 21 (1), 57-59 (2011). \n24. C. Lefevre, R. H. Shin, J. H. Lee, S. H. Oh, F. Roulland, A. Thomasson, E. Autissier, C. \nMeny, W. Jo and N. Viart, Applied Physics Letters 100 (26), 262904-262904 (2012). \n25. M. Trassin, N. Viart, C. Ulhaq-Bouillet, G. Versini, S. Barre, C. Leuvrey and G. Pourroy, \njournal article 105 (10), 106101-106103 (2009). \n26. J. P. Perdew and Y. Wang, Physical Review B 45 (23), 13244-13249 (1992). \n27. G. Kresse and J. Furthmüller, Physical Review B 54 (16), 11169 (1996). \n28. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Physical \nReview B 57 (3), 1505-1509 (1998).  1229. J. P. Perdew, A. Ruzsinszky, G. b. I. Csonka, O.  A. Vydrov, G. E. Scuseria, L. A. Constantin, \nX. Zhou and K. Burke, Physical Review Letters 100 (13), 136406 (2008). \n30. M. Trassin, N. Viart, G. Versini, J. L. Loison, J. P. Vola, G. Schmerbe r, O. Cregut, S. Barre, \nG. Pourroy, J. H. Lee, W. Jo a nd C. Meny, Applied Physics Letters 91 (20), 202504-202503 \n(2007). \n31. A. Garg, Z. H. Barber, M. Dawber, J. F. Sco tt, A. Snedden and P. Lightfoot, Applied Physics \nLetters 83 (12), 2414-2416 (2003). \n32. S. K. Lee, D. Hesse and U. Gosele, journal article 100 (4) (2006). \n33. S. Mukherjee, A. Garg and R. Gupta,  Journal of Physic s: Condensed Matter 23 (44), 445403 \n(2011). \n34. S. K. Mishra, R. Mittal, R. Singh, M. Zbiri,  T. Hansen and H. Schober, journal article 113 \n(17), 174102-174105 (2013). \n35. S. P. Beckman, X. Wang, K. M. Rabe and D. Vanderbilt, Physical Review B 79 (14), 144124 \n(2009). \n36. A. M. Bratkovsky and A. P. Le vanyuk, Physical Review Letters 85 (21), 4614-4617 (2000). \n37. J. Y. Jo, D. J. Kim, Y. S. Kim, S. B. Choe , T. K. Song, J. G. Yoon and T. W. Noh, Physical \nReview Letters 97 (24), 247602 (2006). \n38. A. Roy, R. Prasad, S. Auluck and A. Garg, J. Appl. Phys. 111, 043915 (2012). \n \n \n  13 \n   \n \n \nFigure 1.   (a) -2 XRD scan showing (010) and (001) or ientations of GFO and ITO layers \ndeposited on YSZ (001) substrate.  (b) XRD -scan of {111} planes of YSZ (bottom), ITO (middle) \nand {221} planes of GFO (top) exhibiting four-f old symmetry for YSZ and ITO conducting layer \nwhile GFO showing three variant epitaxy. (c) Reci procal space map (RSM) for 200 nm GFO film on \nITO buffered YSZ substrate near the (020)  reflection of the orthorhombic phase. \n  14 \n \n \n \nFigure 2.   (a) Out of the plane PFM amplitude a nd (b) PFM phase micrographs of GFO (200 \nnm)/ITO (40 nm)/YSZ showing mosaic domain structur e. Local piezoelectric response amplitude (c) \nand phase (d) on b-axis oriented gallium ferrite thin film measured using switching spectroscopy (SS) PFM mode.    15 \n    \n \n \nFigure 3.  Real part of dielectric constant ( ′) vs. temperature plots measur ed at different frequencies \nshowing a dielectric anomaly at ~ 235 K, close to  ferri to paramagnetic transition temperature (T c). \nDielectric anomaly temperature (T m) is marked by a dash-dot  line. Top in set showing ′ vs. \ntemperature plot measured at 10 kHz in presence of different magnetic fields. It  is observed that with \nincreasing magnetic field the diel ectric anomaly vanishes. Bottom inset plots magnetization as a \nfunction of temperature clearly showi ng the magnetic transition temperature (T c). \n  16 \n \n \nFigure 4.  (a) Structural models of centrosymmetric ( Pnna ) and noncentrosymmetroic polar \nstructures ( Pna2 1) depicting the relative changes in the ionic positions, particularly for Fe-O \noctahedra, upon structural transfor mation (red spheres depict O atoms) (b) Switching path between \ntwo polar states via centrosymmet ric phase. Insets show spin-resolv ed total density of states at \ndifferent points on the transition path.  "    },    {        "title": "2012.14232v1.Structural__optical_and_magnetic_properties_of_nanostructured_Cr_substituted_Ni_Zn_spinel_ferrites_synthesized_by_a_microwave_combustion_method.pdf",        "content": "1  Structural, optical and magnetic properties of nanostructured Cr-substituted Ni-Zn spinel ferrites synthesized by a microwave combustion method Abdulaziz Abu El-Fadl1**, Azza M. Hassan1, Mohamed A. Kassem1,2, † 1 Department of Physics, Faculty of Science, Assiut University, Assiut 71516, Egypt, 2 Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan Abstract Nanoparticles of Cr3+-substituted Ni-Zn ferrites with a general formula Ni0.4Zn0.6−xCrxFe2O4 (x = 0.0 - 0.6) have been synthesized via a facile microwave combustion route. The crystalline phase has been characterized by using X-ray diffraction (XRD), transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FT-IR) and X-ray photoelectron spectroscopy (XPS) revealing the spinel ferrite structure without extra phases.  Crystallite sizes of 23 - 32 nm as estimated by XRD analyses, after corrections for crystal stains by Williamson–Hall method, are comparable to the average particle sizes observed by TEM which indicates successfully synthesized nanocrystals. Rietveld refinement analyses of the XRD patterns have inferred a monotonic decrease behavior of the lattice parameter with Cr doping in agreement with Vegard's law of solid solution series. Furthermore, cations distribution with an increased inversion factor indicate the B-site preference of Cr3+ ions. The oxidation states and cations distribution indicated by XPS results imply the Cr3+ doping on the account of Zn2+ ions and a partial reduction of Fe3+ to Fe2+ to keep the charge balance in a composition series of (Ni2+)0.4(Zn2+, Cr3+)0.6(Fe2+, Fe3+)2(O2-)4. The optical properties were explored by optical UV-Vis spectroscopy indicating allowed direct transitions with band gap energy that decreases from 3.9 eV to 3.7 eV with Cr doping. Furthermore, the photocatalytic activity for the degradation of methyl orange (MO) dye was investigated showing largely enhanced photodecomposition up to 30 % of MO dye over Ni0.4Cr0.6Fe2O4 for 6 hours. A vibrating sample magnetometry (VSM) measurements at room temperature show further enhancement in the saturation magnetization of Ni0.4Zn0.6Fe2O4 , the highest in Ni-Zn ferrites, from about 60 to 70 emu/g with the increase of Cr concentration up to x = 0.1, while the coercivity shows a general increase in the whole range of Cr doping.   Key words: Microwave combustion method, spinel ferrites, XRD, FTIR, TEM, VSM  Corresponding authors:  † M. A. Kassem, email: makassem@aun.edu.eg * A. A. El-Fadl , email:  abuelfadl@aun.edu.eg, abulfadla@yahoo.com      2   1. Introduction     Magnetic spinels, AB2O4  with A and B are divalent and/or trivalent transition metals, have attracted much interest particularly in nanosized forms because of their fascinating magnetic, optical and electrical properties with theoretical and technological values [1–5]. Among spinel compounds,  spinel ferrites (AFe2O4) have most remarkable feature of their physical and chemical properties that can also be tuned via substitutions by a divalent or a trivalent transition metal cations at the tetrahedral and octahedral sites [6–11]. A subsequent modified cation distribution after substitutions plays an important role in tailoring their magnetic and optical behavior [8]. Among various spinel ferrites, the antiferromagnetic (AF) zinc ferrite, ZnFe2O4, shows striking changes in its magnetic properties by reducing the grain size to the nanometer-sized range [12,13]. It is well known that bulk zinc ferrite is a normal spinel structure with Zn ions in the tetrahedral (A-sites) and Fe ions in the octahedral (B-sites) [14]. As Fe3+ ions form a pyrochlore networks in the cubic spinel structure, bulk Zn-ferrite has become a model to study the fundamental magnetic frustration. However, Zn-ferrite nanoparticles show ferromagnetic and superparamagnetic order [15]. On another hand, Ni ferrite is soft ferrimagnetic material which has an inverse spinel structure in bulk scale [16]. Mixed Ni-Zn ferrites nanoparticles are the subject of intensive studies [17,18], due to their relation to numerous technological applications [19]. Many researchers have been employed the divalent and trivalent metal ions substitution to upgrade the electrical, optical  and magnetic properties of  Ni-Zn ferrites nanocrystals [20–27]. The effects of replacing Fe3+ by Cr3+on the physiochemical properties of the Ni–Zn ferrite is one of the most common substitution have been reported [27–29]. It was revealed that chromium substitution modified the physical properties of spinel ferrites but does not alter the spinel structure. Furthermore, it is well known that selecting a synthesis route plays a vital role in the physical characteristics of spinel ferrites. Mixed Ni–Zn ferrites have been produced by numerous synthesis methods such as sol-gel [30], oxalate co-precipitation [31], hydrothermal technique [32]. Recently, Ni-Zn ferrites nanoparticles has been synthesized within short time by a simple and cost-effective microwave combustion method [33]. A. Abu El-Fadl et al. [10] have reported the structural and magnetic properties of Ni-Zn ferrites synthesized by microwave combustion and found that the composition Ni0.4Zn0.6Fe2O4 ferrite exhibits optimum magnetic properties. To our knowledge, no much work is done on replacing the divalent ions in spinel materials with trivalent cations, for instance, Cr3+-substitution in Ni1-yZny-xCrxFe2O4, such doping is absence from literature.  As a result, the present study focuses on the easy synthesis of Ni0.4Zn0.6 ferrite and study of their physical properties. The prepared ferrites were characterized using 3  X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR) and transmission electron microscopy (TEM) measurements. Ultraviolet–visible (UV–Vis) spectroscopy measurements are utilized to study the optical properties. The dependences of the optical energy gap, photocatalytic activity and magnetic properties on the concentration of Cr3+ ions are studied in detail. 2. Experimental techniques  2.1. Materials and synthesis Spinel ferrite nanoparticles with the composition Ni0.4Zn0.6−xCrxFe2O4, x=0.0-0.6 were prepared in a step of 0.1 using a microwave combustion route. In a stoichiometric ratio, analytical grade metal nitrates: Zn(NO3)2.6H2O, Ni (NO3)2.6H2O, Fe(NO3)3.9H2O and Cr (NO3)3.6H2O were dissolved with glycine ((NH2)2COOH) as a fuel in small amount of distilled water by a magnetic stirrer. The produced solution was introduced for 20 min into a microwave oven (Olympic electric, KOR-6Q1B) operating at maximum power of 800 W. A brown-to-black voluminous and fluffy product was produced that were ground into fine powders. 2.2. Characterization and measurements Phase identification and structural characterization of the prepared samples were carried out first by powder X-ray diffraction (XRD) using a diffractometer equipped in Bragg-Brentano geometry with an automatic divergent slit (Philips PW1710, Netherlands) uses CuKα-radiation of wavelength, l= 0.15418 nm. The particle size and their morphologies were characterized using high resolution transmission electron microscopy (HR-TEM). Further characterization by Fourier transform infrared spectroscopy was carried out in the range 400-4000 cm-1 by using FT-IR spectrophotometer (470 Shimadzu, 400-4000 cm-1) by employing the KBr pellet method. X-ray photoelectron spectroscopy (XPS) was used to study the phase structure and chemical oxidation states of the synthesized samples. Powder samples have been compressed in pellets shape with highly flat surface and the collected XPS patterns have been corrected for C 1s signal at 285 eV. UV-Visible optical absorbance spectra have been collected from a suspension of the powder samples prepared by adding 10 mg of the sample to 10 mL of a DMSO solvent using a Thermo Evolution 300 UV-Visible spectrophotometer in a wavelength range of 200 -900 nm. Photocatalytic activities for methyl orange (MO) degradation have been studied by measuring the dye UV-Visible optical absorbance spectra after different times of photodegradation. 50 mg of nanoparticles were dispersed into 200 ml of freshly prepared solution of methylene orange (~1.65 ppm). This solution was illuminated by UV irradiation source. Magnetization curves were measured at room temperature by using a Lakeshore-7400 Series vibrating sample magnetometer (VSM).   4  3. Results and discussion 3.1.X-ray diffraction and structural properties The X-ray diffraction patterns for the Ni0.4Zn0.6−xCrxFe2O4 series are shown in Fig. 1(a). The diffraction patterns exhibit a crystalline nature with all possible reflections belong to a spinel ferrite phase, indexed in the figure, without no impurity peaks were detected. The line broadening of diffraction peaks is attributed to the nanocrystalline nature and partial contribution of the internal strain. Further, the peaks show shift position to higher angles, as seen in Fig. 1(b), which indicates lattice shrinkage with increasing the Cr content.     \n Figure 1. XRD patterns of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles. We have performed Rietveld refinement to accurately estimate the structural parameters as well as the cations distribution in Ni0.4Zn0.6−xCrxFe2O4 nanoparticles using the RIETAN-FP system for pattern-fitting structure refinement [34].  Figure 2 shows the XRD Rietveld refinement results for selected samples with x = 0.0, 0.2, 0.4 and 0.6. The XRD patterns were calculated during refinements analysis by assuming the cubic 𝐹𝑑3$𝑚 spinel structure with Wyckoff sites 8a and 16d for atoms in the tetrahedral A- and octahedral B-sites with fixed coordinates (1/8, 1/8, 1/8) and (1/2, 1/2, 1/2), respectively, while the site 32e with refined O coordinates (x = y = z = u). It is well known that both Ni and Cr ions prefer the octahedral B site with large stabilization energy in structures of the inverse spinel ferrite NiFe2O4 and all normal spinel chromites, respectively, while Zn can distribute between both A and B sites in nano spinel ferrites[10,35–37].  Our 44432θ  / deg.(400)(b)Intensity (arb. unit)\n7060504030202θ  / deg.  x = 0.0 Ni0.4Zn0.6-xCrxFe2O4\n x = 0.1  x = 0.2  x = 0.3  x = 0.4 x = 0.5 x = 0.6(111)(220)(311)(222)(400)(422)(511)(440)(a)5  trials, indeed, have confirmed the best Rietveld refinement for the two end members, Ni0.4Zn0.6Fe2O4 and Ni0.4Zn0.6Fe2O4, when we consider these preferences. We have assumed the occupation of Ni and Cr ions in the octahedral B sites for the whole series XRD refinements. The lattice constant (a), oxygen position (u), occupancies of atoms (g) and peaks shape parameters such as FWHM, position, intensity, etc. and atomic displacements were refined during the Rietveld analysis. Structure parameters including lattice constant (a), oxygen position (u), X-ray density (dXRD), crystallite size (DXRD), lattice strain (ε) derived from the Rietveld analysis are summarized in Table 1.  \n Figure 2.  Rietveld analysis of XRD patterns of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles The Cr-content dependence of obtained values of a is shown in Fig. 3(a). It is noticeable from the figure that Cr incorporation decreases the lattice constant first largely from 8.428 to 8.398 Å for x = 0.0 – 0.1 then in a monotonic decrease behavior to a = 8.351 Å for x = 0.5 and finally little decreased by Zn disappearance.  The behavior of a vs x is consistent with the peaks shift in Fig. 1(b) and in a good agreement with Vegard’s law [38], indicating successful substitution. The decrease of lattice constant with increasing Cr3+ concentration is attributed to the smaller size of substituent Cr3+ ions (0.615 Å in radius) relative to the replaced Zn2+ ions (0.074 Å) in the B-site octahedral coordination [39]. The refinement also results in an oxygen position u with a decrease from 0.381 to 0.378 with Cr doping in the whole series.  500040003000200010000Intensity\n7065605550454035302520152  / deg. Rwp =  5.333        Re =  7.269    S = 0.7336    GofF =  0.5382 x = 0.0  Observedcalculated difference  Bragg reflections 2000150010005000Intensity\n7065605550454035302520152  / deg. Rwp = 10.162        Re =  11.136    S = 0.9125    GofF =  0.8327 x = 0.2 \n2000150010005000Intensity\n7065605550454035302520152  / deg. Rwp = 9.238        Re =  11.653    S = 0.7927    GofF =  0.6284 x = 0.4 2000150010005000Intensity\n7065605550454035302520152  / deg. Rwp = 9.586        Re =  12.106    S = 0.7918    GofF =  0.6270 x = 0.6(a)(b)\n(c)(d)6    Figure 3. (a) Lattice constant and inversion factor (inset) as functions of Cr content, x, and (b) W-H analysis plots for Ni0.4Zn0.6-xCrxFe2O4 nanoparticles  The average crystallite sizes D of the prepared spinel ferrites nanoparticles are estimated by using Williamson–Hall method [40]: 𝛽cos=4e\t𝑠𝑖𝑛𝜃+234\t,                      (1) Where k is a constant which depends on the shape of the particle and almost equals 0.9, l is the X-ray wavelength, b is the peak full width at half maximum (FWHM), q is the diffraction angle and e is the internal strain of the lattice. equation (1) represents a linear plot of 𝛽cos𝜃\tagainst sin𝜃 from which the internal strain (ε) and crystallite size (DXRD) can be obtained from the slope and intercept with y-axis, respectively. Figures 3(b) and (c) show the 𝛽cos𝜃\tagainst sin𝜃 plots of the synthesized compositions and the estimated ε and are presented in table 1. The obtained crystallite sizes values of the prepared nanocrystals are in the range of 23–32 nm, and slight positive strain is observed which becomes almost negligible in the lattice of  x = 0.2 and 0.5 samples. The theoretical density can be calculated by using the relation [41]\t∶𝑑9:4=;<=>?@\t,\twhere M is the molecular weight, N is Avogadro’s number, Z is the number of atoms per unit cell and a is the lattice constant. The calculated values of the X-ray density are given in table 1. The X–ray density increases with increasing concentration of Cr up to x ≃ 0.1 and then it starts to 8.448.428.408.388.368.34Lattice constant, a  (Å)\n0.60.50.40.30.20.10.0x  (in Ni0.4Zn0.6-xCrxFe2O4)(a)1.00.90.80.70.6Inversion factor, δ 0.60.40.20.0x 0.00700.00650.00600.0055β cos (θ)x = 0.0x = 0.1x = 0.5x = 0.2(b)\n0.00650.00600.0055β cos (θ)0.600.500.400.30 sin (θ)x = 0.6x = 0.4x = 0.3(c)\nq7  decrease with further Cr incorporation. This behavior can be explained by the competitive decrease in both M and a values with increasing Cr content. Since the lattice constant is drastically decreased with low Cr doping level and then slightly with further doping as seen in Fig. 3(a) while M decreases monotonically, thereby, the ratio (M/a3) shows fluctuation behavior with Cr3+ substitution. Table 1: Structural parameters of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles based on XRD analyses (Rietveld and Williamson–Hall) and TEM microscopy. x a (Å) u ε [± 0.0001] DXRD [± 2] (nm) DTEM [± 5] (nm) dXRD (g/cm3) 0 8.428 0.3805 0.00095 27.0  5.2895 0.1 8.398 0.3795 0.00068 29.2  5.3169 0.2 8.386 0.3799 0.00020 24.1 26  5.3106 0.3 8.378 0.3798 0.00095 32.1  5.2950 0.4 8.362 0.3788 0.00061 26.3 23.20 5.2946 0.5 8.351 0.3779 0.00010 23.0  5.2849 0.6 8.351 0.3776  0.00120 32.6 33.40 5.2553  The cations distribution estimated from XRD analysis is dependent on the Cr content indicated by the inversion factor, δ, that increases with x as shown in the inset of Fig. 3(a). The observed non-monotonic behavior of δ showing a kink at x = 0.3 implies sites preferences. The first relatively slow increase in the inversion of Ni0.4Zn0.6Fe2O4 from 0.62 with Cr doping is explained by Cr3+ substitution for Zn2+ in the B site with movement of both Zn2+ ions and Fe3+ ions from the B site to the A site until  all Zn2+ ions become in the A site at around x = 0.3. For further substitution levels, x > 0.3, Cr3+ still prefers the B site resulting in movement of Fe3+  ions to the A site resulting in higher inversion of the spinel structure. The detailed results of cations distribution and atomic positions in the unit cell are presented in table 2. 3.2.Transmission Electron Microscopy (TEM)  TEM imaging has been reemployed to visualize the shape, size and morphology of the synthesized spinel ferrites. Figure 4 shows TEM micrographs of Ni0.4Zn0.6−xCrxFe2O4 nanoparticles with selected compositions of x = 0.4 and 0.6. The particles are mostly having octahedral as well as cubic shapes reflecting the high high-quality nonocrystals. The particles size varies in the range 5-50 nm and its distribution is shown in the insets of Figs. 3 with averages of 23 to 33 nm matching or slightly greater than the estimated values form XRD patterns. It is also observed that, the 8  particles are agglomerated to some extent due to the fast reaction of the microwave combustion method and due the evolution of large amount of gases during reaction.  \n Figure 4. TEM images for Ni0.4Zn0.6-xCrxFe2O4 nanoparticles with the Cr-contents of (a) x = 0.4 and (b) x = 0.6   Table 2: Cations distributions of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles by XRD Rietveld analysis.  cations distribution Rietveld parameters x (Cr3+) Site (Wyckoff) x = y = z Occupancy δ S GofF 0 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.381Zn + 0.619Fe 0.219Zn + 0.4Ni + 1.38Fe 4O 0.619 0.734 0.538 0.1 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.361Zn + 0.639Fe 0.139Zn + 0.4Ni + 0.1Cr + 1.361Fe 4O 0.639 0.651 0.424 0.2 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.324Zn + 0.676Fe 0.076Zn + 0.4Ni + 0.2Cr + 1.324Fe 4O 0.676 0.913 0.833 0.3 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.295Zn + 0.705Fe 0.005Zn + 0.4 Ni + 0.3Cr + 1.295Fe 4O 0.705 0.942 0.888 0.4 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.198Zn + 0.802Fe 0.002Zn + 0.4 Ni + 0.4Cr + 1.198Fe 4O 0.802 0.782 0.612 0.5 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.098Zn + 0.902Fe 0.002Zn + 0.4 Ni + 0.5Cr + 1.098Fe 4O 0.902 1.087 1.18 0.6 AIV (8a) BVI (16d) O (32e) 0.125 0.5 0.3805 0.0169Ni + 0.983Fe 0.383 Ni + 0.6Cr + 1.017Fe 4O 0.983 0.7918 0.627 \n1520253035051015202530Frequency (Hz) x=0.4\nParticle size (nm)\n1020304050607080010203040Frequency (Hz) x=0.6\nParticle size (nm)(a)(b)9   Moreover; this agglomeration behavior can be raised due to the permanent magnetic character of the present nanoferrite crystals. It is noticeable from the images that the degree of agglomeration between particles decreases with increasing Cr content, which can be attributed to the decrease in the net magnetic moment with further increase of Cr concentration. 3.1. X-ray photoelectron spectroscopy As we have substituted with a trivalent ions Cr3+ for a divalent Zn2+, a partial reduction of some ionic species while the synthesis is expected to keep the charge neutrality. We have employed the XPS spectroscopy to investigate for the oxidation states and further  for the cations distribution. Figure 5(a) shows a survey XPS scan for pellets samples with x = 0.1, 0.3 and 0.5, from which the core photoionization signals of metals Zn 2p, Ni 2p, Fe 2p, Cr 2p, oxygen O 1s and hydrocarbon  C 1s as well as and Auger signals of O KLL, Fe LMM, Ni LMM and Cr LMM are clearly displayed[42]. To investigate for the oxidation states, relative intensities and cations distributions, narrow scans have been collected over sufficiently long time for the Zn 2p, Ni 2p, Fe 2p, Cr 2p signals shown in Figs. 5(b-e). For x = 0.1, the peaks binding-energy positions at 1021.8 and 1036.5 eV are corresponding to the Zn 2p3/2 and its shake-up satellite while the weaker peak at 1033.8 eV is for Zn 2p1/2 signal. The assignment of other metal core signals are as follows, Ni 2p3/2 (855.4 eV) and its satellite (861.8 eV),  Ni 2p1/2 (873 eV) and its satellite (880.3 eV); Fe 2p3/2 (711.4 eV) and its satellite (719.3 eV) , Fe 2p1/2 (725 eV) and its satellite (733.9 eV); Cr 2p3/2 (576.8 eV) and Cr 2p1/2 (586.8 eV) with hardly observed satellites. The most important confirmation result of XPS spectra is the gradual increase in the Cr content on the account of Zn rather than Fe nor Ni content clearly seen in figures change behavior of the signals intensity and shape.  All peaks show slight position shift by Cr doping with almost unchanged peaks intensities for Fe 2p and Ni 2p peaks, Figs. 5(b) and (e), while gradual intensity decrease of Zn 2P and increase of Cr 2p peaks are observed, Figs. 5(c) and (d), with Fe to (Ni+Zn+Cr) relative atomic ratio of about 2. The peaks assignment indicated the most stable oxidation state of Zn2+, Ni2+ and Cr3+ and dominant Fe3+. To elucidate the cations distribution and Fe valance states, the deconvolution of the Fe 2p peaks, including only Fe 2p3/2 satellite for simple Shirley background shape, confirmed the presence of Fe ions in the two lattice sites, tetrahedral (A) and octahedral (B) sites, shown in Fig. 5(f) for x = 0.3. The low binding-energy Fe 2p3/2(2p1/2) sub-peaks centered around 710.25 (723.64) eV are assigned to the Fe2+ at B site while the sub-peaks centered around 711.3 (724.8) eV and 712.96 (727.12) eV are assigned to Fe3+ ions at B and A sites, respectively[43]. The partial reduction of Fe3+ to Fe2+ is expected to occur while this microwave synthesis during quick reaction to compensate for the charge unbalance caused by Cr3+ ions as previously observed in hexaferrite synthesis at high temperatures. The inversion factor, 10  δ, values estimated as the ratio of Fe3+(A-site) relative to the total Fe content match values obtained by Rietveld analysis of the XRD data and are aslo shown in the inset of Fig. 3(a). \n \n Figure 5. XPS spectra of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles: (a) survey scans for x = 0.1, 0.3 and 0.5, (b) – (e) long-time measured patterns of transition metal 2p bands and (f) an example of the Fe-2p band analysis.  Intensity (arb. unit)10008006004002000Binding Enrgy (eV)Ni0.4Zn0.6-xCrxFe2O4\n0.10.30.5Fe2p3/2Zn2p1/2\nFe2p1/2Ni2p3/2Ni2p1/2\nO1sZn LMMCr2p3/2Cr2p1/2\nC1sFe LMM\nFe/Ni 3pFe/Ni 3sO 2sNi LMM\nMg-Kα sourceO KLLx =Zn2p3/2(a)\n880870860850Binding Enrgy (eV)x =0.10.3\n2p3/22p1/2\n0.5Ni-2p3/2 satallite(b)\n590580570Binding Enrgy (eV)x =0.10.3\n2p3/22p1/20.5Cr-2p(d)Intensity (arb. unit)1050104010301020Binding Enrgy (eV)x =0.10.32p3/22p1/2\n0.5Zn-2p3/2 satallite(c)\n730720710Binding Enrgy (eV)x =0.10.3\n2p3/22p1/20.5Fe-2p2p3/2 satallite(e)2p1/2 satallite\n730720710Binding Enrgy (eV)x = 0.3Fe-2p(f)Fe2+ (Oct.)Fe3+ (Oct.)Fe3+ (Tet.)\n2p3/22p1/2sat.11  3.2.Fourier Transform Infrared Spectroscopy (FTIR) Analysis The FTIR spectra of Ni0.4Zn0.6−xCrxFe2O4 nanoparticles were measured in the frequency range 400 – 4000 cm-1 and are shown in Fig. 6(a) below about 1300 cm-1 for clarity. The spectra indicate the two characteristic absorption bands of spinel ferrites as reported by Waldron [44]. One band is completely observed at 565-583 cm-1 while the onset of the other one which occure just below 400 cm-1, lower limit of our measurements[9]. The high frequency band occurs at n1 in the range 565 - 583 cm-1 is related to the anti-symmetric stretching vibrations of the oxygen bond to metal ions in the A site, (Me-O)Teth, and the lower frequency band, n2, is about 360 cm-1 is assigned to anti-symmetric stretching vibration of (Me-O)Octh bonds in B site[9]. This is because the octahedral site bond length is greater than that in the tetrahedral site and it is well known that the frequency band is inversely proportional to the bond length [45]. The n1 band frequency values are presented in table 3. The value of n1 shows an augment trend with increasing Cr content, which could be related to the substitution of relatively lighter Cr ions for Zn  ions. It is well known that Cr ions have strong preference to occupy octahedral sites which also suggest the migration of some Fe ions to the tetrahedral sites [46,47].   3.3.Optical properties  The optical properties of Ni0.4Zn0.6−xCrxFe2O4 nanocrystals were investigated by UV-Visible spectrophotometry and the UV–Vis absorbance spectra are shown in Fig.6(b). The spectra show that the absorption edge is slightly shifted towards higher wavelength with increasing Cr concentration. The optical band gap Eg can be estimated from the optical absorption spectra by using  the well-known Tauc's relation [48]: 𝛼ℎ𝜈=𝛽Eℎ𝜈−𝐸HIJ,                    (4)                                                      Where 𝛼  is the absorption coefficient,n is the frequency of the incident light, h is Plank's constant and n is a constant whose value determines the type of the electron transition. It can take the values 1/2, 2, 3, 3/2 for transition desired direct and indirect allowed transition, indirect forbidden and direct forbidden, respectively. Figs. 6(c) and (d) depicts the Tauc's plots of Ni0.4Zn0.6−xCrxFe2O4 nanocrystals at various substitution levels by Cr ions for direct allowed transitions. The intercept of the straight line on the (hν) axis corresponds to the direct allowed optical band gaps and estimated values are given in table 3. It is clearly shown from the table that the optical band gap of the synthesized nanoparticles are monotonically decreased from 3.9 eV to 3.78 eV with incorporating Cr ions by x from 0.1 to 0.6. The decrease in Eg value with Cr ions doping is possibly a result of  sub-band-gap energy levels formation [49]. Other factors 12  such as  crystallite size, lattice constant, agglomeration and lattice defects may have some effects on the  Eg [50,51]. However, the fine size effects are excluded due to the   absence of change trends in the crystallite size, see table 1. \n Figure 6: (a) FTIR- and (b) UV-visible absorbance spectra of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles. (c) Tauc's plots of direct allowed transition and (d) the Cr-content dependence of the estimated direct energy gap, Eg.   \n   12001000800600400x=0.1x=0.2x=0.3x=0.4x=0.5\n(O-M)oct.(O-M) tet.\nWavenumber (cm-1)Transmittence %x=0.6(a)\nAbsorbance (arb. Unit)800700600500400300Wave length (nm)  x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.6Ni0.4Zn0.6-xCrxFe2O4 (b)\n350300250200150100500(αhν)2 (a. u.)2\n4.24.03.83.63.43.23.0hν (eV)  x = 0.1  x = 0.2  x = 0.3  x = 0.4  x = 0.6 (c)3.953.903.853.80Eg (eV) 0.60.50.40.30.20.10.0xNi0.4Zn0.6-xCrxFe2O4 (d)\nTable 3. The observed optical energy gap values and FT-IR band frequencies of Ni0.4Zn0.6−xCrxFe2O4 nanocrystals. Cr-content (x) Eg (eV)   n1 (cm-1) 0.1 3.90  565 0.2 3.86  570 0.3 3.85  572 0.4 3.83  578 0.5 -  579 0.6 3.78  580 13  3.4.  Photocatalytic dye degradation studies The photocatalytic activity of the synthesized Ni0.4Zn0.6−xCrxFe2O4 nanoparticles is evaluated for some selected compositions (x=0.0, 0.2, 0.4 and 0.6) for the degradation of methyl orange (MO) dye. Figure 7 shows the UV-visible absorbance spectra of MO dye degradation within the time interval of 0–360 min. It noticeable from the spectra figures that the maximum absorbance intensity, which is centered at 463 nm, decreases with increasing irradiation time in the presence of Ni0.4Zn0.6−xCrxFe2O4 photo-catalyst with irradiation by UV-visible light. Fig. 8(a) shows the photo degradation ratio of MO by Ni0.4Zn0.6−xCrxFe2O4 photocatalyst as function of the irradiation time. It is observed that the photocatalytic degradation efficiency was enhanced with increasing the  \n Figure 7. Variation of absorption spectra of orange I in presence of Ni0.4Zn0.6-xCrxFe2O4 nanoparticles under UV-visible light source.  concentration of Cr ions. This can be attributed to the observed decrease of the band gap energy from 3.89 eV to 3.78 eV. The percentage of dye removal shown in Fig. 8(b) was calculated using the following equation: 𝐸=KLMNKL\t%, where C0 and C represent the initial and final concentrations of the dye solution, respectively. From Fig. 8, it is observed that the highest value of photocatalytic activity, about 32 % after irradiation time of 6 hours, is achieved by the sample with Ni0.4Cr0.6Fe2O4 composition. The low activity in MO-dye degradation over the present nanoparticles in relatively to the reported data for ZnFe2-xCrxO4 nanoparticles can be explained by the main  dependence 3504004505005502x=0.0 0.0  0.5  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  6.0 Absorbance (a.u.)wavelength (nm)Time (h) \n3504004505005502x=0.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Absorbance (a.u.)wavelength (nm)Time (h)\n3504004505005501234x=0.4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Absorbance (a.u.)wavelength (nm)Time (h)\n350400450500550 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Wavelength (nm)x=0.6Absorbance (a.u.) Time (h)14  of the photocatalytic effect on the band gap, as lower band gap in which the interaction of light with the material generates electron–hole pairs increases the photocatalytic activity. Other factors such as the particle size and porosity and hence surface area have high impact on the nanoparticles photocatalytic effect [52]. \n Figure 8. (a) relative concentrations (b) removal ration of MO dye over Ni0.4Zn0.6-xCrxFe2O4 nanoparticles  3.5. Magnetic studies  Figure 9(a) shows the magnetic hysteresis loops (M-H curves) for Ni0.4Zn0.6−xCrxFe2O4 nanocrystals measured at room temperature. It is clear from the figure that all samples exhibit a clear behavior of soft ferrimagnetic materials. The magnetic parameters such as saturation magnetization (Ms), remnant magnetization (Mr), coercivity (Hc) and anisotropy constant (𝑘=\tQR<ST.VW) values are listed in table 4. Figure 9(b) shows the variation of Ms and Hc with the Cr-content. It is noticeable from the figure that the saturation magnetization Ms  increases with adding Cr ions up to x = 0.1- 0.2 and then it decreases with further incorporation of Cr ions with (x > 0.2). The initial observed increase of the magnetization from 59.92 emu/g to 67.21 emu/g with addition of small amount of Cr3+ can be discussed in terms of the cations redistribution between both A and B sites after Cr incorporation as well as the magnetic character of the constituent cations on both sites. It is well known that Cr and Ni ions have strong 012345665707580859095100C/C0 %Time (h) x=0.0 x=0.2 x=0.4 x=0.6\n0123456051015202530 x=0.0 x=0.2 x=0.4 x=0.6Dye removal (E%)Irradiation time (h)(a)\n(b)15  preference to occupy the octahedral site [53], thereby, the magnetic Cr3+ ions (3 μB) first replaces the nonmagnetic Zn2+ ions  (0 μB) at B-site. Hence, the net magnetic moment is increased in according to the Néel’s ferrimagnetic theory; the net magnetic moment can be represented as μs = μ(B) - μ(A), where μ(B) and μ(A)are the magnetization of B and A sites, respectively[54,55].  The value of μ(B) and hence μs become maximum when all Zn ions are moved to the A site at x = 0.2. At higher concentrations of Cr ions as a substituent of Zn ions the Ms and Mr values are decreased due to the decreased μ(B) with moving more Fe3+ ions (5 μB) to the A site and replaced by Cr3+ (3 μB)and the emergent Fe2+ ions (4 μB). the magnetization results are in agreement with the cations distribution estimated based on XRD and XPS analyses. Similar behavior of Ms was observed by Rostami and Majles et al. [56] As Mg+2 ions are substituted by Cu+2 ions in Mg0.6Ni0.4Fe2O4. Also Li et al. [57] have found that saturation magnetization of Ni0.5-xZn0.5CrxCo0.1Fe1.9O4 increased with the increase of Cr substitution when x < 0.05, and then decreased when x > 0.05. The coercivity exhibit a general modified trend with increasing Cr content which is mainly could be related to the higher magnetocrystalline anisotropy of Cr in compared to Zn and Fe ions and the variation of crystallite size of the synthesized nanocrystals [58]. \n Figure 9: (a) Room temperature hysteresis loops and (b) variation of magnetic parameters Ms and Hc with the Cr content in Ni0.4Zn0.6-xCrxFe2O4 nanoparticles.  \n  -20-15-10-505101520-60-40-200204060Moment/Mass(emu/g)Field (kG) x=0.1 x=0.2 x=0.3 x=0.4 x=0.5 x=0.6\n-0.2-0.10.00.10.2-20020 x=0.1 x=0.2 x=0.3 x=0.4 x=0.5 x=0.6Moment/Mass(emu/g)\n(a)(b)\nTable 4: Magnetic parameters of  Ni0.4Zn0.6-xCrxFe2O4 nanoparticles   x [Cr3+] Ms (emu/g) Hc  (Oe) Mr  (emu/g) K (ergs/cm2) Hk (Oe) Μ (μB) R 0.0 59.92 44.32 6.43 2709 90 2.55 107 0.1 67.21 57.08 9.05 3915 116 2.85 134 0.2 64.75 90.22 13.91 5960 184 2.73 214 0.3 58.16 79.69 12.92 4729 162 2.44 222 0.4 51.50 78.32 10.53 4116 159 2.14 204 0.5 40.53 86.77 8.84 3589 177 1.68 218 0.6 32.75 97.89 9.47 3272 199 1.35 289 16   4. Conclusion Microwave combustion process was successfully used to fabricate Ni0.4Zn0.6−xCrxFe2O4 nanoparticles. XRD and FT-IR clearly exhibited the formation of single-phase spinel ferrite. The lattice parameters decreased with increasing Cr ion content owing to its smaller ionic radius in compared to Zn ion the octahedral coordination. The crystallite size varied from 20 nm to 30 nm. XPS analysis implies that the Cr3+ doping is on the account of Zn2+ ions and a partial reduction of Fe3+ to Fe2+ occurs which explains the charge balance after Cr3+ doping. Cations distribution that explains the observed magnetic properties have been revealed by XRD-Rietveld and XPS analyses. UV–visible studies show that Cr ion doping caused significant decrease in the optical band gaps Eg, which is attributed to the formation of sub-levels among the energy band gaps. As a result, it was observed that photo catalytic activity of Ni0.4Zn0.6−xCrxFe2O4 nanoparticles or the degradation of MO is enhanced with increasing Cr ions substitutions. Magnetization measurement indicated that the saturation magnetization increased with the increase of Cr content up to about x = 0.2 and then it decreased with further Cr-doping, while the coercivity increases monotonically with Cr-doping.  Acknowledgement  Authors would like to acknowledge the help of Mr. Y Sonobayashi, from the Department of Materials Science and Engineering, Kyoto University, with measurements and great discussion of the XPS data.    17  References   [1] A.-H. Lu, E.L. Salabas, F. Schüth, Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application, Angew. Chemie Int. Ed. 46 (2007) 1222–1244. doi:10.1002/anie.200602866. [2] Q. Zhao, Z. Yan, C. Chen, J. Chen, Spinels: Controlled Preparation, Oxygen Reduction/Evolution Reaction Application, and beyond, Chem. Rev. 117 (2017) 10121–10211. doi:10.1021/acs.chemrev.7b00051. [3] S. Gubbala, H. Nathani, K. Koizol, R.D.K. Misra, Magnetic properties of nanocrystalline Ni-Zn, Zn-Mn, and Ni-Mn ferrites synthesized by reverse micelle technique, Phys. B Condens. Matter. 348 (2004) 317–328. doi:10.1016/j.physb.2003.12.017. [4] M.A. Kassem, A. Abu El-Fadl, A.M. Nashaat, H. Nakamura, Structure, optical and varying magnetic properties of insulating MCr2O4 (M= Co, Zn, Mg and Cd) nanospinels, J. Alloys Compd. 790 (2019) 853–862. doi:10.1016/J.JALLCOM.2019.03.189. [5] V.S. Kirankumar, S. Sumathi, A review on photodegradation of organic pollutants using spinel oxide, Mater. Today Chem. 18 (2020) 100355. doi:10.1016/j.mtchem.2020.100355. [6] W.A. Bayoumy, M.A. Gabal, Synthesis characterization and magnetic properties of Cr-substituted NiCuZn nanocrystalline ferrite, J. Alloys Compd. 506 (2010) 205–209. doi:10.1016/j.jallcom.2010.06.178. [7] A.A. El-Fadl, A.M. Hassan, M.A. Kassem, Structural and spectroscopic studies of nanocrystalline Ni1-xMgxFe2O4 ferrites synthesized by a microwave-assisted combustion route, Phys. Scr. 95 (2020) 055813. doi:10.1088/1402-4896/ab7a39. [8] M.M. Haque, M. Huq, M.A. Hakim, Densification , magnetic and dielectric behaviour of Cu-substituted Mg – Zn ferrites, 112 (2008) 580–586. doi:10.1016/j.matchemphys.2008.05.097. [9] T. Tatarchuk, M. Bououdina, W. Macyk, O. Shyichuk, N. Paliychuk, I. Yaremiy, B. Al-Najar, M. Pacia, Structural, Optical, and Magnetic Properties of Zn-Doped CoFe2O4 Nanoparticles, Nanoscale Res. Lett. 12 (2017) 141. doi:10.1186/s11671-017-1899-x. [10] A. Abu El-Fadl, A.M. Hassan, M.H. Mahmoud, T. Tatarchuk, I.P. Yaremiy, A.M. Gismelssed, M.A. Ahmed, Synthesis and magnetic properties of spinel Zn1−xNixFe2O4 (0.0 ≤ x ≤ 1.0) nanoparticles synthesized by microwave combustion method, J. Magn. Magn. Mater. 471 (2019) 192–199. doi:10.1016/j.jmmm.2018.09.074. [11] T.R. Tatarchuk, M. Bououdina, N.D. Paliychuk, I.P. Yaremiy, V. V. Moklyak, Structural characterization and antistructure modeling of cobalt-substituted zinc ferrites, J. Alloys Compd. 694 (2017) 777–791. doi:10.1016/j.jallcom.2016.10.067. [12] J. Job, A.B. Shinde, P.S.R. Krishna, N. Kalarikkal, ¨ ssbauer studies in Temperature dependent neutron diffraction and Mo zinc ferrite nanoparticles, Mater. Res. Bull. 48 (2013) 1506–1511. doi:10.1016/j.materresbull.2012.12.058. [13] L.D. Tung, V. Kolesnichenko, G. Caruntu, D. Caruntu, Y. Remond, V.O. Golub, C.J.O. Connor, L. Spinu, Annealing effects on the magnetic properties of nanocrystalline zinc ferrite, 319 (2002) 116–121. [14] M.K. Roy, H.C.Ã. Verma, Magnetization anomalies of nanosize zinc ferrite particles prepared using electrodeposition, 306 (2006) 98–102. 18  doi:10.1016/j.jmmm.2006.02.229. [15] J.F. Hochepied, P. Bonville, M.P. Pileni, Nonstoichiometric Zinc Ferrite Nanocrystals: Syntheses and Unusual Magnetic Properties, J. Phys. Chem. B. 104 (2000) 905–912. doi:10.1021/jp991626i. [16] C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, Mixed spinel structure in nanocrystalline NiFe 2 O 4, 63 (2001) 2–7. doi:10.1103/PhysRevB.63.184108. [17] Y. Fu, K. Pan, C. Lin, ferrite powders and their characterizations, 57 (2002) 291–296. [18] D. Ravinder, K.V. Kumar, P. Balaya, High-frequency dielectric behaviour of gadolinium substituted Ni – Zn ferrites, (2001) 210–214. [19] T. Slatineanu, A. Raluca, M. Nicolae, O. Florin, V. Gafton, L. Leontie, Synthesis and characterization of nanocrystalline Zn ferrites substituted with Ni, Mater. Res. Bull. 46 (2011) 1455–1460. doi:10.1016/j.materresbull.2011.05.002. [20] J. Chand, S. Verma, M. Singh, Structural , magnetic and Mössbauer spectral studies of Sm3+ ions doped Mg ferrites synthesized by solid state reaction technique, J. Alloys Compd. 552 (2013) 264–268. doi:10.1016/j.jallcom.2012.10.041. [21] M. Ajmal, M.U. Islam, G.A. Ashraf, M.A. Nazir, M.I. Ghouri, The influence of Ga doping on structural magnetic and dielectric properties of NiCr0.2Fe1.8O4 spinel ferrite, Phys. B Condens. Matter. 526 (2017) 149–154. doi:10.1016/j.physb.2017.05.044. [22] N. Sanpo, C.C. Berndt, C. Wen, J. Wang, Transition metal-substituted cobalt ferrite nanoparticles for biomedical applications, Acta Biomater. 9 (2013) 5830–5837. doi:10.1016/j.actbio.2012.10.037. [23] H. Javed, F. Iqbal, P. Olaleye, M. Azhar, Structural , electrical and magnetic parameters evaluation of nanocrystalline rare earth Nd3+ -substituted nickel-zinc spinel ferrite particles, Ceram. Int. 45 (2019) 11125–11130. doi:10.1016/j.ceramint.2019.02.176. [24] K.V. Babu, G. Satyanarayana, B. Sailaja, G.V.S. Kumar, K. Jalaiah, M. Ravi, Results in Physics Structural and magnetic properties of Ni0 . 8 M0.2Fe2O4 ( M = Cu , Co ) nano-crystalline ferrites, Results Phys. 9 (2018) 55–62. doi:10.1016/j.rinp.2018.01.048. [25] H. Sartaj, R. Ali, F. Shah, B. Ismail, J. Nisar, Improved electrical , dielectric and magnetic properties of Al-Sm co-doped NiFe2O4 spinel ferrites nanoparticles, Mater. Sci. Eng. B. 243 (2019) 47–53. doi:10.1016/j.mseb.2019.03.021. [26] K.V. Kumar, D. Paramesh, P.V. Reddy, Effect of Aluminium Doping on Structural and Magnetic Properties of Ni-Zn Ferrite Nanoparticles, (2015) 68–77. [27] A.M. El-Sayed, Electrical conductivity of nickel -zinc and Cr substituted nickel-zinc ferrites, Mater. Chem. Phys. 82 (2003) 583–587. doi:10.1016/S0254-0584(03)00319-5. [28] M. Ashtar, A. Munir, M. Anis-ur-rehman, A. Maqsood, Effect of chromium substitution on the dielectric properties of mixed Ni-Zn ferrite prepared by WOWS sol – gel technique, Mater. Res. Bull. 79 (2016) 14–21. doi:10.1016/j.materresbull.2016.02.044. [29] M.A. Gabal, W.A. Bayoumy, A. Saeed, Y.M. Al Angari, Structural and electromagnetic characterization of Cr-substituted Ni – Zn ferrites synthesized via Egg-white route, J. Mol. Struct. 1097 (2015) 45–51. 19  doi:10.1016/j.molstruc.2015.04.032. [30] J. Azadmanjiri, Structural and electromagnetic properties of Ni – Zn ferrites prepared by sol – gel combustion method, 109 (2008) 109–112. doi:10.1016/j.matchemphys.2007.11.001. [31] T.J. Shinde, A.B. Gadkari, P.N. Vasambekar, DC resistivity of Ni – Zn ferrites prepared by oxalate precipitation method, 111 (2008) 87–91. doi:10.1016/j.matchemphys.2008.03.028. [32] C. Upadhyay, D. Mishra, H.C. Verma, S. Anand, R.P. Das, Effect of preparation conditions on formation of nanophase Ni – Zn ferrites through hydrothermal technique, 260 (2003) 188–194. [33] M. Sertkol, Y. Köseoǧlu, A. Baykal, H. Kavas, A. Bozkurt, M.S. Toprak, Microwave synthesis and characterization of Zn-doped nickel ferrite nanoparticles, J. Alloys Compd. 486 (2009) 325–329. doi:10.1016/j.jallcom.2009.06.128. [34] F. Izumi, K. Momma, K. Izumi, F.; Momma, Three-Dimensional Visualization in Powder Diffraction, Solid State Phenom. 130 (2007) 15–20. doi:10.4028/www.scientific.net/SSP.130.15. [35] D. Carta, M.F. Casula, A. Falqui, D. Loche, G. Mountjoy, C. Sangregorio, A. Corrias, A Structural and magnetic investigation of the inversion degree in ferrite nanocrystals mfe2o4 (M = Mn, Co, Ni), J. Phys. Chem. C. 113 (2009) 8606–8615. doi:10.1021/jp901077c. [36] C. Suchomski, C. Reitz, K. Brezesinski, C. Tavares De Sousa, M. Rohnke, K.I. Iimura, J.P. Esteves De Araujo, T. Brezesinski, Structural, optical, and magnetic properties of highly ordered mesoporous MCr2O4and MCr2- xFexO4(M = Co, Zn) spinel thin films with uniform 15 nm diameter pores and tunable nanocrystalline domain sizes, Chem. Mater. 24 (2012) 155–165. doi:10.1021/cm2026043. [37] M.A. Kassem, A. Abu El-Fadl, A.M. Nashaat, H. Nakamura, Structure, optical and varying magnetic properties of insulating MCr2O4 (M= Co, Zn, Mg and Cd) nanospinels, J. Alloys Compd. 790 (2019) 853–862. doi:10.1016/j.jallcom.2019.03.189. [38] L. Vegard, Die Konstitution der Mischkristalle und die Raumfüllung der Atome, Zeitschrift Für Phys. 5 (1921) 17–26. doi:10.1007/BF01349680. [39] R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Crystallogr. Sect. A. 32 (1976) 751–767. doi:10.1107/S0567739476001551. [40] G.K. Williamson, W.H. Hall, X-ray line broadening from filed aluminum and wolfram, Acta Metall. 1 (1953) 22. doi:10.1016/0001-6160(53)90006-6. [41] A.K. Zak, M.E. Abrishami, W.H.A. Majid, R. Yousefi, S.M. Hosseini, Effects of annealing temperature on some structural and optical properties of ZnO nanoparticles prepared by a modified sol-gel combustion method, Ceram. Int. 37 (2011) 393–398. doi:10.1016/j.ceramint.2010.08.017. [42] K.D. Moulder, J F; Stickle, W S, Sobol, P E, Bomben, X-ray photoelectron spectroscopy (XPS), Perkin-Elmer Coporation, Minnesota, 2005. doi:10.1002/0470014229.ch22. [43] D. Wilson, M.A. Langell, XPS analysis of oleylamine/ oleic acid capped Fe 3 O 4 nanoparticles as a function of temperature, Appl. Surf. Sci. 303 (2014) 6–13. doi:10.1016/j.apsusc.2014.02.006. [44] R.D. Waldron, Infrared Spectra of Ferrites, 99 (1955). [45] M.H. Abdellatif, A.A. Azab, M. Salerno, E ff ect of rare earth doping on the 20  vibrational spectra of spinel Mn-Cr ferrite, Mater. Res. Bull. 97 (2018) 260–264. doi:10.1016/j.materresbull.2017.09.012. [46] S.F. Mansour, M.A. Abdo, F.L. Kzar, Effect of Cr dopant on the structural , magnetic and dielectric properties of Cu-Zn nanoferrites, J. Magn. Magn. Mater. 465 (2018) 176–185. doi:10.1016/j.jmmm.2018.05.104. [47] A. Lassoued, M. Saber, L. Brahim, D. Salah, A. Abdellatif, Photocatalytic degradation of methyl orange dye by - NiFe 2 O 4 nanoparticles under visible irradiation: effect of varying the synthesis temperature, J. Mater. Sci. Mater. Electron. 29 (2018) 7057–7067. doi:10.1007/s10854-018-8693-0. [48] Y.B. Kannan, R. Saravanan, N. Srinivasan, I. Ismail, Sintering effect on structural, magnetic and optical properties of Ni0.5Zn0. 5Fe2O4 ferrite nano particles, J. Magn. Magn. Mater. 423 (2017) 217–225. doi:10.1016/j.jmmm.2016.09.038. [49] A.A. Al-ghamdi, F.S. Al-hazmi, L.S. Memesh, F.S. Shokr, M. Bronstein, E ff ect of mechanochemical synthesis on the structure , magnetic and optical behavior of Ni 1 − x Zn x Fe 2 O 4 spinel ferrites, 43 (2017) 6192–6200. doi:10.1016/j.ceramint.2017.02.017. [50] M.A. Almessiere, Y. Slimani, M. Sertkol, M. Nawaz, A. Baykal, I. Ercan, The impact of Zr substituted Sr hexaferrite: Investigation on structure, optic and magnetic properties, Results Phys. 13 (2019) 102244. doi:10.1016/j.rinp.2019.102244. [51] B.S. Holinsworth, D. Mazumdar, H. Sims, Q. Sun, M.K. Yurtisigi, S.K. Sarker, A. Gupta, W.H. Butler, Chemical tuning of the optical band gap in spinel ferrites: CoFe2O4 vs NiFe2O4 Chemical tuning of the optical band gap in spinel ferrites: CoFe 2 O 4 vs, 082406 (2014) 2011–2015. doi:10.1063/1.4818315. [52] L. Han, X. Zhou, L. Wan, Y. Deng, S. Zhan, Journal of Environmental Chemical Engineering Synthesis of ZnFe 2 O 4 nanoplates by succinic acid-assisted hydrothermal route and their photocatalytic degradation of rhodamine B under visible light, J. Environ. Chem. Eng. 2 (2014) 123–130. doi:10.1016/j.jece.2013.11.031. [53] W.A. Bayoumy, M.A. Gabal, Synthesis characterization and magnetic properties of Cr-substituted NiCuZn nanocrystalline ferrite, J. Alloys Compd. 506 (2010) 205–209. doi:10.1016/j.jallcom.2010.06.178. [54] J.S. Smart, The Néel Theory of Ferrimagnetism, Am. J. Phys. 23 (1955) 356–370. doi:10.1119/1.1934006. [55] B.D. Cullity, C.D. Graham, Introduction to Magnetic Materials, 2nd ed., John Wiley & Sons, New Jersey, 2009. [56] M. Rostami, M. Hossein, M. Ara, The dielectric , magnetic and microwave absorption properties of Cu- substituted Mg-Ni spinel ferrite-MWCNT nanocomposites, Ceram. Int. 45 (2019) 7606–7613. doi:10.1016/j.ceramint.2019.01.056. [57] L. Li, X. Tu, R. Wang, L. Peng, Journal of Magnetism and Magnetic Materials Structural and magnetic properties of Cr-substituted NiZnCo ferrite nanopowders, J. Magn. Magn. Mater. 381 (2015) 328–331. doi:10.1016/j.jmmm.2015.01.020. [58] R.M. Sebastian, S. Thankachan, S.X.J. M, R. Mary, S. Xavier, S. Joseph, E.M. Mohammed, Structural and Magnetic Properties of Chromium Doped Zinc Ferrite, 91 (2014) 1–5. doi:10.1063/1.4861990.  "    },    {        "title": "1512.01393v1.Magnetoelectric_field_microwave_antennas__Far_field_orbital_angular_momenta_from_chiral_topology_near_fields.pdf",        "content": "Magnetoelectric-field microwave antennas: Far-field  \norbital angular momenta from chiral-topolo gy near fields  \n \nM. Berezin, E. O. Kamenetskii, and R. Shavit   \n \nMicrowave Magnetic Laboratory,  \nDepartment of Electrical and Computer Engineering, \nBen Gurion University of the Negev, Beer Sheva, Israel \n \nDecember 3, 2015 \n \nAbstract \nThe near fields in the proximity of a small fe rrite particle with magnetic-dipolar-mode (MDM) \noscillations have space and time symmetry brea kings. Such MDM-originated fields – called \nmagnetoelectric (ME) fields – carry both spin and orbital angular momentums. By virtue of \nunique topology, ME fields are strongly different  from free-space electromagnetic (EM) fields. \nIn this paper, we show that because of chiral topology of ME fields in a near-field region, far-\nfield orbital angular momenta (OAM) can be obs erved, both numerically and experimentally. \nIn a single-element antenna, we obtain a radiation pattern with an angular squint. We reveal \nthat in far-field microwave radiation a crucial role  is played by the ME energy distribution in \nthe near-field region.  \n \nPACS number(s): 41.20.Jb; 42.50.Tx; 76.50.+g  \nI. INTRODUCTION \n \nIt is well known that EM fields can carry not only energy but also angular momentum. The \nangular momentum is composed of spin angular momentum (SAM) and orbital angular momentum (OAM) describing its polarization state and the phase structure distribution, \nrespectively. The research on OAM of EM fields was not attractive until Allen et al . \ninvestigated the mechanism of OAM in laser modes [1]. Henceforth, more and more attention has been paid to OAM in both optical- and radi o-wave domains. In contrast to SAM, which has \nonly two possible states of left-handed and right -handed circular polarizations, the theoretical \nstates of OAM are unlimited owing to its unique characteristics of spiral  flow of propagating \nEM waves [2]. Therefore, OAM has the potenti al to tremendously increase the spectral \nefficiency and capacity of communication syst ems [3]. Among numerous investigations in \nOAM effects, one of the subjects of intensiv e recent studies in optics concerns relations \nbetween near-field chirality and fa r-field OAM. For different types of chiral polaritonic lenses, \nit was shown that near-field chirality can lead  to tailoring optical OAM in the far-field region \n[4 – 9]. These results offer new opportunities fo r far-field 3D light shaping with distinct \nhandedness.      While numerous experiments on OAM were realized in optical frequencies, the concept of \nOAM in microwave frequencies is relatively no vel. It was shown [10 – 12] that generating \nOAM in microwave frequencies can be realized based on circular antenna arrays. In these \nantenna structures, microwave radiation elements are situated at distances about a half of the \nelectromagnetic (EM) wavelength. It is worth no ting, however, that no chiral polaritonic lenses \nhave been proposed in microwaves till now. Mo reover, no concepts on the microwave near-\nfield chirality that can lead to tailoring microw ave OAM in the far-field, have been suggested.  \n \n  2     The way to realize chiral polaritonic lenses in microwaves is to find subwavelength particles \nwhich exhibit effective resonant interactions with microwave fields. Since resonance \nfrequencies of plasmon- and exciton-polariton states are very far from microwave frequencies, \nthe main ideas and results of the optical subwavelength photonics cannot be used in \nmicrowaves. In microwaves, however, there exis t subwavelength particles (with sizes much \nless than the free-space electromagnetic wavelength 0λ), which are distinguished by specific \nmagnetic-dipolar-mode (MDM) oscillations [13]. In recent studies it was shown that MDM \noscillations in a quasi-2D ferrite disk are m acroscopically coherent quantum states, which \nexperience broken mirror symmetry and also broken time-reversal symmetry. One observes \nvery effective resonant interacti ons of ferrite-disk particles with  microwave fields resulting in \nappearance of MDM-polariton states. Free-space microwave fields, emerging from \nmagnetization dynamics in quasi-2D ferrite disk, carry spin and orbital angular momentums \nand are characterized by power-flow vortices an d non-zero helicity. Symmetry properties of \nthese fields – called magnetoelectric (ME) fiel ds – are different from symmetry properties of \nfree-space electromagnetic (EM) fields. For an in cident electromagnetic field, the MDM ferrite \ndisk looks as a trap with focusing to a ring, rather than a point [14 – 21].  \n     In this paper, we show that due to the chirality and the OAM of near fields originated from \nMDM ferrite particles, the nontrivial far-field OAM can be generated in microwaves. The \ntopological near-field regions with broken symme try we call chiral MDM- polariton lenses. We \ninvestigate a novel microwave antenna with a MDM ferrite disk as a basic building block for \ncontrolling the far-field electromagnetic radiatio n. The antenna has symmetrical geometry. At \nthe MDM resonance, topological singularities of the ME near fields cause chiral electric \ncurrent distributions on metal surfaces of the antenna. This results in the topological \nsingularities in the far-region radiation fields . The MDM antenna continuously modulates both \namplitude and phase in the diffract ion field to shape twisted radiation pattern. This forms a far-\nfield radiation pattern with a strong and contro llable squint. Changing the input/output ports \nand a direction of a bias magnetic field allows  easy manipulation of spatial degrees of freedom \nof microwave photon states. Such an effect of a spatial mode division by a single radiation element is unique from a fundamental point of view. This effect can be attractive for development of novel microwave radiation systems with controllable phase structure \ndistribution. \n     The paper is organized as follows. In S ection II, we describe the MDM-resonance antenna. \nTo find a transfer of the topological ME effect s in the far-field region, this microwave antenna \nhas the MDM-resonance structure as the only res onant element. In Section III, we demonstrate, \nboth numerically and experimentally, the effect  of tailoring ME near-field chirality to a \nmicrowave OAM in the far-field region. This effe ct is verified by the presence of angular \nsquints in radiation patterns. Section IV presents a theoretical insight into the MDM-resonance far-field orbital angular momenta. We analyze the ME-field helicity conservation law. We \nshow that near a ferrite disk at the MDM-re sonance frequencies one has the regions with \npositive helicity and negative helicity. For the entire space volume, we have the “helicity \nneutrality”. We analyze numerically the field to pology in radiation nea r- and far-field regions. \nWe show that the far-field orbital angular momenta, observed at the MDM-resonance frequencies, appear due to the near-field topology of the “helicity dipoles” (“ME dipoles”). In \nSection V, we conclude our studies.   \n \nII. MDM ANTENNA: STRUCTURE AND MICROWAVE CHARACTERISTICS \n \nTo find the transfer of the MDM-resonance topo logical ME effects [14 – 21] in the far-field \nregion, a microwave antenna should not have other resonant elements except the MDM resonant \nstructure. For this purpose, we use a rectangular  waveguide with a hole in a wide wall and the  3diameter of this hole is much less than a ha lf wavelength of microwave radiation. At the MDM \nresonance, the topological singu larities in the far-region radi ation fields appear due to \ntopological singularities of the ME near fields whic h, in their turn, cause chiral electric current \ndistributions on the external surface of a waveguide wall. Such current singularities are well \ndistinguished in a microwave antenna with symmetrical geometry. For this reason, the hole in a \nwaveguide wide wall is situated symmetrically. For the numerical and experimental studies we \nuse a microwave antenna shown in Fig. 1. This is a waveguide radiation structure with a hole in a \nwide wall and a thin-film ferrite disk as a ba sic building block. A hole in a wide wall has a \ndiameter of 8 mm, which is much less than a half wavelength of microwave radiation at the \nfrequency regions from 8.0 GHz till 8.5 GHz, used in our studies. The yttrium iron garnet (YIG) \ndisk is placed inside a 10TE -mode rectangular X-band waveguide symmetrically to its walls so \nthat a disk axis is perpendicular to a wide wall of a waveguide. The disk diameter is 3 mm and \nthe thickness is 0.05 mm. The ferrite disk is normally magnetized by a bias magnetic field \n04760 H= Oe; the saturation magnetization of a ferrite is  1880  4 =sMπ G. For better \nunderstanding the field structures, in a numerical analysis we consider a ferrite disk with a very \nsmall linewidth of 0.1 OeHΔ= . In experimental studies, a ferrite-disk sample has the pointed \nabove parameters except a linewidth which is equal to 0.6 OeHΔ= . \n     Fig. 2 shows the numerical reflection spectral characteristic for the 10TE waveguide mode in \nour microwave antenna. Because of the presence of a radiation hole, the spectrum is quite \nemasculated compared to a multiresonant spectrum of MDM oscillations observed in non-\nradiating microwave structures [16 – 19]. The peaks 1-1′  and 3-3′ correspond to the radial \nMDMs, while the peak 2-2′ is the azimuth-mode magnetic-dipolar resonance [22]. The forms of \nthe resonance peaks in Fig. 2 give evidence for the Fano-type interaction [19, 23, 24]. The underlying physics of the Fano resonances finds it s origin in wave interference which occurs in \nthe systems characterized by discrete energy states  that interact with the continuum spectrum. In \nour structure, the discrete states are due to MDM resonances and an entire continuum is \ncomposed by the internal waveguide and external  free-space regions. The forward and backward \npropagating modes within the waveguide are coupled via the defects. This coupling becomes highly sensitive to the resonant properties of the defect states. For such a case, the coupling can \nbe associated with the Fano resonances. In the corresponding transmission dependencies, the \ninterference effect leads to either perfect tr ansmission or perfect reflection, producing a sharp \nasymmetric response. We have a “bright” a nd a “dark” resonances, which produce the Fano-\nresonance form in the reflection spectra. In our study we will use the first “bright” peak – the peak \n1′ – where the most intensive radiation is observed. At the frequency of the resonance peak \n1′, the field structure near a ferrite disk is typical for the main MDM excited in a closed \nwaveguide system [16 – 19]: there are rotating el ectric and magnetic fields, the active power \nflow vortex, and non-zero field helicity.  \n     Fig. 3 shows the experimental transmissi on spectral characteristic. Experimentally, we \nobserve only the radial MDMs: the resonance peaks 1-1′  and 3-3′. Moreover, because of certain \ngeometrical non-symmetry in an experimental structure, the high-order radial peak 3-3′ in Fig. 3 \nis excited stronger than such a peak in a numerical characteristic (see Fig. 2).   \n      Because of chiral topology of the MDM -resonance near fields [14 – 21], far-field orbital \nangular momenta can be observed both numerically and experimentally. This effect of tailoring \nthe near-field chirality to a microwave OAM in the far-field region can be well verified by \nappearance of angular squints in radiation pa tterns. Usually, angular squints in microwave \nradiation patterns are obtained due to the free-space interference processes with use of an array of \nradiation elements [10 – 12]. In our single-elemen t structure, we obtain radiation patterns with \nthe angular squints due to specific topology of the ME near fields.   4    For an analysis of radiation patterns we use a spherical coordinate system, shown in Fig. 4. \nFig. 5 shows numerically calculated far-field radiat ion patterns (directivity) for two cut planes, zx \nplane ( 0ϕ=o) and zy plane ( 90ϕ=o), at the nonresonance frequency 8.125GHz. The wave in a \nwaveguide propagates from port 1 to port 2. In this case, we have a squint in the zy plane, along a \nnegative direction of y axis. When wave propagates from port 2 to port 1, the squint is along a \npositive direction of y axis. The observed squints in the zy plane are regular squints which take \nplace due to a small phase delay for the wave when it propagates in a region a waveguide hole. \nThere are no squints in the zx plane and the radiation patterns are the same for two opposite \ndirections of a bias magnetic field.  \n    At the frequency of the MDM resonance, squints in the zx plane occur together with the \nexisting regular squints in the zy plane. The squint in zy plane is the same as in Fig. 5. As a \nresult, the angular squints are observed in nume rically calculated far-fiel d radiation patterns. \nSuch angular squints are shown in Figs. 6 – 8.  Fig. 6 shows single-element 2D and 3D \nradiation patterns for two cut planes, 0ϕ=o and 90ϕ=o, at the MDM-resonance frequency \n8.139GHz. The wave in a waveguide propagates from port 1 to port 2. Fig. 7 shows 2D \nradiation patterns in the zx plane ( 0ϕ=o) at the MDM-resonance frequency 8.139GHz and \ntwo opposite directions of the wave propagation  in a waveguide. Fig. 8 shows the resonance-\nfrequency radiation patterns in the planes 0ϕ=o and 90ϕ=o for two opposite directions of \nthe bias magnetic field and the same direction of the wave propagation  in a waveguide (from \nport 1 to port 2).  \n     The numerical results are well verified  by our experimental studies. Fig. 9 shows the \nnumerically simulated and experimentally me asured radiation patterns for a cut plane 0ϕ=o at \nthe MDM-resonance frequency 8.139GHz. Wave pr opagates from port 1 to port 2 and a bias \nmagnetic field is directed upward. The measuremen ts were done in a sector with variation of a \nspherical coordinate from 120 θ=−o to 120θ=o, where the angular squints are expected. \nExperimental radiation patterns in Fig. 10 we ll illustrates a role of the MDM resonance in \nobtaining angular squints. Fig. 10 ( a) shows the measured normalized radiation patterns for \nnonresonant (8.124GHz) and resonant (8.132GHz) frequencies. Figs. 10 ( b) and 10 ( c) present \nenlarged pictures of these radiation patterns.  \n \nIII. MDM-RESONANCE FAR-FIELD ORBITAL ANGULAR MOMENTA:  \nA THEORETICAL INSIGHT \n \nThe shown angular squints in fa r-field radiation patterns is obs erved because of the ME-field \nhelicity and ME-energy distributions in the ra diation near-field area. At the MDM-resonance \nfrequencies, near a ferrite disk one has the regions with positive helicity (positive ME energy) and negative helicity (negative ME energy). These regions constitute the “helicity dipoles” (“ME \ndipoles”). We will show that the far-field or bital angular momenta, observed at the MDM-\nresonance frequencies, appear due to the near-field topology of these “ME dipoles”. \n \nA. ME-field helicity conservation law and “ME dipoles” \n \nAt the MDM resonances (MDM ωω= ), for the ME-field structure in a vacuum region near a \nferrite disk, the magnetic field is a potential field, H ψ =− ∇rr\n, while the electric field has two \nparts: the curl-field component cEr\n and the potential-field component pEr\n. The curl electric field  5cEr\n in vacuum is defined from the Maxwell equation 0 cHEtμ∂∇× =−∂rrr\n. The potential electric \nfield pEr\n in vacuum is calculated by integration over the ferrite-disk region, where the sources \n(magnetic currents,()m mjt∂=∂rr) are given. Here mr is dynamical magnetization in a ferrite disk. \nNumerical studies show that for the ME near fields, we have p c EE>>rr\n. For time-harmonic \nfields (iteω∝ ), and with representation of the potential electric field as pE φ =− ∇rr\n, the time-\naveraged helicity density parame ter in a vacuum near-field region is calculated as [17 – 19, 21]: \n  \n                () ()** * 00 0Re Re Re44 4MDM MDM MDMEB B B Fεε εφφωω ω⎡ ⎤ ⎡⎤ ⋅− ∇ ⋅ = − ∇ ⋅⎣⎦ ⎣ ⎦==rr r r r r\n.          (1)                \n \nHere we took into account that 0B∇⋅ =rr\n. We can also introduce a quantity of the time-\naveraged ME-energy density [21]:   \n \n                                                                   ()*Re Bφ η ⎡⎤∇⋅ ≡−⎣⎦rr\n                                               (2) \n \nand represent the helicity density F as  \n \n                                                                        0\n4MDMFεηω= .                                                  (3) \n \n     An integral of the ME-field helicity dens ity (or ME-energy density) over the entire near-field \nvacuum region of volume V (which excludes a region of a ferrite disk) we define as the helicity \nH: \n \n ()** 00 0Re Re44 4MDM MDM MDM\nVV V SFdv dV B dV B n dSεε εηφ φωω ω⎡⎤ ⎡⎤ ≡ = =− ∇⋅ =− ⋅⎣⎦ ⎣⎦ ∫∫ ∫ ∫rrr rH . (4)  \n \nFrom this integral relation, we can conclude that when the normal component of Br\n vanishes at \nsome boundary inside which the fields are confined (i.e. when 0 Bn⋅=rr at the boundary), the \nquantity H is equal to zero. The quantity H is also equal to zero when the fields are with finite \nenergy and the quantity Bφr\n decreases sufficiently fast at infinity. \n    Inside the vacuum-region volume V there could be a region k (1 )kN≤≤  with volume ()\nkV+ \nwhere the helicity is a non-zero positive quantity: \n \n                                                      \n()() () 004 kMDM\nkkVdVεηω\n+++=>∫H                                                   (5) \n \nand a region l (1 ) lN≤≤  with volume ()\nlV−where the helicity is a non-zero negative quantity: \n \n                                                          \n()() () 004 lMDM\nllVdVεηω\n−−−=<∫H .                                             (6) \n  6For the entire volume () ()\n11NN\nkl\nklVV V+−\n===+∑∑ , we have the “helicity neutrality”: \n \n                                                             () ()\n110NN\nkl\nkl+−\n===+=∑∑HH H .                                              (7) \n \nThe regions with positive and negative helicities are the regions with positive and negative ME \nenergies, respectively. The time-averaged ME-energy density ()η+ can be considered also as the \ntime-averaged density of the positive “helicity charge” while the quantity ()η−– the time-\naveraged density of the negative “helicity char ge”. Because of the “helicity neutrality”, the \n“helicity dipoles” (“ME dipoles”) may occur in a vacuum region near a MDM ferrite disk. More \ngenerally, the “helicity multipoles” (“ME multipoles”) can exist. As we will show in the present \nstudies, just because of the near-field in-plane topology of the “helicity dipoles” (“ME dipoles”) \nthe far-field orbital angular momenta can be  observed at the MDM-resonance frequency. \n      The analyzed above helicity parameter F can be normalized with respect to the field \namplitudes. With such a normalization, one have definite information on the time-averaged angle between the electric and magnetic fields. The normalized helicity parameter is expressed \nas \n \n                                                  (){ } ()*\n* Im\ncosRe EE EH\nEE E Hα⋅∇ × ⋅\n==\n∇×rrr rr\nrr r r .                                 (8)     \n  \nCertainly, for a regular electromagnetic field cos 0α=. For positive helicity (the positive \n“helicity charge”), the time-averaged angle between the electric and magnetic fields is less then \n90o  (cos 0α<). For negative helicity (the negative “helicity charge”), the time-averaged \nangle between the electric and magnetic fields is more then 90o  (cos 0α>). \n \nB. Field topology in radiation near- and far-field regions \n \nThe near-field structure of our antenna can be conventionally divided in two sub-regions. The \nfirst one shows the fields in close proximity of a disk and the second one describes the fields \nnear a radiation hole. In close pr oximity of a ferrite disk (on scales about tens micrometers), the \nMDM-resonance field structure is not different from such a structure in a closed (non-radiating) microwave waveguide with an embedded ferrite disk. This field structure are \ndescribed in details in Refs. [17, 18, 21]. At the same time, near a hole of a radiating \nmicrowave waveguide, the MDM-resonance field structure exhibits very specific topological properties which are strongly dependable on extern al parameters of a system. These properties \nof the fields near a radiation hole are illustrated in Figs. 11 – 17.  \n     Fig. 11 shows the Poynting-vector distributions on a vacuum plane near a radiation hole for \ndifferent combinations of two external parameters: a direction of a bias magnetic field and a \ndirection of the power flow in a waveguide. A vacuum plane is placed below a radiation hole and perpendicular to a disk axis. For the same vacuum plane below radiation hole, Fig. 12 \nshows the normalized helicity parameter, \ncosα. Figs. 11 and 12 clearly illustrate that non-\nsymmetries in power-flow vortices are in definite  correlation with the helicity properties of \nME-field areas on the xy vacuum plane. In Fig. 12, the arrows in right-upper corners show  7directions of “ME dipoles”. There are direct ions from regions of positive ME helicity to \nregions of negative ME helicity. \n    The correlation of the near-field topologi cal structure with the he licity-dipole orientation \n(the ME-dipole orientation) appears also in a vacuum region above a radiation hole. Fig. 13 \nshows the ME-field areas on the cross-section zy plane in the near-field region. One can see \nthat the ME-field areas (originated from a MDM fe rrite disk) significantly “get out” through a \nradiation hole. Fig. 14 shows the ME-field areas on the xy vacuum plane above a radiation \nhole. Similar to Fig. 12, in Fig. 14, the arrows in right-upper corners show directions of “ME \ndipoles”. There are directions from regions of positive ME helicity to regions of negative ME \nhelicity. One can see that “ME dipoles” above a radiation hole are rotated by 90 degrees with \nrespect to “ME dipoles” below a radiation hole. This rotation can be or clockwise, or counterclockwise dependending on direction of a bias magnetic field. Fig. 15 shows Poynting-\nvector distributions in a vacuum cylinder above a hole. In this figure, the regions \nA and B \nconventionally designate the positive (divergenc e of vectors) and negative (convergence of \nvectors) topological charges in the power-flow-d ensity distributions. When we trace the lines \nfrom regions A to regions B, we see that these lines are perpendicular to the directions of ME \ndipoles. \n     ME-field topology strongly influences on dist ributions of the electric fields and currents on \nan external metal surface of a waveguide. Figs. 16 and 17 show such distributions at the MDM \nresonance frequency. The regions C and D designate the positive and negative surface electric \ncharges on a surface of a hole. The observed chir al forms of a front of an electric field and a \nsurface electric current determine chiral-topology of the fields radiating by a MDM microwave \nantenna. The far-field structure is strongly determ ined by ME-field topology of the near fields. \nThis is illustrated by Figs. 18 and 19. Fig. 18 shows intensity of an electric field on the xy \nvacuum plane situated at distance about 03λ above a radiation hole. In this figure, we traced \nprojections on this xy plane the AB lines which connect the regions of positive and negative \ntopological charges of the power-flow-density dist ributions shown in Fig. 15. We also showed, \nby small stars, where on the AB lines we have maximal intensities of the electric field. One can \nsee how the direction of a squint in the far-fiel d radiation pattern is correlated with the non-\nsymmetry of the power-flow-density distribution in a near-field region. There is an evident \ncorrelation between the squint positions and the directions and orientations of the AB-line \nvectors. The same small stars (where on AB lines we have a maximal intensity of an electric \nfield) on the same xy plane are shown in Fig. 19 in correlation with the three vectors. These \nvectors are the following. 0Hr\n is a bias magnetic field, vector pr shows a direction of wave \npropagation in a microwave waveguide, and qr is a unit vector tangent to a curve depicting an \nangular squint. We can state that the three vectors qr,pr,0Hr\n constitute the right-hand triple of \nvectors. \n     \nC. A note on the balance of energy \n \nAt the MDM resonance frequency, near a ferrite disk one observes the regions with positive and negative helicities and the n ear-field topology is distinguishe d by presence of the “helicity \ndipoles” (“ME dipoles”). At the MDM resonance frequency, a robust topological structure of a \npower-flow vortex near a ferrite disk is distorte d (see Fig. 11). We showed that this distortion \nis in evident correlation with orientation of th e ME dipole. We also showed that the far-field \norbital angular momenta appear due to the near-field topology of  the “helicity dipoles” (“ME \ndipoles”). It can be assumed that to create such “ME dipoles”, some additional energy should \nbe taken from RF sources. It means that appearance of the far-field orbital angular momenta  8should be accompanied with reduction of a gain in the radiation pattern. Such an estimation of \nbalance of energy, made based on the numerical analysis, is illustrated in Fig. 20.   \n     At the nonresonance frequency of MDM oscillations, a ferrite di sk behaves as a small \nobstacle in a waveguide. Since the hole diameter is much less than a half wavelength of \nmicrowave radiation and the hole position does  not lead cutting of electric currents in \nwaveguide walls, we have negligibly small radiation power. We should not counting power \nlost due to joule heating in the feedline and refl ections back down the feedline. As a results, at \nthe nonresonance frequency of MDM oscillations, the antenna directivity and antenna gain are \nalmost undistinguishable. This is shown in Fig. 20 ( a).  \n     The situation is completely different at  the MDM resonance frequency. From the radiation \npatterns shown in Fig. 20 ( b) it is evident that difference between the directivity and gain \npowers is about 19 dBi. This amount shows that the power loss due to joule heating in the \nfeedline and reflections back down the feedline is about 98% from the input power in a \nwaveguide. Based on an analysis of the reflec tion characteristic (shown in Fig. 2) and the \ntransmission characteristic (shown in Fig. 20 ( c)), one can easily estimate that the power \nreflection back down the feedline is not more than 40% from the input power. So, we are faced with the fact that a system has extremely big amount of the power losses due to joule heating. \nHowever, a simple analysis shows that the joule heating in the system is negligibly small. From \na numerical reflection characteristics we can see that for the first “bright” peak – the peak \n1′ – \nthe quality factor Q is very big, about 104 (from an experimental re flection characteristic we \nobtain that the quality factor for the peak 1′ is about 321 0× ). It becomes clear that for such a \nquantity Q, joule heating losses inside a ferrite disk are extremely small compared to the entire \npower losses in a MDM resonator. We also have negligibly small joule losses in waveguide \nwalls. The conclusion is that the main losses take place due to absorption of energy necessary for creation of the “ME dipoles”, which result in  distortion of power-flow vortices near a ferrite \ndisk and finally creation of the far-field orbital angular momenta in  radiation characteristics.   \n \nIV. CONCLUSION \n \nIn terms of far-field scattering, the MDM particle s have scattering patterns which are strongly \nnot identical to the conventional electric and magnetic dipole (in general, multipole) structures. \nME fields appear as a result of interaction of  MDM oscillations in a ferrite particle with \nexternal EM fields. In the vicinity of a ferrite disk, at the MDM resonances one observes \nstrongly localized areas of the electric and magn etic fields which are constituents of the ME \nfield. While at the frequency beyond a MDM resonance one observes a current of a regular \nelectric dipole, in a case of a MDM resonance, the surface electric current is a chiral current \nwith an evident deviation of topological charge s. The presence and positions of the in-plane \nregions with positive and negative ME helicity factor strongly influence on the distribution of \npower flows in the vicinity of the antenna radi ation hole. From the pictures of ME-field areas \non a vacuum plane above a radiation hole, one can see that there exist in-plane “ME dipoles” \nand that directions of these “ME dipoles” is stro ngly correlated with directions of the squints in \nradiation patterns. An approximate analysis of the balance of energy shows that the main losses in the antenna take place due to absorption energy necessary for creation of the “ME dipoles”, \nwhich result in distortion of power-flow vortices near a ferrite disk and finally creation of the \nfar-field orbital angular momenta in radiation characteristics.  The approach showing that \nchiral-topology near fields originated from a small ferrite particle with MDM oscillations result \nin generating far-field OAM, bridges and combines the four concepts: (\na) Electromagnetic \n(optical) chirality of the fields; ( b) topological ME effects; ( c) Fano resonances; ( d) OAM \nantennas. \n       9 \nReferences \n[1] L. Allen, M. W. Beijersbergen, R. J. C.  Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, \n8185 (1992). \n[2] L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000). \n[3] R. Celechovsky, Z. Bouchal, New J. Phys. 9, 328 (2007). \n[4] Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 110, 203906 \n(2013). \n[5] H. Yu, H. Zhang, Y. Wang, S. Han, H. Yang, X. Xu, Z. Wang, V. Petrov, and J. Wang,  Sci. \nRep. 3, 3191 (2013). \n[6] A. Žukauskas, M. Malinauskas, and E. Brasselet, Appl. Phys. Lett. 103, 181122 (2013). \n[7] H. Liu, M. Q. Mehmood, K. Huang, L. Ke, H. Ye, P. Genevet, M. Zhang, A. Danner, S. P. \nYeo, C.-W.Qiu, and J. Teng, Adv. Opt. Mater. 2, 1193 (2014). \n[8] F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, ACS Photon. \n1, 762 (2014). \n[9] R. Dall, M. D. Fraser, A. S. Desyatnikov, G. Li, S. Brodbeck, M. Kamp, C. Schneider, S. \nHöfling, and E. A. Ostrovskaya, Phys. Rev. Lett. 113, 200404 (2014). \n[10] B. Thide, H. Then, J. Sjoholm, K. Palmer, J. Bergman, T.D. Carozzi, Ya. N. Istomin, N. H. \nIbragimov and R. Khamitova, Phys. Rev. Lett. 99, 087701 (2007). \n[11] C. Deng, W. Chen, Z. Zhang, Y. Li, and Z. Feng, Int. J. Antenn. Propag. 2013 , 847859 \n(2013).  \n[12] O. Edfors, A. J. Johansson, IEEE Trans. Antenn. Propag. 60, 1126 (2012). \n[13] A. G. Gurevich and G. A. Melkov, Magnetic Oscillations and Waves  (CRC Press, New \nYork, 1996). \n[14] E. O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007). \n[15] E. O. Kamenetskii, J. Phys.: Condens. Matter 22, 486005 (2010). \n[16] E. O. Kamenetskii, R. Joffe, and R. Shavit, Phys. Rev. A 84, 023836 (2011). \n[17] E. O. Kamenetskii, R. Joffe, R. Shavit, Phys. Rev. E 87, 023201 (2013).  \n[18] M. Berezin, E. O. Kamenetskii, and R. Shavit, J. Opt. 14, 125602 (2012). \n[19] M. Berezin, E. O. Kamenetskii, and R. Shavit, Phys. Rev. E 89, 023207 (2014). \n[20] E. O. Kamenetskii, E. Hollander, R. Joffe, R. Shavit, J. Opt. 17, 025601 (2015). \n[21] E. O. Kamenetskii, M. Berezin, R. Shavit, Appl. Phys. B: Lasers Opt. 121, 31 (2015). \n[22] E. O. Kamenetskii, M. Sigalov, and R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005). \n[23] U. Fano, Phys. Rev. 124, 1866 (1961). \n[24] E. O. Kamenetskii, G. Vaisman, and R. Shavit, J. App. Phys. 114, 173902 (2013). \n \n------------------------------------------------------------------------------------------------------------------ \n \n   10\n \nFig. 1. MDM microwave antenna: a waveguide radiation structure with a hole in a wide wall and \na thin-film ferrite disk as a basic building block. A ferrite disk is placed inside a 10TE -mode \nrectangular X-band waveguide symmetrically to its walls so that a disk axis is perpendicular to a \nwide wall of a waveguide. The hole diameter is much less than a half wavelength of microwave \nfree-space radiation at the frequency regions used in the studies. \n    \n \n \nFig. 2. Numerical reflection characteristic in a waveguide radiation structure. \n \n \nFig. 3. Experimental reflection characteri stic in a waveguide radiation structure.  11 \n \nFig. 4. Spherical coordinate system. \n \n \n                                            ( a)                                                             ( b)                                \nFig. 5. Single-element radiation patterns at the nonresonance frequency 8.125GHz for two cut \nplanes, 0ϕ=oand 90ϕ=o. The wave in a waveguide propagates from port 1 to port 2 \n(\n ). (a) 2-D pattern; the squint is observed in the zy plane (marker β). No squint is \nobserved in the zx plane (marker α). (b) 3-D pattern. The radiation patterns are the same for two \nopposite directions of a bias magnetic field. The markers α and β show maximal values of the \ndirectivity.  \n \n  12\n \n                                              ( a)                                                    ( b)        \nFig. 6. Single-element radiation patterns for two cut planes, 0ϕ=o and 90ϕ=o, at the MDM-\nresonance frequency 8.139GHz. The wave in a waveguide propagates from port 1 to port 2. ( a) \n2-D pattern; ( b) 3-D pattern. The squint in zy plane is the same as in Fig. 5. Upward direction \nof a bias field. \n \n \n \nFig. 7. Single-element radia tion patterns for a cut plane 0ϕ=o at the MDM-resonance \nfrequency 8.139GHz and two opposite directions of the wave propagation in a waveguide. Red \nline – wave propagates from port 1 to port 2; blue  line – wave propagates from port 2 to port 1. \nUpward direction of a bias field. \n \n  13\n \n(a)                                                    ( b)        \nFig. 8. Resonance-frequency radi ation patterns in the planes 0ϕ=o and 90ϕ=o for two \nopposite directions of the bias magnetic field and the same direction of the wave propagation in \na waveguide (from port 1 to port 2). ( a) Upward direction of a bias field, ( b) downward \ndirection of a bias field.  \n \n \nFig. 9. Numerically simulated and experimentally  measured radiation patterns for a cut plane \n0ϕ=o at the MDM-resonance frequency 8.139GHz. Wave propagates from port 1 to port 2. \nUpward direction of a bias field. \n \n  \n   14                      ( a)                                                ( b)                                   ( c) \n \nFig. 10. Experimental radiation patterns for nonresonant (8.124GHz) and resonant (8.132GHz) \nfrequencies. ( a) A general picture of the normalized radiation patterns. ( b) An enlarged picture \nof the radiation pattern for a nonresonant frequency. ( c) An enlarged picture of the radiation \npattern for a resonant frequency. The radiation patterns are measured in a zx plane (φ=0°).  \nWave propagates from port 1 to port 2 and a bias magnetic field is upwards directed. \n \nFig. 11. Poynting-vector distributions on a vacuum plane below a radiation hole. ( a) a \nschematic picture of a radiating structure with a vacuum plane; ( b) wave propagation from port \n1 to port 2 and upward direction of a bias fiel d at a frequency beyond a MDM resonance; ( c) \nwave propagation from port 1 to port 2 and upward direction of a bias field; ( d) wave \npropagation from port 2 to port 1 and upw ard direction of a bias field; ( e) wave propagation \nfrom port 1 to port 2 and  downward direction of a bias field; ( f) wave propagation from port 2 \nto port 1 and  downward direction of a bias field. \n  15\n \nFig. 12. ME-field areas on the xy plane on the vacuum plane below a radiation hole. ( a) a \nschematic picture of a radiating structure with a vacuum plane; ( b) wave propagation from port \n1 to port 2 and upward direction of a bias fiel d at a frequency beyond a MDM resonance; ( c) \nwave propagation from port 1 to port 2 an d upward direction of a bias field; ( d) wave \npropagation from port 2 to port 1 and upw ard direction of a bias field; ( e) wave propagation \nfrom port 1 to port 2 and downward direction of a bias field; ( f) wave propagation from port 2 \nto port 1 and adownward direction of a bias field. The arrows in right-upper corners show \ndirections of “ME dipoles”: the directions from regions of the positive ME helicity to regions \nof the negative ME helicity.     \n  \n  16\n \n         ( a)                         ( b)                          ( c)                           ( d) \n \nFig. 13. ME-field areas on the cross-section zy plane in near-field regions.  ( a) Wave \npropagation from port 1 to port 2 and upw ard direction of a bias field; ( b) wave propagation \nfrom port 2 to port 1 and upward direction of a bias field; ( c) wave propagation from port 1 to \nport 2 and downward direction of a bias field; ( d) wave propagation from port 2 to port 1 and \ndownward direction of a bias field. \n \n \nFig. 14. ME-field areas on the xy plane on the vacuum plane above a radiation hole. ( a) a \nschematic picture of a radiating structure with a vacuum plane; ( b) wave propagation from port \n1 to port 2 and upward direction of a bias fiel d at a frequency beyond a MDM resonance; ( c)  17wave propagation from port 1 to port 2 an d upward direction of a bias field; ( d) wave \npropagation from port 2 to port 1 and upw ard direction of a bias field; ( e) wave propagation \nfrom port 1 to port 2 and downward direction of a bias field; ( f) wave propagation from port 2 \nto port 1 and adownward direction of a bias field. The arrows in right-upper corners show \ndirections of “ME dipoles”: the directions from regions of the positive ME helicity to regions \nof the negative ME helicity.      \n \nFig. 15. Poynting-vector distributions in a vacuum cylinder above a radiation hole. ( a) Wave \npropagation from port 1 to port 2 at a frequency beyond a MDM resonance; ( b) MDM-\nresonance wave propagation from port 1 to por t 2 and upward direction of a bias field;  c) \nMDM-resonance wave propagation from port 2 to por t 1 and upward directi on of a bias field; \n(d) MDM-resonance wave propagation from port 1 to port 2 and downward direction of a bias \nfield; (e) MDM-resonance wave propagation from port 2 to port 1 and downward direction of a \nbias field. The regions A and B conventionally designate the regions of positive and negative \ntopological charges in the power-flow-density distributions. \n  18\n \nFig. 16. Electric currents ( a), (b) and fields ( c), (d) on the external metal surface of a \nwaveguide at the frequency MDM resonance, 8.139GHz. ( a), (c) Time phase ( a), (b)  0tω=o; \n(b), (d) time phase 45 tω=o. MDM-resonance wave propagation from port 1 to port 2 and \nupward direction of a bias magnetic field; \n \n  19Fig. 17. Electric currents ( a), (b) and fields ( c), (d) on the external metal surface of a \nwaveguide at the frequency MDM resonance, 8.139GHz. ( a), (c) Time phase ( a), (b)  0tω=o; \n(b), (d) time phase 45tω=o. MDM-resonance wave propagation from port 2 to port 1 and \ndownward direction of a bias magnetic field. \n \n \n \nFig. 18. Intensity of an electric field on the xy vacuum plane situated at distance about 03λ \nabove a radiation hole. The figure shows time aver aged directions of the squints for different \ndirections of a bias field and wave propagation in a waveguide. The AB lines connect the \nregions of positive and negative topological char ges of the power-flow-den sity distributions in \nthe near-field region. Small stars, show the places of maximal intensities of  the electric field on \nAB lines. The squint positions are in strong corre lation with the directions and orientations of \nthe AB-line vectors. \n  20\n \nFig. 19. Distribution of maximal inte nsities of an electric field on the xy vacuum plane in \ncorrelation with directions of the three vectors: a direction of a bias magnetic field, a direction \nof wave propagation in a waveguide, and a unit vector tangent to a curve depicting an angular \nsquint. The three vectors qr,pr,0Hr\n constitute the right-hand triple of vectors. \n \n \nFig. 20. Balance of energy. ( a) The directivity and gain at the nonresonance frequency \n8.125GHz. ( b) The directivity and gain at the MDM-resonance frequency 8.139GHz, when the \norbital angular momentum is observed. ( c) The waveguide transmission coefficient \ncharacteristics. \n \n "    },    {        "title": "1606.02473v1.Magnetoelectric_effect_in_layered_ferrite_PZT_composites__Study_of_the_demagnetizing_effect_on_the_magnetoelectric_behavior.pdf",        "content": "Magnetoelectric effect in layered ferrite/PZT composites. Study of the \ndemagnetizing effect on the magnetoelectric behavior.  \n \nV. Loyau, V. Morin, G. Chaplier, M. LoBue, and F. Mazaleyrat  \nSATIE UMR 8029 CNRS, ENS Cachan, Université  Paris -Saclay , 61, avenue du pré sident \nWilson, 94235 Cachan Cedex, France.  \n \nAbstract.  \nWe report the use of high magnetomechanical coupling ferrites in magnetoelectric (ME) \nlayered composites . Bilayer samples combining (Ni 0.973 Co0.027)1-xZnxFe2O4 ferrites (x=0 -0.5) \nsynthetized  by non conventional reactive Spark Plasma Sintering (SPS) and commercial lead \nzirconate titanate (PZT) were characterized in term of ME voltage coefficients measured at \nsub-resonant frequency. Strong ME effects are obtained and we show that an annealing at \n1000°C and a quench ing in air imp rove the piezomagnetic behavior  of Zn-rich compositions. \nA theoretical model that predict the ME behavior was developed, focusing our work on the \ndemagnetizing effects in the transversal mode as well as the lon gitudinal mode. The model  \nshow s that: (i) high ME coefficients are obtained when ferrites with high magnetomechanical  \ncoupling are used in bilayer ME composites, (ii) the ME behavior in transversal and \nlongitudinal modes are quite  similar, and differences in the shapes of the ME curves are \nmainly due the demagnetizing effects, (iii) in the transversal mode, the magnetic field \npenetration depends on the ferrite layer thickness and the ME coefficient is affected \naccordingly. The two later points are confirmed by measurements on ME samples and \ncalculations. Performances of the ME composites made with high magnetomechanical  \ncoupling ferrites are compared to those obtained using Terfenol -D materials in the same \nconditions of size, shape,  and volume ratio.  It appear s that a ferrite with an optimized \ncomposition has performance s comparable to those  obtained with  Terfenol -D material . \nNevertheless, the fabrication processes of ferrites are quite  simpler. Finally a ferrite/PZT \nbased ME compos ite was used as a current sensor.   \n \nI. Introduction  \nMagnetoelectric1 (ME) materials which exhibit a coupling between magnetic properties and \ndielectric properties have a great interest due to their potential use in smart electronic \napplications. The ME effect consists in an electric polarization change  when a magnetic field \nis applied (direct effect) or , conversely , a magnetization change  when an electric field is \napplied (converse effect). Intrinsic (single phase) ME coupling was first detected in Cr 2O3 at \nlow temperature, but the effect is very weak and it cannot be  used in electronic devic es. More \nrecently, both ferroelectric and ferromagnetic properties were discovered in bismuth ferrite2 at \nroom temperature, however the observed ME magnitudes are still too weak for application purposes. Recently, intrinsic ME effect suitable for some application has been reported in \nmaterials3 derived from barium zirconium titanate with a small substituti on of Fe. A possible \nalternative to the research of new intrinsic ME materials with enhanced effect is represented \nby the use of magnetostrictive/piezoelectric composites. In this case the ME effect arises \nthrough the mechanical coupling between  the two ph ases4. When a constant magnetic bias \nfield is applied to the composite, the magnetostrictive material shows a piezomagnetic \nbehavior and the application of a sma ll alternative field gives rise  to a corresponding \nalternative strain. Due to mechanical coupli ng, an alternative electrical field appears within \nthe piezoelectric phase. ME bulk composites have been made first by sintering together \nBaTiO 3 or PZT with spinel ferrites. However, the low resistivity of the ferrite that short -cut \nthe piezoelectric phase  acts towards a lowering of  the ME effect5. This difficulty is overcome \nwhen using laminated structures6. \nSo, in the 2000s, interest has been focused on layered composite structures based on PZT \nassociated with different ferrimagnetic materials: nickel fer rites, cobalt ferrites, or lanthanum \nmanganites7. Although nickel ferrites exhibit much smaller magnetostriction than cobalt \nferrites, they show a better ME effect which is further strengthened by zinc substitution7. \nFurthermore, ME coupling seems to be dependent on geometric parameters such as layer \nthickness, number of layers, and volume ratio of the two phases. Strongest ME effects were \nobtained for co -sintered thin layers of PZT/nickel -zinc ferrite in the range o f 10µm using the \ntape-casting8 route . Giant magnetostrictive material such as Terfenol -D (Terbium Dysprosium \niron alloy),  were also used in laminated configurations associated with PZT or PMN -PT at \nresonant or sub -resonant frequencies4,9,10. Rare earth -iron alloys have been developed to reach  \nlarge magnetostrictive strains (>1000ppm), and one obtains piezomagnetic coefficients as \nhigh as           at optimum bias field. Although giant ME coupling was obtained, the \nuse of Terfenol -D is not sui table for the following reasons: (i) t his material is extremely brittle  \nand it cannot be machined easily; (ii) i t cannot be co -sinter ed with piezoelectric materials; (iii) \nits high electric conductivity limits the use at low  frequen cy because of the eddy currents; ( iv) \nterbium  and dysprosium  is rare and expensive.  \nA piezoelectric/piezomagnetic bilayer can be modeled as two mechanically coupled \ntransducers. In the 1950s and 1960s, some investigations on cobalt -substituted nickel ferrite \ntransducer s were conducted  and some materials suitable for underwater applications were \nobtained11,12,13.  Although the best composition of ferrite quenched in air achieved a coupling \nfactor as high as 0.37,12 in the 1960s research has turn towards PZT materials which have \nbetter elect romechanical coupling. Nevertheless, in the field of ME composite, replacing \nconventional nickel ferrite with low magnetomechanical  coupling factor11 (k = 0.18) by \ncobalt -substituted nickel ferrite can lead to an improvement of the ME effect.  \nPiezomagnetism is an intrinsic property which depends on the internal DC Bias and AC \nexciting magnetic fields. The demagnetizing field14, depending on the overall geometry of the \nsystem, can greatly influence the ME response of a layered ME composite in th e longitudinal \nas well as the transversal modes. Actually, a layered structure is strongly anisotropic and the \ndemagnetizing field will affect rather differently the response of a system of given diameter \nand thickness under radial or axial excitations.   In the field of ME laminated composites, s ome studies have already be made on the influence \nof the demagnetizing effect  (see Ref. 15, 16, and 17) , but  in the se cases  only the ME \ntransversal mode was considered.  However, here,  we developed a simple model to take into \naccount the i nfluence of the demagnetizing field  in the ME transversal as well as  longitudinal \nmodes  for a layered structure. Especially, we have shown how the ME response in the \nlongitudinal mode can be easily ded uced from the measured response in the transversal mode \n(and vice -versa).  \nThis paper is organized as follow. In section I I, we present a  model derived from the \npiezoelectric and piezomagnetic equations in a two dimensional quasi -static approach where \ndemag netizing corrections are accounted for each ME coupling mode  (longitudinal and \ntransversal) , using the demagnetizing factor N. Useful tables of N values for discs or cylinders \nmagnetized along radius or axis are available in the literature18,19. For a given sample, the \nlinks between the axial and radial ME responses are studied theoretically. For the transversal \nME coupling, the effect of a decrease in the magnetic layer thickness was also theoretically \nstudied in term of demagnetizing effect and field penetration.  \nIn section III , we present the fabrication method of The ME samples . (Ni 0.973 Co0.027)1-\nxZnxFe2O4 compositions, with x = 0, 0.125, 0.25, 0.5 , have been synthesized by reactive Spark \nPlasma Sintering (SPS) method20. To the best of our knowledge, concerning layered ME \ncomposites, no publication in the literature concerns ferrites made by reactive SPS method s. \nHowever, this method permits high densification and an increase of the  magnetostrictive \nproperties can be expec ted. Zinc substitution has been used to help the sintering stage with \nSPS to be accomplished because of the high diffusion capability of the Zn2+ ions. Moreover, \nas showed by some authors7, a certain amo unt of zinc permits to optimize  the piezomagnetic \nbehavior of ME composites. After SPS, all samples were annealed in natural atmosphere at \n1000°C for re -oxidation, and some of them were quenched in air to estimate the effect of a \nheat treatment. All ferrite discs were pasted on commercially availa ble PZT dis cs to form \nbilayers or trilayers and transversal ME coefficient measurements  were performed  at sub -\nresonant frequency (80Hz) . \nIn section IV, the ME response s of the ME samples made with ferrites with different Zn \ncontent s and heat treatments are presented. A possible explanation concerning the quenching \neffect s is given.  In this purpose, we have developed an original set -up to measure the intrinsic \nME coefficients  of ME sample s. The aim of the measurement is to avoid the demagnetizing \neffect in the magnetic material when an AC magnetic field is applied.  In the other hand , the \nlink between the transversal and longitudinal ME modes is studied experimentally and \ntheoretically in t erms of demagnetizing effects and mechanical coupling. In the transversal \nmode, the demagnetizing effect s in ME responses are  also studied for  samples including  \nferrite with various layer thickness es and configurations . The mechanical coupling between \nferrite and PZT layers is an important parameter that influence the ME re sponse and it \ndepends on the configuration s of the layers. Studies were conducted on bilayers and trilayers \nto show what is the configuration with the best mechanical coupling.  For a non-symmetrical \nsample, the possible effe ct of the flexural strain is bri ng out.  The p erformance s of these ferrite/PZT bilayers have  been assessed against other ME \ncomposites with high performances such as Terfenol -D/PZT bilayer. A Terfenol -D disc was \npurchased and pasted on a P ZT disc. For relevant comparison , this ME sample  exhibit  the \nsame geometry, dimension , and volume ratio , as our ferrite/PZT ME samples.  The ME \nresponses were explained estimating the piezomagnetic  and elastic properties of both \nmaterials.  \nFinally,  in section V, we report the fabrication of a passive current sensor prototype based on  \na transversal ME coupling . Layered ME samples made with NiCoZn -ferrites coupled with \nPZT exhibit a magnetic field sensitivity suitable to build non -resonant magnetic field or \ncurrent sensors . It was characterized using square and triangle waveforms and it show s \ncapabilities for high level AC current measurements (          )  in the kHz range with \ngood accuracy.  \nII. Theoretical analysis.  \nIn order to explain the behavior of a layered ME composite, we have first developed a  quasi -\nstatic 2 -dimensional model, with particular attention towards  the demagnetizing effects in \nlongitudinal as well as transversal coupling modes.  The interface of the bilayer is in the (1,2) \nplane and we assumed a perfect mechanical coupling between the two phases. The external \nmechanical influences on the ME composit e are considered negligible. The induced electric \nfield i s always in the (3) direction.  T ransversal ME coupling refers to the case  when ce DC \nbias and AC magnetic fields are both applied in the direction  (1). Longitudinal coupling refers  \nto bias and AC mag netic field applied in the direction  (3) (see Fig. 1).  \n1. Transversal coupling.  \nThe following constitutive equations are used for the direct and converse piezoelectric effects  \n(Einstein summation convention) : \n                                                                                                                                   (1) \n                                                                                                                                   (2) \nwhere     and     are strain and stress tensor components,     and    are electric induction and \nelectric field tensor components, and      ,     ,      are zero field compliance, piezoelectric \ncoefficient, and zero stress permittivity tensor components respectively.  \nIn the same way, the magnetostrictive ferrite can be modeled as a piezomagnetic material, \ngovern ed by the constitutive equations:  \n                                                                                                                                (3) \n                                                                                                                                  (4) \nwhere     and     are strain and stress tensor components,     and    are internal  magnetic \nfield and internal magnetic induction (within the ferrite) tensor components, and      ,     ,      are zero field compliance, piezomagnetic coefficient (which depends on the magnetic bias) , \nand zero stress permeability tensor components respectively.  \nIn the bilayer configuration, the interface coincides with the 1 -2 plane,  and only extensional \nstrain in those directions are considered. S o only the     ,    ,    ,    ,    ,    ,    ,      tensor \ncomponents are to be considered. The electric field is produced in the direction (3) only, so    \nand    reduced to    and   . Lastly, assuming open electrical circuit (no current flowing \nfrom one electrode to the other),     . So Eq. (1) and (2) reduce to:  \n                                                                                                                             (5) \n                                                                                                                             (6) \n                                                                                                                     (7) \nIn the same way, Eq. (3) reduces to:  \n                                                                                                                         (8) \n                                                                                                                       (9) \nif the AC and DC magnetic field are applied along the direction (1). \nAt equilibrium, the force into the ferrite equates the one within the PZT (if we assume no \nforces absorbed by the glue layer), so from  the stress point of view:  \n                                                                                                                                     (10) \n                                                                                                                                     (11) \nwhere         ,    is the volume fraction of PZT and    is the volume fraction of ferrite. \nAssuming ideal coupling at the interface, ferrite and PZT are equally strained , so      equates \nwith     in one part, and     equates with     in the other part.  \nSo, equating Eq. (5 ) with (8) on the one hand and Eq. (6) with (9) on the other, and writing  \nthe two expressions as a function  of the stress within the PZT  (using Eq . (10) and (11)), one \nobtains the formula:  \n                                                                                             (12) \nEq. (7) gives the electric field generated by the stress within the PZT:  \n        \n                                                                                                                          (13) \nLastly, combining Eq. (12) and (13), the electric field    is related to the AC internal \nmagnetic field     : \n                   \n                                                                                                               (14) This formulation for the transversal coupling is similar to the one given by some authors21. \nBut in Eq. (14)  the induced electric field is related to the internal magnetic field.  \n2. Longitudinal coupling.  \nIn this configuration Eq. (5), (6), and (7), governing the piezoelectric material behavior, \nremain unchanged. In Eq. (8) and (9), the direction of the internal magnetic field must be \nchanged from direction (1) to direction (3) and consequently, the piezoma gnetic coefficient is \nnow:  \n                                                                                                                       (15) \n                                                                                                                       (16) \nLastly, the formula coupling the electric field    and the AC internal magnetic field    can be \neasily deduced from Eq. (14):  \n               \n                                                                                                                       (17) \nIt must be noted that a flexural strain exists within an asymmetric bilayer , and it leads to a \nlowering of the extensional strain level. The model proposed here do not take into account the \nflexural behavior, and consequently the calculation may overestimate the ME response of a \nbilayer. Nevertheless, this model gives an overall trend of the mechanic, piezomagnetic, and \npiezoelectric parameter influences.  \n3. Demagnetizing effect.  \nExperimentally, the magnetoelectric effect is measured by applying to the ME sample a small \nAC magnetic field (produced by Helmholtz coils) superimposed to a DC field (produced by \nan electromagnet). The level of the applied AC field can be measured by means of a Hall \neffect probe  or a search coil . Consequently, the ME coefficient is normalized using the \napplied magnetic field Ha. In order to compare theory and experiments, theoretical formulas \n(Eq. (14) and (17)) must be expressed in term of the external field Ha.  The demagnetizing \nfield       created by the sample is opposed to the external  applied  field       produced by the \nHelmholtz coils. Consequently the internal field       is lower than the external one.  Within the \nmagnetic material, the internal  magnetic field15 (in average over the volume)  is: \n                                                                                                                              (18) \nwhere N is the magnetometric demagnetizing factor (      ), and       is the alternative \nmagnetization variation produced by the small AC magnetic field. The alternative \nmagnetization is related to the internal AC field:  \n                                                                                                                                           (19) \nWhere   is the reversible  magnetic susceptibility  (under constant stress) . The internal AC \nfield is expressed as:        \n                                                                                                                                    (20) \nχ can be considered constant for       and practically independent of     if       .  \nIn the same way, the bias DC field produced by the electromagnet is reduced by the \ndemagnet izing effect in the ferrite.  The internal DC field is given by:  \n        \n                                                                                                                               (21) \nWhere           is the static magnetic susceptibility  (under constant  stress) . \nConsequently, t he ME coefficient with respect to the external applied field, for the transversal \ncoupling  mode ,    , and for the longitudinal one,    , are given by : \n      \n                    \n                                        \n                                                                 (22)       \n      \n                \n                                        \n                                                                 (23)         \nWhere   , and     are the radial and axial magnetometric demagnetizing factors respectively.                                                \nIn the  case of cylinders , the demagnetizing factors    and    depend on the ratio of thickness \nto diameter t/d of the magnetic sample and little on the susceptibil ity χ of the material. In Fig. \n2, using data published by D. X. Chen et al. ,18,19 the radial and axial demagnetizing factors \nwere plotted as function of t/d for different values of susceptibility.  Good accuracy are \nobtained for demagnetizing factor         and         expressed as function of thickness to \ndiameter ratio only. For a given piezoelectric material, mechanical, dielectric, and \npiezoelectric properties can be regarded as constants. So, the shape of the ME curves depend \nonly on the intrinsic piezomagnetic coefficients and the static and reversible  susceptibility \n       which are controlled by the internal bias field     . Note that the intrinsic \npiezomagnetic coefficients are relat ed to strain derivatives with respect to the internal field  H. \nAccording to Eq. (20), and (21) demagnetizing effects also influence the ME bilayers \nbehavior .  \nEq. (22) and (23) are quite similar. They differ only in the piezomagnetic  coefficients and the \ndemagnetizing factors. We can expect  similar magnetoelectric behaviors when measurement \nare made in the transversal and longitudinal modes. Because Joules magnetostriction  is a \nconstant volume  deformation (in general, volume magnetost riction can be neglected) , for \npolycrystalline ferrite with random lattice orientations, the piezomagnetic coefficients are \nsimply linked and it can be assumed that                      for the same internal bias \nfield.  \nTheoretically, according to Eq. (22) and (23),  high magnetoelectric effects are obtained when \nthe piezomagnetic material has the following properties: (i) low reversible  magnetic \nsusceptibility χ which permits high internal AC field, (ii) high intrinsic piezomagnetic \ncoefficient d, (iii) low compliance coefficients      and     . It is equivalent to maximize the following ratio:  \n    . This ratio is quite similar to the magnetomechanical  coupling factor22  \n   \n       (where           is the absolute permeability) which indicates the \ncapabilities of a magnetostrictive material to convert magnetic energy t o mechanical one (and \nvice-versa ). In conclusion, good magnetic materials for magnetoelectric applications are to be \nchosen among the  class of high magnetomechanical  coupling piezomagnetic ferrite \ncommonly used in ultrasonic transducer applications. In the 50’S and 60s, many  \ninvestigation s11,12,13  have been made in the field of underwater acoustic. It turns out that \ncobalt substituted nickel ferrites have high magnetomechanical  coupl ing factor , within the \norder of magnitude  of 0.3  (at the optimum bias). These compositions will be the starting point \nfor our study of ME bilayer.  \nIII. Experiment.  \n1. Samples fabrication.  \nNanosized (< 50nm) powders purchased from Sigma -Aldricht  (Fe 2O3, NiO, Co 3O4, ZnO) \nwere used as precursor oxides. The compositions (Ni 0.973 Co0.027)1-xZnxFe2O4, where x = 0, \n0.125, 0.25, 0.5 , were obtained  by mixing  the different powders in appropriate ratios. All \npowders were  mixed by ball milling  (30 min at 200  rpm), and then grinded  at 600  rpm for 1 \nhour.  SPS was used for the spinel structure formation and sintering stage s. Mixtures were \nloaded in a cylindrical graphite  die (10mm inner diameter) between two pistons  applying \nuniaxial stress. Carbon paper was used as separator between powder , carbon die and pistons . \nThe reaction and then the sinter ing were carried out in neutral atmosphere (argon) by heating \nthe powder with a pulsed DC current under application of uniaxial stress. The reaction stage \nwas performed at 600°C under a pressure of 100MPa for 5 minutes. The densification is \nobtained at 850°C for 3 minutes under the same pressure. After sintering, the sample s are \nobtained in the form of 10mm diameter and 2mm thick discs. For each composition,  several  \nsamples were produced . All these samples were annealed in air at 1000°C for 1 hour . For each \ncomposition , we produced two samples:  one quenched in air (except x=0) and the other  \nslowly cooled (approximately 3.5°C/min). Part of  ferrite discs (2mm thickness) were directly \npasted with silver epoxy (Epotek E4110) on PZT discs (PZ27 (Ferroperm)) with the same \ndiameter. One other  part of  ferrit e discs were cut to reduce the  thickness (1mm) and pa sted \non PZT discs (PZ27).  F inally, two ferrite discs were drilled to form rings, and then, they were \npasted on PZT rings (Pic255 (Physik Intrumente)). All the piezoelectric discs or rings are \npolarized  in the thickness direction  (3). The ME sample characteristics are resumed in Table \n1. It must be noted that the SPS sintering process in argon atmosphere produces ferrites with \nsome deficiency in oxygen, and some Fe3+ ions reduce into Fe2+. The anne aling at 1000°C in \nnatural atmosphere do not re -oxidize the ferrite  completely  because of the low porosity. As a \nconsequence, the conducti vity of the material increases, but this is not affecting  layered ME \ncomposites  performances . \n2. ME measurement procedure.  The ME coefficient is measured as a function of external applied DC magnetic field      \nproduced by an electromagnet23. For each      working point, a small external applied AC \nmagnetic field    (1mT, 80Hz) produced by Helmholtz coils is superimposed. Low \nfrequency is used to avoid any resonance effect, so ME bilayers are excited in quasi -static \nmode. The ME voltage is measured by means of a lock -in amplifier (EG&G Princeton \nApplied Research Model  5210) with high input impedance (100MΩ). All the measurement \nwere performed  at room temperature. When the external magnetic field s (AC and DC bias)  \nare perpendicular to the electrical polarization direction, the experimental transversal ME \ncoefficient is : \n      \n                                                                                                                                  (24) \nwhere    is the electric field  within  the PZT layer .     is the external  AC field applied  in the \ndirection  (1). When the magnetic field s (AC and DC bias) are  parallel to the electric \npolarization direction, the experimental  longitudinal ME coefficient is :  \n      \n                                                                                                                                  (25) \nwhere     is the external  AC field applied in the direction  (3). \nIV. Results and discussion.  \n1. Influences of the quench ing and Zn content s in the ferrites . \nIn order to measure the effects of heat treatment and Zn content  on the properties  of ferrites , \nthe transversal ME coefficients were recorded  for the different ferrite compositions (x= 0, \n0.125, 0.25, and  0.5), for slow -cooled and quenched samples  (see Fig. 3 ). The maximum ME \neffect occurs at magnetic DC fields  between  30 kA/m and 55kA/m for all compositions. The \nmaximum ME effect is obtained for x=0.125, and decrease s with Zn content. For x=0.125, the \nME effect is large r for the slow -cooled samples. By opposition, f or x=0.25 and 0.5, the  \nquench ing enhances the ME coefficients. The increase in the non -magnetic Zn2+ content from \nx=0.125 to x=0. 5 produces two effects which work together: (i) the saturation \nmagnetostriction decreases because of the dilution of the magnetostrictive cations (Ni2+, Co2+, \nFe2+), and so, the piezomagnetic coefficient decreases too; (ii) the permeability increase and \nas a consequence the internal field decreases according to Eq. (20). A possible explanation of \nthe effect of heat treatment can be given as follow . CoFe 2O4 is usually consider ed as an \ninverse spinel ferrite, b ut the cations distribution depends on the heat treatment24. At high \ntemperature , Co2+ and Zn2+ ions which have the same radius (82 pm) may be distributed in \nboth sites (tetrahedral and octahedral) because magnetic interaction have no effect.  By \nquenching, a part of Co2+ cations can be frozen into thei r high temperature position s which \ncorrespond to a more randomized distribution25. By opposition , slow -cooling gives time for \ncations to move into their low temperature equilibrium positions. In contrast, for NiFe 2O4 \nferrite, the cations  distribution (inverse spinel) seems to be independent of the heat treatment \nor cooling method of the fabrication process24. In case of Co substituted NiZn -ferrites, a \nreasonable assumption is that the quenching affects the distribution of the Co2+cations in the tetrahedral and octahedral sites. This distribution is also influenced by the Zn2+ rate: Zn2+ \ncations which occupy the tetrahedral sites can affect the migration of Co2+ cations during a \nthermal treatement.  Thus, quenching and Zn2+ rate affects the local electronic symmetry, and \nin turn, spin -orbit coupling dependent properties, namely the magneto -crystalline anisotropy \nand the magnetostriction.  \n2. Link between transversal and longitudinal modes.  \nTo investigate the effects of the coupling  modes, transversal and longitudinal ME coefficients \nwere measured  (see Fig. 4) for the sample #  0.5SC2/1 . As expected, for longitudinal coupling, \nfor which the AC and DC demagnetizing fields are higher, the peak of the ME curve is lower \nand it occurs at higher external bias field. Eq. (22) and (23) show that transversal and \nlongitudinal ME coefficients are strongly linked and that they can be deduce d from each other \nif demagnetizing field corrections are done, knowing the static and reversible magnetic \nsusceptibility of the ferrite. For this purpose, a spherical sample of  ferrite was machined  \n(diameter: 2mm) and characterized using a Vibrating Sample  Magnetometer (VSM) \n(LakeShore 7404). The virgin magnetization curve versus internal field ( after demagnetizing \nfield correction) is given Fig. 5 . From this measurement, the differential  susceptibility \n      was deduced and plotted on the same figure.  From transversal coupling to \nlongitudinal coupling, due to the demagnetizing effects, the amplitude of the ME response \nmust be corrected by the ratio                 . Obviously, at low magnetic bias,  it is \nknown that  the reversible  susceptibility is different from the di fferential susceptibility. But in \nthis case, where both reversible  and differential susceptibility are high, the ratio is \nindependent of the susceptibilities and can be approximated by       .The value of the \nsusceptibility affects the result only if     is within the order of 1 which practically means \n     in the present case ( or for H above 50kA/m). In this region (approach to saturation) \nthe differential and reversible susceptibilities are equal.  According to Eq. (20), (21), (22), and \n(23), the solid line curve in Fig. 4  is deduced from the experimental transversal coupling \ncurve (dashed line), making d emagnetizing field corrections. It is noted that for isotropic \npolycrystalline ferrites,                               in theory. Here, to fit the curves, \nwe have taken piezomagnetic coefficients with a  ratio of                       . This \ndeviation can be explained by a n anisotropic piezomagnetic  behavior of the ferrite. This point \nwill be discussed in section IV.5.  of the paper . Concerning the transversal coupling, the peak \nof the ME coefficient is obtained for a           external applied bias field. At this \nworking point, the reversible  susceptibility i s around 23 and according Eq. (20), the internal \nAC field is four times lower than the external one. Hence, due to the demagnetizing field, the \nME coefficient is correspondingly diminished.  \n3. Ferrite  layer thickness effects on the ME response.  \nAs seen before, radial and axial demagnetizing effects, which are quite different for a given \nsample, have a considerable influence on the ME response . The demagnetizing effect  can be \ntuned  in the same radial mode by changing  the thickness of the magnetic material in the ME \nsamples: according to Fig. 2 , the radial demagnetizing factor    decreases when the thickness \nis decreased for a given diameter. To illustrate this point, a ME bilayer sample was made with a thin ferrite disc of 1mm in thickness pasted  on a 0.5mm PZ27 disc  (sample # 0.125SC1/0.5) . \nIts behavior was compared to the reference ME sample with 2mm thick ferrite layer of the \nsame composition pasted on a 1mm PZ27 disc  (sample # 0.125SC2/1 ). Note that for better \ncomparison, the two ME samples hav e the same PZT/ferrite volume ratio (γ=1/2).  The two \nmeasured ME coefficients are given in Fig. 6 . Both curves have approximately the same \namplitude whereas the main effect of the demagnetizing field is to shift the peaks of the \ncurves. The experimental  ME curve of the reference sample (# 0.125SC2/1) was corrected in \ndemagnetizing effect to obtain the behavior of the 1mm thick ferrite ME sample. The method \nused here is similar to the one used before for the longitudinal ME coefficient calculation: a \nspheri cal shape of ferrite was characterized using a VSM. From the virgin magnetization \ncurve, the susceptibilities were deduced, and then demagnetization corrections were done.  \nThis theoretically corrected cu rve (thi n dashed line in Fig. 6 ) exhibits  correct do wnshift in the \npeak position but the ME amplitude is slightly overestimated with respect to the measured \none. Next, a trilayer ferrite/PZT/ferrite of the same composition with 1mm thick for each \nferrite layer pasted on a 1mm thick PZ27 layer was made  (sample # 0.125SC1/1/1) . Its M E \ncoefficient (plotted in Fig. 6 , thick dotted line) is quite higher than that of the reference \nbilayer sample. This behavior cannot be explained by a demagnetizing effect. In fact, the \ncorrected curve in demagnetizing effect  (thin dotted line) from that of the reference sample \nhave quite lower amplitude compared to the experimental one. We assume that this high ME \neffect is due to a higher mechanical coupling between PZT and ferrite layers because the PZT \nlayer is stressed on  its two faces. Furthermore, due to the symmetric geometry of the trilayer , \nno flexural strain occurs: a higher stress  is transmitted from the two ferrite layers to the \npiezoelectric one.  In this case, the mechanical  behavior of the ME composite is  close r to the \nsimplified  model calculated in section II (see section IV. 5.  for precisions)  Note that for the \ntrilayer sample, the horizontal shift  in the ME curve  is half less than the bilayer  one. Whereas \nin the two cases the ferrite layers have the same thickness (1mm), in the trilayer case there is a \nmagnetic coupling between the two ferrite layer, increasing the demagnetizing factor. We \nestimate that this factor is increased from 0.0881 for  a single ferrite layer (1mm thick) to \n0.115 for two ferrite layers separated by a 1mm PZT layer. To confirm the overall trend of a \nME trilayer, one another sample  (# 0.125SC0.5/0.5/0.5)  was made: two ferrite layer ( 0.5 mm \nthick each) were pasted on both f aces of a PZ27 layer  (0.5mm thick).  Its measured ME \ncoefficient is plotted (dashed line)  in Fig. 7 .  Due to a lower demagnetizing field and a good \nmechanical behavior, the peak ME coefficient is increased up to 0.55 V/A.  \n4. Effect of an inhomogeneous  strain on the ME response . \nThe trilayer sample (# 0.125SC1/1/1) have quite higher ME coefficient compared to the \nbilayer reference sample (# 0 .125SC 2/1),  and the whole difference cannot be explain if we \nconsider only the demagnetizing effect. Firstly, w e may assumed that a flexural strain of the \nbilayer produces a decrease of the stress in the piezoelectric layer compared of the case of a \ntrilayer with no flexural strain. To answer this question, a trilayer sample was made: two \nPZ27 layers (0.5mm thick ea ch) were pasted on both faces of a ferrite layer (2mm thick). This \nsample (# 0.125SC0.5/2/0.5 ) have the same demagnetizing factor and the same volume ratio as \nthe reference sample. But due to its symmetric geometry,  no flexural behavior can occur . The ME coefficient was measured and plotted in Fig. 7 (dotted -dashed line). This trilayer sample \nand the bilayer (reference) sample have comparable ME behavior  with the same peak value of \n0.2V/A.  We can conclude that the flexural strain behavior of the referen ce bilayer sample \nhave negligible influence on the peak of the ME coefficient since the whole thickness (3mm) \nis only 3.3 times lower than the diameter of the sample  (10mm). Lastly, only the in -plane \nstrain have to be considered to predict the ME response.  The exact solution of the strain field  \n(strongly inhomogeneous)  in the whole ME sample can be calculated only by numerical \nmethod s (Finite Element Method, for example). Nevertheless, an experimental estimation of \nthe strain level in each layers of the ME sample can be made. For this purpose, two strain \ngauges (EA -06-062TT -120, Micro -Measurements) were pasted on each free face s of the PZT \nand ferrites layers of the reference bilayer sample (# 0.125SC2/1). The strain gauges were \nchosen because of their small  sensitive areas  (1.8× 1.8 mm2) that permit s local measurement s \nnear the edge of the faces where the strains are expected to be high ly different . The \nlongitudinal strains versus DC magnetic field are  given in Fig. 8. As expected, the strain at the \nsurface of ferrite layer is quite higher than the one measured for the PZT layer.  At saturation,  \nwe obtain            for the ferrite, and            for the PZT. Although t hese \nmeasurements were made on surfaces , average values of the strains in each layer s can be \nestimated when a linear profile for the strain along the direction (3) is assumed.  Using \ngeometric considerations, we obtain                in the ferrite and                \nin the PZT.  The ratio of strain s,                   at saturation , is quite low. In fact, the \nstress is applied on one face of the PT Z layer, the other face staying mechanically free. So, the \npropagation of a longitudinal strain from the ferrite/PZT interface to the  free face of the PZT \nlayer is mainly due to a shear stress  effect . Note that the value of the ferrite strain at saturation  \n(          ) of the ME sample is higher than the magnetostriction saturation (      \n      ) measured for a mechanically fr ee material (see Fig. 13). This difference can be \nexplained as following: (i) the strain gauge was pasted near the edge of the ferrite disc of the \nME sample while the magnetostriction measurement was done with a strain gauge centered \non the surface of the disc where the strain is theoretically lower ; (ii) the PZT layer acts like a \nmechanical load (or  pre-load) on the ferrite layer, and as a consequence , the magnetostriction \nat saturation is increased in comparison to a mechanical ly free ferrite sample. The average \nstrains in ferrite layer and PZT layer are quiet different: we have estimated                  \nand this effect highly deceases the ME response of a bilayer sample . So when the strain ratio \nis introduced for the longitudinal mechanical coupling ,              , as well as  for the \ntransversal mechanical coupling ,                with the same value   , Eq. (22) is modified \nas (transversal ME coupling) : \n      \n                     \n                                         \n                                                                 (26)       \nObviously, an equivalent modification can be applied to Eq. (23) for the longitudinal ME \ncoupling.  \n5. Effect of  the quenc hing  on the ME response.  For Zn-rich samples (x=0.25 and x=0.5), the quench of ferrites permits to enhance the \nmagnetoelectric coupling. According Eq. (22), this enhancement can have two main causes: \nthe improvement of the intrinsic piezomagnetic coefficients or a weakening o f the mag netic \nsusceptibility. To answer this question, the following experiments were made. For the \ncomposition with x=0.25 (quenched and slow -cooled), the ferrite discs were delaminated \nfrom the PZ27 layers. Then, they were drilled to form ferrite rings with a ce ntered 3 mm hole.  \nA thin PZT ring (PIC255, 10mm out er diameter, 5mm internal diameter, 0.25mm thickness) \nwas pasted with silver epoxy on each ferrite rings. Samples are referenced 0.25Q2/0.25  and \n0.25SC2/0.25 . A 8 turns coil was wound on each ME ring . AC tangential magnetic field HAC \n(in the (1,2 ) plane) is forced within the ferrite when the AC current, IAC, is flowing  into the \ncoil:             , where D=6.5mm, is the mean diameter of the ferrite ring , and n=8, is \nthe number of turns  (so the demagnetizing factor N is 0 for HAC). The top electrode of the PZT \nlayers was separated into two part s (two strokes of file in the direction  (1)) and then, the AC \nvoltage  produced by a half piezoelectric layer (parallel to the magnetic field) was measured \nby means of  a lock -in amplifier . The ME samples were placed in a DC m agnetic field applied \nin the directio n (1) and produced by an electromagnet  (see Fig. 9 ). The corresp onding ME \ncoefficients versus external  applied  field     are given in Fig. 10 . The two curves, for \nquenched ferrite sample and slow -cooled ferrite sample, are quite similar: the same maximum \namplitudes are obtained for close DC fields (             ). So the quench do not \nmodify the intrinsic piezomagnetic behaviors of the ferrites. The differences obtained in ME \ncurves for quenched and slow ly cooled ferrite, when the ME coefficients are normalized using \nexternal applied AC field, are assumed to be t he result of the demagnetizing effects. The \ninitial permeability was measured for the two ferrites:       (quenched) and        \n(slow -cooled) and it confirms that a less penetrating magnetic  field in the second case reduces \nthe ME coefficient according  Eq. (22).  \n6. Co-substitued Ni -Zn ferrite properties compared to those of Terfenol -D. \nIn a aim of comparison, Terfenol -D discs with the same size as the NiCoZn -ferrites (10 mm \ndiameter and 2 mm thickness) were purchased from Etrema. One of them was pasted on a \nPz27 disc ( 10mm diameter, 1mm thickness) with silver epoxy. The measured transversal ME \ncoefficient is plotted in  Fig. 11  and compared to that of our best  bilayer sample   # 0.125SC2/1 . \nAs expected, Terfenol -D produces better ME effects but it is only 1.8 times higher. This good \nperformance of the ferrite/PZT composite compared to the Terfenol -D one should be \nexplained estimating the piezomagnetic and elastic properties of both materials. \nMagnetostriction cur ves (parallel and perpendicular to the H field in the (1,2) plane of the \nsample) were measured using a strain gauge (H06A -AC1 -125-700, Micro -Measurements) \npasted on a Terfenol -D disc.      is the magnetostriction measured in the direction (1) when an \nexter nal field is applied in the direction (1).      is the magnetostriction measured in the \ndirection (1) when an external field is applied in the direction (2). The result is given  Fig. 12 . \nOne observes saturation magnetostriction as high as              in the parallel mode and \n            in the perpendicular one, and it is in the range of  the data given by the \nmanufacturer. At the optimal external bias field of             the piezomagnetic \ncoefficients are                                  and                                 . It should be also noted that, in this particular case, the piezomagnetic \ncoefficients       and      are related to strain derivatives with respect to the external applied \nfield Ha, so the effects of the demagnetizing field is already contained in these measurements. \nIn the same way, a strain gauge was pasted on a NiCoZn -ferrite (with x=0.125), and parallel \nand perpendicular in plane magnetostri ctions were measured (see Fig. 13 ). Th e parallel \nmagnetostriction saturation is             which is approximately two times higher than \nthe perpendicular one (            ). One obtains the extrinsic piezomagnetic coefficients \nexpressed as a derivative with respect to the external fi eld:                           \n        and                                  at the optimal bias of      \n            . The      and      compliances were deduced from ultrasonic velocity \nmeasurements along the thickness direction of a NiCoZn -ferrite disc by using a pulse -echo \ntechnique (shear and longitudinal waves) at 20MHz. The longitudinal (           ) and \ntransverse (           ) waves velocities yield :                    , and       \n               . Assuming perfect isotropic polycrystalline ferrite,       and      reduce \nto:           and          . The Terfenol -D disc purchased from Etrema is grain oriented in \nthe thickness direction and exhibit an axial symmetry.  As a consequence, in  the transverse \ndirection, the compliances are rather  high:                    and            \n          (data from Etrema and Dong et al.10). So, we can say that the advantage due to  \nthe high piezomagnetic coefficient of Terfenol -D (17 times higher than the NiCoZn -ferrite \none) is counter balanced by its high compliance (19 times higher than the NiCoZn -ferrite \none). So according Eq. (22) , one can roughly estimate that Terfenol -D and NiCoZn -ferrite \nhave ME performance within  the sa me order when associated with PZT.  \nThe magnetostriction characterization is a helpful tool to estimate the magnetomechanical \nanisotropy of sample s. For the ferrite,  the parallel saturation  magnetostriction,       \n      , is two time s higher (in amplitude) than     . This leads to extrinsic piezomagnetic \ncoefficient s      and      in the same ratio, and consequently , the intrinsic piezomagnetic \ncoefficients     and     have the same ratio . We can conclude to isotropic piezomagn etic \nbehavior in the (1,2) plan. Measurement of saturation magnetostriction in the (1) direction , \nwhen a magnetic field is applied in the (3) direction , gives          , which is 4 times \nlower than     . It can be assumed that the value of the intrinsic piezomagnetic coefficients \n    is roughly               . As a consequence , the value of the ratio               is \n-0.5 which is quite  different from -1, the theoretical value for a perfect isotropic ferrite.  So, \nwe can conclude to large anisotr opic behavior  for 3 -1 piezomagnetic coupling . The physical \nreason of this phenomenon is unclear, but we assumed that a preferred direction is induced  \nwhen the uniaxial  stress is applied in the (3) direction during the reactive and sintering stages \nof the SPS synthesis .  \nUsing data of piezomagnetic, piezoelectric, and elastic p roperties (summarized in Table 2 ), \ntheoretical ME coefficients in transversal coupling at optimal bias were theoretically \ncalculated.  For sample # 0.125SC2/1 , the theory given by Eq. (22) predicts               \nwhich is two times higher than the experimental one.  Nevertheless, when a  strain ratio of \n                  (as measured before) is introduced, the theory predicts (Eq. (26)) \n              which is quite similar to             obtained experimentally. In contrast, for a trilayer of the same composition ( sample # 0.125SC1 /1/1) we obtain \nexperimentally               which is closer to the theoretical value  (corrected in \ndemagnetizing field) given by Eq. (22)              . Using Eq. (26), experiment and \ntheory give the same result  when  a strain ratio of                     is introduced . At \nthis point , it is clearly seen that a  piezoelectric layer stressed on its both faces by two ferrite \nlayers produces average strain 77.5% higher compared to the case of a PZT layer stressed \nonly on one face by a single  ferrite layer. Concerning the Terfenol -D/P27 bilayer, theory  (Eq. \n(22))  leads  to               which is little bit more than tw ice higher than the \nexperimental result. Here again, this discrepancy is assumed to be due to a low average strain \nratio   when the piezoelectric layer is stressed by a single  magnetostrictive layer.  Using Eq. \n(26), theory and experiment give the same result if a strain ratio of                    is \nintroduced. This low strain ratio is assumed to be the result of the high stiffness of the \nTerfenol -D material.  \nFrom  another point of view, the dynamic magnetostrictive properties of a material can be \nexpressed in terms of energy conversion capabilities. The magnetome chanical  coupling factor \n                  is a function of the intrinsic piezomagnetic coefficient    , related to the \ninternal field,                 . This later can be expressed using the extrinsic \npiezomagnetic coefficient                  and the magnetomechanical  coupling factor \nbecome                         . Using data summarized in Table 2 , calculations lead \nto          for the NiCoZn ferrite, and          for the Terfenol -D material which is \nroughly 2 times higher. It is interesting to see that the two ME coefficients of the two \nmaterials have th e same ratio 2:1. This suggests that the magnetomechanical  coupling factor \nis an appropriate criterion to select  magnetostrictive materials to be used into ME multilayer \ncomposites.   \nV. Sensor prototype.  \nLastly , we have made a prototype of a current sensor based on a ME composite. The trilayer \nferrite/PZT/ferrite  (sample # 0.125SC1/1/1)  with             was placed in a small AC -\ncoil made with four turns of an isolated wire. The low bias field required to polarize the ferrite \nmaterial is produced by two small permanent barium ferrite magnets. The distance between \nthe magnets and the trilayer was set to ob tain the highest ME effect. The AC current flowing \ninto the AC -coil was produced by a power amplifier connected in series with a 4Ω power \nresistor. This current was sensing by a commercial active current probe (Tektronic A622) for \ncomparison. The ME voltag e was sensed directly by a passive voltage probe with 10MΩ input \nimpedance connected to an oscilloscope (Lecroy Waverunner 44Xi). 10A peak square and \ntriangle current waveforms at 1kHz were used to characterize the response of the ME sensor \nin the sub -resonant mode. Fig. 14 and Fig. 15  show that, at this frequency, the phase shift is \nnegligible, and the sensor have a good linearity and low noise level. Here, the gain of the ME \ncurrent sensor is approximately 87mV for 1A flowing into the wire. Obviously, thi s gain can \nbe set to a given value by adding or removing some turns to the AC coil or by changing its \nsize.  We have already properly characterized current sensors with the same structure (but \nwith lower sensibility). The results will be given in a paper28 (not yet published ).  VI. Conclusion  \nCo-substituted Ni -Zn ferrite were synthesized using a non conventional solid state reaction \nand sintering route based on a SPS method. These ferrites showing  high magnetomechanical \ncoupling factors are suitable to make multilayer ME composites exhibiting strong ME effects \nas predicted by a theoretical model. ME performances obtained with an optimized \ncomposition of NiCoZn -ferrite/PZT bilayer are comparable to those obtained with the same \nstructure combining Terfenol -D and PZT. It was shown that the low piezomagnetic coupling \nperformance of the ferrite (in comparison to the Terfenol -D) is balanced by a low compliance \nthat permits high stresses produced by low strains. Another important  parameter that \ninfluence the ME behavior is the demagnetizing factor associated with the susceptibility of \nthe magnetic material. By lowering the internal AC and bias magnetic fields, demagnetizing \neffects partially shape the ME coefficient curves. By var ying the thickness of the magnetic \nlayer or by changing the exciting modes (axial or radial), the peak of a ME coefficient curve \ncan be tuned , and its amplitude is affected. In the axial mode, due to better penetration of the \nmagnetic field, the theory pre dicts higher ME coupling for low thickness to diameter ratios \nand as a consequence, the ME curve peak is shift down.  In conclusion, the ME behavior of a \nlayered ME sample  is the result of three intrinsic parameters of the magnetic material: the \nintrinsic piezomagnetic coupling coefficients, the compliance, and the magnetic susceptibility. \nFurthermore, it was shown that the demagnetizing factor and the mechanical coupling \nbetween the layers are  the extrinsic parameter s of the magnetic material that influenc e the ME \nbehavior. Finally, we used Co -substituted Ni -Zn ferrite associated with PZT in a trilayer \nstructure as a ME current sensor. The device was purely passive: the bias field was obtained \nwith two barium ferrite magnets and the ME voltage was directly measured with a passive \nvoltage probe. The characterization in a nonresonant mode have shown a high linearity and a \nnegligible phase shift. The gain of the sensor is closed to 90mV/A for courant in the 0 -10A \nrange that meets performance suitable in the fie ld of power electronic applications.  \n \n \n \n \n \n \n \n \n \n REFERENCES  \n1M. Fiebig, J. Phys. D  : Appl. Phys. 38, R123 (2005).  \n2G. Catalan and J.F. Scott, Adv. Mater. 21, 2463 -2485 (2009).  \n3M. Kumari, C. Prakash, and R. Chatterjee, J. Appl. Phys. 113,17D918 (2013).  \n4C. W. Nan, M. I. Bichurin, S. Dong, D. Viehland, G. Srinivasan, J. Appl. Phys. 103, 031101 \n(2008).  \n5G. Srinivasan, C. P. DeVreugd, and C. S. Flattery, Appl. Phys. Lett. 85, n. 13, 2550 (2004).  \n6G. Srinivasan, V.M. Laletsin, R. Hayes, N. Puddubnaya, E.T. Ra smussen, D.J. Fekel, Solid \nState  Communications 124, 373 -378 (2002).  \n7G. Srinivasan, E.T. Rasmussen, and R. Hayes, Phys. Rev. B 67, 014418 (2003).  \n8G. Srinivasan, E.T. Rasmussen, J. Gallegos, R. Srinivasan, Y.I. Bokhan, V.M. Laletin, Phys. \nRev. B 64, 2144 08 (2001).  \n9S. Dong, J. G. Bai, J. Zhai, J.F. Li, G.Q. Lu, D. Viehland, S. Zhang, T.R. Shrout, Appl. Phys. \nLett. 86, 182506 (2005).  \n10S. Dong, J. Cheng, J.F. Li, and D. Viehland, Appl. Phys. Lett. 83, n. 23, 4812 (2003).  \n11Y. Kikuchi, IEEE Trans. Mag. , VO L. MAG -4, NO.2, June 1968.  \n12S. F. Ferebee and C. M. Davis, Jr, J. Acoust. Soc. Am. Vol. 30, NO. 8, 747 (1958).  \n13A. P. Greifer, J. Appl. Phys. Vol. 35, NO. 3, 1065 -1066 (1964).  \n14S. Chikazumi, Physics of magnetism, pp 19 -24, John Wiley & Sons, INC (1964).  \n15E. Liverts et al.,  J. Appl. Phys. 109, 07D703 (2011).  \n16D. A. Pan, J. Lu, Y. Bai, W. Y. Chu, and L. Qiao, Chinese Science Bulletin, vol. 43, n°14, \n2124 -2128, July 2008.  \n17J. Yang, Y. Wen, P. Li, and X. Dai, PowerMEMS  2009, Washington DC, USA, December \n1-4, 2009  \n18D.X. Chen, E. Pardo, and A. Sanchez, IEEE Trans. Magn. VOL. 37, NO. 6, 3877 (2001).  \n19D.X. Chen, J.A. Brug, R.B. Goldfarb, IEEE Trans. Magn. VOL. 27, NO. 4, 3601 (1991).  \n20K. Zehani, F. Mazaleyrat, V. Loyau, and E. Labouré, J. Appl. Phys. 109, 07A504 (2011).  \n21M.I. Bichurin, V.M. Petrov, G. Srinivasan, Phys. Rev. B 68, 054402 (2003).  \n22Z. Kaczkowsski, J. Magn. Magn. Mater. 41, 338 -340 (1984).  23G.V. Duong, R. Groessinger, M. Schoenhart, D. Bueno -Basques, J. Ma gn. Magn. Mater. \n316, 390 -393 (2007).  \n24G.A. Sawatzky, F. Van Der Woude, and A. H. Morrish, Phys. Rev.  vol. 187, n. 2, pp 747 -\n757 (1969).  \n25I.C. Nlebedim et al. J. Magn. Magn. Mater. 322 (2010), pp 1929 -1933.  \n26 http://www.ferroperm -piezo.com/  \n27http://piceramic.com/  \n28V. Morin et al. , “ A multiferroic composite based magnetic field sensor”,  submitted \n(December 2014) in Sensor & Actuators  (under review) .  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n \n \n \n \n \n \n \n \nSample  #  Ferrite Zn \ncontent  Layer configuration s Layer thickness   \n(mm)  Ferrite thermal \ntreatment  \n0.5Q2/1  x=0.5  Ferrite/PZ27  2/1 quenched  \n0.5SC2/1  x=0.5  Ferrite/PZ27  2/1 slow cooled  \n0.25Q2/1  x=0.25  Ferrite/PZ27  2/1 quenched  \n0.25SC2/1  x=0.25  Ferrite/PZ27  2/1 slow cooled  \n0.125Q2/1  x=0.125  Ferrite/PZ27  2/1 quenched  \n0.125SC2/1  x=0.125  Ferrite/PZ27  2/1 slow cooled  \n0SC2/1  x=0 Ferrite/PZ27  2/1 slow cooled  \n0.25Q2/0.25  x=0.25  Ferrite/Pic255  2/0.25  quenched  \n0.25SC2/0.25  x=0.25  Ferrite/Pic255  2/0.25  slow cooled  \n0.125SC1/0.5  x=0.125  Ferrite/PZ27  1/0.5  slow cooled  \n0.125SC1/1/1  x=0.125  Ferrite/PZ27/Ferrite  1/1/1  slow cooled  \n0.125SC0.5/0.5/0.5  X=0.125  Ferrite/PZ27/Ferrite  0.5/0.5/0.5  slow cooled  \n0.125SC0.5/2/0.5  X=0.125  PZ27/Ferrite/PZ27  0.5/2/0.5  slow cooled  \n \nTable 1: Characteristics of the ME  composite  samples. The different  ferrite compositions are \n(Ni 0.973 Co0.027)1-xZnxFe2O4. \n \n \n \n \n \n \n \n  \n \n \n \n \n \n \n \n \n \n \n      \n(pC/N)       \n(nm/A)       \n(nm/A)       or      \n(m2/N)      or      \n(m2/N) µT or      \n(in relative)  \nPZ27    -170                       1800  \nPic255  -180            - 2400  \nNiCoZn -ferrite   -0.67 0.32                        95 \nTerfenol -D  11.2 -7.3                       10 \n \nTable 2 : Material properties for PZ27 (cited from Ferroperm26), Pic255 (cited from Physik \nIntrumente27), NiCoZn Ferrite (x=0.125) , and Terfenol -D.  \n \n \n \n \n \n \n \n \n \n  \nFIGURE CAPTIONS  \nFig 1. Sketches of the transversal coupling (top)  and longitudinal coupling (bottom). The 1 -2 \nplane coincides with the bases of the cylindrical ME sample . \nFig 2.  Radial demagnetizing factor (triangle symbols) and axial demagnetizing factor (circle \nsymbols) as a function of the thickness/diameter ratio of the magnetic material. Open circles: \n       . Filled circles:      .  Open triangles:    . Filled triangle s:    . Data are \nfrom D. X. Chen et al16,17. \nFig 3 .  Transversal magnetoelectric coefficient     for the various Zn contents in ferrites. \nTop: slow -cooled ferrites. Bottom: quenched ferrites. All ferrites are pasted on PZ27 discs.  \nFig 4 . Transversal (das hed line) and longitudinal (dotted line) magnetoelectric coefficients  \nfor the sample # 0.5SC2/1 .  The solid line is the longitudinal ME coefficient calculated from \nthe transversal one.  \nFig 5 . Magnetization and magnetization derivative measured for the slow -cooled ferrite  with \nx=0.5  Zn content . \nFig 6 . Transversal magnetoelectric coefficients for bilayers and trilayer made with NiCo Zn \nferrite (x=0.125) and PZ27. Thick lines correspond to experimental ME m easurements. Thick \nsolid line: 2 mm/1mm ferrite/PZT bilayer  (reference sample) . Thick dashed line: 1mm/0.5mm  \nferrite/PZT bilayer . Thick dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer. The thin \nlines are curves deduced from the experimental one of the reference sample where \ndemagnetizing effects were corr ected. Thin dashed line: 1mm/0.5 mm ferrite/PZT  bilayer. \nThin dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer.  \nFig 7. Transversal magnetoelectric coefficients for (Ni 0.973 Co0.027)0.875Zn0.125Fe2O4/PZ27 \nbilayers and trilayer.. Solid line: 1mm/2mm PZT/ferrite bilayer (reference sample) . Dotted -\ndashed line: 0.5mm/2mm/0.5mm PZT/ferrite/PZT trilayer . Dotted line: 1mm/1mm/1mm \nPZT/ferrite/PZT trilayer. Dashed line: 0.5mm/0.5mm/0.5mm ferrite/PZT/ferrite trilayer. All \nthe lines correspond to experimental M E measurements.  \nFig 8: Strain curves versus applied external field along the parallel direction for the ME \nsample # 0.125SC2/1 (reference sample) . The closed circles correspond to strain measurement on \nthe ferrite face, and  open circles correspond to strai n measurement on the PZT face. The \nmagnetic field and strain measurements are parallel (and in the disc plane).  \nFig 9 . Top view of the ME device when circumferential AC magnetic field is forced within \nthe ferrite. The PZT top electrode is split into two ha lf electrodes (in grey) which produce two \nopposite voltage s V and V’. Only AC voltage produced by a half piezoelectric layer is \nmeasured.  Fig 10 . Transversal magnetoelectric coefficients when AC magnetic fields are forced within \nthe ferrite. Solid line: sample # 0.25Q2/1  (quenched ferrite ). Dashed line:  sample # 0.25SC2/1  \n(slow cooled ferrite ). \nFig 11 . Transversal magnetoelectric coefficient     for sample # 0.125SC2/1   (solid line) and \nTerfenol -D/Pz27 2mm/1mm bilayer (dotted line).  \nFig 12 .  Magnetostriction curves versus applied external field along parallel (closed circles) \nand perpendicular (open circles) directions for a Terfenol -D disc. The magnetic field and \nstrain measurements are in the disc plane.  \nFig 13 .  Magnetostriction curves vers us applied external field along parallel (closed circles) \nand perpendicular (open circles) directions for a ferrite disc with x=0.125. The magnetic field \nand strain measurements are in the disc plane.  \nFig 14 . Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). \nGrey line: ME voltage obtains at the electrical output of the piezoelectric material. The \ncurrent have a square waveform at 1kHz and 10A peak.  \nFig 15 . Black line: voltage obtains with an commercial active current probe  (gain: 100mV/A). \nGrey line: ME voltage obtains at the electrical output of the piezoelectric material. The \ncurrent have a triangle waveform at 1kHz and 10A peak.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n \n \n \n \n \n \n \n \n \nFig 1. Sketches of the transversal coupling (top)  and longitudinal coupling (bottom). The 1 -2 \nplane coincides with the bases of the cylindrical ME sample . \n \n \n \n \n \n \n \n \n \n \n \n \nFig 2.  Radial demagnetizing factor (triangle symbols ) and axial demagnetizing factor (circle \nsymbols) as a function of the thickness/diameter ratio of the magnetic material.  Open circles: \n       . Filled circles:      .  Open triangles:    . Filled triangles:    . Data are \nfrom D. X. Chen et al16,17. \n               \n     (1) (2) (3) \n                   \n(1) (2) (3) \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig 3 .  Transversal magnetoelectric coefficient     for the various  Zn contents in ferrite s. \nTop:  slow -cooled ferrites. Bottom: quenched ferrites.  All ferrites are pasted on PZ27 discs.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig 4 . Transversal  (dashed line) and longitudinal (dotted line)  magnetoelectric coefficient s  \nfor (Ni 0.973 Co0.027)0.5Zn0.5Fe2O4/Pz27 bilayer.  The solid line is the longitudinal ME \ncoefficient calculated from the transversal one.  \n \n \n \n \n \n \n \n \n \n \n \nFig 5 . Magnetization and magnetization derivative measured for (Ni0.973 Co0.027)0.5Zn0.5Fe2O4 \nslow -cooled ferrite . \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig 6. Transversal magnetoelectric coefficients for (Ni 0.973 Co0.027)0.875Zn0.125Fe2O4/PZ27  \nbilayers and trilayer.  Thick lines correspond to experimental ME measurements. Thick solid \nline: 1mm/2mm PZT/ferrite bilayer  (reference sample) . Thick dashed line:  0.5mm/1mm \nPZT/ferrite bilayer . Thick dotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer. The thin \nlines are curves deduced from the  experimental one of the  reference sample where \ndemagnetizing effects were corrected. Thin dashed line: 1mm/2mm PZT/ferrite bilayer. Thi n \ndotted line: 1mm/1mm/1mm PZT/ferrite/PZT trilayer.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig 7 . Transversal magnetoelectric coefficients for (Ni 0.973 Co0.027)0.875Zn0.125Fe2O4/PZ27 \nbilayers and trilayer.. Solid line: 1mm/2mm PZT/ferrite bilayer  (reference sample) . Dotted -\ndashed line:  0.5mm/2 mm/0.5mm  PZT/ferrite /PZT  trilayer . Dotted line: 1mm/1mm/1mm \nPZT/ferrite/PZT trilayer. Dashed line: 0.5mm/0.5mm/0.5 mm ferrite/PZT/ferrite  trilayer.  All \nthe lines correspond to experimental ME measurements.  \n \n \n \n \n \n \n \n \n \n \nFig 8: Strain curves versus applied external field along the parallel direction  for the ME \nsample # 0.125SC2/1  (reference sample) . The closed circles correspond to strain measurement on \nthe ferrite face, and  open circles correspond to strain measurement on  the PZT face.  The \nmagnetic field and strain measurements are  parallel (and in the disc plane ). \n \n \n \n \n \n \n \n \nFig 9 : Top view of the ME device when circumferential AC magnetic field  is forced within \nthe ferrite.  The PZT top electrode is split into two half electrodes (in grey) which produce two \nopposite voltage s V and V’. Only AC voltage produced by a half piezoelectric layer is \nmeasured.  \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig 10. Transversal magnetoelectric coefficients for (Ni 0.973 Co0.027)0.75Zn0.25Fe2O4/Pic255 \nbilayers when AC magnetic fields are forced within the ferrite. Solid line: quenched ferrite. \nDashed line: slow cooled ferrite.  \n \n \n              \n              \n(1) (2) \n(3) V \nV’  \n \n \n \n \n \n \n \n \n \nFig 11 . Transversal magnetoelectric coefficient     for (Ni 0.973 Co0.027)0.875 Zn0.125Fe2O4 /Pz27 \n2mm/ 1mm bilayer (solid line) and Terfenol -D/Pz27 2mm/1mm bilayer (dotted  line).  \n \n \n \n \n \n \n \n \n \n \n \n \nFig 12 .  Magnetostriction curves versus  applied external field along parallel (closed circles ) \nand perpendicular ( open circles ) directions  for a Terfenol -D disc . The magnetic field and \nstrain measurements are  in the disc plane.  \n \n \n \n \n \n \n \n \n \n \n \n \nFig 13 .  Magnetostriction curves versus  applied external field along parallel (closed circles) \nand perpendicular (open circles) directions for a ferrite disc with x=0.125. The magnetic field \nand strain measurements are in the disc plane.  \n \n \n \n \n \n \n \n \n \n \n \nFig 14 . Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). \nGrey line: ME voltage obtains at the electrical output of the piezoelectric material.  The \ncurrent have a square waveform at 1kHz  and 10A peak . \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig 15 . Black line: voltage obtains with an commercial active current probe (gain: 100mV/A). \nGrey line: ME voltage obtains at the electrical output of the piezoelectric material. The \ncurrent have a triangle waveform at 1kHz  and 10A peak . \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n "    },    {        "title": "1602.05773v1.From_Fe__3_O__4__NiO_bilayers_to_NiFe__2_O__4__like_thin_films_through_Ni_interdiffusion.pdf",        "content": "arXiv:1602.05773v1  [cond-mat.mtrl-sci]  18 Feb 2016From Fe 3O4/NiO bilayers to NiFe 2O4-like thin films through Ni interdiffusion\nO. Kuschel,1R. Buß,1W. Spiess,1T. Schemme,1J. W¨ ollermann,1K. Balinski,1\nT. Kuschel,2A.T. N’Diaye,3J. Wollschl¨ ager,1,∗and K. Kuepper1,†\n1Department of Physics and Center of Physics and Chemistry of New Materials,\nOsnabr¨ uck University, 49076 Osnabr¨ uck, Germany\n2Center for Spinelectronic Materials and Devices, Departme nt of Physics,\nBielefeld University, Universit¨ atsstraße 25, 33615 Biel efeld, Germany\n3Advanced Light Source, Lawrence Berkeley National Laborat ory, California 94720, USA\n(Dated: August 8, 2021)\nFerrites with (inverse) spinel structure display a large va riety of electronic and magnetic prop-\nerties making some of them interesting for potential applic ations in spintronics. We investigate\nthe thermally induced interdiffusion of Ni2+ions out of NiO into Fe 3O4ultrathin films resulting\nin off-stoichiometric nickelferrite-like thin layers. We s ynthesized epitaxial Fe 3O4/NiO bilayers on\nNb-doped SrTiO 3(001) substrates by means of reactive molecular beam epitax y. Subsequently, we\nperformed an annealing cycle comprising three steps at temp eratures of 400◦C, 600◦C, and 800◦C\nunder an oxygen background atmosphere. We studied the chang es of the chemical and electronic\nproperties as result of each annealing step with help of hard x-ray photoelectron spectroscopy and\nfound a rather homogenous distribution of Ni and Fe cations t hroughout the entire film after the\noverall annealing cycle. For one sample we observed a cation ic distribution close to that of the spinel\nferrite NiFe 2O4. Further evidence comes from low energy electron diffractio n patterns indicating\na spinel type structure at the surface after annealing. Site and element specific hysteresis loops\nperformed by x-ray magnetic circular dichroism uncovered t he antiferrimagnetic alignment between\nthe octahedral coordinated Ni2+and Fe3+ions and the Fe3+in tetrahedral coordination. We find a\nquite low coercive field of 0.02T, indicating a rather low def ect concentration within the thin ferrite\nfilms.\nPACS numbers: 68.35.Fx, 75.47.Lx, 75.50.Gg, 75.70.Cn, 75. 70.-i\nI. INTRODUCTION\nIron oxides are of special interest due to a number\nof astonishing properties in dependence of the Fe va-\nlence state and the underlying crystallographic and elec-\ntronic structure. Magnetite (Fe 3O4) is among the most\nstudied ferrites due to its ferrimagnetic ordered ground\nstate with a saturation moment of 4.07 µBper formula\nunit and a high Curie temperature of 860 K for bulk\nmaterial.1,2This magnetic ground state is accompanied\nbyhalfmetallicity, i.e.onlyonespinorientationispresent\nat the Fermi energy,3making this material a potential\ncandidate for future spintronic devices with 100% spin\npolarization.4,5Magnetitecrystallizesinthecubicinverse\nspinel structure (equal distribution of Fe3+on A and B\nsites and Fe2+exclusively on B sites) with lattice con-\nstanta= 0.8396 nm (space group Fd3m). The oxygen\nanions form an fcc anion sublattice.\nOften, Fe 3O4thin films are grown on cubic MgO(001)\nsubstrates by various deposition techniques6,7,8,9,10,11,\nsince the lattice mismatch between the Fe 3O4and\nMgO(001) ( a= 0.42117 nm) is only 0.3%, comparing\nthe oxygen sublattices. A severe limit of epitaxial thin\nfilm growth on MgO substrates is Mg2+segregation into\nthe Fe 3O4film if the substrate temperature is above\n250◦C.12Mg rich interfaces13and Mg interdiffusion have\nbeen studied in detail,14having significant influence on\ninterface roughness or anti phase boundaries. Thus, the\nunderlying electronic and magnetic structure determin-\ning the properties of the magnetite thin film in questionorthetunnelmagnetoresistanceinmagnetictunneljunc-\ntions with magnetite electrodes.15,16,17,18\nPotential approach to minimize or suppress Mg seg-\nregation, besides rather low substrate temperatures dur-\ning magnetite growth, is an additional buffer layer, e.g.\nmetallic iron19or NiO20between the Fe 3O4and the sub-\nstrate. This approach is also of interest with respect to\nthe possibility for building a full oxidic spin valve making\nuse of the exchange bias between the ferrimagnetic mag-\nnetite and the antiferromagnetic nickel oxide.19,20,21The\nusage of other substrates like SrTiO 3could also prevent\nMg interdiffusion. Despite the large lattice mismatch of\n-7.5% between the doubled SrTiO 3bulk lattice constant\n(0.3905nm) andmagnetite it ispossibletogrowepitaxial\nFe3O4films on the SrTiO 3(001) surface.22,23In partic-\nular, concerning coupled Fe 3O4/NiO bilayers grown on\nSrTiO 3, so far only Pilard et al.have reported on the\nmagnetic properties of the Fe 3O4/NiO interface.24On\nthe other hand, NiFe 2O4thin films are of huge interest\nnowadays, since they act as magnetic insulators, which\ncanbe usedtothermallyinducespincurrentsviathespin\nSeebeck effect.25,26Furthermore, electrical charge trans-\nport and spin currents can be manipulated by the spin\nHall magnetoresistance using NiFe 2O4thin films adja-\ncent to nonmagnetic material.27\nHere we go beyond describing a model system of two\ndistinct layers with an epitaxial Fe 3O4/NiO interface\nand study the potential Ni2+interdiffusion from a NiO\nbuffer layer into a Fe 3O4top layer as well as NiO sur-\nface segregation through the Fe 3O4layer if both NiO2\nbuffer layer and Fe 3O4top layer are grown on Nb-\ndoped SrTiO 3(001). Knowledge about the modification\nof the underlying crystallographic, electronic and mag-\nnetic structure by Ni interdiffusion is indispensable for\npotential applications. We also want to learn fundamen-\ntal aspects especially of Ni2+segregation into epitaxial\nFe3O4thin films, since knowledge of diffusion processes\nin oxides appear to be still quite rudimentary for many\nsystems.\nWe perform a systematic three step annealing cycle of\nFe3O4/NiO bilayers after synthesis and simultaneously\ninvestigating surface crystallographic and ”bulk” elec-\ntronic structure changes by means of low energy electron\ndiffraction (LEED) and hard x-ray photoelectron spec-\ntroscopy (HAXPES). Furthermore, we carry out struc-\ntural analysis before and after the overall annealing cy-\ncle employing x-ray reflectivity (XRR) and synchrotron\nbased x-raydiffraction(SR-XRD), aswell aselement and\nsite specific x-ray magnetic circular dichroism (XMCD)\nafter the overall annealing cycle to analyze the resulting\nmagnetic properties in detail.\nII. EXPERIMENTAL DETAILS\nTwo samples with Fe 3O4/NiO ultra thin film bilay-\ners on conductive 0 .05wt.% Nb-doped SrTiO 3(001) sub-\nstrates have been prepared, using the technique of re-\nactive molecular beam epitaxy (RMBE). The substrates\nhave been supplied with a polished surface and were an-\nnealed at 400◦C for one hour in an oxygen atmosphere of\n1×10−4mbar prior to deposition. During film growth,\nthe oxygen pressure was kept at 1 ×10−5mbar for NiO\nand 5×10−6mbar for Fe 3O4, while the substrate was\nheated to 250◦C. One sample has been created with a\n5.6nm NiO film (sample A) and the other with a 1.5nm\nNiO film (sample B). Thereafter, 5.5nm thick Fe 3O4\nfilmsweredepositedontheNiOfilms. Substrateprepara-\ntion, film stoichiometry and surface structure have been\nmonitored in-situby x-ray photoelectron spectroscopy\n(XPS) using Al K αradiation and LEED, respectively.\nThe samples were transported under ambient condi-\ntions to the Diamond Light Source (DLS) synchrotron,\nwhere the effects of annealing on the bilayer system were\nstudied at beamline I09 by heating the samples in three\nstepsat400◦C, 600◦C, and800◦Cfor20to30minutesin\nan oxygen atmosphere of 5 ×10−6mbar. Prior to and af-\nter the annealing studies XRR measurements at 2.5keV\nphoton energy were made to determine the film thick-\nness. After each annealing step, the films were studied\nin-situby softx-rayphotoemissionand HAXPESto clar-\nify the chemical composition in the surface near region\nand in the bulk region, respectively. In addition, LEED\nmeasurements were performed to check the crystallinity\nof the individual layers of the NiO/Fe 3O4bilayer.\nFor HAXPES an energy of hν= 5934eV was used,\ncreating photoelectrons with high kinetic energy, which\nallows a higher probing depth compared to soft x-rayphotoemission ( hν= 1000eV). The information depth,\nfrom which 95% of the photoelectrons originate, is de-\nfined as\nID(95) =−λcosϕln(1−95/100), (1)\nwith the inelastic mean free path λand the off-normal\nemission angle ϕ.28The maximum information depth for\nthe Fe 2p core level for HAXPES and soft x-ray photoe-\nmission measurements is 22nm and 2 .5nm, respectively,\nestimating λby the TPP-2M formula.29As the beam-\nline features a 2D photoelectron detector, which can be\noperated in an angular mode, photoelectron spectra at\ndifferent emission angles were acquired, each with an ac-\nceptance angle of ∼7◦.\nSubsequently, structural analysis of the annealed films\nwas performed using SR-XRD, while the resulting film\nthickness and layer structure of this films were deter-\nmined by means of lab based XRR using Cu K αradia-\ntion. SR-XRD experiments have been carried out ex-situ\nat PETRA III beamline P08 (DESY, Germany) using\na photon energy of 15keV. In both cases the measure-\nments were performed in θ−2θdiffraction geometry.\nFor the analysis of all XRR experiments an in-house de-\nveloped fitting tool based on the Parrattalgorithm30and\nN´ evot-Croce roughness model31was used. The SR-XRD\nmeasurements were analyzed by calculating the intensity\ndistribution within the full kinematic diffraction theory\nto fit the experimental diffraction data.\nXMCD spectroscopy was performed at the Fe L 2,3and\nNi L2,3edges with the samples at room temperature at\nbeamline 6.3.1 of the Advanced Light Source, Lawrence\nBerkeley Laboratory. We have utilized total electron\nyield (TEY) as detection mode. The external magnetic\nfield of 1.5 T has been aligned parallel to the x-ray beam\nand been switched for each energy. The angle between\nsample surface and x-raybeam has been chosen 30◦. The\nresolving power of the beamline has been set to E/∆E\n∼2000,the degreeof circularpolarizationhasbeen about\n55%. For the analysis of the Fe L 2,3XMCD spectra, we\nhave performed corresponding model calculations within\nthe atomic multiplet and crystal field theory including\ncharge transfer using the program CTM4XAS .32,33\nIII. RESULTS\nA. Surface characterisation\nAfter cleaningof the SrTiO 3substratesthe XPS shows\nchemically clean substrates without carbon contami-\nnation (not shown here). The LEED pattern shows\nvery sharp diffraction spots of a (1 ×1) surface with\nsquare structure and negligible background intensity (cf.\nFig. 1a), indicating a clean (001) oriented surface with\nlong range structural order.\nThe LEED image recorded after RMBE of NiO also\nexhibits a (1 ×1) structure. The pattern, however (cf.3\na) \n95eVSrTiO 3 NiO\n75eVFe O 4 3\n95eV\n95eVsample B\n95eVsample Ab) c) \nd) e) \n[010][100]\nFIG. 1: LEED patterns taken after a) preparation of SrTiO 3\nsubstrate, b) deposition of NiO, c) deposition of Fe 3O4, d)\nand e) after annealing at 800◦C of sample A and sample B,\nrespectively . Marked with red squares are the respective\n(1×1) surface unit cells in reciprocal space. The blue square\nindicates the (√\n2×√\n2)R45◦superstructure typical for mag-\nnetite.\nFig. 1b), is rotated by 45◦and∼√\n2 times larger than\nthe pattern of the SrTiO 3(001) substrate as expected for\nthe NiO(001) surface unit cell. The broadening of the\ndiffraction spots is most likely caused by defects due to\nrelaxation processes induced by the high lattice misfit of\n−6.9% for NiO(001) compared to SrTiO 3(001).\nThe LEED pattern of the as prepared Fe 3O4film (cf.\nFig. 1c) reveals a (1 ×1) surface structure with dou-\nbled periodicity compared to NiO, as the real space lat-\ntice constant of the magnetite inverse spinel structure is\nabout twice as large, giving a lattice misfit of only 0 .7%\nfor Fe 3O4(001) on NiO(001). Furthermore, additional\ndiffraction spots of a (√\n2×√\n2)R45◦superstructure can\nbe seen, which is unique for well-ordered Fe 3O4(001)\nsurfaces.34,35,36\nThese results indicate a cube-on-cube growth for both,\nNiO and Fe 3O4films. Additionally, the Ni 2p and Fe\n2p XPS spectra taken directly after preparation of each\nfilm (not shown here) exhibit a characteristic shape for a\nNi2+and a mixed Fe2+/Fe3+valence state, respectively.\nThus, combining the results from XPS and LEED, we\ncan conclude that the as-prepared films are consisting of\nstoichiometric Fe 3O4/NiO bilayers.\nThefirst annealingstepat 400◦C onlyremovedsurface\ncontaminations from the transport, without effecting the\ninitial layer structure of the sample. Soft x-ray photoe-\nmission measurements show a characteristic Fe 2p signal\nindicating a Fe 3O4stoichiometry. Furthermore, no Ni\n2p signal was visible due to the small information depth\ndemonstrating that neither Ni diffused into the Fe 3O4\nfilm nor that the Fe 3O4film was deconstructed.\nAfter the annealing step at 600◦C and 800◦C a dis-\ntinctive satellite typical for trivalent iron becomes visible\nbetween the Fe 2p 1/2and Fe 2p 3/2peaks for soft x-ray\nphotoemissionmeasurements. Thisindicates adeficiency\nof divalent iron in the magnetite layer. Furthermore, thespectra show an intense Ni 2p signal pointing to a pos-\nsible deconstruction or a formation of nickel ferrite as a\nresult of intermixing.\nLEED patterns (cf. Fig. 1d, e) taken after the en-\ntire annealing experiments show a clear (1 ×1) surface\nstructure for both samples. Sample A, however, exhibits\nsharper reflexes than sample B. This structure corre-\nsponds to the inverse spinel surface structure described\nabove for magnetite, but without the (√\n2×√\n2)R45◦\nsuperstructure of the Fe 3O4(001) surface. Therefore, it\nalso can be attributed either to a defect rich magnetite\nsurface, or the formation of several iron oxide species but\nalso to a NiFe 2O4surface.\nB. XRR\nFig. 2 shows the measured and calculated XRR inten-\nsities obtained at DLS prior to the the annealing exper-\niments for both samples. The XRR intensity obtained\nfrom sample A clearly shows the beating of two layers\nwith almost identical thickness while the intensity ob-\ntained from sample B points to two layers with very\ndifferent thickness. For the calculation of the intensity\ndistributions and the exact layer structure a basic model\nwas used (inset Fig. 2), consisting of a magnetite film\non top of a NiO layer on a SrTiO 3substrate. For both\nsamples the data show well defined intensity oscillations\npointingtoadoublelayerstructureandflathomogeneous\ninterfaces and films.\n0.5\n0.5NiFe O x 3-x 4 \n8.2nm \nreflectivity [arb.units]\n0.40.30.20.1\nscatteringvectorq[1/Å]fit\nasprepared \nannealeda)\nreflectivity [arb.units]\n0.40.30.20.1\nscatteringvectorq[1/Å]fit\nasprepared \nannealedb)NiO 5.6nmFeO 3 4 5.5nm\nSrTiO 3NiO 2.0nmannealed asprepared \nNiO 1.5nmFeO 3 4 5.4nm\nSrTiO 3NiFe O x 3-x 4 \n7.2nm\nSrTiO 3annealed asprepared \n00sampleA\nsampleBNiO 1.4nm\nSrTiO 3\nFIG. 2: Reflectivity curves and calculations from XRR mea-\nsurements before and after the annealing experiments a) for\nsample Aand b) for sample B. The insets show the underlying\nmodels.4\nThe measured and calculated XRR intensities of the\nannealed samples as well as the used model are also pre-\nsented in Fig. 2. For both samples the XRR shows clear\nintensity oscillations with a changed periodicity com-\npared to the as prepared films. Taking into account\nthe electron densities and layer structures obtained from\nXRRthiseffectcanbeattributedtoanintermixingofthe\ntwo initial oxide layers. In case of sample A a three layer\nmodel was necessary to describe the data after annealing\n(cf. Fig. 2a). The first layer on top of the substrate is a\nthin nickel oxide layer, the second layer is a 8.2 nm thick\nnickel ferrite film and the third layer on top of the nickel\nferrite film consists again of nickel oxide.\nThe model parameters of the upper NiO layer indi-\ncate a deconstructed film or island formation on the sur-\nface. However, sample B is modeled with only a single\n7.2 nm thick nickel ferrite film on top of the substrate\n(cf. Fig. 2b). For both samples the thicknesses of the\nresidual films coincide almost with the sum of the ini-\ntial thicknesses of the Fe 3O4and NiO films. The slightly\nincrease of the thickness can be attributed to a volume\nincrease of ∼8% due to the formation of nickel ferrite.\nC. HAXPES\nsampleA\n750 740 730 720 710 700satelliteFe2p 1/2 Fe2p 3/2 \n400°C\n600°C\n800°C\nintensity [arb. units]a) \nbinding energy [eV]\nsample B\n750 740 730 720 710 700satelliteFe 2p 1/2 Fe 2p 3/2 \n400°C\n600°C\n800°C\nintensity [arb. units] b) \nbinding energy [eV]\nFIG. 3: HAXPES spectra of Fe 2p core level at 10◦off-normal\nphotoelectron emission after annealing at different temper a-\ntures a) for sample A and b) for sample B.\nIncontrasttosoftx-rayphotoemission, HAXPESmea-\nsurements allow to identify the valence states and chemi-\ncalpropertiesnotonlyatthesurfacenearregionbutwithsample A\n890 880 870 860 850 840satelliteNi 2p 1/2 Ni 2p 3/2 \n400°C\n600°C\n800°C\nintensity [arb. units] a) \nbinding energy [eV]Fe 2s shoulder\nsample B\n890 880 870 860 850 840satelliteNi 2p 1/2 Ni 2p 3/2 \n400°C\n600°C\n800°C\nintensity [arb. units] b) \nbinding energy [eV]Fe 2s \nshoulder700\nFIG. 4: HAXPES spectra of Ni 2p core level at 10◦off-normal\nphotoelectron emission after annealing at different temper a-\ntures a) for sample A and b) for sample B.\nbulksensitivityduetohigherexcitationenergyand, thus,\nincreased information depth.\nFig. 3 shows the HAXPES spectra for the Fe 2p core\nlevel, which is split into the Fe 2p 1/2and Fe 2p 3/2peaks.\nSpectra recorded after each annealing step for both sam-\nples are presented. The shape of the spectra is deter-\nmined by the relative fraction of Fe valence states, which\nis used to identify the material composition37. After the\ninitial annealing step at 400◦C, there is no satellite peak\nvisible between the two main peaks, indicating stoichio-\nmetric Fe 3O4for both samples. After the second and\nthird annealing step, at 600◦C and 800◦C, respectively,\na satellite peak becomes visible between the two main\npeaks for both samples. As it resides on the side of the\nFe 2p1/2peak, it indicates a deficiency of Fe2+ions in\nfavor of Fe3+ions compared to the initial magnetite sto-\nichiometry.\nFig. 4 shows the photoelectronspectra for the Ni 2p 1/2\nand Ni 2p 3/2core level of both samples. The spectra\nafter the annealing step at 400◦C show a shoulder on\nthe high binding energy side of the Ni 2p 3/2peak, which\nis typical for NiO.38This shoulder almost completely\ndisappears after annealing at 600◦C of both samples.\nBiesinger et al.39identified such a peak shape without\na satellite for the spinel type material NiFe 2O4. There-\nfore, an exchange of Fe2+ions with Ni2+ions in the\nFe3O4spinel structure through interdiffusion seems to be\nlikely.40For sample B, the peak shape does not change\nwith the next annealing step at 800◦C (cf. Fig. 4b).\nHowever, for sample A the shoulder on the high bind-5\ning energy side observed for the initial bilayer system\nre-appears (cf. Fig. 4a), suggesting the formation of NiO\nlike structures, which is consistent with the NiO forma-\ntion at the surface seen in the XRR measurements.\nAdditionally, a quantitative analysis of the photoelec-\ntron spectra was performed to prove the possible forma-\ntion of nickel ferrite. After subtracting a Shirley back-\nground, the intensities IFeandINiofthe Fe 2p peaks and\nthe Ni 2p 1/2peak (due to the overlap with the Fe 2s,\nthe Ni 2p 3/2peak has not been considered) have been\nnumerically integrated. From these results, the relative\nphotoelectron yield\nYNi=INi/σNi\nINi/σNi+IFe/σFe=NNi\nNNi+NFe·C(ϕ)(2)\nof Ni has been calculated, using the differen-\ntial photoionization cross sections σreported by\nTrzhaskovskaya et al.41Newberg et al. derived,thatthis\nyield is equal to the atomic ratios42, but with a factor\nC(ϕ), that depends on the angle of photoemission. The\nresultingyieldsfromdifferentdetectionanglesareplotted\nin Fig. 5. The curves from the data of the first annealing\nsteps show for both samples a decreasing yield for higher\nemission angles as indicated by the blue dashed lines.\nThis behavior points to an intact stack of oxide films\ndue to a longer pathway of the photoelectrons for higher\nemission angles. The lines are calculated for a stack of\ntwo separated Fe 3O4/NiO films using the thicknesses ob-\ntainedfromXRRanalysis. With thesuccessiveannealing\nsteps, the photoelectron yield from Ni increases, which\nindicates that there is diffusion of Ni into the Fe 3O4film\nand/or Fe into the NiO film.\nIn case of sample A the intensity ratios (Fig. 5a) show\na continuous increase of the nickel intensity with higher\nannealing temperature. The calculation of the photo-\nelectron yield after the third annealing step at 800◦C\n(dashed red line) was done using the layer structure and\nthicknesses obtained from the XRR analysis (cf. inset\nFig. 2a). This model is based on a stochiometric 8.2 nm\nthick NiFe 2O4film between two NiO films. Since there\nis no evidence of NiO in the Ni 2p HAXPES spectra\nafter annealing at 600◦C, a model consisting of a sto-\nichiometric 8.2 nm thick NiFe 3O4on top of a 3.4 nm\nthick NiO layer was used (green dashed line Fig. 5a).\nWith further annealing at 800◦C more Ni atoms are dif-\nfusing/transported through the nickel ferrite layer to the\nvery surface forming NiO as detected by XRR and HAX-\nPES (see discussion of Ni 2p 3/2shoulder) after the entire\nannealing experiment. This segregation behavior of Ni\nand the formation of NiO at the surface is explained by\nits lower surface energy of 0.863 J/m2compared to the\nsurface energy of 1.235 J/m2for NiFe 2O4(001).43\nIn case of sample B one can conclude that a single\nhomogeneous film was formed by the interdiffusion pro-\ncess already after the second annealing step. Its stoi-\nchiometry does not change from the second to the third\nannealing step (cf. Fig. 5b). The ratio of Ni and Fe, as-\nsuming a complete intermixing, can be determined fromequation (2), as then the angular factor C(ϕ)≡1. The\namountofnickelandirondoesnotmatchtheratioof1:2\nfor stoichiometric nickel ferrite, but is 1 : 2.6 for the sam-\nple B indicating an excess ofFe atoms. The experimental\ndata are in good agreement with the calculated behav-\nior (dashed red line) for a homogeneously mixed single\nlayer. Thus, the resulting stoichiometry of the sample B\nis NixFe3−xO4withx= 0.83.\nAll calculations of the HAXPES intensity indicate the\nsamelayerstructureandthicknessesasobtainedfromthe\nXRR measurements were used, indicating a consistent\nmodel.\n400°C\n600°C\n800°CsampleAa)\n0° 10°20°30°40°50°\nangleofphotoemissionφ relative photoelectron yield YNi\n0.10.20.30.40.50.60.70.8\n0\n0° 10°20°30°40°50°\nangleofphotoemissionφ sampleB\n0.10.20.30.4\nrelative photoelectron yield YNi\n0b) \n400°C\n600°C\n800°C\nFIG. 5: Relative photoelectron yield at different off-normal\nemission angles a) for sample A and b) for sample B. The\ndashed lines show the calculated intensities using the mode ls\nobtained from XRR analysis.\nD. SR-XRD\nFig.6showsSR-XRDmeasurementsandcalculatedin-\ntensity of the crystal truncation rod (CTR) along (00 L)\ndirection close to the SrTiO 3(002)Pand spinel (004) S\nBragg peak for both samples after annealing. Here, L\ndenotes vertical scattering vector in reciprocal lattice\nunits (r.l.u.) with respect to the layer distance of the\nSrTiO 3(001)substrate. Indices PandSindicatethebulk\nnotationforperovskitetype andspinel type unit cells, re-\nspectively. The structural parameters, e.g. vertical layer\ndistances, are determined by analyzing the CTRs apply-\ningfull kinematic diffractiontheory. Forthe analysis, the\nsame layer model as for the XRR calculations was used\nto describe the data (cf. inset Fig. 2a, b). For both sam-\nples a clearpeak from the SrTiO 3(001)substrateat L=2\nand a broad Bragg peak originating from the oxide film\naroundL≈1.87 is observed. Additionally, for sample A\nclearoscillations close to the Braggpeak of the oxide film\n(Laue fringes) are visible which can be clearly attributed\nto the nickel ferrite layer indicating a well ordered ho-\nmogeneous film of high crystalline quality. Furthermore,\nthe vertical lattice constant of sample A obtained from6\ncurve fitting is c= 0.8334nm and is in good agreement\nwith the bulk value of NiFe 2O4(abulk= 0.8339nm).\nintensity [arb.units]\n2.102.001.901.801.70\nL[r.l.u.[SrTiO(001)]]3fit\nannealed\n1.60FeO 3 4 (004)SbulkNiFeO(004) 2 4 S bulk\nL[r.l.u.[SrTiO(001)]]3intensity [arb.units]\n2.102.001.901.801.70fit\nannealed\n1.60a) \nb) sampleASrTiO(002) 3 P \nsampleBSrTiO(002) 3 P \nNiFeO(004) bulk 2 4 S \nFeO 3 4 (004) bulkS\nFIG. 6: SR-XRD measurements along (00 L) direction and\ncalculated intensities. For the calculation the same model as\nobtained from the analysis of the XRR was used (cf. inset\nFig. 2).\nFor sample B the oscillations completely vanish, point-\ning to an inhomogeneous film. This effect is possibly\ncaused by the excess of Fe atoms in the film as observed\nby HAXPES. In addition, the vertical lattice constant\nc = 0.8304nm obtained from the calculations confirms\nthe presence of a strongly distorted structure of the an-\nnealed film, since it notably comes below the value of\nbulk NiFe 2O4.\nE. XMCD\nXMCD has been employed after the overall annealing\ncycle to analyze the resulting magnetic properties ele-\nment specifically after annealing at 800◦C. Fig. 7 de-\npicts the XMCD spectra of samples A and B performed\nat the Fe L 2,3and Ni L 2,3edges, respectively. Both sam-\nples show a strong Ni dichroic signal (cf. Fig. 7a), and in\norder to extract the spin magnetic moments we use the\nspin sum rule developed by Chen et al.44The number\nof holes are determined from the charge transfer multi-\nplet simulations for each sample. We also account for the\ncore hole interactions which mix the character of the L 3\nand L 2edges45,46by considering the spin sum rule cor-\nrection factors obtained by Teramura et al.45We find a\nNi spin moment of 0.51 µBper Ni atom and an orbital\ncontribution of 0.053 µB/Ni atom summing up to a total\nNi moment of 0.56 µBfor sample A. In case of sample B\nwe derive mspin= 0.91µB/Ni atom, morb= 0.122µB/Ni\natom, and hence a total Ni moment of 1.03 µBper for-mulaunit. Thelattervalueisratherclosetothatrecently\nfound by Klewe et al.47on a stoichiometric NiFe 2O4thin\nfilm.\nTurning to the Fe moments we find strong indica-\ntions that our heat and diffusion experiments lead to a\nNixFe3−xO4layer or cluster formation in both samples.\nSince we obtain mspin= -0.028 (+0.11) µB/Fe atom and\nmorb= +0.015 (+0.007) µB/Fe atom at the Fe sites of\nsampleA(sample B) wefind verysmallnet contributions\nto the overall magnetic moments. In comparison Klewe\net al.47found an iron spin moment of around 0.1 µB/Fe\natom and a further orbital contribution of around 10-\n15% of that value. This indicates an (almost complete)\nstructural inversion of the prior bilayer system, i.e. the\niron ions occupy in equal parts octahedral and tetrahe-\ndral positions within the crystal. Since the moments of\nthese octahedrally and tetrahedrally coordinated cations\nare aligned antiparallel the moments cancel each other\nnearly out in a perfect inverse spinel structure.\nFig. 7c presents the charge transfer multiplet calcula-\ntions for the single iron cations in octahedral and tetra-\nhedral coordination as well as the best fits to the exper-\nimental Fe L 2,3-XMCD spectra of sample A and B with\n(red) and without (blue) consideration of Fe2+\noctions. The\nresulting lattice site occupancies are 16.3% Fe2+\noct, 32.2%\nFe3+\noct, 51.5% Fe3+\ntet(42.6% Fe3+\noct, 57.4% Fe3+\ntet) for sam-\nple A, and 24.0% Fe2+\noct, 31.5% Fe3+\noct, 44.5% Fe3+\ntet(55.6%\nFe3+\noct, 44.4% Fe3+\ntet) for sample B including (not includ-\ning) Fe2+\noctions into the respective fit. The result that\nfor sample A over 50% are in Fe3+\ntetcoordination as to\nthe calculations also corresponds with the small negative\nspin moment determined by the spin sum rule.\nFrom the overallmultiplet fits (Fig. 7c) one can clearly\nsee that feature i(Fig. 7b) is very small if Fe2+\noctcations\nare not explicitly considered in the respective simula-\ntions. The origin of this feature in ferrites with in-\nverse spinel structure other than magnetite is still not\nentirely understood.47,48,49In both Fe L 2,3-XMCD spec-\ntra of samples A and B peak iis significantly smaller\nthan results obtained veryrecentlyon NiFe 2O4thin films\ngrownby pulsed laserdeposition (PLD),49but somewhat\nmore intense than it is in the result of Klewe et al.47\nAlso their corresponding multiplet simulation resembles\nourapproach(not consideringthe Fe2+\noctsites) ratherwell.\nThe presence of peak iin the Fe L 2,3-XMCD of sample B\ncan at least partly be explained by the lack of Ni2+\noctions\nas to the HAXPES measurements. Since peak ialso oc-\ncurs in XMCD experiments on bulk material48one can\nthink about several additional reasons about the pres-\nence of some Fe2+\noctions. For instance, a small fraction of\nthe Ni ions might be present in form of Ni3+or coordi-\nnated on tetrahedral sites as result of the interdiffusion\nprocess. Despite the fact that Ni2+prefersoctahedralco-\nordination, even measurements on NiFe 2O4bulk crystals\nindicate a few of the Ni ions to be on tetrahedral sites.48\nFurthermore, oxidation or reduction of a fraction of the\nFe at the verysurface ofthe thin films can not be entirely\nexcluded as the probing depth of the total electron yield7\n840 850 860 870 880 890 900 910 sample B XMCD [arb. units] \nPhoton Energy [eV] Ni L 2,3  edges: \nsample A P-, P+\n XMCD \n XMCD integr. a)\n690 700 710 720 730 740 750 760 b)\niii ii P-, P+\n XMCD \n XMCD integr. \nPhoton Energy [eV] XMCD [arb. units] sample B Fe L 2,3  edges: \nsample A \ni\n705 710 715 720 725 730  sample A: XMCD \n CTM4XAS: Best fit (with Fe 2+ \noct )\n CTM4XAS: Best fit (no Fe 2+ \noct )\n sample B: XMCD \n CTM4XAS: Best fit (with Fe 2+ \noct )\n CTM4XAS: Best fit (no Fe 2+ \noct )CTM4XAS: \nmodel \nspectra XMCD intensity [arb. units] \nPhoton Energy [eV]  Fe 2+ \noct  Fe 3+ \noct  Fe 3+ \ntet c)\nFIG. 7: a) Ni L 2,3-XMCD spectra of samples A and B. b) Fe\nL2,3-XMCD spectra of samples A and B. c) Experimental Fe\nL2,3edge XMCD of samples A and B and the corresponding\nXTM4XAS fits with and without consideration of octahedral\ncoordinated Fe2+ions present.\nis only around 2nm at the Fe L 2,3and Ni L 2,3resonances\nof oxides.48,50\nFor sample B we also recorded element specific hys-\nteresis loops at the Ni L 3edge and the site specific loops\nat Fe L 3resonances for peaks i−iii(cf. Fig. 7b). Fig. 8\ndisplays the resulting magnetization loops. One can see\nthe ferrimagnetic ordering between the Fe3+\ntetcations and\nthe other Fe and Ni cations. For all octahedrally coordi-\nnated cations we probe an in-plane coercive field Hcof-0.4 -0.2 0.0 0.2 0.4 -4 -2 024sample B TEY XMCD ratio [arb. units] \nH [T] XMCD hysteresis \n Ni 2+  Fe 2+ \noct \n Fe 2+ \ntet  Fe 3+ \noct a)\n-0.4 -0.2 0.0 0.2 0.4 -4 -2 024XMCD out of plane \nhysteresis \n Ni 2+ \nsample B TEY XMCD ratio [arb. units] H[T] \n-0.06 -0.03 0.00 0.03 0.06 -1.0 -0.5 0.0 0.5 1.0 b)\nsample B TEY XMCD ratio [arb. units] \nH [T] XMCD hysteresis \n Ni 2+  Fe 2+ \noct \n Fe 2+ \ntet  Fe 3+ \noct \n-0.10 -0.05 0.00 0.05 0.10 -1.0 -0.5 0.0 0.5 1.0 \nXMCD out of plane \nhysteresis \n Ni 2+ \nsample B TEY XMCD ratio [arb. units] H[T] \nFIG. 8: (a) Element and site specific hysteresis loops of the\nNi L3- and Fe L 3intensities of sample B. (b) Expanded view\nof the loops near H=0 T. Insets show the Ni hysteresis loop\nmeasured in perpendicular (out of plane) geometry.\naround0.02 T, whereasthe Fe3+\ntetcations exhibit a closed,\nparamagnetic magnetization curve. In out-of plane con-\nfiguration we only probed the Ni sites and find a Hcof\naround 0.01 T (see insets in Fig. 8). This is a signifi-\ncant different result compared to recently reported val-\nues ofHc=0.1 T or more for NiFe 2O4thin films.47,49,51\nA number of reasons might be responsible for a strongly\nincreased Hcsuch as exchange coupled grains51or a high\ndefect density.47Onthe otherhand, similarvaluesforthe\ncoercivefieldmeasuredherehavebeenfoundonpolycrys-\ntalline as well as epitaxial Ni xFe3−xO4thin films.52The\nbulk value of NiFe 2O4has been reported to be 0.01 T53\nwhich is close to the values obtained here.\nIV. CONCLUSION\nWe investigated the modification of the crystal-\nlographic, electronic, and magnetic properties of\nFe3O4/NiO-bilayers due to thermally induced interdif-\nfusion of Ni ions out of the NiO layer into the magnetite\nfilm. We annealed two bilayers, sample A (B) comprising\ninitially 5.6nm (1.5nm) NiO and 5.5nm (5.4nm) Fe 3O4in\nthree steps ` a 20 - 30 minutes in an oxygen atmosphere of8\n5×10−6mbar. LEEDdemonstratestheextinctionofthe\nmagnetite specific (√\n2×√\n2)R45 superstructure, how-\never, a spinel like (1 ×1) surface structure occurs after\nthe overall annealing cycle.\nStructural analysis reveals that the annealing cycles\nlead to homogenous layers of Ni xFe3−xO4. In case of\nsampleAconsiderationofanadditionalNiOsurfacelayer\non the surface leads to the best agreement between cal-\nculated and experimentally observed XRR and SR-XRD\nresults. For sample B SR-XRD indicates a strongly\ndistorted structure with a vertical lattice constant of\nc= 0.8334nm whereas the vertical lattice constant of\nsample A is close to that of bulk NiFe 2O4.\nThese findings are supported by the HAXPES experi-\nments. Firstly, the formation of Fe3+upon annealing is\nconfirmed by the Fe 2p core level HAXPES data. Sec-\nondly, for sample B the shape of the Ni 2p-HAXPES in-\ndicate the formation of an inverse spinel ferrite, whereas\nin case of sample A NiO characteristic features first di-\nminish after annealing at 600◦C and re-appear after the\nentire annealing cycle at 800◦C. This may be associ-\nated with the much thicker initial NiO layer of sample\nA maybe leading to NiO rich grains at the interface or\nNiO clusters at the sample surface. Thirdly, we deter-\nmined a Ni:Fe ratio of 1:2.6 for sample B, the resulting\nstoichiometry of sample B is Ni 0.83Fe2.17O4. For sample\nA an increasing amount of Ni2+ions with increasing an-\nnealing temperature is found due to the Ni diffusion to\nthe surface.\nWe employed XMCD to study the internal magnetic\nproperties of the thin films resulting from the Ni interdif-\nfusion process. In excellent agreement to complementary\ncharge transfer multiplet simulations we find a strong in-\ncrease of Fe3+\ntetcoordinated cation fraction (around 50%)comparedtostoichiometricFe 3O4, resultinginverysmall\nFe net magnetic moments as determined from the exper-\nimental XMCD data by applying the sum rules. The\nmagnetic properties after the annealing cycle are in both\nsamples dominated by the contribution of the Ni2+ions,\nwhich exhibit magnetic moments of 0.56 µB/f.u. (sample\nA) and 1.03 µB/f.u. (sample B). The latter value cor-\nresponds quite well to the value very recently reported\nfor a stoichiometric NiFe 2O4thin film.47The lower value\nfound for sample A can be explained by the formation\nof (antiferromagnetic) NiO-rich islands or clusters at the\nsurface of the sample which contribute to the Ni L 2,3-\nXAS signal but not to the correspondingXMCD. Finally,\nperformed element specific hysteresis loops on sample\nB find a rather small in-plane coercive field of around\n0.02 T. This is a further indication for the formation a\nquite high quality NiFe 2O4-like thin film by means of\nthermal interdiffusion of Ni2+ions into magnetite from\nFe3O4/NiO bilayers.\nAcknowledgments\nFinancial support by the Deutsche Forschungsgemein-\nschaft (DFG) (KU2321/2-1 and KU3271/1-1) is grate-\nfully acknowledged. We thank Diamond Light Source for\naccess to beamline I09 (SI10511-1) that contributed to\nthe results presented here. Additionally, parts of this re-\nsearch were carried out at the light source PETRA III at\nDESY. We would like to thank F. Bertram for assistance\nusing beamline P08. Furthermore, part of this work has\nbeen performed at the Advanced Light Source, which is\nsupported bythe Director, Office ofScience, OfficeofBa-\nsic Energy Sciences, of the U.S. Department of Energy\nunder Contract No. DE-AC02-05CH11231.\n∗Electronic address: jwollsch@uos.de\n†Electronic address: kkuepper@uos.de\n1P. Weiss and R. Forrer, Ann. Phys. (Paris) 12, 279 (1929).\n2P. I. Slick, Ferromagnetic Materials: A Handbook on the\nProperties of Magnetically Ordered Substances (Wohlfarth\n(ed.), E. P., North-Holland Publishing Company, Amster-\ndam, 1980).\n3M. I. Katsnelson, V. Y. Irkhin, L. Chioncel, A. I. Licht-\nenstein, and R. A. de Groot, Rev. Mod. Phys. 80, 315\n(2008).\n4R. Bliem, E. McDermott, P. Ferstl, M. Setvin, O. Gamba,\nJ. Pavelec, M. A. Schneider, M. Schmid, U. Diebold,\nP. Blaha, et al., Science 346, 1215 (2014).\n5J. M. Byrne, N. Klueglein, C. Pearce, K. M. Rosso, E. Ap-\npel, and A. Kappler, Science 347, 1473 (2015).\n6K. Balakrishnan, S. K. Arora, and I. V. Shvets,\nJ. Phys.: Condens. Matter 16, 5387 (2004).\n7G. E. Sterbinsky, J. Cheng, P. T. Chiu, B. W. Wessels, and\nD. J. Keavney, J. Vac. Sci. Technol., B 25, 1389 (2007).\n8F. Bertram, C. Deiter, O. Hoefert, T. Schemme, F. Tim-\nmer, M. Suendorf, B. Zimmermann, and J. Wollschl¨ ager,\nJ. Phys. D: Appl. Phys. 45, 395302 (2012).9F. Bertram, C. Deiter, T. Schemme, S. Jentsch, and\nJ. Wollschl¨ ager, J. Appl. Phys. 113, 184103 (2013).\n10J. A. Moyer, S. Lee, P. Schiffer, and L. W. Martin, Phys.\nRev. B 91, 064413 (2015).\n11T. Schemme, N. Path´ e, G. Niu, F. Bertram, T. Kuschel,\nK. Kuepper, and J. Wollschl¨ ager, Mat. Res. Exp. 2, 016101\n(2015).\n12N.-T. H. Kim-Ngan, A. G. Balogh, J. D. Meyer, J. Br¨ otz,\nM. Zaj¸ ac, T. ´Sl¸ ezak, and J. Korecki, Surf. Sci. 603, 1175\n(2009).\n13K. A. Shaw, E. Lochner, and D. M. Lind, J. Appl. Phys.\n87, 1727 (2000).\n14N.-T. H. Kim-Ngan, A. G. Balogh, J. D. Meyer, J. Br¨ otz,\nS. Hummelt, M. Zaj¸ ac, T. ´Sl¸ ezak, and J. Korecki, Surf. Sci.\n602, 2358 (2008).\n15J. F. Anderson, M. Kuhn, U. Diebold, K. Shaw, P. Stoy-\nanov, and D. Lind, Phys. Rev. B 56, 9902 (1997).\n16L. A. Kalev, P. Schurer, and L. Nielsen, Phys. Rev. B 68,\n165407 (2003).\n17H. C. Wu, R. Ramos, R. S. G. Sofin, Z. M. Liao, M. Abid,\nand I. V. Shvets, Appl. Phys. Lett. 101, 052402 (2012).\n18L. Marnitz, K. Rott, S. Nieh¨ orster, C. Klewe, D. Meier,9\nS. Fabretti, M. Witziok, A. Krampf, O. Kuschel,\nT. Schemme, et al., AIP Adv. 5, 047103 (2015).\n19T. Schemme, A. Krampf, F. Bertram, T. Kuschel,\nK. Kuepper, and J. Wollschl¨ ager, J. Appl. Phys. 118,\n113904 (2015).\n20C. Gatel, E. Snoeck, V. Serin, and A. R. Fert,\nEur. Phys. J. B 45, 157 (2005).\n21J. Keller, P. Milt´ enyi, B. Beschoten, G. G¨ untherodt,\nU. Nowak, and K. D. Usadel, Phys. Rev. B 66, 014431\n(2002).\n22M. Monti, M. Sanz, M. Oujja, E. Rebollar, M. Castillejo,\nF. J. Pedrosa, A. Bollero, J. Camarero, J. L. F. Cu˜ nado,\nN. M. Nemes, et al., J. Appl. Phys. 114, 223902 (2013).\n23J. Rubio-Zuazo, L. Onandia, E. Salas-Colera, A. Munoz-\nNoval, and G. R. Castro, J. Phys. Chem. C 119, 1108\n(2015).\n24M. Pilard, O. Ersen, S. Cherifi, B. Carvello, L. Roiban,\nB. Muller, F. Scheurer, L. Ranno, and C. Boeglin, Phys.\nRev. B 76, 214436 (2007).\n25D. Meier, T. Kuschel, L. Shen, A. Gupta, T. Kikkawa,\nK. Uchida, E. Saitoh, J.-M. Schmalhorst, and G. Reiss,\nPhys. Rev. B 87, 054421 (2013).\n26D. Meier, D. Reinhardt, M. van Straaten, C. Klewe, M. Al-\nthammer, M. Schreier, S. T. B. Goennenwein, A. Gupta,\nM. Schmid, C. H. Back, et al., Nat. Commun. 6, 8211\n(2015).\n27M. Althammer, S. Meyer, H. Nakayama, M. Schreier,\nS. Altmannshofer, M. Weiler, H. Huebl, S. Gepr¨ ags,\nM. Opel, R. Gross, et al., Phys. Rev. B 87, 224401 (2013).\n28C. J. Powell and A. Jablonski, Nucl. Instrum. Methods\nPhys. Res., Sect. A 601, 54 (2009).\n29S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Inter-\nface Anal. 35, 268 (2003).\n30L. G. Parratt, Phys. Rev. 95, 359 (1954).\n31L. N´ evot and P. Croce, Revue de Physique Applique 15,\n761 (1980).\n32F. M. F. de Groot, Coord. Chem. Rev. 249, 31 (2005).\n33E. Stavitski and F. M. F. de Groot, Micron 41, 687 (2010).\n34S. A.Chambers andS. A.Joyce, Surf. Sci. 420, 111 (1999).\n35J. Korecki, B. Handke, N. Spiridis, T. Slezak, F. Flis-\nKabulska, and J. Haber, Thin Solid Films 412, 14 (2002).\n36R. Pentcheva, W. Moritz, J. Rundgren, S. Frank,\nD. Schrupp, and M. Scheffler, Surf. Sci. 602(7), 1299\n(2008).37T. Yamashita and P. Hayes, Appl. Surf. Sci. 254, 2441\n(2008).\n38A. P. Grosvenor, M. C. Biesinger, R. S. C. Smart, and\nN. S. N. Stewart McIntyre, Surf. Sci. 600, 1771 (2006).\n39M. C. Biesinger, B. P. Payne, A. P. Grosvenor, L. W. M.\nLau, A. R. Gerson, and R. S. C. Smart, Appl. Surf. Sci.\n257, 2717 (2011).\n40R. M. Cornell and U. Schwertmann, The Iron Oxides\n(WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim,\n2003), 2nd ed.\n41M. B. Trzhaskovskaya, V. I. Nefedov, and V. G. Yarzhem-\nsky, At. Data Nucl. Data Tables 77, 97 (2001).\n42J. T. Newberg, D. E. Starr, S. Yamamoto, S. Kaya,\nT. Kendelewicz, E. R. Mysak, S. Porsgaard, M. B.\nSalmeron, G. E. Brown Jr., A. Nilsson, et al., Surf. Sci.\n605, 89 (2011).\n43C. J. OBrien, Z. Rak, and D. W. Brenner, J. Phys.: Con-\ndens. Matter 25, 445008 (2013).\n44C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith,\nG. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette,\nPhys. Rev. Lett. 75, 152 (1995).\n45Y. Teramura, A. Tanaka, and T. Jo, J. Phys. Soc. Jap. 65,\n4, 1053 (1996).\n46C. Piamonteze, P. Miedema, and F. M. F. de Groot, Phys.\nRev. B 80, 184410 (2009).\n47C. Klewe, M. Meinert, A. Boehnke, K. Kuepper, E. Aren-\nholz, A. Gupta, J.-M. Schmalhorst, T. Kuschel, and\nG. Reiss, J. Appl. Phys. 115, 123903 (2014).\n48R. Pattrick, G. Van der Laan, C. Henderson, P. Kuiper,\nE. Dudzik, and D. Vaughan, Eur. J. Mineral. 14, 1095\n(2002).\n49M. Hoppe, S. D¨ oring, M. Gorgoi, S. Cramm, and\nM. M¨ uller, Phys. Rev. B 91, 054418 (2015).\n50G. F. M. Gomes, T. E. P. Bueno, D. E. Parreiras, G. J. P.\nAbreu,A.deSiervo, J.C.Cezar, H.-D.Pfannes, andR.Pa-\nniago, Phys. Rev. B 90, 134422 (2014).\n51G. H. Jaffari, A. K. Rumaiz, J. C. Woicik, and S. I. Shah,\nJ. Appl. Phys. 111, 093906 (2012).\n52C. Jin, Q. Zhang, W. B. Mi, E. Y. Jiang, and H. L. Bai,\nJ. Phys. D: Appl. Phys. 43, L5001 (2010).\n53A. Shan, X. Wu, J. Lu, C. Chen, and R. Wang, CrystEng-\nComm17, 1603 (2015).a)\n(00)(01)\n(10)\nb)\n(00)(01)\n(10)\nc)\n(00)\n(20)(02)\nd)\n(00)\n(10)(01)\nBinding Energy [eV]Intensity [arb. unit]a)\n  \nFe 2p3/2 Fe 2p1/2\nsatellite\n700 710 720 730 740 750400°C\n600°C\n800°Csample ABinding Energy [eV]Intensity [arb. unit]a)\n  \nNi 2p3/2\nNi 2p1/2\nFe 2s\nsatelliteshoulder\n840 850 860 870 880 890400°C\n600°C\n800°Csample AAngle of Photoemission ϕRelative Photoelectron Yield YNia)\n  \n−10°0°10°20°30°40°50°60°0.20.30.40.50.60.70.8400°C\n600°C\n800°Csample AL [r. l. u. SrTiO 3(001)]Intensity [arb. unit]a)\n  \n1.7 1.8 1.9 2 2.110−2100102104106\nexp.\nsim.Sample AScattering Vector [ ˚A−1]Intensity [arb. unit]a)\n  \n00.1 0.2 0.3 0.4 0.510−610−410−2100102\nbefore\nafter\nsim.sample ABinding Energy [eV]Intensity [arb. unit]b)\n  \nFe 2p3/2 Fe 2p1/2\nsatellite\n700 710 720 730 740 750400°C\n600°C\n800°Csample BBinding Energy [eV]Intensity [arb. unit]b)\n  \nNi 2p3/2\nNi 2p1/2 Fe 2s\nsatelliteshoulder\n840 850 860 870 880 890400°C\n600°C\n800°Csample BAngle of Photoemission ϕRelative Photoelectron Yield YNib)\n  \n−10°0°10°20°30°40°50°60°0.10.20.30.40.5400°C\n600°C\n800°Csample BL [r. l. u. SrTiO 3(001)]Intensity [arb. unit]b)\n  \n1.7 1.8 1.9 2 2.110−2100102104106\nexp.\nsim.Sample BScattering Vector [ ˚A−1]Intensity [arb. unit]b)\n  \n00.1 0.2 0.3 0.4 0.510−610−410−2100102\nbefore\nafter\nsim.sample B"    },    {        "title": "2009.08084v1.Magnetoelectric_near_fields.pdf",        "content": " \n Magnetoelectric near fields \n \nEugene Kamenetskii \n  \nMicrowave Magnetic Laboratoty  \nBen Gurion University of the Negev, Israel \nE-mail: kmntsk@bgu.ac.il \n \nAbstract \nSimilar to electromagnetic (EM) phenomena, described by Maxwell equations, physics of \nmagnetoelectric (ME) phenomena deals with the fundamental problems of the relationship between \nelectric and magnetic fields. The different nature of these two notions is especially evident in dynamic \nregimes. Analyzing the EM phenomena inside the ME material, the question arises: What kind of the \nnear fields, originated from a sample of such a material, can be measured? Observation of the ME \nstates requires an experimental technique characterized by a violation of spatial and temporal inversion \nsymmetries in a subwavelength region. This presumes the existence of specific near fields. Recently, \nsuch field structures, called ME fields, were found as the near fields of a quasi-2D subwavelength-size \nferrite disk with magnetic-dipolar-mode (MDM) oscillations. The key physical characteristics that \ndetermine the configurations of the ME near fields are the spin and orbital angular momenta of the \nquantum states of the MDM spectra. This leads to the appearance of subwavelength power-flow \nvortices. By virtue of unique topology, the ME quantum fluctuations in vacuum are different from \nvirtual EM photons. While preserving the ME properties, one observes strong enhancing the near-field \nintensity. The main purpose of this chapter is to review and analyze the studies of the ME fields. We \nconsider the near-field topological singularities originated from the MDM ferrite-disk particle. These \ntopological features can be transmitted to various types of nonmagnetic material structures. \n \n1. Introduction \n \nSymmetry principles play an important role in the laws of nature. Maxwell added an electric \ndisplacement current to put into a symmetrical form the equations which couple together the electric \nand magnetic fields. The dual symmetry between electric and magnetic fields underlies the \nconservation of energy and momentum for electromagnetic fields [1]. Recently, it was shown that this \ndual symmetry determines the conservation of optical (electromagnetic) chirality [2, 3]. Based on an \nanalysis of the interaction of chiral light and chiral specimens, new mechanisms of enantiomer \ndiscrimination and separation in optics have been proposed [2 – 8]. Since chiroptical effects are usually \nhampered by weak chiral light-matter interaction, it is argued that to enhance the chiral effects it is \nnecessary that the near field remains chiral in the process. Different plasmonic and dielectric \nnanostructures have recently been proposed as a viable route for near-field enhancement of chiral \nlight-matter interactions [9 – 11]. In a more general sense, one can say that this is an attempt to enhance \nthe near-field intensity while preserving the ME properties. However, the following fundamental \nquestions arise: Can one really observe effects of the near-field magnetoelectricity in dynamic \nregimes. What are the symmetry properties of such dynamic ME fields?  \n     The question on relationships between magnetoelectricity and electromagnetism is a subject of a \nstrong interest and numerous discussions in microwave and optical wave physics and material  \n sciences. The problem of the near-field magnetoelectricity in electromagnetism is a topical problem. \nEvanescent fields are oscillating fields whose energy is spatially concentrated in the vicinity of the \noscillating currents. In classical electrodynamics we know only two types of local (subwavelength) \nelectric currents: linear and circular. These types of currents determine elementary electric and \nmagnetic dipole oscillations in matter. The electric polarization is parity odd and time-reversal even. \nAt the same time, the magnetization is parity even and time-reversal odd [1]. These symmetry relation \ncast doubt on the idea of a local (subwavelength) coupling of two, electric and magnetic, small dipoles. \nWhen the violation of the invariances under space reflection parity and time inversion are necessary \nconditions for the emergence of the ME effect, the same symmetry properties should be observed for \nthe near fields – the ME near fields.  \n     The uniqueness of the proposed ME near fields can be shown by analyzing vacuum near fields \noriginated from a scatterer made of a ME structure. In this connection, it is worth noting that in a case \nof usual (non-ME) material structures one can distinguish two kinds of the EM near fields: (a) near \nfields originated from EM wave resonances and (b) near fields originated from dipole-carrying \nresonances. The former fields, abbreviated as EM NFs, are obtained based on the full-Maxwell-\nequation solutions with use of Mie theory [12]. The latter fields, abbreviated as DC NFs, are observed \nwhen the electric or magnetic dipole-carrying oscillations (such, for example, as surface plasmons [13 \n– 15] and magnons [16 – 18]) take place. Notably, in accordance with Mie theory one can observe EM \nNFs with magnetic responses originated from small nonmagnetic dielectric resonators, both in \nmicrowaves [19] and optics [20 – 22]. In a case of DC NFs, strong coupling of EM waves with electric \nor magnetic dipole-carrying excitations, called polaritons, occur [16, 23]. Importantly, the spatial scale \nof the DC NFs is much smaller than the spatial scale of the EM NFs in the same frequency range. Due \nto strong coupling of EM waves with dipole-carrying excitations and temporal dispersion of the \nmaterial, polaritons display enhanced field localization to surfaces and edges. Properties of vacuum \nnear-fields originated from a small non-ME (dielectric or magnetic) sample become evident when this \nsample has sizes significantly smaller than the EM wavelength in all three spatial dimensions . The \nmatter of fact is that near such a scatter we can only measure the electric E\n or the magnetic field H\n \nwith accuracy. As volumes smaller than the wavelength are probed, measurements of EM energy \nbecome uncertain, highlighting the difficulty with performing measurements in this regime. There is \nHeisenberg’s uncertainty principle binding E\n and H\n fields of the EM wave [13, 24].  \n     Taking all this into account, let us consider now a subwavelength ME sample . The near-field \nstructure of such a point scatterer is dominated by two types of the fields: the electric and magnetic \nfields, which are mutually coupled  due to the intrinsic properties of a ME material. This fact gives us \nmuch greater uncertainty in probing of the fields. In total, such fields can be represented as the \nstructures of cross E H \nor dot E H \n products in a subwavelength region. Due to  symmetry of \nME structure, the ME near fields of a subwavelength sample should be characterized by a certain \npseudoscar parameter. Moreover, supposing that in a subwavelength region both structures of cross \nE H \nand dot E H \n products exist, one should assume the presence of helicity properties of the fields. \nIt is evident that such a near-field structure – the ME-field structure – is beyond the frames of the \nMaxwell theory description [1].  \n     When we are talking on ME dynamics, we have to refer also to an analysis of artificial structures \n– bianisotropic metamaterials. The notion “bianisotropic media” had been introduced to generalize \ndifferent effects of coupling between magnetic and electric properties [25]. The local bianisotropic \nmedia is supposed as the media composed by structural subwavelength elements with “glued” pairs of \nelectric and magnetic dipoles. The consideration of high-order quadrupole and multipole transitions is \nactually an account of spatial dispersion [26, 27]. It is assumed that bianisotropy (chirality) in  \n metamaterials arises from a “local ME effect” [28 – 31]. Such a “first-principle”, “microscopic-scale” \nME effect of a structure composed by “glued” pairs of electric and magnetic dipoles raises a basic \nquestion on the ways of probing the dynamic parameters, since the near field structure of such a probe \nshould violate both the spatial and temporal inversion symmetries. However, in metamaterial \nbianisotropic (chiral) structures, the known experimental retrieval of the cross-polarization parameters \nis via far-field measurement  of the scattering-matrix characteristics [32 – 34]. Far-field retrieved \npermittivity and permeability frequently retain non-physical values, especially in the regions of the \nmetamaterial resonances where most interesting features are expected. Far-field retrieved cross-\npolarization parameters of “bianisotropic particles\" retain much greater non-physical value. The \nobserved far-field phenomena of bianisotropy (chirality) can be very weakly related to the near-field \nmanipulation effects. We can say that the cross-polarization properties of small “glued-pair” \nbianisotropic particles are incompatible with the effects of Rayleigh scattering.  \n     In this chapter, we consider near fields originated from subwavelength resonators, that are the \nsystems with quantum-confinement effects of dipolar-mode quasistatic oscillations. We analyze the \npossibilities of these resonances to exhibit near-field ME properties. An analysis of such dipole-\ncarrying excitations allows finding a proper way in realizing polariton structures with properties of \nstrong ME interactions.  \n \n2. Subwavelength resonators with dipole-carrying excitations \n \nAn interaction between the photon and medium dipole-carrying excitation becomes strong enough \nnear the resonance between the light mode and the mode of the medium excitation. At the resonance \nregion, the dispersion curves of these modes transform into two split polaritonic branches showing \nanticrossing behavior. The examples are exciton polaritons, surface-plasmon polaritons, and magnon \npolaritons. Semiclassically, polaritons are described using Maxwell equations and constitutive \nrelations that include the frequency dependent response functions. Quantum mechanically, polaritons \nare described as hybrid collective excitations that are linear superpositions of matter collective \nexcitations and photons. There are the effects of interaction between real and virtual photons . When \ndipole-carrying excitations are observed in a high-quality confined structure, the coupling modes can \nappear as composite bosons. Strong long-range dipole-dipole interactions significantly modify the \nmean-field predictions of the quantum phases of microscopic short-range excitations by stabilizing the \ncondensate phase. It can persist up to densities high enough to support quantum liquidity with very \nlong lifetimes. In exciton-polariton condensates , in particular, this effect leads to sustained trapping \nof the emitted photon [35 – 39].  \n     Excitons in semiconductor resonators are dipole-carrying oscillations. Plasmons and magnons in \nconfined structures are also dipole-carrying oscillations. Plasmons are optical responses of metal \nstructures arising from collective oscillations of their conduction electrons. The microwave responses \nof ferrite samples – magnons – arise from collective oscillations of their precessing electrons. Both \nplasmons and magnons are bosons. In increasing the capabilities of the optical and microwave \ntechniques further into the subwavelength regime, small plasmon and magnon resonant structures have \nattracted considerable interest. These oscillations in subwavelength resonators, however, are not \ncomposite bosons , as in the case of exciton resonances. No dipole-dipole plasmon condensate and \ndipole-dipole magnon condensate in confined resonant structures are observed, to the best to our \nknowledge. The problem of creating a condensate with linked (electric and magnetic) dipole-carrying \nexcitations confined in a high-quality resonant structure appears as a lot more exotic. Is it even possible \nto observe tightly bound ME excitations, which turns into a composite boson (or fermion) and behaves  \n as quasiparticle? Can we, in general, solve the problem of creation of the ME-polariton condensate? \nTo answer these questions, we should analyze the possibility of finding ME properties in \nsubwavelength resonators with quasistatic (dipolar-mode) oscillations.  \n \nA. On the possibility to observe the quantum confinement effects of electrostatic and \nmagnetostatic oscillations \n \nElectromagnetic (EM) responses of plasmon oscillations in optics and magnon oscillations in \nmicrowaves give rise to a strong enhancement of local fields near the surfaces of subwavelength \nresonators. We can classify these oscillations as electrostatic (ES) and magnetostatic (MS) resonances, \nrespectively [18, 40]. In ES resonances in small metallic samples, one neglects a time variation of \nmagnetic energy in comparison with a time variation of electric energy. It means that one neglects a \nmagnetic displacement current and an electric field is expressed via an ES potential, E \n[40]. \nHowever, the Ampere–Maxwell law gives the presence of a curl magnetic field. In like manner, in the \ncase of MS resonances in ferrite samples, one neglects a time variation of electric energy in \ncomparison with a time variation of magnetic energy. It means that the MS-resonance problem is \nconsidered as zero-order approximation of Maxwell’s equations when one neglects the electric \ndisplacement current and expresses a magnetic field via a MS potential, H \n[18]. While \nFaraday’s law gives the presence of a curl electric field. Importantly, from a classical electrodynamics \npoint of view, one does not have a physical mechanism describing the reverse effect of transformation \nof a curl magnetic field to a potential electric field in the case of ES resonances. Also, one does not \nhave a physical mechanism describing the reverse effect of transformation of a curl electric field to a \npotential magnetic field a case of the MS resonance [1, 41]. It means that, fundamentally, \nsubwavelength sizes of the particles should eliminate any EM retardation effects. We can say that for \nan EM wavelength   and particle of a characteristic size a, the quasistatic approximation 2 1a  \nimplies the transition to a small EM phase.  \n     What kind of the time-varying field structure one can expect to see when an electric or magnetic \ndisplacements currents are neglected and so the electromagnetic-field symmetry (dual symmetry) of \nMaxwell equations is broken?  When one neglects a displacement current (magnetic or electric) and \nconsiders the scalar-function [ ( , )r t\n or ( , )r t\n] solutions, as the wave-propagation solutions, one has \nto accept the possibility to observe the quantum confinement effects of electrostatic and magnetostatic \noscillations. Such an analysis of quasistatic resonances is based on postulates about a physical meaning \nof scalar function as a complex scalar wavefunction, which presumes a long-range phase coherence in \ndipole–dipole interactions. These solutions should be based on the Schrödinger-like equation. \n     For quasi-ES resonances in subwavelength metal structures characterised by non-homogeneous \nscalar permittivity, we have Poison’s equation  [42 – 45] \n \n                                                          21 0r        .                                                     (1) \n \nAt the same time, for quasi-MS resonances in subwavelength microwave ferrite structures with tensor \npermeability , there is Walker’s equation [18, 46]: \n   \n                                                       2\n00 I               \n.                                                   (2) \n \nSolutions of both these equations are harmonic functions. Nevertheless, it appears that in spite of a \ncertain similarity between Eqs. (1) and (2), the physical properties of the ES and MS oscillation spectra \nare fundamentally different in many aspects. The most important factor distinguishing the MS \nresonance from the ES resonance is the tensorial form of permeability and the presence off-diagonal \ngyrotropic elements in this tensor. \n     In Ref. [47] it was discussed that in a case of the surface plasmon resonances in subwavelength \noptical metallic structures no retardation processes characterized by the electric dipole-dipole \ninteraction and described exclusively by electrostatic wave function ( , )r t take place. There is no \npossibility to describe these resonances by the Schrödinger-equation energy eigenstate problem. \nNevertheless, for MS resonances in ferrite specimens we have bulk wave process, which are \ndetermined by a scalar wave function ( , )r t. Due to the retardation processes caused by the magnetic \ndipole-dipole interaction in a subwavelength ferrite particle, we have a possibility to formulate the \nenergy eigenstate boundary problem based on the Schrödinger-like equation for scalar-wave \neigenfunctions ( , )r t. Such a behavior can be obtained in a ferrite particle in a form of a quasi-2D \ndisk. The oscillations in a quasi-2D ferrite disk, analyzed as spectral solutions for the MS-potential \nscalar wave function ( , )r t, have evident quantum-like attributes. Quantized forms of such \noscillations we call the MS magnons or the magnetic-dipolar-mode (MDM) magnons. The \nmacroscopic nature of MDMs, involving the collective motion of a many-body system of precessing \nelectrons, does not destroy a quantum behavior. The long-range dipole-dipole correlation in positions \nof electron spins can be treated in terms of collective excitations of a system as a whole. \n     Analyzing the confinement effects of electrostatic and magnetostatic oscillations in subwavelength \nresonators, it is also worth making another important remark. Considering light interaction with \nphotonic and plasmonic resonances, the authors of review in Ref. [48] noted that as the optical mode \nbecomes deeply subwavelength in all three dimensions, independent of its shape, the Q-factor of the \nresonances is limited to about 10 or less. As they argue, the reason is that in such small volumes, self-\nsustaining oscillations are no longer possible between the electric-field and magnetic-field energies \nand, at the same time, no effects of the electric dipole-dipole oscillations can be assumed. At the same \ntime, in the case of a microwave MDMs in a deeply subwavelength ferrite disk resonator, we have the \nQ-factor about several thousand [49 – 51]. For such MDM resonances, subwavelength sizes of the \nferrite particle allow eliminate any electromagnetic retardation effects and consider only the magnetic \ndipole-dipole interaction effects. \n     To make the MDM spectral problem analytically integrable, two approaches were suggested. These \napproaches, distinguished by differential operators and boundary conditions used for solving the \nspectral problem, give two types of MDM oscillation spectra in a quasi-2D ferrite disk. These two \napproaches are conditionally called as the G and L modes in the magnetic dipolar spectra [52 – 57]. \nThe MS-potential wave function ( , )r t manifests itself in different manners for each of these types \nof spectra. In the case of the G-mode spectrum, where the physically observable quantities are energy \neigenstates, the MS-potential wave function appears as a Hilbert-space scalar wave function. In the \ncase of the L modes, the MS-potential wave function is considered as a generating function for the \nvector harmonics of the magnetic and electric fields.     \n  \n B. Spectral problems for MDM magnetostatic oscillations: G modes \n \nThe MDM-resonance spectral solutions obtained from the second-order differential equation – the \nWalker’s equation [18, 46] – are constructed in accordance with basic symmetry considerations for \nthe sample geometry. For an open quasi-2D ferrite disk normally magnetized along the z axis, we can \nuse separation of variables. In cylindrical coordinate system ( , , )z r, the solutions are represented as \n[52 – 57]  \n \n                                                              , , , , , , , ( ) ( , )p q p q p q qA z r       ,                                             (3)   \n \nwhere , ,p qA is a dimensional amplitude coefficient, , ,( )p qz is a dimensionless function of the MS-\npotential distribution along z axis, and ,( , )qr  is dimensionless membrane function. The membrane \nfunction  is defined by a Bessel-function order  and a number of zeros of the Bessel function \ncorresponding to a radial variations q. The dimensionless “thickness-mode” function ( )z is \ndetermined by the axial-variation number p.  \n     In a quasi-2D ferrite disk, one can formulate the energy eigenstate boundary problem based on the \nSchrödinger-like equation for scalar-wave eigenfunctions ( , )r t\n with using the Dirichlet-Neumann \n(ND) boundary conditions. The energy eigenvalue problem for MDMs is defined by differential \nequation \n \n                                                                          ˆ\nn n nG E  ,                                                             (4) \n \nwhere ˆGis a two-dimensional (on the ,r disk plane) differential operator. The quantity nE is \ninterpreted as density of accumulated magnetic energy of mode n. This is the average (on the RF \nperiod) energy accumulated in the ferrite-disk region of unit in-plane cross-section and unit length \nalong z axis [52 – 57]. The operator ˆG and quantity nE are defined as   \n \n                                                                        2 0\n4n n n ngE    ,                                                    (5) \n \nwhere  \n                                                                               20\n4n ngE .                                                    (6)              \n \nHere 2\n is the two-dimensional (on the circular cross section of a ferrite-disk region) Laplace \noperator, g is a dimensional normalization coefficient (with the unit of dimension 2) for mode n \nand nis the propagation constant of mode n along the disk axis z. The parameter n (which is a \ndiagonal component of the permeability tensor [18]) should be considered as an eigenvalue. Outside \na ferrite 1n. The operator ˆG is a self-adjoint operator only for negative quantities n in a ferrite.  \n For self-adjointness of operator ˆG, the membrane function ( , )nr  must be continuous and \ndifferentiable with respect to the normal to lateral surface of a ferrite disk. The homogeneous boundary \nconditions – the ND boundary conditions – for the membrane function are: \n \n                                                                        0n nr r                                                        (7) \n \nand  \n \n                                                                    0n n\nr rr r \n                \n ,                                         (8) \n \nwhere  is the disk radius. MDM oscillations in a ferrite disk are described by real eigenfunctions: \n*\nn n  . For modes n and n, the orthogonality conditions are expressed as  \n \n                                                                         *\ncn n nn\nSdS    ,                                                         (9) \n \nwhere cS is a square of a circular cross section of a ferrite-disk region and nnis the Kronecker delta. \nThe spectral problem gives the energy orthogonality relation for MDMs:  \n \n \n                                                                    *0\ncn n n n\nSE E dS      .                                                  (10) \n \n     Since the space of square integrable functions is a Hilbert space with a well-defined scalar product, \nwe can introduce a basis set. A dimensional amplitude coefficient we write as n nA ca, where c is \na dimensional unit coefficient and nais a normalized dimensionless amplitude. The normalized scalar-\nwave membrane function  can be represented as n n\nna   . The amplitude is defined as  \n2\n2 *\ncn n\nSa dS .   The mode amplitude can be interpreted as the probability to find a system in a \ncertain state n. Normalization of membrane function is expressed as 21n\nna  [52 – 57].  \n     The analysis of discrete-energy eigenstates of the MDM oscillations, resulting from structural \nconfinement in a normally magnetized ferrite disk, is based on a continuum model. Using the principle \nof wave-particle duality, one can describe this oscillating system as a collective motion of \nquasiparticles. There are “flat-mode” quasiparticles at a reflexively-translational motion behavior \nbetween the lower and upper planes of a quasi-2D disk. Such quasiparticles are called “light” magnons. \nIn our study we consider MS magnons in ferromagnet as quanta of collective MS spin waves that \ninvolves the precession of many spins on the long-range dipole-dipole interactions. It is different from \nthe short-range magnons for exchange-interaction spin waves with a quadratic character of dispersion.  \n The meaning of the term “light”, used for the condensed MDM magnons, arises from the fact that \neffective masses of these quasiparticles are much less, than effective masses of “real” magnons – the \nquasiparticles describing small-scale exchange-interaction effects in magnetic structures. The \neffective mass of the “light” magnon for a monochromatic MDM is defined as [53]: \n \n                                                                           2\n( )\n2eff n\nlmnm\n.                                                    (11) \n \n     In solving boundary value problems for MS resonances, one encounters some questions when using \nboundary conditions. As is known, in solving a boundary value problem that involves the \neigenfunctions of a differential operator, the boundary conditions must be in a definite correlation with \nthe type of this differential operator [58, 59]. In an analysis of MDM resonances in a ferrite disk, we \nused the homogeneous ND boundary conditions, which mean continuity of the MS wave functions \ntogether with continuity of their first derivatives on the sample boundaries. Only in this case the \nfunctions form a complete set of orthogonal basis functions and thus the field expansion in terms of \northogonal MS-potential functions can be employed.  \n     However, the ND boundary condition (7), (8) are not the EM boundary conditions. While the \nconsidered above ND boundary conditions are the so-called essential boundary conditions, the EM \nboundary conditions are the natural boundary conditions [58]. For the EM boundary conditions, on a \nlateral surface of a ferrite disk we have to have continuity of membrane function  and a radial \ncomponent of the magnetic flux density 01n n\nr aBr r          . Here  and a are diagonal \ncomponent and off-diagonal components of the permeability tensor [18]. With such EM boundary \nconditions, it becomes evident that the membrane function   must not only be continuous and \ndifferentiable with respect to a normal to the lateral surface of a disk, but (because of the presence of \na gyrotropy term a) be also differentiable with respect to a tangent to this surface. There is evidence \nof the presence of an azimuthal magnetic field on the border circle with clockwise and \ncounterclockwise rotation asymmetry. In this case, the membrane functions  cannot be considered \nas single-valued functions, and the question arises of the validity of the energy orthogonality relation \nfor MS-wave modes.   \n     To restore the ND boundary conditions and thus the completeness of eigenfunctions , we need \nintroducing a certain surface magnetic current  ( )m\nstopjcirculating on a lateral surface of the disk. \nThis is a topological current, which compensates the term 1\na\nrir  \n  \nin the EM boundary \nconditions [55, 56, 60].  Evidently, for a given direction of a bias magnetic field (that is, for a given \nsign of a), there can be two, clockwise and counterclockwise, quantities of the circulating magnetic \ncurrent. The topological current ( )m\nstopjis defined by the velocity of an irrotational border flow. This \nflow is observable via the circulation integral of the gradient 1\nre \n     \n ,   where  is a \ndouble-valued edge wave function on contour 2 . On a lateral surface of a quasi-2D ferrite  \n disk, one can distinguish two different functions , which are the counterclockwise and clockwise \nrotating-wave edge functions with respect to a membrane function . The spin-half wave-function  \nchanges its sign when the regular-coordinate angle  is rotated by 2. As a result, one has the \neigenstate spectrum of MDM oscillations with topological phases accumulated by the edge wave \nfunction . A circulation of gradient \n along contour 2  gives a non-zero quantity when \nan azimuth number is a quantity divisible by 1\n2. A line integral around a singular contour : \n2\n* *\n01( )  ( )\nri d i d\n     \n \n                     \n  is an observable quantity. Because of the existing \nthe geometrical phase factor on a lateral boundary of a ferrite disk, MDM oscillations are characterized \nby a pseudo-electric field (the gauge field) €\n. The pseudo-electric field €\n can be found as \n( )m\n€ €  \n. The field €\n is the Berry curvature. The corresponding flux of the gauge field €\n \nthrough a circle of radius  is obtained as:      ( ) ( )2m e\n€\nSK € dS K d K q             \n , \nwhere ( )e\n are quantized fluxes of pseudo-electric fields, K is the normalization coefficient. Each \nMDM is quantized to a quantum of an emergent electric flux. There are the positive and negative \neigenfluxes. These different-sign fluxes should be nonequivalent to avoid the cancellation. It is evident \nthat while integration of the Berry curvature over the regular-coordinate angle  is quantized in units \nof 2, integration over the spin-coordinate angle  1\n2     is quantized in units of . The \nphysical meaning of coefficient K concerns the property of a flux of a pseudo-electric field. The Berry \nmechanism provides a microscopic basis for the surface magnetic current at the interface between \ngyrotropic and nongyrotropic media. Following the spectrum analysis of MDMs in a quasi-2D ferrite \ndisk one obtains pseudo-scalar axion-like fields and edge chiral magnetic currents. The anapole \nmoment for every mode n is calculated as [55, 56, 60].   \n \n                                                             ( ) ( )\n0( )  d\ne m\nsn topna j z dldz     \n ,                                      (12) \n \nwhere d is the disk thickness. The edge magnetic current ( )m\nstopj is a persistent current appearing \ndue to the mesoscopic effect: the magnitude of such a resonant current becomes appreciable when the \nparameters of the ferrite disk are reduced to the scale of the dipole-dipole quantum phase coherence \nlength of precessing electrons. At the MDM resonances, one has the “spin-orbit” interaction between \nprecessing magnetic dipoles and a persistent orbital magnetic current. When the frequency of the \norbital rotation of MDM resonances in a ferrite disk is close to the ferromagnetic resonance frequency, \nthe precessing magnetic dipoles become strongly correlated and one observers fermionization of the \nsystem composed of bosons. There are the macroscopic quantum phenomena related to the collective \nmotion of magnetic dipoles coalescing into the same quantum state, described by a single coherent  \n wavefunction of the condensate. This is a fundamentally distinctive feature from a boson condensate \ncreated by small-scale exchange-interaction magnons [61].  \n     It is worth noting that along with the circulation of the surface magnetic current ( )m\nstopj caused \nby the edge wave function, there is also the quadratic-form circulation due to this function. For the \ndouble-valued edge wave functions , we have the following orthonormality condition on contour \n2 [55]:  \n \n                                         \n       2 *\n*\n0\n2\n*\n00n n\na a n n\nr\na n n n nri i d\nq q d\n      \n     \n \n\n                         \n        \n\n\n.                                   (13)        \n \nFor mode n, there are the normalisation relations for the edge functions \n \n                                                               2\n*\n0n n nrd N\n                                                                    (14) \nand  \n \n                                                                2\n*\n0n n nrd N\n                                                      (15)                       \nwhere nN and nNare real quantities, which we characterize as surface power flow density of \nthe MDM mode. For a given direction of a bias magnetic field, the wave described by functions n\npropagates only in one direction along the edge. Also, the wave described by function n − \npropagates in one direction (opposite to the former case) along the edge. It is evident that a complex \nconjugate ‘particle’ configuration is an ‘antiparticle’ configuration and vice versa. This fact is related \nto the existence of only a single edgemode excitation for each wavenumber q. In other words, the \n‘particle’ configurations are their own ‘antiparticle’ configurations. This resembles the well-known \nproperties of the Majorana fermions [62]. So, we have a “chiral Majorana fermion field” [63, 64] on \nthe lateral wall of the MDM ferrite disk. \n     Due to the presence of surface power flow density, membrane eigenfunction  of every MDM \nrotates around the disk axis. When for every MDM we introduce the notion of an effective mass \n( )eff\nlmnm, expressed by Eq. (11), we can assume that for every MDM there exists also an effective \nmoment of inertia  eff\nznI. With this assumption, an orbital angular momentum a mode is expressed  \n as   eff\nz znnL I   . At the first approximation, let us suppose that the membrane eigenfunction n \nis viewed as an infinitely thin homogenous disk of radius . In other words, we assume that for every \nMDM, the radial and azimuth variation of the MS-potential function, are averaged. In such a case, we \ncan write  \n                                 \n                                                                ( ) 21\n2eff eff\nz lmn nI m d .                                                  (16) \n \nand  \n                                                               \n                                                          2 2\n4eff eff\nz z nn nL I d     .                                              (17)                         \n \nC. Spectral problems for MDM magnetostatic oscillations: L modes \n \nIn the above spectral analysis of the G modes, we used the ND boundary conditions. To bridge this \nspectral problem with the EM boundary conditions, we introduced the contour integrals determining \nsurface magnetic current ( )m\nstopj and surface power flow density of the MDM modes. However, the \nMDM spectral can be solved directly based on the EM boundary conditions. This approach is called \nthe L-mode spectral analysis. The solution for MS-potential wave function of a L-mode is written as \n \n                                                            , , , , , , , ( ) ( , )p q p q p q qC z r       ,                                                         (18)  \n \nwhere , ,p qC is a dimensional amplitude coefficient and  is a membrane function. For solutions in \na cylindrical coordinate system, one uses the following the boundary condition on a lateral surface of \na ferrite disk [52, 53, 55, 56]: \n \n                                           0a\nr r rir r                                \n   ,                                        (19)  \n \nwhich are different from the boundary conditions (8). A function  is not a single-valued function. It \nchanges a sign when angle  is turned on 2. For any mode n, the function n is a two-component \nsprinor pictorially denoted by two arrows:  \n                                            \n                                               1\n2\n1\n2, ,i\nn\nn n\niner r\ne\n   \n\n\n             \n                                                      (20) \n  \n      For MS waves in a ferrite medium, described by a L-mode scalar wave function ( , )r t, we define \na magnetic flux density: B H         . In this case, the power flow density can be viewed as \na current density, is expressed as [55]: \n \n                                                          * *\n4iB B   \n  .                                                             (21) \n \nSuch a power flow can appear because of dipole-dipole interaction of magnetic dipoles. With use of \nseparation of variables and taking into account a form of tensor  [18], we decompose a magnetic \nflux density by two components:  \n \n                                                                        || B B B   \n.                                                             (22) \n \nThe component B\n are given as \n \n                                                ( ) ( , )n n n B C z r e                       ,                             (23) \n \nwhere e is a unit vector laying in the ,r plane, and  \n                                       \n                                                     0a\nai\ni      .                                                                  (24 )                        \n \n For the component B\n we have \n \n                                      0 || 0( )( , )en\nn n zzB C rz           ,                                                 (25)   \n \nwhere ez is a unit vector directed along the z axis. \n     The above representations allow considering two components of the power flow density (current \ndensity). For mode n, we can write Eq. (21) as   \n \n                                                         nn n   \n     ,                                                                (26) \n \nwhere      * *\n4n nn n niB B        \n   and      * *\n4n nn n niB B        \n  . Along every of the \ncoordinates , , and r z , we have the power flows (currents):   \n \n      *\n2 2 *\n01 1,         4n n n n\nr n n n a n a rniC i i er r r r                                                         (27)  \n  \n      *\n2 2 *\n01 1,4\n        n n n n\nn n n a n aniC i i er r r r                                                                 (28) \n  \n       *\n2 2 *\n04n n\nz n n n zniC ez z                     ,                                                                           (29) \n \nwhere re,e, and ze are the unit vectors. We can see that for membrane function , defined by Eq. \n(20), there is a non-zero real azimuth component of the power-flow density. So, there is a non-zero \nquantity of the power flow circulation (clockwise or counterclockwise) around a circle 2L r, where \n0r . At the same time, homogeneous EM boundary conditions imposed on a ferrite disk on the \nr and z axes give standing waves without real power flows. \n \n3. Near fields of MDM oscillations – the ME near fields  \n \nThe L-mode wave function ( , )r t can define a magnetic flux density in a ferrite disk, as shown \nabove. This scalar wave function is considered as a generating function for other types of the fields \nboth inside and outside a ferrite disk. It allows analyzing complex topological properties of vectorial \nfields, associated with orbital angular momentum properties of MDM resonances.   \n     When the spectral problem for the MS-potential scalar wave function ( , )r t, expressed by Eq. \n(18),  is solved, distribution of magnetization in a ferrite disk is found as m  , where \n is \nthe susceptibility tensor of a ferrite [18]. Based on the known magnetization m, one can find the \nmagnetic field distribution at any point outside a ferrite disk [1, 65]: \n \n                                        \n3 31( )4V Sm r r r n m r r r\nH r dV dS\nr r r r                           \n   .                 (30)              \n \nAlso, the electric field in any point outside a ferrite disk is defined as [56, 65] \n \n                                                     ( )\n31( )  4m\nVj r r rE r dV\nr r    \n  \n  ,                                   (31) \n \nwhere ( )\n0mj i m \n is the density of a bulk magnetic current and frequency  is the MDM \nresonance frequency. In Eqs. (30) and (31), V and S are a volume and a surface of a ferrite sample, \nrespectively. Vector n is the outwardly directed normal to surface S.   \n      Depending on a direction of a bias magnetic field, we can distinguish the clockwise and \ncounterclockwise topological-phase rotation of the fields. At the MDM resonances, for the magnetic \nand electric fields defined by Eqs. (30) and (31) one can compose a vector \n \n                                                          * 1Re2MDMS E H   \n.                                                             (32)                                         \n \nThe vector MDMS\n can be considered as a power flow density vector. Really, based on the vector \nrelation * * * *E H H E E H            \n with taking into account  equations E i B   \n, \nH  \n and 0B \n, one has as a result * *E H i B         \n. The right-hand side of this \nequation is a divergence of the power flow density of monochromatic MS waves [55]. So, vector \nMDMS\n can be interpreted as the power flow density as well. Nevertheless, this is not the “EM \nPoynting vector”. Compare to the case of EM wave propagation (with both curl electric and curl \nmagnetic fields), we have here the modes with curl electric and potential magnetic fields. As we noted \nabove, that there is no EM laws describing transformation of the curl electric field to the potential \nmagnetic field. \n     In the MDM resonance, the orbital angular-momentum of the power flow density is expressed as \n \n                                                           * 1Re2zr E H       .                                                         (33) \n \nDepending on a direction of a bias magnetic field, we can distinguish the clockwise and \ncounterclockwise topological-phase rotation of the fields outside the ferrite disk. The direction of an \norbital angular-momentum z\n is correlated with the direction of a bias magnetic field 0H\n (along +z \naxis or –z axis). The active power flow of the field both inside and outside a subwavelength ferrite \ndisk has the vortex topology. In Refs. [65 – 67] it was shown that for every MDM mode, the power \nflow circulation calculated by Eq. (28) have the same distributions on the ,r plane, as the circulation \nof the power flow vector MDMS\n. Such the analytically derived distributions coincide with the \nnumerical patterns of the power flows. The analysis was made for a YIG ferrite disk of a 3 mm \ndiameter and thickness of 0.050 mm at the frequency region 8 – 9 GHz. Fig. 1 gives an example of \nthe analytically derived power-flow-density distribution. Fig. 2 shows some numerical patterns of the \npower flows. One can see a strong confinement of the fields arising from the vortices of the MDM \nresonances. In Fig. 3, we give a schematic representation of the circulation of the power flow, depicted \non the surface of the vacuum sphere and on the surface of the solid angle. Direction of an orbital \nangular-momentum of a ferrite disk is correlated with the direction of a bias magnetic field. \n       A persistent edge magnetic current circulating along the contour 2  on a lateral surface of \nferrite disk determines an angular momentum – the anapole moment. Another type of an angular \nmomentum is associated with the power-flow circulation. In a lossless ferrite disk, circulation of the \npower flow density can be considered as a persistent current as well. The divergentless power-flow-\ndensity persistent current, circulating on the ,r plane, is an intrinsic property of the fields at the \nMDM resonances unrelated to the rigid-body rotation of a ferrite-disk. In the Introduction, we asked  \n a question about the possibility of observing a dot product E H \n together with a cross product E H \nin the near-field region of a subwavelength sample. This question concerned the samples with ME \nproperties. When, for MDM oscillations in a subwavelength ferrite disk, we observe the cross-product \nof the fields, can we classify this field structure as the ME fields, which are also characterized by the \nproperties of -symmetry and dot-product  E H \n of the fields? In Ref. [56] it was shown that in \nthe near-field region adjacent to the MDM ferrite disk, there exists also another quadratic parameter \ndetermined by the scalar product between the electric and magnetic field components: \n  \n                                              ** 0 0 0Im Re 04 4F E E E H             \n.                                (34)                         \n  \nThis effect is due to the presence of both the curl and potential electric fields in the subwavelength \nregion of the MDM ferrite disk. At the same time, the magnetic near field is pure potential.      \nParameter F is the ME-field helicity density. It appears only at the MDM resonances. A sign of the \nhelicity parameter depends on a direction of a bias magnetic field. Because of time-reversal symmetry \nbreaking, all the regions with positive helicity become the regions with negative helicity (and vice \nversa), when one changes a direction of a bias magnetic field:   \n \n                                                                      0 0H HF F   \n.                                                            (35) \n \nAn integral of the ME-field helicity over an entire near-field vacuum region should be equal to zero \n[68, 69]. This “helicity neutrality” can be considered as a specific conservation law of helicity. The \nhelicity parameter F is a pseudoscalar: to come back to the initial stage, one has to combine a reflection \nin a ferrite-disk plane and an opposite (time-reversal) rotation about an axis perpendicular to that plane. \nThe helicity-density distribution is related to the angle between the spinning electric and magnetic \nfields. Figs. 4 and 5 show the magnetic and electric field distributions on the upper plane of a ferrite \ndisk for the first MDM resonance at different time phases. For such a field structure one can observe \nboth the cross E H \n and dot E H \n products in the near-field region. The dot-product distributions \n(the helicity density distributions) are showed in Fig. 6.  When one moves from the ferrite surfaces, \nabove or below a ferrite disk, one observes reduction of the field amplitudes and also variation of the \nangle between spinning electric and magnetic fields. This angle varies from 0° or 180° (near the disk \nsurfaces) to 90° (sufficiently far from a ferrite disk). The “source” of the helicity factor is the \npseudoscalar quantity of the magnetization distribution in a ferrite disk at the MDM resonances [68] \n \n                                                              \n *Im 0\nVm m dV\n      ,                                               (36) \n \nwhere V are volumes of the upper and lower halves of the ferrite disk. These magnetization \nparameters are distributed asymmetrically with respect to the z-axis (see Figure 7). Thus, the \ndistribution of the helicity factor is also asymmetric. The regions with nonzero helicity factors we can \ncharacterize as the regions with nonzero ME energies. The area with positive helicity factor ( )F is \nthe area with positive ME energy, ( )\nMEW. The area with negative helicity factor ( )F is the area with  \n negative ME energy, ( )\nMEW. The total “ME potential energy” is related to the “ME kinetic energy” of \nthe power-flow rotation. It a symmetrical structure, we have “magnetoelectrically neutral” condensate.  \n     At the MDM resonances, both the power-flow vortices and the helicity states of ME fields are \ntopologically protected quantumlike states. In Ref. [69], it was shown that the power-flow density and \nthe helicity are the complex quantities. In the absence of losses and sources, there exist also the vector \n*ImE H \n. This vector can be classified as the reactive power flow density. Fig. 8 illustrates the active \nand reactive power flows distributions at the MDM resonance above and below a ferrite disk. We can \nsee that while the active power flow is characterized by the vortex topology, the reactive power flow \nhas a source which is originated from a ferrite disk. The regions of localization of the active and \nreactive power flows are different. While the active power flow is localized at the disk periphery, the \nreactive power flow is localized at a central part of the disk. It was shown [69] that above and below \na quasi-2D ferrite disk, the real part of the helicity density (defined by Eq. (34)) is related to an \nimaginary part of the complex power-flow density:  \n                                                                 \n                                                          * * 1 1Re Im2 2zE H E H         \n                                              (37) \n \nThe numerical results in Ref. [69] clearly show that in a vacuum region where the helicity-density \nfactor exist, the reactive power flow is observed as well. So, in a region near a ferrite disk, the reactive \npower flow is accompanied by the helicity factor or, in other words, by the ME-energy density. \n    The pseudoscalar parameter (36) and the helicity factor F, arise due to spin-orbit interaction. Such \nPT-symmetric parameters, mixing electric and magnetic fields, are associated with the axion-\nelectrodynamic term, leading to modification of inhomogeneous Maxwell equations [57, 70, 71]. It \nmeans that the ME fields appear as the fields of axion electrodynamics. With such a unique topological \nstructure of ME near fields, two types of polaritons should be observed: right-handed ME polaritons \nand left-handed ME polaritons. When an external microwave structure is geometrically symmetrical, \nthe two types of ME polaritons are indistinguishable. Otherwise, different microwave responses could \nbe observed depending on the direction of the bias magnetic field. When an external microwave \nstructure contains any elements with geometrical chirality, the right-hand and left-hand ME polaritons \nbecomes nondegenerate, and microwave responses depend on the direction of the bias magnetic field. \nThis fact was confirmed both numerically and experimentally [56]. \n \n4. MDM particles inside waveguides and cavities.  \n  \nIn microwaves, we are witnesses that long-standing research in coupling between electrodynamics and \nmagnetization dynamics noticeably reappear in recent studies of strong magnon-photon interaction \n[72 – 76]. In a small ferromagnetic particle, the exchange interaction can lead to the fact that a very \nlarge number of spins to lock together into one macrospin with a corresponding increase in oscillator \nstrength. This results in strong enhancement of spin-photon coupling. In a structure of a microwave \ncavity with a yttrium iron garnet (YIG) sphere inside, the avoided crossing in the microwave reflection \nspectra verifies the strong coupling between the microwave photon and the macrospin magnon. In \nthese studies, the Zeeman energy is defined by a coherent state of the macrospin-photon system when \na magnetic dipole is in its antiparallel orientation to the cavity magnetic field.  Together with an \nanalysis of the strong coupling of the electromagnetic modes of a cavity with the fundamental Kittel \nmodes, coupling with non-uniform modes – the Walker modes – in a YIG sphere was considered. In \nthe microwave experiments, identification of the Walker modes in the sphere was made based an effect  \n of overlapping between the cavity and spin waves due to relative symmetries of the fields [77, 78]. \nNevertheless, the experimentally observed effects of strong magnon-photon interaction, cannot be \ndescribed properly in terms of a single magnon-photon coupling process. In a view of these aspects, \nthe theory based on solving coupled Maxwell and Landau-Lifshitz-Gilbert equations without making \nthe conventional magnetostatic approximation have been suggested [79, 80]. Currently, the studies of \nstrong magnon-photon interaction are integrated in a new field of research called cavity spintronics \n(or spin cavitronics) [81]. \n     The coupling strength in the magnon-photon system is proportional to the probability of conversion \nof a photon to a magnon and vice versa. An effective way for strong coupling is to confine both \nmagnons and photons to a small (subwavelength) region. Long-range spin transport in magnetic \ninsulators demonstrates that the dipolar interactions alone generate coherent spin waves on the scales \nthat are much larger than the exchange-interaction scales and, at the same time, much smaller than the \nelectromagnetic-wave scales. Because of symmetry breakings, the MDM ferrite disk, being a very \nsmall particle compared to the free-space electromagnetic wavelength, is a singular point for \nelectromagnetic fields in a waveguide or cavity. When we consider a ferrite disk in vacuum \nenvironment, the unidirectional power-flow circulation might seem to violate the law of conservation \nof an angular momentum in a mechanically stationary system. In a microwave structure with an \nembedded ferrite disk, an orbital angular momentum, related to the power-flow circulation, must be \nconserved in the process. It can be conserved if topological properties of electromagnetic fields in the \nentire microwave structure are taken into account. Thus, if power-flow circulation is pushed in one \ndirection in a ferrite disk, then the power-flow circulation on metal walls of the waveguide or cavity \nto be pushed in the opposite direction at the same time. It means that, in a general consideration, the \nmodel of MDM-vortex polaritons appears as an integrodifferential problem. Fig. 9 presents a \nschematic picture of an interaction of a MDM ferrite disk with an external microwave structure. In \nRef. [68] it was shown that due to the topological action of the azimuthally unidirectional transport of \nenergy in a MDM-resonance ferrite sample there exists the opposite topological reaction (opposite \nazimuthally unidirectional transport of energy) on a metal screen placed near this sample. It is obvious \nthat the question of the interaction of a MDM ferrite disk with an external microwave structure is far \nfrom trivial. To illustrate this nontriviality in more details, we adduce here some topological problems \nrelated to our studies.   \n \nA. On Rayleigh scattering by a thin ferrite rod \n  \nIn the above studies of the MDM oscillation spectra in an open quasi-2D ferrite disk, the separation \nof variables in a cylindrical coordinate system was used. Analytically, we cannot apply a 2D model to \nconsider scattering of EM waves by a subwavelength ferrite disk. Nevertheless, based on a simple \nqualitative analysis of a 2D structure, we can illustrate the role of topology in the EM-wave scattering \nby a ferrite sample. For this purpose, we will view some properties of the EM-wave scattering by a \nthin endless ferrite rod in comparison with the EM-wave scattering by a thin endless metal rod.  \n     In Fig. 10, we give a schematic illustration of charges and currents on the cross-section of the rods \nat the dipole-like scattering. Let us consider, initially, Rayleigh scattering by a thin endless cylindrical \nrod made from a perfect electric conductor (PEC). A rod oriented along the z axis is acted upon by an \nexternal alternating electric field in the plane ,r of a plane electromagnetic wave. Assuming that the \nrod diameter is much less than the EM wavelength, the analysis can be viewed as a quasi-electrostatic \nproblem. The electric field of the EM wave induces positive and negative electric charges on \ndiametrically opposite points of the ,r plane, which cause two, clockwise (CW) and counter  \n clockwise (CCW), azimuthal electric currents on the rod surface. Creating an azimuthally symmetric \nstructure, each of these surface currents passes over a regular-coordinate angle . In such a structure \nwe have both the azimuthal and time symmetries. In Fig. 10 ( a), the ,  surface electric charges \ncorrespond to the maximum, minimum of the charge distributions in the azimuth coordinates. One can \nadduce other examples of the azimuthal and time symmetries (the PT symmetry) at the dipole-like \nscattering from subwavelength structures. This includes also the electric-dipole eigenmodes of the \nsurface plasmon resonances [82 – 84].  \n     We consider now a thin endless cylindrical rod made from a magnetic insulator, YIG. A plane EM \nwave propagates along the rod axis. The rod diameter is much less than the EM wavelength and the \nanalysis is considered as a quasi-magnetostatic problem. The rod is axially magnetized up to saturation \nby a bias magnetic field directed along the z axis.  Due to the anisotropy (gyrotropy) induced by bias \nmagnetic field, the RF magnetic field of the EM wave, which lies in the ,r plane, causes the \nprecessional motion of the alternating magnetization vector about the z axis. In this structure, magnetic \ncharges at diametrically opposite points of a ferrite rod can appear due to the divergence of \nmagnetization. It is known that at the ferromagnetic resonance frequency in an infinite medium, no \ndivergence of the magnetization exists. Also, it is known that a divergence of the DC magnetization \nexists in a ferrite ellipsoid (in an endless cylindrical ferrite rod, in particular) with the homogeneous-\nprecession mode (Kittel’s mode) [18]. The divergence of both the DC and RF magnetizations may \noccur in a ferrite sample in a case of nonhomogeneous-precession modes. These magnetic-dipole \nmodes – Walker’s modes – in a thin endless cylindrical ferrite rod were studied in Ref. [85]. For these \neigenmodes, the RF magnetic field of the incident EM wave induces a magnetic dipoles, which lies in \nthe ,r plane of a ferrite rod. In Fig. 10 ( b), the ,m m  surface  magnetic charges correspond to the \nmaximum, minimum of the charge distributions in the azimuth coordinates. Due to the time-reversal \nsymmetry breaking, these surface magnetic charges cannot cause two, clockwise (CW) and counter \nclockwise (CCW), azimuthal magnetic currents. For the given direction of bias magnetic field, we \nmay have only CW or CCW induced magnetic current, which passes over a regular-coordinate angle \n at the time phase of . In Fig. 10 ( b), this is shown as the CW blue-arrow current. We can suppose, \nhowever, that there exists a polaritonic structure with an additional (non-electromagnetic) phase shift, \nwhen the gradient of twisting angle plays the role of the phase gradient. A global phase texture with \ncoflowing an EM-wave induced magnetic current and topological magnetic current will provide us \nwith the possibility to have rotational symmetry by a turn over a regular-coordinate angle 2 at the \ntime phase of . This situation is shown in Fig. 10 ( b), where the CW magnetic current of a polaritonic \nstructure is conventionally represented as a circle composed by the blue and red arrows. It is worth \nnoting, however, that one can view such a phenomenon not in a ferrite rod, but in the ,r plane of a \nferrite disk with MDM oscillations, where the non-electromagnetic torque is caused by the \ntopological-phase effects. In the MDM ferrite-disk resonator, the non-zero circulation of such a \nmagnetic current, observed at the time phase shift of , results in appearance of a constant angular \nmomentum directed along the  z axis. This is possible due to an additional phase shift of the magnetic \ncurrent along the z axis. The magnetic currents have a helical structure. When such helical currents \n(and so helical waves) cannot be observed in a smooth ferrite rod, they can be seen in a MDM ferrite \ndisk [86]. \n \nB. Testing the topological properties of the ME field with small metal rods and rings in a \nmicrowave waveguide  \n  \n In a structure of a MDM particle embedded in a microwave waveguide, photons interact strongly and \ncoherently with magnetic excitations. The creation of certain non-classical states in such a \nmacroscopic system can be observed with help of small metallic elements placed inside a microwave \nwaveguide near the ferrite disk. Here we show some of the topological properties of the ME field using \nsmall metallic rods and rings.  \n     A structure of microwave waveguide with a ferrite disk and small metallic rod, shown in Fig. 11 \n(a), was studied experimentally in Ref. [87] and numerically in Ref. [88]. The rod is oriented along an \nelectric field of a rectangular waveguide. Its diameter is a very small compared to the disk diameter \nand to the free-space electromagnetic wavelength. On the basis of a comparative analysis of \nexperimental oscillation spectra, it was argued in Ref. [87] that the fact that an additional small \ncapacitive coupling (due to a piece of a nonmagnetic wire) strongly affects magnetic oscillation proves \nthe presence of the electric-dipole moments (anapole moments) of the MDMs in a quasi-2D ferrite \ndisk. In numerical studies [88], a metal rod is made of a PEC. At frequencies far from the MDM \nresonances, the field structure of an entire waveguide is not noticeably disturbed. The electric field on \nthe rod demonstrates a trivial picture of the field induced on a small electric dipole inside a waveguide \n[Fig. 11 ( b)].  At the same time, in the case of the MDM resonance, there is a strong reflection of \nelectromagnetic waves in a waveguide. The PEC rod behaves as a small line defect on which rotational \nsymmetry is violated. The observed evolution of the radial part of the electric polarization, giving, as \na result, a circulating electric current, indicates the presence of a geometrical phase in the vacuum-\nregion field of the MDM-vortex polariton [Fig. 11 ( c)]. \n     Let us bend the metallic rod into a ring and rigidly connect the ends. At the MDM resonance, \nrotating electric charges and circulating electric currents arise on a ring placed above the ferrite disk. \n[89]. Fig.12 shows circulation of a surface electric current along a PEC ring. The ferrite disk has a \ndiameter of 3 mm. A metallic ring made from a wire of a diameter of 0,05 mm, has a diameter of 1.5 \nmm. The ring is located above a ferrite disk at a distance of 0.05 mm. The circulating current will give \nan angular-momentum flux. The intensity of the flux is proportional to the gradient of twisting angle, \nwhich plays the role of the phase gradient. A critical phase gradient is required to enable the process. \nThis occurs only at the MDM resonance. In this case, the persistent charge current in the ring is \ncorrelated to the persistent magnetic current in a ferrite disk. The electric current on the surface of the \nmetallic ring has the spin degree of freedom [see Fig. 12 ( c)]. When using 2D models in our main \nstudies of MDM oscillations, we can conclude now that, generally, an analysis of ME fields should be \nmade based on the 3D model. At the MDM resonance, the current induces on a test metal ring is a \ntopological soliton structure which is quantized simultaneously in poloidal and toroidal directions. \nThis 3D continuous vector-field structure – a hopfion (or Hopf soliton) – cannot be unknotted without \ncutting [90, 91]. It is also worth noting that the helicity properties of the 3D structure of the ME field \nin vacuum reflect its own topologically nontrivial structure at each mode  of the MDM-oscillation \nspectrum. \n     It is worth noting that in a remarkable paper [92], the authors had measured the low-temperature \nmagnetization response of an isolated mescoscopic copper ring to a slowly varying magnetic flux. \nThey showed that the total magnetization response oscillates as a function of the enclosed magnetic \nflux on the scale of half a flux quantum . In our study, a numerical analysis made in Ref. [89] shows \nthat the currents induced on a metal ring at the MDM resonances, strongly perturb the electric, but not \nthe magnetic, field in a vacuum region above the ferrite disk. This means that the ring is threaded \nmainly by an electric flux. Taking into account the above-analyzed properties of the anapole, we have \nevidence of the presence of the enclosed electric flux on the scale of half a flux quantum .   \n  \n C. MDM cavity electrodynamics \n \nFor the case of MDM resonances in a small ferrite disk, characterizing by non-uniform magnetization \ndynamics, the above-mentioned model of coherent states of the macrospin/photon system in a ferrite \nsphere [72 – 76, 81], is not applicable. In Refs. [57, 93], it was shown that multiresonance microwave \noscillations observed in experiments [49 – 51, 93], are related to the fact that magnetization dynamics \nof MDM oscillations in a quasi-2D ferrite disk have a strong impact on the phenomena associated with \nthe quantized energy fluctuation of microwave photons in a cavity. Fig. 13 gives a sketch showing the \nrelationship between quantized states of microwave energy in a cavity and magnetic energy in a MDM \nferrite disk. The microwave structure is a rectangular waveguide cavity with a normally magnetized \nferrite-disk sample. The operating frequency, which is a resonant frequency of the cavity, is constant. \nThe only external parameter, which varies in the experiment, is a bias magnetic field. The observed \ndiscrete variation of the cavity impedances is related to discrete states of the cavity fields. Since the \neffect was obtained at a given resonant frequency, the shown resonances are not conventional cavity \nmodes related to the frequency-dependent quantization of the photon wave vector. These resonances \nare caused by the quantized variation of energy of a ferrite disk, which appear due to variation of \nenergy of an external source – the bias magnetic field. \n     At the regions of a bias magnetic field, designated in Fig. 13 as A, a, b, c, d,  …, we do not have \nMDM resonances. In these regions, a ferrite disk is “seen” by electromagnetic waves, as a very small \nobstacle which, practically, does not perturb a microwave cavity. In this case, the cavity (with an \nembedded ferrite disk) has good impedance matching with an external waveguiding structure and a \nmicrowave energy accumulated in a cavity is at a certain maximal level. At the MDM resonances, the \nreflection coefficient sharply increases (the states designated in Fig. 13 by numbers 1, 2, 3, …). The \ninput impedances are real, but the cavity is strongly mismatched with an external waveguiding \nstructure. It means that at the MDM-resonance peaks, the cavity receives less energy from an external \nmicrowave source. In these states of a bias magnetic field, the microwave energy stored in a cavity \nsharply decreases, compared to its maximal level in the A, a, b, c, d,  … Since the only external \nparameter, which varies in this experiment, is a bias magnetic field, such a sharp release of the \nmicrowave energy accumulated in a cavity to an external waveguiding structure should be related to \nthe emission of discrete portions of energy from a ferrite disk. This means that at the MDM resonances, \na strong and sharp decrease in the magnetic energy of the ferrite sample should be observed. \n     When speaking about the eigenstates of the microwave-cavity spectrum observed at the bias-field \nvariation and constant frequency, we should answer the question about the eigenfunctions of this \nspectrum. In general, microwave resonators with the time-reversal symmetry breakings give an \nexample of a nonintegrable, i.e., path dependent, system. The time-reversal symmetry breaking effect \nleads to creation of the Poynting-vector vortices in a vacuum region the microwave resonators with \nenclosed lossless ferrite samples [94 – 97]. In an analysis of the cavity eigenfunctions, it makes no \nsense to consider the reflection of electromagnetic waves from magnetized ferrites from the standpoint \nof energy flow and ray propagation [98]. One cannot use an interpretation which allows viewing the \nmodes as pairs of two bouncing electromagnetic plane waves. This interpretation clearly shows that \nfor a structure with an enclosed magnetized ferrite sample given, for example, in Fig. 14, there can be \nno identity between the rays 1 1F   and 1 1F   in the sense that these rays can acquire \ndifferent phases when are reflected by the ferrite. \n     At the same time, it is argued [99] that in quantum mechanics the distinction between integrable \nand nonintegrable systems does not work any longer. The initial conditions are defined only within  \n the limits of the uncertainty relation 1\n2x p   . Since the Schrödinger equation is linear, a quantum \nmechanical wave packet can be constructed from the eigenfunctions by the superposition principle. \nWhat do we have in our structure of a MDM ferrite disk in a cavity? We use the Walker equation for \na MS scalar wave function. It also allows to construct a wave packet from the eigenfunctions by the \nsuperposition principle. We have to use a description of the spectral response functions of the system \nwith respect to two external parameters – a bias magnetic field 0H and a signal frequency  – and \nanalyze the correlations between the spectral response functions at different values of these external \nparameters. It means that, in neglect of losses, there should exist a certain uncertainty limit  stating that  \n \n                                                               0f H    uncertainty limit .                                               (38)     \n \nThis uncertainty limit is a constant which depends on the disk size parameters and the ferrite material \nproperty (such as saturation magnetization) [57]. Beyond the frames of the uncertainty limit (38) one \nhas continuum of energy. The fact that there are different mechanisms of quantization allows to \nconclude that for MDM oscillations in a quasi-2D ferrite disk both discrete energy eigenstate and a \ncontinuum of energy can exist. In quantum mechanics, the uncertainty principle says that the values \nof a pair of canonically conjugate observables cannot both be precisely determined in any quantum \nstate. In a formal harmonic analysis in classical physics, the uncertainty principle can be summed up \nas follows: A nonzero function and its Fourier transform cannot be sharply localized. This principle \nstates also that there exist limitations in performing measurements on a system without disturbing it. \nBasically, formulation of the main statement of the MDM-oscillation theory is impossible without \nusing a classical microwave structure. If a MDM particle is under interaction with a “classical \nelectrodynamics” object, the states of this classical object change. The character and value of these \nchanges depend on the MDM quantized states and so can serve as its qualitative characteristics. The \nmicrowave measurement reflects interaction between a microwave cavity and a MDM particle. It is \nworth noting that for different types of subwavelength particles (ferrite disks), the uncertainty limits \nmay be different. \n     The fact of the existence of the uncertainty limit (38) is indirectly confirmed by the experimental \nresults presented in Ref. [100]. In the microwave structure shown in Fig. 15 ( a), a ferrite disk is placed \nin a cavity with a very low Q factor. The wide bandwidth is due to losses caused by the test samples \nembedded in the cavity. Fig. 15 ( b) shows how a bias magnetic field tunes the shape of the MDM \nresonance. It can be seen that as one approaches the top of the cavity resonance curve, the effect of \nFano resonance collapses, the Fano line shape is completely decays, and a single Lorentz peak is \nobserved. The Lorentzian response is a narrow, highly symmetric peak. The scattering cross section \ncorresponds to a pure dark mode. All this means that, within uncertainty limit (38), it is possible to \ncarry out observations for a very wide linewidth of the cavity mode ( fis very big) and an extremely \nnarrow linewidth of the MDM resonance peak (0His very small).  \n     In the above studies, we considered the G modes (with a scalar MS membrane function  and the \nND BC) and the L modes (with vector MS membrane function BV\n \n   \n and the EM BC). The G-\nmode spectral analysis is more appropriate to use at the regime of a constant frequency and the bias  \n magnetic-field variation, while the L-mode analysis – at a constant bias magnetic field and the \nfrequency variation. These two spectral problems are bridged within uncertainty limit (38). \n \n5. Transfer of angular momentum to dielectric materials, metals and biological structures \nfrom MDM resonators \n \nDue to unique structures of twisted ME near fields, one can observe angular momentums (spin and \norbital) transfer to electric polarization in a dielectric sample (Fig. 16). Experiments [101, 102] show \nexplicit shifts of the MDM resonance peaks due to the dielectric loading of the ferrite disk. This effect \nwas explained in Refs. [56, 57, 102]. The mechanical torque exerted on a given electric dipole in a \ndielectric sample is defined as a cross product of the MDM electric field and the electric moment of \nthe dipole. The torque exerting on the electric polarization in a dielectric sample due to the MDM \nelectric field should be equal to reaction torque exerting on the magnetization in a ferrite disk. Because \nof this reaction torque, the precessing magnetic moment density of the ferromagnet will be under \nadditional mechanical rotation at a certain frequency . The frequency  is defined based on both, \nspin and orbital, momentums of the fields of MDM oscillations. It was shown experimentally that the \nchiral structure of near-field ME provides the potential for microwave chirality discrimination in \nchemical and biological objects [103].  \n     Because of a chiral topology of near fields originated from MDM oscillations in a ferrite disk, one \nhas helical electric currents induced on a surface of a metal wire electrode placed on a surface of a \nferrite disk. On a butt end of a wire probe one can observe twisted near fields (Fig. 17). The handedness \nof these fields depends on a direction of a bias magnetic field applied to a MDM ferrite resonator \n[102]. Using helical electric currents induced on a metal wire electrode, one can obtain the angular \nmomentum transfer to localized regions in dielectric samples (Fig. 18). \n     Due to strong reflection and absorption of electromagnetic waves in conductive layers and \nbiological tissue, standard microwave techniques cannot be used for testing such structures. Twisted \nmicrowave near fields with strong energy concentration, originated from MDM ferrite disk with a \nmetal wire electrode, allow probing effectively high absorption conductive layers. This effect can be \nexplained by a simple physical model. When the electromagnetic wave incidents on a conductive \nmaterial, the induced electric current is almost parallel to the electric field (Ohm’s law). Joule losses \nin conductive materials are defined by a scalar product of an induced electric current and an electric \nfield. When, however, a conductive material is placed in a twisted microwave near field, the RF \nelectric current and an RF electric field become mutually nonparallel. It means that for Joule losses, \none has cos J E J E     \n with cos 1. Extremely small Joule losses result in strong enlargement \nof a penetration length  – the skin depth – in a sample. Fig. 19 presents numerical results illustrating \nthe effect of penetration of the twisted-field microwave power through a thin metal screen [104].  \n \n6. Conclusion \n \nME fields are subwavelength-domain fields with specific properties of violation of spatial and \ntemporal inversion symmetry. When searching for such fields, we consider near fields originated from \nsubwavelength resonators, that are the systems with quantum-confinement effects of dipolar-mode \nquasistatic oscillations. We show that the near fields of a quasi-2D subwavelength-size ferrite disk \nwith magnetic-dipolar-mode (MDM) oscillations have the properties of ME fields. The ME fields, \nbeing originated from magnetization dynamics at MDM resonances, appear as the pseudoscalar \naxionlike fields. Whenever the pseudoscalar axionlike fields, is introduced in the electromagnetic  \n theory, the dual symmetry is spontaneously and explicitly broken. This results in non-trivial coupling \nbetween pseudoscalar quasistatic ME fields and the EM fields in microwave structures with an \nembedded MDM ferrite disk. \n     Long range magnetic dipole-dipole correlation can be treated in terms of collective magnetostatic \nexcitations of the system. In small ferromagnetic-resonance ferrite disk, macroscopic quantum \ncoherence can be observed. In a case of a quasi-2D ferrite disk, the quantized forms of these collective \nmatter oscillations – the MDM magnons – were found to be quasiparticles with both wave-like and \nparticle-like behaviors, as expected for quantum excitations. With use of MS-potential scalar wave \nfunction  we formulate properly the energy eigenstate problem based on the Schrödinger-like \nequation. We obtain currents (fluxes) for MS modes. We show that in a subwavelength ferrite-disk \nparticle one can observe an angular momentum due to the power-flow circulation of double-valued \nedge MS-wave functions. For incident electromagnetic wave, this magnon subwavelength particle \nemerges as a singular point carrying quanta of angular momenta. In a ferrite-disk sample, the \nmagnetization has both the spin and orbital rotations. There is the spin-orbit interaction between these \nangular momenta. The MDMs are characterized by the pseudoscalar magnetization helicity parameter, \nwhich can be considered as a certain source of the helicity properties of ME fields. \n     Quantized ME fields arising from nonhomogeneous ferromagnetic resonances with spin-orbit \neffect, suggest a conceptually new microwave functionality for material characterization. Due to \nunique structures of twisted ME near fields, one can observe angular momentums (spin and orbital) \ntransfer to electric polarization in a dielectric sample. The chiral structure of near-field ME provides \nthe potential for microwave chirality discrimination in chemical and biological objects. Twisted ME \nfields allow deep penetration of the microwave power into materials with high conductivity.  \n  \nReferences \n \n[1] J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).  \n[2] Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, \n163901 (2010).  \n[3] K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Dual electromagnetism: Helicity, spin, momentum \nand angular momentum,” New J. Phys. 15, 033026 (2013).  \n[4] E. Hendry, T. Carpy, J. Johnston et al., “Ultrasensitive detection and characterization of \nbiomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783 (2010). \n[5] M. M. Coles and D. L. Andrews, “Chirality and angular momentum in optical radiation,” Phys. \nRev. A 85, 063810 (2012).  \n[6] R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” \nNew J. Phys. 16, 013020 (2014).  \n[7] A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of \nchiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).  \n[8] A. Canaguier-Durand and C. Genet, “Chiral route to pulling optical forces and left-handed optical \ntorques,” Phys. Rev. A 92, 043823 (2015). \n[9] E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, \n“Nanophotonic platforms for enhanced chiral sensing”, ACS Photonics 5, 2669 (2018). \n[10] S. Droulias and L. Bougas, “Surface plasmon platform for angle-resolved chiral sensing”, ACS \nPhotonics 6, 1485 (2019). \n[11] T. V. Raziman, R. H. Godiksen, M. A. Müller, and A. G. Curto, “Conditions for enhancing chiral \nnanophotonics near achiral nanoparticles”, ACS Photonics 6, 2583 (2019).  \n [12] C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles  (John \nWiley & Sons, New York, 1983). \n[13] W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics”, Nature \n424, 824 (2003). \n[14] E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions”, Science \n311, 189 (2006). \n[15] S. A. Maier, Plasmonics: Fundamentals and Applications  (Springer, New York, 2007).  \n[16] M. I. Kaganov, N. B. Pustyl'nik, and T. N. Shalaeva, “Magnons, magnetic polaritons, \nmagnetostatic waves”, Physics-Uspekhi 40, 181 (1997). \n[17] V. V. Kruglyak, S. O. Demokritov, and D. Grundler, “Magnonics“, J. Phys. D: Appl. Phys. 43, \n264001 (2010). \n[18] A. G. Gurevich and G. A. Melkov, Magnetic Oscillations and Waves  (CRC Press, New York, \n1996). \n[19] S. B. Cohn, “Microwave bandpass filters containing high-Q dielectric resonators”, IEEE Trans. \nMicrow. Theor. Techn. MTT-16, 218 (1968). \n[20] J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. \nWarne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric \nmetamaterials,” Phys. Rev. Lett. 108, 097402 (2012). \n[21] A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic \nlight”, Sci. Rep. 2, 492 (2012). \n[22] G. T. Papadakis, D. Fleischman, A. Davoyan, P. Yeh, and H. A. Atwater, “Optical magnetism in \nplanar metamaterial heterostructures”, Nature Commun. 9, 296 (2018).  \n[23] J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons \nand surface-plasmon polaritons”, Rep. Prog. Phys.  70, 1 (2007) \n[24] B. Bêchea and E. Gaviot, “About the Heisenberg’s uncertainty principle and the determination of \neffective optical indices in integrated photonics at high sub-wavelength regime”, Optik 127, 3643 \n(2016). \n[25] J. A. Kong, “Theorems of bianisotropic media”, Proc. IEEE 60, 1036 (1972). \n[26] C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials”, \nIEEE J. Select. Top. Quant. Electron. 16, 367 (2010).   \n[27] N. Guth, B. Gallas, J. Rivory, J. Grand, A. Ourir, G. Guida, R. Abdeddaim, C. Jouvaud, and J. de \nRosny, “Optical properties of metamaterials: Influence of electric multipoles, magnetoelectric \ncoupling, and spatial dispersion”, Phys. Rev. B 85, 115138 (2012). \n[28] S. A. Tretyakov, C. R. Simovski, and M. Hudlička, “Bianisotropic route to the realization and \nmatching of backward-wave metamaterial slabs”, Phys. Rev. B 75, 153104 (2007). \n[29] A. Kwadrin and A. F. Koenderink, “Probing the electrodynamic local density of states with \nmagnetoelectric point scatterers”, Phys. Rev. B 87, 125123 (2013).  \n[30] J. Proust, N. Bonod, J. Grand, and B. Gallas, “Optical monitoring of the magnetoelectric coupling \nin individual plasmonic scatterers”, ACS Photonics 3, 1581 (2016). \n[31] C. Caloz and A. Sihvola, ”Electromagnetic chirality”, arXiv:1903.09087. \n[32] X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive \nparameters of bianisotropic metamaterials”, Phys. Rev. E 71, 046610 (2005). \n[33] Z. F. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of \nbianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610, \n(2009).  \n [34] Y. Moritake and T. Tanaka, “Bi-anisotropic Fano resonance in three-dimensional metamaterials”, \nScient. Rep. 8, 9012 (2018). \n[35] C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-\nphoton mode splitting in a semiconductor quantum microcavity”, Phys. Rev. Lett. 69, 3314 (1992). \n[36] J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. \nMarchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and \nL. S. Dang, “Bose–Einstein condensation of exciton polaritons”, Nature 443, (2006). \n[37] H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation”, Rev. \nMod. Phys. 82, 1489 (2010). \n[38] D. Snoke and P. Littlewood, “Polariton condensates”, Phys. Today 63, 42 (2010). \n[39] T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton–polariton condensates”, Nature Phys. 10, 803 \n(2014). \n[40] T.J. Davis and D.E. Gómez, “Colloquium: An algebraic model of localized surface plasmons \nand their interactions”, Rev. Mod. Phys. 89, 011003 (2017). \n[41] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media  (Pergamon Press, Oxford, \n1960). \n[42] D. J. Bergman, “The dielectric constant of a composite material—A problem in classical physics”, \nPhys. Rep. 43, 377 (1978). \n[43] M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localization versus delocalization of surface \nplasmons in nanosystems: Can one state have both characteristics?,\" Phys. Rev. Lett. 87, 167401 \n(2001). \n[44] V. Klimov, G.-Y. Guo, and M. Pikhota, “Plasmon resonances in metal nanoparticles with sharp \nedges and vertices: a material independent approach”, J. Phys. Chem. C 118, 13052 (2014). \n[45] R. Yu, L. M. Liz-Marzán, and F. J. Garcia de Abajo, ”Universal analytical modeling of plasmonic \nnanoparticles”, Chem. Soc. Rev. 46, 6710 (2017). \n[46] L. R. Walker, “Magnetostatic modes in ferromagnetic resonance”, Phys. Rev. 105, 390 (1957). \n[47] E. O. Kamenetskii, “Quasistatic oscillations in subwavelength particles: Can one observe energy \neigenstates?”, Ann. Phys. (Berlin) 531, 1800496 (2019). \n[48] P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic \nand plasmonic resonances”, Laser Photonics Rev. 12, 1700113 (2018). \n[49] J. F. Dillon Jr., “Magnetostatic modes in disks and rods”, J. Appl. Phys. 31, 1605 (1960). \n[50] T. Yukawa and K. Abe, “FMR spectrum of magnetostatic waves in a normally magnetized YIG \ndisk”, J. Appl. Phys. 45, 3146 (1974). \n[51] E. O. Kamenetskii, A. K. Saha, and I. Awai, \"Interaction of magnetic-dipolar modes with \nmicrowave-cavity electromagnetic fields”, Phys. Lett. A 332, 303 (2004). \n[52] E. O. Kamenetskii, “Energy eigenstates of magnetostatic waves and oscillations”, Phys. Rev. E \n63, 066612 (2001). \n[53] E. O. Kamenetskii, R. Shavit and M. Sigalov, “Quantum wells based on magnetic-dipolar-mode \noscillations in disk ferromagnetic particles”, Europhys. Lett., 64, 730 (2003). \n[54] E. O. Kamenetskii, M. Sigalov, and R. Shavit, “Quantum confinement of magnetic-dipolar \noscillations in ferrite discs”, J. Phys.: Condens. Matter 17, 2211 (2005). \n[55] E. O. Kamenetskii, \"Vortices and chirality of magnetostatic modes in quasi-2D ferrite disc \nparticles\", J. Phys. A: Math. Theor . 40, 6539 (2007). \n[56] E. O. Kamenetskii, R. Joffe, and R. Shavit, \"Microwave magnetoelectric fields and their role in \nthe matter-field interaction,\" Phys. Rev. E 87, 023201 (2013). \n[57] E. O. Kamenetskii, “Quantization of magnetoelectric fields”, J. Modern Opt. 66, 909 (2019).  \n [58] S. G. Mikhlin, Variational Methods in Mathematical Physics  (McMillan, New York, 1964). \n[59] M. A. Naimark , Linear Differential Operator s (Frederick Ungar Publishing, New York,1967). \n[60] E. O. Kamenetskii, “The anapole moments in disk-form MS-wave ferrite particles”, Europhys. \nLett. 65, 269 (2004). \n[61] S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and \nA. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under \npumping”, Nature 443, 430 (2006). \n[62] A. S. Davydov, Quantum Mechanics , 2nd ed. (Oxford, Pergamon, 1976). \n[63] D. A. Ivanov, “Non-Abelian statistics of half-quantum vortices in p-wave superconductors”, \nPhys. Rev. Lett. 86, 268 (2001). \n[64] N. Read and D. Green, “Paired states of fermions in two dimensions with breaking of parity and \ntime-reversal symmetries and the fractional quantum Hall effect”, Phys. Rev. B 61, 10267 (2000). \n[65] R. Joffe, E. O. Kamenetskii, R. Shavit, “Microwave magnetoelectric fields: An analytical study \nof topological characteristics”, J. Magn. Magn. Mater. 392, 6 (2015). \n[66] M. Sigalov, E. O. Kamenetskii, and R. Shavit, “Magnetic-dipolar and electromagnetic vortices in \nquasi-2D ferrite discs”, J. Phys.: Condens. Matter 21, 016003 (2009). \n[67] E. O. Kamenetskii, M. Sigalov, and R. Shavit, “Manipulating microwaves with magnetic-dipolar-\nmode vortices”, Phys. Rev. A 81, 053823 (2010). \n[68] R. Joffe, E. O. Kamenetskii, and R. Shavit, “Azimuthally unidirectional transport of energy in \nmagnetoelectric fields: Topological Lenz’s effect“, J. Mod. Opt. 64, 2316 (2017). \n[69] E. O. Kamenetskii, M. Berezin, and R. Shavit, “Microwave magnetoelectric fields: Helicities and \nreactive power flows,” Appl. Phys. B: Lasers Opt. 121, 31 (2015). \n[70] F. Wilczek, Two applications of axion electrodynamics”, Phys. Rev. Lett 58, 1799 (1987).  \n[71] L. Visinelli, “Dual axion electrodynamic”, arXiv 1111.2268 (2011). \n[72] Ö. O. Soukal and M. E. Flatté, “Strong field interactions between a nanomagnet and a photonic \ncavity”, Phys. Rev. Lett. 104, 077202 (2010); “Size dependence of strong coupling between \nnanomagnets and photonic cavities”, Phys. Rev. B 82, 104413 (2010).  \n[73] X. Zhang, C. L. Zou, L. Jiang, and H. X. Tang, “Strongly coupled magnons and cavity microwave \nphotons” Phys. Rev. Lett. 113, 156401 (2014).  \n[74] Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “Hybridizing \nferromagnetic magnons and microwave photons in the quantum limit”, Phys. Rev. Lett. 113, 083603 \n(2014).  \n[75] M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, “High-\ncooperativity cavity QED with magnons at microwave frequencies,” Phys. Rev. Appl. 2, 054002 \n(2014).  \n[76] J. A. Haigh, N. J. Lambert, A. C. Doherty, and A. J. Ferguson, “Dispersive readout of \nferromagnetic resonance for strongly coupled magnons and microwave photons,” Phys. Rev. B 91, \n104410 (2015). \n[77] N. J. Lambert, J. A. Haigh, and A. J. Ferguson, “Identification of spin wave modes in yttrium iron \ngarnet strongly coupled to a co-axial cavity”, J. Appl. Phys. 117, 053910 (2015).  \n[78] A. Leo, A. Grazia Monteduro, S. Rizzato, L. Martina, and G. Maruccio, “Identification and time-\nresolved study of ferrimagnetic spin-wave modes in a microwave cavity in the strong-coupling \nregime”, Phys. Rev. B 101, 014439 (2020). \n[79] Y. Cao, P. Yan, H. Huebl, S. T. B. Goennenwein, and G. E. W. Bauer, “Exchange magnon-\npolaritons in microwave cavities”, Phys. Rev. B 91, 094423 (2015).  \n [80] B. Zare Rameshti, Y, Cao, and G. E. W. Bauer, “Magnetic spheres in microwave cavities”, Phys. \nRev. B 91, 214430 (2015). \n[81] M. Harder  and C.-M. Hu, “Cavity spintronics: An early review of recent progress in the study of \nmagnon–photon level repulsion”, Solid State Phys. 69, 47 (2018). \n[82] D. Tzarouchis and A. Sihvola, “Light scattering by a dielectric sphere: Perspectives on the Mie \nresonances”, Appl. Sci.  8, 184 (2018).   \n[83] I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in \nnanoparticles”, Phys. Rev. B 72, 155412 (2005). \n[84] B. S. Luk’yanchuk and V. Ternovsky, “Light scattering by a thin wire with a surface-plasmon \nresonance: Bifurcations of the Poynting vector field”, Phys. Rev. B 73, 235432 (2006). \n[85] R. I. Joseph and E. Schlomann, “Theory of magnetostatic modes in long, axially magnetized \ncylinders”, J. App. Phys. 32, 1001 (1961). \n[86] E. O. Kamenetskii, “ Helical-mode  magnetostatic resonances in small ferrite particles and singular \nmetamaterials”, J. Phys.: Condens. Matter 22, 486005 (2010). \n[87] M. Sigalov, E. O. Kamenetskii, and R. Shavit, “Eigen electric moments and magnetic–dipolar \nvortices in quasi-2D ferrite disks”, Appl. Phys. B 93, 339 (2008). \n[88] E. O. Kamenetskii, R. Joffe, and R. Shavit, “Coupled states of electromagnetic fields with \nmagnetic-dipolar-mode vortices: Magnetic-dipolar-mode vortex polaritons’, Phys. Rev. A 84, 023836 \n(2011). \n[89] E. O. Kamenetskii and Y. Peretz, “Topological properties of magnetoelectric fields”, Unpublished \npaper (2015). \n[90] Y. M. Bidasyuk, A. V. Chumachenko, O. O. Prikhodko, S. I. Vilchinskii, M. Weyrauch, and A. \nI. Yakimenko, “Stable Hopf solitons in rotating Bose-Einstein condensates”, Phys. Rev. A 92, 053603 \n(2015).  \n[91] B. A. Malomed, “Vortex solitons: Old results and new perspectives”, Physica D: Nonlinear \nPhenom. 399, 108 (20019). \n[92] L. P. Lévy, G. Dolan, J. Dunsmuir, and H. Bouchiat, “Magnetization of mesoscopic copper rings: \nEvidence for persistent currents”,  \nPhys. Rev. Lett. 64, 2074 (1990). \n[93] E. O. Kamenetskii, G. Vaisman, and R. Shavit, “Fano resonances in microwave structures with \nembedded magneto-dipolar quantum dots”, J. Appl. Phys. 114, 173902 (2013). \n[94] P. So, S. M. Anlage, E. Ott, and R. N. Oerter, “Wave chaos experiments with and without time \nreversal symmetry: GUE and GOE statistics”, Phys. Rev. Lett. 74, 2662 (1995). \n[95] M. Vraničar, M. Barth, G. Veble, M. Robnik, and H.-J. Stöckmann, “Persistent currents’ and \neigenfunctions in microwave resonators with broken time-reversal symmetry”, J. Phys. A: Math. Gen. \n35, 4929 (2002). \n[96] H. Schanze, H.-J. Stöckmann, M. Martinez-Mares, and C. H. Lewenkopf, “Universal transport \nproperties of open microwave cavities with and without time-reversal symmetry”, Phys. Rev. E 71, \n016223 (2005). \n[97] E. O. Kamenetskii, M. Sigalov, and R. Shavit, “Microwave whirlpools in a rectangular waveguide \ncavity with a thin ferrite disk”, Phys. Rev. E 74, 036620 (2006).  \n[98] S. S. Gupta and N. C. Srivastava, “Physics of microwave reflection at a dielectric-ferrite \ninterface”, Phys. Rev. B 19, 5403 (1979). \n[99] H.-J. Stöckmann, “Microwave billiards and quantum chaos”, Scholarpedia 5, 10243 (2010). \n[100] G. Vaisman, E. O. Kamenetskii, and R. Shavit, “Magnetic-dipolar-mode Fano resonances for \nmicrowave spectroscopy of high absorption matter”, J. Phys. D: Appl. Phys. 48, 115003 (2015).  \n [101] M. Sigalov, E. O. Kamenetskii, and R. Shavit, “Electric self-inductance of quasi-two-\ndimensional magnetic-dipolar-mode ferrite disks”, J. Appl. Phys. 104, 053901 (2008). \n[102] R. Joffe, E. O. Kamenetskii and R. Shavit, “Novel microwave near-field sensors for material \ncharacterization, biology, and nanotechnology,” J. Appl. Phys. 113, 063912 (2013). \n[103] E. Hollander, E. O. Kamenetskii, R. Shavit, “Microwave chirality discrimination in enantiomeric \nliquids”, J. Appl. Phys. 122, 034901 (2017). \n[104] E. O. Kamenetskii and A. Davidov, “Twisted microwave near fields for probing high \nabsorption conductive layers and biological tissue ”, Unpublished paper (2019). \n \n \n \n                                                            \n \nFig 1. Analytically derived power-flow-density distribution for the main MDM inside a ferrite disk of \ndimeter 3 mm (arbitrary units). \n \n \n            \n                                                                                                                 (g) \nFig. 2. Field confinement originating from the MDM vortices in a ferrite disk. (a) The Poynting vector \ndistributions for the field on plane A at the frequency (f = 8.5225 GHz) of the first resonance. (b) The \nsame at the frequency (f = 8.5871 GHz) between the resonances. (c) The same at the frequency (f = \n8.6511 GHz) of the second resonance. (d) The Poynting vector distributions inside a ferrite disk at the \nfrequency of the first resonance. (e) The same at the frequency between resonances. (f) The same at \nthe frequency of the second resonance. (g) The plane A is a vacuum plane inside a waveguide situated \nabove an upper plane of a MDM ferrite disk. Ref. [67]. \n \n                                               \n \n Fig. 3. Schematic representation of the circulation of the power flow, depicted on the surface of the \nvacuum sphere and on the surface of the solid angle. Direction of an orbital angular-momentum of a \nferrite disk is correlated with the direction of a bias magnetic field. \n \n                                         \nFig. 4. Magnetic field distributions on the upper plane of a ferrite disk for the first MDM resonance at \ndifferent time phases. \n \n                                            \n  \nFig. 5. Electric field distributions on the upper plane of a ferrite disc for the first MDM resonance at \ndifferent time phases. \n \n \n           \nFig. 6. The helicity density distributions above and below a ferrite disk at the MDM resonance at two \nopposite directions of a bias magnetic field. The electric and magnetic fields outside a ferrite disk are \nrotating fields which are not mutually perpendicular. The helicity parameter F is a pseudoscalar: to \ncome back to the initial stage, one has to combine a reflection in a ferrite-disk plane and an opposite \n(time-reversal) rotation about an axis perpendicular to that plane. In a green region F = 0: the angle \nbetween the electric and magnetic fields is 90.   \n \n                      \n \nFig. 7. Pseudoscalar quantity of the magnetization in a ferrite disk as a “source” of the helicity factor \nat the MDM resonance. \n \n \n                                                         \nFig. 8. The active and reactive power flows of the ME field at the MDM resonance.  a) An upward \ndirected bias magnetic field; b) a downward directed bias magnetic field. The active and reactive \npower flows are mutually perpendicular. These flows constitute surfaces, which can be considered as \ndeformed versions of the complex planes, i.e., as Riemann surfaces. When one changes a direction of \n \n a bias field, the active power flow changes its direction as well. At the same time, the reactive power \nflow does not change its direction when the direction of a bias field is changed. \n \n \n                                        \n \nFig. 9. An interaction of a MDM ferrite disk with a microwave waveguide. The structure is viewed as \nthe P + Q space. It consists of a localized quantum system (the MDM ferrite disk), denoted as the \nregion Q, which is embedded within an environment of scattering states (the microwave waveguide), \ndenoted as the regions P. The coupling between the regions Q and P is regulated by means of the two \n“contact regions” in the waveguide space.  \n       \n                                                 (a)                                                                                      (b) \n               \nFig. 10. Schematic illustration of charges and currents on the cross-section of the rods at the dipole-\nlike scattering. ( a) Electric charges and currents on a surface of a thin metal rod induced by RF electric \nfield in a ,r plane.  (b) Magnetic charges and currents on a surface of a thin ferrite rod induced by \nRF magnetic field in a ,r plane. Magnetic current of a polaritonic structure is conventionally \nrepresented as a circle composed by the blue and red arrows. In this case, the entire cycle of rotation \ncorresponds to the -shift of a dynamic phase. \n \n                                       \n                                                                       ( a) \n \n  \n                                                \n                                              ( b)                                                                                             ( c)         \n \nFig. 11. (a) A structure of microwave waveguide with a ferrite disk and small metallic rod. ( b) Electric \nfield on a small PEC rod for the frequency far from the MDM resonance at different time phases. \nThere is a trivial picture of the fields of a small electric dipole inside a waveguide. ( c) Electric field \non a small PEC rod in the MDM resonance at different time phases. A PEC rod behaves as a small \nline defect on which rotational symmetry is violated. The observed evolution of the radial part of \npolarization gives evidence for the presence of a geometrical phase in the vacuum-region field of the \nMDM-vortex polariton. \n                                             \n                                                                                          ( a) \n             \n  \n                                                                                  ( b) \n \n            \n                                                                                   ( c) \n \nFig. 12. ( a) A structure of microwave waveguide with a ferrite disk and small metallic ring. ( b) \nCirculating surface electric current on a metallic ring. ( c) The electric current on the surface of a \nmetallic ring has the spin degree of freedom. \n \n \n \nFig. 13. A sketch showing the relationship between quantized states of microwave energy in a cavity \nand magnetic energy in a ferrite disk. ( a) A structure of a rectangular waveguide cavity with a normally \nmagnetized ferrite-disk sample. ( b) A typical multiresonance spectrum of modulus of the reflection \ncoefficient. ( c) Microwave energy accumulated in a cavity; ( )n\nRFw are jumps of electromagnetic energy \nat MDM resonances. \n      \n                       \n \n \n Fig. 14.  The rays 1 1F   and 1 1F  acquire different phases when are reflected by the \nferrite. \n            \n                                            ( a)                                                                            ( b) \n \nFig. 15. ( a) A structure of a rectangular waveguide cavity. ( b) Modification of the Fano-resonance \nshape. At variation of a bias magnetic field, 0 0 01 2 3H H H  , the Fano line shape of a MDM \nresonance can be completely damped. The scattering cross section of a single Lorentzian peak \ncorresponds to a pure dark mode.  \n \n                                              \nFig. 16. Angular momentums (spin and orbital) transfer to electric polarization in a dielectric sample.  \n \n                 \n                                       ( a)                                                                             ( b) \n \nFig. 17. (a) Microwave probing structure with a MDM ferrite-disk resonator and a wire electrode. ( b) \nSchematic illustration of twisted near fields. \n    \n \n                                           \n \nFig 18. Angular momentum transfer to localized regions in dielectric samples.  \n \n                                      \n                                                  \nFig. 19. Numerical results showing the twisted-field effect of penetration microwave power through a \nthin metal screen. \n \n"    },    {        "title": "0901.2704v1.Generation_of_pulse_trains_by_current_controlled_magnetic_mirrors.pdf",        "content": "arXiv:0901.2704v1  [cond-mat.other]  18 Jan 2009Generation of pulse trains by current-controlled magnetic mirrors\nA. A. Serga,∗T. Neumann, A. V. Chumak, and B. Hillebrands\nFachbereich Physik and Forschungszentrum OPTIMAS\nTechnische Universit¨ at Kaiserslautern, 67663 Kaisersla utern, Germany\n(Dated: November 15, 2018)\nThe evolution of a spin-wave packet trapped between two dire ct current-carrying wires placed\non the surface of a ferrite film is observed by Brillouin light scattering. The wires act as semi-\ntransparent mirrors confining the packet. Because the spin- wave energy partially passes through\nthese mirrors, trains of spin-wave packets are generated ou tside the trap. A numerical model of this\nprocess is presented and applied to the case when the current in the wires is dynamically controlled.\nThis dynamical control of the mirror reflectivity provides n ew functionalities interesting for the field\nof spin-wave logic like that of a spin-wave memory cell.\nPACS numbers: 75.30.Ds, 85.70.Ge\nSpin-wave logic has attracted much attention, espe-\ncially since the experimental realization of XOR- and\nNAND-gates [1, 2, 3, 4]. The principle design of these\nbasic elements relies on the interaction of a spin-wave\npacket propagating in a waveguide with the magnetic\ninhomogeneity formed by the Oersted field of a direct\ncurrent-carrying wire placed on the waveguide surface.\nThis interaction allows one to control the spin-wave am-\nplitude and phase as necessary [5, 6].\nFor several reasons a main focus of interest is given\nto multi-wired structures, which represent a particular\nrealization of so called magnonic crystals [7]. Such struc-\ntures potentially decrease the required current. More-\nover, since they can trap spin-wave packets, they possess\nnew functionalities, for instance, as spin-wave memory\nelements, spin-wave delay lines or multipliers.\nHere, we investigate the propagation of a spin-wave\npacket across a double-wire structure consisting of two\nparallel, current-conducting wires placed on the surface\nof a spin-wave waveguide. Different from the observa-\ntion of resonant tunneling [8] when a static current was\napplied to both wires and, consequently, the spin-wave\npacket had to pass both of them simultaneously, we dy-\nnamically switch the current in one wire in such a way,\nthat the spin-wave packet is trapped between the wires.\nIn the experiment the generation of pulse trains in trans-\nmission and reflection was observed by time- and space-\nresolved Brillouin light scattering spectroscopy. Numer-\nical simulations on the basis of our previous experimen-\ntal data [9] obtained for a single-wire structure support\nthe results. In particular, the time interval between two\nconsecutively generated packets is mainly determined by\nthe distance between the wires while their relative in-\ntensity is governed by the applied direct currents. As\na consequence, by dynamically changing the applied di-\nrect currents the intensity of the spin-wave packets can\nbe modified according to any desired functional depen-\ndence. This is illustrated by discussing the generation\n∗Electronic address: serga@physik.uni-kl.de\nFIG. 1: Sketch of the experimental section.\nof pulse trains consisting of spatially or temporally equal\npulses.\nFigure 1 shows the experimental setup using a macro-\nscopic yttrium iron garnet (YIG) stripe for easy experi-\nmental conditions. An 18 ns long input microwave pulse\nwith a carrier frequency 7 .125 GHz was sent to an in-\nput microstrip antenna placed on the surface of an YIG\nwaveguide. The 1 .5 mm wide and 25 mm long YIG-film\nof thickness 5 .7µm was magnetized along its longitudi-\nnal axis by a magnetic field H= 1836 Oe. In the cho-\nsen configuration the microwave pulse excites a packet of\nbackward volume magnetostatic spin waves with a wave\nvectork= 112 rad /cm parallel to the bias magnetic field\nand a group velocity of 30 µm/ns.\nIn the center of the YIG-film, two parallel 50 µm thick\nwires were placed at a distance of 0 .8 mm from each\nother. To these wires direct currents I1= 1.2 A and\nI2= 0.8 Awere applied. While current I2wasconstantly\noperating, current I1was dynamically switched on only\nafter the spin-wave pulse had passed the wire. This way\nthe spin-wave pulse was trapped between two barriers\nformed by the current-carrying wires. We emphasize at\nthis point that the polarity of the currents was chosen\nin such a way, that the magnetic field locally decreases\nthe bias field and a barrier for the spin-wave propagation\nis formed [5]. This ensures that the transmission of the\nspin-wave packets depends monotonically on the applied\ncurrent and that the frequency and, consequently, the2\nFIG. 2: (Color online) Space-resolved Brillouin light scat ter-\ning images of the 6 mm wide central part of the sample at dif-\nferent times after the initial pulse was launched. The dotte d\nvertical lines indicate the positions of the wires. The dash ed\ndiagonal lines and the central zigzag line illustrate the ev o-\nlution of the generated wave packets and of the initial pulse ,\nrespectively.\nwave-numberdependenceofthetransmissionisnegligible\n[9]. The latter aspect is noteworthy considering the short\npulse duration which was used.\nThetimeandspatialevolutionofthespin-wavespacket\nwas detected by means of time- and space-resolved Bril-\nlouin light scattering [10]. The obtained results are\nshown in Fig. 2. Each frame represents the space dis-\ntribution of the dynamic magnetization in the sample\ndetected at a specific moment in time as indicated in the\nright upper corner. The initial pulse (Frame 1) prop-\nagates from left to right and passes the first wire - to\nwhich at this time no current is applied. The pulse is\nreflected from the barrier formed by the second current-\ncarrying wire (Frames 2 and 3). At this point, current\nI1is switched on. Consecutively, the spin-wave packet\nstarts wobbling between the two current-carrying wires\nwhich is illustrated by the central zigzag line in Fig. 2.\nEach time the pulse is reflected from one of the two\nwires, a certain fraction of the spin-wave energy tunnels\nthroughthebarrier(seeforinstanceFrame4). Thetrans-\nmitted part of the spin-wavepacket is detected as a pulse\nof the same duration as the original pulse outside of the\ntrap. It continues its propagation to either side of the\nsampleasindicatedbythedashedlines. Overall,thegen-eration of five, clearly distinguishable spin-wave packets\nwas observed. These five packets as well as the central\ntrapped spin-wave pulse are shown in Fig. 3(a), which\ncontains a horizontal cut obtained by summing up the\nintensities in Frame 5 along a vertical line. Each packet\nis identified by a number, which indicates the position in\nthe sequence, at which the packet was generated.\nIn order to model the pulse train generation, we write\nthe initial amplitude A(x,t= 0) of the wave packet as\nA(x,t= 0) =/summationdisplay\nkAkeikx\nwhere the coefficients Akare found by a Fourier transfor-\nmation of the rectangular excitation pulse. Damping is\nincluded in this formulationasan imaginarycontribution\nto the spin-wave frequency ω.\nThe amplitude distribution after a specific time tis\nthen given as the sum of partial amplitudes from differ-\nent transmitted and reflected waves. Hence, for the cen-\ntral section of the sample between the two wires we have\nA(x,t) =A+(x,t)+A−(x,t) with two contributions, one\nsummand from waves propagating in the same direction\nas the initial pulse\nA+(x,t) =/summationdisplay\nk/parenleftbig\nAk+AkR(1)\nkR(2)\nkei2kx0\n+Ak(R(1)\nk)2(R(2)\nk)2ei4kx0+.../parenrightbig\nei(ω(k)t+kx)\n=/summationdisplay\nkAk1\n1−R(1)\nkR(2)\nkei2kx0ei(ω(k)t+kx)\nand one summand from waves reflected on the second\nwire and propagating in the opposite direction\nA−(x,t) =/summationdisplay\nkAkR(1)\nkei2kx0\n1−R(1)\nkR(2)\nkei2kx0ei(ω(k)t−kx).\nHere, we have chosen x= 0 for simplicity to coincide\nwith the position of the first wire. x0denotes the dis-\ntance between the two wires, which restricts the region\nof applicability for the last two equations to 0 < x < x 0.\nIn the equations, R(1)\nkandR(2)\nkare factors describing the\nreflection of the spin-wave amplitude for the first and\nsecond wire, respectively.\nAccordingly, equations can be found which in-\nvolve the amplitude transmission coefficients T(1,2)\nk=/radicalBig\n1−R(1,2)2\nkin order to describe the spin-wave ampli-\ntude to the right of the second wire (i.e. for x > x0) and\nto the left of the left of the first wire ( x <0).\nIn the simulation, the signal pulse duration was set\nto 18 ns and the distance between the wires was chosen\nasx0= 0.44 mm. This value is smaller than the ge-\nometric distance between the wires because the implicit\nassumptionmadeabove, thatthe reflectiontakesplaceat\nthe position of the wire, is only approximately satisfied.\nIn fact, the larger the currents, the more the current-\ninduced Oersted fields of the wires reduce the area of\nlocalization where the spin-wave packet is trapped.3\nFIG. 3: (Color online) (a) Comparison of the intensity profil e\nfrom Brillouin light scattering measurements after 180 .6 ns\nwith numerical simulations. (b) Numerical simulations wit h\ndynamically adjusted currents and reflection coefficients.\nTwo types of simulations were performed. Simula-\ntion 1 used previouslymeasured datafor asingle current-\ncarrying wire [9] from which the reflection coefficients\nR(1,2)\nkwere interpolated. In order to determine the influ-\nence ofthe k-dependence of Ron the results, a secondset\nof simulations was run using k-independent coefficients\nR(1,2)\nk=R(1,2)(Simulation 2). The values of Rused in\nthesesimulationscanbeconsideredasaveragedreflection\ncoefficients and display the ratio of energy transmitted\nand reflected at the wires more clearly than the current\nvalues do.\nThe results of these simulations are presented in\nFig. 3(a). There is a large discrepancy for the central\npeak which is a result of the simplicity of the proposed\nmodel.\nTheintensityofthecentralpeakisverysensitivetothe\nexact interference conditions for the spin waves reflected\nfrom the wires. However, the phase change due to the\ncurrent induced barrier is not included in our considera-\ntions, neither is any change in wave-vector or a resulting\nchangein group velocity caused by the magnetic inhomo-\ngeneity. Despite these limitations, the simulationsforthe\ngenerated pulses agree well with the experimental data\nwhich shows that the model is actually working.\nFor suitable parameters R(1)= 0.69 A and R(2)=\n0.92 A, Simulation 1 and Simulation 2 in Fig. 3 can be\nbrought to perfect coincidence. From this, we conclude\nthat it is indeed possible to replace the k-dependent setsR(1,2)\nkby twok-independent parameters. We would like\nto attract the reader’s attention to the fact, that the\nreflectiononwire2ishigherthanonwire1-whichresults\ninthefirstgeneratedspin-wavepacketbeingsmallerthan\nthe second one - though the current applied to wire 2 is\nsmaller. The reason for this effect is the thermal heating\nof the sample around the wire 2 due to the constantly\napplied current which leads to an increased scattering.\nOne main advantage of the section design is the con-\ntrollability of the current on very short time scales com-\npared to the spin-wave relaxation time. As a conse-\nquence, the current-carrying wires can be used like a set\nof mirrors, whose reflectivity can be adjusted dynami-\ncally. Due to the high reflectivity, that can be reached,\nit is possible to store a signal packet for a certain pe-\nriod of time between the mirrors and afterwards release\nit. This realizes the functionality of a spin-wave mem-\nory cell. Of course, the storage time of the spin-wave\npacket is limited by the damping of the packet inside the\ntrap. However,itispossibleto compensatethe spin-wave\ndamping between the magnetic mirrors, for instance by\nmeans of parametric amplification [11].\nEven without parametric amplification it is possible to\nuse the dynamic propertiesofthe mirrorsin orderto gain\nfunctionality. As a first example, we consider the gen-\neration of pulse trains consisting of spatially separated\npulses with equal intensity for a fixed time.\nFigure 3(b) shows two simulations of such pulse trains,\nwhich were generated by a time-dependent variation of\nthe reflection characteristics. As previously, the param-\netersR(1,2)\nkin Simulation 1 are taken from experimen-\ntal data. The current was manually adjusted to generate\npulsesofequalheight. In Simulation2 the k-independent\ncoefficients R(1,2)were chosen according to\nR(1) =RandR(n+1) =/radicalBigg\n1−1−R2\n1−n(1−R2)(1)\nwherenis the number of the packet which is generated.\nThis analytically guarantees the same amplitudes for all\nwave numbers and all generated pulses. In Simulation 2,\nR= 0.92 was chosen so that the first pulse has the same\nintensity as the pulse 1 in Fig. 3(a).\nClearly, the number ofspin-wavepacketswith an equal\nintensity, whichcanbegeneratedbysimplyturningdown\nthe current and, thereby, adjusting the reflectivity is lim-\nited. According to Eq. (1), the maximal number nmax\nis a function of the initial reflection coefficient R, which\ndetermines the intensity of the first packet\nnmax=⌊R2\n1−R2⌋+1.\nFor microwave applications it is more interesting to\nrequire that the temporally separated pulses picked up\nat an antenna (which is located at a fixed position in\nspace) are of equal intensity. In this case, in Eq. (1)4\nR(n+1) has to be modified to\n/radicaltp/radicalvertex/radicalvertex/radicalbt1−(1−R2)e2nΓx0\nvG\n1−(1+e2Γx0\nvG+...+e2(n−1)Γx0\nvG)(1−R2)\nwhere Γ is the relaxation frequency and vGthe group\nvelocity of the spin-wave packet.\nIn conclusion, we have experimentally demonstrated\nthe generation of pulse trains from a single spin-wave\npacket by using two current-carrying wires as magnetic\nmirrors between which the spin-wave packet is trapped.\nTheperformednumericalsimulationsbasedonthepre-\nsentedmodel arein goodagreementwith theexperiment.\nIt was shown, that for the tunneling regime, when thecurrent creates a barrier for the spin-wave propagation,\nthe frequency dependence of the transmission and reflec-\ntion can be neglected and is replaced by a single param-\neter even for short pulses with a wide Fourier spectrum.\nBy dynamically changing the current, the generated\npulse trains can be modified in any desired way. This\nwas illustrated by simulations with variable reflection co-\nefficients. In particular, the important examples of pulse\ntrains consisting of pulses with equal intensity which are\nobserved (i) at different positions in space but at a fixed\nmoment in time and (ii) at different times but at a fixed\nposition in space were discussed.\nOurworkhasbeenfinanciallysupportedbytheMatcor\nGraduate School of Excellence and DFG SE 1771/1-1.\n[1] M. P. Kostylev, A. A. Serga, T. Schneider, B. Leven, and\nB. Hillebrands, Appl. Phys. Lett. 87, 153501 (2005).\n[2] S. V. Vasiliev, V. V. Kruglyak, M. L. Sokolovskii, and\nA. N. Kuchko, J. Appl. Phys. 101, 113919 (2007).\n[3] T. Schneider, A. A. Serga, B. Leven, B. Hillebrands,\nR. L. Stamps, and M. P. Kostylev, Appl. Phys. Lett.\n92, 022505 (2008).\n[4] Ki-Suk Lee, and Sang-Koog Kim, Jour. Appl. Phys. 104,\n053909 (2008)\n[5] S.O.Demokritov, A. A.Serga, A.Andr´ e, V.E. Demidov,\nM. P. Kostylev, and B. Hillebrands, Phys. Rev. Lett. 93,\n047201 (2004).\n[6] M. P. Kostylev, A. A. Serga, T. Schneider, T. Neumann,\nB. Leven, B. Hillebrands, and R. L. Stamps, Phys. Rev.B76, 184419 (2007).\n[7] H. Puszkarski, and M. Krawczyk, Solid State Phenomena\n94, 125 (2003).\n[8] U.-H. Hansen, M. Gatzen, V. E. Demidov, and S. O.\nDemokritov, Phys. Rev. Lett. 99, 127204 (2007).\n[9] T. Neumann, A. A. Serga, B. Hillebrands and M. P.\nKostylev, accepted at APL (2009).\n[10] O. B¨ uttner, M. Bauer, S. O. Demokritov, B. Hillebrands ,\nYu. S. Kivshar, V. Grimalsky, Yu. Rapoport, and A. N.\nSlavin, Phys. Rev. B 61, 11576 (2000).\n[11] G. A. Melkov, A. A. Serga, A. N. Slavin, V. S. Tiberke-\nvich, A. N. Oleinik, and A. V. Bagada, JETP 89, 1189\n(1999)."    },    {        "title": "1911.05070v2.Diamond_magnetometer_enhanced_by_ferrite_flux_concentrators.pdf",        "content": "Diamond magnetometer enhanced by ferrite \rux concentrators\nIlja Fescenko,1,\u0003Andrey Jarmola,2, 3Igor Savukov,4Pauli Kehayias,1, 5Janis Smits,1, 6\nJoshua Damron,1Nathaniel Risto\u000b,1Nazanin Mosavian,1and Victor M. Acosta1,y\n1Center for High Technology Materials and Department of Physics\nand Astronomy, University of New Mexico, Albuquerque, NM, USA\n2ODMR Technologies Inc., El Cerrito, CA, USA\n3Department of Physics, University of California, Berkeley, CA, USA\n4Los Alamos National Laboratory, Los Alamos, NM, USA\n5Sandia National Laboratory, Albuquerque, NM, USA\n6Laser Center of the University of Latvia, Riga, Latvia\nMagnetometers based on nitrogen-vacancy (NV) centers in diamond are promising room-\ntemperature, solid-state sensors. However, their reported sensitivity to magnetic \felds at low fre-\nquencies ( .1 kHz) is presently &10 pT s1=2, precluding potential applications in medical imaging,\ngeoscience, and navigation. Here we show that high-permeability magnetic \rux concentrators, which\ncollect magnetic \rux from a larger area and concentrate it into the diamond sensor, can be used to\nimprove the sensitivity of diamond magnetometers. By inserting an NV-doped diamond membrane\nbetween two ferrite cones in a bowtie con\fguration, we realize a \u0018250-fold increase of the magnetic\n\feld amplitude within the diamond. We demonstrate a sensitivity of \u00180:9 pT s1=2to magnetic\n\felds in the frequency range between 10 and 1000 Hz, using a dual-resonance modulation technique\nto suppress the e\u000bect of thermal shifts of the NV spin levels. This is accomplished using 200 mW\nof laser power and 20 mW of microwave power. This work introduces a new dimension for diamond\nquantum sensors by using micro-structured magnetic materials to manipulate magnetic \felds.\nI. Introduction\nQuantum sensors based on nitrogen-vacancy (NV) cen-\nters in diamond have emerged as a powerful platform\nfor detecting magnetic \felds across a range of length\nscales [1]. At the few-nanometer scale, single NV cen-\nters have been used to detect magnetic phenomena in\ncondensed-matter [2, 3] and biological [4, 5] samples.\nAt the scale of a few hundred nanometers, diamond\nmagnetic microscopes have been used to image biomag-\nnetism in various systems, including magnetically-labeled\nbiomolecules [6] and cells [7, 8] and intrinsically-magnetic\nbiocrystals [9, 10]. At the micrometer scale, diamond\nmagnetometers have detected the magnetic \felds pro-\nduced by neurons [11], integrated circuits [12, 13], and\nthe nuclear magnetic resonance of \ruids [14, 15].\nDiamond magnetometers with larger active volumes\nare expected to o\u000ber the highest sensitivity [16]. How-\never, in order to be competitive with existing technolo-\ngies, they must overcome several technical drawbacks,\nincluding high laser-power requirements and poor sensi-\ntivity at low frequencies. The most sensitive diamond\nmagnetometer reported to date featured a projected sen-\nsitivity of\u00180:9 pT s1=2using 400 mW of laser power [17].\nHowever this magnetometer used a Hahn-echo pulse se-\nquence which limited the bandwidth to a narrow range\naround 20 kHz. For broadband, low-frequency operation,\nthe highest sensitivity reported to date is \u001815 pT s1=2in\nthe 80{2000 Hz range, using &3 W of laser power [11]. A\ndiamond magnetometer based on infrared absorption de-\n\u0003iliafes@gmail.com\nyvmacosta@unm.edutection realized a sensitivity of \u001830 pT s1=2at 10{500 Hz,\nusing 0:5 W of laser power [18].\nTo understand the interplay between sensitivity and\nlaser power, we consider a diamond magnetometer based\non continuous-wave, \ruorescence-detected magnetic res-\nonance (FDMR) spectroscopy. Here, the sensitivity is\nfundamentally limited by photoelectron shot noise as:\n\u0011psn\u0019\u0000\n\rnvCp\n\u0018Popt=Eph; (1)\nwhere\rnv= 28 GHz=T is the NV gyromagnetic ratio,\n\u0000 is the FDMR full-width-at-half-maximum linewidth,\nandCis the FDMR amplitude's fractional contrast. The\nfactor\u0018Popt=Ephconstitutes the photoelectron detection\nrate, where Poptis the optical excitation power, \u0018is the\nfraction of excitation photons converted to \ruorescence\nphotoelectrons, and Eph= 3:7\u000210\u000019J is the excitation\nphoton energy (532 nm). To set an optimistic bound on\n\u0011psn, we insert the best reported values ( \u0018= 0:08 [17],\n\u0000=C= 1 MHz=0:04 [11]) into Eq. (1) to obtain \u0011psn\u0019\n2 pT s1=2W1=2. Even in this ideal case (Appendix XIII),\n\u00184 W of optical power is needed to realize a sensitivity of\n1 pT s1=2, and further improvements become impractical.\nThe need for such a high laser power presents chal-\nlenges for thermal management and has implications for\nthe overall sensor size, weight and cost. Applications\nwhich call for sub-picotesla sensitivity, such as magne-\ntoencephalography (MEG) [19] and long-range magnetic\nanomaly detection [20, 21], may require alternative ap-\nproaches to improve sensitivity. Avenues currently be-\ning pursued often focus on reducing the ratio \u0000 =C[16].\nApproaches to reduce \u0000 include lowering13C spin den-\nsity and mitigating strain and electric-\feld inhomogene-\nity [22, 23], increasing the nitrogen-to-NV\u0000conversionarXiv:1911.05070v2  [physics.ins-det]  14 Nov 20192\na)10mm10mm\nBext\nθzx\n370µmδ=43µmRelative magnetic field, |B  (r )| / |Bext| \nr0MN60 ferrite\n(μr=6500)\n1100200300\n20 40 60 80 1000200400\nGap,    (µm)Enhancement factor, /uni0454\n0 3000 6000 90000100200\nRelative permeability, μ rMN60 ferrite300b)\nd) e)\nμr = 6500\n= 0°θ\nθ  = 43 µm\n= 0°\nδδ\nμr = 6500\n  = 43 µmδBext\nθ(  = 0°)\nEnhancement factor, /uni0454\n0 45 90 135 180-300-1500150300\nField polarangle,θ(°)Relative magnetic fieldc)\nFit: /uni0454 cosθ Bz (r0) / |Bext|\n Bx (r0) / |Bext|x\nz\nFIG. 1. Simulations of magnetic \rux concentrators. (a) Model geometry. Two identical solid cones, con\fgured in a\nbowtie geometry, are placed in an external magnetic \feld, Bext. (b) Simulated x-z plane cut of the relative magnetic \feld\namplitude,jB(r)j=jBextj, for cones with relative permeability \u0016r= 6500 and a tip gap of \u000e= 43 \u0016m, upon application of\nBextat\u0012= 0. Arrows indicate the direction and magnitude of B(r). The point at the geometric center is labeled r0. (c)\nVector components of the relative magnetic \feld amplitude at r0as a function of \u0012, for cones with \u0016r= 6500 and \u000e= 43 \u0016m.\nThe relative axial magnetic \feld amplitude is \ft to the function Bz(r0)=jBextj=\u000fcos\u0012, where in this case \u000f= 280. (d)\nEnhancement factor as a function of \u000efor cones with \u0016r= 6500. (e) Enhancement factor as a function of \u0016rfor\u000e= 43 \u0016m.\nyield [24{26], and designing techniques to decouple NV\ncenters from paramagnetic spins [23, 27]. Methods to\nincreaseCinclude using preferentially-aligned NV cen-\nters [28, 29], detecting infrared absorption [18, 30], and\ndetecting signatures of photo-ionization [31{33].\nIn this Manuscript, we report a complementary ap-\nproach to improve the sensitivity of diamond magnetome-\nters. Our approach uses microstructured magnetic \rux\nconcentrators to amplify the external magnetic \feld am-\nplitude by a factor of \u0018250 within the diamond sensor.\nUsing a dual-resonance magnetometry technique to sup-\npress the e\u000bect of thermal shifts of the NV spin levels,\nwe realize a sensitivity of \u00180:9 pT s1=2in the 10{1000 Hz\nrange, using a laser power of 200 mW. We show that,\nwith further improvements, a magnetic noise \roor of\n\u00180:02 pT s1=2at 1000 Hz is possible before ferrite ther-\nmal magnetization noise limits the sensitivity.\nII. Experimental design\nMagnetic \rux concentrators have previously been used\nto improve the sensitivity of magnetometers based on the\nHall e\u000bect [34], magnetoresistance [35], magnetic tunnel\njunctions [36], superconducting quantum interference de-\nvices [37], and alkali spin precession [38]. Typically, the\nmagnetometer is positioned in the gap between a pairof ferromagnetic structures which collect magnetic \rux\nfrom a larger area and concentrate it into the gap. The\nfractional increase in magnetic \feld amplitude due to the\n\rux concentrators, \u000f, is a function of their geometry, gap\nwidth, and relative permeability ( \u0016r). Ideally, the con-\ncentrators are formed from a soft magnetic material with\nlow remanence, high \u0016r, low relative loss factor [38], and\nconstant susceptibility over a broad range of magnetic\n\feld amplitudes and frequencies. The improvement in\nsensitivity is generally accompanied by a reduction in\nspatial resolution, as the total magnetometer size is larger\n(Appendix II). Diamond sensors usually have sub-mm di-\nmensions, whereas the \rux concentrators used here have\ndimensions of\u001810 mm. Thus our device is best suited\nfor applications that require a spatial resolution &10 mm,\nsuch as MEG and magnetic anomaly detection.\nThe optimal \rux concentrator geometry depends on a\nnumber of factors, which include the sensor dimensions\nand target application. Here, we consider a pair of iden-\ntical cones (height: 10 mm, base diameter: 10 mm), with\n\u0018370{\u0016m diameter \rat tips, arranged in a bowtie con-\n\fguration, Fig. 1(a). A static magnetic \feld, Bext, is\napplied at an angle \u0012from the cone symmetry axis ( ^z)\nand the resulting magnetic \feld, B(r), is simulated us-\ning \fnite-element magnetostatic methods. Figure 1(b)\nshows a plane-cut of the relative magnetic \feld ampli-3\n0.960.981.002840 2860 2880Fluorescence (norm.)Microwave frequency (MHz)\n■■■■■■■■■■■■■■■■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■■■■■■■■■■■■■■■■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■■■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■■■■■■■■■■■■■■■■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■\n■■■■■■■■■■■■■■■■■■■\n■\nFit (/uni0454=254)\n-40 -20 0 20 4027002800290030003100\nExternal field, Bext (µT)FDMR freqnency (MHz)f+ f-\nf+\nf-Laser \n(532 nm, 200 mW)\nFluorescence \n(650-800 nm)Dichroic\nmirror\nLens\nmu-metal shieldDiamond microwave loop\nBalanced\nphotodetector\nBeam\nsplitterFerrite \ncones\nHelmholtz coilsa) b)\nc)\n300 µmmicrowave loop\nMN60 ferrite[100]\ndiamondBext\nBgap\nFIG. 2. Experimental setup and enhancement measurement. (a) Schematic of the experimental setup. Inset:\nphotograph of the diamond membrane in the gap between ferrite cones. (b) Fluorescence-detected magnetic resonance (FDMR)\nspectrum obtained at Bext= 2:62\u0016T. Two peaks are present, with central frequencies f\u0006extracted from Lorentzian \fts. (c)\nMeasured FDMR frequencies as a function of Bext. Error bars are smaller than the plot markers. The gray solid lines are a \ft\nusing the NV spin Hamiltonian (Appendix I), assuming Bgap=\u000fBext, with\u000f= 254.\ntude,jB(r)j=jBextj, for cones with \u0016r= 6500 and a\ntip gap of \u000e= 43 \u0016m, upon application of Bextat\n\u0012= 0. Throughout the gap (Appendix II), B(r) is\naligned along ^zwith a uniform relative magnetic \feld\njB(r)j=jBextj\u0019280.\nFigure 1(c) shows the vector components of the rela-\ntive magnetic \feld at the center of the bowtie geometry\n(r=r0) as a function of \u0012. The relative axial mag-\nnetic \feld is well described by Bz(r0)=jBextj\u0019\u000fcos\u0012,\nwhere\u000fis the enhancement factor (in this simulation\n\u000f= 280). On the other hand, the relative transverse\nmagnetic \feld, Bx(r0)=jBextj, is less than 0.1 for all val-\nues of\u0012. Thus, the structure acts as a \flter for the axial\ncomponent of external magnetic \felds, producing a uni-\nform \feld throughout the gap of:\nBgap\u0019\u000fjBextjcos\u0012^z: (2)\nFor the remainder of the manuscript, we consider only\nexternal magnetic \felds applied along ^z(\u0012= 0) and de-\nscribe Bgapaccording to Eq. (2).\nFig. 1(d) shows simulation results of the enhance-\nment factor as a function of gap length for cones with\n\u0016r= 6500. For \u000ein the 20{100 \u0016m range,\u000fvaries from\n560 to 120, indicating that large enhancement factors are\npossible for typical diamond membrane thicknesses. Fig-\nure 1(e) is a plot of the simulated \u000fas a function of \u0016r\nfor\u000e= 43 \u0016m. For\u0016r&500 the enhancement factor is\nrelatively constant at \u000f\u0019280. This indicates that a wide\nrange of magnetic materials can be used for \rux concen-\ntration and minor variations in \u0016r(due, for example, to\ntemperature variation) have a negligible impact on Bgap.\nWe elected to use MN60 ferrite ( \u0016r\u00196500) as the ex-\nperimental concentrator material, owing to its low ther-mal magnetic noise [38, 39]. The ferrite cones were micro-\nmachined to have approximately the same dimensions\nas simulated in Fig. 1. Figure 2(a) depicts the experi-\nmental setup. An NV-doped diamond membrane with\n[100] faces is positioned in the gap between the ferrite\ncones. The membrane was formed from a commercially-\navailable, type Ib diamond grown by high-pressure high-\ntemperature (HPHT) synthesis. The diamond had been\nirradiated with 2{MeV electrons at a dose of \u00181019cm\u00002.\nIt was subsequently annealed in a vacuum furnace at\n800{1100 °C [9] and mechanically polished and cut into\na membrane of dimensions \u0018300\u0002300\u000243\u0016m3.\nApproximately 200 mW of light from a 532 nm laser\nis focused by a 0.79 NA lens to a \u001840\u0016m diameter\nbeam that traverses the diamond membrane parallel to\nits faces. The same lens is used to collect NV \ruores-\ncence, which is then refocused onto one of the channels\nof a balanced photodetector, producing \u00181:2 mA of pho-\ntocurrent. A small portion of laser light is picked o\u000b from\nthe excitation path and directed to the other photode-\ntector channel for balanced detection. Microwaves are\ndelivered by a two-turn copper loop wound around one\nof the ferrite cones. The ferrite cones provide a &2-fold\nenhancement in the microwave magnetic \feld amplitude\nwithin the diamond (Appendix IX). All measurements\nwere performed using .20 mW of microwave power.\nThe ferrite-diamond assembly is positioned at the cen-\nter of a pair of Helmholtz coils (radius: 38 mm), which\nproduce a homogenous magnetic \feld parallel to the\ncone axis of amplitude Bext. The coils' current response\nwas calibrated using three di\u000berent magnetometers (Ap-\npendix X). A 1.5-mm-thick cylindrical mu-metal shield\n(diameter: 150 mm, height: 150 mm) surrounds the4\nDual resonance\n0.5 1.0 1.5 2.0 2.5 3.0-20-1001020200 400 600 800AC photocurrent amplitude (µArms)Field indiamond, Bgap (µT)\nSingle resonance, f-\nSingle resonance,  f+\nExternal field, Bext (µT)TimeMicrowave frequency modulation\nMicrowave frequency2fdFDMR signal\n1/fmod\nf-\nf+a) c)\n0Lock-in Signal (V)-0.4\n-0.80.40.8\nπ\nDiamond \nsensor\n(Fig. 2a) Lock-in\namplifiersignal\ncos(2   fmod t)πreference signal:b)\nfrequency-modulated\nmicrowaves inphotodetectorphase shift\n3.5\nFIG. 3. Dual-resonance magnetometry concept. (a) Microwave frequency modulation used for dual-resonance magne-\ntometry. (b) Schematic of the lock-in technique. Both microwave signals depicted in (a) are combined and delivered through\nthe microwave loop. NV \ruorescence is continuously excited and its time-varying intensity is recorded by the balanced pho-\ntodetector. This signal is then fed to a lock-in ampli\fer and demodulated by the reference signal. (c) Lock-in signal as a\nfunction of Bextfor both single-resonance and dual-resonance modulation protocols. The microwave frequencies were centered\nabout thef\u0006values measured by FDMR spectroscopy at Bext= 1:73\u0016T. In all cases, fmod= 15 kHz and the lock-in uses a 12\ndB/octave low-pass \flter with a 100 \u0016s time constant. For the f\u0000scan, the lock-in reference signal had a \u0019phase shift relative\nto the modulation function. The right vertical axis converts the lock-in signal to the amplitude of photocurrent oscillations at\nfmod, which is used to estimate the photoelectron-shot-noise-limited sensitivity, Appendix XIII.\nHelmholtz coils, providing a shielding factor of \u0018100.\nTo measure the enhancement factor, we recorded the\nNV FDMR spectrum as a function of Bext. Figure 2(b)\nshows a typical FDMR spectrum acquired at Bext=\n2:62\u0016T. Two peaks are present, with central frequencies\nf\u0006. These frequencies correspond to NV electron-spin\ntransitions between the ms= 0 andms=\u00061 magnetic\nsublevels (Appendix I). For magnetic \feld amplitudes\nwithin the diamond in the range 0 :5 mT.\u000fBext.5 mT,\nthe transition frequencies may be approximated as:\nf\u0006\u0019D(\u0001T)\u0006\rnv\u000fBext=p\n3; (3)\nwhere, in our experiments (Appendix IV), D(\u0001T)\u0019\n2862 MHz + \u001f\u0001Tis the axial zero-\feld splitting param-\neter which shifts with changes in temperature, \u0001 T, as\n\u001f\u0019\u00000:1 MHz=K [40]. The 1 =p\n3 factor in Eq. (3) comes\nfrom projecting Bgaponto the four NV axes which are\nall aligned at 55 °with respect to the cone axis.\nFigure 2(c) plots the \ftted f\u0006values as a function of\nBext. These data were obtained by scanning Bextback\nand forth between \u000650\u0016T two times. For a given Bext,\nthe extracted f\u0006are nearly identical regardless of scan\nhistory, indicating negligible hysteresis (Appendix XII).\nThe data were \ft according to the NV spin Hamiltonian\n(Appendix I), which reveals an experimental enhance-\nment factor of \u000f= 254\u000619. The uncertainty in \u000fis pri-\nmarily due to uncertainty in the Bextcurrent calibration\n(Appendix X). The experimental enhancement factor is\n\u001810% smaller than the one simulated in Fig. 1(b). This\ncould be explained by a \u00184\u0016m increase in \u000edue to adhe-\nsive between the diamond and ferrite tips (Appendix III).\nHaving established that the ferrite cones provide a\u0018250-fold \feld enhancement, we now turn to methods of\nusing the device for sensitive magnetometry. A common\napproach in diamond magnetometry [41, 42] is to mod-\nulate the microwave frequency about one of the FDMR\nresonances and demodulate the resulting \ruorescence sig-\nnal using a lock-in ampli\fer (Appendix VI). We call this\nmethod \\single-resonance\" magnetometry, as each reso-\nnance frequency is measured independently. For exam-\nple, to measure f+, the microwave frequency is varied as\nF(t)\u0019f++fdcos (2\u0019fmodt), wherefdis the modulation\ndepth andfmodis the modulation frequency. The lock-\nin ampli\fer demodulates the photodetector signal using\na reference signal proportional to cos (2 \u0019fmodt). The re-\nsulting lock-in output is proportional to variations in f+.\nHowever, a single FDMR resonance can shift due to\nchanges in temperature in addition to magnetic \feld, see\nEq. (3). To isolate the shifts due only to changes in mag-\nnetic \feld, the di\u000berence frequency ( f+\u0000f\u0000) must be\ndetermined. Previous works accomplished this by mea-\nsuring both resonances either sequentially [43] or simulta-\nneously by multiplexing modulation frequencies [44, 45].\nThe magnetic \feld was then inferred by measuring f+\nandf\u0000independently and calculating the di\u000berence.\nHere, we use an alternative \\dual-resonance\" ap-\nproach, which extracts the magnetic \feld amplitude di-\nrectly from a single lock-in measurement (Appendix VI).\nTwo microwave signal frequencies, centered about f\u0006, are\nmodulated to provide time-varying frequencies, F\u0006(t)\u0019\nf\u0006\u0006cos (2\u0019fmodt). In other words, each tone is mod-\nulated with the same modulation frequency and depth,\nbut with a relative \u0019phase shift, Fig. 3(a). The photode-\ntector signal is then demodulated by the lock-in ampli-5\n0 20 40 60 80 100-4-2024\n80.00 80.05123\nTime (s)Magneti cfield (nT)\n0200400600\nTest field frequency (Hz)Amplitude (pT rms)\n1 10 100 10000.11101001000\nFrequency (Hz)Magneti cnoise (pT  s1/2)testfields\nPhotoelectron shot-noise limitMagneti cfield (nT)\n1 10 100 1000a)\nb)c)\nTime (s)Dual resonance\nSingle resonance, f -\nMN60 ferrite magnetization-noise limit Single resonance, f+\nDual resonanceSingle resonance, f-\nMicrowaves off0.01\nFIG. 4. Sub-picotesla diamond magnetometry. (a) Time-domain lock-in signals for single-resonance ( f\u0000) and dual-\nresonance modulation. Throughout, fmod= 15 kHz and the lock-in uses a 12 dB/octave low-pass \flter with a 100 \u0016s time\nconstant. The adjacent plot is a zoom of the dual-resonance signal where the 580 pTrms test \feld at 135 Hz can be seen. The\ntest-\feld frequency for f+andf\u0000single-resonance experiments were 125 and 130 Hz, respectively, with the same 580 pTrms\namplitude. (b) Magnetic noise spectra of single-resonance (two shades of gray) and dual-resonance (blue) signals. A reference\nspectrum obtained with microwaves turned o\u000b (green) shows noise from the un-modulated photodetector signal. Each spectrum\nwas obtained by dividing a 100{s data set into one hundred 1{s segments, taking the absolute value of the Fourier Transform of\neach segment, and then averaging the Fourier Transforms together. Spectra were normalized such that the test \feld amplitudes\nmatched the calibrated 580 pTrms values (Appendix VIII). The dashed red line is the projected value of \u0011psnfor dual-resonance\nmagnetometry (Appendix XIII). The dashed magenta line is the calculated thermal magnetization noise produced by the ferrite\ncones (Appendix XIV). (c) Frequency dependence of the test \feld amplitude measured by dual-resonance magnetometry.\n\fer using a reference signal proportional to cos (2 \u0019fmodt),\nFig. 3(b). In this way, the lock-in output is proportional\nto (f+\u0000f\u0000) and is una\u000bected by thermal shifts of D(\u0001T).\nFurthermore, the dual-resonance lock-in signal's response\nto magnetic \felds is larger than in the single-resonance\ncase. Figure 3(c) shows the experimental lock-in signal\nas a function of Bextfor dual-resonance modulation and\nboth of the f\u0006single-resonance modulation protocols.\nThe slope for dual-resonance modulation is \u00181:3 times\nlarger than that of single-resonance modulation. This is\nclose to the expected increase of 4 =3 (Appendix VII).\nIII. Results\nWe next show that the combination of \rux concentration\nand dual-resonance modulation enables diamond mag-netometry with sub-pT s1=2sensitivity over a broad fre-\nquency range. A 1 :73\u0016T bias \feld and 580 pTrms oscil-\nlating test \feld in the 125{135 Hz range were applied\nvia the Helmholtz coils. The lock-in signal was con-\ntinuously recorded for 100 s using either dual-resonance\nor single-resonance modulation. Figure 4(a) shows the\nmagnetometer signals as a function of time. For single-\nresonance modulation, the signals undergo low-frequency\ndrifts, likely due to thermal shifts of D(\u0001T). These drifts\nare largely absent for dual-resonance modulation.\nFigure 4(b) shows the magnetic noise spectrum for\nthe di\u000berent modulation techniques. In addition to the\ncalibrated test \feld signals, numerous peaks appear for\nboth single and dual-resonance modulation. We attribute\nthese peaks to ambient magnetic noise that is not su\u000e-\nciently attenuated by the single-layer mu-metal shield. In6\n1 10 100 10001101001000\nFrequency (Hz)Magneti cnoise (pT  s1/2) testfields\nTwinlea fVMR\n270pT  s1/2\nFluxgate\n22 pT  s1/2SENSYS\nNV-ferrite\n0.9 pT  s1/2\nFIG. 5. Magnetometer comparison. Magnetic noise spec-\ntra of a commercial magnetoresistive magnetometer (Twinleaf\nVMR), \ruxgate magnetometer (SENSYS FGM-100) and our\ndual-resonance NV-ferrite magnetometer reproduced from\nFig. 4(b). Each magnetometer was placed in a similar location\nwithin the experimental apparatus and subject to the same\nbias and test \feld amplitudes. The test \feld frequency was\n130 Hz for both commercial sensors and 135 Hz for NV-ferrite.\nThe manufacturer-speci\fed sensitivities are 300 pT =p\nHz and\n10 pT=p\nHz for the VMR and \ruxgate, respectively.\nregions without peaks, the noise \roor for single-resonance\nmagnetometry is \u00181:5 pT s1=2for frequencies &300 Hz,\nbut it exhibits nearly 1 =fbehavior for lower frequencies.\nOn the other hand, the noise \roor for dual-resonance\nmagnetometry is \u00180:9 pT s1=2for frequencies &100 Hz\nand remains at this level, to within a factor of two, for\nfrequencies down to \u001810 Hz. The remaining noise be-\nlow 10 Hz may be due to thermal variation in the gap\nlength,\u000e(Appendix XVI). For reference, a spectrum ob-\ntained with the microwaves turned o\u000b is also shown. It\nfeatures a constant noise \roor of \u00180:8 pT s1=2through-\nout the 1{1000 Hz frequency range. This level is con-\nsistent with the projected photoelectron shot-noise limit,\n\u0011psn= 0:72 pT s1=2, which was calculated based on the\naverage photocurrent and lock-in slope (Appendix XIII).\nThe frequency response of the magnetometer was de-\ntermined by recording magnetic spectra at di\u000berent test-\n\feld frequencies, while holding the amplitude of the driv-\ning current constant. Figure 4(c) plots the test-\feld am-\nplitude, recorded by dual-resonance diamond magnetom-\netry, as a function of frequency. The amplitude decays by\nless than a factor of two over the 1{1000 Hz range. The\nobserved decay is due to a combination of the lock-in am-\npli\fer's low-pass \flter and a frequency-dependent mag-\nnetic \feld attenuation due to metal components within\nthe Helmholtz coils (Appendix VIII).\nFinally, we compared the performance of our magne-\ntometer with two commercial vector sensors: a magne-\ntoresistive magnetometer and a \ruxgate magnetometer.\nFigure 5 shows the magnetic noise spectra obtained under\ncomparable experimental conditions. Evidently, the NV-\nferrite magnetometer outperforms the commercial mag-\nnetometers throughout the frequency range.IV. Discussion and conclusion\nThe demonstration of broadband, sub-picotesla diamond\nmagnetometry is a signi\fcant step towards applications\nin precision navigation, geoscience, and medical imaging.\nSince only 200 mW of laser power and 20 mW of mi-\ncrowave power were used, the device holds promise for\nfuture miniaturization and parallelization e\u000borts. More-\nover, our magnetometer operates at microtesla ambient\n\felds, which raises the intriguing possibility of operating\nin Earth's magnetic \feld without an additional bias \feld.\nOur implementation used a commercially-available,\ntype Ib HPHT diamond processed using standard\nelectron-irradiation and annealing treatments [24]. This\nmaterial exhibits relatively broad FDMR resonances\n(\u0000\u00199 MHz), which leads to a photoelectron-shot-noise-\nlimited sensitivity of \u0011psn= 0:72 pT s1=2even after the\n\u0018250-fold \rux-concentrator \feld enhancement. State-of-\nthe-art synthetic diamonds have recently been fabricated\nthat feature several orders of magnitude narrower reso-\nnances [23, 46]. The excitation photon-to-photoelectron\nconversion e\u000eciency in our experiments ( \u0018\u001910\u00002) could\nalso be improved by at least an order of magnitude with\noptimized collection optics [17]. With these additions,\n\u0011psncould be further improved by several orders of mag-\nnitude, Eq. (1). However, at this level, thermal magne-\ntization noise intrinsic to the \rux concentrators becomes\nrelevant.\nThermal magnetic noise originating from dissipative\nmaterials can be estimated using \ructuation-dissipation\nmethods [38, 47]. The noise has contributions due to\nthermal eddy currents and magnetic domain \ructuations.\nAs discussed in Appendix XIV, we \fnd that thermal eddy\ncurrents in the ferrite cones produce an e\u000bective white\nmagnetic noise of \u00187\u000210\u00005pT s1=2. This negligibly-\nlow noise level is a consequence of our choice of low-\nconductivity ferrite. On the other hand, thermal mag-\nnetization noise results in a larger, frequency-dependent\nmagnetic noise. At 1 Hz, this noise is 0 :5 pT s1=2, and it\nscales with frequency as f\u00001=2, reaching\u00180:02 pT s1=2at\n1 kHz. This noise, shown in Fig. 4(b), is not a limiting\nfactor in our experiments, but it may have implications\nfor future optimization e\u000borts. If a material with a lower\nrelative loss factor could be identi\fed, it would result in\nlower thermal magnetization noise (Appendix XV).\nIn summary, we have demonstrated a diamond mag-\nnetometer with a sensitivity of \u00180:9 pT s1=2over the\n10{1000 Hz frequency range. The magnetometer oper-\nates at ambient temperature and uses 0 :2 W of laser\npower. These improved sensor properties are enabled\nby the use of ferrite \rux concentrators to amplify mag-\nnetic \felds within the diamond sensor. Our results may\nbe immediately relevant to applications in precision nav-\nigation, geoscience, and medical imaging. More broadly,\nthe use of micro-structured magnetic materials to manip-\nulate magnetic \felds o\u000bers a new dimension for diamond\nquantum sensors, with potential applications in magnetic\nmicroscopy [6{13] and tests of fundamental physics [48].7\nAcknowledgments\nThe authors acknowledge advice and support from A.\nLaraoui, Z. Sun, D. Budker, P. Schwindt, A. Mounce,\nM. S. Ziabari, B. Richards, Y. Silani, F. Hubert, and\nM. D. Aiello. This work was funded by NIH grants\n1R01EB025703-01 and 1R21EB027405-01, NSF grant\nDMR1809800, and a Beckman Young Investigator award.\nCompeting interests I. Fescenko, A. Jarmola, and\nV. M. Acosta are co-inventors on a pending patent appli-\ncation. A. Jarmola is a co-founder of ODMR Technolo-\ngies and has \fnancial interests in the \frm. The remaining\nauthors declare no competing \fnancial interests.\nAuthor contributions V. M. Acosta and I. Savukov\nconceived the idea for this study in consultation with I.\nFescenko and A. Jarmola. I. Fescenko carried out sim-\nulations, performed experiments, and analyzed the data\nwith guidance from V. M. Acosta. P. Kehayias, J. Smits,\nJ. Damron, N. Risto\u000b, N. Mosavian, and A. Jarmola con-\ntributed to experimental design and data analysis. All\nauthors discussed results and helped write the paper.8\nAppendix I.\nNV electron spin Hamiltonian\nNeglecting hyper\fne coupling (which is not resolved\nin our experiments), the NV ground-state electron spin\nHamiltonian can be written as [49]:\n^H\nh=DS2\nz0+E(S2\nx0\u0000S2\ny0) +\rnvBBB\u0001SSS; (AI-1)\nwherehis Planck's constant, \rnv= 28:03 GHz=T is the\nNV gyromagnetic ratio, and E\u00193 MHz is the transverse\nzero-\feld splitting parameter. The axial zero-\feld split-\nting parameter, D\u00192862 MHz, is temperature depen-\ndent, as discussed in Appendix IV. SSS= (Sx0;Sy0;Sz0) are\ndimensionless electron spin operators, and the zzz0direc-\ntion is parallel to the NV symmetry axis. For a magnetic\n\feld of amplitude Bgapapplied normal to a diamond with\n[100] faces, the Hamiltonian for NV centers aligned along\nany of the four possible axes is the same. In matrix form,\nit is:\n^H\nh=0\nBBBBB@D+\rnvBgapp\n3\rnvBgapp\n3E\n\rnvBgapp\n30\rnvBgapp\n3\nE\rnvBgapp\n3D\u0000\rnvBgapp\n31\nCCCCCA;\n(AI-2)\nThe eigenstates and eigenfrequencies can be found by\ndiagonalizing the Hamiltonian. The two microwave tran-\nsition frequencies observed in our experiments, f\u0006, cor-\nrespond to the frequency di\u000berences between the eigen-\nstate with largely ms= 0 character and the eigenstates\nwith largely ms=\u00061 character. We used this Hamil-\ntonian to \ft the f\u0006versusBextdata in Fig. 2(c). We\nassumedBgap=\u000fBextand used solutions to Eq. AI-2 to\n\ft for\u000f= 254. The values of EandDwere determined\nseparately from low-\feld FDMR data and were not \ft\nparameters.\nNote that Eq. (3) in the main text, which approxi-\nmatesf\u0006as being linearly dependent on Bext, is merely\na convenient approximation. As can be seen in Fig. 2(c),\nthe exact values of f\u0006are generally nonlinear functions\nofBext. This is especially pronounced near zero \feld,\n\u000fjBextj.E=\rnv\u00190:1 mT, where f\u0006undergo an avoided\ncrossing, and also at high \feld, where mixing due to\ntransverse \felds produces nonlinear dependence. How-\never, for magnetic \felds 0 :5 mT .\u000fBext.5 mT,\nthe transition frequencies f\u0006are approximately linear in\nBext.\nAppendix II.\nFlux concentrator simulations\nOur \rux concentrator model and simulations are de-\nscribed in Sec. II and Fig. 1 of the main text. Here we\ndescribe supplementary results demonstrating the \feld\nhomogeneity in the gap, the enhancement factor as the\nFIG. A6. Enhancement factor and \feld homogeneity.\n(a) The model geometry. See Fig. 1(a) for additional dimen-\nsions. (b) Enhancement factor, \u000f, as a function of the gap\nlength,\u000e. (c) Enhancement factor as a function of the axial\ndisplacement z. The gap is shaded in light gray, while the fer-\nrite concentrators are shaded in dark gray. (d) Enhancement\nfactor as a function of the transverse displacement x.\ngap length approaches zero, and the approximate point\nspread function. Figure A6(a) describes the geometry\nused for the simulations. Figure A6(b) shows the en-\nhancement factor as a function of \u000e, with the range\nextending to \u000e\u00190. The largest enhancement factors\nare observed for small gaps, approaching \u000f= 5000 for\n\u000e= 0. We chose a gap of \u000e\u001943\u0016m in our exper-\niments as a compromise that o\u000bers moderate enhance-\nment (\u000f\u0019250) while still providing substantial optical\naccess and straightforward fabrication and construction.\nTo visualize the homogeneity of the magnetic \feld\nwithin the gap, we plot line cuts of the relative \feld am-\nplitude along the axial and transverse directions. Fig-\nure A6(c) shows the relative magnetic \feld along the\ncone symmetry axis. Figure A6(d) shows the relative\n\feld along a transverse line passing through r0. Both\nplots predict a high degree of magnetic \feld homogeneity;\nresidual variations of the relative \feld are .1% through-\nout the region \flled by the diamond membrane.\nFuture NV-\rux concentrator devices may involve the\nuse of sensor arrays to perform imaging. While a detailed\nanalysis of the design space for imaging applications is\nbeyond the scope of this work, we performed simulations\nto estimate the point spread function of our device. A\nsmall (1{mm diameter) current loop was positioned to\nhave an axial displacement of 1 mm below the base of the\nbottom cone. The magnetic \feld amplitude in the gap,\nBgap, was simulated as a function of the current loop's\nlateral displacement, x. Figure A7 shows the resulting\nmagnetic \feld pro\fle. While it does not a have simple\nGaussian shape, it can be approximated as having a full-\nwidth-at-half-maximum (FWHM) resolution of \u001811 mm.9\n-40 -20 0 20 40010203040\nLateral displacemen t,x(mm)Field ingap,Bgap(arb.)\nFWHM  ≈ 11 mm\ncurrent loop1 mm\nFIG. A7. Flux concentrator point spread function.\nThe value of Bgapdue to a small current loop located below\nthe device is recorded as a function of lateral displacement.\nThe resulting \feld pro\fle has a FWHM linewidth of \u001811 mm.\nInset: geometry for scanning.\nAppendix III.\nExperimental setup: cones\nThe ferrite cones were ordered from Precision Ferrites\n& Ceramics, Inc. The diamond membrane was glued\non the tip of one of the ferrite cones with LOCTITE\nAA3494 UV-curing adhesive. The second cone with the\nmicrowave loop was mounted inside a metallic holder and\nmicro-positioned to contact the exposed face of the dia-\nmond membrane by use of a Thorlabs MicroBlock Com-\npact Flexure Stage MBT616D. When in the desired po-\nsition, the holder was glued to the support of the bottom\ncone by superglue, and then detached from the micro-\npositioning stage.\nAppendix IV.\nExperimental setup: optics\nTo excite NV \ruorescence, a Lighthouse Photonics\nSprout-G laser is used to form a collimated beam of 532\nnm light. The beam is focused with a Thorlabs aspheric\ncondenser lens ACL25416U-B (NA=0.79) onto the edge\nof the diamond membrane. Fluorescence is collected by\nthe same lens and is spectrally \fltered by a Semrock\nFF560-FDi01-25x36 dichroic mirror. A second lens re-\nimages the \ruorescence onto a photodetector. For mag-\nnetometry experiments, including all data in the \fgures\nin the main text, we used a Thorlabs PDB210A balanced\nphotodetector. For beam characterization (Fig. A8), we\nused a CMOS image sensor, and for observing Rabi os-\ncillations (Fig. A13), we used a Thorlabs PDA8A high-\nspeed photodetector. Figure A8(a) shows an image of the\n\ruorescence spot from the entrance edge of the diamond\nmembrane. The FWHM spot diameter of \u001840\u0016m was\nselected to match the diamond membrane thickness. It\nwas adjusted by tailoring additional telescoping lenses in\nthe excitation path.\nWith this optical system, we obtained a excitation\nFIG. A8. Beam pro\fle and absorption length. (a)\nImage of the \ruorescence spot at the entrance edge of the di-\namond membrane. The FWHM spot diameter is \u001840\u0016m.\nThe dashed lines indicate the approximate edges of the dia-\nmond. (b) Fluorescence intensity produced by a \u00181 mm di-\nameter laser beam entering the edge of a diamond membrane.\nThe inset shows a \ruorescence image of the top face. Red\nmarkers depict the normalized \ruorescence intensity along\nthe cut shown by the dashed line in the inset. The black solid\nline is an exponential \ft, revealing a 1 =eabsorption length of\n0:6 mm.\nphoton-to-photoelectron conversion e\u000eciency of \u0018\u0019\n0:01. The primary factors limiting \u0018are due to the lim-\nited optical access a\u000borded by the ferrite cones, loss of \ru-\norescence exiting orthogonal faces of the diamond mem-\nbrane, and incomplete absorption of the excitation beam\nwithin the diamond. To characterize the latter, we used\na separate apparatus to image the \ruorescence from the\ntop face of a larger membrane, Fig. A8(b). This larger\nmembrane was the starting piece from which we cut the\nsmaller membrane used in magnetometry experiments.\nWe found that the 1 =eabsorption length of this material\nis 0:6 mm. Thus we expect that only \u001840% of the laser\nlight was absorbed in the \u0018300\u0016m-long diamond mem-\nbrane used in magnetometry experiments. This approx-\nimation neglects the e\u000bects of laser light that is re\rected\nat the air-diamond interfaces.\nThe large absorbed optical power results in signi\fcant\nheating of the diamond membrane. The experimentally-\nmeasured axial zero-\feld splitting parameter D\u0019\n2862 MHz, Fig. 2(c), indicates a local diamond temper-\nature of\u0018385 K [40]. While the elevated temperature\nleads to a large shift in D, it does not signi\fcantly di-10\nDiamond\nsensor\n(Fig.2a)\nLaserAmplifierPower\ncombiner\nlock-in\nDemodu-\nlator\nLPFFunction\ngenerator\nCurrent\nsupplyVtest\nto HCsto MW loop\nBalanced PD\nLabVIEW DAQ cardφmod=π\nφmod=0�+\n�-\nfmod\nVpdclock sync.\nVoutMW generatorsa) b)\nc)VCO\nVCOf++f -\n2\nfdcos(2πf modt)f+-f -\n2to MW loop\nMixerTfeedback\nBfeedback\nf- f+fdf++f -\n2\nf+-f -\n2\nFDMRMW\nFIG. A9. Electronics. (a) Schematic of the electronics portion of the experimental apparatus. Vpdis the photodetector signal,\nVoutis the lock-in ampli\fer's in-phase output signal, Vtestis the test signal waveform, and fmodis the modulation frequency.\n(b) Alternative electronic scheme for dual-resonance microwave signal generation and feedback. A voltage-controlled oscillator\n(VCO) produces a carrier frequency fcar= (f++f\u0000)=2\u0019D(\u0001T) that is mixed with the signal from a second VCO with\nfrequencyfdi\u000b= (f+\u0000f\u0000)=2, creating two sidebands at the FDMR frequencies. The sidedand frequencies are modulated\nby adding a reference signal fdcos (2\u0019fmodt) to the second VCO. This arrangement allows for rapid feedback to correct for\ntemperature and magnetic \feld drifts by adjusting the bias voltage to the VCOs. (c) Microwave signal spectrum resulting from\nthe alternative electronics scheme in (b). A typical FDMR spectrum is shown in red for reference. DAQ: data acquisition card;\nHC: Helmholtz coils; LPF: low-pass \flter; MW: microwave; PD: photodetector.\nminish the contrast or broaden the FDMR resonances.\nFuture devices may employ active cooling or optimized\nheat sinks to reduce the diamond temperature.\nAppendix V.\nExperimental setup: electronics\nFigure A9(a) shows a schematic of the electronic de-\nvices used in our experimental setup. Microwaves are\nsupplied by two Stanford Research SG384 signal gener-\nators. The clocks of the generators are synchronized by\npassing the 10 MHz frequency reference output of one\ngenerator to the frequency reference input of the other.\nBoth generators are con\fgured to modulate the mi-\ncrowave frequency with a modulation frequency fmod=\n15 kHz and depth fd= 3:3 MHz. In dual-resonance\nmodulation, the signal generators are con\fgured such\nthat their modulation functions, F\u0006, have a relative \u0019\nphase shift (see Sec. II). The signals from both generators\nare combined with a Mini-Circuits ZAPD-30-S+ 2-way\npower combiner, ampli\fed by a Mini-Circuits ampli\fer\nZHL-16W-43-S+, and \fnally delivered to a two-turn mi-\ncrowave loop made from polyurethane-enameled copper\nwire (38 AWG). Prior to performing dual-resonance mag-\nnetometry, the microwave powers for each f\u0006resonance\nwere independently adjusted to give approximately the\nsame lock-in slope Fig. 3(c).The photodetector output signal, Vpd, is fed to a Signal\nRecovery 7280 lock-in ampli\fer using 50 \n termination.\nThe lock-in multiplies Vpdby a reference signal, propor-\ntional to cos (2 \u0019fmodt), output from one of the signal\ngenerators. The demodulated signal is processed by the\nlock-in's low pass \flter, which was set to 12 dB/octave\nwith a 100 \u0016s time-constant. The lock-in ampli\fer's in-\nphase component, Vout, is digitized at 50 kS/s by a Na-\ntional Instrument USB-6361 data acquisition unit.\nExternal \felds, Bext, are produced by a pair of\nHelmholtz coils (radius: 38 mm) driven by a Twinleaf\nCSUA-50 current source. To create oscillating test sig-\nnals, a Teledyne LeCroy WaveStation 2012 function gen-\nerator provides a sinusoidal waveform, Vtest, to the mod-\nulation input of the current source. The same function\ngenerator was used to slowly sweep the magnetic \feld\nfor the lock-in signals shown in Fig. 3c (in this case, no\noscillating test signals were applied).\nWhile our tabletop prototype uses scienti\fc-grade mi-\ncrowave generators, a simpler system could be used to de-\nliver the requisite dual-resonance microwave waveforms.\nFigures A9(b) shows an alternative scheme which uses\nonly voltage-controlled oscillators and a mixer. This\nscheme has the bene\ft of allowing for rapid feedback to\ncompensate for thermal and magnetic \feld drifts, which\nwould enable a higher dynamic range [45].11\nAppendix VI.\nDual-resonance magnetometry\nWe perform our magnetometry experiments with a\nlock-in ampli\fer in order to reduce technical noise, par-\nticularly at low frequencies. Such noise could arise from\na variety of sources, but a common source in NV mag-\nnetometry experiments is due to intensity \ructuations of\nthe laser that are not fully canceled by balanced pho-\ntodetection. The lock-in method allows us to tune our\nphotodetector signal to a narrow frequency band, where\nsuch technical noise is minimal. In our experiments,\nthis is accomplished by modulating the microwave fre-\nquency at a modulation frequency fmod= 15 kHz and\ndepthfd= 3:3 MHz. The resulting photodetector sig-\nnal,Vpd, has components at fmodand higher harmonics,\nin addition to the DC level. The lock-in ampli\fer iso-\nlates the component at fmod, in a phase-sensitive man-\nner, by multiplying Vpdby a reference signal proportional\nto cos (2\u0019fmodt). The product signal is passed through a\nlow-pass \flter, and the in-phase component, Vout, serves\nas the magnetometer signal.\nThe lock-in signal, Vout, can be converted to magnetic\n\feld units by one of two methods. In the \frst case, one\ncan sweep the magnetic \feld and measure the depen-\ndence ofVoutonBext, as in Fig. 3(c) of the main text.\nThe slope can be used to infer the conversion of Voutto\nmagnetic \feld units. This method works well provided\nthat the slope never changes. In practice, the slope can\nchange due to drifts of the laser or microwave powers. It\nalso can't account for any dependence of Vouton mag-\nnetic \feld frequency, as the slope is measured at DC.\nThus, we always apply a calibrated oscillating test \feld\nand re-normalize our magnetometer conversion based on\nthe observed amplitude. Typically the di\u000berence in con-\nversion factors using the two methods is small ( .10%).\nWe now turn to describing the principle of dual-\nresonance magnetometry. In single-resonance magne-\ntometry, the microwave frequency is modulated about\none of the FDMR resonances (for example, f+) and de-\nmodulated at the same frequency. The in-phase lock-in\noutputVoutis proportional to small deviations in f+.\nThis allows one to infer both the magnitude and sign\nof changes in f+. If the relative phase between the mi-\ncrowave modulation function, F+, and the reference sig-\nnal were shifted by \u0019radians, the magnitude of Vout\nwould be the same but the sign would reverse.\nIn dual-resonance magnetometry, we exploit this fea-\nture of phase-sensitive detection. The microwave mod-\nulation function for one resonance has a \u0019phase shift\nwith respect to the modulation function of the second\nresonance. The reference signal has the phase of the \frst\nmodulation function. In this way, if both f+andf\u0000\nshift by equal amounts in the same direction [due to a\nchange inD(\u0001T)], their contributions to the lock-in sig-\nnal cancel and Vout= 0. Iff+andf\u0000shift by equal\namounts but in opposite directions (due to a change in\nBext), their contributions to the lock-in signal add to-\ngether and Voutchanges in proportion to their shift. In\nms = -1ms = +1\nms = 0\nDual resonance: \nP(ms = 0) = 1/3ms = -1ms = +1\nms = 0\nSingle resonance: \nP(ms = 0) = 1/2FIG. A10. Single and dual-resonance spin popula-\ntions. NV spin level populations, represented by the num-\nber of magenta circles, are shown under single-resonance and\ndual-resonance microwave excitation.\nother words, the lock-in output is una\u000bected by ther-\nmal shifts of the NV spin levels (which shift f+andf\u0000\nby equal amounts in the same direction), but it remains\nproportional to changes in magnetic \feld (which shift f+\nandf\u0000by approximately equal amounts in opposite di-\nrections).\nNote that dual-resonance modulation could also be\nused to make an NV thermometer which is una\u000bected by\nchanges in magnetic \feld. This would be accomplished\nby applying the same modulation phase to both F\u0006sig-\nnals and monitoring the in-phase lock-in signal.\nAppendix VII.\nSensitivity enhancement in dual-resonance\nmagnetometry\nThe dual-resonance magnetometry approach was pri-\nmarily used because it is una\u000bected by thermal shifts of\nthe NV spin levels. This enabled better low-frequency\nperformance. However the dual-resonance approach also\nhas a fundamental advantage in sensitivity for all fre-\nquencies. Compared to the single-resonance approach,\nit o\u000bers a\u00184=3-fold improvement in photoelectron-shot-\nnoise-limited sensitivity. This improvement comes about\ndue to a\u00184=3-fold increase in the FDMR contrast.\nTo understand where the factor of 4 =3 arises, consider\nthe limiting case when the microwave excitation rate is\nmuch larger than the optical excitation rate. In this\nregime, a resonant microwave \feld drives the spin levels\nit interacts with into a fully mixed state, Fig. A10. For\nsingle-resonance excitation, when the microwave \feld is\non resonance, the probability that NV centers will be in\nthems= 0 level is P0= 1=2. For dual-resonance ex-\ncitation, both microwave transitions share the ms= 0\nlevel and thus P0= 1=3 when both microwave \felds are\non resonance. De\fning the \ruorescence intensity of an\nNV center in the ms= 0 level as I0and the \ruorescence\nintensity of an NV center in either of the ms=\u00061 levels\nasI1, the FDMR contrast is given by:\nC=I0\u0000[P0I0+ (1\u0000P0)I1]\nI0: (AVII-1)12\nFor the single-resonance case, the contrast is Cs=\n1\n2I0\u0000I1\nI0. In the dual-resonance case, the contrast is\nCd=2\n3I0\u0000I1\nI0. The ratio is therefore Cd=Cs= 4=3.\nSince the photoelectron-shot-noise-limited sensitivity is\nproportional to 1 =C[Eq. (1)], this corresponds to a 4 =3\nreduction in the magnetic noise \roor.\nTo derive the factor of 4 =3 we assumed that the mi-\ncrowave excitation rate was larger than the optical ex-\ncitation rate. In experiments, we use 20 mW of mi-\ncrowave power. This corresponds to a microwave Rabi\nfrequency of\u00180:7 MHz (Appendix IX) or a spin \rip rate\nof\u00181:4\u0002106s\u00001. The optical intensity used in our exper-\niments was Iopt\u00190:2 W=(40\u0016m)2= 12:5 kW=cm2(Ap-\npendix IV). The NV absorption cross section at 532 nm\nis\u001bnv\u00193\u000210\u000017cm2[24], so this corresponds to an\noptical excitation rate of Iopt\u001bnv=Eph\u0019106s\u00001. Thus,\nin our experiments, the microwave excitation rate is com-\nparable to, or slightly larger than, the optical excitation\nrate. The improvement in dual-resonance sensitivity was\nthus not exactly 4 =3, but it was close ( \u00181:3). Another\nassumption that we implicitly made is that the FDMR\nlinewidth is the same under single-resonance and dual-\nresonance excitation. This assumption is reasonably ac-\ncurate in our experiments, see Fig. 3(c) of the main text.\nAppendix VIII.\nMagnetometer frequency response\nFigure 4(c) of the main text shows the amplitude of\ntest \felds, recorded by dual-resonance diamond magne-\ntometry, as a function of their frequency. A moderate\ndecay (\u001840%) of the signal amplitude was observed over\nthe 1{1000 Hz range. In order to determine the causes\nof this signal decay, we performed a series of frequency-\nresponse measurements under di\u000berent conditions.\nFigure A12 shows the results of these experiments.\nIn all cases, we use fmod = 15 kHz and the lock-in\nuses a 12 dB/octave low-pass \flter with a time constant\n\u001cli= 100 \u0016s. We \frst isolated the lock-in ampli\fer's\nfrequency response by applying a sinusoidal voltage, os-\ncillating at fmod = 15 kHz, with an amplitude mod-\nulation of constant depth and variable modulation fre-\nquency. The resulting lock-in response is well described\nby a second-order Bessel \flter with a cuto\u000b frequency of\n1=(2\u0019\u001cli). While this \flter is largely responsible for the\nmagnetometer decay at frequencies &1 kHz, it can only\naccount for a small fraction of the decay observed over\nthe 1{1000 Hz range.\nNext, we removed the ferrite cones from the assem-\nbly and performed dual-resonance magnetometry. The\nobserved frequency response is similar to that observed\nwith the ferrite cones in place. The decay is slightly less\npronounced, but evidently the ferrite cones do not ac-\ncount for the observed decay.\nFinally, we removed the metal mounting hardware used\nin the apparatus that were located within the Helmholtz\ncoils, Fig. A11. We again performed dual-resonance di-\namond magnetometry without the ferrite cones in place.\nBrass c reww Brass screw\nCu\nmount\nAl postFIG. A11. Photo of apparatus with shield removed.\nMetal mounting components that were removed to generate\nthe data in Fig. A12 are labeled. The brass screw was used\nfor mounting to a translation stage during initial alignment\n(Appendix III). Other unlabeled metal parts, such as brass\nnuts, were not found to contribute to the frequency-dependent\nmagnetic \feld attenuation.\nFIG. A12. Frequency response of di\u000berent magne-\ntometer con\fgurations. The blue trace is the normalized\nmagnetometer frequency response, reproduced from Fig. 4(c).\nThe red trace is the same NV magnetometer setup except\nwithout the ferrite cones. The brown trace is the NV mag-\nnetometer without ferrite cones and with metal components\n(Fig. A11) removed from the interior of the Helmholtz coils.\nThe black trace is the lock-in \flter response as measured by\namplitude-modulated voltage inputs.\nIn this case, we observe a frequency response which is\nnearly identical to the lock-in ampli\fer's frequency re-\nsponse.\nWe therefore conclude that metal components within\nthe Helmholtz coils are responsible for most of the decay\nin the 1{1000 Hz range observed in Fig. 4(c). The lock-\nin ampli\fer's low-pass \flter contributes as well, but to\na lesser degree. The ferrite cones may also contribute\na small amount to the observed decay, but future work\nwould be needed to isolate their response independently.\nThe frequency dependence of our magnetometer leaves\nan ambiguity as to how best to normalize the magnetic\nnoise spectra in Fig. 4(b). As seen in Fig. 4(c), when we13\napply a test current which is expected to produce an am-\nplitude of 580 pTrms, it produces the correct amplitude\nat 1 Hz, but at 125{135 Hz it produces an amplitude of\n\u0018540 pTrms. Since 125{135 Hz is the frequency range of\nthe test \felds applied in Fig. 4(b), we therefore had to\ndecide whether to normalize the noise spectra so that the\ntest-\feld peaks appeared at 580 pT s1=2or\u0018540 pT s1=2.\nConservatively, we chose the former. We multiplied each\nspectrum by 580 =540 = 1:07, which raised the test \feld\npeaks to 580 pT s1=2and also raised the noise \roor by 7%.\nIf we had instead chosen to normalize the test-\feld peaks\nto 540 pT s1=2, our noise \roor estimates would improve\nby\u00187% to\u00180:84 pT s1=2.\nAppendix IX.\nFerrite microwave \feld enhancement\nA feature of our magnetometer is that it uses a sim-\nple, non-resonant coil for microwave excitation and only\nrequires 20 mW of microwave power. This is partially\nenabled by an enhancement of the microwave magnetic\n\feld provided by the ferrite cones. Figure A13 shows\nRabi oscillations of the same diamond-coil con\fguration\nwith and without ferrite cones. The Rabi frequency with\nferrite is a &2-times larger, indicating an equivalent &2-\nfold enhancement in the microwave magnetic \feld.\n●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●\n0 100 200 300 400 5000.951.001.05\nTime(ns)Fluorescence (norm.)\nno ferrite, fRabi=7 MHz\nwith ferrite, fRabi=16 MHzLaser\nMW\nreadout500ns\nFIG. A13. Rabi frequency with and without ferrite.\n(top) Protocol used to observe continuous-wave Rabi oscilla-\ntions. (bottom) Rabi oscillations observed with and without\nferrite cones (the setup was identical otherwise). Black solid\ncurves are \fts to an exponentially-damped sinusoidal function\nrevealingfRabi = 16 MHz with ferrite and fRabi = 7 MHz\nwithout ferrite. A microwave power of \u001810 W was used for\nboth traces in order to clearly visualize the Rabi oscillations.\nAppendix X.\nCalibration of Helmholtz coils\nOur magnetometer signal's accuracy relies on a care-\nful calibration of the conversion between the current ap-\nplied to the Helmholtz coils and Bext. Here, we callthis conversion factor Mcal. Theoretically, we estimated\nMcal= 165 \u0016T=A based on the known coil geometry\nand number of turns. We veri\fed this estimate experi-\nmentally by applying currents to the Helmholtz coils and\nmeasuring the resulting magnetic \feld using three di\u000ber-\nent magnetometers.\nFG,shield, 174.6µT/A\nFG,noshield, 166.0µT/A\nVMR, shield,150.6 µT/A\n0.00 0.05 0.1005101520\nCurrent(A)External field, Bext(µT)a)\nf+\nf-\nFitwithMcal=175µT/A\n0 2 4 6 8 102830284028502860287028802890\nCurrent(A)Frequency (MHz)b)\nFIG. A14. Helmholtz coils current calibration. (a)\nHelmholtz coils current calibration performed with two com-\nmercial vector magnetometers. FG: SENSYS FGM3D/100\n\ruxgate magnetometer; VMR: Twinleaf VMR magnetometer.\n(b) NV FDMR frequencies versus current in the Helmholtz\ncoils. Solid lines are a \ft using Eq. AI-2, where Mcal=\n175\u0016T=A is the \ft parameter.\nFirst, two commercial vector magnetometers (Twinleaf\nVMR and SENSYS \ruxgate, see Fig. 5) were used to\ncalibrate the Helmholtz coils. Each magnetometer was\nplaced in the center of the coils at approximately the\nsame location as the NV-ferrite structure would be. The\ncurrent in the Helmholtz coils was varied and the axial\nmagnetic \feld component was recorded. Figure A14(a)\nshows the resulting calibration curves. The data were \ft\nto linear functions, revealing Mcal(listed in the legend).\nFor the \ruxgate magnetometer, Mcalis approximately\nthe same as the theoretical estimate when the top of the\nmagnetic shields was removed. When the shield remained\nin place, the calibration factor was \u00185% larger. The\nVMR magnetometer reported a lower magnetic \feld than\nother methods. In both cases we relied on conversion\nconstants between voltage and magnetic \feld units as\nprovided by the manufacturers.\nNote that when the current was turned o\u000b, we still ob-\nserved a small residual axial \feld of Bext=\u00000:2\u0016T using\nboth magnetometers. This is due to the \fnite attenuation14\nprovided by the shields. When the shields were removed,\nthe axial component of the lab \feld was approximately\n\u000020\u0016T. Since the shields provide a \u0018100-fold attenua-\ntion, this leads to a small residual \feld of \u00000:2\u0016T.\nNext, we used NV magnetometry, with the ferrite\ncones removed from the setup (Appendix VIII), to mea-\nsure the FDMR frequencies as a function of the current\nin the coils. Figure A14(b) shows the observed f\u0006values\nalongside a \ft according to the NV spin Hamiltonian,\nEq. AI-2, with Mcal= 175 \u0016T=A as a \ftting parameter.\nThe value of Mcalused throughout the main text was\nthe average of all three values reported by the magne-\ntometers with the shields on. It is Mcal= 167\u000614\u0016T=A,\nwhere the uncertainty is the standard deviation. If we\nhad removed the VMR magnetometer from the analy-\nsis, we would have obtained Mcal\u0019175\u0016T=A. This\nwould decrease the reported sensitivity by \u00185% to\u0018\n0:95 pT s1=2.\nAppendix XI.\nSensitivity without ferrite\nWe used the same dual-resonance magnetometry tech-\nnique described in the main text to record the dia-\nmond magnetometry signal with the ferrite cones re-\nmoved. Fig. A15 shows the resulting magnetic noise\nspectrum alongside the spectrum with ferrite [repro-\nduced from Fig. 4(b)]. The noise \roor without ferrite is\n\u0018300 pT s1=2. This is slightly larger than the expected\n254-fold increase, most likely due to a suboptimal choice\nof microwave power.\nFIG. A15. Sensitivity with and without ferrite cones.\nMagnetic noise spectra for dual-resonance magnetometry with\n(blue) and without (red) the ferrite cones.\nAppendix XII.\nFlux concentrator hysteresis\nThe data in Fig. 2(c) of the main text were obtained by\nsweepingBextfrom zero to +50 \u0016T, then from +50 \u0016T\nto\u000050\u0016T, and \fnally from \u000050\u0016T back to zero. To\ncheck whether hysteresis results in any remanent \feldsover the course of these measurements, we separated the\nf\u0006data into three segments: 0{ + 50 \u0016T, +50{\u000050\u0016T,\nand\u000050{0 \u0016T. We \ft the three data sets separately\naccording to Eq. AI-2 with a residual magnetic \feld o\u000bset\nofBextas the only \ftting parameter. The resulting o\u000bset\nmagnetic \felds were found to be 8.8 nT, -9.2 nT, and\n9.8 nT, respectively. This variation lies within the \ft\nuncertainty, so we take 10 nT as an upper bound. Note\nthat this corresponds to a remanent \feld within the gap\nof.2:5\u0016T.\nAppendix XIII.\nPhotoelectron shot-noise limit\nThe photoelectron-shot-noise-limited sensitivity of our\nmagnetometer is given by:\n\u0011psn=pqIdc\ndIac=dB ext; (AXIII-1)\nwhereIdc= 2:3 mA is the sum of the average pho-\ntocurrent in both channels of the balanced photodetector,\ndIac=dB ext= 33 Arms=T is the lock-in slope expressed in\nterms of the AC photocurrent rms amplitude [Fig. 3(c)],\nandq= 1:6\u000210\u000019C is the electron charge. Thus\nEq. (AXIII-1) evaluates to \u0011psn= 0:58 pT s1=2. This\nnoise can be thought of as the standard deviation of the\ntime-domain magnetometer data obtained in 1 second\nintervals. In the frequency domain it corresponds to the\nstandard deviation of the real part of the Fourier Trans-\nform expressed in pT s1=2. In our experiments, we report\nthe absolute value of the Fourier Transform. In order to\nrepresent\u0011psnin this way, it must be multiplied by 1.25 to\nreveal a magnetic noise \roor of \u0011psn= 0:72 pT s1=2. This\nconversion was checked by simulating Poissonian noise\nand observing the noise \roor in the absolute value of the\nFourier Transform.\nA similar value \u0011psn\u00190:75 pT s1=2was obtained by\ninserting experimental values from FDMR spectra into\nEq. 1 in the main text. In this case, we used \u0018= 0:01,\nPopt= 200 mW, \u0000 = 9 MHz, and C= 0:04. The e\u000bect of\n\rux concentrators is incorporated by multiplying \rnvby\n\u000f. Note that the expression in Eq. 1 refers to the sensitiv-\nity to the magnetic \feld component along the NV axis.\nSince we use this measurement to infer the total \feld am-\nplitude (which is directed at 55 °with respect to the NV\naxes), the right hand side of Eq. 1 must be multiplied by\n1=cos 55 °=p\n3.\nIn Sec. I of the main text, we claimed that the lowest\nvalue of \u0000=C[11] was 1 MHz =0:04. To be accurate, the\nreported contrast in this paper was 0 :05 and the linewidth\nwas 1 MHz. However this experiment measured the pro-\njection of the \feld onto NV axes that were aligned at 35 °\nwith respect to the \feld (the \feld was aligned normal to\na [110]-cut diamond face). Incorporating the projection\nfactor (cos 35 °= 0:82) in Eq. 1 has the same e\u000bect as\nscaling down the ratio \u0000 =Cby the same proportion. We\nthus reported the ratio as \u0000 =C\u00191 MHz=0:04.15\nFinally, we would like to clarify some issues with the\noptimistic estimation of \u0011psnmade in Sec. I of the main\ntext. There, we combined the highest-reported value\nof\u0018with the lowest reported value of \u0000 =C. In reality\nsuch a combination may be di\u000ecult to achieve as there\nare competing factors. For example, realizing high \u0018re-\nquires high optical depth. This is challenging to realize\nwhen \u0000 is small, because the latter implies a low NV\ndensity. In principle this could still be accomplished\nwith a multipass con\fguration or by using a large dia-\nmond. However, as one moves to lower \u0000, the optimal\nexcitation intensity also decreases (since the optical ex-\ncitation rate should not exceed \u0000). This means that, for\na \fxed power, the beam area must increase, which fur-\nther constrains the geometry and favors larger diamond\ndimensions. A lower excitation intensity also results in a\nsmaller magnetometer bandwidth, since the optical repo-\nlarization rate is lower. Finally, realizing a high value of\n\u0018requires getting waveguides and/or lenses very close to\nthe diamond. Realizing such a high optical access may\ninterfere with other magnetometer components (concen-\ntrators, microwave loop, heat sinks, etc.). Most of these\ntechnical challenges are not insurmountable, but they\nneed to be addressed. Our \rux concentrator solution\no\u000bers a complementary path that may alleviate some of\nthese engineering constraints.\nAppendix XIV.\nFerrite thermal magnetic noise\nThermal magnetic noise originating from dissipative\nmaterials can be estimated using \ructuation-dissipation\nmethods [38, 47]. The noise is inferred by calculating\nthe power loss ( P) incurred in the material due to a hy-\npothetical oscillating magnetic \feld (angular frequency:\n!) produced by a small current loop (area: A, current:\nI) situated at the location of the magnetometer. The\nmagnetic noise detected by the sensor is then given by:\n\u000eBgap=p\n8kTP\nAI!; (AXIV-1)\nwherekis the Boltzmann constant. The power loss has\nseparate contributions due to thermal eddy currents and\nmagnetic domain \ructuations:\nPeddy=Z\nV1\n2\u001bE2dV; P hyst=Z\nV1\n2!\u001600H2dV:\n(AXIV-2)\nHere\u001bis the electrical conductivity, \u001600is the imaginary\npart of the permeability ( \u0016=\u00160\u0000i\u001600),EandHare the\namplitudes of the induced electric and magnetic \felds,\nand the integration is carried out over the volume Vof\nthe dissipative material. In the small excitation limit,\nEandHscale linearly with the driving dipole moment\n(AI), so the magnetic noise in Eq. (AXIV-1) is indepen-\ndent of the size and driving current in the loop.\nWe numerically calculated magnetic noise contribu-\ntions due to Peddy andPhystfor our \rux concentratorgeometry [Figs. 1(a-b)]. We used MN60 material param-\neters [38] (\u001b= 0:2 \n\u00001m\u00001,\u00160= 6500\u00160,\u001600= 26\u00160,\nwhere\u00160is the vacuum permeability) and a cone gap of\n\u000e= 47 \u0016m, which resulted in the experimental enhance-\nment factor \u000f= 254. We \fnd that thermal eddy currents\nproduce white magnetic noise at the level of \u000eBgap\u0019\n0:02 pT s1=2. Since we are interested in our sensitivity\nin relation to the external \feld [38], noise produced lo-\ncally by the ferrite cones translates to an equivalent ex-\nternal \feld noise of \u000eBext=\u000eBgap=\u000f\u00197\u000210\u00005pT s1=2.\nThis negligibly-low noise level is a consequence of our\nchoice of low-conductivity ferrite materials. On the other\nhand, thermal magnetization noise results in a larger,\nfrequency-dependent magnetic noise. At 1 Hz, the ef-\nfective noise is 0 :5 pT s1=2, and it scales with frequency\nasf\u00001=2. The thermal magnetization noise is annotated\nin Fig. 4(b). It is not a limiting factor in our present\nexperiments, but it may have implications for future op-\ntimization e\u000borts. If a material with a lower relative\nloss factor ( \u001600=\u001602) could be identi\fed, it would result in\nlower thermal magnetization noise (Appendix XV).\nAppendix XV.\nThermal magnetic noise for various materials\nWe also used Eqs. (AXIV-1) and (AXIV-2) to estimate\nthe magnetic noise produced by cones of the same dimen-\nsions as in Fig. 1(a), but made from di\u000berent magnetic\nmaterials. Speci\fcally, we considered low-carbon steel\n1018 [50], MnZn ferrite MN80 [51], and mu-metal [38].\nThe results of these estimates are listed in Tab. A1 along\nwith the material parameters used for the analysis. In\nall cases, the hysteresis noise is dominant for frequencies\n.10 Hz.\n125\n0.5\n1 2 5Steel 1018\nMN80 ferrite\nMN60 ferrite\nmu-metal\n-1/2\nFIG. A16. Magnetization noise vs. relative loss factor.\nCalculated hysteresis magnetic noise (at 1 Hz) as a function\nof the square root of the relative loss factor,p\u001600=\u00160in four\nmagnetic materials.\nTo minimize hysteresis noise, one must limit the rel-\native loss factor ( \u001600=\u001602). We found that the hysteresis\nnoise scales proportional top\n\u001600=\u001602, Fig. A16. Another16\nMaterial \u00160=\u00160\u00160=\u00160\u00160=\u00160\u001600=\u00160\u001600=\u00160\u001600=\u00160\u001b\u001b\u001b(S/m) Enhancement, \u000f \u000eB hyst\u000eBhyst\u000eBhyst(1 Hz) , pT s1=2\u000eBeddy\u000eBeddy\u000eBeddy, pT s1=2\nSteel 1018 250 5 5.18 \u0002106223 6.8 0.4\nMnZn MN80 2030 6.1 0.2 251 0.85 0.00007\nMnZn MN60 6500 26 0.2 254 0.54 0.00007\nmu-metal 30000 1200 1.6 \u0002106255 0.8 0.2\nTABLE A1. Thermal magnetic noise for di\u000berent cone materials. Magnetic noise arising from Hysteresis and Johnson\nnoise were numerically calculated by the method described in Refs. [38, 47] using \fnite-element methods. The values of \u00160,\n\u001600, and\u001bare taken from references: low-carbon steel 1018 [50], MnZn ferrite MN80 [51], MnZn ferrite MN60 [38], and mu-\nmetal [38]. Note that \u00160and\u001600are in general frequency dependent. Here we take the values for the lowest reported frequency\nand assume that the response is relatively \rat below 1 kHz. The enhancement \u000fis determined from magnetostatic simulations\nas in Fig. 1 of the main text. The e\u000bective external magnetic noises \u000eBext=\u000eBgap=\u000fare de\fned by Eqs. AXIV-2-AXIV-1.\n\u000eBextis reported at 1 Hz. It scales with frequency as f\u00001=2.\ndesign consideration is the geometry of the \rux concen-\ntrators, but such an optimization is beyond the scope\nof this work. If the Johnson noise matters, as in the\nconductive mu-metal, it could be further decreased by\npassivating the skin e\u000bect with a lamination.\nFinally, we estimated the magnetic noise produced\nby the mu-metal magnetic shield used in our experi-\nments. Here, we used an analytical expression for a\n\fnite closed cylinder [47] and inserted mu-metal pa-\nrameters from Tab. A1 along with the shield dimen-\nsions (height: 150 mm, diameter: 150 mm, thickness:\n1:5 mm). The calculated Johnson noise for our shield is\n\u000eBeddy= 0:02 pT s1=2and the hysteresis noise at 1 Hz is\n\u000eBhyst= 0:007 pT s1=2. These are much lower than the\nobserved noise \roors and can safely be neglected. Note\nthat the noise from the shields is enhanced by the \rux\nconcentrators. This e\u000bect was incorporated in the calcu-\nlations, but we still arrived at negligibly-low values.\nAppendix XVI.\nSensitivity to variation of the gap length\nAn important systematic e\u000bect in our device could\narise from temporal variations in the cone gap length.\nAccording to the data in Fig. 1(d), a small change in gap\nlength in the vicinity of \u000e\u001943\u0016m produces a change\nin the enhancement factor given by d\u000f=d\u000e\u00196=\u0016m. This\nvariation extrapolates to a variation in the magnetometerreading given by:\ndBext\nd\u000e=d\u000f\nd\u000eBext\n\u000f: (AXVI-1)\nFor\u000f\u0019254 andBext= 2\u0016T, Eq. (AXVI-1) predicts\nthat a change in \u000eof just 20 pm produces an error in\nestimation of Bextof 1 pT.\nFortunately the gap length remains relatively stable\nin our construction such that this e\u000bect may only be a\nproblem at low frequencies. If the material in the gap\nexpands and contracts due to changes in temperature,\nthis produces a thermal dependence of the magnetometer\noutput given by:\ndBext\ndT=dBext\nd\u000ed\u000e\ndT: (AXVI-2)\nIf the material in the gap has a thermal expansion\ncoe\u000ecient\u000b, then the temperature dependence of the\ngap length is d\u000e=dT =\u000b\u000e. For diamond, \u000b\u00190:7\u0002\n10\u00006K\u00001. Using this value, and inserting Eq. (AXVI-1)\ninto Eq. (AXVI-2), we \fnd a magnetometer temperature\ndependence of dBext=dT\u00191:5 pT=K. This temperature\ndependence is more than 6 orders of magnitude smaller\nthan the thermal dependence in single-resonance magne-\ntometry (Sec. II). Nevertheless, to reach this limit, care\nmust be taken to mechanically stabilize the gap using\nan approach which does not signi\fcantly increase d\u000e=dT .\nFor example, using mechanical clamping and/or very thin\nadhesive layers would be bene\fcial.\n[1] C. L. Degen, F. Reinhard, and P. Cappellaro, \\Quantum\nsensing,\" Reviews of Modern Physics 89, 035002 (2017).\n[2] F. Casola, T. van der Sar, and A. Yacoby, \\Probing\ncondensed matter physics with magnetometry based on\nnitrogen-vacancy centres in diamond,\" Nature Reviews\nMaterials 3, 17088 (2018).[3] V. M. Acosta, L. S. Bouchard, D. Budker, R. Folman,\nT. Lenz, P. Maletinsky, D. Rohner, Y. Schlussel, and\nL. Thiel, \\Color centers in diamond as novel probes\nof superconductivity,\" Journal of Superconductivity and\nNovel Magnetism 32, 85 (2019).\n[4] R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen,17\n\\Nitrogen-vacancy centers in diamond: nanoscale sen-\nsors for physics and biology,\" Annual Review of Physical\nChemistry 65, 83 (2014).\n[5] Y. Wu, F. Jelezko, M. B. Plenio, and T. Weil, \\Dia-\nmond quantum devices in biology,\" Angewandte Chemie\nInternational Edition 55, 6586 (2016).\n[6] S. Lourette, L. Bougas, M. Kayci, S. Xu, and\nD. Budker, \\Noncovalent force spectroscopy using wide-\n\feld optical and diamond-based magnetic imaging,\"\narXiv:1908.10052 (2019).\n[7] S. Steinert, F. Ziem, L. T. Hall, A. Zappe, M. Schweik-\nert, N. G otz, A. Aird, G. Balasubramanian, L. Hollen-\nberg, and J. Wrachtrup, \\Magnetic spin imaging under\nambient conditions with sub-cellular resolution,\" Nature\nCommunications 4, 1607 (2013).\n[8] D. R. Glenn, K. Lee, H. Park, R. Weissleder, A. Ya-\ncoby, M. D. Lukin, H. Lee, R. L. Walsworth, and C. B.\nConnolly, \\Single-cell magnetic imaging using a quantum\ndiamond microscope,\" Nature Methods 12, 736 (2015).\n[9] I. Fescenko, A. Laraoui, J. Smits, N. Mosavian, P. Ke-\nhayias, J. Seto, L. Bougas, A. Jarmola, and V. M.\nAcosta, \\Diamond magnetic microscopy of malarial\nhemozoin nanocrystals,\" Physical Review Applied 11,\n034029 (2019).\n[10] J. M. McCoey, M. Matsuoka, R. W. de Gille, L. T. Hall,\nJ. A. Shaw, J.-P. Tetienne, D. Kisailus, L. C. L. Hollen-\nberg, and D. A. Simpson, \\Quantum magnetic imaging\nof iron biomineralisation in teeth of the chiton Acantho-\npleura hirtosa ,\" arXiv:1902.09637 (2019).\n[11] J. F. Barry, M. J. Turner, J. M. Schloss, D. R. Glenn,\nY. Song, M. D. Lukin, H. Park, and R. L. Walsworth,\n\\Optical magnetic detection of single-neuron action po-\ntentials using quantum defects in diamond,\" Proceedings\nof the National Academy of Sciences 113, 14133 (2016).\n[12] A. Nowodzinski, M. Chipaux, L. Toraille, V. Jacques, J.-\nF. Roch, and T. Debuisschert, \\Nitrogen-vacancy cen-\nters in diamond for current imaging at the redistributive\nlayer level of integrated circuits,\" Microelectronics Reli-\nability 55, 1549 (2015).\n[13] A. Horsley, P. Appel, J. Wolters, J. Achard, A. Tal-\nlaire, P. Maletinsky, and P. Treutlein, \\Microwave device\ncharacterization using a wide\feld diamond microscope,\"\nPhysical Review Applied 10, 044039 (2018).\n[14] D. R. Glenn, D. B. Bucher, J. Lee, M. D. Lukin, H. Park,\nand R. L. Walsworth, \\High-resolution magnetic reso-\nnance spectroscopy using a solid-state spin sensor,\" Na-\nture555, 351 (2018).\n[15] J. Smits, J. T. Damron, P. Kehayias, A. F. McDowell,\nN. Mosavian, I. Fescenko, N. Risto\u000b, A. Laraoui, A. Jar-\nmola, and V. M. Acosta, \\Two-dimensional nuclear mag-\nnetic resonance spectroscopy with a micro\ruidic diamond\nquantum sensor,\" Science Advances 5, eaaw7895 (2019).\n[16] J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner,\nC. A. Hart, L. M. Pham, and R. L. Walsworth, \\Sen-\nsitivity optimization for NV-diamond magnetometry,\"\narXiv:1903.08176 (2019).\n[17] T. Wolf, P. Neumann, K. Nakamura, H. Sumiya,\nT. Ohshima, J. Isoya, and J. Wrachtrup, \\Subpicotesla\ndiamond magnetometry,\" Physical Review X 5, 041001\n(2015).\n[18] G. Chatzidrosos, A. Wickenbrock, L. Bougas, N. Leefer,\nT. Wu, K. Jensen, Y. Dumeige, and D. Budker, \\Minia-\nture cavity-enhanced diamond magnetometer,\" Physical\nReview Applied 8, 044019 (2017).[19] E. Boto, R. Bowtell, P. Krger, T. M. Fromhold, P. G.\nMorris, S. S. Meyer, G. R. Barnes, and M. J. Brookes,\n\\On the potential of a new generation of magnetometers\nfor MEG: A beamformer simulation study,\" PLoS ONE\n11, e0157655 (2016).\n[20] J. Lenz and S. Edelstein, \\Magnetic sensors and their\napplications,\" IEEE Sensors Journal 6, 631 (2006).\n[21] P. Frontera, S. Alessandrini, and J. Stetson, \\Shipboard\ncalibration of a diamond nitrogen vacancy magnetic \feld\nsensor,\" in 2018 IEEE/ION Position, Location and Nav-\nigation Symposium (PLANS) (2018) pp. 497{504.\n[22] K. Fang, V. M. Acosta, C. Santori, Z. Huang, K. M.\nItoh, H. Watanabe, S. Shikata, and R. G. Beausoleil,\n\\High-sensitivity magnetometry based on quantum beats\nin diamond nitrogen-vacancy centers,\" Physical Review\nLetters 110, 130802 (2013).\n[23] E. Bauch, C. A. Hart, J. M. Schloss, M. J. Turner, J. F.\nBarry, P. Kehayias, S. Singh, and R. L. Walsworth, \\Ul-\ntralong dephasing times in solid-state spin ensembles via\nquantum control,\" Physical Review X 8, 031025 (2018).\n[24] V. M. Acosta, E. Bauch, M. P. Ledbetter, C. Santori,\nK.-M. C. Fu, P. E. Barclay, R. G. Beausoleil, H. Linget,\nJ. F. Roch, F. Treussart, S. Chemerisov, W. Gawlik, and\nD. Budker, \\Diamonds with a high density of nitrogen-\nvacancy centers for magnetometry applications,\" Physi-\ncal Review B 80, 115202 (2009).\n[25] S. Chakravarthi, C. Moore, A. Opsvig, E. Hunt,\nA. Ivanov, I. Christen, S. Dunham, and K.-M. C. Fu,\n\\A window into NV center kinetics via repeated anneal-\ning and spatial tracking of thousands of individual NV\ncenters,\" arXiv:1907.07793 (2019).\n[26] T. R. Eichhorn, C. A. McLellan, and A. C. B. Jayich,\n\\Optimizing the formation of depth-con\fned nitrogen va-\ncancy center spin ensembles in diamond for quantum\nsensing,\" arXiv:1901.11519 (2019).\n[27] G. de Lange, T. van der Sar, M. Blok, Z.-H. Wang, V. Do-\nbrovitski, and R. Hanson, \\Controlling the quantum dy-\nnamics of a mesoscopic spin bath in diamond,\" Scienti\fc\nReports 2, 382 (2012).\n[28] H. Ozawa, Y. Hatano, T. Iwasaki, Y. Harada, and\nM. Hatano, \\Formation of perfectly aligned high-density\nNV centers in (111) CVD-grown diamonds for magnetic\n\feld imaging of magnetic particles,\" Japanese Journal of\nApplied Physics 58, SIIB26 (2019).\n[29] C. Osterkamp, M. Mangold, J. Lang, P. Balasubrama-\nnian, T. Teraji, B. Naydenov, and F. Jelezko, \\Engineer-\ning preferentially-aligned nitrogen-vacancy centre ensem-\nbles in CVD grown diamond,\" Scienti\fc Reports 9, 5786\n(2019).\n[30] K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M.\nAcosta, P. Kehayias, B. Patton, and D. Budker, \\Cavity-\nenhanced room-temperature magnetometry using ab-\nsorption by nitrogen-vacancy centers in diamond,\" Phys-\nical Review Letters 112, 160802 (2014).\n[31] B. J. Shields, Q. P. Unterreithmeier, N. P. de Leon,\nH. Park, and M. D. Lukin, \\E\u000ecient readout of a sin-\ngle spin state in diamond via spin-to-charge conversion,\"\nPhysical Review Letters 114, 136402 (2015).\n[32] E. Bourgeois, A. Jarmola, P. Siyushev, M. Gulka,\nJ. Hruby, F. Jelezko, D. Budker, and M. Nesladek,\n\\Photoelectric detection of electron spin resonance of\nnitrogen-vacancy centres in diamond,\" Nature Commu-\nnications 6, 8577 (2015).\n[33] D. A. Hopper, R. R. Grote, A. L. Exarhos, and L. C.18\nBassett, \\Near-infrared-assisted charge control and spin\nreadout of the nitrogen-vacancy center in diamond,\"\nPhysical Review B 94, 241201 (2016).\n[34] P. Leroy, C. Coillot, A. F. Roux, and G. M. Chanteur,\n\\High magnetic \feld ampli\fcation for improving the sen-\nsitivity of Hall sensors,\" IEEE Sensors Journal 6, 707\n(2006).\n[35] M. J. Caruso, T. Bratland, C. H. Smith, and R. Schnei-\nder, \\A new perspective on magnetic \feld sensing,\" Sen-\nsors (Peterborough, NH) 15, 34 (1998).\n[36] R. C. Chaves, P. P. Freitas, B. Ocker, and W. Maass,\n\\MgO based picotesla \feld sensors,\" Journal of Applied\nPhysics 103, 07E931 (2008).\n[37] S. Bondarenko, A. Shablo, P. Pavlov, and S. Perepelkin,\n\\Ferromagnetic concentrator of a magnetic \feld for the\nplanar HTSC SQUID,\" Physica C: Superconductivity\n372-376 , 158 (2002).\n[38] W. C. Gri\u000eth, R. Jimenez-Martinez, V. Shah,\nS. Knappe, and J. Kitching, \\Miniature atomic mag-\nnetometer integrated with \rux concentrators,\" Applied\nPhysics Letters 94, 023502 (2009).\n[39] Y. J. Kim and I. Savukov, \\Ultra-sensitive magnetic mi-\ncroscopy with an optically pumped magnetometer,\" Sci-\nenti\fc Reports 6, 24773 (2016).\n[40] D. M. Toyli, D. J. Christle, A. Alkauskas, B. B. Buckley,\nC. G. Van de Walle, and D. D. Awschalom, \\Measure-\nment and control of single nitrogen-vacancy center spins\nabove 600 K,\" Physical Review X 2, 031001 (2012).\n[41] R. S. Schoenfeld and W. Harneit, \\Real time magnetic\n\feld sensing and imaging using a single spin in diamond,\"\nPhysical Review Letters 106, 030802 (2011).\n[42] C. S. Shin, C. E. Avalos, M. C. Butler, D. R. Trease,\nS. J. Seltzer, J. Peter Mustonen, D. J. Kennedy, V. M.\nAcosta, D. Budker, A. Pines, and V. S. Bajaj, \\Room-\ntemperature operation of a radiofrequency diamond mag-netometer near the shot-noise limit,\" Journal of Applied\nPhysics 112, 124519 (2012).\n[43] H. Clevenson, M. E. Trusheim, C. Teale, T. Schr oder,\nD. Braje, and D. Englund, \\Broadband magnetometry\nand temperature sensing with a light-trapping diamond\nwaveguide,\" Nature Physics 11, 393 (2015).\n[44] J. M. Schloss, J. F. Barry, M. J. Turner, and R. L.\nWalsworth, \\Simultaneous broadband vector magnetom-\netry using solid-state spins,\" Physical Review Applied\n10, 034044 (2018).\n[45] H. Clevenson, L. M. Pham, C. Teale, K. Johnson, D. En-\nglund, and D. Braje, \\Robust high-dynamic-range vec-\ntor magnetometry with nitrogen-vacancy centers in dia-\nmond,\" Applied Physics Letters 112, 252406 (2018).\n[46] H. Zheng, J. Xu, G. Z. Iwata, T. Lenz, J. Michl,\nB. Yavkin, K. Nakamura, H. Sumiya, T. Ohshima,\nJ. Isoya, J. Wrachtrup, A. Wickenbrock, and D. Bud-\nker, \\Zero-\feld magnetometry based on nitrogen-vacancy\nensembles in diamond,\" Physical Review Applied 11,\n064068 (2019).\n[47] S. K. Lee and M. V. Romalis, \\Calculation of magnetic\n\feld noise from high-permeability magnetic shields and\nconducting objects with simple geometry,\" Journal of\nApplied Physics 103(2008).\n[48] P.-H. Chu, Y. J. Kim, and I. Savukov, \\Search for\nexotic spin-dependent interactions with a spin-exchange\nrelaxation-free magnetometer,\" Physical Review D 94,\n036002 (2016).\n[49] S. Rochester and D. Budker, \\\"Nitrogen-Vacancy centers\nin diamond\",\" Budker Group Physics Tutorials (2013).\n[50] N. Bowler, \\Frequency-dependence of relative perme-\nability in steel,\" AIP Conference Proceedings 820, 1269\n(2006).\n[51] T. W. Kornack, S. J. Smullin, S.-K. Lee, and M. V.\nRomalis, \\A low-noise ferrite magnetic shield,\" Applied\nPhysics Letters 90, 223501 (2007)."    },    {        "title": "1804.09599v1.Nonreciprocity_in_microwave_optomechanical_circuits.pdf",        "content": "Nonreciprocity in microwave optomechanical circuits\nN. R. Bernier,1L. D. T\u0013 oth,1A. K. Feofanov,1,\u0003and T. J. Kippenberg1,y\n1Institute of Physics, \u0013Ecole Polytechnique F\u0013 ed\u0013 erale de Lausanne, Lausanne 1015, Switzerland\n(Dated: April 26, 2018)\nNonreciprocal devices such as isolators and circulators are necessary to protect sensitive apparatus\nfrom unwanted noise. Recently, a variety of alternatives were proposed to replace ferrite-based\ncommercial technologies, with the motivation to be integrated with microwave superconducting\nquantum circuits. Here, we review isolators realized with microwave optomechanical circuits and\npresent a gyrator-based picture to develop an intuition on the origin of nonreciprocity in these\nsystems. Such nonreciprocal optomechanical schemes show promise as they can be extended to\ncirculators and directional ampli\fers, with perspectives to reach the quantum limit in terms of\nadded noise.\nI. INTRODUCTION\nNonreciprocal devices, such as isolators, circulators,\nand directional ampli\fers, are pivotal components for\nquantum information processing with superconducting\ncircuits because they protect sensitive quantum states\nfrom readout electronics backaction. The commercial\nFaraday-e\u000bect devices typically used in these applica-\ntions have a large size and weight that require bigger\nand more powerful dilution refrigerators, contain ferro-\nmagnetic material that does not allow them to be placed\nclose to the quantum processor, and cause losses that\nlimit the readout \fdelity of the measurement chain. In\nrecent years, with major advances in superconducting\nquantum circuits [1] and attempts to scale-up quantum\nprocessors, these shortcomings have called for chip-scale\nlossless nonreciprocal devices without ferromagnetic ma-\nterials [2].\nThere have been numerous demonstrations of para-\nmetric nonreciprocal devices harnessing three-wave mix-\ning in dc-SQUIDs or Josephson parametric converters\n(JPCs). A three-mode nonlinear superconducting cir-\ncuit using a dc-SQUID and two linear LC-resonators\nwas engineered to implement a recon\fgurable frequency-\nconverting three-port circulator or directional ampli-\n\fer [3, 4]. Similar functionality was achieved using a\nsingle-stage JPC [5]. Meanwhile, two coupled JPCs en-\nabled implementation of frequency-preserving Josephson\ndirectional ampli\fers [6{8] and a gyrator [9], which can\neasily be converted into a four-port circulator. A four-\nport on-chip superconducting circulator was also demon-\nstrated using a combination of frequency conversion and\ndelay [10], which can be viewed as a \\synthetic rota-\ntion\" [11].\nAnother class of superconducting devices that ex-\nhibit directionality is travelling-wave parametric am-\npli\fers (TWPAs) [12]. Near-quantum-limited TWPAs\nwere realized employing nonlinearity of Josephson junc-\ntions [13, 14] and kinetic inductance [15, 16]. The direc-\n\u0003alexey.feofanov@ep\r.ch\nytobias.kippenberg@ep\r.chtionality of the TWPA gain arises from phase matching\nof the parametric interaction, since ampli\fcation occurs\nonly when the signal is copropagating with the pump.\nTherefore, the signal travelling in the reverse direction\nstays unmodi\fed: the reverse gain of an ideal TWPA\nis 0 dB. Another intrinsically directional ampli\fer uti-\nlizes a superconducting low-inductance undulatory gal-\nvanometer (SLUG, a version of a dc-SQUID) [17] in a\n\fnite voltage state. In contrast to TWPAs, SLUG mi-\ncrowave ampli\fers feature reverse isolation comparable\nto commercial isolators [18].\nSimilarly, nonreciprocal devices can be engineered us-\ning the nonlinearity of the optomechanical coupling [19]\nboth in the optical and microwave domains. The \frst\nproposal of an optomechanical nonreciprocal device con-\nsidered a travelling-wave geometry [20] and was imple-\nmented in the optical domain [21, 22].\nA general approach to engineer nonreciprocal photon\ntransport compatible with optomechanical systems was\noutlined by Metelmann and Clerk [23]. The framework\nwas formulated in terms of interference between coherent\nand dissipative coupling channels linking two electromag-\nnetic modes. Closely following this proposal, an optical\nisolator and directional ampli\fer was demonstrated [24].\nAn alternative scheme that does not employ direct co-\nherent coupling between electromagnetic modes but only\noptomechanical interactions was implemented with su-\nperconducting circuits resulting in electromechanical iso-\nlators and circulators [25{27]. Near-quantum-limited\nphase-preserving and phase-sensitive electromechanical\nampli\fers can be engineered in a similar way [28].\nHere we explain the origin of nonreciprocity in elec-\ntromechanical circuits by using the gyrator-based isola-\ntor as a conceptual starting point. We then discuss the\nlimitations of the current experimental implementations\nof electromechanical nonreciprocal devices as well as the\nfuture prospects.\nII. THE GYRATOR-BASED ISOLATOR\nAny linear two-port device can be described by its scat-\ntering matrix S, linking the incoming modes ^ ai;into thearXiv:1804.09599v1  [quant-ph]  25 Apr 20182\noutgoing modes ^ ai;outby\n\u0012\n^a1;out\n^a2;out\u0013\n=\u0012\nS11S12\nS21S22\u0013 \u0012\n^a1;in\n^a2;in\u0013\n: (1)\nA starting de\fnition for nonreciprocity is that a device\nis nonreciprocal when S216=S12. Physically this corre-\nsponds to a modi\fcation of the scattering process when\ninput and output modes are interchanged.\nIn order to develop an intuitive picture for nonreciproc-\nity, we introduce the gyrator as a canonical nonreciprocal\nelement. The gyrator is a 2-port device which provides a\nnonreciprocal phase shift [29], as illustrated in \fg. 1a. In\none direction, it imparts a phase shift of \u0019, while in the\nother direction it leaves the signal unchanged. The scat-\ntering matrix of a lossless, matched gyrator is given by\nSgyr= (0 1\n\u00001 0). Recently, new implementations of mi-\ncrowave gyrators relying on the non-commutativity of\nfrequency and time translations [30] have been demon-\nstrated with Josephson junctions [9, 10]. The gyrator in\nitself is not commonly used in technological applications,\nbut rather as a fundamental nonreciprocal building block\nto construct other nonreciprocal devices.\nAn isolator is a useful nonreciprocal device that can be\nassembled from a gyrator and additional reciprocal ele-\nments [29]. A beam splitter can divide a signal in two;\none part goes through a gyrator while the other propa-\ngates with no phase shift. Recombining the signals with a\nsecond beam splitter results in a 4-port device that inter-\nferes the signal nonreciprocally, as illustrated in \fg. 2a.\nFor a signal injected in port 1, the recombined signal af-\nter the second beam splitter interferes destructively in\nport 4, but constructively in port 2. In contrast, a sig-\nnal injected from port 2, reaches port 3 instead of port\n1, since one arm of the signal is in this case subjected\nto a\u0019shift. Overall, the device is a four-port circula-\ntor that redirects each port to the next. To obtain a\ntwo-port isolator, two of the four ports are terminated\nby matched loads to absorb the unwanted signal. The\nscattering matrix for the remaining two ports is that of\nan ideal isolator, Sis= (0 0\n1 0):\nThe gyrator-based scheme helps to summarize three\nsu\u000ecient ingredients to realize an isolator. Firstly, an\nelement breaks reciprocity by inducing a nonreciprocal\nphase shift. Secondly, an additional path is introduced\nfor signals to interfere such that the scattering matrix\nbecomes asymmetric in the amplitude with jS21j6=jS12j.\nFinally, dissipation is required for an isolator, since its\nscattering matrix between the two ports is non-unitary\nand some signals must necessarily be redirected to an\nexternal degree of freedom. The gyrator-based isolator\nprovides a framework to understand how nonreciprocity\narises in microwave optomechanical implementations.\na\na\naineiπ\nainb\nˆa1 ˆa2e±iϕ\naing gΓm\nˆin\nˆˆˆFIG. 1. Gyrator and optomechanical coupling. a . The\ngyrator is a canonical nonreciprocal component. It is a two-\nport device, which adds a \u0019phase shift when a wave is travel-\ning one way but no phase shift in the reverse direction. b. A\nsimple multimode optomechanical system consists of two elec-\ntromagnetic modes coupled to the same mechanical oscillator.\nDue to the two microwave drive tones which linearize the op-\ntomechanical coupling, the conversion from ^ a1to ^a2formally\nimparts a nonreciprocal phase shift, similarly to the gyrator.\nIn the case of frequency conversion, this phase shift between\ntones at di\u000berent frequencies is not measureable, as it depends\non the reference frame.\nIII. NONRECIPROCITY IN\nOPTOMECHANICAL SYSTEMS\nMicrowave optomechanical schemes for nonreciprocity\nrely on scattering between coupled modes [3, 12]. As a\n\frst step towards optomechanical isolators, we introduce\noptomechanical frequency conversion [31] and how it re-\nlates to the gyrator.\nThe simplest optomechanical scheme to couple two\nelectromagnetic modes ^ a1and ^a2involves coupling them\nboth to the same mechanical oscillator ^b(\fg. 1b). The\noptomechanical coupling terms ~g0;i^ay\ni^ai(^b+^by) (i=\n1;2), whereg0;iis the vacuum coupling rate of ^ aiand\n^b, can be linearized by two applied tones, detuned by \u0001 i\nwith respect to each cavity resonance [19]. In a frame\nrotating at the pump frequencies, and keeping only the\nlinear terms and taking the rotating-wave approximation,\nthe e\u000bective Hamiltonian becomes [19]\nH=\u0000~\u00011^ay\n1^a1\u0000~\u00012^ay\n2^a2+~\nm^by^b\n+~g1\u0010\nei\u001e1^a1^by+e\u0000i\u001e1^ay\n1^b\u0011\n+~g2\u0010\nei\u001e2^a2^by+e\u0000i\u001e2^ay\n2^b\u0011\n;\n(2)\nwhere \n mis the mechanical frequency, gi=g0;ipnc;iis\nthe coupling rate enhanced by the photon number nc;i\ndue to the pump \feld, and \u001eiis the phase of each pump\n\feld. For the resonant case \u0001 1= \u0001 2=\u0000\nm, the fre-\nquency conversion between the two modes through me-\nchanical motion is characterized by the scattering matrix\nelements (at the center of the frequency conversion win-\ndow) [32]\nS21=2pC1C2\n1 +C1+C2ei(\u001e1\u0000\u001e2)andS12=S\u0003\n21;(3)\nwhere\u0014iis the energy decay rate of mode ^ ai, and\nCi= 4g2\ni=(\u0014i\u0000m) is the cooperativity with \u0000 mthe energy3\n50:50 50:50\ndiss.diss.in/out\nin/outa\nb c\nde\nˆa1 ˆa2g g1\n34\n2π\nφ\nJ\n ˆa1 ˆa2g g\nφ\ng gTransmissionTransmission\nFIG. 2. Gyrator-based isolator compared to op-\ntomechanical multimode schemes. a . An isolator can\nbe built by combining the gyrator with other reciprocal ele-\nments. By combining the gyrator with two beam splitters and\na transmission line, a four-port circulator is realized. Dissipa-\ntion (provided by line terminations) eliminates the unwanted\nports. b. The three-mode optomechanical isolator in which\ntwo electromagnetic modes have a direct coherent J-coupling,\nand interact through a shared mechanical mode. c. The four-\nmode optomechanical isolator, in which two electromagnetic\nmodes interact through to di\u000berent mechanical modes. d. In\nthe scheme (b), frequency conversion through the J-coupling\n(light blue) and through the mechanical modes (green) inter-\nfere di\u000berently in the forward and backward direction when\ncombined. e. In the scheme (c), the frequency conversion\nthrough each mechanical mode (green curves) are o\u000bset in\nfrequency to interfere in a nonreciprocal manner.\ndecay rate of the mechanical oscillator (for simplicity, the\ncavities are assumed to be overcoupled).\nWhile eq. (3) apparently ful\flls the condition S216=\nS12for nonreciprocity, the situation is more subtle due\nto the fact that the two modes are in fact at di\u000berent fre-\nquencies in the laboratory frame. The time-dependence\nfor the two modes can be written explicitly to under-\nstand where the issue lies. The \frst incoming mode\n^a1;in(t) =e\u0000!1tA1results in ^a2;out(t) =S21e\u0000i!2tA1and\nreciprocally the other mode ^ a2;in(t) =e\u0000i!2tA2results\nin ^a1;out(t) =S12e\u0000i!1tA2, where!iare the mode angu-\nlar frequencies and Aiare constant amplitudes. If a new\norigin of time t0is chosen, the \felds transform as ^ a0\ni(t) =\ne\u0000i!it0ai(t), equivalent to a frequency-dependent phase\nshift for each mode. In this new reference frame, the scat-\ntering matrix transforms as S0\n21=S21e\u0000i(!2\u0000!1)t0and\nS0\n12=S12e+i(!2\u0000!1)t0. For di\u000berent frequencies !16=!2,\nthere always exists a t0for which the phases of S21and\nS12are the same. A nonreciprocal phase shift is there-\nfore unphysical for frequency conversion, as the phase\ndepends on the chosen reference frame. For this reason,Ranzani and Aumentado [3] pose the stricter requirement\njS12j 6=jS21jfor nonreciprocity in coupled-modes sys-\ntems. The pump tones that linearize the optomechanical\ncoupling break reciprocity, as they are held \fxed when\ninput and output are interchanged and impose a \fxed\nphase\u001e1\u0000\u001e2for the coupling. Nevertheless, there is\nalways a frame with a di\u000berent origin of time in which\nthe two pumps have the same phase and \u001e0\n1\u0000\u001e0\n2= 0.\nIn that frame, the symmetry between the two ports is\napparently restored.\nWhile a change of the origin of time turns a phase-\nnonreciprocal system reciprocal for coupled-mode sys-\ntems, it simultaneously turns reciprocal systems phase-\nnonreciprocal. The isolator in \fg. 1B provides an ex-\nample (adding frequency conversion as a thought exper-\niment). With ( !2\u0000!1)t0=\u0019=2, the gyrator scatter-\ning matrix transforms from Sgyr= (0 1\n\u00001 0) toS0\ngyr=\nei\u0019=2(0 1\n1 0) while the transmission line scattering matrix\ntransforms from Stl= (0 1\n1 0) toS0\ntl=ei\u0019=2(0 1\n\u00001 0). In ef-\nfect, gyrators and transmission lines are mapped to each\nother. Importantly, the combination of a gyrator and\na transmission line is preserved. One interpretation is\nthat the frame-dependent nonreciprocal phase acts as a\ngauge symmetry, that can realize the Aharonov-Bohm\ne\u000bect when a loop is created [33{35]. To build an op-\ntomechanical isolator, one method is to realize two paths\nbetween ^a1and ^a2, one similar to a gyrator and the other\nto a transmission line, which can be done following one\nof two proposed schemes.\nThe \frst scheme, shown in \fg. 2b, combines an op-\ntomechanical link between two electromagnetic modes\n^a1and ^a2and a direct coherent coupling of strength\nJ. The interaction term of the latter, given by Hcoh=\n~J(ei\u0012^a1^ay\n2+e\u0000i\u0012^ay\n1^a2) induces by itself conversion be-\ntween the two modes as\nS21=2pCcoh\n1 +Ccohiei\u0012andS12=2pCcoh\n1 +Ccohie\u0000i\u0012(4)\nwhereCcoh= 4J2=(\u00141\u00142). Compared to eq. (3), there\nis an intrinsic reciprocal phase shift of i=ei\u0019=2. By\nchoosing the phases \u001e1=\u001e2and\u0012=\u0019=2, the op-\ntomechanical link realizes a reciprocal transmission line\nwhile the coherent link breaks the symmetry and real-\nizes a gyrator. The combination, with matching cou-\npling rates, functions as an isolator between the modes\n^a1and ^a2. One cannot tell which of the optomechan-\nical or direct link breaks reciprocity, as it depends on\nthe chosen frame. Nonetheless, there is a gauge-invariant\nphase\u001e=\u001e1\u0000\u001e2+\u0012that globally characterizes the bro-\nken symmetry and can be seen as a synthetic magnetic\n\rux[24, 36].\nThe second scheme to realize isolation, shown in \fg. 2c,\nuses two optomechanical conversion links with two di\u000ber-\nent mechanical modes. From eq. (3), one cannot realize\nthe scattering matrices of a gyrator and a transmission\nline with the same reciprocal phase factor. Dissipation of\nthe mechanical modes is the key to tune the overall re-\nciprocal phase factor of conversion. By detuning the two4\nmechanical modes in frequency, the mechanical suscepti-\nbilities induce di\u000berent phases. Advantageously over the\n\frst scheme, no direct coherent coupling must be engi-\nneered and the modes ^ a1and ^a2do not need to have the\nsame frequency.\nThe \frst scheme (\fg. 2b) derives from a proposal by\nMetelmann and Clerk [23], who describe the optome-\nchanical link as an e\u000bective dissipative interaction be-\ntween the modes ^ a1and ^a2. This coupling is equiv-\nalent to a non-Hermitian Hamiltonian term Hdis=\n\u0000i~\u0000dis(ei(\u001e1\u0000\u001e2)^a1^ay\n2+e\u0000i(\u001e1\u0000\u001e2)^ay\n1^a2) with \u0000 dis=\n2g1g2=\u0000m. With suitable parameters, the total interac-\ntionHcoh+Hdiscan be made unidirectional, with for in-\nstance a term proportional to ^ ay\n1^a2but not ^a1^ay\n2. We note\nthat while only the case of resonant modes is considered\nhere, a direct coherent J-coupling can also be realized\nbetween modes at di\u000berent frequencies using parametric\ninteractions. The second scheme (\fg. 2c) can also be un-\nderstood in that framework, as each detuned mechanical\nconversion link is equivalent to an e\u000bective interaction\nbetween the modes ^ a1and ^a2with both a coherent and\na dissipative component. The total e\u000bective interaction\ncan be made unidirectional when the total direct coher-\nent interaction matches the total dissipative interaction\nand they interfere.\nBoth methods to achieve nonreciprocal isolation can be\ndecomposed in terms of the three ingredients identi\fed\nin the gyrator-based isolator. At the heart is the break-\ning of reciprocity that occurs through the time-dependent\ndrives applied to the system that impart a complex phase\nto the interaction. Then a loop constituted by two arms\nallow the unwanted signal to be canceled in the backward\ndirection through destructive interference while preserv-\ning it in the forward direction. The mechanical dissipa-\ntive baths are used to eliminate the backward signal. As\na consequence, the nonreciprocal bandwidth (where S21\nandS12di\u000ber) is limited by the mechanical dissipation\nrates, as illustrated in \fg. 2d and e. Dissipation plays a\ndouble role here, since it also gives the di\u000berent recipro-\ncal phase shift in each arms necessary to implement both\na gyrator and a transmission line.\nIV. EXPERIMENTAL REALIZATIONS\nMicrowave optomechanics is uniquely suited to im-\nplement the mode structure presented in \fg. 2b,c and\nachieve the nonreciprocal frequency conversion described\nabove. The electromagnetic (EM) modes are here modes\nof a superconductive LC resonator and the mechanical\nmodes are modes of the vibrating top plate of a vacuum-\ngap capacitor.\nIt turns out that the \frst, seemingly simplest, scheme\nshown in \fg. 2c, in which two EM modes are coupled to\none mechanical element as well as to each other through\na direct coherent coupling, poses engineering challenges.\nThe two EM modes must have the same resonance fre-\nquencies (within their linewidth) and the \fxed direct\na\nb\nc\ndFIG. 3. Experimental realization of nonreciprocal fre-\nquency conversion in a microwave optomechanical cir-\ncuit. (\fgure adapted from Bernier et al. [25]) a. In order the\nrealize the mode structure of \fg. 2c, a multimode electrome-\nchanical circuit can be constructed. In the example shown,\nthe circuit supports two modes, each coupled to the motion\nof the top plate of a vacuum-gap capacitor that supports two\nvibrational modes. b. Transmission linear response of the\nfrequency conversion between the modes ^ a1and ^a2, in both\ndirection, for two phases \u001efor which the circuit acts as an\nisolator in one direction and the other. c. Noise emission\nNfwin the forward direction of the isolator, corresponding to\nthe added noise to the signal. d. Noise emission Nbwin the\nbackward direction, displaying large power in the isolation\nbandwidth, as the mechanical bath noise is directly coupled\nto the input port.\nJ-coupling must be strong enough to achieve Ccoh\u0019\n1. Despite these di\u000eculties, an analogous scheme has\nbeen implemented in the optical domain, in which two\nphotonic-crystal modes are each coupled to a phononic-\ncrystal mode and two direct coherent optical-optical and\nmechanical-mechanical link are realized through waveg-\nuide buses [24]. The scheme is equivalent to the mode\nstructure in \fg. 2b as the e\u000bective interaction through\nthe two mechanical modes is similar to that through a\nsingle one.\nBy contrast, the simpler plaquette of the second\nscheme in \fg. 2c, that requires only optomechanical inter-\nactions and no frequency tuning, has been realized in mi-\ncrowave optomechanical circuits [25{27]. Two microwave\nmodes of a superconducting circuit are both coupled to\ntwo vibrational modes of the top plate of a capacitor. An5\nexample circuit is shown in \fg. 3a [25]. These systems\nare inherently frequency converting as the two microwave\nmodes have di\u000berent resonance frequencies. The optome-\nchanical couplings are established through four phase-\nlocked microwave pump tones slightly detuned from the\nlower motional sidebands of each mode. Two frequency\nconversion windows open, one through each mechanical\nmode, and interfere with each other. By varying the rel-\native phases of each pump tone, the gauge-independent\nphase\u001ecan be tuned, realizing the isolator scheme of\n\fg. 2c,e. An example of the measured nonreciprocal\ntransmission is shown in \fg. 3b for two values of \u001efor\nwhich the system isolates in each direction. There is no\nlimitation on the achievable depth of isolation in these\nsystems. However, since the scheme relies on the me-\nchanical dissipation to absorb the unwanted backward\nsignal, the nonreciprocal bandwidth is limited the bare\nenergy decay rate of the mechanical modes, typically in\nthe 10 - 100 Hz range, although it can be e\u000bectively in-\ncreased by external damping.\nAn important aspect of the nonreciprocal devices\nbased on the optomechanical interaction is their noise\nperformance. It is apparent from the gyrator scheme pre-\nsented in section II and shown in \fg. 2a that the dissipa-\ntive elements terminating the unwanted ports modes in\nturn emit back their respective thermal noise into the sys-\ntem. In the forward direction (\fg. 3c), the emitted noise,\ncorresponding to the added noise to the signal, is spread\nover a wide bandwidth and can be made quantum-limited\nin the high-cooperativity regime. In the backward direc-\ntion however (\fg. 3d), noise commensurate with the high\nthermal occupancy of the mechanical baths is directly\nemitted back from the input port, within the isolation\nbandwidth. External cooling of the mechanical modes\nis therefore required for the optomechanical isolator to\nprotect sensitive quantum devices from back-propagatingnoise.\nV. CONCLUSION AND OUTLOOK\nMicrowave optomechanical circuits form a new plat-\nform to design nonreciprocal devices that could be inte-\ngrated with superconducting quantum circuits. Current\nrealizations for isolators su\u000ber from a narrow bandwidth,\nlimited by the mechanical dissipation rates, as well as\nfrom high back-propagating noise. External cooling of\nthe mechanical oscillators can mitigate both issues. Mi-\ncrowave circulators realized with the same technology[27]\nprovide a better solution leading to quantum-limited\nnoise and a nonreciprocal bandwidth only limited by\nthe dissipation rates of the cavities [25]. Furthermore,\ndirectional ampli\fcation can be implemented with the\nsame structures as isolators, both phase-preserving and\nquadrature dependent, with prospects to reach the quan-\ntum limit in terms of added noise [28]. Optomechanical\nnonreciprocal devices have intrinsic limits to their band-\nwidth, but their frequencies can be made adjustable [37]\nand certain applications might bene\ft from the versatil-\nity of such tunable narrow-band nonreciprocal devices.\nComment This manuscript was submitted as a contri-\nbution to a special issue titled \\Magnet-less Nonreciproc-\nity in Electromagnetics\" to appear in IEEE Antennas and\nWireless Propagation Letters.\nACKNOWLEDGMENTS\nThis work was supported by the SNF, the NCCR\nQSIT, and the EU H2020 programme under grant agree-\nment No 732894 (FET Proactive HOT). T.J.K. acknowl-\nedges \fnancial support from an ERC AdG (QuREM).\n[1] M. H. Devoret and R. J. Schoelkopf, \\Superconducting\ncircuits for quantum information: An outlook,\" Science ,\nvol. 339, p. 1169, 2013.\n[2] A. Kamal, J. Clarke, and M. H. Devoret, \\Noiseless\nnon-reciprocity in a parametric active device,\" Nature\nPhysics , vol. 7, no. 4, pp. 311{315, Apr. 2011. [Online].\nAvailable: http://www.nature.com/nphys/journal/v7/\nn4/abs/nphys1893.html\n[3] L. Ranzani and J. Aumentado, \\Graph-based analysis of\nnonreciprocity in coupled-mode systems,\" New Journal\nof Physics , vol. 17, no. 2, p. 023024, 2015. [Online].\nAvailable: http://stacks.iop.org/1367-2630/17/i=2/a=\n023024\n[4] F. Lecocq, L. Ranzani, G. A. Peterson, K. Cicak,\nR. W. Simmonds, J. D. Teufel, and J. Aumentado,\n\\Nonreciprocal microwave signal processing with a \feld-\nprogrammable josephson ampli\fer,\" Phys. Rev. Applied ,\nvol. 7, p. 024028, Feb 2017. [Online]. Available: https:\n//link.aps.org/doi/10.1103/PhysRevApplied.7.024028\n[5] K. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio,R. Schoelkopf, and M. Devoret, \\Recon\fgurable\nJosephson Circulator/Directional Ampli\fer,\" Physical\nReview X , vol. 5, no. 4, p. 041020, Nov. 2015. [Online].\nAvailable: http://link.aps.org/doi/10.1103/PhysRevX.\n5.041020\n[6] B. Abdo, K. Sliwa, L. Frunzio, and M. Devoret,\n\\Directional Ampli\fcation with a Josephson Circuit,\"\nPhysical Review X , vol. 3, no. 3, p. 031001, Jul.\n2013. [Online]. Available: http://link.aps.org/doi/10.\n1103/PhysRevX.3.031001\n[7] B. Abdo, K. Sliwa, S. Shankar, M. Hatridge, L. Frunzio,\nR. Schoelkopf, and M. Devoret, \\Josephson Directional\nAmpli\fer for Quantum Measurement of Superconducting\nCircuits,\" Physical Review Letters , vol. 112, no. 16,\np. 167701, Apr. 2014. [Online]. Available: http:\n//link.aps.org/doi/10.1103/PhysRevLett.112.167701\n[8] B. Abdo, N. T. Bronn, O. Jinka, S. Olivadese, M. Brink,\nand J. M. Chow, \\Multi-path interferometric josephson\ndirectional ampli\fer for qubit readout,\" Quantum\nScience and Technology , vol. 3, no. 2, p. 024003, 2018.6\n[Online]. Available: http://stacks.iop.org/2058-9565/3/\ni=2/a=024003\n[9] B. Abdo, M. Brink, and J. M. Chow, \\Gyrator Opera-\ntion Using Josephson Mixers,\" Physical Review Applied ,\nvol. 8, no. 3, p. 034009, Sep. 2017.\n[10] B. J. Chapman, E. I. Rosenthal, J. Kerckho\u000b, B. A.\nMoores, L. R. Vale, J. A. B. Mates, G. C. Hilton, K. La-\nlumi\u0012 ere, A. Blais, and K. W. Lehnert, \\Widely Tun-\nable On-Chip Microwave Circulator for Superconducting\nQuantum Circuits,\" Physical Review X , vol. 7, no. 4, p.\n041043, Nov. 2017.\n[11] J. Kerckho\u000b, K. Lalumi\u0012 ere, B. J. Chapman, A. Blais, and\nK. W. Lehnert, \\On-Chip Superconducting Microwave\nCirculator from Synthetic Rotation,\" Physical Review\nApplied , vol. 4, no. 3, p. 034002, Sep. 2015.\n[12] L. Ranzani and J. Aumentado, \\A geometric description\nof nonreciprocity in coupled two-mode systems,\" New\nJournal of Physics , vol. 16, no. 10, p. 103027, 2014.\n[Online]. Available: http://stacks.iop.org/1367-2630/\n16/i=10/a=103027\n[13] T. C. White, J. Y. Mutus, I.-C. Hoi, R. Barends,\nB. Campbell, Y. Chen, Z. Chen, B. Chiaro,\nA. Dunsworth, E. Je\u000brey, J. Kelly, A. Megrant, C. Neill,\nP. J. J. O'Malley, P. Roushan, D. Sank, A. Vainsencher,\nJ. Wenner, S. Chaudhuri, J. Gao, and J. M. Marti-\nnis, \\Traveling wave parametric ampli\fer with Joseph-\nson junctions using minimal resonator phase matching,\"\nApplied Physics Letters , vol. 106, no. 24, p. 242601, Jun.\n2015.\n[14] C. Macklin, K. O'Brien, D. Hover, M. E. Schwartz,\nV. Bolkhovsky, X. Zhang, W. D. Oliver, and\nI. Siddiqi, \\A near{quantum-limited Josephson traveling-\nwave parametric ampli\fer,\" Science , vol. 350, no.\n6258, pp. 307{310, Oct. 2015. [Online]. Available:\nhttp://science.sciencemag.org/content/350/6258/307\n[15] B. Ho Eom, P. K. Day, H. G. LeDuc, and\nJ. Zmuidzinas, \\A wideband, low-noise superconducting\nampli\fer with high dynamic range,\" Nature Physics ,\nvol. 8, pp. 623{627, 07 2012. [Online]. Available:\nhttp://dx.doi.org/10.1038/nphys2356\n[16] M. R. Vissers, R. P. Erickson, H.-S. Ku, L. Vale,\nX. Wu, G. C. Hilton, and D. P. Pappas, \\Low-\nnoise kinetic inductance traveling-wave ampli\fer using\nthree-wave mixing,\" Applied Physics Letters , vol.\n108, no. 1, p. 012601, 2016. [Online]. Available:\nhttps://doi.org/10.1063/1.4937922\n[17] D. Hover, Y.-F. Chen, G. J. Ribeill, S. Zhu,\nS. Sendelbach, and R. McDermott, \\Superconducting\nlow-inductance undulatory galvanometer microwave\nampli\fer,\" Applied Physics Letters , vol. 100, no. 6, p.\n063503, 2012. [Online]. Available: https://doi.org/10.\n1063/1.3682309\n[18] T. Thorbeck, S. Zhu, E. Leonard, R. Barends, J. Kelly,\nJ. M. Martinis, and R. McDermott, \\Reverse isolation\nand backaction of the slug microwave ampli\fer,\"\nPhys. Rev. Applied , vol. 8, p. 054007, Nov 2017.\n[Online]. Available: https://link.aps.org/doi/10.1103/\nPhysRevApplied.8.054007\n[19] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt,\n\\Cavity optomechanics,\" Rev. Mod. Phys. , vol. 86,\npp. 1391{1452, Dec 2014. [Online]. Available: http:\n//link.aps.org/doi/10.1103/RevModPhys.86.1391\n[20] M. Hafezi and P. Rabl, \\Optomechanically induced\nnon-reciprocity in microring resonators,\" Optics Express ,vol. 20, no. 7, pp. 7672{7684, Mar. 2012. [Online].\nAvailable: http://www.osapublishing.org/abstract.cfm?\nuri=oe-20-7-7672\n[21] Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-\nF. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and\nC.-H. Dong, \\Experimental realization of optome-\nchanically induced non-reciprocity,\" Nature Photonics ,\nvol. 10, no. 10, pp. 657{661, Oct. 2016. [Online].\nAvailable: http://www.nature.com/nphoton/journal/\nv10/n10/full/nphoton.2016.161.html\n[22] F. Ruesink, M.-A. Miri, A. Al\u0012 u, and E. Verhagen, \\Non-\nreciprocity and magnetic-free isolation based on optome-\nchanical interactions,\" Nature Communications , vol. 7,\np. 13662, Nov. 2016.\n[23] A. Metelmann and A. Clerk, \\Nonreciprocal Pho-\nton Transmission and Ampli\fcation via Reser-\nvoir Engineering,\" Physical Review X , vol. 5,\nno. 2, p. 021025, Jun. 2015. [Online]. Available:\nhttp://link.aps.org/doi/10.1103/PhysRevX.5.021025\n[24] K. Fang, J. Luo, A. Metelmann, M. H. Matheny,\nF. Marquardt, A. A. Clerk, and O. Painter, \\Generalized\nnon-reciprocity in an optomechanical circuit via synthetic\nmagnetism and reservoir engineering,\" Nat Phys , vol. 13,\nno. 5, pp. 465{471, 05 2017. [Online]. Available:\nhttp://dx.doi.org/10.1038/nphys4009\n[25] N. R. Bernier, L. D. T\u0013 oth, A. Koottandavida, M. A.\nIoannou, D. Malz, A. Nunnenkamp, A. K. Feofanov,\nand T. J. Kippenberg, \\Nonreciprocal recon\fgurable\nmicrowave optomechanical circuit,\" Nature Communica-\ntions , vol. 8, no. 1, p. 604, Sep. 2017. [Online]. Available:\nhttps://www.nature.com/articles/s41467-017-00447-1\n[26] G. Peterson, F. Lecocq, K. Cicak, R. Simmonds,\nJ. Aumentado, and J. Teufel, \\Demonstration of\nE\u000ecient Nonreciprocity in a Microwave Optomechanical\nCircuit,\" Physical Review X , vol. 7, no. 3, p. 031001,\nJul. 2017. [Online]. Available: https://link.aps.org/doi/\n10.1103/PhysRevX.7.031001\n[27] S. Barzanjeh, M. Wulf, M. Peruzzo, M. Kalaee, P. B.\nDieterle, O. Painter, and J. M. Fink, \\Mechanical\non-chip microwave circulator,\" Nature Communications ,\nvol. 8, no. 1, p. 953, Oct. 2017. [Online]. Available:\nhttps://www.nature.com/articles/s41467-017-01304-x\n[28] D. Malz, L. D. T\u0013 oth, N. R. Bernier, A. K. Feofanov,\nT. J. Kippenberg, and A. Nunnenkamp, \\Quantum-\nlimited directional ampli\fers with optomechanics,\"\nPhys. Rev. Lett. , vol. 120, p. 023601, Jan 2018.\n[Online]. Available: https://link.aps.org/doi/10.1103/\nPhysRevLett.120.023601\n[29] D. M. Pozar, Microwave Engineering , 4th ed. Wiley,\n2011.\n[30] E. I. Rosenthal, B. J. Chapman, A. P. Higginbotham,\nJ. Kerckho\u000b, and K. W. Lehnert, \\Breaking Lorentz\nReciprocity with Frequency Conversion and Delay,\"\nPhysical Review Letters , vol. 119, no. 14, p. 147703, Oct.\n2017.\n[31] F. Lecocq, J. Clark, R. Simmonds, J. Aumentado, and\nJ. Teufel, \\Mechanically Mediated Microwave Frequency\nConversion in the Quantum Regime,\" Physical Review\nLetters , vol. 116, no. 4, p. 043601, Jan. 2016.\n[Online]. Available: http://link.aps.org/doi/10.1103/\nPhysRevLett.116.043601\n[32] A. H. Safavi-Naeini and O. Painter, \\Proposal for an op-\ntomechanical traveling wave phonon{photon translator,\"\nNew Journal of Physics , vol. 13, no. 1, p. 013017, 2011.7\n[33] K. Fang, Z. Yu, and S. Fan, \\Photonic Aharonov-Bohm\nE\u000bect Based on Dynamic Modulation,\" Physical Review\nLetters , vol. 108, no. 15, p. 153901, Apr. 2012.\n[34] ||, \\Experimental demonstration of a photonic\nAharonov-Bohm e\u000bect at radio frequencies,\" Physical\nReview B , vol. 87, no. 6, p. 060301, Feb. 2013.\n[35] L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan,\nand M. Lipson, \\Non-reciprocal phase shift induced\nby an e\u000bective magnetic \rux for light,\" Nature\nPhotonics , vol. 8, no. 9, pp. 701{705, Sep. 2014.\n[Online]. Available: http://www.nature.com/nphoton/journal/v8/n9/full/nphoton.2014.177.html#ref8\n[36] V. Peano, C. Brendel, M. Schmidt, and F. Marquardt,\n\\Topological Phases of Sound and Light,\" Physical\nReview X , vol. 5, no. 3, p. 031011, Jul. 2015. [Online].\nAvailable: http://link.aps.org/doi/10.1103/PhysRevX.\n5.031011\n[37] R. W. Andrews, A. P. Reed, K. Cicak, J. D. Teufel, and\nK. W. Lehnert, \\Quantum-enabled temporal and spec-\ntral mode conversion of microwave signals,\" Nature Com-\nmunications , vol. 6, p. 10021, Nov. 2015."    },    {        "title": "2309.15860v1.Greener_processing_of_SrFe___12__O___19___ceramic_permanent_magnets_by_two_step_sintering.pdf",        "content": "Ceramics International 47 (2021) 31765–31771\nAvailable online 12 August 2021\n0272-8842/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license\n(http://creativecommons.org/licenses/by-nc-nd/4.0/ ).Greener processing of SrFe 12O19 ceramic permanent magnets by \ntwo-step sintering \nJ.C. Guzm ˘an-Míngueza, V. Fuertesa,b, C. Granados-Mirallesa, J.F. Fern˘andeza, A. Quesadaa,* \naInstitute of Ceramics and Glass Materials (CSIC), Kelsen 5, 28049, Madrid, Spain \nbCenter for Optics, Photonics, and Lasers, Laval University, 2375 Terrasse street, Quebec, QC, G1V 0A6, Canada   \nARTICLE INFO  \nKeywords: \nPermanent magnets \nFerrites \nSintering \nMagnetic properties \nHard-soft composites ABSTRACT  \nWith an annual production amounting to 800 kilotons, ferrite magnets constitute the largest family of permanent \nmagnets in volume, a demand that will only increase as a consequence of the rare-earth crisis. With the global \ngoal of building a climate-resilient future, strategies towards a greener manufacturing of ferrite magnets are of \ngreat interest. A new ceramic processing route for obtaining dense Sr-ferrite sintered magnets is presented here. \nInstead of the usual sintering process employed nowadays in ferrite magnet manufacturing that demands long \ndwell times, a shorter two-step sintering is designed to densify the ferrite ceramics. As a result of these processes, \ndense SrFe 12O19 ceramic magnets with properties comparable to state-of-the-art ferrite magnets are obtained. In \nparticular, the SrFe 12O19 magnet containing 0.2% PVA and 0.6% wt SiO2 reaches a coercivity of 164 kA/m along \nwith a 93% relative density. A reduction of 31% in energy consumption is achieved in the thermal treatment with \nrespect to conventional sintering, which could lead to energy savings for the industry of the order of 7.109 kWh \nper year.   \n1.Introduction \nHexaferrites, particularly SrFe 12O19 (SFO), cover 80% of the volume \nof magnets that are sold every year, reaching an annual production of \n800 kilotons. This is due to the main advantages they offer that include \navailability, price and environmental friendliness during both mining \nand production [1,2]. Ferrite magnets are widely used in a variety of \napplications, of which electrical motors and sensors represent their \nlargest markets [3]. As for its magnetic properties, SFO presents high \ncoercivity and a moderate saturation magnetization [4–6]. This implies \nthat it is often the case that remanence magnetization is the limiting \nfactor in the energy density that a ferrite magnet can store, i.e. its energy \nproduct BHmax. Nevertheless, it is mandatory to achieve competitive \ncoercivity and density values in order to maximize BHmax, and both \nproperties strongly depend on the ceramic processing involved in the \nfabrication of ferrite sintered magnets [7–9]. \nThe pre-consolidation processing of the powder is important to \nensure a low degree of agglomeration of the ferrite particles for subse -\nquent magnetic alignment and compaction. One of the key balances in \nhexaferrite ceramics comes from the fact that massive grain growth, \nwhich damages coercivity, is activated at the temperatures required for proper densification [5,8,10–13]. It is well know that the use of addi-\ntives is crucial in tuning an appropriate microstructure. In particular, \nCaO and SiO2 are used together to control grain growth and its impact on \ncoercivity [11,14,15]. Recently, we have shown that it is possible to \nobtain dense ferrite ceramics with high coercivity using only SiO2 as an \nadditive [16,17]. Moreover, carefully designing the sintering schedule \nplays of course an important role as well in the final microstructure \n[18–20]. The most employed process at industrial level requires long \ndwell times, typically between 2 and 4 h, at 1200 •C and above (Fig. 1a), \nwhich has yielded traditionally high densities and moderate grain sizes \nin the presence of the aforementioned additives. \nGiven the remarkable volume of ferrite magnets that is produced \nevery year, efforts towards reducing the dwell time associated with their \nsintering could lead to significant energy savings. An alternative sin-\ntering treatment, that allows reducing the dwell time during sintering \ntreatment, is the well-known two-step sintering (TSS) process [17], with \nwhich high density values can be achieved without excessive grain \ngrowth. \nIn this work, we analyze the possibility to obtain high density and \nhigh coercivity SrFe 12O19 sintered magnets by combining for the first \ntime a pre-processing of the hexaferrite starting powder with a TSS \n*Corresponding author. \nE-mail address: jesus.guzman@icv.csic.es (A. Quesada).  \nContents lists available at ScienceDirect \nCeramics International \nu{�~zkw! s{yo|kr o>!ÐÐÐ1ow�o �to~1m{y2w{m k�o2mo~kyt z�!\nhttps://doi.org/10.1016/j.ceramint.2021.08.058 \nReceived 26 May 2021; Received in revised form 3 August 2021; Accepted 6 August 2021   Ceramics International 47 (2021) 31765–31771\n31766schedule that significantly reduces the overall duration of the consoli -\ndation step. \n2.Experimental \nFirstly, 0.2 wt% of PVA (Aldrich Chemical Company, Inc.) was added \nto an aqueous dissolution of commercial SrFe 12O19 (SFO) powders (Max \nBaermann GmbH 99.9%). This dissolution was homogenized and \ndispersed with the help of a high-shear mixer (Dissolver Simplex SL-1) \nby using a 5 cm in diameter cowless rotor and high solid content in \nwater suspension, typically 60% wt, by applying 1500 rpm during 10 \nmin. \nAfterwards, different percentages of SiO2 (0.2-0.4-0.6-1 %wt) were \nadded to the SFO/PVA solution and dispersed again with the help of \nDisolver Simplex SL-1. The resultant mix was dried, pressed under 200 MPa and sintered by way of a two-step sintering (TSS) process. In our \nsintering treatment (Fig. 1b 1c), a pressed sample is heated to an in-\ntermediate temperature (T1 1100 •C) at 5•/min, then quickly \nannealed at 20•/min to a higher temperature (T2 1225•C-1275 •C), \nafter a dwell between 0 and 10 min, the temperature rapidly drops (20•/ \nmin) to T1 and finally decreases to room-temperature at 3•/min. The use \nof this type of two-step cycle significantly reduces the sintering times \nfrom the 360 min required for conventional treatment to 240 min for \nTSS1 or 235 min for TSS2. \nNext, we subjected selected samples (SrFe 12O19 - 0.2% wt PVA with \n0.6% wt of SiO2) to a Spray drying process (SDP). The Spray drying \nmethod consists of two phases: 1) Particle formation: the atomization \nand the solvent evaporation take place and 2) Particle collection: dry \nand rounded particles are obtained. The rounded and dried powder \nobtained was pressed (while applying an external magnetic field in the \nfinal samples) and sintered by TSS. \nThe morphological and microstructural characterizations were car-\nried out by means of secondary electron images of field emission scan-\nning electron microscopy, FE-SEM (Hitachi S-4700). Powder X-ray \ndiffraction (PXRD) data were collected in a Bruker D8 Advance \ndiffractometer equipped with a Lynx Eye detector and a Cu target \n(λCuα1 1.54060 Å), after milling the sintered dense ceramics to \npowder. The PXRD data were fitted to a Rietveld model including \nSrFe 12O19 as the only phase and using the software FullProf. Crystallo -\ngraphic densities were calculated based on the refined unit cell param -\neters, a and c, and assuming all atomic sites of SrFe 12O19 are fully \noccupied by the due atoms. The relative density values were measured \nusing by the Archimedes method and 5.1 g/cm3 as the density value of \nSrFe 12O19, which was calculated from the PXRD patterns [1]. The \nmagnetic properties were evaluated using a homemade vibrating sample \nmagnetometer (VSM) [21]. The magnetization curves were measured at \nroom temperature by applying a maximum magnetic field of 1.3T. \n3.Results \nFig. 2 shows SEM micrographs of the SFO powder before and after \ndispersion in high shear with PVA. As can be seen in Fig. 2a and b, the \ninitial SFO powder contains agglomerates showing a bimodal size dis-\ntribution of particles consisting of irregular small particles 200–600 nm \nin size and large platelet type particles 1–5 μm in size. \nAfter mixing with PVA (Fig. 2c and d), we observe changes in the \nmorphology and distribution of the particles. The average size of the \nlarger particles is reduced to 1–2 μm and a more spherical shape is \nattained (without corners). These changes are likely the consequence of \nthe high shear forces occurring in the Dissolver mixer. In Fig. 2d, we \nobserve that the new agglomerates, although composed of smaller par-\nticles, appear to be arranged in larger structures. This is attributed to the \nencapsulation effect of adding PVA [22–24]. Higher amounts of PVA \n(not shown) resulted in larger agglomerates with more limited \ncompaction capability. \nOnce the PVA is optimally dispersed around the SFO particles, \ndifferent SiO2 contents (0.2, 0.4, 0.6 and 1 %wt) were added to the \nmixture. As discussed in previous studies [16], the addition of SiO2 has \nan inhibitory role on grain growth during the consolidation treatment. \nSFO pellets of samples with different SiO2 contents (0.2-0.4-0.6-1 % \nwt) and containing 0.2%wt PVA were pressed. The green bodies, with \nrelative densities between 63 and 67% (density of SFO is 5.1 g/cm3), \nwere then subjected to various TSS processes. \nThe magnetization curves are shown in Fig.3 . Furthermore, the \nvalues of coercivity, magnetization and relative density for each sample \nare collected in Table 1. As expected [11,16,25], increasing the SiO2 \ncontent (%wt) tends to increase the value of coercivity (Hc) while \nmagnetization at 1.3 T (M1.3T) tends to slightly decrease. This is due to \nthe grain growth inhibition induced by silica that lowers the average \ngrain size, which increases Hc [11]. Unfortunately, the grain growth \ninhibition process promotes a certain formation of secondary \nFig. 1.a) Heating treatment for conventional sintering (CS); Heating treat-\nments for two-step sintering b) (TSS 1) and c) (TSS 2). J.C. Guzm ˘an-Mínguez et al.                                                                                                                                                                                                                  Ceramics International 47 (2021) 31765–31771\n31767\nFig. 2.SEM images of SFO particles (a, b) after the dispersion process without PVA and (c, d) after dispersion process with PVA.  \nFig. 3.Magnetization curves of samples with different SiO2 contents sintered using different TSS-modified) processes a) 1100 –1200(10 min)-1100, b) 1100 –1225 \n(10 min)-1100 and c) 1100 –1250(10 min)-1100. J.C. Guzm ˘an-Mínguez et al.                                                                                                                                                                                                                  Ceramics International 47 (2021) 31765–31771\n31768non-magnetic phases, such as hematite, which hinders magnetization. \nFor the 0.2%wt SiO2 content, it can be seen that, for all TSS treatments, \nthe Hc values are in the 160–168 kA/m range. For 0.4%wt and 0.6%wt, \nHc values are between 152 and 184 kA/m for all TSS studied. For \nsamples with 1%wt, the Hc reaches values between 152 and 192 kA/m, \nalthough at the expense of an average 6% decrease in M1.3T compared to \nthe other contents, which makes us discard the 1% wt SiO2 samples. \nIncreasing T2 in TSS treatments increases relative density at the \nexpense of Hc. This competition between density and coercivity is \ncommon in SFO ceramics, as usually higher density is associated with \nslightly larger grain sizes. Indeed, for T2 1225 •C, the highest Hc and \nlower densities are measured. The grain growth inhibition promoted by \nSiO2 is a process that involves two different chemical reactions: the \ndissolution of Si inside the SFO grains (which is the one that actually \nopposes grain growth) and the decomposition of SFO onto α-Fe2O3. \nThese two competing reactions have different kinetics and thermody -\nnamic windows [11]. We speculate that the sintering treatment that \nemploys T2 1225 •C favors the dissolution reaction over the decom -\nposition reaction more than the other sintering schedules, leading to \nsmaller grain sizes and thus lower density and higher coercivity. This is \nhowever not entirely true for all samples under study, which we suspect \nis related with the experimental error in the determination of both \nrelative density and coercivity that we estimate in the 5–10% range. For \nsamples treated at T2 1200 •C, acceptable values of Hc between 160 \nand 176 kA/m are measured, although relative densities are below 91%. \nAs we increase T2 (T2 1225-1250 •C) the density improves and the \nM1.3T values hardly varies. In this scenario, samples with a content of \n0.6%wt of SiO2, treated at T2 1225-1250 •C reach a reasonable \ncompromise between the relevant magnetic and density values. \nThe Hc values measured here are significantly higher, on average \n15%, than the ones reported in our previous work using a conventional \nsintering procedure with a 4 h dwell time. Fig. 4 compares the micro -\nstructure of a pellet sintered at 1250 •C for 4 h and a pellet sintered using TSS with T2 1250 •C. For both thermal treatments, a bimodal grain \nsize distribution can be observed, although the relative fraction of the \nlarger grains is decreased in number and in size for TSS sintering. \nMoreover, the most relevant differences arise in the decrease in size of \nthe finer grains for the TSS treatment. The average grain size determined \nby automatic image analysis is 3.1 ±0.9 μm for conventional sintering \nand 1.1 ±0.9 μm for TSS. Thus, a clear reduction in grain size is obtained \nusing TSS, even for a lower SiO2 content. Thus, the microstructure \nrefinement for the TSS treatment is consequence of the grain growth \ncontrol and is likely the cause for the improved Hc. \nThe coercivity of these systems is commonly described by the \nequation [11]:  \nHc αHA - NeffMs                                                                                 \nWhere HA is the anisotropy field of SFO, which is approximately 1.8 T \n[1] and Neff the effective demagnetization constant. However, this \nmodel, which can describe successfully systems where both coherent \nrotation and domain wall propagation mechanisms are occurring, is not \nentirely accurate for systems where magnetization reversal is dominated \nby domain wall propagation [4,5]. Given that the \nsingle-to-multi-domain grain size threshold for SFO is slightly below 1 \nμm and the grain sizes observed in Fig. 4, it seems reasonable to assume \nthat the SFO grains of the ceramics studied here are in a multi-domain \nstate and that domain wall propagation is dominating the demagneti -\nzation process. Under these circumstances, the main mechanism \nresponsible for the changes in coercivity is that reducing grain size to-\nwards the single-domain threshold significantly increases Hc [8]. \nAt this stage, after choosing the appropriate additive contents (SiO 2 \nand PVA) and optimizing the TSS parameters, the effect of processing \nthe powders with a Spray Drying Process (SDP) was investigated. \nFig. 5 shows SEM micrograph of the powders before (5a, 5b and 5c) \nand after (5d, 5e and 5f) the SDP. As can be seen, in Fig. 5a, b and 5c, the \nSFO particles present a bimodal distribution, where larger particles with \nsizes above 1 μm coexist with smaller ones. In addition, it is observed \nthat the SFO particles present their characteristic platelet morphology. \nHowever, in the micrographs of the powder after SDP (Fig. 5d, e and 5f), \nthe particle distribution is narrowed and less bimodal than for the un-\nmodified SFO powder. The particle morphologies are slightly rounder, \nwhich may improve the final density of the samples by permitting an \nincreased degree of packing. \nOn the other hand, the improvement in the dispersion of the addi-\ntives (SiO 2 and PVA) in the ceramic matrix should be highlighted. If we \nfocus on Fig. 5c, we see how the SiO2 nanoparticles appear agglomerated \non top of the SFO particles, while in Fig. 5f this does not occur. We do not \nobserve small agglomerates in the micrographs, suggesting a successful \ndispersion that rends the nanoparticles not detectable at this magnifi -\ncation. We suggest this effect is due to the fast drying of the solutions in \nthe spray drying chamber (typically in the range of few minutes). In the \ncase of the powder without SDP, the drying in the laboratory stove was \nquite slow (in the range of several hours), causing part of the SiO2 and Table 1 \nThe table displays the values of coercivity (Hc), magnetization at 1.3T (M1.3T), \nand relative density for all SiO2 content and each TSS treatment.  \nSintering Treatment x (% wt \nSiO2) Hc (kA/ \nm) M1.3T \n(Am2/kg) Relative density \n(%) \na) 1100 –1200(10 \nmin)-1100 0,2 160 57 84 \n0,4 168 54 90 \n0,6 160 56 91 \n1 176 53 90 \nb) 1100 –1225(10 \nmin)-1100 0,2 168 55 89 \n0,4 184 52 83 \n0,6 152 56 92 \n1 192 49 87 \nc) 1100 –1250(10 \nmin)-1100 0,2 160 56 90 \n0,4 168 52 90 \n0,6 160 55 92 \n1 152 52 95  \nFig. 4.a) SEM micrograph of a 1%SiO 2 SFO pellet sintered for 4 h at 1250 •C. b) SEM micrograph of a 0.6%SiO 2 SFO pellet sintered by TSS using T2 1250 •C.  J.C. Guzm ˘an-Mínguez et al.                                                                                                                                                                                                                  Ceramics International 47 (2021) 31765–31771\n31769PVA to float so that when the solution dries, it accumulates or ag-\nglomerates on the surface of the SFO particles. It should be noted here \nthat the role that PVA plays in this process is to keep the SiO2 nano-\nparticles dispersed on the surface of the ferrite particles. In this sense, \nthe high shear dispersion process favors the dispersion of micro and \nnanoparticles. The subsequent fast drying process in the SDP ensures \nthat the encapsulation of the ferrite particles is maintained. \nTo further fine tune the properties, samples were then sintered using \ntwo different firing profiles: 1100 –1225 [10 min dwell]-1100 will be \ncalled TSS 1 and 1100-1250-1100 will be named TSS 2. Fig. 6 shows the \nPXRD diffraction patterns of the SDP samples TSS1 and TSS2. Only \ndiffraction maxima corresponding to SFO were observed, confirming the \nabsence of secondary up to the resolution limit of the technique. In \naddition, the fitting of the patterns yielded a density of 5.1 g/cm3, which \nis in agreement with the theoretical value for SFO [1]. \nAs can be observed in Table 2, SDP samples show up to a 5% \nimprovement in density value, reaching ρ 97%, with respect to their \nnon-SDP counterpart. \nWith the aim of comparing sintered magnets fabricated following our \nprocedure with current commercial ferrite magnets, the magnetization \ncurves of different oriented dense pellets are represented in Fig.7 , \nalongside that of a commercial magnet (grade Y-35). \nTable 3 shows magnetic properties and relative density values of the \nsamples and the commercial magnet. On one hand, although non-SPD \nsamples have high coercivity values (160 kA/m), their densities are \nrelatively low (89–90%). On the other hand, both coercivity and relative density are significantly enhanced when SPD processing the powders. In \nparticular, the sample SFO/PVA0.6%SiO 2 using SPD and the TSS 2 \ntreatment, shows an Hc value of 164 kA/m, M1.3T 58 Am2/kg and a \nrelative density of 93%. These are almost identical values as the refer-\nence state-of-the-art commercial ferrite magnet Y-35. \nOur Mr/M1.3T ratio is in the 0.78 –0.82 range, while the commercial \nmagnet reaches 0.93. This is likely the consequence of the fact that our \norientation method, which is a delicate process, is not as optimized as \nthat of industrial magnet manufacturers. Tokar ’s study demonstrated \nthat the degree of orientation increased during sintering [26]. In \nparticular, optimizing the viscosity of the slurred prepared with the SFO \npowders prior to compaction and increasing the magnetic field during \nthe compaction process would be needed. \nIt is important to remark that, through the processing developed \nhere, state-of-the-art nominal magnetic performance values are reached \nusing a sintering schedule without dwell time. This implies a significant \nFig. 5.SEM images of powder of SrFe 12O19 - 0.2% PVA with 0.6% wt of SiO2 before (a, b and c) and after (d, e and f) the SDP.  \nFig. 6.PXRD patterns of the SSDP samples sintered using a) TSS1 and b) TSS2 schedules.  Table 2 \nValues of relative density (%) of samples with and without SPD, sintered \nusing two different TSS treatments.  \nSample Relative density (%) \nSFO-PVA-SiO 2 SDP TSS 1 94 \nSFO-PVA-SiO 2 Non-SDP TSS 1 92 \nSFO-PVA-SiO 2 SDP TSS2 97 \nSFO-PVA-SiO 2 Non-SDP TSS 2 92  J.C. Guzm ˘an-Mínguez et al.                                                                                                                                                                                                                  Ceramics International 47 (2021) 31765–31771\n31770reduction in the energy consumption required to sinter ferrite magnets. \n4 h at 1200 •C demand approximately 29 kWh, while TSS employs 20 \nkWh, leading to energy savings of the order of 30%. Given the 800 ki-\nlotons of ferrite magnets produced every year; industrial implementa -\ntion of the sintering process presented in this work would lead to a \nglobal annual reduction in energy consumption of the order of 7⋅109 \nkWh. \n4.Conclusions \nWith the purpose of developing a greener SFO ferrite magnet \nmanufacturing process, the sintering parameters of a TSS schedule are \noptimized. The influence of additives such as SiO2 and PVA on the \nmicrostructure has been studied, as well as the application of the Spray \ndrying process to modify the morphology of the SFO particles. By \ncombining the encapsulating capacity of PVA with a high power \ndispersion (SDP) process, more dispersed and agglomerate-free/smaller \nparticles are obtained. As expected, increasing the SiO2 content in \nSrFe 12O19 - 0.2%wt PVA mixtures increases the coercivity (Hc) value. \nSimilarly, an increase in T2 in TSS treatments generates an increase in \nthe relative density values. It is found that annealing up to 1100 •C at 3•/ \nmin and subsequently rapidly increasing the temperature to \n1225 –1250 •C before cooling back down leads to the best density and \nmagnetic properties. The refinement of the grain size in the TSS treat-\nment causes the notable increase of coercivity in sintered samples. \nFinally, the samples were oriented and compared with a commercial \nferrite magnet (Y-35). Using the novel methodology proposed here for producing sintered ferrite magnets, that leads to energy savings of the \norder of 31%, we obtain practically the same coercivity (164 kA/m), \nmagnetization (58 Am2/kg) and relative density (93%) as for commer -\ncial ferrite magnets. Our results open the door to implementing signif -\nicantly greener sintering cycles for ferrite magnets with no loss of \nmagnetic performance. \nDeclaration of competing interest \nThe authors declare that they have no known competing financial \ninterests or personal relationships that could have appeared to influence \nthe work reported in this paper. \nAcknowledgments \nThis work is supported by the Spanish Ministerio de Economía y \nCompetitividad through Projects no. RTI2018-095303-A-C52 \nMAT2017-86450-C4-1-R, MAT2015-64110-C2-1-P, MAT2015-64110- \nC2-2-P, FIS2017-82415-R and through the Ram ˘on y Cajal Contract RYC- \n2017-23320; and by the European Comission through Project H2020 no. \n720853 (AMPHIBIAN). V.Fuertes holds a Sentinel North Excellence \nPostdoctoral Fellowship and acknowledges the economic support from \nthe Sentinel North program of Universit ˘e Laval, made possible, in part, \nthanks to funding from the Canada First Research Excellence Fund. \nReferences \n[1]R.C. Pullar, Hexagonal ferrites: a review of the synthesis, properties and \napplications of hexaferrite ceramics, Prog. Mater. Sci. 57 (2012) 1191 –1334, \nhttps://doi.org/10.1016/j.pmatsci.2012.04.001 . \n[2]D. Chen, D. Zeng, Z. Liu, Synthesis, structure, morphology evolutionand magnetic \nproperties of single domain strontium hexaferrite particles, Mater. Res. Express 3 \n(2016), https://doi.org/10.1088/2053-1591/3/4/045002 . 045002. \n[3]M.M. Maqableh, X. Huang, S.-Y. Sung, K.S.M. Reddy, G. Norby, R.H. Victora, B.J. \nH. Stadler, Low-resistivity 10 Nm diameter magnetic sensors, Nano Lett. 12 (2012) \n4102 –4109, https://doi.org/10.1021/nl301610z . \n[4]R. Skomski, J.M.D. Coey, Magnetic anisotropy - how much is enough for a \npermanent magnet? Scripta Mater. 112 (2016) 3–8, https://doi.org/10.1016/j. \nscriptamat.2015.09.021 . \n[5]J.C. Faloh-Gandarilla, S. Díaz-Casta ~n˘on, B.E. Watts, Magnetization reversal and \ninteractions in SrFe 12O19, Phys. Status Solidi Basic Res. 254 (2017) 1–7, https:// \ndoi.org/10.1002/pssb.201600393 . \n[6]L.H. Lewis, F. Jim˘enez-Villacorta, Perspectives on permanent magnetic materials \nfor energy conversion and power generation, Metall. Mater. Trans. 44 (2012) 2–20, \nhttps://doi.org/10.1007/s11661-012-1278-2 . \n[7]M. Getzlaff, Fundamentals of Magnetism_M. Getzlaff. Pdf, Springer, Berlin, \nHeidelberg, 2007, https://doi.org/10.1007/978-3-540-31152-2 . \n[8]A.Z. Eikeland, M. Stingaciu, A.H. Mamakhel, M. Saura-Múzquiz, M. Christensen, \nEnhancement of magnetic properties through morphology control of SrFe 12O19 \nnanocrystallites ”, Sci. Rep. 8 (2018) 1–9, https://doi.org/10.1038/s41598-018- \n25662-8 . \n[9]D. Niarchos, G. Giannopoulos, M. Gjoka, C. Sarafidis, V. Psycharis, J. Rusz, \nA. Edstr om, O. Eriksson, P. Toson, J. Fidler, E. Anagnostopoulou, Toward rare- \nearth-free permanent magnets: a combinatorial approach exploiting the \npossibilities of modeling, shape anisotropy in elongated nanoparticles, and \ncombinatorial thin-film approach ”, JOM 67 (2015) 1318 –1328, https://doi.org/ \n10.1007/s11837-015-1431-7 . \n[10] A. Quesada, G. Delgado, L. Pascual, A.M. Arag ˘on, P. Marín, C. Granados-Miralles, \nM. Foerster, L. Aballe, J.E. Prieto, J. De La Figuera, J.F. Fern˘andez, P. Prieto, \nExchange-spring behavior below the exchange length in hard-soft bilayers in \nmultidomain configurations, Phys. Rev. B 98 (2018) 1–7, https://doi.org/10.1103/ \nPhysRevB.98.214435 . \n[11] F.X.N.M. Kools, “Science and Technology of Ferrite Magnets : Modelling of \nCoercivity and Grain Growth Inhibition ”, Technische Universiteit Eindhoven, 2003 \nhttps://doi.org/10.6100/IR562293 . \n[12] M. Biesuz, S. Grasso, V.M. Sglavo, “What ’s new in ceramics sintering? A short \nreport on the latest trends and future prospects ”, Curr. Opin. Solid State Mater. Sci. \n24 (2020), 100868 https://doi.org/10.1016/j.cossms.2020.100868 . \n[13] R.E. El-Shater, E.H. El-Ghazzawy, M.K. El-Nimr, Study of the sintering temperature \nand the sintering time period effects on the structural and magnetic properties of \nM-type hexaferrite BaFe 12O19, J. Alloys Compd. 739 (2018) 327–334, https://doi. \norg/10.1016/j.jallcom.2017.12.228 . \n[14] J. Topfer, S. Schwarzer, S. Senz, D. Hesse, Influence of SiO2 and CaO additions on \nthe microstructure and magnetic properties of sintered Sr-hexaferrite, J. Eur. \nCeram. Soc. (2005), https://doi.org/10.1016/j.jeurceramsoc.2004.06.003 . \n[15] S. Hussain, A. Maqsood, Influence of sintering time on structural, magnetic and \nelectrical properties of SiO2-Ca added Sr-hexaferrites ”, J. Magn. Magn Mater. \n(2007) https://doi.org/10.1016/j.jmmm.2007.03.206 . \nFig. 7.Magnetization curves of samples of SrFe 12O19 - 0.2% PVA with 0.6% wt \nof SiO2, SPD and non-SPD sintered using a) TSS 1 and b) TSS 2. \nTable 3 \nMagnetic properties and values of relative density of the oriented samples \ntreated to two different TSS-modified treatments and of the commercial magnet \nY-35.  \nSample Hc \n(kA/ \nm) Mr \n(Am2/ \nkg) M1.3T \n(Am2/ \nkg) Mr/ \nM1.3T \n(%) Relative \ndensity (%) \nY-35 166 55 59 93 99 \nSFO/PVA0.6% \nSiO2 SDP TSS 1 147 41 54 76 92 \nSFO/PVA0.6% \nSiO2 Non-SDP \nTSS 1 160 44 58 76 90 \nSFO/PVA0.6% \nSiO2 SDP TSS 2 164 46 58 80 93 \nSFO/PVA0.6% \nSiO2 Non-SDP \nTSS 2 154 44 57 77 89  J.C. Guzm ˘an-Mínguez et al.                                                                                                                                                                                                                  Ceramics International 47 (2021) 31765–31771\n31771[16] J.C. Guzm ˘an-Mínguez, L.M. Vicente-Arche, C. Granados-Miralles, J.F. Fern˘andez, \nA. Quesada, Improvement of the magnetic properties of SrFe 12O19 ceramics by \ntailored sintering with SiO2 addition, J. Alloys Compd. (2020) 157890, https://doi. \norg/10.1016/j.jallcom.2020.157890 . \n[17] I.W. Chen, X.H. Wang, Sintering dense nanocrystalline ceramics without final-stage \ngrain growth, Nature 404 (6774) (2000) 168–171, https://doi.org/10.1038/ \n35004548 . \n[18] X.H. Wang, I.W. Chen, Two-step sintering of ceramics with constant grain-size, I. \nY2O3, J. Am. Ceram. Soc. 89 (2) (2006) 431–437, https://doi.org/10.1111/j.1551- \n2916.2005.00763.x . \n[19] X.H. Wang, X.Y. Deng, H.L. Bai, H. Zhou, W.G. Qu, I.W. Chen, Two-step sintering of \nceramics with constant grain-size, II. BaTiO 3 and Ni-Cu-Zn ferrite, J. Am. Ceram. \nSoc. 89 (2) (2006) 438–443, https://doi.org/10.1111/j.1551-2916.2005.00728.x . \n[20] J. Du, T. Zhou, L. Lian, Y. Liu, Y. Du, Two-Step sintering of M-type strontium ferrite \nwith high coercivity, Ceram. Int. 45 (2019) 6978 –6984, title\", https://doi.org/10 \n.1016/j.ceramint.2018.12.197 . \n[21] V. Lopez-Dominguez, A. Quesada, J.C. Guzm ˘an-Mínguez, L. Moreno, J. Lere, \nJ. Spottorno, F. Giacomone, J.F. Fern˘andez, A. Hernando, M.A. García, A simple vibrating sample magnetometer for macroscopic samples ”, Rev. Sci. Instrum. 89 \n(2018) https://doi.org/10.1063/1.5017708 . \n[22] G. Ghosh, M.K. Naskar, A. Patra, M. Chatterjee, Synthesis and characterization of \nPVA-encapsulated ZnS nanoparticles, Opt. Mater. 28 (2006) 8–9, https://doi.org/ \n10.1016/j.optmat.2005.06.003 , 1047-1053. \n[23] F.N. Tenorio Gonzalez, I.R. Barajas Rosales, P. Vera Serna, F. S˘anchez de Jesus, A. \nM. Bolarin Mir˘o, A. Garrido Hern ˘andez, Martin Kusý, Reducing the crystallite and \nparticle size of SrFe 12O19 with PVA by high energy ball milling, J. Alloys Compd. \n771 (2019) 464–470, https://doi.org/10.1016/j.jallcom.2018.08.297 . \n[24] G. Nabiyouni, A. Ahmadi, D. Ghanbari, H. Halakouie, SrFe 12O19 ferrites and hard \nmagnetic PVA nanocomposite: investigation of magnetization, coercivity and \nremanence, J. Mater. Sci. Mater. Electron. 27 (2016) 4297 –4306, https://doi.org/ \n10.1007/s10854-016-4296-9 . \n[25] I. Lorite, L. P˘erez, J.J. Romero, J.F. Fernandez, Effect of the dry nanodispersion \nprocedure in the magnetic order of the Co3O4 surface ”, Ceram. Int. 39 (4) (2013) \n4377 –4381, https://doi.org/10.1016/j.ceramint.2012.11.025 . \n[26] M. Tokar, Increase in preferred orientation in lead ferrite by firing ”, J. Am. Ceram. \nSoc. 51 (10) (1968) 601–602, https://doi.org/10.1111/j.1151-2916.1968. \ntb13331.x . J.C. Guzm ˘an-Mínguez et al.                                                                                                                                                                                                                  "    },    {        "title": "2203.12102v1.Effect_of_ECAP_and_heat_treatment_on_mechanical_properties__stress_relaxation_behavior_and_corrosion_resistance_of_a_321_type_austenitic_steel_with_increased_delta_ferrite_content.pdf",        "content": "Effect of ECAP and heat treatment on mechanical properties, stress relaxation \nbehavior and corrosion resistance of a 321-type austenitic steel with increased -\nferrite content \nV.N. Chuvil’deev1, A.V. Nokhrin1,(*), N.A. Kozlova1, M.K. Chegurov1, V.I. Kopylov1,2,  \nM.Yu. Gryaznov1, S.V. Shotin1, N.V. Melekhin1, C.V. Likhnitskii1, N.Yu. Tabachkova3,4 \n1 Lobachevsky State University of Nizhniy Novgorod, Nizhniy Novgorod, Russia \n2 Physical-Technical Institute, National Academy of Sciences of Belarus, Belarus, Minsk \n3 A.M. Prokhorov Institute of General Physics, RAS, Russia, Moscow \n4 National University of Science and Technology “MISIS”, Russia, Moscow \nnokhrin@nifti.unn.ru  \n \nAbstract \nHot rolled commercial metastable austenitic steel 0.8C-18Cr-10Ni-0.1Ti (Russian industrial \nname 08X18H10T, analog 321L) with strongly elongated thin -ferrite particles in its \nmicrostructure was the object of investigations. The lengths of these -particles were up to 500 m, \nthe thickness was 10 m. The formation of the strain-induced martensite as well as the grinding of \nthe austenite and of the -ferrite grains take place during ECAP. During the annealing of the UFG \nsteel, the formation of the -phase particles takes place. These particles affect the grain boundary \nmigration and the strength of the steel. However, a reduction of the Hall-Petch coefficient as \ncompared to the coarse-grained (CG) steel due to the fragmentation of the -ferrite particles was \nobserved. The samples of the UFG steel were found to have 2-3 times higher stress relaxation \nresistance as compared to the CG steel (a higher macroelasticity stress and a lower stress relaxation \nmagnitude). The differences in the stress relaxation resistance of the UFG and CG steels were \ninvestigated. ECAP was shown to result in an increase in the corrosion rate and in an increased \ntendency to the intergranular corrosion (IGC). The reduction of the corrosion resistance of the UFG \nsteel was found to originate from the increase in the fraction of the strain-induced martensite during \nECAP. \nKeywords : Austenitic steel, fine-grained microstructure, strength, relaxation resistance, \ncorrosion resistance  \n  \n \n(*) Corresponding author ( nokhrin@nifti.unn.ru )  Introduction \nCoarse-grained austenitic stainless steels Fe-Cr-Ni are used widely in nuclear power \nengineering, in oil and chemical industry. The austenitic steels are applied in fabricating the highly \nresponsible products intended for operation in corrosion-aggressive ambient [1-8].  \nThe problem of increasing the strength of the austenitic steels preserving their high \nresistance to the intergranular corrosion (IGC) is one of the key problems of the materials science \n[5-11]. This makes the traditional approach to increasing the strength consisting in annealing \nleading to the nucleation of the chromium carbide particles at the austenite grain boundaries \ninapplicable [12-16]. In this connection, engineers are developing novel methods of simultaneous \nincreasing the strength and the corrosion resistance of the austenite steels. \nForming the ultrafine-grained (UFG) structure is one of the popular methods of improving \nthe strength and the operational characteristics of stainless alloys [17-22]. At present, various \nmethods of Severe Plastic Deformation (SPD) are applied to form the UFG structure – Equal \nChannel Angular Pressing (ECAP) [17-21], high pressure torsion [22-24], rotary swaging [25, 26], \nextrusion [26, 27] etc. In spite of certain success in the improvement of the hardness and strength of \nsteels, it should be noted that the application of SPD leads to strain-induced decomposition of \naustenite often [17, 19, 21, 29-31]. It may affect the corrosion resistance of the UFG austenitic \nsteels negatively. In this connection, the applied problem of choice of the optimal regimes of heat-\ndeformation processing of austenitic steels, which allow increasing the strength of the ones without \nthe reduction of the corrosion resistance is relevant. \nA problem of providing a high stress relaxation resistance of the austenitic steels is even \nmore complex. The problem of increasing the relaxation resistance is especially important in the \ndevelopment of machine-building hardware providing simultaneously high characteristics of \nfatigue, creep resistance, stress corrosion cracking resistance, etc. [32-36]. The high stress \nrelaxation resistance determines the capability of the hardware to provide the necessary level of \ndownforce during a long operation time [37, 38]. The improvement of the stress relaxation resistance of the materials with simultaneous proving a high strength will allow increasing the \ndownforce of the hardware and keeping it during a notably longer operation time. Plenty of \nexperimental and theoretical works was devoted to the problem of investigation of the stress \nrelaxation resistance mechanisms for the coarse-grained (CG) materials [39-42]. For CG materials, \nit is supposed usually that the higher the level of internal stresses, the lower the stress relaxation \ndepth (the magnitude of the decrease in the stress in given time interval). Therefore, the strain \nstrengthening is a traditional method of increasing the stress relaxation resistance. From this \nviewpoint, the fine-grained metals and alloys fabricated using the SPD methods are promising \ncandidates for application as the base materials for the heavy-duty relaxation-proof hardware.  \nThe analysis of the literature shows that SPD may lead to an increase as well as in a \ndecrease in the stress relaxation resistance of metals [43-52]. One should outline the works [43-47], \nwhere a faster and stronger reduction of the stresses in time in the UFG metals was demonstrated. \nSome authors related it to grain boundary sliding [43, 44, 48-51] or to interaction of the lattice \ndislocations with the grain boundaries [43, 46, 47, 50, 51], which may occur during the stress \nrelaxation tests of the UFG materials along with accommodative redistribution of lattice \ndislocations. \nThe present work was aimed at studying the effect of SPD and annealing on the relaxation \nresistance and the resistance to IGC of the Russian metastable austenitic steels 0.8%C-18%Cr-\n10%Ni-0.1%Ti (Russian industrial name 08X18H10T, Russian analog of steel 321L). This steel is \nused widely in nuclear mechanical and power engineering for making the machine building \nhardware operated in the condition of simultaneous impact of elevated temperatures, mechanical \nloads, and corrosion-aggressive ambients. In particular, a low strength and high stress relaxation \nrate in the austenite steels result in difficulties in operations of assembling and disassembling the \nproducts after long-term operation. An increased content of -ferrite is a special feature of the \nobject of investigations. It is a defect of casting or of heat treatment of the cast workpieces but is \npresent in the bulk austenite steel often.  \nMaterials and methods \nThe Russian commercial metastable austenitic steel 08Х18Н10Т (composition: Fe-\n0.08wt.%С-17.9wt.%Cr-10.6wt.%Ni-0.5wt.%Si-0.1wt.%Ti) was the object of investigations. The \nformation of the UFG microstructure in the steel was performed by ECAP. The workpieces of \n1414140 mm in sizes were cut out from hot-rolled rods of 20 mm in diameter. Prior to ECAP, the \nrods were annealed at 1050 оC for 30 min followed by quenching in water. ECAP was performed \nusing Ficep  HF400L press (Italy). The angle of crossing the working channel and the output one \nwas /2. In the ECAP regime used, the workpiece rotated at the angle of  around its longitudinal \naxis during every cycle (regime “С”, see [52]). The ECAP rate was 0.4 mm/s. The ECAP \ntemperatures were 150 and 450 C, the number of pressing cycles (N) varied from one to four. \nThe investigations of the steel microstructure were carried out using Jeol JSM-6490 and \nTescan Vega Scanning Electron Microscopes (SEMs) and Jeol JEM-2100F Transmission \nElectron Microscope (TEM). X-ray diffraction (XRD) phase analysis of the stainless steels was \ncarried out using Shimadzu XRD-7000 X-ray diffractometer (CuK  emission, recording in the \nBragg-Brentano scheme in the range of angles 2  = 30-80о with the scan rate 1 о/min). The crystal \nlattice parameters were determined and the mass fractions of the phases were calculated by Rietveld \nmethod. \nThe microhardness (H v) of the steel was measured with Duramin Struers 5 \nmicrohardness tester. The uncertainty of the microhardness measurements was ±50 MPa. \nFor the mechanical tests, flat double-blade shaped specimens were made by electric spark \ncutting. The sizes of the working part were 2 23 mm. The tension tests were carried out using \nTinius Olsen H25K-S machine with the strain rate 3.3 10–3 s–1 (the tension rate was 10-2 mm/s). \nThe tension tests were performed at the room temperature (RT) and in the temperature range 450–\n900 C. The specimens were heated up to the testing temperatures in 5 min. The specimens were \nkept at the testing temperatures for 10 min to establish the thermal equilibrium. In the course of the tests, the curves stress ( ) – strain ( ) were recorded. From these curves (), the magnitudes of the \nultimate strength ( b) and of the maximum relative elongation to failure ( ) were determined.  \nThe fractographic analysis of the fractures after the tension tests was carried out using Jeol \nJSM-6490 SEM. The macrostructure of the specimens after the failure tests was investigated using \nLeica IM DRM metallographic optical microscope. The investigations of microstructure and the \nmicrohardness measurements were performed in the fracture zones (“deformed area”) and in the \nnon-deformed areas near the capturers. \nThe stress relaxation tests were performed according the technique described in Appendix A \nto the paper [53]. For the tests, the rectangular specimens of 3×3 mm in cross-sections and of 6 mm \nin height were made. The specimens were loaded with the rate 0.13%/s during 0.3 s. Afterwards, \nthe specimens were kept under a constant stress ( i) during given stress relaxation time (t r = 60 s). \nIn the course of stress relaxation, a curve of the stress on the testing time i(t) was acquired. \nAfterwards, the next loading step was performed. As a result of experiment, a dependence of the \nstress relaxation magnitude i on the magnitude of the summary load applied i() was obtained. \nThe dependence obtained was used also to determine the macroelasticity stress ( 0) and the yield \nstrength ( y). \nThe resistance of the steels to the intergranular corrosion (IGC) was investigated using R-8 \npotentiostat-galvanostat according to Russian National Standard GOST 9.914-91 by double loop \nelectrochemical potentiokinetic reactivation (DLEPR) method. The DLEPR tests were conducted at \nRT in an aqueous solution 10%H 2SO4 +0.0025 g/l KSCN. An auxiliary electrode was made from a \nPt grid, the reference electrode – from chlorine silver, the investigated specimen served as the \nworking electrode. The investigated specimen was cathode polarized at the potential φ = –550 mV \nfor 2 min. The curves voltage – current density were recorded in the range of potentials from –550 \nmV to +1200 mV with a rate of 3 mV/s. The tendency of the steel to IGC was determined from the \nratio of the areas under the passivation curve (S 1) and under the reactivation one (S 2): K = S 1/S2. \nAccording to GOST 9.914-91, the increasing of the coefficient K up to K = 0.11 means that the austenite steel demonstrates an increased tendency to IGC.  \nThe Tafel curves ln(i) – E were measured in the same medium. From the Tafel curves, the \ncorrosion current densities (i corr, mA/cm2) and the corrosion potentials (E corr, mV) were obtained by \nstandard method. Prior to the corrosion investigations, the surfaces of specimens of 5 1010 mm in \nsize were subjected to mechanical grinding and polishing. From the results of measuring the i corr, \nthe corrosion rate was calculated using the formula: V corr = 8.76i corrM/F, where  is the density of \niron [g/cm3], М – molar mass [g/mol], F = 96500 C – Faraday's constant. The verification tests of \nresistance against IGC were conducted according to GOST 6232-2003 by the boiling of the \nspecimens in a solution of 25% H 2SO4 + CuSO 4. The character of the surface destruction after the \ncorrosion tests was analyzed using Leica IM DRM metallographic optical microscope. \nTo study the thermal stability of the structure and properties of the UFG steel, the specimens \nwere annealed in air in the temperature range from 100 up to 900 C. The isothermic holding time \nwas 60 min. Th uncertainty of maintaining the temperature was ± 10 C. The specimens were cooled \ndown in water.  \n \nResults \nMicrostructure investigations \nAs initial state, stainless steel had a uniform austenite microstructure (Figs. 1a-1d). The \nmean austenite grain sizes were ~20 m. The thin (up to 10 m in thickness) strips of the ferrite -\nphase elongated along the deformation direction were observed in the microstructure of the CG \nsteel (Figs. 1a-1d). The lengths of the -ferrite stripes were ~500 m. The lattice dislocations (Fig. \n1f) as wee as few micron- and submicron-sized titanium carbide and carbonitride particles (Fig. 1e) \nwere observed inside the austenite grains. \nAfter the first ECAP cycle, the macrostructure of the steel workpieces comprised of \nalternating macro-bands of localized strain (Fig. 2). After N = 4 ECAP cycles, the specimens had a \nuniform macrostructure. Fig. 3a presents the XRD curves from the steel specimens in the initial state and after ECAP. \nAn XRD peak 111 ()-phase (PDF 00-006-0696) is seen clearly in the XRD curve of the CG steel \nat the diffraction angel 2  ~ 45о near the highly intensive XRD peak 110 -Fe (PDF 01-071-4649). \nThe results of the XRD phase analysis evidence the mean mass fraction of the -phase in the steel in \nthe initial state to be ~1.5–3 %. The lattice parameter of the -phase in the steel Fe-Cr-Ni-Ti was \n2.8869 Å, the one of the -phase was 3.5875 Å. \nECAP leads to an increase in the fraction of the -phase because of appearing the strain-\ninduced martensite. The scale and dynamics of the increasing of the strain-induced martensite with \nincreasing the number of cycles depends on the ECAP temperature (Fib. 3b). After ECAP at 150 \nС, the mass fraction of the ()-phase was 5.9–7.7% and didn’t change essentially with increasing \nnumber of ECAP cycles up to N  = 4. The increasing of the SPD temperature up to 450 C resulted in \nmore intensive decomposition of the -phase (austenite) – the mass fraction of the ()-phase \nincreased from 3.6% after N  = 1 cycle up to 17.4% after N  = 4 ECAP cycles. Note that the effect of \nstrain-induced decomposition of the -phase during ECAP of the austenitic steel is known for a long \nenough time [19-23]. At the same time, it is worth noting that the effect of accelerated strain-\ninduced decomposition of austenite at higher SPD temperatures is an unexpected ones (see [24]). \nECAP resulted in a decreasing of the intensity and in the broadening of the XRD peaks from \nthe - and -phases. The half width at half maximum (HWHM) of the 111 XRD peaks of ()-Fe \nand of the (110) ones of -Fe for the coarse-grained steel were 0.196о and 0.193о, respectively. In \nthe UFG steel after N=4 ECAP cycles at 150 оC, the HWHMs of the 111 ()-Fe and (110) -Fe \nXRD peaks were 0.300о and 0.277о, respectively while for the UFG steel specimens after N=4 \nECAP cycles at 450 оC – 0.407о and 0.289о, respectively. The lattice constants of ()-Fe and -Fe \nfor the UFG steel after N = 4 ECAP cycles ( a = 2.8718 Å, a = 3.5863 Å – T ECAP = 150 оС; a = \n2.8780 Å, a = 3.5897 Å – T ECAP = 450 оС) were close to the ones of ferrite and austenite in the \ncoarse-grained steel. This allow suggesting small grain sizes (small sizes of the coherent scattering regions) to introduce the major contributions in the broadening of the XRD peaks after N=4 ECAP \ncycles. \nAlong with the austenite strain-induced decomposition during ECAP, a grinding of the steel \ngrain microstructure was observed. After N  = 4 ECAP cycles at 150 and 450 C, an UFG \nmicrostructure with mean grain sizes of 0.3 and 0.5 m, respectively formed in steel (Fig. 4). For \nthe specimens of steel obtained by ECAP at 150 оC, the crossing localization micro-bands, which \nlead to different orientation of the austenite grains were observed at the microscopic level (Fig. 4a, \nc, d). The microstructure of the specimens after ECAP at 450 оC was more uniform, no shear \nmicrobands manifested clearly were observed (Fig. 4d). The nanotwins are seen in some austenite \ngrains (Fig. 4d), which can be classified as the strain-induced martensite according to [17-20]. No \nnucleation of the chromium carbide particles was observed in the steel microstructure after ECAP. \nNo -phase particles were reveled in the UFG microstructure during the metallographic and SEM \ninvestigations that allows making a conclusion on a strong fragmentation of these ones during \nECAP. The presence of separate point reflections in the electron diffraction pattern evidenced the \npresence of the high-angle grain boundaries in the UFG steel obtained by ECAP at 450 оC (Fig. 4f). \nThe electron diffraction patterns from the specimens of the UFG steel after ECAP at 150 оC were \nmore blurry (Fig. 4b). \nThe investigations of the thermal stability of the UFG microstructure during annealing \ndemonstrated the temperature of recrystallization in the UFG steel (N = 4, T ECAP = 450 C) to be Т 1 \n= 750 C. The recrystallization had a clearly expressed abnormal character accompanied by a \nformation of a multi-grained structure. After annealing at 750 C, 1 hour, the recrystallized metal \nregions with the mean grain sizes of 5-7 m were observed in the microstructure of the UFG steel. \nThe volume fraction of these regions was ~3% or less. At increased annealing temperatures, an \nincrease in the volume fraction of the recrystallization metal as well as an increase in the mean \ngrain sizes were observed – after annealing at 900 C, 1 hour, an equiaxial austenite microstructure \nwith the mean grain sizes of 8-12 m formed in the steel (Fig. 5). Increasing the number of ECAP cycles up to N = 4 at Т ECAP = 450 C didn’t result in any change of the recrystallization temperature \nТ1 but was accompanied by a decrease in the mean recrystallized grain sizes (Fig. 5).  \nThe XRD phase analysis demonstrated a decrease in the mass fraction of the ()-phase \nwith increasing annealing temperature up to 600°C (1 h). After annealing at 800 оC, the mass \nfraction of the ()-phase was beyond the measurement uncertainty ±1 wt.% (the intensity of the \nXRD peaks from the ()-phase didn’t exceed the noise level) regardless to the ECAP regimes. \nThe in situ TEM investigations demonstrated the nucleation of the light-colored \nnanoparticles in the UFG steel when heating up to 600 оC. The mean size and the volume fraction \nof the particles increased with increasing heating temperature. After heating up to 800 оC and \nholding for 0.5 hrs, the mean particle size was about 50 nm (Figs. 6, 7). Because of the presence of \nthe ()-phase having an essential residual magnetization in the steel, we failed to analyze the \ncomposition of the nucleated second phase nanoparticles by EDS. We suggest these particles to be \nthe -phase ones. The peaks from the -phase were absent in the XRD curves from the annealed \nspecimens, probably, due to small sizes of the nucleated particles. Earlier, the possibility of \nnucleation of the -phase particles during annealing of UFG steel 08Х18Н10Т was reported in [18, \n19]. \n \nMechanical properties at room temperature \nAs shipped, the CG steel had the macroelasticity stress ( о) and the yield strength ( y) equal \nto 205 MPa and 380 MPa, respectively. The processing by ECAP resulted in an improvement of the \nmechanical properties of the steel. The о increased up to 340 MPa and 425 MPa and the y – up to \n940 and 1070 MPa, respectively with increasing number of ECAP cycles from N  = 2 to 4 at Т ECAP = \n450 C (Fig. 8a). The magnitudes of the yield strength and of the macroelasticity stress of the UFG \nsteel depended on the ECAP temperature weakly – the y increased from 1070 to 1145 MPa and the \no decreased from 425 to 410 MPa with decreasing ECAP temperature from 450 down to 150 °C \n(N = 4). The analysis of the yield strength dependence on the mean grain sizes has shown that this \ndependence can be interpolated by a straight line in the y – d-1/2 axes with a good precision (Fig. \n8b). This evidences the Hall-Petch relation to hold:  \ny = о + K·d-1/2,       (1) \nwhere K is the grain boundary hardening coefficient (Hall-Petch coefficient) describing the \ncontribution of the grain boundary structure in the strength of the metal. The mean value of the \ncoefficient K determined from the dependence in Fig. 8b is K = 0.46 MPa m1/2. \nFig. 9 presents the dependencies of the macroelasticity stress (Fig. 9a) and of the yield \nstrength (Fig. 9b) on the temperature of 1 hour annealing of the UFG steel. One can see in Fig. 9a \nthat the dependencies σ о(Т) have a three-stage character. The first stage (RT–300 оC) is \ncharacterized by a constant value σ о. At the second stage of annealing (500–600 оC), an increase in \nthe macroelasticity stress was observed, which probably originates from the nucleation of the \nsecond phase particles (see above). At the third stage of annealing, at the temperatures greater than \n600 оC, a decrease of σ о down to the values typical for the CG steel in the as–shipped state was \nobserved. The softening of the UFG steel at this stage of annealing was related to the \nrecrystallization leading to an increase in the grain sizes.  \nThe dependence of the yield strength on the annealing temperature had usual two-stage \ncharacter (Fig. 9b). Note that the increase in the macroelasticity stress at 600 оC originating from \nthe nucleation of the second phase particles didn’t lead to the increase in the yield strength as one \ncould expect because of the Hall-Petch law (see (1)). This result evidences active grain boundary \nrecovery processes to go at this stage. These processes lead to a decrease in the defect density in the \ngrain boundaries [50].  \nNote also that the values of the macroelasticity stress and of the yield strength of the CG \nsteel almost didn’t change when annealing at the temperatures up to 700 оС. After heating up to \nhigher temperatures, an insufficient decrease in σ о and in σ y was observed. After annealing at 900 \nоC, the values of the macroelasticity stress and of the yield strength for the CG steel and for the UFG one were close to each other. \nThe stress–strain tension curves () of the CG steel specimens and of the UFG ones at RT \nare presented in Fig. 10. The () curve of the CG steel had a classical form, with a long strain \nhardening stage. The magnitude of the tensile strength of the CG steel was b = 720 MPa. This is a \nvery high value, which probably originates from the presence of the –ferrite particles and from \nrelatively small grain sizes in austenite (~20 m) in the hot-deformed steel. In the stress–strain \ntension curves () of the UFG steel specimens, there are a short stage of stable strain flow, which \ntransforms into a stage of localization of the strain. Increasing the ECAP temperature from 150 up \nto 450 оC resulted in an insufficient increase in the duration of the uniform strain stage. \nThe tension tests of the CG and UFG steel specimens demonstrated the formation of the \nUFG structure by ECAP (N = 4 at Т = 150 оC) to result in a decreasing of the elongation to failure \n() of the steel from 125 down to 45% and in an increasing of the ultimate strength from 720 up to \n1100 MPa (Table 1). ECAP at higher temperature (450 оC) resulted in an insufficient decreasing of \nthe ultimate strength down to 1020 MPa and in an increasing of the elongation up to  ~ 60%. \nThe fractographic analysis revealed three characteristic zones on the fractures of the CG \nsteel specimens and of the UFG ones after the tension tests. These are: the fibrous zone, the radial \none, and the break (cut) zone (Fig. 11). It is worth noting that the cut zones in the CG steel occupied  \n~50 % of the whole fracture area. In the UFG steel after ECAP (N  = 4), the cut zones occupied \n~70%. So far, the formation of the UFG microstructure resulted in an increasing of the cut zone \nfraction of the fracture area and, hence, in a decreasing of the viscous component of the fracture.  \n \nStress relaxation resistance \nFig. 12a presents the stress relaxation curves i() for the specimens of the CG steel and of \nthe UFG ones. The stress relaxation curve i() for the CG steel had a classical three-stage \ncharacter: one can distinguish the macroelasticity strain stage, the microplastic strain stage, and the \nmacroplastic strain one clearly enough. Note that one can see the stress relaxation curves i() to be close to each other at the stresses < 150-170 MPa; no essential differences in the stress relaxation \nmagnitudes were observed. In the microplastic strain range (where the stress increased from 150-\n170 MPa up to 300-320 MPa), the stress relaxation magnitude i of the CG steel specimens began \nto increase drastically and reached ~15 MPa at the stress of 320 MPa. At further increasing of the \nstress up to 580-600 MPa (in the macroplastic strain region), a smooth increasing of the stress \nrelaxation magnitude up to i ~20 MPa was observed. \nThe stress relaxation curves for the UFG steel specimens had more smooth character than \nthe curves i() for the CG steel ones. Note that the fairly expressed macroplastic strain stage was \nalmost absent – as one can see in Fig. 12a, the microplastic strain stage transforms into the \nmacroplastic strain one smoothly enough. The increasing of the of the number of the ECAP cycles \nresulted in a displacement of the curves i() towards the higher stresses. One can see in Fig. 12a \nthat the stress relaxation magnitude i ~20 MPa in the UFG steels subjected to N = 1 ECAP cycle \nwas achieved at the stress of 670-690 MPa whereas in the UFG steels obtained by N = 4 cycles of \nprocessing by ECAP, this stress relaxation magnitude was achieved at the stress of 935–950 MPa \n(TECAP = 450 оC) and 990–1010 MPa (T ECAP = 150 оC). \nSo far, one can conclude the processing of the austenitic steel by ECAP to result in the \nincreasing of its stress relaxation resistance – in the increasing of the macroelasticity stress o (see \nabove) and in the decreasing of the stress relaxation magnitude i at increased loads. \nThe recrystallization annealing resulted in a decreasing of the stress relaxation resistance \nparameters of the UFG steels – as one can see in Fig. 12b, the increasing of the annealing \ntemperature above 650-700 оC resulted in a displacement of the stress relaxation curves i() \ntowards the smaller stresses. After annealing at 800-900 оC, the stress relaxation curves of the \ndeformed steel specimens had usual tree-stage character corresponding to the stress relaxation curve \ni() of the coarse-grained steel specimens (Fig. 12a). \n  Tension testing at elevated temperatures \nTable 2 presents the dependencies of the ultimate strength and of the elongation to failure on \nthe testing temperature for the coarse-gained steel specimens and for the UFG ones obtained in \ndifferent ECAP temperatures. Fig. 13 presents the stress–strain curves () for the tension tests at \nelevated temperatures. \nThe stress–strain curves () for the CG steel specimens had the form typical for high-\nplasticity materials (Fig. 13a). The duration of the localized plastic strain stage was much smaller \nthan of the uniform strain one. The curves () for the UFG steel specimens at the testing \ntemperatures of 750 and 800 оC had the form typical for highly plasticity materials – the stage of an \ninsufficient strain hardening transformed into a long state of stable strain flow (Figs. 13b, c). The \nanalysis of the dependencies presented in Fig. 13 demonstrated the increasing of the temperature \nfrom RT up to 750 C to result in a monotonous decreasing of the ultimate strength (the flow stress) \nfrom 720 MPa down to 250 MPa for the CG steel and from 950–1100 MPa down to 240–290 MPa \nfor the UFG steel, respectively.  \nNote that the increasing of the testing temperature resulted in a nonmonotonous variation of \nthe elongation to failure for the UFG steel that differs from the same dependencies for the CG steel. \nThe analysis of the data presented in Fig. 13b shows the elongation to failure for the CG steel to \ndecrease monotonously from 125% down to 70% with increasing testing temperature from RT up to \n750 C. The character of the dependence (Т) for the UFG steel was more complex – the elongation \nto failure decreased insufficiently with increasing testing temperature from RT up to 450 C. At \nfurther increasing of the temperature from 450 C up to 750–800 C, the elongation to failure of the \nUFG steel increased and was several times higher than the  of the CG steel. For the UFG steel \nspecimens obtained by ECAP at Т ECAP = 150 C, the elongation to failure at the testing temperature \nof 750 C reached 250 %. Further increasing of the testing temperature resulted in a decreasing of \nthe elongating to failure for the UFG steel specimens again. The fractographic analysis of the fractures (Fig. 14) demonstrated the areas of the fibrous \nzones and of the radial ones to increase and the areas of the cut zones – to decrease with increasing \ntesting temperature. At the testing temperature of 600 C, the cur zone area didn't exceed 5–10% of \nthe whole fracture area. For the UFG steels (T ECAP = 450 C), the cut zones were absent that also \nevidences an increased plasticity of the UFG material as compared to the coarse-grained state. \nIn our opinion, the non-monotonous character of the dependence of the elongation to failure \non the testing temperature for the UFG steel originates from the recrystallization processes in the \nUFG steel starting after annealing at ~650–700 C. \nIn particular, the microhardness testing results (Table 2) evidence the intensive \nrecrystallization at the high-temperature strain of the UFG steel. The microhardness measurements \nof the specimens after the tension tests demonstrated the increasing of the testing temperature from \n450 up to 800 C to result in a decreasing of the microhardness both in the deformed areas and in \nthe non-deformed ones. This conclusion is supported by the results of the microstructure \ninvestigations in the deformed areas of the UFG steel specimens and in the non-deformed ones after \nthe tension tests (Fig. 15). As one can see from Fig. 15 and from the data presented in Table 3, the \ntesting at 800 оС resulted in the formation of a well uniform fine-grained structure. No essential \ngrain growth was observed. The mean grain sizes in the deformed parts were slightly smaller than \nin the non-deformed ones. \n \nCorrosion resistance \nFig. 16a presents the Tafel curves ln(i)–E for the coarse-grained steel specimens and for the \nUFG ones. The results of the electrochemical testing are summarized in Table 3. The curves ln(i)–E \nhad usual character. One can see the coarse-grained steel specimens to have smaller corrosion rates \nthan the UFG ones. For the UFG steel specimens obtained by ECAP at Т = 450 оC, the values of \nmean corrosion current density i corr (of the mean corrosion rate V corr) were 10–15% greater than the \nsame characteristics for the UFG steel specimens obtained by ECAP at 150 оC.  Fig. 16b presents the curves i(E) illustrating the results of testing by the DLEPR method \naccording to GOST 9.914-91. The results of these tests are summarized in Table 3. It follows from \nthe data presented in Table 3 that the ratios of the areas under the passivation curves (S 1) and the \nreactivation ones (S 2) (K = S 1/S2) were small and appeared to be much less than the ultimate value \nKmax = 0.11. This result evidences both coarse–grained steel and UFG one to be highly resistant \nagainst IGC. At the same time, the magnitudes of the coefficient K for the UFG steel specimens \nwere 1.5–2.5 times higher than for the CG ones. The metallographic analysis of the surfaces has \nshown the large elongated -ferrite particles to be the places of accelerated corrosion destruction of \nthe surfaces in the DLEPR testing (Fig. 17a). No IGC traces were observed on the surfaces of the \nUFG steel specimens (Fig. 17b). \nThe results of standard tests of the resistance against IGC according to GOST 6232-2003 \nconfirmed high corrosion resistance of the UFG steels. As one can see in Fig. 18a, after testing \nduring 24 hrs, the corroded elongated -ferrite particles were observed on the CG steel surfaces. In \nsome areas of the surfaces, the IGC corrosion defects or the pitting corrosion no more than 10–15 \nm in depth are seen. On the surfaces of the steel specimens with the UFG structure formed as a \nresult of 1 or 2 ECAP cycles, few corrosion pits were observed. On the surfaces of the UFG steel \nspecimens (N = 3, 4), the corrosion defects were absent (Fig. 18b). \nSo far, the UFG steel specimens have high strength, stress relaxation resistance, and high \nresistance against the intergranular corrosion simultaneously. It allows an efficient application of \nthe UFG steel for making the stress relaxation–proof machine–building hardware utilized in the \nconditions of enhanced loads and corrosion–aggressive media. \n \nDiscussion \nInvestigation of thermal stability \nFirst, one should pay attention to the fact of nucleation of the second phase particles during \nthe annealing of the UFG austenitic stainless steel. It is interesting to note that the nucleation of the second phase particles was observed not in all grains. In our opinion, the nucleation of the particles \ngoes preferentially inside the grains of –phase, the lattice constant of which is much less than the \none of the –phase. It leads to a formation of a strongly supersaturated solid solution (of chromium) \nin the –phase grains and, as a consequence, to its nucleation at further heating up. This assumption \nallows suggesting the nucleation of ferromagnetic –phase particles Fe-Cr to take place in the \ncourse of heating up. We suppose the nucleation of chromium carbide Cr 23C6 particles to be hardly \nprobable in this case since steel contains titanium, which reacts chemically with carbon and forms \ntitanium carbide TiC [10, 18, 20, 22]. The possible nucleation of the -phase particles during \nannealing of metastable UFG austenitic steel Fe-Cr-Ni-Ti was reported in [18, 19]. \nThe analysis of the grain growth process revealed the grain growth activation energy (Q R) \ndetermined from the slope of the dependence ln(dn-d0n) – Tm/T to be 6.0–8.3 kT m (~ 90–125 kJ/mol) \n(Fig. 5). The uncertainty of determining the activation energy Q R was ±1 kT m. The calculated \nactivation energy depends on the number of ECAP cycles or on the ECAP temperature weakly. In \nthe calculations, the magnitude of coefficient n was taken to be n = 4 that corresponds to the case of \nthe migration of grain boundary with the particles nucleated at the ones [52]. The melting point of \nsteel was taken to be T m = 1810 K. Note that the recrystallization activation energy was ~20–30% \nsmaller than the equilibrium activation energy of the grain boundary diffusion in austenite Q b ~ 10.6 \nkTm (159 kJ/mol [52]). In our opinion, this result evidences the nonequilibrium grain boundaries in \nthe UFG steel obtained by ECAP to contain an increased concentration of defects – the orientation \nmismatch dislocations (OMDs) and the products of the delocalization of the ones (the tangential \ncomponents of Burgers vectors of the delocalized dislocations) [52]. The increased density of \ndefects in the grain boundaries leads to an increasing of the free volume of the grain boundaries in \nthe UFG material [52] and, as a consequence, to a decreasing of the activation energy of the grain \nboundary diffusion [52]. \nNote also that at n = 2, the recrystallization activation energy Q R takes non-physical values \n(3–4.3 kT m ~ 45–63 kJ/mol), which appear to be smaller than the activation energy of diffusion in the iron melt (see [52]). In our opinion, it evidences indirectly the nucleating nanoparticles to affect \nthe grain boundary migration in the deformed austenite steel essentially. \n \nMechanical properties \nThe yield strength in the austenitic steel can be calculated using Hall-Petch equation (1) \nwhere the magnitude of the macroelasticity stress in the first approximation can be calculated as the \nsum of the following contributions: \nσ= σ+∑A୧C୧+αଵMGbඥρ୴+2ଶMGb⁄,     (2) \nwhere PN is the stress of resistance of the crystal lattice (the Peierls-Nabarro stress), с=∑A୧C୧ \naccounts for the contributions of the doping elements into the strengthening of austenite (A i is the \ncontribution of the ith doping element, the concentration of which is C i into the hardening of \naustenite) [55], σୢ= αଵMGbඥρ୴ is the contribution of the hardening dislocations ( v being the \ndensity of the lattice dislocations) [55], σ୮= 2ଶMGb⁄ is the contribution of the second phase \nparticles (  is the distance between the particles), where G = 81 GPa is the shear modulus, b = \n0.258 nm is the Burgers vector, 1 = 0.3-0.67 is a numerical coefficient depending on the character \nof the distribution and of the interaction of the lattice dislocations, 2 = 0.5 is a numerical \ncoefficient, M = 3.1 is the orientation factor (the Taylor coefficient). \nAccording to [55, 56], the contribution of the crystal lattice of the doped austenite for steel \nand the heat-resistance nickel alloys is PN = 60-70 MPa. The contribution of the second phase \nparticles can be neglected in the first approximation since the nucleated particles were large enough \n(Fig. 1d) and were located far enough from each other: at  = 5-10 m, the contribution of the \nsecond phase particles is d ~ 10 MPa.  \nSince the contribution of Ni in the hardening of austenite is small [55], one can suggest the \ndislocation hardening makes the major contribution in the magnitude of the macroelasticity stress of \nthe austenite steel ( 0 = 240 MPa). The magnitude of d = 0 - PN = 170–180 MPa at 1 = 0.3 corresponds to the density of lattice dislocations of v ~ 8·1013 m-2 whereas at 1 = 0.67 to v ~ \n1.5·1013 m-2. This estimate of v matches well to the data reported in the literature [17-20]. \nFor the mean value of K = 0.46 MPa m1/2 (see above) and d  ~ 20 m, the contribution of the \ngrain boundary hardening gb = K·d-1/2 in the CG austenitic steel is ~105 MPa.  \nThe calculated value of the yield strength of the CG austenitic steel y = 240 MPa + 105 \nMPa = 245 MPa was lower than the experimentally measured value (380 MPa). \nIn our opinion, there are two main origins of the discrepancy between the results of \ncalculations and the experimental data. \nFirst, it is worth noting the large particles of -ferrite in the microstructure of austenitic \nsteel, which can impede the micro- and macroplastic strain. Traditional approach to the calculation \nof the yield strength of the steel with such a composite structure consists in accounting for the \nvolume fraction and the yield strength of -ferrite: σ୷= fஓσ୷(ஓ)+fσ୷() where f  and f  are the \nvolume fractions of austenite ( -Fe) and of -ferrite, y() and y() are the yield strength of austenite \nand -ferrite, respectively. Unfortunately, at present it is impossible to measure the yield strength of \n-ferrite y() correctly. In this connection, it is impossible to estimate the effect of such meso-\nbarriers on the ultimate strength correctly at present. \nThe second origin is, from our viewpoint, is the effect of the structural and phase state of the \ngrain boundary on the magnitude of the Hall-Petch coefficient K. It leads to an essential difference \nof the mean value of K calculated from the dependence y – d-1/2 from the Hall-Petch coefficients in \nthe coarse–grained steel (K 0) and in the UFG steel (K 1). \nNote also that the intensities of increasing of the macroelasticity stress о and of the yield \nstrength y with increasing number of ECAP cycles (N) were different (Fig. 9a). Analysis of the \ndata presented in Fig. 9a shows the magnitude of gb = y - о = Kd-1/2  in the initial state to be 175 \nMPa and to increase up to gb = 645-655 MPa with increasing N up to 3–4 (Т ECAP = 450 C). Note \nthat at the same time, the magnitude of the grain boundary hardening coefficient K calculated according to the formula K = ( y - о)d1/2 (see (1)) decreased monotonously with increasing number \nof ECAP cycles. The magnitude of the Hall-Petch coefficient K for the CG steel was 0.78 \nMPa·m1/2. After N = 3 and N = 4 ECAP cycles at 450 С, it decreased down to 0.46 and 0.35 \nMPa1/2, respectively. Similar effect was observed for the UFG steel specimens obtained by ECAP at \nТECAP = 150 C. \nIn our opinion, the decreasing of the coefficient K in ECAP is related to the fragmentation of \nstrongly elongated -ferrite particles (up to 10 m in thickness and up to 500 m long). The harder \n-ferrite particles crossing the austenite grains often (Fig. 1) can impede the propagation of the \nstrain in the austenite grains as well as the “transfer” of the strain from one austenite grain to \nanother. In our opinion, strong fragmentation of the harder particles during ECAP helps eliminating \nthe additional type of the “barrier” obstacles and promotes the strain at the micro- and macrolevels. \nIn our opinion, the fragmentation of the large elongated -ferrite particles is one of the possible \norigins of the presence of the uniform strain flow stage in the stress–strain tension curves at room \ntemperature (Fig. 10). \nTaking for the CG steel K = 0.78 MPa m1/2 (see above) and d  ~ 20 m, one gets the \ncontribution of the grain boundary hardening in the CG steel gb ~ 175 MPa. In this case, one gets \nthe value of yield strength of the CG austenite steel calculated taking into account the correction for \nthe magnitude of K y = 240 MPa + 175 MPa = 415 MPa. The calculated value of the yield strength \nmatches well to the one measured experimentally ( y = 380 MPa). \nThe magnitudes of the macroelasticity stress and of the yield strength for the UFG steel after \nN = 4 ECAP cycles were 410–425 MPa and 1070–1145 MPa, respectively. \nSince the contributions PN, c, and p don't change doting ECAP, in our opinion, the \nincreasing of the macroelasticity stress in 30-45 MPa originated from the increase in the density of \nthe lattice dislocations  up to ~1.2·1014 m-2 (at 1 = 0.3) whereas the increasing of the yield strength \n– from the decrease in the grain sizes down to the submicron level. \n Stress relaxation resistance \nAs it has been shown above, the UFG steel has a higher stress relaxation resistance – the \nstress relaxation magnitude i in the UFG steel were much smaller at the same stress applied (Fig. \n12a). Let us analyze the stress relaxation mechanisms in UFG steel underlying its improved stress \nrelaxation resistance. \nIn general, the accommodative reconstruction of the defect structure (first of all – of the \ndislocation one) is well known to be the primary stress relaxation mechanism. In the coarse-grained \nmaterials at RT, the lattice dislocation glide in the field of the point defects distributed uniformly is \nsuch a mechanism most often. The dependence of the strain rate ε̇ on the stress  in this case can be \ndescribed by the following formula \nε̇= ε̇expቀ−∆\n୩ቄ1−\n∗ቅቁ,      (3) \nwhere ε̇ is the pre-exponential factor, F is the activation energy of dislocation glide depending on \nthe obstacles type, k is the Boltzmann constant, Т is the testing temperature, and * is the non-\nthermal flow stress, which can be taken to be equal to the ultimate strength [55]. \nIn the first approximation, the strain rate in the stress relaxation tests can be accepted to be \nproportional to the stress relaxation one: ε̇= σ̇/E, where E is the elastic modulus. The stress \nrelaxation rate can be calculated as σ̇=t୰⁄. Since the stress relaxation time t r = 60 s and Е = 217 \nGPa were the same for all specimens, the magnitude of the activation energy F/kT can be \ndetermined from the slope of the dependence ln( ) – 1-/b (Fig. 19a).  \nAs one can see in Fig. 19a, the dependence ln( ) – 1-/y for the CG steel has a two-stage \ncharacter. The activation energy of dislocation glide in the microplastic strain range is F1 ~4.8 kT \n(~0.62 Gb3) that matches well to the data published in the literature (~ 0.5 Gb3 for the steels AISI \n304 and AISI 316 [57]). It allows concluding the gliding of lattice dislocations in the long-range \nstress field from other lattice dislocations to be main stress relaxation mechanism within the \nmicroplastic strain stage. At increased stresses, the activation energy of overcoming the obstacles \ntends to F2 ~ 0.9 kT (~0.12 Gb3). According to the classification of [57], the obstacles with F < 0.2 Gb3 are the classified as the “weak” ones for the dislocation motion. In the case of the coarse-\ngrained steel deformed in the macroscopic strain range, obviously, the austenite grain boundaries \ncan be such obstacles. \nIn the case of the UFG steel, the stage with the increased F1 ~4.9–6.2 kT (~0.63–0.80 Gb3) \nwas observed at small stresses only. In the range of micro- and macroplastic strain, the magnitude \nof activation energy of overcoming the obstacles was F2 ~2.2–2.3 kT (~0.28–0.30 Gb3). In the \nUFG metals, the grain boundaries are the main type of the obstacles for the gliding of the lattice \ndislocations. In this connection, one can suggest that the long microplastic strain stage characterizes \nthe overcoming of the grain boundaries by the lattice dislocations.  \nNote that the magnitude of F2 in the UFG steel (~0.28–0.30 Gb3) is considerably greater \nthan the one in the coarse-grained steel (~0.12 Gb3). \nThe nonequilibrium grain boundaries in the UFG metals are known to contain an increased \ndensity of the OMDs featured by the density bb and of the products of delocalization of the ones \n– the tangential (“sliding”) components of the Burgers vectors of the delocalized dislocations and of \nthe normal ones featured by the densities w t and w n, respectively [52]. The defects introduced into \nthe grain boundaries during ECAP generate the long–range internal stress fields, which impede the \nsliding of the lattice dislocations inside the austenite grains and prevent the formation of the \ndislocation clusters at the grain boundaries [52]. In our opinion, this factor is the primary origin of \nthe increasing of the activation energy for overcoming the grain boundaries by the lattice \ndislocations F2 in the UFG steel. This assumption is supported indirectly by the change of the \nactiation energy F2 at the annealing of the UFG steel (Fig. 19b). As one can see in Fig. 12b, the \nrecrystallization annealing of the UFG steel leads to the change in the character of the stress \nrelaxation curves (). The annealing of the UFG steel at the temperatures below 700 оC \n(corresponding to the start of recrystallization) doesn't lead to any essential change of F2 ~ 2.70–\n2.92 kT (0.34–0.37 Gb3). After annealing at 750-800 оC, the form of the ln( ) – 1-/b \ndependence turned into a two-stage one while the magnitude of F2 decreases monotonously from 1.39–1.49 kT (0.17–0.19 Gb3). It is interesting to note that the magnitude of the activation energy \nF1 for the annealed UFG steel decreases monotonously from 5.6 kT (0.70 Gb3) at Т = 800 оC up to \n9.2 kT (1.16 Gb3) at Т = 900 оС (Fig. 19b). In our opinion, this result is related to the nucleation of \nthe second phase particles in the course of heating up (Fig. 7). \nSo far, the formation of the long–range internal stress fields from the nonequilibrium grain \nboundaries, which prevent the free motion of the lattice dislocations (prevent the accommodative \nreconstruction of the defect structure) is the origin of the increased stress relaxation resistance of the \nUFG steel. \nThe change of the phase composition of the steel can be an additional factor increasing the \nstress relaxation resistance at ECAP. As follows from the analysis of the results of the XRD \ninvestigations, the stainless steel after N = 4 ECAP cycles contains from ~ 7–8% (Т ECAP = 150 оC) \nup to 17–18% (Т ECAP = 450 оC) of stronger ()-phase particles. At the same external stress, the \nstress relaxation magnitude (the accommodation reconstruction of the defect structure) in the \nstronger ()–phase will be smaller than the one in the -phase. In this connection, the increasing of \nthe content of the stronger ()–phase particles can promote the increase in the stress relaxation \nmagnitude of the UFG steel. \n \nCorrosion resistance \nAnalysis of the results of the corrosion tests demonstrated ECAP to result in an insufficient \nincrease in the uniform corrosion rate V corr calculated according to the Tafel method. Besides, the \nanalysis of the results of the electrochemical testing by the DLEPR method demonstrated the UFG \nsteel to have a higher tendency to the IGC as compared to the coarse–grained steel. It should be \nstressed here that in spite of the increased tendency to the IGC, the UFG steel satisfies the \nrequirements of GOST 9.914-91 in the resistance against IGC completely. \nIn our opinion, the increasing of the volume fraction of strain–induced martensite and, \nhence, the formation of the two–phase + microstructure is the main origin of increased corrosion rate and of reduction of the resistance against to IGC in the UFG steels. The strain–induced \nmartensite particles having a different chemical composition (unlike austenite) have a higher \ncorrosion (dissolving) rate. Therefore, the increasing of the volume fraction of strain–induced \nmartensite will lead to increasing of the uniform corrosion rate according to the ordinary rule: V corr \n= fV + fV where V  and V  are the dissolving rates for the – and –phases, respectively.  \nThe formation of the two–phase microstructure leads to the appearing of the microgalvanic \ncouples austenite – martensite in the material. These ones are the places of accelerated corrosion \ndestruction during the electrochemical tests for IGC. So far, the increasing of the volume fraction of \nstrain–induced martensite provides the conditions for the increase in the uniform corrosion rate and \nin the intergranular corrosion one. \nThe second factor promoting the reduction of the resistance of the stainless steel against IGC \nafter ECAP can be the redistribution of the doping elements (chromium and nickel) during SPD. In \n[58], the grain boundaries in the nanocrystalline austenitic steel Fe-12%Cr-30%Ni with the grain \nsize ~60 nm were shown to be enriched with nickel after SPD but to have a reduced chromium \nconcentration. The width of the near-boundary zone enriched with nickel was predicted \ntheoretically to increase with increasing temperature [58]. The strain-induced segregation of the Ni \natoms at the austenite grain boundaries was utilized to explain the formation of the ferromagnetic \nclusters at the grain boundaries in the Fe-12%Cr-30%Ni and Fe-12%Cr-40%Ni steels during SPD \n[59]. Such a deformation-stimulated bundle of the solid solution would promote an accelerated \nelectrochemical corrosion near the grain boundaries in the UFG steel Fe-18%Cr-10%Ni-0.1%Ti. \n \nConclusions  \n1. The samples of the UFG steel with improved mechanical properties were obtained by \nECAP. After N = 4 ECAP cycles at 150 and 450 оC, the values of the ultimate strength of the steel \nwere 1100 and 1020 MPa, respectively. The main contribution into the increasing of the strength of \nsteel during ECAP is made by the increasing of the dislocation density and by the modification of the grain structure down to the submicron scale. The stages of the uniform strain flow were \nobserved in the stress–strain tension curves () of the specimens of the UFG steel at RT. The \nspecimen fractures had a viscous character. The XRD phase analysis revealed the strain–induced \nmartensite to form during ECAP. The strain–induced martensite content in the UFG steel \nmicrostructure achieves 17-18%. \n2. The annealing of the UFG steel at the temperatures over 700 оC leads to the beginning of \nthe recrystallization processes, which is accompanied by the decreasing of the volume fraction of \nthe strain–induced martensite and by the nucleation of the light–colored nanometer-sized particles, \nwhich presumably consist of –phase. The activation energy of the grain boundaries migration \n(6.0–8.3 kT m) is 20-30% smaller than the one of the diffusion along the austenite grain boundaries. \nThe reduction of the activation energy is caused by the presence of the excess density of defects – \nthe orientation mismatch dislocations and of the products of the delocalization of these ones – at the \nnonequilibrium grain boundaries. \n3. The UFG steel is featured by an improved stress relaxation resistance – by a higher \nmacroelasticity stress and a smaller stress relaxation magnitude (at given magnitude of the stress \napplied). The increased stress relaxation resistance of the UFG steel is caused by a special internal \nstress relaxation mechanism related to the interaction of the lattice dislocations with the \nnonequilibrium grain boundaries in the UFG steel. The second probable origin of the increased \nstress relaxation resistance of the UFG steel can be the presence of stronger strain–induced \nmartensite particles, which the accommodation reconstruction of the dislocation structure is \ndifficult in. \n4. The ECAP process leads to the reduction of the corrosion resistance of the austenite steel \n– the increase in the uniform corrosion rate and the increasing of the tendency of the steel to the \nintergranular corrosion were observed. The reduction of the corrosion resistance is caused, first of \nall, by the presence of the strain–induced martensite particles, which have a greater dissolving rate. \nThe presence of the strain–induced martensite particles leads to the appearance of the microgalvanic couples martensite – austenite in the steel microstructure, at the grain boundaries of which an \naccelerated intergranular corrosion is possible. \n \nAcknowledgements \nThe present study was supported by Ministry of Science and Higher Education of the \nRussian Federation (Grant No. 0729-2020-0060).  \nThe TEM microstructure were carried out the equipment of shared research facility \n“Materials Science and Metallurgy” NUST “MISIS” funded by Ministry of Science and Higher \nEducation of the Russian Federation (Project No. 075-15-2021-696). \n \nAuthor Contribution Statement \nV.N. Chuvil’deev - Project administration, Writing - review & editing, Funding acquisition \nA.V. Nokhrin – Investigation (fractography, SEM) & Analysis of experimental results & Writing of \nmanuscript & Data curation \nN.A. Kozlova – Investigation (corrosion test) \nM.K. Chegurov – Investigation (corrosion test,  fractography) \nM.Yu. Gryaznov, S.V. Shotin – Investigation (mechanical tensile tests) \nV.I. Kopylov – Investigation (obtained by UFG steel by ECAP, optimization of ECAP modes) \nN.V. Melekhin – Investigation (relaxation test) \nC.V. Likhnitskii – Investigation (microhardness, optical microscopy) \nN.Yu. Tabachkova - Investigation (TEM) \n \nConflict of interest . The authors declare that they have no conflict of interest.  \nReferences  \n1. K.H. Lo, C.H. Shek, J.K.L. Lai, Recent developments in stainless steels, Materials Science and \nEngineering R. 65 (4-6) (2009) 39-104. doi:10.1016/j.mser.2009.03.001 \n2. V.V. Sagaradze, Yu.I. Filippov, M.F. Matvienko, et al., Corrosion cracking of austenitic and \nferrite-pearlite steels, Russia, Yekaterinburg: UB RAS. (2004). (in Russian). \n3. V.V. Sagaradze, A.I. Uvarov, Hardening and properties of austenitic steels. Russia, \nYekaterinburg: M.N. Mikheev Institute of Metal Physics RAS. (2013). (in Russian). \n4. X. Mao, W. Zhao, Electrochemical polarization method to detect aging embrittlement of 321 \nstainless steel, Corrosion. 49 (3) (1993) 335-342. doi:10.5006/1.3316058  \n5. J. Ryi, A. Arutunow, M.T. Tobiszewski, J. Wysocka, Aspects of intergranular corrosion of AISI \n321 stainless steel in high-carbon-containing environments, Anti-Corrosion Methods and \nMaterials. 61 (5) (2014) 328-333. doi:10.1108/ACMM-04-2013-1260 \n6. A. Pardo, M.C. Merino, A.E. Coy, et al., Influence of Ti, C and N concentration on the \nintergranular corrosion behavior of AISI 316Ti and 321 stainless steel, Acta Materialia. 55 (7) \n(2007) 2239-2251. doi:10.1016/j.actamat.2006.11.021 \n7. M. Matula, L. Hyspecka, M. Svoboda, et al., Intergranular corrosion of AISI 316L steel, \nMaterials Characterization. 46 (2-3) (2001) 203-210. doi:10.1016/S1044-5803(01)00125-5 \n8. I.L. Rosenfeld, Corrosion and protection of metals. Russia, Moscow: Metallurgy. (1969). (in \nRussian). \n9. V. Moura, A.Y. Kina, S.S.M. Tavares, et al., Influence of stabilization heat treatments on \nmicrostructure, hardness and intergranular corrosion resistance of the AISI 321 stainless steel, \nJournal of Materials Science. 43 (2008) 536-540. doi:10.1007/s10853-007-1785-5 \n10. A.S. Grot, J.E. Spruiell, Microstructural stability of titanium-modified type 316 and type 321 \nstainless steel, Metallurgical Transactions A. 6 (1975) 2023-2030. doi:10.1007/BF03161827 11. V.Y. Gertsman, S.M. Bruemmer, Study of grain boundary character along intergranular stress \ncorrosion cracks paths in austenitic alloys, Acta Materialia. 49 (9) (2001) 1589-1598. \ndoi:10.1016/S1359-6454(01)00064-7 \n12. M.S. Laws, P.J. Goodhew, Grain boundary structure and chromium segregation in a 316 \nstainless steel, Acta Metallurgica et Materialia. 39 (7) (1991) 1525-1533. doi:10.1016/0956-\n7151(91)90238-V \n13. S.M. Bruemmer, L.A. Charlot, Development of grain boundary chromium depletion in type 304 \nand 316 stainless steels, Scripta Metallurgica. 20 (7) (1986) 1019-1024. doi:10.1016/0036-\n9748(86)90428-X \n14. E.L. Hall, C.L. Briant, Chromium depletion in the vicinity of carbides in sensitized austenitic \nstainless steels, Metallurgical Transactions A. 15 (1984) 793-811. doi:10.1007/BF02644554 \n15. H.U. Hong, B.S. Rho, S.W. Nam, Correlation of the M 23C6 precipitation morphology with grain \nboundary characteristics in austenitic stainless steel, Materials Science and Engineering A. 318 \n(1-2) (2001) 285-292. doi:10.1016/S0921-5093(01)01254-0 \n16. D.N. Wasnik, V. Kaim, I. Samajdar, et al., Resistance of sensitization and intergranular \ncorrosion through extreme randomization of grain boundaries, Acta Materialia. 50 (18) (2002) \n4587-4601. doi:10.1016/S1359-6454(02)00306-3 \n17. O.V. Rybal’chenko, S.V. Dobatkin, L.M. Kaputkina, et al., Strength of ultrafine-grained \ncorrosion-resistance steels after severe plastic deformation, Materials Science and Engineering \nA. 387-389 (1-2) (2004) 244-248. doi:10.1016/j.msea.2004.03.097 \n18. S.V. Dobatkin, O.V. Rybal’chenko, G.I. Raab, Formation of submicrocrystalline structure in \naustenitic 08KH18N10T steel during equal-channel angular pressing followed by heating, \nRussian Metallurgy (Metally), 2006 (1) (2006) 42-48. doi:10.1134/S0036029506010083 \n19. S.V. Dobatkin, O.V. Rybal’chenko, G.I. Raab, Structure formation, phase transformations and \nproperties in Cr-Ni austenitic steel after equal-channel angular pressing and heating, Materials \nScience and Engineering A, 463 (1-2) (2007) 41-45. doi:10.1016/j.msea.2006.07.156 20. S.V. Dobatkin, V.F. Terent’ev, O.V. Rybal’chenko, et al., Structure and fatigue properties of \n08KH18N10T after Equal-Channel Angular Pressing and heating, Russian Metallurgy \n(Metally). 2012 (11) (2012) 954-962. doi:10.1134/S0036029512110043  \n21. I.I. Kositsyna, V.V. Sagaradze, V.I. Kopylov, Formation of high-strength and high-plastic state \nin metastable austenitic steels by the method of equal-channel angular pressing, Physics of \nMetals and Metallography. 88 (5) (1999) 493-498.  \n22. S.V. Dobatkin, O.V. Rybalchenko, N.A. Enikeev, et al., Formation of fully austenitic ultrafine-\ngrained high strength state in metastable Cr-Ni-Ti stainless steel by severe plastic deformation, \nMaterials Letters. 166 (2016) 276-279. doi:10.1016/j.matlet.2015.12.094 \n23. S.S. Tavares, D. Gunderov, V. Stolyarov, J.M. Neto, Phase transformation induced by severe \nplastic deformation in the AISI 304L stainless steel, Materials Science and Engineering A. 358 \n(1-2) (2003) 32-36. doi:10.1016/S0921-5093(03)00263-6 \n24. C. Du, G. Liu, B. Sun, et al., A 2.9 GPa strength nano-gradient and nano-precipitated 304L-type \naustenitic stainless steel, Materials. 13 (23) (2020) 5382. doi:10.3390/ma13235382 \n25. D.O. Panov, R.S. Chernichenko, S.V. Naumov, et al., Excellent strength-toughness synergy in \nmetastable austenitic stainless steel due to gradient structure formation, Materials Letters. 303 \n(2021) 130585. doi:10.1016/j.matlet.2021.130585 \n26. D. Panov, E. Kudryavtsev, R. Chernichenko, et al., Mechanisms on the reverse martensite-to-\naustenite transformation in metastable austenitic stainless steel, Metals. 11 (4) (2021) 599. \ndoi:10.3390/met11040599 \n27. E. Ura-Bińczyk, Effect of grain refinement on the corrosion resistance of 316L stainless steel, \nMaterials. 14 (24) (2021) 7517. doi:10.3390/ma14247517 \n28. A.T. Krawczynska, W. Chrominski, E. Ura-Binczyk, et al., Mechanical properties and corrosion \nresistance of ultrafine grained austenitic stainless steel processed by hydrostatic extrusion, \nMaterials and Design. 136 (2017) 34-44. doi:10.1016/j.matdes.2017.09.050 29. J. Singh, Influence of deformation on the transformation of austenitic stainless steel, Journal of \nMaterials Science. 20 (1985) 3157-3166. doi:10.1007/BF00545181 \n30. M. Smaga, F. Walther, D. Eifler, Deformation-induced martensitic transformation in metastable \naustenitic steels, Materials Science and Engineering A. 483-484 (2008) 394-397. \ndoi:10.1016/j.msea.2006.09.140 \n31. I.Yu. Litovchenko, S.A. Akkuzin, N.A. Polekhina, et al., Effect of liquid nitrogen and warm \ndeformation on the microstructure and mechanical properties of 321-type metastable austenitic \nsteel, Materials Science and Engineering A. 824 (2021) 141525. \ndoi:10.1016/j.msea.2021.141525 \n32. X. Xiao, D. Li, Y. Li, S. Lu, Intergranular precipitation behavior and its influence on the stress \nrelaxation cracking susceptibility of Super304H austenitic stainless steel weld metal during \nlong-term aging, Materials Characterization. 178 (2021) 111309. \ndoi:10.1016/j.matchar.2021.111309 \n33. M. Yamashita, Y. Wada, The stress-relaxation behavior of type 304 stainless steel, International \nJournal of Pressure Vessels and Piping, 42 (2) (1990) 203-216. doi:10.1016/0308-\n0161(90)90020-I \n34. I. Dayalan, P.F. Crasta, S. Pradhan, R. Gupta, A review on stress relaxation cracking in \naustenitic stainless steel, In: Vasudevan H., Kottur V., Raina A. (eds) Proceedings of \nInternational Conference on Intelligent Manufacturing and Automation. Lecture Notes in \nMechanical Engineering. Springer, Singapore, (2020) 427-434. doi:10.1007/978-981-15-4485-\n9_44 \n35. K.B. Yoon, J.M. Yu, T.S. Nguyen, Stress relaxation cracking in 304H stainless steel weld of a \nchemical reactor serviced at 560 oC, Engineering Failure Analysis. 56 (2015) 288-299. \ndoi:10.1016/j.engfailanal.2015.01.014 36. Y.Q. Wang, M.W. Spindler, C.E. Truman, D.J. Smith, Critical analysis of the prediction of \nstress relaxation from forward creep of type 316H austenitic stainless steel, Materials and \nDesign. 95 (2016) 656-668. doi:10.1016/j.matdes.2016.01.118 \n37. M. Tendo, K. Yamada, Y. Shimura, Stress relaxation behavior at high-tension bolted \nconnections of stainless-steel plates, Journal of Engineering Materials and Technology. 123 (2) \n(2001) 198-202. doi:10.1115/1.1338481 \n38. M.J. Anciaux, Stress relaxation of austenitic stainless steels at 290 oC, Metallurgical \nTransactions A. 12 (1981) 1981-1985. doi:10.1007/BF02643812 \n39. A.M. Bordzyuka, L.B. Getsov, Stress relaxation in metals and alloys. Moscow, Nauka. (1978). \n(in Russian). \n40. B. Chen, D.J. Smith, P.E.J. Flewitt, M.W. Spindler, Constitutive equations that describe creep \nstress relaxation for 316H stainless steel at 550 oC, Materials at High Temperatures. 28 (3) \n(2011) 155-164. doi:10.3184/096034011X13119593388654 \n41. F. Povolo, R.J. Tinivella, J.F. Reggiardo, G.B. Botteri, Stress relaxation in bending of type \nAISI304 stainless steel at 773 and 823 K, Journal of Materials Science. 27 (1992) 1505-1513. \ndoi:10.1007/BF00542911 \n42. H. Yamada, C.-Y. Li, Stress relaxation and mechanical equation of state in austenitic stainless \nsteels, Metallurgical Transactions. 4 (1973) 2133-2136. doi:10.1007/bf02643278 \n43. H.-L. Peng, X.-F. Li, X. Chen, et al., Effect of grain size on high-temperature stress relaxation \nbehavior of fine-grained TC4 titanium alloy, Transactions of Nonferrous Metals Society of \nChina (English Edition). 30 (3) (2020) 668-677. \n44. M.K. Akhtar, F.A. Khwaja, M.Z. Butt, Effect of grain size on the stress-relaxation rate in Ti-6.5 \nat%Nb alloy crystals, Physica Status Solidi (a). 143 (1) (1994) 59-63. \ndoi:10.1002/pssa.2211430107 45. M.Z. Butt, M.S. Khiliji, On the strength and stress-relaxation response of fine-grained Cu-\n42.2at%Zn-0.6at%Pd alloy polycrystals, Journal of Alloys and Compounds. 479 (1-2) (2009) \n252-256. doi:10.1016/j.jallcom.2009.01.027 \n46. Y. Suzuki, K. Ueno, K. Murasawa, et al., Effect of surface area of grain boundaries on stress \nrelaxation behavior in pure copper over wide range of grain size, Materials Science and \nEngineering A. 794 (2020) 139585. doi:10.1016/j.msea.2020.139585 \n47. M.S. Mohebbi, A. Akbarazadeh, Y.-O. Yoon, S.-K. Kim, Stress relaxation and flow behavior of \nultrafine grained AA1050, Mechanics of Materials. 89 (2015) 23-34. \ndoi:10.1016/j.mechmat.2015.06.001 \n48. Y.M. Wang, A.V. Hamza, E. Ma, Temperature-depended strain rate sensitivity and activation \nvolume of nanocrystalline Ni, Acta Materialia. 54 (10) (2006) 2715-2726. \ndoi:10.1016/j.actamat.2006.02.013 \n49. R. Kapoor, J.K. Chakravartty, Deformation behavior of an ultrafine-grained Al-Mg alloy \nproduced by equal-channel angular pressing, Acta Materialia. 55 (16) (2007) 5408-5418. \ndoi:10.1016/j.actamat.2007.05.049 \n50. Y.G. Ko, J.H. Kim, C.S. Lee, et al., Load relaxation behavior of ultra-fine grained Ti-6Al-4V \nalloy, Materials Science Forum. 475-479 (IV) (2005) 2955-2960. \ndoi:10.4028/www.scientific.net/MSF.475-479.2955 \n51. A. Goyal, V. Doquet, A. Pouya, Grain boundary sliding and strain rate sensitivity of coarse and \nfine/ultrafine grained 5082 aluminum alloys, Metallurgical and Materials Transactions A. 51 (3) \n(2020) 1109-1122. doi:10.1007/s11661-019-05583-5 \n52. V.M. Segal, I.J. Beyerlein, C.N. Tome, V.N. Chuvil’deev, V.I. Kopylov, Fundamentals and \nEngineering of Severe Plastic Deformation. New York: Nova Science Publishers. (2010). \n53. V.N. Chuvil’deev, A.V. Nokhrin, M.S. Boldin, et al., Impact of mechanical activation on \nsintering kinetics and mechanical properties of ultrafine-grained 95W-Ni-Fe tungsten heavy alloys, Journal of Alloys and Compounds. 773 (2019) 666-688. \ndoi:10.1016/j.jallcom.2018.09.176 \n54. J. Martin, R. Doerty, Stability of microstructure of metallic systems, Cambridge Univ. Press: \nCambridge, (1976). \n55. F.B. Pickering, Physical Metallurgy and the design of steels. Applied Science Publ. Ltd., \nLondon (1978). \n56. M.I. Gol’dshteyn, V.S. Litvinov, B.M. Bronfin, Metal Physics of high-strength alloys, Moscow, \nMetallurgiya. (1986). \n57. H.J. Frost, M.F. Ashby, Deformation-mechanism maps: the plasticity and creep of metals and \nceramics, Pergamon Press, Oxford (1982). \n58. A.R. Kuznetsov, S.A. Starikov, V.V. Sagaradze, et al., Studying deformation-induced \nsegregation in the Fe-Cr-Ni alloy, Physics of Metals and Metallography. 98 (3) (2004) 294-299. \n(in Russian). \n59. A.I. Deryagin, V.A. Zavalishin, V.V. Sagaradze, A.R. Kuznetsov, Low-temperature strain-\ninduced atomic segregation in chromium-nickel steels, Physics of Metals and Metallography.  \n89 (6) (2000) 610-621. (in Russian) \n \n  Table 1. Results of mechanical testing. The magnitudes of the ultimate strength ( b, MPa) and of \nthe elongation to failure ( , %) for the samples of stainless steel for the tension tests at different \ntemperatures  \n \nТtest, \nC CG steel N = 2 N = 3 N = 4 \nТECAP=450 С ТECAP=150 С ТECAP=450 С Т ECAP=150 С ТECAP=450 С \nb  b  b  b  b  b  \nRT 720 125 950 70 1100 40 950 65 1100 45 1020 60 \n450 420 65 800 40 870 35 720 20 920 22 760 30 \n600 350 65 650 50 600 50 600 48 630 45 640 45 \n750 250 70 -  120 250 290 105 240 185 290 120 \n800 220 75 250 110 150 200 200 150 152 220 205 160 \n900 - - - - - - 98 190 - - - - \n \n  Table 2. Microhardness of the samples of steel after tension testing at different temperatures. The \nmean recrystallized grain sizes [d, m] for the samples tested at 800 and 900 оC are given in braces \n \nТtest, \nС Microhardness (H v, GPa) \nCG steel N = 2 N = 3 N = 4 \nТECAP=450C ТECAP=150C ТECAP=450С ТECAP=150C ТECAP=450C \nZone \nI Zone \nII Zone \nI Zone \nII Zone \nI Zone \nII Zone \nI Zone \nII Zone \nI Zone \nII Zone \nI Zone \nII \nRT 2.15 3.71 3.49 4.34 3.91 4.45 3.47 4.38 3.99 4.50 3.51 4.46 \n450 1.87 2.95 - - - - 3.64 3.55 4.07 4.13 3.76 3.75 \n600 1.88 2.68 2.94 3.38 4.05 3.63 3.56 3.49 4.25 3.75 3.77 3.60 \n750 1.76 2.38 - - - - 2.79 2.77 3.33 2.52 3.38 2.71 \n800 1.84 \n(33) 2.26 \n(41) 2.40 \n(21.5) 2.54 \n(2.0) 2.13 \n(2.7) 2.39 \n(2.3) 2.15 \n(2.9) 2.48 \n(1.6) 2.96 \n(2.5) 3.05 \n(1.9) 2.21 \n(2.6) 2.29 \n(1.6) \n900 - - - - - - 1.90 \n(6.8) 1.99 \n(4.4) - - - - \nNote: Zone I is the non-deformed one, Zone II is the deformed one (the destruction zone) \n \n  Table 3. Results of the electrochemical corrosions testing of the coarse-grained and UFG steel  \n \nSteel Tafel test results DLEPR test results \n(GOST 9.914-91) IGC test (GOST \n6232-2003) \nЕcorr, \nmV icorr, \nmA/cm2 Vcorr, \nmm/year S1/S2, 104 Corrosion \ncharacter Corrosion \ncharacter \nInitial state  -403 0.073 0.58 0.93 IGC IGC or PC \nECAP, N = 1, \nТ = 150°С -402 0.072 0.56 1.64 UC  PC \nECAP, N = 2, \nТ = 150°С -403 0.083 0.64 1.96 UC PC \nECAP, N = 3, \nТ = 150°С -404 0.084 0.65 2.07 UC  - \nECAP, N = 4, \nТ = 150°С -404 0.084 0.65 2.34 UC - \nECAP, N = 1, \nТ = 450°С -404 0.092 0.71 2.78 UC PC \nECAP, N = 2, \nТ = 450°С -406 0.084 0.64 3.25 UC - \nECAP, N = 3, \nТ = 450°С -406 0.099 0.77 2.41 UC - \nECAP, N = 4, \nТ = 450°С -403 0.097 0.75 2.22 UC - \nNote: IGC – intergranular corrosion, UC – uniform corrosion, PC – pitting corrosion \n \n  List of Figures \n \nFigure 1 – Microstructure of stainless steel in the initial state: (a, b, c, d); the -phase nuclei in steel \nin the initial state (a, b – optical microscopy; c, d – SEM); (e, f) microstructure of the austenite \ngrains. TEM \n \nFigure 2. Macrostructure of the steel specimens after the first ECAP cycle at 150 (a) and 450 оС (b) \n \nFigure 3 – Results of XRD phase analysis of the steel samples in the initial state and after ECAP: \n(a) XRD curves for the steel samples after different numbers of ECAP cycles at Т = 450 оC; (b) \ndependence of the mass fraction of the –phase on the number of the ECAP cycles at 150 and 450 \nоC \n \nFigure 4. Microphotographs (a, c, d, e) and the electron diffraction patterns (b, f) of the steel \nmicrostructure after ECAP (N = 4) at 150 C (a, b, c, d) and 450 С (e, f) \nFigure 5. Dependencies of the grain sizes on the annealing temperature for the UFG steel specimens \nsubjected to ECAP at Т ECAP = 450 С \n \nFigure 6. Nucleation of the second phase particles at the heating up of the UFG steel samples (N = \n4, ТECAP = 450 оC): a – initial state; b – heating up to 500 оС, holding 60 min; c – heating up to 600 \nоC, holding 60 min; d – heating up to 700 оC, holding 60 min; e – heating up to 800 оC, holding 30 \nmin; f – heating up to 800 оC, holding 60 min \n \nFigure 7. Enlarged image of the nucleation of the second phase particles in the UFG steel (N = 4, \nТECAP = 450 оC) after at heating up to 800 оС and holding for 60 min. The regions of intensive \nparticle nucleation are marked by the dashed lines \n \nFigure 8: Results of investigations of the mechanical properties of UFG steel (Т ECAP = 450 оC): a) \ndependencies of the mean grain sizes and of the mechanical properties of steel on the number of \nECAP cycles; b) dependence of the yield strength on the grain size in the axes y – d-1/2 axes \n \nFigure 9. Dependencies of the macroelasticity stress (a) and of the yield strength (b) on the \ntemperature of the 1-hour annealing of UFG steel \n \nFigure 10 – Stress–strain tension curves for the CG and UFG steel samples at RT  \nFigure 11. Fractographic analysis of the fractures of steel after the tension tests at RT: (a, b) coarse \ngrained steel, (c, d) UFG steel (N = 4, Т ECAP = 150 С), (e, f) UFG steel (N = 4, Т ECAP = 450 С). In \nFigs. 11a, b: Zone 1 – the fibrous fracture zone; Zone 2 – the radial zone; Zone 3 – the cut zone; in \nFig. 11d – the fibrous zone consisting of a set of pits and featuring the viscous destruction \n \nFigure 12 Results of the stress relaxation tests: (a) the stress relaxation curves of the CG and UFG \nsteel specimens; (b) the stress relaxation curves of the UFG steel specimens (ECAP, N = 1, 150 oC) \nafter annealing at different temperatures \n \nFigure 13. Tension diagram for the CG (a) and UFG (b, c) steel at elevated temperatures: (а) CG \nsteel; (b) UFG steel (N = 4, 150 oC), (c) UFG steel (N = 4, 450 oC) \n \nFigure 14. Fractographic analysis of the steel fractures after the superplasticity tests at 600 C: (a, b) \nCG steel, (c, d) UFG steel (N = 4, Т ECAP = 150 C), (e, f) UFG steel (N = 4, Т ECAP = 450 оC). \nDesignations in the figures are the same as in Figure 11 \n \nFigure 15. Results of the microstructure investigations of the nondeformed areas (a, c, e) and of the \ndeformed ones (b, d, f) of the specimens after the tension tests at 800 оC: (a, b) CG steel; (c, d) UFG \nsteel (ECAP, N = 3, 150 oC); (e, f) UFG steel (ECAP, N = 4, 450 oC) \n \nFigure 16. Results of the electrochemical investigations of the coarse–grained and UFG steel \nsamples: a) Tafel curves ln(i)–E; b) results of the DLEPR tests \n \nFigure 17. Surfaces of the CG steel specimen (a) and of the UFG one (N = 4, 450 oC) (b) after the \nDLEPR tests according to GOST 9.914-91 \n \nFigure 18. The surfaces of the CG steel specimen (a) and of the UFG one (N = 4, 450 oC) after \ntesting in boiling acid solution according to GOST 6232-2003 \n \nFigure 19. Dependencies of the stress relaxation magnitude on the stress applied in the ln( ) – 1-\n/* axes: (а) comparison of the course grained and UFG steels (analysis of the data presented in \nFig. 12a); (б) effect of the annealing temperature on the relaxation curves for UFG steel (analysis of \nthe data presented in Fig. 12b)  \n   \n \n  \n \n  \n \n  \n \n \n \n \n \nFigure 1  \n  \n(b) \n(c) (d) (a) \n(e) (f)  \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 2 \n  \n(a) \n(b)  \n \n \n \n \n \n \nFigure 3  \n  40 45 50 55 60 65 70 75 80Initial state\nN=1\nN=2\nN=3\nN=4\n05101520\n0 1 2 3 4 5, %\nN150\n450-Fe \n-Fe -Fe -Fe (a) \n(b)  \n  \n \n  \n \n  \n \nFigure 4 \n(a) (b) \n(c) (d) \n(e) (f)  \n \n \n \n \n \n \n \n \n \n   \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 5 \n  \n0246810\n0 200 400 600 800 1000d, m\nТ, °СN=3\nN=4\n y = -8,3101x + 18,368y = -5,9486x + 16,963\n0246810\n1 1,2 1,4 1,6 1,8 2 2,2Tm/Tln(d4-d04)   \n  \n  \n  \n  \n \n \n \nFigure 6 \n  \n(а) (b) \n(c) (d) \n(e) (f)  \n  \n \n \n \n \n \n \n \nFigure 7 \n  \n \n \n \n \n \n \n \n \n \n \n \nFigure 8 \n  0,1110100\n0200400600800100012001400\n0 1 2 3 4 5d, m , MPa\nNy\n0\nd\ny = 0,4574x + 300,31\nR² = 0,9586y = 0,4909x + 281,58\nR² = 0,9906\n030060090012001500\n0 500 1000 1500 2000 2500y, MPa\nd-1/2, m150\n450(а) \n(b)  \n \n \n \n \n \n \n \n \n \nFigure 9 \n  \n0200400600800\n0 200 400 600 800 10000, MPa\nT, oC\nCoarse-grained steel\nECAP (N=2, 450C)\nECAP (N=3, 450C)\nECAP (N=4, 450C)\nECAP (N=4, 150C)\n030060090012001500\n0 200 400 600 800 1000y, MPa\nT, oC\nCoarse-grained steel\nECAP (N=2, 450C)\nECAP (N=3, 450C)\nECAP (N=4, 450C)\nECAP (N=4, 150C)(а) \n(b)  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure 10 \n  030060090012001500\n0 20 40 60 80 100 120 140 160, MPa\n, %CG steel\nECAP (150 С, N=3)\nECAP (150 С, N=4)\nECAP (450 С, N=2)\nECAP (450 С, N=3)\nECAP (450 C, N=4) \n \n \n \n \n  \n \n \n  \n \n \n \n \n \n \nFigure 11 \n  \n(а) (b) \n(c) (d) \n(e) (f)  \n \n \n \n  \n \n \n \n \n \n \nFigure 12  \n  05101520253035\n0 300 600 900 1200, MPa\n, MPaCG steel\nECAP (N=1, 150 С)\nECAP (N=1, 450 С)\nECAP (N=4, 450 C)\nECAP (N=4, 150 C)\n05101520253035\n0 200 400 600 800 1000 1200, MPa\n, MPaRT\n600\n700\n750\n800\n850\n900(а) \n(б)  \n \n \n \nFigure 13 \n  020040060080010001200\n0 50 100 150 200 250, MPa\n, %RT\n450\n600\n750\n800\n020040060080010001200\n0 50 100 150 200 250, MPa\n, %RT\n450\n600\n750\n800\n020040060080010001200\n0 50 100 150 200 250, MPa\n, %RT\n450\n600\n750\n800(а) \n(b) \n(c)   \n  \n  \n \n \n \n \n \n \nFigure 14 \n  \n(а) \n(b) \n(c) (d) \n(e) (f)  \n \n \n \n  \n  \n  \n \n \n \n \nFigure 15 \n  \n(d) (b) \n(c) (а) \n(e) (f)  \n \n \n \n \n \n \n \nFigure 16 \n  -6-5-4-3-2-101\n-500 -450 -400 -350 -300lg(i), \nmA/cm2\nЕ, mVCoarse-grained steel\nECAP (N=1, 150C)\nECAP (N=2, 150C)\nECAP (N=4, 150C)\nECAP (N=1, 450C)\nECAP (N=2, 450C)\nECAP (N=4, 450C)\n-5-4-3-2-1012\n-600 -300 0 300 600 900 1200lg(i), \nmA/cm2\nЕ, mVCoarse-grained steel\nN=4, 150C\nN=1, 150C\nN=4, 450C\nN=1, 450C(а) \n(b)  \n \n \n \n \n \n \n \n \nFigure 17 \n  \n(a) \n(b)  \n \n \n \n \n \n \n \n \nFigure 18 \n  \n(b) (a)  \n \n \n \n \n \n \n \n \n \n \nFigure 19 y = -4,83x + 5,42y = -0,91x + 3,28\ny = -4,88x + 5,65y = -6,22x + 7,04y = -2,18x + 3,27\ny = -2,28x + 3,1303\n012345\n-0,3 -0,1 0,1 0,3 0,5 0,7 0,9 1,1 1,3ln(), MPa\n1-/bCoarse-grained steel\nECAP (N=4, 450C)\nECAP (N=4, 150C)\n00,511,522,533,544,5\n-0,3 -0,1 0,1 0,3 0,5 0,7 0,9 1,1ln[], MPa\n1-/b900\n850\n800\n750\n600\n500\nRT\n00,20,40,60,811,21,4\n0200 400 600 8001000F1, \nGb3\nT, oC(а) \n(b) "    },    {        "title": "1908.00343v2.Size_dependent_spatial_magnetization_profile_of_manganese_zinc_ferrite_Mn0_2Zn0_2Fe2_6O4_nanoparticles.pdf",        "content": " \n \nSize-dependent spatial magnetiz ation profile of Mangan eseZinc  ferrite \nMn 0.2Zn 0.2Fe2.6O4 nanoparticles  \n \n \nMathias Bersweiler ,1 Philipp Be nder,1 Laura G . Vivas ,1 \nMartin Albino,2 Michele Petrecca,2,3 \nSebastian Mühlbauer ,4 \nSergey Erokhin ,5 Dmitry Berkov ,5 \nClaudio Sangregorio ,2,3 and Andreas Michels1 \n \n1Physics and Materials Science Research Unit, University of Luxembourg , 162A Avenue de la Faïencerie,  \nL-1511 Luxembourg, Grand Duchy of Luxembourg  \n2Università degli Studi di Firenze , Dipartimento di Chimica “U. Schiff ”, Via della Lastruccia 3, \n50019 Sesto Fiorentino , Italy  \n3ICCOM -CNR via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy  \n4Heinz Maier -Leibnitz Zentrum  (MLZ), Technische Universität München, D -85748 Garching, Germany  \n5General Numerics Research Lab, An der Leite 3B, D -07749 Jena, Germany  \n \n \nWe report the results of a n unpolarized  small -angle neutron scattering  (SANS) study  on Mn-Zn ferrite \n(MZFO) magnetic nanoparticles  with the aim  to elucidate the interplay between their particle size and the \nmagnetization configuration . We study  different samples  of single -crystalline MZFO nanoparticle s with \naverage diameter s ranging between  8 to 80 nm , and demonstrate that the smallest particles are \nhomogeneously magnetized. However, with increasing nano particle size, we observe the transition from \na uniform to a nonuniform magnetization state.  Field -dependent results for the correlation  function  \nconfirm  that the internal spin disorder is suppressed with increasing field strength . The experimental \nSANS data are supported by the resul ts of micromagnetic simulations, which confirm an increasing \ninhomogeneity of the magnetization profile of the nano particle with increasing size.  The r esults presented \ndemonstrate the unique ability of SANS to detect even very small deviations of the magnetization state \nfrom the homogeneous one.  \n \n \n  \n \nI. INTRODUCTION  \n \nThe Manganese -Zinc ferrite (MZFO)  material system  \npossesses favorable  physical properties such as high \nmagnetic permeability, reasonable saturation magnetization  \ncombined  with low eddy current losses, high electrical \nresistivity as well as a good flexibility and chemical stability. \nThese features render MZFO a  very promising candidate for \nmany technological and biomedical  applications, e.g., as \nmagnetic reading head s [1], constituent s of temperature -\nsensitive ferrofluid s [2], microwave absorber s [3], \ninductors  [4], drug delivery  [5,6] , and MRI contrast \nenhancing agent s [7]. A problem arises because  the \nmacroscopic  magnetic properties of MZFO are strongly \ndependent e.g. on their chemical composition  [8–10], the \nsynthesis methods  [11,12] , and on the distribution o f cation s \nbetween interstitial tetrahedral and octahedral  sites [9,13,14] . \nMoreover, even for the same chemical composition, the \nmagnetic properties may sensitively depend on  the MZFO  \nparticle  size  [8,10,15,16] . \nPrevious studies  on MZFO nanoparticles along these lines  \nusing conventional magnetometry have reported a transition \nfrom single - to multi -domain structure for critical size s \nbetween abou t 20-40 nm  [8,15] . In th e present work, we \nemploy  magnetic -field-dependent unpolari zed small -angle \nneutron scattering (SANS) to obtain mesos copic  information \non the  magneti zation  profile  within MZFO nanoparticles  of \ndifferent  sizes. Magnetic SANS provides volume -averaged \ninformation about variations of the magnetization vector \nfield on a nanometer  length scale of   1 – 100 nm  (see \nRefs.  [17,18]  for reviews ). The SANS technique  has been  used in several other \nstudies to investigate intra and interparticle magnetic \nmoment correlations  in various nanoparticle systems ; for \ninstance , SANS was applied to study interacting nanoparticle \nensembles  [19,20] , including ordered arrays of \nnano wires  [21,22] , it was employed to reveal the domain \norienta tion in nanocrystalline soft magnets  [23], or to \ninvestigate the response of magnetic colloids  [24–26] and \nferrofluids  [27–29] to external fields. In Refs.  [20,30 –32] the \nSANS method  has been utilized  to disclose  the intrapa rticle  \nmagnetization profile  on different magnetic nanoparticle  \nsystems . These studies indicate  the presence of spin disorder \nand canting , particular ly at the nanoparticle  surface . A \nnonuniform spin texture obviously affects the macroscopic \nmagnetic properties, and hence the application potential. \nHere, we also use magnetic SANS to disclose the \nmagnetization profile, however, in contrast to the previous \nwork s we focus  our analysis on model -independent  \napproaches . Additionally , we use large -scale  micromagnetic  \ncontinuum  simulations to support our finding s and to disclose  \nthe delicate interplay between particle size and magnetization \nprofile within MZFO nanoparticles . \nThe article  is organized as follow s: In Section II , we \ndiscuss the nanoparticle  synthesis, the characterization \nmethods , and the details of the SANS experiment . In Section \nIII, we summarize briefly the expressions for the unpolarized \nSANS cross section , the intensity ratio , and the correlat ion \nfunction . Section IV presents and discusses the experimental \nresults of the characterization of the samples by X-ray \nfluorescence spectrometry, X-ray diffraction, transmission \nelectron microscopy , magnetometry, and in particular the  \n \nSANS measurements ; a paragraph on the micromagnetic \nsimulation results completes  this section . Section V \nsummarizes the main f indings of  this paper . \n \n \nII. EXPERIMENTAL  \n \nMn 0.2Zn0.2Fe2.6O4 nanoparticles  covered with a \nmono layer of oleic acid (capping agent)  were  synthesized by \nco-precipitation from aqueous solution s and by thermal \ndecomposition  of iron and manganese acetylacetonates in \nhigh-boiling solvent (benzyl ether) in the presence of \nsurfactants and of ZnCl 2 (see Appendix A and B for details \non the nanopart icle synthesis ). In the following , the particles \nwill be labeled as MZFO -x, where x denotes their average \nparticle size.  \nThe chemical composition of the nanoparticles was \ndetermined by a Rigaku ZSX Primus II X-ray fluorescence \nspectrometer (XRF), equipped with a Rh Kα radiation source \nand a wavelength dispersive detector. The average  crystallite  \nsize and the structural properties of the nanoparticles were  \nestimated by transmission electron microscopy (TEM) , using \na CM12 Philips microscope with a LaB 6 filament operating \nat 100 kV , and by X-ray diffraction (XRD), using a Bruker \nNew D8 ADVANCE ECO diffractometer with Cu Kα \nradiation. The amount of organic layer was estimated by \nCHN analysis, using a CHN -S Flash E1112 Thermofinnigan. \nThe magnetic analysis at room temperature was performed \non tightly packed powder samples using a Quantum Design  \nMPMS superconducting quantum interference device \n(SQUID)  magnetometer . \nFor the SANS experiments, the nanoparticles were \npressed into circular pellets with a diameter of 8 mm and  a \nthickness of 1.3 ± 0.1  mm. The neutron experiments were \nperformed at the instrument  SANS -1 [33] at the Heinz \nMaier -Leibnitz Zentrum (MLZ), Garching, G ermany . The \nmeasurements were  done using  an unpolarized incident \nneutron  beam  with a mean wavelength of λ = 4.5 1 Å and a \nwavelength broadening of Δλ /λ = 10 % (FWHM). All the \nmeasurement s were conducted at room temperature and \nwithin a q-range of about 0.06 nm-1 ≤ q ≤ 3.0 nm-1. A \nmagnetic field H0 was applied perpendicular to the incident \nneutron beam (H0 ⊥ k0). The experimental setup used for \nthese experiments is sketched in Fig. 1. Neutron data were \nrecorded by increasing the applied  magnetic  field from 0  T to \n4 T following  the magnetization curve . The neutron -data \nreduction (correction for background and empty cell \nscattering, sample transmission, detector efficiency , and \nwater calibration ) was carried out using the GRASP software \npackage  [34]. \n \n \nIII. SANS CROSS SECTION , INTENSITY RATIO , \nAND CORRELATION  FUNCTION  \n \nA. Elastic unpolarized SANS cross section  \n \nAs detailed in Refs. [17,18] , when the applied magnetic \nfield H0 is perpendicular to the incident neutron beam ( H0 ⊥ \nk0), the elastic  nuclear and magnetic  unpolarized SANS cross section  dΣ/dΩ at momentum -transfer vector q can be written \nas: \n \nd𝛴\nd𝛺(𝒒)=8𝜋3\n𝑉𝑏H2(𝑏H−2|𝑁̃|2+|𝑀̃𝑥|2+|𝑀̃𝑦|2cos2(𝜃)+ |𝑀̃𝑧|2sin2(𝜃)\n−(𝑀̃𝑦𝑀̃𝑧∗+𝑀̃𝑦∗𝑀̃𝑧)sin(𝜃)cos(𝜃)),(1) \n \nwhere V is the scattering volume , bH = 2.91  108 A-1m-1 \nrelates the atomic magnetic moment to the  atomic magnetic \nscattering length , 𝑁̃(𝒒) and 𝑀̃(𝒒)=[𝑀̃𝑥(𝒒),𝑀̃𝑦(𝒒),\n𝑀̃𝑧(𝒒)] represent the Fourier transforms of the nuclear \nscattering length density N(r) and of the magnetization vector \nfield M(r), respectively,  θ specifies the angle between H0 and \nq (see Fig. 1), and the asterisks “*” denote the com plex \nconjugated quantity.  Generally , the Fourier components \n𝑀̃𝑥,𝑦,𝑧 depend on both the magnitude and the orientation of \nthe scattering (wave) vector q. This dependence is influenced  \nby the applied magnetic field , the various intra and \ninterparticle magnetic interactions , and by the particle size \nand shape . It is also worth emphasizing that in the small -\nangle approximation (scattering angle  << 1) only \ncorrelations in the plane perpe ndicular to the incoming \nneutron beam are probed  (compare Fig. 1) ; this means that \nthe above Fourier components are to be evaluated at qx  0. \n \n \nB.  SANS  intensity ratio  \n \nDeviations from the uniform magnetization state in \nnanoparticle systems had already become evident in the early \nSANS study by Ernst, Schelten, and Schmatz  [35]. These \nauthors investigated the transition from single to multi -\ndomain configurations of Co precipitates in a Cu single \ncrystal  and analyzed the following ratio (q) of SANS cross \nsections ( H0 ⊥ k0) [35]: \n \n𝛼(𝒒)=d𝛴\nd𝛺(𝒒)|\n𝑯0 = 0 T\nd𝛴\nd𝛺(𝒒)|\n𝒒 ∥ 𝑯0⟶ ∞=[d𝛴\nd𝛺nuc(𝒒)+d𝛴\nd𝛺mag(𝒒)]|\n𝑯0 = 0 T\nd𝛴\nd𝛺nuc(𝑞)|\n𝒒 ∥ 𝑯0⟶ ∞.   (2) \n \nThe total unpolarized SANS cross section 𝑑𝛴 𝑑𝛺⁄  at zero \napplied magnetic field equals the sum of nuclear and \nmagnetic contributions, while the cross section at a saturating \nfield H0 applied parallel to the scattering vector q yields (for \n𝒌0⊥𝑯0) the purely nuclear SANS cross section 𝑑𝛴 nuc/𝑑𝛺. \nWe emphasize that the interpretation of 𝛼(𝒒) is highly \nnontrivial , since it depends on a number of both structural \nand magnetic parameters; for instance, on the particle volume \nfraction, at high packing densities also on the shape and size \ndistribution of  the particles, and not the least on the internal \nspin structure of the nan oparticles, which depends e.g. on the \nparticle size and the applied field, but also on the strength of \nthe magnetodipolar int eraction between the particles.  \nConsider the s pecial cas e of a dilute  assembly of \nrandomly -oriented single -doma in particles: if for H0 = 0, the \nmagnetizations of the particles are randomly oriented, then \nthe two -dimensional 𝑑𝛴 𝑑𝛺⁄ is isotropic, whereas it exhibits \nthe well -known sin2θ angular anisotropy for the saturated \ncase, 𝒌0⊥𝑯0, and for a not too strong nuclear signal   \n \n[compare Eq. (1)] . For this par ticular situation, the ratio α \ndepends only on the magnitude q of the scattering vector:   \n \n𝛼(𝑞)=[d𝛴\nd𝛺nuc(𝒒)+d𝛴\nd𝛺mag(𝒒)]|\n𝒒 ∥ 𝑯0 = 0 T\nd𝛴\nd𝛺nuc(𝑞)|\n𝒒 ∥ 𝑯0⟶ ∞=1+d𝛴\nd𝛺mag(𝑞)\nd𝛴\nd𝛺nuc(𝑞),       (3) \n \nwhere the isotropic zero -field SANS cross section has also \nbeen averaged for  𝒒∥𝑯0. By contrast, for a globally \nanisotropic microstructure, e.g.,  for oriented shape -\nanisotropic particles  or for a system exhib iting a large \nremanence  [33], the α-ratio may depend on th e orientation of \nq. Moreover, if in the dilute ensemble of randomly -oriented \nsingle -domain particles  the chemical  (nuclear)  and magnetic \nparticle sizes  coincide , then Eq. (3) simplifies to the q-\nindependent value:  \n \n𝛼calc=1+2\n3(𝜚mag\nΔϱnuc)2\n,      (4) \n \nwhere Δ𝜚nuc is the difference between the nuclear scattering \nlength densities of the nanoparticles and the matrix, and \n𝜚mag =𝑏𝐻𝑀𝑆𝑀𝑍𝐹𝑂  is the magnetic scatter ing length density \nof the MZFO nanoparticles. The factor 2/3 in Eq. ( 4) results \nfrom an orientational average of the sin2(𝜃) factor in Eq. (1) \nin the remanent state (assuming the absence of other \nmagnetic scattering contributions in line with the assumption  \nof the presence of only single -domain particles). Under the \nabove a ssumptions, deviations from the  constant value  given \nby Eq. (4)  may indicate the presence of intra -particle spin \ndisorder.  \n \n \nC. Correlation  function  \n \nTo obtain real -space information about the magnetic \nmicrostructure, we have computed the following correlation  \nfunction  [36–39]: \n \n𝑝(𝑟)=𝑟2∫𝐼(𝑞)𝑗0(𝑞𝑟)𝑞2𝑑𝑞∞\n0,      (5) \n \nwhere 𝑗0(𝑥)=sin(𝑥)/𝑥 denotes the spherical Bessel \nfunction of zero order , and I(q) represents the azimuthally -\naveraged magnetic SANS cross section . In nuclear SANS \nand small -angle X -ray scattering  p(r) is known as the pair -\ndistance distribution function, which provides information on \nthe particle size and shape, and on the presenc e of \ninterparticle interactions; for magnetic systems it may also \nindicate the presence of intraparticle spin disorder.  \n \n \n \nIV. RESULTS AND DISCUSSION  \n \nA.  Structural and magnetic pre-characterization  \n \nXRF analyses confirmed that the synthesized nanoparticle \nsamples all have a similar composition, i.e., Mn 0.2Zn0.2Fe2.6O4 \n(see Table 1). XRD results for the nanoparticle  powder s are shown in Fig. 2(a). All the diffraction peaks observed can be \nwell indexed  with the AB2O4 spinel structure, indicating a \npure cubic phase of Mn 0.2Zn0.2Fe2.6O4. Moreover, impurity \npeaks or secondary  phase s are not observed in our XRD \npattern, which confirm s the high quality of the nanoparticle s \nsynthetized by co -precipitation and thermal decomposition . \nThe structural parameters  were determined by the method of \nthe fundamental parameter approach (FDA) implemented in \nthe TOPAS software , considerin g the  cubic s pace group  \n𝐹𝑑3̅𝑚. The average crystal lite sizes are reported in Table 1. \nThe lattice parameter  a varies in the range from 0.8407 (2) to \n0.8421 (1) nm, as expected for  doped  Mn-Zn ferrite  \nnanoparticles  [9]. \nTEM images of the nanoparticles are displayed  in Fig. 2(b) \nand the average particle sizes are listed in Table 1. It should \nbe emphasized  that the  small nanoparticles look spherical , \nwhereas the  larger nanoparticles seem to have a faceted  cubic  \nstructure . This morphology evolution is the result of the \ninterplay between surface tension and preferential growth \nalong the <100> directions  [40]. For all samples, the average \nparticle  size determined by TEM is nearly identical to the \nXRD crystallite size , suggesting  that the nanoparticles are  \nsingle crystal s. The CHN analysis indicates  that the relative  \namount of surfactant decreases with the nanoparticle surface -\nto-volume ratio, from 11.2 % for MZFO -8 to 1.1 % for \nMZFO -80. For all the samples, this corresponds \napproximately to a monolayer of surfactant, as evaluated by \nassuming that each ligand molecule occupies a surface area \nof 0.5 nm2 [19,41] . Figure 3 shows a typical scanning \nelectron microscopy  (SEM)  image  of a MZFO sample  after \nthe powder has been  pressed into a circular pellet ; this \nmicrostructure is characteristic of  the SANS samples in our \nstudy . \nThe normalized room -temperature  magnetization curves \nM(H) of the nanoparticle  powder s are shown  in Fig. 4(a) and \nin Fig. 4(b), respectively . From these  curves, we determined \nthe saturation  and remanent  magnetization s (MS and MR \nrespectively ) and the coercive fiel d HC (see Table 1 ). The \nM(H) curve of MZFO -8 shows no hysteresis , indicat ing \nsuperparamagnetic behavior . However, for larger particle \nsizes , the M(H)  curves  start to open up and  an increase of  MS, \nMR, and HC is observed . \nFrom the M(H) curve of MZFO -8, we have extract ed the \nunderlying effective moment distribution PV(μ) using  the \napproach outlined in  Bender et al.  [42] [see Fig. 4(c)], where \na Langevin -type magnetization behavior is assumed . The \nobtained distribution exhibits one main peak at ~ 10-19 Am2 \nand addi tional contributions in the low -moment range. We \nsurmise that the main peak corresponds to the distribution of \nthe individual  particle moments μi = MSVi of the whole \nensemble (where Vi is the particle volume) , and that the low -\nmoment contributions can be attributed to dipolar \ninteractions  within the ensemble , similar as in Bender et \nal.  [42]. As shown in Fi g. 4(c), the main peak can be well \nadjusted with a lognormal distribution  function , which  can be \nfurther transformed to the number -weighted particle -size \ndistribution  shown in Fig . 4(d); for this transformation we  \nassumed a spherical particle shape and  used a value of MS = \n301 kA/m  to relate the particle moments to the particle sizes . \nThis distribution is in a good agreement with the size \nhistogram determined with TEM, which in turn verifies the  \n \nsuperparamagnetic m agnetization behavior of MZFO -8. For \nthe larger particles , the same appr oach  (which assumes a \nLangevin -type magnetization behavior ) results in size \ndistribution s that significantly deviate from the TEM results  \n(data not shown) . This is in line with  the observed  transition \nfrom superparamagnetic to  ferromagnetic -like behavior  with \nincreasing size , similar to results reported in the \nliterature  [8,10,15] . \n \n \nB.  Unpolarized SANS  measurements  \n \nWe measured the total unpolarized SANS cross sections \ndΣ/dΩ of each sample at 10 different applied magnetic fields \nfrom 0 to 4  T at room temperature . Figure 5 (left panel)  shows \nsome selected  two-dimensional  SANS patterns  (remanent \nstate and 4 T) , which c ontain nuclear and magnetic \ncontributions. According  to magnetometry , all the samples \nare nearly magnetically saturated  at a field of 4 T [Fig. 4(a)]. \nHence, the sector average  of dΣ/dΩ parallel to the applied \nfield ( q // H0) at 4 T is a good approximation  to the purely \nnuclear SANS cross section d Σnuc/dΩ [compare also Eq. (1)] . \nAs shown in Fig. 6, dΣnuc/dΩ in the high -q range can be well \ndescribed by a power  law, dΣnuc/dΩ  q -4, which is expected \nin the Porod regime for orientationally -averaged  particles \nwith a discontinuous  interfac e [37]. For b oth the MZFO -27 \nand MZFO -38 samples we observe peak  structures in  the \nscattering curves, which might be related to the narrow \nparticle -size di stribution [compare Fig. 2(b)]. By contrast, the \nMZFO -8 and MZFO -80 exhibit a relatively broad size \ndistribution, which results in the absence of such features in \nthe nuclear SANS . \nRegarding the 2D patterns, Fig. 5 shows that  the total  \n(nuclear and magnetic)  SANS cross sections dΣ/dΩ exhibit \nfor all samples a weakly field -dependent (compare top panel \nin Fig. 7) and a nearly isotropic intensity distribution . This \nobservation points towards  the dominance of the isotropic \nnuclear scattering contribution. Since  in general  the nuclear \nSANS cross section is field independent, t he magnetic SANS  \ncross section  dΣM/dΩ can be  determined by subtracting , for \neach sample , the total dΣ/dΩ measured at the highest field of \n4 T from the data at lower fields . The field-depen dent dΣM/dΩ \nobtained in this way are displayed in Fig. 5 (right panel ). It is \nseen that the  intensity distributions of MZFO -8 and MZFO -\n80 are slightly anisotropic, elongated along the horizontal \nfield direction , while the  2D dΣM/dΩ of MZFO -27 and \nMZFO -38 are isotropic . For MZFO -8 the angular anisotropy  \nof dΣM/dΩ is found in a q-range that corresponds to an \ninterparticle length scale, whereas MZFO -80 exhibits  this \nanisotropy on an intraparticle length scale. This observation \nsuggests  for MZFO -80 the presence of transversal \n(perpendicular to H0) spin components , in line with  the \n|𝑀̃𝑦|2cos2(𝜃) scattering contribution in Eq. (1) . \nThe used procedure of subtracting the total unpolarized \nSANS scattering at a field close to saturation from data at \nlower fields (Fig s. 5 and 7 ) suggests that it may not always \nbe necessary to resort to polar ization -analysis experiments in \norder to obtain the magnetic (spin -flip) SANS cross section. \nIf nuclear -spin-dependent SANS  and chiral scattering \ncontributions are ignored , the comparison of the spin -flip SANS cross section (Eq. (1 8) in Ref.  [18]) with the so-called \nspin-misalignment SANS cross section [ obtained by \nsubtracting from Eq. (1)  the scattering at saturation  ∝|𝑁̃|2+\n |𝑀̃𝑧|2sin2(𝜃)] reveals that the subtraction procedure yields, \nexcept for the longitudinal magnetic term, a combination of \n(difference) Fourier components that is very similar to the \nspin-flip SANS cross section  (albeit with different \ntrigonometric weights) . If the nuclear particle microstructure \nof the material under study does not change with the applied \nfield (leaving aside magnetostriction effects) , this procedure \nmight be a practicabl e alternative to time -consuming and \nlow-intensity polarization -analysis measurements.  \nThe azimuthal ly average d (over 2π)  dΣ/dΩ and dΣM/dΩ \nfor each magnetic field  value  H0 are summarized in Fig. 7. \nThe magnitude of d ΣM/dΩ is reduced  compared to dΣ/dΩ, \nwhich is due to the dominance of the nuclear scattering \ncontributions  in our system s. In the following, we will \ndistinguish between the intra particle  (q > qc) and  the \ninterparticle ( q < qc) q-ranges, which are roughly defined by \nthe average particle sizes D of the respective system (i.e. , qc \n= 2π/D). For each sample , dΣ M/dΩ exhibits a strong  and more \npronounced magnetic field dependence  as compared to \ndΣ/dΩ (Fig. 7). \nFigure 8 displays the SANS results for the experimental \nintensity ratio  αexp as defined by  Eq. (3). Dividing the  q-range \nin regions corresponding to values larger or smaller than qc = \n2/D, we can obtain information on either inter - or \nintraparticle moment cor relations of the nanoparticles (w e \nnote that the high -q range may also contain weak features due \nto interparticle correlations ). Regarding the interparticle q-\nrange ( q < qc), exp exhibits for all samples a strong q-\ndependence, which might  be explained by a difference \nbetween the nuclear and magnetic structure factors  [43]. \nHowever, within  the intraparticle q-range , corresponding \napproximately to q/qc > 1, we observe very distinct features.  \nFor the smallest nano particles  (MZFO -8), αexp is independent \nof q and a lmost  equals the theoretical limit given by Eq. ( 4). \nBased on the consideration s of Sec. III . B, this then suggest s \na single -domain configuration of MZFO -8 with a  \nhomogeneous magnetization profile.  For the case of \nnanoparticles with an intermediate diameter ( MZFO -27 an d \nMZFO -38), we observe a more or less pronounced  peak  in \nthe intraparticle q-range , at q  0.34 nm-1 (MZFO -27) and at \nq  0.22 nm-1 (MZFO -38), while for the largest particles \n(MZFO -80) we observe a weak monotonic decrease of αexp \nover the whole q-range. Similar peaks were reported in  \nRef. [35] and were  attributed to inhomogeneous \nmagnetization profiles.  By increasing the applied  magnetic \nfield,  the magni tude of the peak  feature  of the MZFO -38 \nsample decreases ( Fig. 8 right panel ), which strongly  \nsuggest s the transition from an inhomogeneous to a \nhomogenous  spin structure , where the canted spin s tend to \nalign with respect to the magnetic  field H0. As we will see \nbelow (Sec. IV .C), these observations are consistent with our \nmicromagnetic simulations. In Fig. 8(a,b ) the mere deviation \nfrom the horizontal line at large q-values may indicate the \npresence of an inhomogeneous internal spin structure of the \nlarger nanoparticles.  \nTo analyze in more detail  the possible field-dependent \ntransition from an inhomogeneous to a homogeneous spin   \n \nstructure for MZFO -38, we have extracted the corresponding  \npair-distance distribution function s p(r) [Eq. (5 )] from \ndΣM/dΩ. We restricted  our analysis to the intraparticle  q-\nrange, as visualized by the d ashed vertical  line in Fig. 9(a), \nand obtained the field -dependent  p(r) profiles shown in Fig. \n9(b). Accord ingly, these profiles approximately describe the \nscattering behavior in the intraparticle q-range. As can be \nseen in Fig. 9(b), at the highest field of 1.0 T the extracted \ndistributio n p(r) is nearly bell -shaped  [37], which  indicates a \nhomogeneous magnetization profile within the spherical \nnanoparticles, whereas with decreasing field  the deviation of \nthe profile from this ideal case increases . This feature is an \nadditional strong indication for the transition fr om a \nhomogeno us to an inhomogeneous spin structure within the \nparticle with de creasing  field, and vice versa . We note that \nthere exist many studies in the literature, employing other \ntechniques such as Mössbauer  spectroscopy, magnetic X -ray \nscattering, or photoemission electron microscopy, which also \nreport an inhomogeneous nanoparticle spin structure and/or \nthe presence of interparticle moment correlations (e.g. \nRef [44–48]). To further suppo rt our experimental \nobservations , we have performed numerical micromagnetic \nsimulations of the size -dependent magnetization behavior  of \nMZFO nanoparticle ensembles ; these are discussed in the \nfollowing.  \n \n \nC. Micromagnetic simulations  \n \nIn the micromagnetic simulations we have considered the \nfour standard contributions to the total magnetic energy: \nenergy in the external field, cubic magnetocrystalline \nanisotropy energy, and exchange and dipolar interaction \nenergies. The nanoparticle microstructure, consistin g of a \ndistribution of Mn -Zn based nanoparticles, was generated by \nemploying an algorithm described in Refs.  [49–54]. The \nsimulation volume ( = sample volume) is a cubic box of size \n 300  300  300 nm3, which was discretized into 4  105 \nmesh elements with an average mesh size of 4 nm. The \nvolume fraction of the nanoparticles was kept fixed at 80 %, \nleaving 20 % void. Materials parameters are: s aturation \nmagnetization MS = 480 kA/m (typical for ferrites, see page \n423 in Ref.  [55]), anisotropy constant K = 3  103 J/m3 [56], \nand exchange -stiffness constant A = 7  10-12 J/m [53]. The \nequilibrium magnetization state of the system was found , as \nusual, by minimizing the total magnetic energy at a given \nvalue of the applied magnetic field. Periodic boundary \nconditions were applied in the simulations. For more details \non our micromagnetic methodology, see Refs.  [49–54]. \nFigure 10 depicts the sample microstructures used in the \nsimulations. Since the sample volume is kept constant, an \nincrease in the average particle size D from 14 to 74 nm  leads \nto a reduction of the particle number N, from N  40.000 at \n14 nm to N  40 at 74 nm.  \nFigure 1 1 shows the field dependence of the quantity \nM/MS for different particle sizes. This parameter is defined \nas: \n \n|𝑀|\n𝑀S=1\n𝑁∑ (𝑀𝑥,𝑖2+𝑀𝑦,𝑖2+𝑀𝑧,𝑖2)1/2𝑁\n𝑖=1\n𝑀S,       (6)  \nwhich is a measure for the average deviation of the particle’s \nmagnetization state from the single -domain state, \ncorresponding  to M/MS = 1. It becomes visible in Fig. 1 1 \nthat (small) deviations from the uniform particle \nmagnetization state appear for D-values  ranging  between 20 -\n30 nm , which is in reasonable agreement with our \nconclusions from the SANS data analysis  (compare Figs. 8 \nand 9). Since the micromagnetic algorithm does not tak e into \naccount superparamagnetic fluctuations, the computed \nhysteresis curves in the inset of Fig. 1 1 cannot reproduce the \nexperimentally observed transition from the \nsuperparamagnetic to the blocked regime [compare Fig. 4(a) \nand (b)]. It is seen that the quasi -static magnetization \ndecrease s with increasing particle size, since larger particles \ntend to be in a more nonuniform spin state than smaller \nparticles. This is shown in Fig. 1 2, which displays the \nevolution of the parameter M/MS for each magnetic particle \n“i” and as a function of the applied field. Also shown are \nsnapshots of the spin structure at selected fields, where the \nlargest deviations from the uniform state are observed.  \n \n \nV. CONCLUSION  \n \nIn summary,  the structure and magnetic properties of  Mn-\nZn ferrite (MZFO) single crystalline nanoparticles with \naverage diameters ranging from 8 to 80 nm were investigated  \nusing a suite of experimental and simulation techniques . The \nincrease  of the remanent  magnetization  as well as  the \ncoercive field , determined from the magnetization cu rves, is \na clear evidence  for a  transition from the superparamagnetic \nto the blocked state with increasing particle diameter . The \nanalysis of the magnetic -field-dependent unpolarized SANS \ndata demonstrate s that the magnetization profiles of the \nlarger nanoparticles deviate from the perfect single -domain \nstate. This conclusion has mainly become possible by \nplotting a special intensity ratio (Eq. ( 3) and Fig. 8), \noriginally introduced by  Ernst, Schelten, and Schmatz  [35]. \nAnother important clue for the nonuniform internal spin \nstructure was obtained by the computation of the pair -\ndistance distribution  function  p(r) (Fig. 9). The p(r) data \nnicely confirm the field-dependent internal spin structure  of \nthe nanoparticles . In reasonable agreement with the outcome \nof the experimental data analysis, l arge-scale micromagnetic \nsimulations reveal  that slight deviations from single -domain \nbehavior occur for Mn-Zn ferrite particle sizes above about \n20-30 nm.  In general, we emphasize that a fundamental \nunderstanding of magnetic SANS can only be obtained by \ncomparing experimental data, both in Fourier and real space, \nto the results of simulations.  The used procedure of \nsubtracting the total unpolarized SANS scat tering at or close \nto saturation from data at lower fields suggests that it may not \nalways be necessary to perform  challenging  polarization -\nanalysis experiments in order to obtain the magnetic SANS \ncross section.  If the nuclear particle microstructure of the \nmaterial under study does not change with the applied field, \nthis procedure might be a practicable alternative  to time -\nconsuming and low-intensity  polarized neutron \nmeasurement s. Finally , we n ote that o ur stud y demonstrates \nthe unique ability of SANS to detect even very small  \n \ndeviations of  the magnetization configuration from the \nhomogeneously magnetized state . \n \n \nACKNOWLEGDEMENTS  \n \nThe authors acknowledge  the Heinz Maier -Leibnitz \nZentrum for provision of neutron  beamtime . We thank Jörg \nSchwarz  and Jörg Schmauch (Universität des Saarlandes) for \nthe technical support with the hydraulic press  and for the \nSEM investigations . It is also a pleasure to thank Dirk \nHonecker for fruitful discussion s. This research was \nsupporte d by the EU-H2020 AMPHIBIAN Project  (n. \n720853).  Philipp Bender and Andreas Michels  thank the \nFonds National de la Recherche of Luxembourg for financial \nsupport (CORE SANS4NCC grant).  \n \n \nAPPENDIX  \n \nA. Materials  \n \nAll the samples were prepared using commercially \navailable reagents used as received. Benzyl ether (99  %), \ntoluene (99  %), oleic acid (OA, 90  %), oleylamine (OAM, ≥ \n98 %), manganese (II) acetylacetonate (Mn(acac) 2·2 H 2O ≥ \n99 %), zinc chloride (ZnCl 2, ≥ 98  %), iron (III) chloride hexa -\nhydrate (FeCl 3·6 H 2O, 98  %), iron (II) chloride tetra -hydrate \n(FeCl 2·4 H 2O, 98  %), manganese chloride tetra -hydrate \n(MnCl 2·4 H 2O, ≥ 99  %), sodium hydroxide (NaOH, ≥ 98  %) \nwere purchased from Aldrich Chemistry. Iron (III) \nacetylacetonate (Fe(acac) 3, 99 %) was obtained from Strem \nChemicals and absolute ethanol (EtOH) was purchased from \nFluka.  \n \nB. Synthesis  \n \nThe samples MZFO -27 and MZFO -38 were synthesized \nby thermal decomposition of iron and manganese \nacetylacetonates in high -boiling solvent (benzyl ether) in the \npresence of surfactants (OA, OAM) and of ZnCl 2. Instead,  \nthe samples MZFO -8 and MZFO -80 were prepared by the \nco-precipitation method using manganese chloride tetra -\nhydrate, zinc chloride, iron (I I) chloride tetra -\nhydrate,iron (III) chloride hexa -hydrate , and sodium \nhydroxide as starting materials.  \nMZFO -27: Fe(acac) 3 (0.612 g, 1.733 mmol), Mn (acac) 2·2 \nH2O (0.038 g, 0.133 mmol), ZnCl 2 (0.018 g, 0.133 mmol), \nOAM (2.675 g, 10 mmol), OA (2.825 g, 10 mmol) and benzyl \nether (30 mL) ) were mixed and magnetically stirred under a \nflow of nitrogen in a 100 mL three -neck round -bottom flask \nfor 15 min. Th e resulting mixture was heated to reflux (~ 290 \n°C) at 9 °C/min and kept at this temperature for 30 min under \na blanket of nitrogen and vigorous stirring. The black -brown \nmixture was cooled to room temperature and EtOH (60 mL) \nwas added causing the precipi tation of a black material. The \nobtained product was separated with a permanent magnet, \nwashed several times with ethanol , and finally re -dispersed \nin toluene.  \nMZFO -38: The synthesis and purification of this sample \nwas carried out by following the same pro tocol used for MZFO -27, but using the metal/oleic acid/oleylamine ratio \n1:5:5 and keeping the reaction mixture to reflux for 1 h.  \nMZFO -80: FeCl 3·6 H 2O (2.7 g, 10 mmol), FeCl 2·4 H 2O \n(0.597 g, 3 mmol), MnCl 2·4 H 2O (0.198 g, 1 mmol), ZnCl 2 \n(0.136 g, 1 mmol) a nd degassed water (10 ml) were mixed \nand magnetically stirred under a flow of nitrogen. The \nresulting mixture was added to a basic solution at 100 °C, \nobtained dissolving NaOH (1.72 g, 43 mmol) in degassed \nwater (100 ml), and kept at this temperature for 2  h under a \nblanket of nitrogen and vigorous stirring. The black -brown \nmixture was cooled to room temperature and the obtained \nproduct was separated with a permanent magnet, washed \nseveral times with water, 2 times with ethanol and finally \ndried under nitro gen. The obtained product was annealed  at \n725 °C for 2 h under N 2 in a tubular furnace. The powder was \nfinally mixed with OA and toluene, sonicated for 30’, \nprecipitated with a permanent magnet , and washed three \ntimes with ethanol.  \nMZFO -8: The synthesis a nd purification of this sample \nwas carried out by following the same protocol used for \nMZFO -80, but using a larger amount of NaOH (2 g, 50 \nmmol) and OA (2 g, 7 mmol) as surfactant. This sample did \nnot undergo any annealing  step. \n \n \nREFERENCE S \n \n[1] D. Stoppels, J. Magn. Magn. Mater. 26, 306 (1982).  \n[2] T. Upadhyay, R. V. Upadhyay, R. V. Mehta, V. K. Aswal, and \nP. S. Goyal, Phys. Rev. B 55, 5585 (1997).  \n[3] D. Stoppels, J. Magn. Magn. Mater. 160, 323 (1 996).  \n[4] C. C. Agrafiotis and V. T. Zaspalis, J. Magn. Magn. Mater. \n283, 364 (2004).  \n[5] A. M. Cojocariu, A. Doaga, W. Amin, P. Bender, R. \nHempelmann, and O. F. Caltun, Dig. J. Nanomater. \nBiostructures 8, 519 (2013).  \n[6] Z. Beji, A. Hanini, L. S. Smiri, J. Gavard, K. Kacem, F. \nVillain, J. M. Grenèche, F. Chau, and S. Ammar, Chem. Mater. \n22, 5420 (2010).  \n[7] U. I. Tromsdorf, N. C. Bigall, M. G. Kaul, O. T. Bruns, M. S. \nNikolic, B. Mollwitz, R. A. Sperling, R. Reimer, H. \nHohenberg, W. J. Parak, S. Förster, U. Beisiegel, G. Adam, \nand H. Weller, Nano Lett. 7, 2422 (2007).  \n[8] T. Sun, A. Borrasso, B. Liu, and V. Dravid, J. Am. Ceram. \nSoc. 94, 1490 (2011).  \n[9] Z. Klencsár, G. Tolnai, L. Korecz, I. Sajó, P. Németh, J. Osán, \nS. Més záros, and E. Kuzmann, Solid State Sci. 24, 90 (2013).  \n[10] L. Sun, J. Guo, Q. Ni, E. Cao, Y. Zhang, W. Hao, and L. Ju, J. \nMater. Sci. Mater. Electron. 29, 5356 (2018).  \n[11] C. Rath, K. K. Sahu, S. Anand, S. K. Date, N. C. Mishra, and \nR. P. Das, J. Magn. Magn. Mater. 202, 77 (1999).  \n[12] S. A. Morrison, C. L. Cahill, E. E. Carpenter, S. Calvin, and \nV. G. Harris, J. Appl. Phys. 93, 7489 (2003).  \n[13] G. Thirupathi and R. Singh, IEEE Trans. Magn. 50, 2006704 \n(2014).  \n[14] R. U. Ichikawa, J. P. R. L. L. Parra, O. Vallcorba, I. Peral, W. \nK. Yoshito, M. J. Saeki, X. Turrillas, and L. G. Martinez, \nEurophys. Lett. 124, 56001 (2018).  \n[15] P. Mathur, A. Thakur, and M. Singh, J. Magn. Magn . Mater. \n320, 1364 (2008).  \n[16] P. J. Van Der Zaag, M. T. Johnson, and A. Noordermeer, J. \nMagn. Magn. Mater. 99, L1 (1991).  \n[17] A. Michels, J. Phys. Condens. Matter 26, 383201 (2014).  \n[18] S. Mühlbauer, D. Honecker, E. A. Périgo, F. Bergner, S. \nDisch, A. Heinemann, S. Erokhin, D. Berkov, C. Leighton, M. \nR. Eskildsen, and A. Michels, Rev. Mod. Phys. 91, 015004 \n(2019).   \n \n[19] P. Bender, E. Wetterskog, D. Honecker, J. Fock, C. Frandsen, \nC. Moerland, L. K. Bogart, O. Posth, W. Szczerba, H. Gavilán, \nR. Costo, L. F. Barquín, and C. Johansson, Phys. Rev. B 98, \n224420 (2018).  \n[20] Y. Ijiri, K. L. Krycka, I. Hunt -Isaak, H. Pan, J. Hsieh, J. A. \nBorchers, J. J. Rhyne, S. D. Oberdick, A. Abdelgawad, and S. \nA. Majetich, Phys. Rev. B 99, 094421 (2019).  \n[21] A. Günther, J. -P. Bick, P. Szary, D. Honecker, C. D. Dewhurst, \nU. Keiderling, A. V. Feoktystov, A. Tschöpe, R. Birringer, and \nA. Michels, J. Appl. Crystallogr. 47, 992 (2014).  \n[22] T. Maurer, S. Gautrot, F. Ott, G. Chaboussant, F. Zighem, L. \nCagnon, and O. Fruchart, Phys . Rev. B 89, 184423 (2014).  \n[23] N. Ito, A. Michels, J. Kohlbrecher, J. S. Garitaonandia, K. \nSuzuki, and J. D. Cashion, J. Magn. Magn. Mater. 316, 458 \n(2007).  \n[24] P. Bender, A. Günther, D. Honecker, A. Wiedenmann, S. \nDisch, A. Tschöpe, A. Michels, and R. Birringer, Nanoscale 7, \n17122 (2015).  \n[25] V. V. Krishnamurthy, G. J. Mankey, B. He, M. Piao, J. M. \nWiest, D. E. Nikles, L. Porcar, and J. L. Robertson, Phys. Rev. \nE 77, 031403 (2008).  \n[26] V. V. Krishnamurthy, A. S. Bhandar, M. Piao, I. Zoto, A. M. \nLane, D. E. Nikles, J. M. Wiest, G. J. Mankey, L. Porcar, and \nC. J. Glinka, Phys. Rev. E 67, 051406 (2003).  \n[27] F. Gazeau, E. Dubois, J. C. Bacri, F. Boué, A. Cebers, and R. \nPerzynski, Phys. Rev.  E 65, 031403 (2002).  \n[28] G. Mériguet, E. Wandersman, E. Dubois, A. Cēbers, J. de \nAndrade Gomes, G. Demouchy, J. Depeyrot, A. Robert, and \nR. Perzynski, Magnetohydrodynamics 48, 415 (2012).  \n[29] B. Frka -Petesic, E. Dubois, L. Almasy, V. Dupuis, F. Cousin, \nand R. Perzynski, Magnetohydrodynamics 49, 328 (2013).  \n[30] S.Disch, E. Wetterskog, R. P. Hermann, A. Wiedenmann, U. \nVaino, G. Salazar -Alvarez, L. Bergström, and T. Brückel, \nNew J. Phys. 14, 013025 (2012).  \n[31] S. D. Oberdick, A. Abdelgawad, C. Moya, S. Me sbahi -Vasey, \nD. Kepaptsoglou, V. K. Lazarov, R. F. L. Evans, D. Meilak, \nE. Skoropata, J. Van Lierop, I. Hunt -Isaak, H. Pan, Y. Ijiri, K. \nL. Krycka, J. A. Borchers, and S. A. Majetich, Sci. Rep. 8, \n3425 (2018).  \n[32] K. L. Krycka, R. A. Booth, C. R. Hogg, Y. Ijiri, J. A. Borchers, \nW. C. Chen, S. M. Watson, M. Laver, T. R. Gentile, L. R. \nDedon, S. Harris, J. J. Rhyne, and S. A. Majetich, Phys. Rev. \nLett. 104, 207203 (2010).  \n[33] S. Mühlbauer, A. Heinemann, A. Wilhelm, L . Karge, A. \nOstermann, I. Defendi, A. Schreyer, W. Petry, and R. Gilles, \nNucl. Inst. Methods Phys. Res. A 832, 297 (2016).  \n[34] C. D. Dewhurst, https://www.ill.eu/users/support -labs-\ninfrastructure/software -scientif ic-tools/g rasp/ (2018).  \n[35] M. Ernst, J. Schelten, and W. Schmatz, Phys. Stat. Sol 7, 477 \n(1971).  \n[36] O. Glatter, J. Appl. Cryst. 10, 415 (1977).  [37] D. I. Svergun and M. H. J. Koch, Reports Prog. Phys. 66, 1735 \n(2003).  \n[38] G. Fritz and O. Glatter, J. Phys. Condens. Matter 18, S2403 \n(2006).  \n[39] P. Bender, L. K. Bogart, O. Posth, W. Szczerba, S. E. Rogers, \nA. Castro, L. Nilsson, L. J. Zeng, A. Sugunan, J. Sommertune, \nA. Fornara, D. González -Alonzo, L. F. Barquín, and C. \nJohansson, Sci. Rep. 7, 46990 (2017).  \n[40] A. López -Ortega, E. Lottini, C . D. J. Fernández, and C. \nSangregorio, Chem. Mater. 27, 4048 (2015).  \n[41] M. Klokkenburg, J. Hilhorst, and B. H. Erné, Vib. Spectrosc. \n43, 243 (2007).  \n[42] P. Bender, C. Balceris, F. Ludwig, O. Posth, L. K. Bogart, W. \nSzczerba, A. Castro, L. Nilsson, R. Co sto, H. Gavilán, D. \nGonzáley -Alonso, I. de P. L. F. Barquin, and C. Johansson, \nNew J. Phys. 19, 073012 (2017).  \n[43] D. Honecker, L. F. Barquín, and P. Bender, ArXiv:1904.06243 \n(2019).  \n[44] J. B. Kortright, O. Hellwig, K. Chesnel, S. Sun, and E. E. \nFullerto n, Phys. Rev. B 71, 012402 (2005).  \n[45] K. Chesnel, D. Griner, D. Smith, Y. Cai, M. Trevino, B. \nNewbold, T. Wang, T. Liu, E. Jal, A. Reid, and R. Harrison, \nMagnetochemistry 4, 42 (2018).  \n[46] J. Rackham, B. Newbold, S. Kotter, D. Smith, D. Griner, R. \nHarri son, A. H. Reid, M. Transtrum, and K. Chesnel, AIP Adv. \n9, 035006 (2019).  \n[47] S. Mørup, E. Brok, and C. Frandsen, J. Nanomater. 2013 , \n720629 (2013).  \n[48] A. Fraile Rodríguez, A. Kleibert, J. Bansmann, A. Voitkans, \nL. J. Heyderman, and F. Nolting, Phys. Re v. Lett. 104, 127201 \n(2010).  \n[49] S. Erokhin, D. Berkov, N. Gorn, and A. Michels, IEEE Trans. \nMagn. 47, 3044 (2011).  \n[50] S. Erokhin, D. Berkov, N. Gorn, and A. Michels, Phys. Rev. B \n85, 024410 (2012).  \n[51] S. Erokhin, D. Berkov, N. Gorn, and A. Michels, P hys. Rev. B \n85, 134418 (2012).  \n[52] A. Michels, S. Erokhin, D. Berkov, and N. Gorn, J. Magn. \nMagn. Mater. 350, 55 (2014).  \n[53] S. Erokhin, D. Berkov, and A. Michels, Phys. Rev. B 92, \n014427 (2015).  \n[54] S. Erokhin, D. Berkov, M. Ito, A. Kato, M. Yano, and A. \nMichels, J. Phys. Condens. Matter 30, 125802 (2018).  \n[55] J. M. D. Coey, Magnetism and Magnetic Materials  \n(Cambridge University Press, 2010).  \n[56] T. Gaudisson, Z. Beji, F. Herbst, S. Nowak, S. Ammar, and R. \nValenzuela, J. Magn. Magn. Mater. 387, 90 (2015).  \n \n \n \n   \n \nFIGURE 1  \n \n \n \n \nFig. 1: Schematic drawing of the SANS setup. The scattering vector q is defined as the difference between the wave \nvectors of the scattered and incident neutrons, i.e. , q = k1-k0. The magnetic field H0 is applied perpendicular to the \nincident neutron beam, i.e. , k0 // ex ⊥ H0 // ez. In the small -angle approximation  ( << 1), t he component of q along k0 is \nneglected, i.e. , 𝒒≅{0,𝑞𝑦,𝑞𝑧}=𝑞{0,sin(𝜃),cos (𝜃)}, where the angle θ specifies the orientation of q on the two -\ndimensional detector.  \n \n   \n \n \nFIGURE 2  \n \n \nFig. 2: (a) X-ray diffraction patterns of Mn 0.2Zn0.2Fe2.6O4 nanoparticles (8, 27, 38, 80 nm diameter particle size) compared \nto the reference pattern of the cubic spinel structure (red color bars; taken from the JPCD  database , JCPDS -221086 ). (b) \nTEM images of  the Mn 0.2Zn0.2Fe2.6O4 nanoparticles (8, 27, 38 and 80 n m diameter particle size).  \n \n  \n \nFIGURE 3  \n \n \nFig. 3: Scanning electron microscopy (SEM) image of the MZFO -38 sample after press ing into a circular pellet. Inset: \nSEM cross view at the edge of the pellet.   \n \n \n \nFIGURE 4 \n \n \nFig. 4: (a) Normalized M(H) curves of Mn 0.2Zn0.2Fe2.6O4 nanoparticle powder s measured at room temperature in a field \nrange of ± 5  T (8 (green), 27 (black), 38 (blue) and 80 (pink) nm diameter particle size).  The experimental MS has been \napproximated by the high -field value (5 T). (b) Zoom in the low -field region of the M(H) curves.  (c) Extracted m agnetic \nmoment distribution PV(μ) of MZFO -8 determined by numerical inversion of the M(H) in Fig. 4(a) (green squares ). The \nmain peak has been fitted assuming a log-normal  distribution of the magnetic moment μ (red dashed line ). (d) Histogram \nof the particle -size distribution  of MZFO -8 determined by TEM  (green) and number -weighted log -normal distribution \ndetermined by transforming the main peak of the magnetic moment distri bution PV(μ) observed in Fig. 4(c) (red solid \nline).   \n   \n \nFIGURE 5 \n \n \nFig. 5: Experimental two -dimensiona l total unpolarized SANS cross section s dΣ/dΩ (left and middle panel ) and magnetic \nSANS cross section s dΣM/dΩ (right panel ) of Mn 0.2Zn0.2Fe2.6O4 nanoparticles. The dΣM/dΩ in the remanent state were \nobtained by subtracting the total scattering at the  (near)  saturation field of 4  T from the data at H = 0 T. The applied \nmagnetic field H0 is horizontal in the plane of the detector ( H0 ⊥ k0). All measurements were performed at room \ntemperature. Note that the d Σ/dΩ and d ΣM/dΩ scale s are plotted in polar coordinates ( q in nm-1, θ in degree and the \nintensi ty in arbitrary units normalized between 0 and 1 ).   \n \nFIGURE 6 \n \n \nFig. 6: Nuclear SANS cross section s dΣnuc/dΩ of Mn 0.2Zn0.2Fe2.6O4  nanoparticles as a function of  momentum  transfer  q \n(8 (green), 27 (black), 38 (blue) and 80 (pink) nm diameter particle size)  (log-log scale) . The d Σnuc/dΩ were determined \nby  10° horizontal averages ( q // H0) of the total d Σ/dΩ at an applied magnetic field of μ 0H0 = 4 T. Note that the data \nare displ ayed as a function of q/qc, where  qc = 2π/ D with D the respective  mean  nanoparticle size. Measurements were \nperformed at room temperature (300  K). Black solid lines: power law fits to dΣnuc/dΩ ∝ K/(qD)4. Dashed vertical line: q \n= qc = 2π/ D. The error bars of d Σnuc/dΩ are smaller than the data point size.  \n   \n \nFIGURE 7 \n \n \n \nFig. 7: Magnetic field dependence of the (over 2) azimuthally -averaged total nuclear and magnetic (top panel ) and \npurely magnetic (bottom  panel ) SANS cross section s of Mn 0.2Zn0.2Fe2.6O4 nanoparticles  (log-log scale) . Solid filled \ncircles  in the inset : magnetic field values in Tesla decrease from 4.0 T (bottom) to 0 T (top). All measurements were \nperformed at room temperature . The error bars of d Σ/dΩ and dΣM/dΩ are smaller than the data point size.  \n   \n \nFIGURE 8 \n \n \nFig. 8: Left: e xperimental intensity ratio αexp(q) determined from the averaged SANS cross section s at zero field and at \n0H0 = 4 T with q // H0 [Eq. ( 3)]. Right: magnetic field dependence of αexp around q = 0.22 nm-1 for MZFO -38. Note that \nthe data are displayed as a function of q/qc, where qc = 2π/ D with D the respective mean nanoparticle size. Dashed \nvertical lines: q = qc = 2π/D. Dashed horizontal lines: αcalc = 1.027 [Eq. (4)] computed using the Mn 0.2Zn0.2Fe2O4 bulk \ndensity of 4 084 kg/m3, 𝛥𝜚nuc=𝜚Mn 0.2Zn0.2Fe2O4−𝜚Oleic  acid =5.15510−6\nÅ2, and 𝜚mag =𝑏𝐻𝑀S𝑀𝑍𝐹𝑂=1.04610−6\nÅ2, where \n𝑀S𝑀𝑍𝐹𝑂=359 .4 kA/m corresponds to the mean value of MS (compare Table 1) . \n \n   \n \nFIGURE 9  \n \n \nFig. 9: (a) Selected field-dependent 2π -azimuthal averages of the magnetic SANS cross section 𝑑𝛴 M/𝑑𝛺 of MZFO -38 \n(taken from Fig. 7). Color  solid lines:  reconstruction of 𝑑𝛴 M/𝑑𝛺 in the intraparticle q-range ( marked by the dashed \nvertical  line) using the extracted p(r) profiles fro m (b). (b) Field -dependent pair-distance distribution functions p(r) [Eq. \n(5)] extracted by an indirect Fourie r transform  of 𝑑𝛴 M/𝑑𝛺 in the intraparticle q-range . Dashed line: expected  p(r) = r2 \n[1 – 3r/(4R) + r3/(16R3)] for a homogeneous sphere of D = 2R = 38 nm size.  \n    \n \nFIGURE 1 0 \n \n \n \nFig. 1 0: Microstructures used in the micromagnetic simulations. The volume fraction of the particle phase was set to 80 \n% in all computations. The simulation volume  300  300  300 nm3 is constant in the simulations (mesh size: 4 nm), \nso that an increase in the average particle size D is accompanied by a reduction of the number N of particles, from N  \n40.000 at 14 nm to N  40 at 74 nm.  \n  \n \n \nFIGURE 11 \n \n \n \nFig. 11: Applied field dependence  of the quantity M/MS [Eq. (6 )] for different average particle sizes D. Inset: \nCorresponding normalized magnetization curves.  \n   \n \nFIGURE 1 2 \n \n \nFig. 1 2: (top panel ) Particle -size-dependent evolution of the parameter M/MS [Eq. (6 )] for each magnetic particle “ i” \nand as a function of the applied magnetic field. ( bottom panel)  Snapshots of spin structures at selected fields, where the \nlargest deviations from the uniform magnetization state are observed . \n \n \n   \n \nTABLE 1  \nSample  Composition  \n(XRF)  Particle size  \n(TEM)  \n(nm)  Crystal size  \n(XRD)  \n(nm)  MS \nat 300 K  \n(Am2/kg) MR \nat 300 K  \n(Am2/kg) μ0HC \nat 300 K  \n(mT)  \nMZFO -8 Mn 0.18Zn0.25Fe2.57O4 8±2 8(1) 73 1 0.8 \nMZFO -27 Mn 0.24Zn0.21Fe2.55O4 27±3 26(1)  95 1 0.4 \nMZFO -38 Mn 0.20Zn0.17Fe2.63O4 38±5 38(1)  90 4 2.7 \nMZFO -80 Mn 0.20Zn0.25Fe2.55O4  80 79(1)  94 10 9.4 \n \nTable 1: Structural and magnetic parameters of Mn 0.2Zn0.2Fe2.6O4 nanoparticle powder s. The average  particle sizes were \ndetermined by means of transmission electron microscopy (TEM) and wide -angle X -ray diffraction (XRD) . The \nsaturation  and remanent magnetization s (MS and MR) and the coercive field ( HC) have been determined from the M(H) \ncurves.  \n \n \n "    },    {        "title": "2201.07087v1.Growth_and_characterization_of_ultrathin_cobalt_ferrite_films_on_Pt_111_.pdf",        "content": "Growth and characterization of ultrathin cobalt ferrite films on Pt(111)\nG.D. Soria,1K. Freindl,2J. E. Prieto,1A. Quesada,3J. de la Figuera,1N. Spiridis,2J. Korecki,2, 4and J. F. Marco1\n1Instituto de Química Física “Rocasolano”, CSIC, Madrid E-28006, Spain\n2Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, 30-239 Kraków, Poland\n3Instituto de Cerámica y Vidrio, CSIC, Madrid E-28049, Spain\n4AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, 30-259 Kraków, Poland\nCoFe 2O4thin films (5 nm and 20 nm thick) were grown by oxygen assisted molecular beam epitaxy on\nPt(111) at 523 K and subsequently annealed at 773 K in vacuum or oxygen. They were characterized in-\nsituusing Auger Electron Spectroscopy, Low-Energy Electron Diffraction, Scanning Tunneling Microscopy\nand Conversion Electron Mössbauer Spectroscopy. The as-grown films were composed of small, nanometric\ngrains. Annealing of the films produced an increase in the grain size and gave rise to magnetic order at room\ntemperature, although with a fraction of the films remaining in the paramagnetic state. Annealing also induced\ncobalt segregation to the surface of the thicker films. The measured Mössbauer spectra at low temperature were\nindicative of cobalt ferrite, the both films showing very similar hyperfine patterns. Annealing in oxygen or\nvacuum affected the cationic distribution, which was closer to that expected for an inverse spinel in the case of\nannealing in an oxygen atmosphere.\nI. INTRODUCTION\nHard magnetic ferrites have many technological applica-\ntions, including permanent magnets, recording media, spin-\ntronic and microwave devices1–6. Since for many of these ap-\nplications the use of ferrite thin films with well-defined prop-\nerties is of paramount importance, we have focused in this\nwork on the preparation and characterization of cobalt fer-\nrite (CoFe 2O4, CFO) thin films. Cobalt ferrite has the high-\nest magnetocrystalline anisotropy among the cubic ferrites,\nshows large magnetostriction effects and presents both a high\nCurie temperature and a large saturation magnetization1. In\nthin film form it has been proposed as a spin filter in spin-\ntronic devices7–14.\nAn ideal CFO has an inverse spinel crystal structure\n(AB 2O4) with space group Fd \u00163m, in which all cobalt cations\n(Co2+) together with half of the iron cations (Fe3+\nB) occupy\noctahedral sites (B), while the other half of iron cations (Fe3+\nA)\nare located at tetrahedral sites (A), resulting in the chemical\nformula Fe3+\nAFe3+\nBCo2+\nBO4. Real samples always present a\npartial Co2+occupation of the tetrahedral sites, whose partic-\nular value depends on the preparation method and the sam-\nple history15–20. The high magnetocrystalline anisotropy is at-\ntributed to the high orbital moment of the Co2+cations. The\nnet magnetization is smaller than that of the isostructural mag-\nnetite (pure iron inverse spinel), as the Co2+cations have a\nsmaller spin moment compared with the Fe2+of the latter. A\ntechnique often used to study the cationic distribution in CFO\nis Mössbauer spectroscopy15. In this case, iron in octahedral\nand tetrahedral positions give rise to two sextets in the Möss-\nbauer spectrum. However, the two sextets overlap strongly\nat room temperature, and low temperature experiments are\nrequired to separate both signals. Even at low temperature,\nthe overlap is significant21requiring the application of exter-\nnal magnetic fields for a non-ambiguous determination of the\noctahedral and tetrahedral populations and, therefore, of the\ninversion degree17,18. Nevertheless, Mössbauer spectroscopy\nremains one of the most useful techniques to characterize fer-\nrites and, in particular, CFO.CFO films have been grown by many different methods,\nsuch as sol-gel process22,23, dual ion beam sputtering24,25,\npulsed laser deposition26–30, magnetron sputtering26,31,32, and\nmolecular beam epitaxy to cite a few. The latter method has\nbeen performed depositing Co and Fe in atomic oxygen9,33or\nmolecular oxygen34,35enviroments, followed by subsequent\noxidation steps of the deposited metal layers20, by depositing\nCo on magnetite36or even by annealing oxide layers37,38. In\nnearly all those cases, the substrates have been oxides or in-\nsulators. However, there are cases where the growth of thin\nfilms of CFO on metal substrates is desirable. With an ap-\nplied goal in spintronic applications, it would allow study-\ning the possible modification of magnetic domains by current\nflow, either due to spin-orbit or spin-transfer torque. From\nthe characterization point of view, it allows using the full\nrange of electron-based surface probes on ultrathin films to\ndetermine the structural, chemical and magnetic properties\nof the grown films. While the growth of magnetite films,\ni.e. pure-iron spinel with mixed valence, has been performed\non a variety of metal substrates such as Au, Ag, Pt, Ru and\nW39,40, their use has been much more scarce in the case of\ncobalt ferrite. Santis et al.20used a post annealing step after\ndepositing Co and Fe on Ag(100), obtaining (100)-oriented\nfilms. Recently, we have grown cobalt ferrite films on hexag-\nonal single crystal substrates, such as Ru(0001), by oxygen-\nassisted high temperature molecular beam epitaxy34,35obtain-\ning (111) oriented crystallites. However, in a similar manner\nto other spinels such as magnetite41–43and nickel ferrite44, the\ngrowth typically does not provide single-phase films with a\nflat morphology. Instead, it gives rise to crystallites of non-\nstoichiometric CFO islands sitting on a wetting layer of Fe(II)-\nCo(II) mixed oxide. In many applications, a continuous uni-\nform film is desired. Thus, in the present work, we investigate\na method to obtain continuous CFO films on top of a metal\nsubstrate, Pt (111), by oxygen-assisted molecular beam epi-\ntaxy, but keeping the substrate at much lower temperatures to\nprevent the phase separation observed at high temperatures35.\nIn this study, we use in-situ Mössbauer spectroscopy to iden-\ntify the environment of the iron cations, and we complement\nit with Auger electron spectroscopy (AES), low-energy elec-arXiv:2201.07087v1  [cond-mat.mtrl-sci]  18 Jan 20222\ntron diffraction (LEED), and scanning tunnelling microscopy\n(STM).\nII. EXPERIMENTAL METHODS\nCobalt ferrite films were prepared and characterized in-\nsituin an ultra-high vacuum (UHV) multichamber system.\nThe system included a preparation chamber equipped with\na molecular beam epitaxy doser, a LEED difractometer\n(OCI Vacuum Microengineering), which can be also used\nto record AES data using it as a Retarding Field Analyser\n(RFA), a chamber with STM (Burleigh Instruments micro-\nscope with Digital Instruments control electronics), and a\nchamber devoted to Conversion Electron Mössbauer Spec-\ntroscopy (CEMS). The home-made CEMS spectrometer, fit-\nted with a channeltron to detect the electrons emitted from\nthe sample, and a 100 mCi Mössbauer57Co(Rh) \r-ray source\nlocated outside the vacuum chamber, has been described in\nRef.45. The spectra were measured with the incoming \r-rays\nalong the surface normal.\nThe substrate was a Pt(111) single crystal. Its temperature\nwas controlled by a PtRh-Pt thermocouple pressed against the\nback side of the crystal. It was cleaned by cycles of sputtering\nwith argon ion bombardment (500 eV , 5 \u0016A, for 35 min), flash-\ning in UHV and annealing in atmosphere of oxygen (1 \u000210\u00007\nmbar, 10 min, 825 K). The cycles were repeated until a sharp\n(1\u00021) Pt (111) LEED pattern was obtained. Nonetheless,\nsome residual iron contamination could be detected by CEMS\nafter numerous preparation cycles due to iron impurities di-\nluted deeper into the substrate.\nThe cobalt ferrite films were grown by co-deposition of\niron, enriched to 95 %in57Fe, and cobalt in an oxygen atmo-\nsphere on a heated Pt substrate. The oxygen partial pressure\nwas8\u000210\u00006mbar, and the substrate temperature was kept\nat 523 K. The growth rates of iron and cobalt and the anneal-\ning treatments for each film are explained in their respective\nsections.\nAt each preparation step, the films were characterized by\nLEED and AES. At selected steps, STM and CEMS measure-\nments were performed. The latter were acquired both at room\ntemperature (RT) and low temperature (LT, 115–125 K). The\nspectra and the magnetic field distributions were fitted using\nthe Recoil program and the NORMOS code46. As mentioned\nabove, the Auger spectra were acquired by means of the four-\ngrid LEED spectrometer (in RFA mode) using a primary elec-\ntron beam (I P) of 1.7 keV .\nIII. RESULTS\nA. 20 nm film\nThis sample was deposited using growth rates of approxi-\nmately 0.28 nm/min for Fe and 0.14 nm/min for Co, respec-\ntively, i.e. keeping the nominal Fe flux approximately twice as\nlarge as that of Co, in order to obtain a nominal film of compo-sition close to CoFe 2O4. Subsequently, the film was annealed\nat 673 K and 773 K in UHV for 15 min in both treatments.\nFigure 1 shows the AES spectra recorded from the as-grown\nfilm, as well as for the film subjected to annealing at 673 and\n773 K. All spectra show the expected oxygen KLL, iron LMM\nand cobalt LMM lines. Due to the overlap of several of the Co\nand Fe LMM lines, we used the peaks at 598 and 775 eV of\nFe and Co, respectively, to monitor changes in the film com-\nposition. The data show an increase in the intensity of the Co\nLMM lines with respect to the Fe LMM lines upon anneal-\ning, going from a ratio of Fe (598eV)/Co (775eV)0.95 to 0.81\n(673 K) and 0.60 (773 K). Assuming the nominal composi-\ntion for the as-prepared film, this intensity evolution implies\nthe change of the Fe to Co ratio from approximately 2:1 to\n4:3. We note that the electron beam energy used to acquire\nthe AES spectra is rather low, 1.7 keV . The inelastic mean\nfree path for Auger electrons at I Pof 600 eV is close to 1\nnm, so here we are collecting electrons coming from a sur-\nface layer 2-3 nm thick47. Therefore, the annealing treatment\ncauses an increase in the ratio of cobalt atoms to iron atoms\nnear the surface. This increase in cobalt atoms or decrease in\niron atoms on the surface with the annealing step is also re-\nflected in the oxygen peak (512 eV). The ratios between the\nintensity of the O KLL lines with respect to the Fe LMM in-\ntensity line, Fe (598eV)/O(512eV), after growth and after the an-\nnealing treatments at 673 K and 773 K are 0.115, 0.110, and\n0.095, respectively. This data trend from the Fe/O ratio con-\nfirms the decrease in the number of iron atoms on the surface\nupon annealing.\n500 600 700 800\nElectron Energy (eV)-6-4-2024Intensity (arb. units)\nAs-grown\nAnnealed at 673 K\nAnnealed at 773 K750760770780  0\n  -1  1\nFeFe+Co Fe+Co Co\nO\nFigure 1. Auger spectra recorded from the 20 nm film. The spectra\nwere normalized to the intensity of the Fe peak at 598 eV . Inset:\nAuger Co LMM peak at 775 eV .\nThe LEED patterns of the 20 nm thick CFO sample\nrecorded at different stages of its preparation are shown in fig-\nure 2. In the first panel, the pattern from the substrate is pre-\nsented, showing the Pt(111) first-order spots. The as-grown\nfilm also shows a 1\u00021pattern, with the same symmetry as the\nsubstrate and somewhat smaller spacing, which corresponds\nto a larger surface unit cell of 0.30 nm compared to 0.277 nm3\nfor Pt(111). No significant changes are observed in the pattern\nupon annealing. Although hexagonal symmetry is expected\nfor the (111) surface of the cobalt ferrite, the observed surface\nunit cell is smaller by a factor of two than that expected for the\n(111) plane of bulk cobalt ferrite which has a 0.59 nm period-\nicity. We will comment on this observation in the discussion\nsection.\na)\n b) c) d) a)\nFigure 2. Diffraction patterns for: a) Platinum substrate, 20 nm CFO\nfilm, b) as-grown, c) annealed at 673 K, and d) at 773 K. LEED\npatterns were acquired at an energy of 66 eV .\nFigure 3a shows an STM image of the as-grown film. The\nimage shows the presence of particles with a size around 15–\n20 nm and a surface rms roughness of 0.3 nm. Figure 3b,\nwhich corresponds to the sample after annealing at 773 K in\nUHV , shows a film with somewhat larger clusters 20–25 nm\nin size and slightly larger 0.4 nm rms roughness.\n50 nm 50 nma) b)\nFigure 3. STM images of the 20 nm CFO thin film: a) as-grown and\nb) annealed to 773 K.\nThe Mössbauer spectrum recorded from the as-grown sam-\nple is depicted on top of figure 4. The spectrum is dominated\nby intense paramagnetic signals (a singlet and two doublets)\nin its central part. A low intensity, broad magnetic component\nis also observed. The values of the hyperfine parameters for\nthe various components obtained from the fit of this spectrum\nare collected in table I. The paramagnetic singlet is due\nto the presence of Fe0dissolved in the platinum substrate,\nsomething which is quite common in this type of systems.\nThe most intense doublet is characteristic of a high spin Fe3+\nspecies in distorted octahedral oxygen coordination, while\nthe minor doublet can be associated with a high spin Fe2+\nspecies also in octahedral coordination. The weak magnetic\ncomponent reflects the occurrence of a broad hyperfine\nmagnetic field distribution, most probably arising from the\npoor crystallinity or from the presence of a distribution of\nsmall-sized particles (as revealed by STM) in the depositedfilm, whose Mössbauer parameters are characteristic of Fe3+.\nWe should mention that the inclusion of a paramagnetic\nFe2+doublet results from the evident occurrence of a bump\nat around +1.5 mms\u00001which makes the central “paramag-\nnetic” part of the spectrum to be asymmetric. However, as\nit occurs in the case of magnetite thin films, where strong\nsuperparamagnetism is observed due to the occurrence of\nstructural domains, this spectrum can be also fitted using\nhyperfine magnetic field distributions to account for super-\nparamagnetic components. An example of this type of fit\nis shown in Figure 1 of the Supplementary Information.\nIt is interesting to note (see also Table in the SI) that the\nisomer shifts of these magnetic field distributions are very\nhigh (0.53-0.56 mms\u00001) suggesting also the presence of\nFe2+in the film. In this case, the result would indicate that\nthose components would have a “magnetite-like” behavior,\nshowing the occurrence of electron hopping. Importantly,\nboth fitting approaches are suggestive of the presence of Fe2+\nin the as-grown film. As it happens very often, the fit of such\na spectrum cannot be unique and several models are possible.\nIn any case, independently of the final fit chosen, the evident\nrelaxation components and the likely presence of Fe2+in the\nspectrum forced us to anneal the film as a means to get rid out\nof such contributions which are not the expected for CFO.\nThus, the Mössbauer spectra recorded at 298 K and LT from\nthe film annealed up to 773 K are also shown in figure 4. The\nresults clearly indicate that the annealing treatment has a sig-\nnificant effect on the nature of the deposited film.\nThe 298 K spectrum shows the presence of a broad in-\ntense magnetic component and some other small paramag-\nnetic components (the Fe0singlet, a Fe3+doublet and a Fe2+\ndoublet). The fit of the magnetic component can be performed\nin different ways. After trying different fitting models, we\nadopted finally a model considering two discrete magnetic\nsextets and a sextet with a hyperfine magnetic field distribu-\ntion. The Mössbauer parameters of the discrete sextets (table\nI) are typical of those shown by the tetrahedral and octahe-\ndral Fe3+cations of oxides with spinel-related structure. The\nmagnetic field distribution component has a difficult assign-\nment since its isomer shift is intermediate between those of\nthe octahedral and tetrahedral discrete sextets. Most proba-\nbly, it contains both octahedral and tetrahedral contributions.\nThe assignment of the paramagnetic components remains as\nexplained above.\nThe 125 K Mössbauer spectrum presents much narrower\nlines than the RT one and the two discrete sextets are now\nmuch better resolved. However, the spectrum still shows some\nrelaxation character and an additional broad (characterized by\na hyperfine magnetic field distribution) magnetic component,\nwas included in the fit. Apart from this, the spectrum contin-\nues showing the small Fe0and Fe2+contribution. It is well-\nknown30,48that annealing promotes both cation rearrangement\namong the tetrahedral and octahedral sites as well as an in-\ncrease in the size of the small particles which compose the\nfilm. Specifically for small particles, the Mössbauer spec-\ntra reflect the change in the magnetic behaviour by a transi-\ntion from a doublet (superparamagnetic) to a sextet (magnetic4\n100.0100.5101.0101.5\nEffect (%)\n-12-8-404812\nVelocity (mm/s)100.0100.5101.0101.5Effect (%)102.0102.5102.0Effect (%)\n100.0104.0106.0\na) 298 K \n102.0As-grown \nAnnealed at 673 K / 773 K\nb) 298 K\nc) 125 KFe0\nFe3+\nFe3+ Dist. \nFe2+ \nFe3+ Td (A)\nFe3+ Oh\n (B)\nFe0Fe2+Fe3+ Dist.Fe3+ Td (A)Fe3+ Oh (B)Fe0Fe3+Fe2+Fe3+ Dist.Fe3+ Td (A)Fe3+ Oh (B)Fe0Fe3+Fe2+Fe3+ Dist.\nFigure 4. Mössbauer spectra obtained for the 20 nm cobalt ferrite\nthin film for the different stages: a) as-grown (measured at 298 K),\nb) and c) annealed to 673 K and 773 K, measured at 298 K and 125\nK, respectively.\ncharacter) with the temperature decrease as well as the particle\nsize distribution causing line broadening since the magnetic\nmoment stabilization does not occur at the same temperature\nfor all particles.\nThe superparamagnetic character in thin films caused by\nthe small size of the particles has already been reported in\nthe literature. J.G. S. Duque22studied this phenomenon for\nCFO films with particle sizes between 10-20 nm. Also, López\net al.49commented on the influence of the grain size (10-40\nnm in average) in their CoFe 2O4films. In addition, Yanagi-\nhara/acute.ts1s group50working on 13 nm thick cobalt ferrite films on\n\u000b-Al2O3(0001) pointed out the occurrence of a broad mag-\nnetic component which was interpreted as a result of a ther-\nmally fluctuating magnetic order near the blocking tempera-Spectrum Site \u000e \u0001- 2\" H Area\n(\u00060.03 mms\u00001)(\u00060.05 mms\u00001) (\u00060.05 T) (%)\nAs-grown Fe00.33 - - 11\n298 K Fe2+1.25 0.75 - 14\nFe3+0.41 0.80 - 58\nFe3+0.43 0.02 25.1 17\nAnnealed Fe00.23 - - 5\n298 K Fe3+\nB 0.38 -0.09 49.3 12\nFe3+\nA 0.30 -0.01 46.4 37\nFe3+0.31 0.93 - 6\nFe2+0.87 0.78 - 6\nFe3+0.35 -0.04 44.0 (H AV G - 37.1)a34\nAnnealed Fe00.30 - - 1\n125 K Fe3+\nB 0.51 -0.04 52.4 27\nFe3+\nA 0.41 -0.03 49.1 57\nFe2+1.10 1.10 - 3\nFe3+0.45 -0.09 43.0 (H AV G - 34.6)a12\naIn the case of the distribution component, H corresponds to the maximum\nof the distribution while H AV G refers to the average field of distribution.\nTable I.57Fe Mössbauer parameters obtained from the fit of the spec-\ntra shown in figure 4. The symbols \u000e,\u0001, 2\", H correspond to isomer\nshift, quadrupole splitting, quadrupole shift and and hyperfine mag-\nnetic field, respectively. The isomer shift values are quoted relative\nto\u000b-Fe at room temperature.\nture associated to a superparamagnetic behavior of the films.\nThe values of the hyperfine parameters of the two discrete\nsextets are very similar to those expected for cobalt ferrite. It\nis worth noting that the line intensity ratio of the magnetic\ncomponents is 3:3.3:1:1:3.3:3. This indicates that the film\nmagnetization is mostly in-plane at 72 deg with respect to the\n\r-rays direction in average. Considering that in this particu-\nlar spectrometer the average deviation from normal incidence\ndue to the solid angle of the sample ilumination is approxi-\nmately 6\u000e, the angle between the hyperfine magnetic field and\nthe surface plane would be 18\u000e\u00066\u000e. The relative areas of the\ndiscrete sextets (Fe3+\nA/Fe3+\nB) are in the ratio 2.1, i.e. quite far\nfrom the expected ratio (1.0) for a perfect CFO inverse spinel.\nThis would imply that the magnetic field distribution compo-\nnent contains mostly octahedral contributions. We will come\nback to this point later.\nB. 5 nm film\nThe growth of this film was performed at rates of approx-\nimately 0.16 nm/min for Fe and 0.08 nm/min for Co, thus\nkeeping the nominal Fe flux approximately twice as large as\nthat of Co in order to obtain a film with nominal composi-\ntion close to CoFe 2O4. Afterwards, the film was annealed at\n673 K for 15 min and subsequently at 773 K for other 15 min,\nwith both processes being carried out in UHV . An additional\nannealing treatment at 773 K in oxygen ( 1\u000210\u00006mbar) for\n15 min was performed to check if this could improve the for-\nmation of a CFO inverse spinel.\nThe AES spectra recorded from the as-grown 5 nm thick\nCFO film as well as from the annealed films both in vacuum\nand in oxygen are shown in figure 5. Again, the lines arising5\nfrom O KLL, Fe LMM and Co LMM are observed. However,\nunlike the case of the 20 nm thick film, which showed a clear\nCo enrichment upon annealing, now within the error limits of\nthe quantitative determination, there is no clear trend.\n500 600 700 800\nElectron Energy (eV)-4-2024Intensity (arb. units)\nAs-grown\nAnnealed at 673 K\nAnnealed at 773 K\nAnnealed in O2 at 773 K750760770780  0\n  -0.4  0.4\nFigure 5. Auger spectra of the 5 nm film recorded after the different\ntreatment steps. The spectra were normalized to the intensity of the\nFe peak at 598 eV . Inset: Auger Co LMM peak at 775 eV .\nThe LEED patterns from the as-grown and annealed films\nare shown in Figure 6. First, the diffraction pattern of the\nsubstrate, Pt(111), is shown (figure 6a). As for the thicker\nfilm, all the patterns are hexagonal with the same symmetry\nand orientation as the substrate. The as-grown film presents\nbroader spots with considerably larger lattice spacing than the\nsubstrate (figure 6b). Annealing at 673 K and 773 K in vac-\nuum produces a small increase in the spot separation towards\nthe substrate lattice spacing, an effect which is more clear af-\nter annealing in O 2(figures 6c, 6d and 6e, respectively). Us-\ning the Pt as a reference (0.28 nm), we show in figure 6f the\nobserved evolution of the lattice spacing in the 5 nm film.\nSTM images recorded from the as-grown film, as well as\nfrom the film annealed at 773 K both in vacuum and in oxy-\ngen, are shown in figure 7. They show particles 10-15 nm\nin size with a rms roughness of 0.3 nm, 15-18 nm and a rms\nroughness value of 0.4 nm and 20-25 nm with a rms roughness\nof 0.5 nm, respectively.\nFigure 8 collects the Mössbauer data recorded from the as-\ngrown sample at 298 K, the vacuum-annealed film both at 298\nK and 115 K, and the film annealed in oxygen also both at 298\nK and 125 K.\nThe RT spectrum recorded from the as-deposited sample is\ncharacterized by an intense, broad magnetic component that\nis accompanied by some other minor paramagnetic compo-\nnents: the Fe0singlet mentioned before and an Fe3+doublet\nin distorted octahedral oxygen coordination. Because of the\nbroadness of the magnetic component, the presence of a Fe2+\ncontribution to the spectrum has not been considered in the fit\nsince this would imply a large uncertainty in the determination\nof both its Mössbauer parameters and its spectral area. The\nspectrum is compatible with a broad distribution of the parti-\n300 400 500 600 700 800\nTemperature (K)0.270.280.290.300.31Lattice parameter (nm)\nPt(111)\nAs-grown\nAnnealed at 673 K\nAnnealed at 773 K\nAnnealed in O2\n at 773 Kf)a)b) c) d) e)Figure 6. Top panel: LEED diffraction patterns recorded from: a)\nplatinum substrate, 5 nm CFO film, b) as-grown, b) annealed in UHV\nat 673 K, d) annealed in UHV at 773 K e) annealed in O 2at 773 K.\nBottom panel: f) lattice parameters calculated from the LEED pat-\nterns after each processing step.\na) b) c)\n50 nm 50 nm 50 nm\nFigure 7. STM images recorded from the 5 nm thick CFO film: a)\nas-grown, b) annealed at 773 K in vacuum, and c) annealed at 773 K\nin oxygen.\ncles sizes ranging from sufficiently small as to remain param-\nagnetic at RT to large enough as to give a relatively high hy-\nperfine magnetic fields (46 T) (see Table II). It is worth men-\ntioning that comparing the spectra of the as-grown 5 nm and\n20 nm films, we find that the former shows only a small para-\nmagnetic contribution. Increasing the thickness of thin films\nusually confer them structural and magnetic properties similar\nto those expected for the bulk compound. However, the oppo-\nsite behavior is observed here. This result will be commented\nin the discussion section.\nAs in the case of the thicker film, the annealing treat-\nments induce significant changes in the nature of the deposited\nfilm. The RT spectra acquired from the annealed film both\nin vacuum and in the presence of oxygen are very similar,\nand they are also similar to the RT spectrum recorded from\nthe annealed 20 nm CFO film: they show much better de-\nfined magnetic components and significantly less intense (su-\nper)paramagnetic contributions. Therefore, they have been all\nfitted using a similar model and, consequently, the same con-\nsiderations mentioned in the case of the 20 nm-thick annealed\nfilm are of application here. At LT, the spectra show much nar-\nrower sextet lines although, again, some magnetic relaxation\nis still present, hence the need of including a low-intensity\nmagnetic component having a hyperfine magnetic field distri-6\n100.0100.5101.0101.5\nEffect (%)a) 298 K\n-12-8-404812\nVelocity (mm/s)As-grown\nFe0\nFe3+\nFe3+ Dist. \nFe2+\nFe3+ Td (A)\nFe3+ Oh (B)\n100.0100.5101.0101.5Effect (%)\n100.0100.5101.0101.5\n-12-8-404812\nVelocity (mm/s)100.0100.5100.1101.5Effect (%) Effect (%)\n100.0100.5101.0101.5Effect (%)\n-12-8-404812\nVelocity (mm/s)d) 298 K\ne) 125 K c) 115 Kb) 298 KAnnealed at 673 K / 773 KAnnealed in O2\n at 773 KFe0Fe3+Fe3+ Dist.\nFe0Fe3+Fe2+Fe3+ Dist.Fe3+ Td (A)Fe3+ Oh (B)\nFe0Fe2+Fe3+ Dist.Fe3+ Td (A)Fe3+ Oh (B)Fe0Fe3+Fe2+Fe3+ Dist.Fe3+ Td (A)Fe3+ Oh (B)\nFe0Fe2+Fe3+ Dist.Fe3+ Td (A)Fe3+ Oh (B)\nFigure 8. Mössbauer spectra recorded from the 5 nm CFO thin film\nfor the different stages: a) as-grown film measured at 298K, b) and\nc) film annealed at 673 K /773 K in UHV measured at 298 K and 115\nK, respectively, d) and e) film annealed in oxygen atmosphere at 773\nK measured at 298 K and 125 K, respectively.\nbution. Similarly to the LT spectrum of the thick film, the 125\nK spectra of these films continue to show a Fe2+contribu-\ntion. Slight differences between the LT spectrum correspond-\ning to the thick film and the two reported in this section refer\nto the Fe3+\nA/Fe3+\nBdiscrete sextets intensity ratio. While in the\nformer this ratio amounts to 2.1, in the present case, the val-\nues obtained are 1.9 (annealed in vacuum) and 1.1 (annealed\nin oxygen). For the 5 nm-thick film, the line intensity ratio\nin the sextet is 3:3.1:1:1:3.1:3, which corresponds to an angle\nbetween the sample average magnetization and the gamma ra-\ndiation direction of 70\u000e. This indicates that the sample mag-\nnetization direction forms an angle respect to the surface plane\nclose to 20\u000e\u00066\u000e. Therefore, in the present film the magneti-\nzation is slightly more out-of-plane than in the case of the 20\nnm-thick film.\nIV . DISCUSSION\nWe first consider the morphology observed by STM. The\nas-grown films are composed of nanometric particulates hav-\ning sizes of tenths of nanometers. This explains the in-\ntense paramagnetic components and broad magnetic contri-\nbutions observed in the corresponding Mössbauer spectra.\nHowever, despite having similar grain size in both as-grownSpectrum Site \u000e \u0001- 2\" H Area\n(\u00060.03 mms\u00001)(\u00060.05 mms\u00001) (\u00060.05 T) (%)\nAs-grown Fe00.30 - - 6\nFe3+0.40 0.85 - 13\nFe3+0.34 -0.03 46.5 (H AV G - 33.7)a81\nAnnealed, RT Fe00.23 - - 4\nFe3+\nB 0.39 -0.05 49.4 14\nFe3+\nA 0.29 0.02 46.7 31\nFe3+0.31 0.93 - 5\nFe2+0.82 0.97 - 5\nFe3+0.41 -0.03 43.5 (H AV G - 34.9)a41\nAnnealed, 115 K Fe00.30 - - 3\nFe3+\nB 0.46 -0.08 51.4 24\nFe3+\nA 0.36 0.00 48.0 47\nFe2+0.99 0.88 - 3\nFe3+0.41 -0.04 44.0 (H AV G - 30.5)a23\nAnnealed in O 2, RT Fe00.23 - - 4\nFe3+\nB 0.37 -0.05 48.8 7\nFe3+\nA 0.31 0.01 45.5 37\nFe3+0.31 0.93 - 4\nFe2+0.86 1.08 - 5\nFe3+0.33 -0.02 43.0 (H AV G - 35.5)a43\nAnnealed in O 2, 125 K Fe00.30 - - 1\nFe3+\nB 0.49 -0.03 51.9 37\nFe3+\nA 0.36 -0.01 48.9 43\nFe2+0.93 1.21 - 4\nFe3+0.40 -0.16 45.2 (H AV G - 30.5)a15\naIn the case of the distribution component, H corresponds to the maximum\nof the distribution while H AV G refers to the average field of distribution.\nTable II.57Fe Mössbauer parameters obtained from the fit of the\nspectra shown in figure 8. The symbols \u000e,\u0001, 2\", H correspond\nto isomer shift, quadrupole splitting, quadrupole shift and hyperfine\nmagnetic field, respectively. The isomer shift values are quoted rela-\ntive to\u000b-Fe at room temperature.\nfilms, a higher magnetic ordering is observed for the thinner\nfilm. Such evidence is surprising since one might think that\nan increase in the film thickness promotes a smaller (super-\npara)magnetic relaxation and not vice versa. This behavior\nmight be related with the different deposition rates used to\ngrow both films. As mentioned in the corresponding section,\ndeposition rates for the 5 nm film were slower than for the\nthicker film by a factor of almost two. Taking into account the\nlow temperature of growth (523 K), slower deposition rates\nwould favour either the formation or larger surface aggrea-\ngates and/or induce the formation of a more ordered crystal\nstructure.\nThe LEED patterns are 1\u00021, i.e. they show the same\nsymmetry and orientation as the substrate, with similar lattice\nparameter. This suggests that the films grow epitaxially on\nthe substrate, although it is not expected that they are single-\ncrystalline. The lattice parameter of a spinel phase is close to\ndouble in size compared to the in-plane Pt spacing (0.59 nm\nvs 0.27 nm). Thus one expects for an epitaxial spinel film a\npattern with a periodicity close to a 2\u00022pattern. This is in\nfact observed in magnetite grown on Pt(111)39,40,45,51, or in the\nstructure of highly perfect but non-stoichiometric cobalt fer-\nrite grown on Ru(0001) at higher temperatures34. There are\ntwo possible reasons for the lack of 2\u00022diffracted beams in\nthe LEED patterns of both as-grown and annealed films.\nFirst, the films might be structurally quite disordered at the\ncationic level. Especially for the as-grown films, this is in line\nwith the observed Mössbauer patterns. This would imply that7\nthe only unit cell that is observed is actually the one corre-\nsponding to the in-plane oxygen-oxygen spacing in the films,\nwhich is half the size of the full spinel unit cell. We note\nthat we have reported a similar effect during the deposition\nof Co on Fe 3O4(100) where at some point only the oxygen\nunit cell was observed in LEED36. The second explanation is\nthat the LEED patterns correspond to a near-surface region of\nthe films with a rocksalt structure and thus with a Fe xCo1\u0000xO\ncomposition. In support of this explanation, we note that the\nMössbauer spectra show a small Fe2+contribution. There are\na few reported results in support of this explanation. First,\nin the growth of magnetite on Pt(111) and Ru(0001), a sur-\nface reconstruction, the so-called bi-phase reconstruction, has\noften been observed upon molecular oxygen growth. It has\nbeen explained by a FeO-terminated spinel phase45. A simi-\nlar reconstruction has been observed in cobalt ferrite grown at\nhigh temperature on Ru(0001)34. Furthermore, annealing of\nCoO/Fe 3O4has also been reported to result in surface segre-\ngation of a CoO layer37, where it was suggested that the origin\nis the lower surface energy of CoO. We thus suggest that our\nconditions are such as to promote a rocksalt termination of the\nfilms.\nFrom the two explanations proposed for the observation of a\n1\u00021LEED pattern relative to Pt, we consider more likely\nthat the origin is cationic disorder, specially for the thinner\nfilm and the thicker one before Co segregation. Although a\nrock salt termination, as mentioned, has been observed as a\nreconstruction in (111) oriented spinels, that termination is\nquite thin and a moiré is observed in LEED arising from the\ncoincidence pattern of the underlying spinel and the rocksalt\nstructure. A similar effect should give weak 2\u00022spots in our\ncase arising from lower spinel layers. This is not observed.\nAdditionally, the low growth (and annealing, for oxides) tem-\nperatures used make it likely that cationic disorder is present,\nsomething which is also supported by the Mössbauer observa-\ntions.\nAnnealing the samples in vacuum brings two main effects.\nFirst, it induces an enrichment in cobalt at the surface of the\nthicker film. This enrichment could be readily accommodated\nin such a Fe xCo1\u0000xO termination, and for both, it increases\nthe size of the particles. The latter is not too surprising, as\nannealing is expected to activate surface transport and pro-\nmote coarsening of the films. The increase in the size of\nthe particles is reflected in the appearance of well-developed,\nmuch better defined magnetic components in the RT Möss-\nbauer spectra. However, the Mössbauer spectra still show the\npresence of some magnetic relaxation, hence the need of in-\ncluding a broad hyperfine magnetic field distribution, together\nwith a Fe3+doublet associated with very small particles that\nremain in superparamagnetic state at RT.\nIt is also interesting to note that the differences among\nthe RT Mössbauer spectra of the annealed films are really\nminute: they show a larger contribution of the tetrahedral\nsextet as compared to that of the octahedral sextet, the area\ncorresponding to the hyperfine magnetic component amounts\nto ca. 34-40% of the total spectral area and the paramagnetic\ncontributions together do not represent more than 14% of\nthe spectral area. Therefore, it is difficult to conclude fromthe RT Mössbauer data if the difference in thickness of the\nfilms and/or the different annealing treatments (in vacuum or\nin the presence of oxygen atmosphere) have some influence\non the structural and magnetic characteristics of the films.\nFortunately, the LT Mössbauer spectra help significantly in\nestablishing such differences. It is well-known that the cation\ndistribution of cobalt ferrite cannot be precisely determined\nfrom its RT Mössbauer spectrum. In general, the tetrahe-\ndral/octahedral site ratio is usually overestimated from such\nmeasurement. In a recent publication, we have discussed this\nissue in detail19,21. This is mainly due to the strong overlap\nof the sextets corresponding to Fe3+in both sites, the result\nbeing very much dependent on the constraints imposed on\nthe linewidths of both sextets during fitting. In general, the\ntetrahedral sextet tends to be broader, and this appears to be\nrelated to the occurrence of supertransferred magnetic fields\nin the spinel structure52. Due to the supertransfer mechanism,\na significant percentage of the Fe3+at the octahedral sites\nexperience hyperfine magnetic fields, which can be very\nsimilar and even smaller than the average hyperfine field felt\nby the tetrahedral Fe3+cations. This broadens the tetrahedral\nsextet and, thus, it results in an area that is larger than that\nexpected. This effect in the spectra is mitigated at low\ntemperatures: due to different temperature variation of the\nMössbauer parameters for both sites, the two sextets appear\nto be much better-resolved19,21.\nIn the case of the spectra of the present paper, there is an ad-\nditional complication since the superparamagnetic relaxation\nhas not disappeared completely at the lowest Mössbauer ac-\nquisition temperature (125 K). The hyperfine magnetic distri-\nbution included to account for this remanent relaxation varies\nbetween 12%-20% depending on the cases. Therefore, given\nthat this broad magnetic component appears to contain both\ntetrahedral and octahedral contributions, it seems that it would\nnot have a significant influence in changing the tetra/octa ra-\ntio determined at low temperature (or at least the trend ob-\nserved) once it had been completely eliminated at lower tem-\nperatures (which we cannot reach with the present experimen-\ntal set up). As mentioned above, these ratios are 2.1, 1.9 and\n1.1 for the 20 nm-thick annealed in vacuum and 5 nm-thick\nfilm annealed in vacuum and annealed in an oxygen atmo-\nsphere, respectively. Such large values (for a perfectly in-\nverse spinel a value of 1.0 would be expected) are usually\nobtained from the evaluation of low-temperature Mössbauer\nspectra recorded in the absence of applied magnetic field from\ncobalt ferrite19,21,25. This has been observed not only for films\nbut also for the bulk material, and although some explanations\nhave been advanced19,21the final reason remains uncertain. In\nany case, from the results described here, it seems that the\nthickness of the film does not play a relevant role in the char-\nacteristics of the film and that, contrarily, annealing in oxygen\nhas a significantly larger influence on the cation distribution\nof the final cobalt ferrite.\nThe annealed films studied in this paper present signifi-\ncantly larger superparamagnetic relaxation than CFO films of\ncomparable thickness prepared by IBAD19but are compara-8\nble in this respect with CFO films prepared by UV-PLD30.\nThis reflects once again the influence of the preparation con-\nditions and how the properties of the films can be modified\nusing different deposition methods, substrate temperature and\ncomposition of the environment atmosphere. It seems, how-\never, that among all the preparation parameters, annealing at\nhigh temperatures after deposition, or deposition on a sub-\nstrate maintained at high temperature, is one of the most rele-\nvant to obtain “genuine” or “standard” CFO films and that this\nappears to be relatively independent of the substrate. How-\never, annealing or growing at much higher temperatures (over\n1000 K) provides highly perfect structural cobalt ferrite34\nbut at the cost of phase separation on the film between non-\nstoichiometric cobalt ferrite and a rocksalt oxide35. Finer tun-\ning of the films before reaching such a high temperature can\nbe achieved by the proper choice of the deposition atmosphere\nand/or method.\nThese ferrite ultrathin films grown on a metallic substrate\nare relatively unexplored and relevant to consider for spin-\ntronic applications. A cobalt ferrite film might provide an\nefficient spin-polarized current from an unpolarized current\ninjected from the metallic substrate due to the spin-filtering\neffect. A possible consequence of such current flow could be\nto reverse the magnetization of the CFO magnetic domains, of\nuse in magnetic information storage devices14,20,53,54.\nV . SUMMARY\nCobalt ferrite thin films of different thicknesses (5 and\n20 nm) have been synthesized by molecular beam epitaxy\non Pt(111) and characterized in-situ under UHV conditions.\nDeposition at 523 K gives rise to superparamagnetic/poorlycrystalline thin films composed by a distribution of Fe3+\ncontaining-particles of different sizes in the nanometer scale.\nThe results show that together with the deposition of these\nFe3+-containing particles, a minor Fe2+contribution devel-\nops. The thinner film presents higher magnetic ordering than\nthe thicker sample. This might be due to the lower deposition\nrate employed, which allows a cation distribution more similar\nto canonical CFO. Annealing in vacuum to 663 K and 773 K\npromotes an increase in size of the Fe3+particles which re-\nsults in the development of magnetic ordering at RT, although\nthe heating treatment has not completely eliminated the su-\nperparamagnetic relaxation. Annealing of the films also pro-\nduces a cobalt enrichment of the thicker films surface, prob-\nably associated with the segregation of CoO. The low tem-\nperature Mössbauer spectra recorded from the various films\nindicate differences in the cation distribution of the deposited\nCFO films. In particular, annealing in oxygen atmosphere ap-\npears to promote the formation of a CFO film with a cation\ndistribution close to that expected for an inverse spinel.\nACKNOWLEDGMENTS\nThis work is supported by the Spanish Ministry of Sci-\nence, Innovation and Universities through Projects RTI2018-\n095303-B-C51, RTI2018-095303-B-C53, MAT2017-86450-\nC4-1-R, RTI2018-095303-A-C52, through the Ramón y\nCajal Contract RYC-2017-23320 and RTI2018-095303-C52\n(MCIU/AIE/FEDER,EU), by the Regional Government of\nMadrid through project S2018-NMT-4321 and by the PROM\nProgramme - International scholarship exchange of PhD stu-\ndents and academics; and by the European Commission\nthrough the H2020 Project no. 720853 (AMPHIBIAN).\n1Brabers V A M 1995 Progress in spinel ferrite research Handbook\nof Magnetic Materials vol 8 pp 189–324\n2Murdock E, Simmons R and Davidson R 1992 IEEE Transactions\non Magnetics 283078–3083\n3Sugimoto M 2004 Journal of the American Ceramic Society 82\n269–280\n4Bibes M and Barthelemy A 2007 Ieee Trans. Elect. Dev. 541003–\n1023\n5Harris V G 2012 IEEE Transactions on Magnetics 481075–1104\n6Coll M, Fontcuberta J, Althammer M, Bibes M, Boschker H,\nCalleja A and Cheng G F M 2019 App. Surf. Sci. 4821–93\n7Carey M J, Maat S, Rice P, Farrow R F C, Marks R F, Kellock A,\nNguyen P and Gurney B A 2002 Appl. Phys. Lett. 811044–1046\n8Chen Y F and Ziese M 2007 Phys. Rev. B 76014426\n9Ramos A V , Moussy J B, Guittet M J, Gautier-Soyer M, Gatel C,\nBayle-Guillemaud P, Warot-Fonrose B and Snoeck E 2007 Phys-\nical Review B 75224421\n10Ramos A V , Santos T S, Miao G X, Guittet M J, Moussy J B and\nMoodera J S 2008 Phys. Rev. B 78180402\n11Foerster M, Rigato F, Bouzehouane K and Fontcuberta J 2010 J.\nPhys. D: Appl. Phys. 43295001\n12Bibes M, Villegas J E and Barthélémy A 2011 Adv. Phys. 605–8413Takahashi Y K, Kasai S, Furubayashi T, Mitani S, Inomata K and\nHono K 2010 Appl. Phys. Lett. 96072512\n14Chen X, Zhu X, Xiao W, Liu G, Feng Y P, Ding J and Li R W\n2015 ACS Nano 94210–4218\n15Takahashi M and Fine M E 1972 Journal of Applied Physics 43\n4205–4216\n16Martens J W D, Peeters W L, van Noort H M and Erman M 1985\nJ. Phys. Chem. Sol. 46411–416\n17de Bakker P, Vandenberghe R and De Grave E 1994 Hyperfine\nInteractions 942023–2027\n18Le Trong H, Presmanes L, De Grave E, Barnabé A, Bonningue C\nand Tailhades P 2013 J. Magn. Magn. Mater. 33466–73\n19de la Figuera J, Quesada A, Martín-García L, Sanz M, Oujja M,\nCastillejo M, Mascaraque A, T N’Diaye A, Foerster M, Aballe L\nand F Marco J 2015 Croatica Chemica Acta 88453–460\n20De Santis M, Bailly A, Coates I, Grenier S, Heckmann O, Hri-\ncovini K, Joly Y , Langlais V , Ramos A Y , Richter C, Torrelles X,\nGaraudée S, Geaymond O and Ulrich O 2019 Acta Cryst B 75\n21Sánchez-Arenillas M, Oujja M, Moutinho F, de la Figuera J, Caña-\nmares M V , Quesada A, Castillejo M and Marco J F 2019 Appl.\nSurf. Sci. 470917–922\n22dos S Duque J G, Macêdo M A, Moreno N O, Lopez J L and\nPfanes H D 2001 Journal of Magnetism and Magnetic Materials9\n226-230 1424–1425\n23Lee J G, Park J Y , Oh Y J and Kim C S 1998 Journal of Applied\nPhysics 842801–2804\n24Okuno S N, Hashimoto S and Inomata K 1992 Journal of Applied\nPhysics 715926–5929\n25Prieto P, Marco J F, Prieto J E, Ruiz-Gomez S, Perez L, del Real\nR P, Vázquez M and de la Figuera J 2018 Applied Surface Science\n4361067–1074\n26Foerster M, Iliev M, Dix N, Martí X, Barchuk M, Sánchez F and\nFontcuberta J 2012 Adv. Funct. Mater. 224344–4351\n27Bilovol V , Pampillo L G and Saccone F D 2014 Thin Solid Films\n562218–222\n28Valvidares M, Dix N, Isasa M, Ollefs K, Wilhelm F, Rogalev A,\nSánchez F, Pellegrin E, Bedoya-Pinto A, Gargiani P, Hueso L E,\nCasanova F and Fontcuberta J 2016 Phys. Rev. B 93214415\n29Eskandari F, Porter S B, Venkatesan M, Kameli P, Rode K and\nCoey J M D 2017 Physical Review Materials 1074413\n30Oujja M, Martín-García L, Rebollar E, Quesada A, García M A,\nFernández J F, Marco J F, de la Figuera J and Castillejo M 2018\nApplied Surface Science 45219–31\n31Lee J G, Chae K P and Sur J C 2003 Journal of Magnetism and\nMagnetic Materials 267161–167\n32Rigato F, Geshev J, Skumryev V and Fontcuberta J 2009 Journal\nof Applied Physics 106113924\n33Horng L, Chern G, Chen M C, Kang P C and Lee D S 2004 Jour-\nnal of Magnetism and Magnetic Materials 270389–396\n34Martín-García L, Quesada A, Munuera C, Fernández J F, García-\nHernández M, Foerster M, Aballe L and de la Figuera J 2015 Ad-\nvanced Materials 275955–5960\n35Ruiz-Gómez S, Mandziak A, Prieto J E, Aristu M, Trapero E M,\nSoria G D, Quesada A, Foerster M, Aballe L and de la Figuera J\n2020 J. Chem. Phys. 152074704\n36Gargallo-Caballero R, Martín-García L, Quesada A, Granados-\nMiralles C, Foerster M, Aballe L, Bliem R, Parkinson G S, Blaha\nP, Marco J F and Figuera J d l 2016 J. Chem. Phys. 144094704\n37Rodewald J, Thien J, Pohlmann T, Hoppe M, Timmer F, Bertram\nF, Kuepper K and Wollschläger J 2019 Phys. Rev. B 100155418\n38Thien J, Bahlmann J, Alexander A, Hoppe M, Pohlmann T,\nRuwisch K, Meyer C, Bertram F, Küpper K and Wollschläger J2020 J. Phys. Chem. C 12423895–23904\n39Weiss W and Ranke W 2002 Prog. Surf. Sci. 701–151\n40Parkinson G S 2016 Surf. Sci. Rep. 71272–365\n41Santos B, Loginova E, Mascaraque A, Schmid A, McCarty K and\nde la Figuera J 2009 J. Phys-Cond. Mat. 21314011\n42Monti M, Santos B, Mascaraque A, Rodríguez de la Fuente O,\nNiño M A, Mente¸ s T O, Locatelli A, McCarty K F, Marco J F and\nde la Figuera J 2012 Phys. Rev. B 85\n43Ruiz-Gomez S, Perez L, Mascaraque A, Quesad A, Prieto P, Pala-\ncio I, Martin-Garcia L, Foerster M, Aballe L and de la Figuera J\n2018 Nanoscale 105566–5573\n44Mandziak A, Figuera J d l, Ruiz-Gómez S, Soria G D, Pérez L,\nPrieto P, Quesada A, Foerster M and Aballe L 2018 Sci. Rep. 8\n17980\n45Spiridis N, Freindl K, Wojas J, Kwiatek N, Madej E, Wilgocka-\n´Sl˛ ezak D, Dró ˙zd˙z P,´Sl˛ ezak T and Korecki J 2019 J. Phys. Chem.\nC1234204–4216\n46Brand R 1995 1–123\n47Powell C J 2020 Journal of Vacuum Science and Technology A 38\n023209\n48Cheng F, Peng Z, Liao C, Xu Z, Gao S, Yan C, Wang D and Wang\nJ 1998 Solid State Communications 107471–476\n49López J, Serrano W P and Pfannes H 2006 Rev. Colomb. Fís 38\n1074–1077\n50Yanagihara H, Uwabo K, Minagawa M, Kita E and Hirota N 2011\nJournal of Applied Physics 10907C122\n51Spiridis N, Wilgocka- ´Sl˛ ezak D, Freindl K, Figarska B, Giela T,\nMły´nczak E, Strzelczyk B, Zaj ˛ ac M and Korecki J 2012 Phys.\nRev. B 85075436\n52Vandenberghe R E and Grave E D 1989 Mössbauer Effect Studies\nof Oxidic Spinels Mössbauer Spectroscopy Applied to Inorganic\nChemistry (Modern Inorganic Chemistry no 3) pp 59–182\n53Takahashi Y K, Kasai S, Furubayashi T, Mitani S, Inomata K and\nHono K 2010 Applied Physics Letters 96072512\n54Ostler T A, Barker J, Evans R F L, Chantrell R W, Atxitia U,\nChubykalo-Fesenko O, El Moussaoui S, Le Guyader L, Mengotti\nE, Heyderman L J, Nolting F, Tsukamoto A, Itoh A, Afanasiev D,\nIvanov B A, Kalashnikova A M, Vahaplar K, Mentink J, Kirilyuk\nA, Rasing T and Kimel A V 2012 Nature Communications 3666"    },    {        "title": "1807.00060v1.High_quality_cobalt_ferrite_ultrathin_films_with_large_inversion_parameter_grown_in_epitaxy_on_Ag_001_.pdf",        "content": "\t\n1\t\t      High quality cobalt ferrite ultrathin films with large inversion parameter grown in epitaxy on Ag(001). M. De Santis,a* A. Bailly, a I. Coates,a S. Grenier,a O. Heckmann,b K. Hricovini,b Y. Joly,a V. Langlais,c A. Y. Ramos,a M. C. Richter,b X. Torrelles.d S. Garaudée,a O. Geaymond,a O. Ulrich.e aUniversité Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38042 Grenoble, France bLMPS, Université de Cergy-Pontoise, Neuville/Oise, 95031 Cergy-Pontoise, France cCNRS, CEMES (Centre d’Elaboration des Matériaux et d’Etudes Structurales), B.P. 94347, 29 rue Jeanne Marvig, F-31055 Toulouse, France dInstitut de Ciència de Materials de Barcelona, ICMAB-CSIC, Bellaterra, 08193 Barcelona, Spain eUniversité Grenoble Alpes, CEA, INAC/MEM, 38054 Grenoble, France  Abstract Cobalt ferrite ultrathin films with inverse spinel structure are among the best candidates for spin-filtering at room temperature. We have fabricated high-quality epitaxial ultrathin CoFe2O4 layers on Ag(001) following a three-step method: an ultrathin metallic CoFe2 alloy was first grown in coherent epitaxy on the substrate, and then treated twice with O2, first at RT and then during annealing. The epitaxial orientation, the surface, interface and film structure were resolved combining LEED, STM, Auger and in situ GIXRD. A slight tetragonal distortion was observed, that should drive the easy magnetization axis in plane due to the large magneto-elastic coupling of such a material. The so-called inversion parameter, i.e. the Co fraction occupying octahedral sites in the ferrite spinel structure, is a key element for its spin-dependent electronic gap. It was obtained through in-situ x-ray resonant diffraction measurements collected at both the Co and Fe K edges. The data analysis was performed using the FDMNES code and showed that Co ions are predominantly located at octahedral sites with an inversion parameter of 0.88±0.05. Ex-situ XPS gave an estimation in accordance with the values obtained through diffraction analysis. Keywords: Cobalt ferrite; Spinel structure; Epitaxial growth; Surface x-ray diffraction; Resonant x-ray diffraction.  1) Introduction Cobalt ferrite is an insulating (ferri)magnetic oxide with a high Curie temperature (Tc=793 K) and a large saturation magnetization [Brabers]. Alongside its low cost, these properties make it attractive for a wide range of applications. The spinel crystal structure (space group Fd-3m) is comprised of a face-centered cubic (fcc) sublattice of oxygen anions in which, one eighth of the tetrahedral lattice holes and one half of the octahedral lattice holes are occupied by cations. This results in the general formula AB2O4, where A and B refer to the cations located in the tetrahedral and octahedral sites respectively. In the normal spinel structure, A sites are occupied by divalent cations, and B sites by trivalent cations. In the inverse spinel structure, the divalent cations \t\n2\t\toccupy half of B sites and the trivalent cations occupy the remaining A and B sites [Proskurina]. For cobalt ferrite, the inverse structure is the most stable. However, in general, this inversion is not complete and a fraction of cobalt ions remain located at tetrahedral sites. The degree of inversion typically depends on the sample preparation conditions. Due to the ferromagnetic interactions between ions in octahedral sites, and antiferromagnetic interactions between ions in octahedral and tetrahedral sites, cobalt ferrite is ferrimagnetic. Various density of state (DOS) calculations have accordingly predicted that the electronic band gap at the Fermi level differs for majority and minority spins. [Ref. Fritsch, Caffrey, Szotek]. The size of the band gap, however, depends on the degree of inversion [Fritsch2].  The use of ferromagnetic or ferrimagnetic insulators in multilayered structures is an efficient way to generate highly spin-polarized currents due to the exponential relationship between tunneling probability and the spin-dependent barrier height.  This so-called spin-filtering effect was first observed in EuS at low temperature [Moodera], but in the last decade, the research have focused on ferrites because of their high Curie temperatures, that create the possibility spin-filter tunneling at room temperature. A second important property of cobalt ferrite is its significant magnetostriction [Bozorth] that results in a large strain-dependent magnetocrystalline anisotropy energy in ultrathin epitaxial films. A compressive strain favors an in-plane magnetization as in the case of CoFe2O4/MgAl2O4(001) [Matzen], while tensile strain induces a perpendicular magnetization, observed for CoFe2O4/MgO(001) [Chambers, Lisfi Yanagihara]. These findings have been confirmed by theoretical calculations [Fritsch]. Therefore, the incorporation of cobalt ferrite in artificial multiferroic heterostructures may result in new phenomena that opens the way to a large range of applications. It was shown, for example, that an elastic strain-mediated magnetoelectric coupling can be used to reverse the magnetization in columnar CoFe2O4 nanostructures embedded in ferroelectric BiFeO3 [Zavaliche]. To fine-tune the inversion parameter and induce epitaxial strain, a precise growth methodology is essential. The growth of transition metal oxides on fcc (001) metallic substrates is strongly influenced by the lattice misfit. For example CoO films grow (001) oriented on Ag(001) [Torelli] while in the case of CoO/Ir(100), (111) films are usually obtained [Meyer]. However, in this latter system the CoO orientation can be changed to (001) by depositing a Co buffer layer of ~ 2 monolayers (ML) thickness prior to oxidation [Gubo]. This layer is pseudomorphic and forms, after a moderate oxidation, a c(4x2)-Co3O4/Co/Ir(001) reconstructed surface, which acts as a precursor for the growth of CoO(001). A similar method for growing high quality (001) magnetite ultrathin films on Ag(001) has already been previously demonstrated [Lamirand]. Facilitated by a lattice mismatch of only 0.8 %, iron grows pseudomorphically on Ag(001). Provided that a few monolayers of Fe are initially deposited, the lattice expands during oxidation, but its relative orientation is maintained. Here, the same technique is employed to obtain high quality ultrathin cobalt ferrite films with a sharp interface, a relatively flat surface, and a large inversion parameter. In the next section, the experimental setups and deposition methods are described together with a qualitative characterization of the surface. In section 3 the film structure is solved by grazing incidence x-ray diffraction (GIXRD). Sections 4 and 5 are devoted to the determination of the \t\n3\t\tinversion parameter, by x-ray photoelectron spectroscopy (XPS) and resonant x-ray diffraction (RXD), respectively.      2) Setups, sample growth and characterization.  All films were prepared in a similar manner using one of two distinct experimental setups, both of which are fully equipped for sample preparation and analysis in an ultra-high vacuum (UHV) environment. The first setup (LEED/STM) is located at the Néel Institute and possesses a commercial scanning tunneling microscope (Omicron VT STM/AFM), a low-energy electron diffractometer (LEED) and an Auger electron spectrometer (AES). Samples grown at this location were then transferred to the LMPS laboratory in Cergy-Pontoise, where photoelectron spectra were measured using a Mg Kα X-ray emission source (1253.6 eV) and a hemispherical analyzer. The second setup (GIXRD) is installed at the French BM32 beamline (CRG-IF) of the European Synchrotron Radiation Facility (ESRF). This setup consists of a UHV chamber equipped with evaporation sources for MBE growth and with AES. The system is mounted on a Z-axis diffractometer with additional degrees of freedom for sample positioning provided by a hexapod. This setup was used for resonant and non-resonant x-ray diffraction experiments in-situ.  The oxide layers were grown on a Ag(001) single crystal with a miscut of less than 0.1°. Prior to deposition, the substrate was cleaned by repeated cycles of Ar+ ion sputtering followed by annealing at approximately 850 K. Cleanliness was checked by AES, such that all contaminants were below the detection limit. Iron and cobalt were evaporated from pure rods using water-cooled electron-beam evaporators. The base pressure was in the low 10-11 (10-10) mbar range for the STM (GIXRD) setup. The Fe (Co) deposition rate was typically 1 ML per 5 minutes (10 minutes), calibrated with a quartz crystal microbalance. STM images were obtained in constant current mode using a voltage bias (Vsample) applied to the sample. The non-resonant GIXRD measurements were performed with a photon energy of 9500 eV. Resonant measurements were carried out scanning both Co and Fe K absorption edge regions. To increase the signal to noise ratio, the incidence angle was set at the critical angle for total x-ray reflection for Ag at the different energies (0.37°, 0.46° and 0.50° for 9500 eV, 7709 eV, and 7112 eV,  respectively). The diffraction data were collected using a 2D detector (MAXIPIX, ESRF). A cobalt ferrite seed layer was initially prepared in the LEED/STM setup by a three-step method. Firstly, Co (2 ML as referred to the Ag surface atomic density) and Fe (4 ML) were codeposited on the substrate kept at room temperature (RT) under UHV, forming an epitaxial metallic alloy. After deposition, the oxide layer was formed by dosing with 10-6 mbar O2 for 10 minutes at RT. This step is essential to avoid intermixing with Ag. Finally, the O2 partial pressure was maintained whilst the sample was annealed up to 750 K for 10 minutes via an intermediate 10 minute interval at 570 K. Following the deposition of the seed layer, the film thickness was increased by reactive codeposition of cobalt and iron (2 ML and 4 ML respectively) in the presence of molecular oxygen (10-6 mbar) at 750 K, resulting in a cobalt ferrite film about 4 nm thick. For the GIXRD experiments, the samples were grown following the same procedure, with the exception that oxygen annealing was performed up to a higher temperature of ~870 K with more temperature intervals during the heating process. During annealing, the film structure was monitored at each interval. The higher temperature was also maintained during the reactive deposition which subsequently ensured a large average crystallite domain size in the surface plane. A value of about 30 nm was found applying the Scherrer equation to the ferrite peak width. \t\n4\t\tThis allows a proper measurement of the diffraction rod intensity without the need for corrections of the detector area. Figure 1 shows AES spectra measured in the LEED/STM set-up (continuous line, red online) and in the GIXRD one (black circles) after oxide growth. The principal peaks of O, Fe and Co are labelled. The peaks at 598 and 775 eV, arising from Fe and Co levels respectively, were used to infer the ferrite stoichiometry. The two samples have the same composition within error. We measure a signal ratio AES(Fe598)/AES(Co775) of ~ 0.75, while the corresponding cross section ratio is σ(Fe598)/ σ (Co775) ~ 0.46. Then the ratio Fe : Co ~1.63, i.e. the ferrite is slightly enriched in Co with respect to the desired composition. As will be discussed later, the more quantitative x-ray resonant diffraction analysis gives a ratio of ~1.86. Some Ag surface segregation is observed in the sample annealed at 870 K (peak at 356 eV). A rough estimation based on the relative cross sections gives about 0.5 equivalent ML of Ag on the surface.   \n     Fig.1 Derivative Auger spectra of the samples elaborated in the GIXRD chamber (black circles) and in the LEED/STM chamber (continuous line, red online).   Figure 2 shows the LEED pattern of the Ag substrate (a) and of the final oxide (b). The latter is generated by an epitaxial oxide layer with P4mm symmetry and lattice constant almost twice that of Ag. This fits well with a (001)-oriented CoFe2O4 film. In addition, weaker spots of two domains at 90° of a (3×1) surface reconstruction are observed.  A (30×30 nm2) medium resolution STM image recorded at room temperature of the same oxide sample is shown in Fig.3. The surface is flat on such a length scale and rows spaced by about 1.7 nm, the period of the (3×1) reconstruction, are clearly observed. The step height between dark \n\t\n5\t\tand clear regions in the figure is about 0.22+/-0.03 nm.  Large size images show that this value is the most often encountered as step height (while scanning with VSample =2 V). \n Fig. 2. LEED pattern of (a): clean Ag(001); (b): CoFe2O4/Ag(001). The ferrite films grows (001) oriented and exhibits a (3×1) surface reconstruction. The Ag, magnetite, and (3×1) reciprocal space surface unit cells are represented by the black square, blue square, and red rectangles, respectively (color version online). \n             Fig. 3. STM image recorded at room temperature of the cobalt ferrite ultrathin film, 30×30 nm2, VSample =2 V, IBias=0.1 nA   The ferrite structure can be viewed along the (001) direction as a stacking of eight unique layers that alternate between planes containing oxygen anions and B-site cations, and planes containing only A-site cations . The interplanar spacing between planes of the same type is 0.21 nm, which is \n\t\n6\t\tdirectly comparable to the observed step height. It can therefore be concluded that the surface termination of the cobalt ferrite structure is dominated by one of these two types of planes. A similar result was observed at the surface of (001) bulk magnetite which exhibits B-type termination [Stanka].  3) XRD. GIXRD data were collected to quantitatively solve the structure. The diffraction pattern has a 4--fold symmetry as already observed by LEED. The in-plane [100] direction is aligned with the [100] of the silver substrate, indicating epitaxial growth. The film is relaxed and its diffraction pattern does not interfere with that of the substrate. Two sets of sharp peaks are therefore observed while scanning the momentum transfer, Q, parallel to the surface. The first set is given by the so-called crystal truncation rods (CTRs) of Ag [Robinson2], the second set corresponds to the rods originating from the film. They are located at integer (HK) values, once indexed in the film mesh reference. Perpendicular to the surface, an intensity distribution, the so-called diffraction rod, is observed for each (HK) value [Robinson]. It exhibits wide peaks and thickness intensity oscillations. The in-plane film lattice constant afilm was obtained by scanning across some diffraction rods at Qz = 2π/acfo, where acfo, the bulk cobalt ferrite lattice constant, is 838.6 pm [Proskurina], [Mohamed].  The position of 6 rods (including 5 non-equivalent ones) was carefully measured. A linear regression analysis gives afilm = 836±2 pm. With the objective to achieve a representative portion of reciprocal space, a large set of intensities along Bragg rods, IHK(L), was measured. The standard procedure is to set the diffractometer angles to define each (HKL) point in the sample’s reciprocal space and then rock the sample azimuth to integrate the intensity across the rod at a given L-value. The structure factors FHKL are then extracted by applying standard correction factors [Vlieg]. A set of 416 reflections distributed along 14 rods was collected. The set averaged to 293 non-equivalent reflections according to the substrate’s P4mm surface symmetry (10 non-equivalent rods). An agreement factor of 7% between equivalent reflections was found and used as systematic error estimation for the final experimental error calculation [Robinson]. The sampling interval ΔQz required to describe the rod shape decreases with respect to the inverse of the film thickness, and the required acquisition time increases accordingly. In this study, an initial ΔQz value of 0.1×2π/acfo was used, which proved to be insufficient to describe the film thickness oscillations. Subsequently, line scans along each rod were collected (stationary- or L-scans, ΔQz = 0.02×2π/acfo) to which specific corrections were applied to extract the structure factors. These FHKL curves were interpolated and multiplied by a specific scaling factor to fit the data obtained from the rocking scans. The resulting rods are plotted in Fig.4. The Qz values have been renormalized using a factor calculated from the cobalt ferrite density, to take into account the x-ray refraction of the incident beam at the vacuum-film interface [FEIDENHANS'L].    \t\n7\t\t Fig. 4 Experimental CoFe2O4 film rods with error bars (black symbols) and best fit (continuous line, red online). The corresponding (H K) values are indicated on each panel. L is related to the cfilm lattice constant. \n\t\n8\t\tThe first step in the analysis was the calculation of the average film interlayer spacing by fitting the peak positions along the rods. Using a linear regression based on the 14 non-equivalent peaks, cfilm value of 841±3 pm was found, resulting in a slight tetragonal distortion whereby cfilm/afilm = 1.006±0.006. The unit cell volume was found to be equal to that of the bulk material within the error, (Vfilm-Vcfo)/ Vcfo = (-2±8) ×10-3. Before resolving the film structure, the interface roughness, that modifies the rods’ shape, was studied by analyzing the Ag CTRs. A set of 47 reflections belonging to three different CTRs was collected. Their structure factors are reported in Fig.5, indexed within the Ag(001) surface cell (𝑎!!=!!\"![110], 𝑎!!=!!\"![110], and 𝑎!!=𝑎!\"[001]). The error is evaluated using the agreement factor obtained from film reflections.  Since the oxide film exists in incoherent epitaxy, it does not contribute to the CTRs intensity, which depends only on the substrate parameters and the interface roughness. An initial best fit of the (11) CTR is shown in Fig. 5a (dashed line, red online). It is calculated using bulk interlayer distances and Debye-Waller (DW) factors (BAg=0.7×104 pm2). The roughness, considered within the β model [Robinson2], is therefore the only remaining physical parameter to be optimized. A value β=0.12±0.03 is obtained, resulting in a normalized χ2 of 0.84.   \n   Fig. 5. Experimental Ag(001) CTRs (black symbols with error bars), calculations with best β fit only (dashed line, red online) and with best surface in-plane DW fit (continuous line).  However, as shown in Fig.5, this model fails to give an accurate fit of the relative intensity of the different rods. The χ2 increases to about 10 upon considering the full data-set of three CTRs. A better description is achieved by considering the role of the oxide film. The stress exerted by the film on the silver at the interface induces a localized displacement field in the silver substrate. Periodic displacements in the substrate give rise to satellite peaks close to the Bragg ones [Prevot]. Fig. 6 shows an H-scan close to the Ag (101) Bragg where such satellites are observed. The distance between satellites corresponds roughly to the period of the Moiré generated by the Ag and CoFe2O4 lattices.  The stress caused by the oxide film induces displacements that are predominantly parallel to the interface. Their amplitude decreases while going deeper into the crystal. A detailed analysis would require the introduction of a large superstructure cell, with a consequently large number of variables. However, the average structure can be qualitatively described by a structural disorder within the Ag surface unit cell. The CTRs were therefore analyzed further by introducing in-\n\t\n9\t\tplane DW factors. A simultaneous fit of the CTRs (Fig.5, continuous black line) results in an in-plane Debye factor gradient over the first five atomic layers of the silver substrate at the interface (Bi,IP). The out-of-plane component was kept fixed at the bulk value (Table I). Note that the DW factors observed in the surface layers decreases the scattering factor amplitude relative to the bulk values, therefore its effect on a single rod is similar to that of increasing interface roughness. Within this model, the best fit β value is close to zero. It was also observed that the first Ag interlayer distance at the interface (dAg1) is slightly contracted, which accounts for the observed shift in the CTR’s minima. The corresponding χ2 when considering the full data set of the three CTRs is 2.5.   \n Fig.6 Ag (H 0 1.2) scan.  TABLE I Best fit structural parameters of the interfacial Ag including the interfacial interlayer distance, dAg1; the DW factor at the ith layer parallel to the surface, Bi,IP; and the roughness parameter, β.  dAg1  (pm).  201±1 B1,IP  (×104 pm2).  6.3±0.5 B2,IP  (×104 pm2).  3.9±0.5 B3,IP  (×104 pm2).  2.3±0.3 B4,IP  (×104 pm2).  1.4±0.3 B5,IP  (×104 pm2).  0.9±0.1 β  0.05±0.03 χ2  2.5  In summary, the CTR analysis shows that the interface is quite sharp, despite the high annealing temperature, as indicated by the calculated β parameter of 0.05, which corresponds to a root mean square roughness of 43 pm [Robinson2]. In the following, the film structure is studied via the analysis of its rods considering a sharp interface. The bulk CoFe2O4 unit cell is formed by eight equispaced atomic layers along the growth axis, as shown in Fig.7. The diffraction pattern of the film was calculated for a structure which follows \n\t\n10\t\tthis same layer stacking, starting with a B type layer at the interface (layer 1). Since the non-resonant iron and cobalt scattering factors are close in magnitude, standard diffraction methods cannot give reliable values for the film’s inversion parameter, i.e. the relative Co and Fe occupancies of tetrahedral and octahedral sites. These values were obtained by XRD, as described in the following, and are used here in the best-fit of the structure. From our calculation, the film is composed of 33 complete atomic layers, on top of which, the surface is terminated by five partially occupied bilayers, corresponding to the observed surface roughness. Each bilayer was assumed to be B terminated, in accordance with the observed termination of the magnetite (001) surface [Stanka]. A further parameter of the crystal structure is the shift of the oxygen anion positions, Δ, relative to a standard fcc sublattice in accordance with the Fd-3m symmetry, whereby Δ=±(0.25-u) times the unit cell and u=0.261 for the bulk material [Proskurina]. The (3×1) reconstruction rods were not observed in the GIXRD experiment. We believe that this is due, in large part, to the Ag segregation that was present in the GIXRD-system-prepared samples, which inhibits the establishment of large reconstructed surface regions. The (3×1) superstructure was therefore neglected in the model. A fixed DW factor, averaged from the Fe and Co bulk values (B=0.5×104 pm2), was used for the simulation. The most reliable film structure was obtained from the refinement agreement between experimental and calculated data using a model considering only a limited number of parameters: the bilayer occupancies (Occi), the oxygen displacement (u), and the first A-B interlayer distance at Ag interface (d1). The remaining interlayer distances were kept fixed at the value d=cfilm/8=105.1 pm. In the fit, the intensities of four equioccupied domains with equivalent structures rotated by 90° were added to restore the substrate symmetry. Scattering factors of Fe, Co and O ions were used. By refining these few structural parameters a relatively good agreement with the experimental data is obtained. The best-fit values are reported in Table II and the fit is plotted in Fig. 4. This fit definitively confirms the CoFe2O4 structure of the film. The most significant discrepancies between simulated and experimental data originate from regions close to the main peaks, where deep minima are calculated but not observed experimentally. This results in a relatively high χ2 of 6.9. It should be emphasized, however, that most of the discrepancies likely arise from the observed Ag segregation at the surface. It is known that silver deposited on the (√2×√2)R45°- Fe3O4(001) surface grows both on specific crystallographic sites and forms clusters, depending on the annealing conditions [Bliem2]. A fraction of a Ag monolayer located at specific sites on the surface would correspond in modulus to a few percent of the CoFe2O4 film’s scattering amplitude at Q=0. While this interference can be neglected for strong peaks, it may substantially change the diffracted intensity close to minima. Nevertheless, the comparison between the crystallographic model and the experimental x-ray diffraction data using another figure of merit, the so-called R-factor, which neglects experimental errors, gives a very reasonable value of 17%. CoFe2O4 has the same spinel structure as magnetite. In the absence of 1/6 of cations in octahedral sites in magnetite, Fe2O3 with maghemite structure is obtained. For this reason, the octahedral site occupancy of the cobalt ferrite film was also checked. The resulting occupancy Occ(B) was found to be between 0.95 and 1.  \t\n11\t\tFinally, TABLE III reports the experimental structure factor values obtained for each peak position together with the corresponding fitted values and the bulk CoFe2O4 values. In both cases, the agreement is fairly good. TABLE II Structural parameters of the CoFe2O4 film Occ1  0.85±0.05 Occ2 0.62±0.05 Occ3 0.56±0.05 Occ4 0.23±0.05 Occ5 0.23±0.05 u 0.254±0.001 d1 (pm) 94±1 Occ(B) 1+0/-0.05 xA,Co 0.13±0.05 xB,Co  0.46±0.03 χ2 6.9  TABLE III experimental, fitted and bulk CoFe2O4 structure factors. Reflection index Exp. Fit Bulk [Proskurina] (111) 38±3 41.1 40.5 (202) 89±7 91.3 88.2 (311) 168±12 153.5 137.3 (313) 18±1 24.4 9.45 (331) 19±1 23.4 9.45 (333) 102±7 118.3 96.8 (422) 69±5 72.9 68.5 (511) 120±9 130.6 132.1 (513) 22±2 26.0 25.3 (531) 23±2 25.3 25.3 (533) 94±7 104.2 98.9 (551) 21±2 25.6 33.3 (553) 77±6 93.2 96.6 (602) 50±4 60.4 56.3 χ2  6 14  4) Photoemission \tX-ray photoelectron spectra were collected ex-situ on the sample grown in the STM setup after degassing for a few hours at approximately 450 K in UHV to remove adsorbed molecules (no trace of carbon contamination was detected by XPS). Fig.8 (a) and (b) show the Co 2p and Fe 2p core-level photoemission regions, respectively. Each level is comprised of the 2p3/2 and 2p1/2 sublevels. Their binding energy depends on the valence state and on the local structural \t\n12\t\tenvironment. Co ions in ferrite are divalent, and a splitting is observed for atoms in octahedral (B, D3d symmetry) and tetrahedral (A, Td symmetry) sites. 1 2 3 4 5 6 7 8  A B O       Fig. 7. Layer-by-layer structure of bulk CoFe2O4 unit cell, following the stacking order. A and B correspond to the tetrahedral and octahedral sites, respectively. The interlayer spacing is cfilm/8  Each sublevel has a shake-up satellite, due to the excitation of a 3d electron by the core level photoelectron. Therefore the Co 2p level has been fitted with 6 Gaussian peaks, after subtraction of a suitable background (a Shirley background plus a linear one which represents the energy loss contribution of peaks at lower binding energy). Iron is trivalent in CoFe2O4 [Aghavnian]. The analysis of its 2p level is difficult due to the presence of the oxygen Auger peak and due to the fact that the shake-up satellites are poorly defined. Therefore, in this case, a reliable fit cannot be found without constraints. Aghavnian et al. [Aghavnian] determined the inversion degree in CoFe2O4/BaTiO3 films by X-ray Magnetic Circular Dichroism (XMCD) and used their results to fit XPS 2p data. Here, for both elements, we have focused on the most reliable 2p3/2 level constraining the energy splitting between A and B sites to the values given in ref. [Aghavnian] (2.4 eV and 2.65 eV for Co and Fe, respectively). The areas of the Co 2p3/2-D3d and Co 2p3/2-Td peaks give directly the fraction of cobalt in octahedral sites, i.e. the inversion parameter. A value of about 0.79 is obtained. On the other hand, equivalent analysis of the Fe 2p3/2 doublet provides an estimation that 47% of iron is located on tetrahedral sites. These results have to be compared \n\t\n13\t\twith those obtained by the quantitative resonant diffraction analysis (0.88±0.05 and 45±3%, respectively, see next section).  \n  Fig. 8. Experimental Co (a) and Fe (b) 2p core level photoemission lines and best fits.    5) Resonant x-ray diffraction RXD exploits the change in the atomic scattering factor close to an absorption edge to study the composition and the atomic environment of a given crystallographic site [Grenier]. In the present experiment, the intensity changes of several ferrite film diffraction peaks were measured by scanning the energy close to both the Fe and the Co absorption K edges. Experimentally, this requires the diffractometer circles to move in such a way that the (HKL) position is kept fixed while scanning the energy. These energy scans are shown in Fig. 9 for a set of 6 peaks at both edges and for 5 additional peaks at the iron edge only. Some of these peaks exhibit a very strong intensity variation, which makes this technique very powerful in determining the stoichiometry of the octahedral and tetrahedral sites of the spinel structure. The CoFe2O4 unit cell structure factors can be written as the sum of three contributions originating from the A, B and oxygen sites:   𝐹(𝐻𝐾𝐿)=𝐹!+𝐹!+𝐹!.        (1) While most of the reflections are sensitive to all atomic sites, it is easy to calculate that: 𝐹2+4𝑛,0,2=(−1)!!!×8𝑓!+𝐹!,  (2) and: 𝐹2+4𝑛,2,2=16𝑓!+𝐹!,  (3) where fA =fCo × xA,Co + fFe × (1-xA,Co), and xA,Co is the fraction of A sites occupied by Co  (analogously for fB).  \n\t\n14\t\t Fig.9. Experimental RXD of selected (HKL) reflections at the iron (left and central columns) and cobalt (right) K edges (black symbols), calculated intensity for best fit occupancy (continuous red lines) and for statistical occupancy (dashed green lines).  This means that the (202) and (602) reflections plotted in Fig. 9 are sensitive to the tetrahedral cation sites only, while the (222) and (622) ones to the octahedral ones only. A first inspection of the respective curves brings the conclusion that the inversion parameter is quite high, because, for example, the intensity variation of the (202) reflection is much larger at the Fe edge than at the Co one, i.e. the tetrahedral site is iron rich. A more quantitative analysis requires the precise knowledge of the resonant contribution to the scattering factors, which is very sensitive to the oxidation state and to the environment of the selected element. This resonant contribution was calculated using FDMNES [Bunau], an ab initio code already extensively used to simulate XANES and RXD. Its density functional theory (DFT) full potential approach makes it especially \n\t\n15\t\tappropriate for simulating absorption edges of chemical elements embedded in non-close packed surroundings or in low symmetry sites. The specific Co and Fe scattering factors were calculated for atoms located both in octahedral and tetrahedral sites, taking a spinel structure with statistical occupancy of the cation sites. Then they were inserted in the unit cell structure factor to calculate the intensities. The occupancy of each site was obtained through a best fit of the experimental data (continuous line in Fig.9, red online). It was found that tetrahedral and octahedral sites are occupied at 13±5% and 46±3% by Co, respectively. This results in an inversion parameter of 0.88±0.05 and in an average stoichiometry of Co1.05Fe1.95O4. In Fig.9, the intensity calculated assuming statistical occupancy of the cation sites is also shown for comparison (dashed line, green online). 6) Summary and conclusions. Ultrathin cobalt ferrite layers were grown on Ag(001) by MBE following a three-step method. The films are (001) oriented and have a sharp interface, a relatively flat surface, and a bulk-like crystallographic structure. The substrate induces a slight compressive strain and the inversion parameter, determined by RXD, is close to 1. These characteristics make such films an ideal insulating barrier for spintronic applications, particularly for RT spin filtering, since the inversion parameter is linked to the height of the spin-dependent energy gap at the Fermi level [Szotek]. Theoretical calculations have also shown that strain and degree of inversion are correlated; a decrease in the lattice constant favors the inverse configuration with respect to the normal state [Fritsch2]. Therefore, the nature of the substrate and the growth mode can have a strong influence on the cation distribution. Both calculations [Fritsch] and experiments [Gao] agree that a compressive strain in cobalt ferrite films induces an in-plane magnetization. Such layers can then be combined with other transition metal oxides to form model multilayered structures whose properties can be tuned and calculated theoretically. For example, cobalt ferrite, magnetite, MgO, and other transition metal oxides can be layered-up to form magnetic tunnel junctions [Chapline] and other functional devices in coherent epitaxy. This will help to develop an understanding of the influence of the structural parameters on the physical properties.  Acknowledgments Financial support through ANR EQUIPEX ANR-11-EQPX-0010 and beam time at the French CRG BM32 beamline of the ESRF are acknowledged. V. L. and X. T. also acknowledge European financial support through the EFA194/16 TNSI (POCTEFA/UE-FEDER) project.    *Corresponding author. E-mail address: Maurizio.De-Santis@neel.cnrs.fr \t\n16\t\t[Brabers] V. A. M. Brabers, in Handbook of Magnetic Materials, edited by K. H. J. Buschow (Elsevier, Amsterdam, 1995), pp. 189–324. [Fritsch] Daniel Fritsch and Claude Ederer, Phys. Rev. B 82, 104117 (2010) [Caffrey] Nuala M. Caffrey, Daniel Fritsch, Thomas Archer, Stefano Sanvito, and Claude Ederer Phys. Rev. B 87, 024419 (2013) [Szotek] Z. Szotek, W. M. Temmerman, D. Ködderitzsch, A. Svane, L. Petit, and H. Winter, Phys. Rev. B 74, 174431 (2006) [Fritsch2] Daniel Fritsch and Claude Ederer, Appl. Phys. Lett. 99, 081916 (2011) [Moodera] J. S. Moodera, X. Hao, G. A. Gibson, and R. Meservey, Phys. Rev. Lett. 61, 637 [Bozorth] R. M. Bozorth, E. F. Tilden, and A. J. Williams, Phys. Rev. 99, 1788 (1955). [Matzen] S. Matzen, J.-B. Moussy, R. Mattana, F. Petroff, C. Gatel, B. Warot-Fonrose, J. C. Cezar, A. Barbier, M.-A. Arrio, and Ph. Sainctavit, Appl. Phys. Lett. 99, 052514 (2011);  [Chambers] S.A. Chambers, R.F.C. Farrow, S. Maat, M.F. Toney, L. Folks, J.G. Catalano, T.P. Trainor, G.E. Brown Jr., JMMM 246, 124 (2002) 124 [Lisfi] A. Lisfi, and C. M. Williams, Journal of Applied Physics 93, 8143 (2003). [Yanagihara] H. Yanagihara, K. Uwabo, M. Minagawa, Eiji Kita, and Noriyuki Hirota, Journal of Applied Physics 109, 07C122 (2011) F. Zavaliche, H. Zheng, L. Mohaddes-Ardabili, S. Y. Yang, Q. Zhan, P. Shafer, E. Reilly, R. Chopdekar, Y. Jia, P. Wright, D. G. Schlom, Y. Suzuki and R. Ramesh, Nano Letters 5, 1793 (2005). [Torelli] P. Torelli, E.A. Soares, G. Renaud, S. Valeri, X.X. Guo, P. Luches, Surf. Sci. 601 (2007) 2651. [Meyer] W. Meyer, D. Hock, K. Biedermann, M. Gubo, S. Müller, L. Hammer, K. Heinz, Phys. Rev. Lett. 101 (2008) 016103. [Gubo] M. Gubo, C. Ebensperger, W. Meyer, L. Hammer, K. Heinz, F. Mittendorfer, J. Redinger, Phys. Rev. Lett. 108 (2012) 066101. [Lamirand] A. D. Lamirand, S. Grenier, V. Langlais, A. Y. Ramos, H. C. N. Tolentino, X. Torrelles, M. De Santis, Surface Science 647, 33 (2016). [Stanka] B. Stanka, W. Hebenstreit, U. Diebold, S.A. Chambers, Surf. Sci. 448 (2000) 49. \t\n17\t\t[Aghavnian] T. Aghavniana, J.-B. Moussy, D. Stanescu, R. Belkhou, N. Jedrecy, H. Magnan,P. Ohresser, M.-A. Arrio, Ph. Sainctavit, A. Barbier, Journal of Electron Spectroscopy and Related Phenomena 202 (2015) 16–21 [Robinson 2] I.K. Robinson, Phys. Rev. B 33 (1986) 3830. [E. Vlieg] E. Vlieg  J. Appl. Crystallogr. 30, 532 (1997) [Robinson] I. K. Robinson, in Handbook on Synchrotron Radiation, edited by G. S. Brown and D. E. Moncton (North-Holland, Amsterdam, 1991), Vol. 3, p. 221. [Prevot] Geoffroy Prévot, Alessandro Coati, Bernard Croset and Yves Garreau, J. Appl. Cryst. (2007). 40, 874–882 [Proskurina] N. V. Proskurina, V. A. Cherepanov, O. S. Golynets, and V. I. Voronin, Inorganic Materials, Vol. 40, No. 9, 2004, pp. 955–959. [Mohamed] Mohamed Bakr Mohamed, M. Yehia, Journal of Alloys and Compounds 615 (2014) 181–187 [Bleim] R. Bliem, E. McDermott, P. Ferstl, M. Setvin, O. Gamba, J. Pavelec, M. A. Schneider, M. Schmid, U. Diebold, P. Blaha, L. Hammer, G. S. Parkinson, Science 346 (2014) 1215. [Rieck] G. D. Rieck and J. J. M. Thijssen, Acta Cryst. (1968) B24, 982. [FEIDENHANS'L] R. Feidenhans’l, Surface Science Reports 10 (1989) 105-188 [Bunau] Bunǎu, O.; Joly, Y., J. Phys.: Condens. Matter 2009, 21, 345501. [Chapline] Michael G. Chapline and Shan X. Wang, Phys. Rev. B 74, 014418 (2006). [Gao] X S Gao, D H Bao, B Birajdar, T Habisreuther, R Mattheis, M A Schubert, M Alexe and D Hesse, 2009 J. Phys. D: Appl. Phys. 42 175006 [Grenier] S. Grenier and Y. Joly\"Basics of Resonant Elastic X-ray Scattering theory\", Proceedings of REXS 2013 - Workshop on Resonant Elastic X-ray Scattering in Condensed Matter, Oxford, UK, (15-19 July 2013), Journal of Physics: Conference Series 519, 012001 (2014).  [Bliem2] R. Bliem, R. Kosak, L. Perneczky, Z. Novotny, O. Gamba, D. Fobes, Z. Mao, M. Schmid, P. Blaha, U. Diebold, and G. S. Parkinson, ACS Nano 8(2014)7531–7537.  "    },    {        "title": "2306.13108v1.Onion_like_Fe3O4_MgO_CoFe2O4_magnetic_nanoparticles__new_ways_to_control_magnetic_coupling_between_soft_hard_phases.pdf",        "content": " 1 Onion -like Fe 3O4/MgO/CoFe 2O4 magnetic \nnanoparticles: new ways to control magnetic \ncoupling between soft/hard phases  \nJorge M. Nuñez 1,2,3 ,4, Simon  Hettler4,5, Enio Lima Jr .1,2, Gerardo. F. Goya ,4,5,6, Raul \nArenal4,5,6,7, Roberto D. Zysler1,2,3, Myriam H. Aguirre4,5,6 and Elin L. Winkler1,2,3* \n1 Resonancias Magnéticas -Centro Atómico Bariloche (CNEA, CONICET) S. C. Bariloche \n8400, Río Negro, Argentina  \n2Instituto de Nanociencia y Nanotecnología, CNEA, CONICET, S. C. Bariloche 8400, Río \nNegro, Argentina . \n3 Instituto Balseiro (UNCuyo, CNEA), Av. Bustillo 9500, S.C. de Bariloche 8400, Río \nNegro, Argentina.  \n4 Instituto de Nanocienc ias y Materiales de Aragón, CSIC -Universidad de Zaragoza, C/ \nMariano Esquillor s/n, Zaragoza 50018, Zaragoza, Spain  \n5 Laboratorio de Microscopías Avanzadas, Universidad de Zaragoza, Mariano Esquillor s/n, \nZaragoza 50018, Zaragoza, Spain  \n6 Dept. Física de la Materia Condensada, Universida d de Zaragoza, C/ Mariano Esquillor s/n, \nZaragoza 50018, Zaragoza, Spain  \n7 ARAID Foundation, Av. de Ranillas, Zaragoza 50018, Zaragoza, Zaragoza, Spain  \n  2 KEYWORDS  Onion -like nanoparticles, core/shell/shell nanoparticles, Exchange Bias, \nmagnetic coupling, EELS.  \nABSTRACT    \nThe control of the magnetization inversion dynamics is one of the main challenges driving  \nthe design of new nanostructured magnetic materials for magnetoelectronic applications.  \nNanoparticles with onion -like architecture offer a unique opportunity to expand the \npossibilities allowing to combin e different phases at the nanoscale and also modulate the \ncoupling between magnetic phases  by introducing spacers in the same structure .  Here we \nreport the fabrication , by a three -step high temperature decomposition method, of \nFe3O4/MgO/CoFe 2O4 onion -like nanoparticles and their detailed structural analysis , \nelemental compositional  maps  and magnetic response . The core/shell/shell nanoparticles \npresent epitaxial grow th and cubic shape with  overall size of (29 ±6) nm .  These nanoparticles \nare formed by cubic iron oxide core of (22±4) nm cover ed by  two shells, the inner  of \nmagnesium oxide and the outer of cobalt ferrite  of ~1 and ~2.5 nm of thickness, respectively .  \nThe magnetization measurements show a single reversion magnetization curve and the \nenhancement of the coercivity field, from H C~608 Oe for the Fe3O4/MgO  to H C~5890 Oe to \nthe Fe3O4/MgO/CoFe 2O4 nanoparticles at T=5 K, ascribed  to the coupling betwe en both \nferrimagnetic phases with a coupling constant of     =2 erg/cm2. The system also exhibits  \nexchange bias effect, where the exchange bias field increases up to H EB~2850 Oe at 5 K \naccompanied with the broadening of the magnetiza tion loop of HC~6650 Oe. Th is exchange  \nbias effect originates from  the freezing of the surface spins below the freezing temperature \nTF=32 K that pinned the magnetic moment of the cobalt ferrite shell .  \n   3 INTRODUCTION  \nOne of the main challenges driving  the development of nanostructured magnetic materials is \nthe control of the magnetization response with the magnetic field. The magnetic inversion \ndynamic s, the shape of the hysteresis loop, the coercive field and the saturation magnetization \ndetermine the  application range of each material which can be tune d for biomedical \napplication, new magnets or magneto -electronic devices .1 These parameters can be adjusted  \nby combining compounds  at the nanoscale  with different magnetic characteri stic.2,3 For \nexample, the microfabrication techniques allow the design of exchange coupled magnetic \nmultilayers combining magnetic phases with different magnetic orders as antiferromagnetic \n(AFM), ferromagnetic (FM) or ferrimagnetic (FiM) and different magnetic anisotropies, that \ncan exhibit both shifting and  broadening of the hysteresis loop .3–7 The coupling between the \nmagnetic phases can be modulated by introducing a non -magnetic spacer that, depending on \nthe thickness, can even decouple the m.8–11 In the  latter case, the response of the \nmagnetization with the field presents steps associated with the coercive fields of each \nphase.8,12 The combination and manipulation of these features makes it possible to design \ninnumerable devices wit h different responses for the development of field sensors, MRAM , \nspin valves, etc.13–16 Anot her interesting approach is the design of nanostructures from \nbottom -up chemical route, which could allow combining in a single nanoparticle phase s with \ndifferent functionalities in an onion -like architecture.17–19 These architectures permit \ncombining different properties in a single nanoparticle, reducing the size of the functional \nactive unit  and also reducing the cost and simplifying the fabrication process.20 The control of \nthe different synthesis parameters  that determine  the nanoparticles ´ characteristic  results in \nreproducible systems with defined size, interfaces, low dispersion and high crystallinity.18–21 \nDifferent AFM/FiM(FM) or FiM(FM)/AFM core/she ll NPs with exchange bias field, \ncoercivity enhancement22–29, or exchange spring effect30 have been fabricated and their  4 magnetic properties have been tuned for different applications.  There are some reports o n the \nsynthesis of s ystems with enhanced  energy product , intended for  new rare -earth -free \npermanent magnets by coating hard magnetic nanoparticles FePt or FePd with a soft \nmagnetic shell Fe, Fe 3Pt, Fe 3O4.20,31 –35 Also, core/shell NPs can be applied to  magnetic \nrecording devices with smaller  elemental magnetic units (bit) and therefore increase d density \nof information, in order to avoid the deleterious effects of  thermal fluctuation s. This can be \nachieved  by fine-tuning the magnetic anisotropy  through a combination of a core/shell \n(soft/hard) architecture . In this way , the thermal stability  can be enhanced  and the switching \nfield can be adjusted to invert the magnetization of a bit within the capability of the write \nhead .20,36 Magnetic NPs can generate building blocks fo r more complex nanostructures \narrangement allowing th eir integration in thin films for  spin-valves design.37–41 The \ndevelopment of core/shell nanoparticles also finds a wide field of applications in biomedical \narea. For instance , adjusting the magnetic anisotropy by combining soft  and hard magnetic \nmaterials in  core/s hell architecture  provides control on the contribution from  Brown and Néel \nrelaxation mechanism s to the power absorption for magnetic hyperthermia , optimiz ing the \nfinal heating efficie ncy.21,35,42,43 Despite  the great potent ial of design new heterostructures, a \nfew steps have been done to develop  more complex magnetic onion -like NPs, in these \nstructures the physicochemical properties are determined by the interfaces and the local \ncharacterization at a few nanometer scale is a  challenge.44–48  \nIn this context and with the aim to move forward the design of novel nanostructure s to \ncontrol the magnetization invers ion at the nanoscale, we develop ed core/shell/shell NPs \nformed by soft and hard magnetic components separated by a non -magnetic insulator layer. \nThe system w as fabricated by a three -step high temperature decomposition method and \nconsists in ~22 nm Fe 3O4 soft magnetic core encapsulated by a MgO intermediate shell of ~1 \nnm thickness that separate s the core from a CoFe 2O4 hard magnetic outer shell of ~2.5 nm  5 thickness. We found that the growing of the third layer results in an enhancement of the \ncoercivity field as a consequence of the coupling of the ferrimagnetic phases even in presence \nof the MgO separator. The system also exhibit s an exchange -bias field which is ascribed to \nthe spin glass order of the CoFe 2O4 surface spins that effectively pin the outer shell  spins \nresulting in an unidirectional exchange anisotropy.  \nEXPERIMENTAL SECTION  \nCore/Shell/Shell Nanoparticle Synthesis  \nFe3O4/MgO/ CoFe 2O4 core/shell/shell (CSS) monodispersed nanoparticles (NPs) were \nsynthesized by thermal decomposition of organomet allic precursors in presence of oleic acid \n(OA) and oleylamine (OL) as surfactants in a three -step process based on the method \ndescribed in 34,49 and illustrated in the Fig. 1. Briefly, Fe3O4 core is synthesized from 3 mmol \nof iron (III) acetylacetonate  (Fe(acac) 3) in presence of 1,5 mmol of 1,2 -octanediol, 9 mmol of \nOA, 3 mmol of Ol and 60 mL of 1 -octadecene as solvent. Firstly, the solution was heated up \nto 120 °C during 3 h under a N 2 flow to degas the precursors, then the solution was heated up  \nto 200 ºC, and k ept there for 10 minutes for core nucleation, and finally it was slowly heated \nup to promote the growth of the NPs. In a second stage, when the solution reaches 290  ºC, 3 \nmmol of magnesium acetylacetonate  (Mg(acac) 2), dissolved in a solution of 1 .5 mmol of  1,2-\nhexadecanediol, 3 mmol of OA, 1 mmol of OL and 15 mL of 1 -octadecene , was injected to \nthe solution, to form the first shell, and heat up to 315  ºC for 2 hours.  After the cooling \nprocess, 30 mL of the resulting solution were separated to overgrow the second shell. \nCore/shell/shell  NPs were prepared in a similar reaction, but in presence of the Fe3O4/MgO \nNPs that act as seeds for the growing of the CoFe 2O4 shell. The as -prepared nanoparticles \nwere precipitated by adding 3 times in volume of a solution c ontaining acetone and hexane  6 (14:1) followed by centrifugation (3900 rpm during 30 minutes). Finally, the samples in \npowder form were dispersed in hexane.  \nStructural c haracterization  \nStructural characterization of the systems was performed by means of powd er X -ray \ndiffraction experiments in a PANAlytical X´Pert diffractometer with Cu Kα radiation using a \nglass sample holder. The crystalline structure, morphology  and size dispersion of the NPs \nwere analyzed by transmission electron microscopy (TEM) and high-resolution TEM \n(HRTEM)  with an aberration corrected Titan3 60–300 (ThermoFisher Scientific, formerly \nFEI) microscope operating at 300 kV at room temperature . High -resolution scanning TEM \n(HRSTEM ) images acquired with a high-angle annular dark field (HAADF)  detector  \n(Fischione)  were obtained in a CS-probe -corrected Titan (ThermoFisher Scientific, formerly \nFEI) at a working voltage of 300 kV.  Electron energy -loss spectra (EELS)  were acquired in \nthis Cs -probe corrected microscope using a  Tridiem Energy Filter  (Gatan) spectrometer  at an \nenergy dispersion of 0.5 e V/pixel . Spectrum images were acquired with 500 ms dwell time \nand a pixel step size of 0.7 nm. The collection semiangle ( β) was 51.3 mrad for a camera \nlength of 10 mm and a spectrometer entrance apertur e of 1 mm. The convergence semiangle \n(α) was 24.8 mrad. The energy resolution, estimated from the full width at half -maximum \n(FWHM ) of the zero -loss peak, was 0.8 eV. \nMagnetic characterization  \nThe magnetic properties were studied by means of a commercial s uperconducting quantum \ninterference device magnetometer (SQUID, MPMS Quantum Design) . The magnetization \nwas measured as function of temperature using the field -cooling (FC) and zero -field-cooling \n(ZFC) protocols, with a field from  50 Oe  to 50 kOe. Magnetization as function  of an applied \nfield up to 50 kOe was measure d with a ZFC and FC protocol s; in this last case the sample s  7 were cooled  from room temperature down to the measured temperature with an applied field \nof 10 kOe . To perform th e magnetic measurements , 3 mg of nanoparticles were dispersed and \nfixed in 1 g of epoxy resin to reduce the  interparticle interactions  and to suppress mechanical \nmovement  of the NPs . In order to normalize the magnetization with the magnetic \nnanoparticles m ass, the proportion of the organic compound in the as -made nanoparticles was \ndetermined by means of thermogravimetric analysis (TGA) in a Shimadzu DTG -60H \nequipment. AC susceptibility measurements were performed in a Quantum Design PPMS \nac/dc magnetometer using an excitation field of Hac = 4 Oe and  frequencies 1 Hz  f  1.5 \nkHz, as a function of temperature . \nRESULTS AND DISCUSSION  \nFigure 1 schematizes the three -step seed -mediated high temperature decomposition synthesis \nroute . This figure indicates the first synthesis stage where the nucleation and growth of the \nFe3O4 core take place . In the second stage the respective precursors , which are detailed in the \nexperimental section,  are hot injected in order to nucleate and grow  the MgO over the cores , \nand then the solution was cooled down . Finally, in the third s tage,  the solution is heated up \nand the precursors to grow the second shell  of CoFe 2O4 were hot inject ed as signaled in the \nfigure . It is important to remark that proper so lvents should be selected to reach the reflux \ncondition at a higher temperature than the decomposition temperature of the organic \nprecursors. This guarantees to reach the metal ions supersaturation condition and the \nnucleation of the metal oxides phase. Th e Mg(acac) 2 precursor has a decomposition \ntemperature of T~538 K, larger than the Fe(acac) 3 (T~453 K) and Co(acac) 2 (T~440 K), \ndetermining the use of 1 -octadecene as solvent (T~587 K). The requested reflux condition \nalso restricts the use of surfactants to  those with larger decomposition temperature, such as \n1,2-hexadecanediol (T~ 576 K). Representative low and HRTEM image s of the Fe3O4/MgO  8 sample obtained in the second st age of the synthesis, are shown in Fig. 2 -(a) and (b). From \nthis figure , nanoparticles with cubic shape and uniform size can be observed . The size \nhistogram shown in Fig. 2 -(c) was obtained by measuring more than  300 NPs. The mean \ndiameter and size dispersion was obtaine d from the fitting with  a log-normal distributio n \n ( ) (  √  )    [   (    )    ], from where the mean diameter               and \nthe standard deviation      [     ]    were calculated,  resulting  (24±4) nm  for the \ncore/shell NPs . Figure 2 -(d) and ( e) shows the Fe3O4/MgO/ CoFe 2O4 nanoparticles obtained \nafter the third st age of the syntheses , where again cubic shape nanoparticles are observed . \nFigure 2 -(f) shows the size histogram, constructed by measuring the size of more than 300 \nNPs, fitted with a log -normal distribution from wh ere the mean nanoparticle size and size \ndispersion was obtained  (29±6) nm.  The analysis from high  resolution TEM (HRTEM) \nimages reveal s that the nanoparticles are single crystal line, and the successive layers gr ew \nepitaxial ly due to the negligible lattice mismatch between the Fe3O4, MgO and CoFe 2O4 \n(≈0.34-0.38%). The analysis of the images also showed interplanar distance s d=2.10(2) Å and \nd=2.94(2)  Å that could be identified in the core/shell and core/shell/shell nanoparticles , \nconsistent  with the interplanar distance of the (400) and (220) planes of  the spinel phase, \nrespectively . Also, t he distance d=2.1 1(2) Å agrees well with the corresponding (200) \ncrystalline plane of the MgO phase. The fast Fourier transformation ( FFT) images of the \ncore/shell and core/shell/shell confirm ed the single -crystal  growth with the plane indexation \nshown in the inset of Fig.2 -(b) and (d). These features are also evidenced in the XRD  pattern \nof the Fe3O4/MgO/ CoFe 2O4 nanoparticles, Fig. 3, where the overlap of the peaks \ncorresponding to the iron and cobalt spinel and the MgO phase are observed , with no other \ndetected phases .  Using  the diffraction peaks position, the spinel lattice parameter, aspinel, was \ncalculated f rom the relationship between the Miller indices (h,k,l)  and the corresponding \ninterplanar distance dhkl for a cubic structure: a=d hkl (h2+k2+l2)1/2, resulting a=0.841(3) nm.  9 Analogously, the lattice parameter of the magnesium oxide aMgO=0.422 (2) nm was obt ained. \nThe calculated lattice parameters, aspinel and aMgO, are in agreement with the reported for \nmagnetite ( aFe3O4=0.8392 nm), cobalt ferrite ( aCoFe2O4 =0.8392 nm) and magnesium oxide \n(aMgO=0.4211 nm) 5,50.  Also the crystallite size of the core/shell/shell NPs was obtained from \nthe x -ray powder pattern. To perform this analysis the peaks were fitted with a pseudo -Voigt \nfunction in order to obtain the full width at half maximum  (FWHM) , and then the crystallite \nsize was calculated by using the Scherrer equation, re sulting in a median value of 22 (2) nm. \nThe smaller crystallite size obtained from XRD compared to the mean size obtained by TEM \nindicates the presence of surface disorder in the core/shell/shell structure.  \n \nFigure 1: Temperature ramp profile use d in the three -step high temperature decomposition \nmethod and schematic illustration of the Fe 3O4/MgO/CoFe 2O4 nanoparticles growth . Left \npanel: In the first synthesis step the precursors were heating (Fe(acac) 3, 1,2-octanediol, OA, \nOl and 1 -octadecene ) up to 120 °C for 3 h under N 2 flow (1), then the solution was heated up \nto 200 ºC for 10 minutes for the Fe 3O4 cores nucleation (2), followed by a ramp to 290 ºC to \npromote the growth of the Fe 3O4 NPs (3). In the second stage Mg(acac) 2, 1,2-hexadecanediol, \n0 100 200 300 400050100150200250300350\nFe3O4\nMgOFe3O4\nTemperature (ºC)\nTime (min)\n(1)(2)(4)\n(3)(5)\n0 50 100 150 200 250050100150200250300350\nCoFe2O4MgOFe3O4\nMgOFe3O4\nTemperature (ºC)\nTime (min)(6)(7) (8)\n(a) \n (b)  10 OA, OL and  1 -octadecene were injected at 290 ºC (4), then the solution was heated up to 315 \nºC for 2 hours to grow the MgO shell (5), followed by the cooling process. Right Panel: \nSketch of the final synthesis step  including the heating of the  solution co ntaining Fe 3O4/MgO \nNPs seeds up to 315 ºC (6), where the precursors Fe(acac) 3, Co(acac) 2, OA, OL and 1 -\noctadecene were injected  (7) for the growing of the CoFe 2O4 outer shell ( 8).  \n  \nFigure 2: Bright -field TEM micrographs of (a) Fe3O4/MgO and (d) Fe3O4/MgO/CoFe2O4 \nnanoparticles. Aberration -corrected HRTEM image of a (b) Fe3O4/MgO nanoparticle and (e) \n220} 2,94 Å\n220\n400/200\n10 15 20 25 30 35 40051015202530\nFrecuency (%)\nParticle size (nm)<d> = (244)Fe3O4/MgO Fe3O4/MgO/CoFe2O4\n(c)(d)\n(e)\n(f)\n10 15 20 25 30 35 40051015202530Frecuency (%)\nParticle size (nm)<d> = (296)(a)\n(b)\n(b)  11 Fe3O4/MgO/CoFe2O4 nanoparticle and their corresponding FFT images of the whole NPs \nare shown in the insets.  Size histograms fitted with a l og-normal distribution for (c) \nFe3O4/MgO and (f) Fe 3O4/MgO/CoFe 2O4 nanoparticles. From the fitting (24±4) nm and \n(29±6) nm were obtained for the core/shell and core/shell/shell, respectively, corresponding \nto an C oFe2O4 outer layer of 2.5 nm thickness.   \n \n  \nFigure 3:  (a) XRD pattern of Fe3O4/MgO/CoFe 2O4 nanoparticle s, where the diffraction \npeaks of the Fe 3O4 (black),  CoFe 2O4 (red) and  MgO  (blue)  are indexed . (b) STEM -HAADF \nimage where the annular  magnesium oxide shell can be detected  by Z contrast , showing  core \nof size ~22 nm coated with a n intermediate (MgO)  thin layer of ~1 nm thickness and a n outer  \n1 0  n m\n2 0  n m\n(d) \n (c) \n(a) \n (b)  12 thicker layer  (CoFe 2O4) of ~2.5 nm thickness . (c) Selected area diffraction  pattern , wher e the \nrings were  indexed with the Fm3m MgO (green) and Fd3m Fe 3O4/ CoFe 2O4 (cyan ) space \ngroups . (d) Dark -field TEM images of Fe3O4/MgO/CoFe 2O4 NPs selecting  a section  of the \n(311) spinel diffraction ring  using a small objective aperture .  \nDue to the epitaxial grow th and the negligible mismatch between the different phases , the \nonion -like architecture could not be resolved from HRTEM lattice -fringe image s (Figure 2 -\n(b) and (d)) . However , dark-field images , selecting a section of the (311) spinel diffra ction \nring using a small objective aperture , show ed a bright contrast only for the Fe3O4 and \nCoFe 2O4 spinel phases, unveiling  the core/shell/shell structure  as shown in Fig. 3 -(c). This \nonion -like architecture was confirmed by HAADF -STEM  imaging that is a known technique \nfor material characterization with high spatial resolution and with a contrast proportional to \n~Z1.7, known as Z -contrast.51–53 Figure 3 -(b) shows representative HAADF -STEM images \nwhere a clear dark annular contrast is observed in the inner shell c orresponding to the MgO \nphase.  From these measurements a mean core nanoparticle size (22±4) nm and the thickness \nof the inner MgO shell of ~1 nm was measured.  It is worth to mention that from the \ncomparison between the size histograms of core/shell and core/shell/shell  (see Fig. 2 -(c) and \n(f)) the thickness of the outer shell could be calculated , obtaining a value of  ~2.5 nm.  13  \n  \nFigure 4:  Elemental profile performed by EDS on  (a) isolated Fe3O4/MgO  nanoparticles and \n(b) Fe3O4/MgO/CoFe 2O4 nanoparticles  (O in red + Fe in blue + Mg in green  + Co in yellow ).  \nElemental mapping of the core/shell and core/shell/shell nanoparticles were analyzed by \nenergy dispersive X -ray spectroscopy (EDS) and electron energy -loss s pectroscopy  (EELS) . \nFigure 4 -(a) shows an EDS elemental profile on a single core/shell nanoparticle, where Fe, \nMg and O were detected. From the atomic percentage elemental profile , the Fe3O4/MgO \nstructure is corroborated. Analogously, Fig.4 -(b) shows the EDS profile scanning over two \nnanoparticles  confirming the onion -like architecture. More accurate  nanoparticles elemental \nmapping was investigated by EELS  and a representative spectrum  is shown in Fig. 5-(e). In \nthis figure  the peaks associated to  O-K edge (red), Fe -L edge (blue), Co -L edge ( yellow ) and \n0 10 20 30 40010203040506070\nAtomic percentage (a.u.)\nLength (nm) O % at\n Fe % at\n Mg % at(a)\n0 10 20 30 40 500102070\nAtomic percentage (a.u.)\nLength (nm) O At%\n Fe At%\n Mg At%\n Co At%(b) 14 Mg-K edge  (green)  are identified in the  spectrum . By performing spectrum imaging  (SI) and \nintegration of the background -subtracted edge areas in every pixel , the spatial elemental \ndistribution was obtained  (Fig.5 -(a-d)). The maps confirm the highest concentration of \nmagnesium  in the inner shell and cobalt in the outer shell consistently  with the \ncore/shell/shell architecture. This observation can be quantified by a linear profile \ncomposi tion analysis, shown in Fig. 5 -(g), confirmin g the increase of magnesium with the \ncorresponding decline  of iron oxide in the intermediate  shell, and also the increase of cobalt \nand iron  in the outer shell.  Notice that, in some interface sect ions, a thinning of the MgO \nintermediate layer can be observ ed, Fig. 5 -(e). The lineal profile atomic distribution, Fig.5 -\n(g), also shows that the magnesium is concentrated in a ring with average diameter of ~23 nm \nand it s concentration extend s to the nanoparticle edge , suggesting that the cobalt ferrite oxide \nis doped with magn esium. The doping of the outer shell with magnesium could be related to \neither interface interdiffusion during the synthesis, or the presence of Mg excess ions \nremaining from the second st age of the synthesis. The core /shell /shell architecture of the NPs \nis also revealed by an energy loss near edge structure (ELNES) analysis of the O -K core -loss \nedge  shown in Fig. S1 of the Supporting Information . This figure presents  the comparison of \nthe O -K edge at 530 eV obtained from core, core -shell and core -shell -shell areas of a NP. The \nthree spectra are compared with a Fe 3O4 magnetite and a MgO reference.47,54 –57 The major \ndifference is observed in the p re-peak located at 530 eV, which is strong in the core region \nand the outer shell, while shows a decreased intensity in the inner MgO shell. This \nobservation corresponds well to the reference spectra, as magnetite shows a prominent pre -\npeak, while it is co mpletely absent for MgO. The spectrum of the outer  shell does not \nperfectly agree with the magnetite reference,  as the pre -peak intensity is reduced in cobalt \nferrite when compared to Fe 3O4,47 and also due to the  presence of Mg that it is expected to  15 alter the O -K edge.  These results have important implications in the magnetic response of the \nnanoparticles  discussed below . \n400 600 800 1000 1200 140001×1052×1053×1054×1055×1056×105\nCounts (arb. units)\nEnergy (eV)Mg-K edgeO-K edge\nFe-L edge\nCo-L edge\nCobalt\nIron\nOxygen\nMagnesium\n(a) (b) (c) (d)(e)\n(f)\n(g)\n0 5 10 15 20 25 30 350102030405060Atomic percentage (a.u.)\nLenght (nm)\n \nFigure 5. Elemental mapping performed by EELS -SI on an isolated Fe3O4/MgO/CoFe 2O4 NP \nof (a) O in red , (b) Fe in blue , (c) Co in yellow , (d) Mg in green and (e) the composition map. \n(f) EELS sum spectra of SI with the O−K edge (532 eV, red vertical line), Fe−L (713 eV, \nblue vertical line) edges, Co−L edge (781 eV, yellow vertical line) as well Mg−K edge (1323 \neV, green vertical line) are indicated . (g)  Line profile  across the NP , extracted from this \nEELS dataset, of atomic percentages, where  the core/shell/shell structure  is evidenced . \n \nFigure 6 compares t he field d ependence of the magnetization at 5K of  the Fe3O4/MgO and \nFe3O4/MgO/ CoFe 2O4 nanoparticles . From this measurement  the enhancement of the  16 coercivity field is clearly observed from H C=608 Oe for the core/shell NPs to H C=5890 Oe \nwhen the third shell of cobalt ferrite is grown.   Figure 6 -(b) shows the magnetization loops as \na function of the temperature in the ZFC condition  for the Fe 3O4/MgO/ CoFe 2O4 \nnanoparticles . It is noteworthy that a single reversion curve is observed for all the \ntemperature s, signaling that the FiM phases are coupled even though they are separated by a \nMgO diamagnetic insulator interlayer. This result is consistent with the  magnetic response \nreported by Zaag et al. for multi layers.8,9 These authors studied the coupling in  \nFe3O4/MgO/ Fe3O4/Co xFe3-xO4 thin films  as a functio n of the MgO thickness ( tMgO) and \nidentified two different coupling regime: i) a weaker interlayer interaction for tMgO >1.3 nm , \nwhere a stepped hysteresis loop is observed due to the different coercive fields of the \nmagnetic layers and ii) a rapid increase  of the coercivity for tMgO <1.3 nm due to the \nenhancement of the ferromagnetic coupling between the layers, wh ere the magnetization loop \ntends to a single reversion magnetization behaviour .8,9 In this work, t he authors assume d that \nthe change from weak to strong coupling is due to irregularities at the interface , where Fe 3O4 \nbridges through the  MgO are formed. In the present case, t he magnetic reversion curve  of the \nFe3O4/MgO/ CoFe 2O4 nanoparticles  (tMgO~1 nm)  is consistent with  the behavio ur observed in \nmultilayers for the strong coupling regime (t Mg<1.3 nm) . Moreover , Fig. 5  shows  the \npresence of ferrimagnetic bridges through the MgO shell, confirming the hypothesis \npresented to explain the increasing coupling in nanostructures for thinner spacers. The \nmagnitude of the surface coupling energy (   ) can be estimated from the differ ence in the \ncoercivity fields between  the uncoupled Fe 3O4 NPs (      ) and the coupled  onion  (       ) \nsystem : 9,58 \n    (              )           ,   (1)  17 where tcore and        are the thickness and satura tion magnetization of the non -interacting \nFe3O4 phase . From this equation    = 2 erg/cm2 was calculated using              , \n               , tcore=22 nm,       =35 emu/g. This value is larger than the obtained for \nthe Fe 3O4/MgO/Fe 3O4/Co xFe3-xO4 multilayers in the strong ly-coupled regimen,   ~0.3 \nerg/cm2,8 probably because the surface -to-volume  ratio of the Fe 3O4 core is 10 time larger \nthan the Fe 3O4 phase in the multilayer, resulting in a larger effective coupling surface; \nfurthermore heterogeneous seed mediated growth of core/shell/shell architecture could results \nin larger interface imperfect ions, in particular in the thinner MgO shell, than in the multilayer \nfabricated by molecular beam deposition. For uniaxial, randomly oriented and non -interacting \nnanoparticles where the magnetization reverts coherently with the magnetic field it is \npredict ed that the coercive field follow the  relation   ( )    [  ( \n  )   \n], where     is \nthe coercive field extrapolated at zero temperature  value .59 Despite the complexity of this \nonion -like nanoparticles  system , Fig. 6 -(c) shows that the coercive field follows a T1/2 \ndependence supporting the single magnetization reversion of the NPs  due to the strong \ncoupling of the ferrimagnetic phases . From the fitting curve    =(7033 ±264) Oe and \nTB=(216 ±37) K  were obtained .  On the other hand, the calculation of the effective ma gnetic \nanisotropy from the blocking temperature (              ); in this three -layer NPs is not \nstraightforward due to the presence of a non -magnetic interlayer.   18  \nFigure 6.  (a) Hysteresis cycles of the Fe 3O4/MgO and Fe3O4/MgO/CoFe 2O4 NPs systems , \nmeasured at 5  K. (b) ZFC and (d ) FC, from 320 K with 10  kOe, hysteresis loops of \nFe3O4/MgO/CoFe 2O4 NPs systems measured in the 5  K – 300 K temperature range. (c) \nTemperature dependence of the H C measured wit h the ZFC ( black  dot) and FC ( blue dot) \nprotocol s, and H EB (red triangle ) of the Fe 3O4/MgO/CoFe 2O4 system.  The inset shows the \ndependence of H C(T) with T1/2. \n \n 19 Figure 6 -(d) shows the magnetization loop s measured after cooling the Fe3O4/MgO/CoFe 2O4 \nsample from room temperature  without a magnetic field (ZFC)  and with an applied field of \n10 kOe  (FC). From th is figure a single reversion curve is observed in the whole  temperature \nrange and also a systematic increase of the coe rcive field as the temperature decreases . \nMoreover, in t he FC magnetization measurements a clear shift toward negative field is \nobserved for temperature T< 75 K evidencing the presence of exchange bias effect. It is \nimportant to remark  that no exchange bias effect was observed in the Fe 3O4/MgO  core/ shell \nsystem.   Figure 6-(c) shows  the temperature evolution of  the exchange bias field which  grows \nup to 2850 Oe at 5  K. The shifting of the hysteresis cycles is also accompanied by an \nenha ncement of the coercivity field .  It is known that the e xchange bias effect is present  in \nnanoparticles with AFM/FM  (FIM)  interfaces3,26,60,61 and also in systems with interface  \nexchange coupling between the magnetically  ordered core with disordered and frozen surface \nspins .62–65 In these systems the FM (FiM)  phase has pinned spins at the interfaces due to the \ncoupling with the more anisotropic AFM state or with the surface spin glass phase . Even \nlarger exchange bias and coercivity field enhancement  were  found when  the ferromagnetic \nphase is coupled with the more disorder ed spin glass state, when compared with the coupling \nwith AFM ph ase, indicating a larger amount of pinned spins at the interface.66 Based on the \ncomposition al and the morpholog ical analysis of the Fe 3O4/MgO/ CoFe 2O4 nanoparticles , the \norigin of the exchange bias is ascribed to the formation of spin glass -like state s at the outer \nFiM shell. This hypothesis is supported by previous reports, in particular the magnetic \nbehavio ur of ferromagnetic hollow nanoparticles whose morphology is similar  to the \nCoFe 2O4 shell growth over the non -magnetic MgO shell.67–69 These systems present  a larger \ndegree of spins surface disorder that freeze at low temperature increasing its surface \nanisotropy and show ing large exchange bias effects as a consequence of the magnetic \ncoupling with the FiM order phase . In addition, the doping  of the CoFe 2O4 shell with non - 20 magnetic magnesium ions, as shown by the EELS analysis, introduce a larger degree of \nmagnetic disorder spins that  froze  at lower tempe rature. In order to  support this picture,  we \nanalyze the evolution of the magnetization with the temperature.  \n \nFigure 7: ZFC and FC temperature dependence of the magnetization curves of the core/shell \n(a) and core/shell/shell (b) nanoparticles, measured w ith H=50 Oe (black dots) and H=5000 \nOe (blue  dots). The inset shows   (  )  \n  (    ( )    ( ))\n   curve (red dot s), where the \nmaximum corresponds to the most probab e blocking temperature , TB. (c) Field dependence of \nTB and the freezing temperature T F of the Fe3O4/MgO/ CoFe 2O4 nanoparticles systems. The \ninset shows the  (    ( )    ( ))\n   used to determine  TF (dash line) , also the maximum \nassociated to TB  is signaled  (red triangles) . \n \nFigure 7-(a) and ( b) present the ZFC-FC magnetization curves of the Fe3O4/MgO  and the \nFe3O4/MgO/ CoFe 2O4 nanoparticles systems , respectively . The magnetization  of the \nFe3O4/MgO NPs shows  a change from reversible to irreversible behavio ur in agreement with \n01234\nH = 50 Oe\nFe3O4CoFe2O4\nMgO\nFe3O4MgO(a)\n(b)H = 50 Oe\n0 50 100 150 200 250 300 350 4000.00.51.01.52.02.5\nTemperature (K)M (emu/g)H = 5000 Oe\n051015\nM (emu/g)100 150 200f (TB)\nTemperature (K)TV TB\n0 200 400 600 800 1000 1200 1400050100150200250\nTFT (K)\nH2/3 (Oe2/3)TB\n(c)-50 0 50 100 150 200 250 300 350 400d(MZFC-MFC)/dT (a.u.)\nTemperature (K) 50 Oe\n 500 Oe\n 1000 Oe\n 2500 Oe\n 5000 Oe\n 10000 Oe 21 the change from superparamagnetic to blocked regime. Fr om this measurement the \ndistribution of blocked temperature  (  )  \n  (    ( )    ( ))\n   can be calculated,  where the \nmost probabl e blocking temperature is obtained from the maximum of the distribution <T B> \n= 177 K. From this figure it is also notice a kink at T V= 101(2) K associated with the Fe3O4 \nVerwey transition , present at  lower  temperature  compared to the bulk T V ~120 K ,70 due to \nsize ef fects and deviation from stoichiometry .71–74 When the CoFe 2O4 is grown over the \nFe3O4/MgO the  irreversibility  in the ZFC -FC magnetization is shifted to higher temperature \nsignaling an increase of the energy barrier of the system  in agreement with the magnetic \ncoupling of both phases . From the  (  ) curves  calculated from  the magnetizat ion of the \nFe3O4/MgO/ CoFe 2O4 NPs measured  with H=50 Oe ( Fig. 7-(b)) the most probabl e blocking \ntemperature  is obtained  resulting <TB> =237 K. Notice that this value is in agreement with \nthe one obtained from the fitting of the temperature dependence of H C, shown in Fig. 6 -(c). \nAlso the non -monotonous behavio ur of the core/shell/shell FC magnetization curve  is \nnoteworthy , an anomaly  that is more evident when the measurement is collected  applying \nlarger magnetic  fields.  The inset of Fig. 7 -(c) shows the  (    ( )    ( ))\n   curve s for different \nmeasuring applied field  where, beside the broad peak associated to the distribution of \nblocking temperature, a narrower peak center ed at T F with lower field dependence  is clear ly \nidentified . Figure 7 -(c) shows that both T B and T F have a linear dependence with H2/3. This \nfield dependence is consistent with the Almeida -Tholousse (AT) line      (      ) for \nspin glass transition  63,75,76 but also with the field dependence of the blocking temperature as \npredicted by Brown77 and Dormann et al.78 However, the emergence of exchange bias effect \nsuggests  the formation of spin glass state at low temperature  as observed in several NPs \nsystems .63,65,68,79 –84 The onsets of the freezing process can be identified by the low \ntemperature increasing of the derivative curve at T ~ 70 K in agreement with the appearance \nof exchange bias field, and the  freezing temperat ure of the system can be  obtained  from the   22 extrapolation to zero field of the AT -line resulting T F~ 32 K. To further explore the magnetic \ndynamic s of the NPs we perform ed ac susceptibility measurements as a function of the \ntemperature under different ac excitation frequencies.  \n \nFigure 8(a):  Imaginary component () of the ac susceptibility measured (Hac= 4  Oe; 1 Hz \nf 1.5 kHz ) for the Fe3O4/MgO/ CoFe 2O4 system . The inset shows a detail of the low \n0.006 0.007 0.008 0.009-10-8-6-4-2ln (t)\n1/(T-T0) (K-1)\n1.6 1.8 2.0 2.2 2.4 2.6-8-6-4-2ln(t)\nln(TF/(T-TF))\n0 50 100 150 200 250 300 350-0.10.00.10.20.30.40.50.60.70.80.91.0\n25 50 750.000.02\n´´ (arb.units)\nTemperature (K)  1500 Hz\n 1000 Hz\n  200 Hz\n  100 Hz\n  10 Hz\n    1 Hz´´ (arb. units)\nTemperature (K)(a)\n(b)\n(c) 23 temperature region. (b) Frequency dependence of the high-temperature maximum and the \nfitting curve with the Vogel -Fulcher law. ( c) Frequency dependence of the low -temperature \nmaximum and the corresponding fit with a power law.  \nFrom t he real () and imaginary ( ) component s of the ac magnetic susceptibility two \ndifferent maxima in the data were observed at rather different temperature s. These „peaks‟  \nare more clearly defined in the curve  (see Figure 8 -(a)), with a  high temperature pe ak \nthat shifts with increasing fre quencies from T~293 K to T~ 333 K, and a  low temperature \npeak that shifts from T~33.4 K to T~37 K in the same frequency range. We used the relative \nshift of temperature T m of the maximum in  curves, per frequency decade      \n      ( ) \nas an indicator of the magnetic moment dynamic, obtaining          and 0.032 for the \nhigh- and low -maxima, respectively . These values show smaller  frequency dependence than \nthe expected for thermally activated superparamagnetic blocking mechanism in non-\ninteracting NPs  system s, and closer to values observed for spin glasses or strongly interacting \nsingle -domain magnetic NPs .65,85,86 Consistently with these findings, the fitting of the high -\ntemperature maxima using  the Arrhenius law          (      ),  where τ = 1/ 2f and τ0 \nis the characteristic relaxation time of the  system , returns unreasonable physical results, \nevidencing the presence of interactions that affect the relaxation process. Therefore we used a \nphenomenological Vogel -Fulcher law        *     \n(    )+ to fit the frequency dependence of \nthe high temperature peak , where T0  account the  interactions presents.  From the fitting of \nthe experimental results, shown in Fig. 8 -(b), the following parameters were obtained: τ0 \n=2x10-12 s, EA=2869(300) K, and T0=180 (20) K. This values are consistent with a thermally \nactivated process of interacti ng magnetic moments , where the interactions are attributed to \nintrapartic le effects due to the complex internal magnetic structure of the core/shell/shell \nnanoparticles . Instead, the low temperature peak is not consistent with a thermally activated  24 process, and different model that account its slow dynamic should be applied. The critically \nslowing down relaxation time is usually  model by a Power law     (  \n    )  \n,  where TF is \nthe static freezing temperature, and zν is the dynamic exponent. Figure 8 -(c) shows the \nfrequency dependence of the low temperature maximum and the corresponding fit with a \nPower Law ,  from where  TF = 31(6) K, zν = 7(1), and τ0 = 1.5×10−8 s were obtained. The \nparameters obtained from the fitting  are in agreement with the reported for spin -glass, surface \nspin-glass  like nanoparticles behaviour61,82,87 and super spin -glass,61,88 supporting the \ncollective freezing  model  of the surface spins at low temperature.   \nThe above results show that  the onion -like nanoparticles present  an enhancement of their \ncoercivity H C compared with the single magnetic phase  Fe3O4/MgO NPs, and the \nmagnetization displayed a field dependence consistent with a single reversion that reflects the \nstrong coupling between the Fe3O4 core with CoFe 2O4 shell, notwithstanding the presence of \nthe MgO spacer.  This coupling c ould be due to  surface irregularities , such as the FiM bridges \nobserved by TEM where both FiM phases could be  coupled by exchange interaction s and, \nconsequently , invert its magnetization together . Therefore, the magnetic moment of the \nonion -like nanoparticles behave superparamagnetically at room temperature and change to a \nblock ed regime at T B=237 K and below .  Moreover, the do ping of the cobalt ferrite  with \nmagne sium ions  induce s magnetic disorder evidenced by the reduction of the magnetic \nanisotropy of this phase and also by the presence of surface spins disorder that froze into a \nstatic and randomly oriented configuration at TF=32 K. At the  onsets of th is spin glass \ntransition, defined from the increases of the magnetization curve , emerge the exchange bias \neffect , manifested by the shifting of the FC magnetization loop and the enhancement of the \ncoercivity field . The surface spin glass state is effective t o pin the spins of the ferrimagnetic \nlayer inducing large values of exchange bias field at low temperature as H EB=2850 Oe at 5  K.  25  \nCONCLUSIONS  \n \nWe successfully fabricated three -layer Fe 3O4/MgO/CoFe 2O4 core/shell/shell magnetic \nnanoparticle s using a thermal decomposition method, with an  onion-like architecture \nconfirmed by TEM and STEM microscopy. The resulting structure is formed by a magnetite \ncore of 22 nm, encapsulated with a n inner  shell of MgO having   ~1 nm thickness , and a n \nouter  cobal t ferrite shell of ~2.5 nm. We have identified the presence of FiM bridges through \nthe diamagnetic MgO phase by  EDS and EELS analysis, as well as partial Mg diffusion into \nthe CoFe 2O4 layer resulting in partial Mg -doping of the outer layer.  The magnetic \ncharacterization showed that the magnetic moments of the Fe3O4/MgO/CoFe 2O4  system \nfluctuate with a superparamagnetic regime  in the time window of dc measurement (~100 s), \nchanging to blocking regime at   TB=237K , higher than the T B=177 K of the Fe3O4/MgO  \nnanoparticles, showing an effective magnetic coupling between the two magnetic phases \nthrough the MgO layer . An enhancement of the coercivity field is found when the third shell \nis grown due to the coupling between both FiM shells. The coupling is ascribe d to the \nexchange interaction that is established through the MgO separator due to the presence of \nFiM bridges . At low temperature t he disorder outer surface spins freeze  in a spin glass state, \nthat effectively pin the magnetic ions of the doped cobalt ferrite and, as a consequence, the \nsystem evidence exchange bias effects , which is  manifested by the shifting and enhancement \nof the hysteresis cycle . The present results sh ow the potential of the synthesis method for the \ndesign of new multiphase magnetic nanostructures in a single nanoparticle, and also it \nhighlights the relevance of the structural, compositional, and interface details to the resulting \nmagnetic phenomena at the level of individual particles.  \nASSOCIATED CONTENT   26 Supporting Information .  \nAdditional data related to EELS spectra and EELS -SI mapping.  \n \nAUTHOR INFORMATION  \nCorresponding Author  \n*e-mail: winkler@cab.cnea.gov.ar   \nAuthor Contributions  \nThe manuscript was written throug h contributions of all authors. All authors have given \napproval to the final version of the manuscript.   \nACKNOWLEDGMENT  \nThe authors acknowledge financial support of Argentinian governmental agency ANPCyT \nthrough Grant No. PICT -2019 -02059, PICT -2018 -02565 and UNCuyo for support through \nGrants No.  06/C604 and 06/C605. The authors gratefully acknowledge the EU  Commission \nfor financial support through MSCA -RISE projects  #734187 ( SPICOLOST ) and #101007629 \n(NESTOR) . SH was supported by the German Research Foundation (DFG project He \n7675/1 -1). G.F.G. thanks Spanish State Agency AEI for financial support through project \nPID2019 -106947RB -C21. R.A.  gratefully acknowledge the support fro m the Spanish \nMICINN (PID2019 -104739GB -100/AEI/10.13039/501100011033), Government of Aragon \n(projects DGA E13 -20R and from the European Union H2020 program “ESTEEM3” (Grant \nnumber 823717).  \nREFERENCES  \n(1)  Coey, J. M. D. Magnetism and Magnetic Materials ; 2009.   27 (2)  Kneller, E. F.; Hawig, R. The Exchange -Spring Magnet: A New Material Principle for \nPermanent Magnets. IEEE Trans. Magn.  1991 , 27 (4), 3588 –3560. \nhttps://doi.org/10.1109/20.102931.  \n(3)  Nogués, J.; Sort,  J.; Langlais, V.; Skumryev, V.; Suriñach, S.; Muñoz, J. S.; Baró, M. \nD. Exchange Bias in Nanostructures. Phys. Rep.  2005 , 422 (3), 65 –117. \nhttps://doi.org/10.1016/j.physrep.2005.08.004.  \n(4)  Tan, A.; Li, J.; Jenkins, C. A.; Arenholz, E.; Scholl, A.; Hwang, C.; Qiu, Z. Q. \nExchange Bias in Epitaxially Grown CoO/MgO/Fe/Ag(001). Phys. Rev. B - Condens. \nMatter Mater. Phys.  2012 , 86 (6), 1 –6. https://doi.org/10.1103/PhysRevB.86.064406.  \n(5)  Lavorato , G.; Winkler, E.; Rivas -Murias, B.; Rivadulla, F. Thickness Dependence of \nExchange Coupling in Epitaxial Fe 3 O 4/ CoFe 2 O 4 Soft/Hard Magnetic Bilayers. \nPhys. Rev. B  2016 , 94 (5), 1 –6. https://doi.org/10.1103/PhysRevB.94.054405.  \n(6)  Rivas -Murias, B.; Lucas, I.; Jiménez -Cavero, P.; Magén, C.; Morellón, L.; Rivadulla, \nF. Independent Control of the Magnetization in Ferromagnetic \nLa2/3Sr1/3MnO3/SrTiO3/LaCoO3Heterostructures Achieved by Epitaxial Lattice \nMismatch. Nano Lett.  2016 , 16 (3), 1736 –1740. \nhttps://doi.org/10.1021/acs.nanolett.5b04657.  \n(7)  Kiwi, M. Exchange Bias Theory. J. Magn. Magn. Mater.  2001 , 234 (3), 584 –595. \nhttps://doi.org/10.1016/S0304 -8853(01)00421 -8. \n(8)  van der Heijden, P. A. A.; Bloemen, P. J. H.; Metselaar, J. M.; W olf, R. M.; Gaines, J. \nM.; van Eemeren, J. T. W. M.; van der Zaag, P. J.; de Jonge, W. J. M. Interlayer \nCoupling between Fe3O4 Layers Separated by an Insulating Nonmagnetic MgO \nLayer. Phys. Rev. B  1997 , 55 (17), 11569 –11575. \nhttps://doi.org/10.1103/PhysRev B.55.11569.  \n(9)  Van Der Zaag, P. J.; Bloemen, P. J. H.; Gaines, J. M.; Wolf, R. M.; Van Der Heijden,  28 P. A. A.; Van De Veerdonk, R. J. M.; De Jonge, W. J. M. On the Construction of an \nFe3O4 -Based All -Oxide Spin Valve. J. Magn. Magn. Mater.  2000 , 211 (1), 3 01–308. \nhttps://doi.org/10.1016/S0304 -8853(99)00751 -9. \n(10)  Gökemeijer, N. J.; Ambrose, T.; Chien, C. L. Long -Range Exchange Bias across a \nSpacer Layer. Phys. Rev. Lett.  1997 , 79 (21), 4270 –4273. \nhttps://doi.org/10.1103/PhysRevLett.79.4270.  \n(11)  Garcia, F.; Sort, J.; Rodmacq, B.; Auffret, S.; Dieny, B. Large Anomalous \nEnhancement of Perpendicular Exchange Bias by Introduction of a Nonmagnetic \nSpacer between the Ferromagnetic and Antiferromagnetic Layers. Appl. Phys. Lett.  \n2003 , 83 (17), 3537 –3539. https:/ /doi.org/10.1063/1.1619562.  \n(12)  Brück, S.; Sort, J.; Baltz, V.; Suriñach, S.; Muñoz, J. S.; Dieny, B.; Baró, M. D.; \nNogués, J. Exploiting Length Scales of Exchange -Bias Systems to Fully Tailor \nDouble -Shifted Hysteresis Loops. Adv. Mater.  2005 , 17 (24), 2 978–2983. \nhttps://doi.org/10.1002/adma.200500544.  \n(13)  Žutić, I.; Fabian, J.; Das Sarma, S. Spintronics: Fundamentals and Applications. Rev. \nMod. Phys.  2004 , 76 (2), 323 –410. https://doi.org/10.1103/RevModPhys.76.323.  \n(14)  Bibes, M.; Barthélémy, A. Oxide Spintronics. IEEE Trans. Electron Devices  2007 , 54 \n(5), 1003 –1023. https://doi.org/10.1109/TED.2007.894366.  \n(15)  Freitas, P. P.; Ferreira, R.; Cardoso, S.; Cardoso, F. Magnetoresistive Sensors. J. \nPhysicsCondensed Matter  2007, 19 (16), 165221. https://doi.org/10.1088/0953 -\n8984/19/16/165221.  \n(16)  Bader, S. D.; Parkin, S. S. P. Spintronics. Annu. Rev. Condens. Matter Phys.  2010 , 1, \n71–88. https://doi.org/10.1146/annurev -conmatphys -070909 -104123.  \n(17)  Lavorato, G.; Lima, E.; Vasquez Mansilla, M.; Troiani, H.; Zysler, R.; Winkler, E. \nBifunctional CoFe 2 O 4 /ZnO Core/Shell Nanoparticles for Magnetic Fluid  29 Hyperthermia with Controlled Optical Response. J. Phys. Chem. C  2018 , 122 (5), \n3047 –3057. https://doi.org/10.1021/acs.jpcc.7 b11115.  \n(18)  Rui, H.; Xing, R.; Xu, Z.; Hou, Y.; Goo, S.; Sun, S. Synthesis, Functionalization, and \nBiomedical Applications of Multifunctional Magnetic Nanoparticles. Adv. Mater.  \n2010 , 22 (25), 2729 –2742. https://doi.org/10.1002/adma.201000260.  \n(19)  Murr ay, C. B.; Kagan, C. R.; Bawendi, M. G. Synthesis and Characterization of \nMonodisperse Nanocrystals and Close -Packed Nanocrystal Assemblies. Annu. Rev. \nMater. Sci.  2000 , 30 (1), 545 –610. https://doi.org/10.1146/annurev.matsci.30.1.545.  \n(20)  López -Ortega, A.; Estrader, M.; Salazar -Alvarez, G.; Roca, A. G.; Nogués, J. \nApplications of Exchange Coupled Bi -Magnetic Hard/Soft and Soft/Hard Magnetic \nCore/Shell Nanoparticles. Phys. Rep.  2015 , 553 (February 2016), 1 –32. \nhttps://doi.org/10.1016/j.physrep.2014.09.007 . \n(21)  Noh, S. H.; Na, W.; Jang, J. T.; Lee, J. H.; Lee, E. J.; Moon, S. H.; Lim, Y.; Shin, J. S.; \nCheon, J. Nanoscale Magnetism Control via Surface and Exchange Anisotropy for \nOptimized Ferrimagnetic Hysteresis. Nano Lett.  2012 , 12 (7), 3716 –3721. \nhttps: //doi.org/10.1021/nl301499u.  \n(22)  Liu, X.; Pichon, B. P.; Ulhaq, C.; Lefèvre, C.; Grenèche, J. -M.; Bégin, D.; Bégin -\nColin, S. Systematic Study of Exchange Coupling in Core –Shell Fe 3−δ O 4 @CoO \nNanoparticles. Chem. Mater.  2015 , 27 (11), 4073 –4081. \nhttps:/ /doi.org/10.1021/acs.chemmater.5b01103.  \n(23)  Baaziz, W.; Pichon, B. P.; Lefevre, C.; Ulhaq -Bouillet, C.; Greneche, J. M.; Toumi, \nM.; Mhiri, T.; Bégin -Colin, S. High Exchange Bias in Fe3 -ΔO4@CoO Core Shell \nNanoparticles Synthesized by a One -Pot Seed -Mediated Growth Method. J. Phys. \nChem. C  2013 , 117 (21), 11436 –11443. https://doi.org/10.1021/jp402823h.  \n(24)  Lavorato, G. C.; Lima Jr, E.; Tobia, D.; Fiorani, D.; Troiani, H. E.; Zysler, R. D.;  30 Winkler, E. L. Size Effects in Bimagnetic CoO/CoFe2O4 Core/Shell Nanoparticles. \nNanotechnology  2014 , 25 (35), 35 5704. https://doi.org/10.1088/0957 -\n4484/25/35/355704.  \n(25)  Lavorato, G. C.; Lima, E.; Troiani, H. E.; Zysler, R. D.; Winkler, E. L. Exchange -\nCoupling in Thermal Annealed Bimagnetic Core/Shell Nanoparticles. J. Alloys \nCompd.  2015 , 633, 333 –337. https://doi .org/10.1016/j.jallcom.2015.02.050.  \n(26)  Lavorato, G. C.; Lima, E.; Troiani, H. E.; Zysler, R. D.; Winkler, E. L. Tuning the \nCoercivity and Exchange Bias by Controlling the Interface Coupling in Bimagnetic \nCore/Shell Nanoparticles. Nanoscale  2017 , 9 (29),  10240 –10247. \nhttps://doi.org/10.1039/c7nr03740f.  \n(27)  Lima, E.; Winkler, E. L.; Tobia, D.; Troiani, H. E.; Zysler, R. D.; Agostinelli, E.; \nFiorani, D. Bimagnetic CoO Core/CoFe 2 O 4 Shell Nanoparticles: Synthesis and \nMagnetic Properties. Chem. Mater.  2012, 24 (3), 512 –516. \nhttps://doi.org/10.1021/cm2028959.  \n(28)  Li, H.; Wang, C.; Li, D.; Homm, P.; Menghini, M.; Locquet, J. -P.; Van Haesendonck, \nC.; Van Bael, M. J.; Ruan, S.; Zeng, Y. -J. Magnetic Orders and Origin of Exchange \nBias in Co Clusters Embedded O xide Nanocomposite Films. J. Phys. Condens. Matter  \n2019 , 31 (15), 155301. https://doi.org/10.1088/1361 -648X/aafff0.  \n(29)  Xing, M.; Mohapatra, J.; Elkins, J.; Guragain, D.; Mishra, S. R.; Ping Liu, J. Exchange \nBias and Verwey Transition in Fe5C2/Fe3O4core/ Shell Nanoparticles. Nanoscale  \n2021 , 13 (37), 15837 –15843. https://doi.org/10.1039/d1nr04520b.  \n(30)  Carnevale, D. J.; Shatruk, M.; Strouse, G. F. Ligand Passivated Core –Shell FePt@Co \nNanomagnets Exhibiting Enhanced Energy Product. Chem. Mater.  2016 , 28 (15), \n5480 –5487. https://doi.org/10.1021/acs.chemmater.6b02062.  \n(31)  Lottini, E.; López -Ortega, A.; Bertoni, G.; Turner, S.; Meledina, M.; Tendeloo, G.  31 Van; De Julián Fernández, C.; Sangregorio, C. Strongly Exchange Coupled Core|Shell \nNanoparticles with Hig h Magnetic Anisotropy: A Strategy toward Rare -Earth -Free \nPermanent Magnets. Chem. Mater.  2016 , 28 (12), 4214 –4222. \nhttps://doi.org/10.1021/acs.chemmater.6b00623.  \n(32)  Lavorato, G. C.; Das, R.; Xing, Y.; Robles, J.; Litterst, F. J.; Baggio -Saitovitch, E.; \nPhan, M. -H.; Srikanth, H. Origin and Shell -Driven Optimization of the Heating Power \nin Core/Shell Bimagnetic Nanoparticles. ACS Appl. Nano Mater.  2020 , 3 (2), 1755 –\n1765. https://doi.org/10.1021/acsanm.9b02449.  \n(33)  Sartori, K.; Cotin, G.; Bouillet, C.; Halté, V.; Bégin -Colin, S.; Choueikani, F.; Pichon, \nB. P. Strong Interfacial Coupling through Exchange Interactions in Soft/Hard Core -\nShell Nanoparticles a s a Function of Cationic Distribution. Nanoscale  2019 , 11 (27), \n12946 –12958. https://doi.org/10.1039/c9nr02323b.  \n(34)  Fabris, F.; Lima, E.; De Biasi, E.; Troiani, H. E.; Vásquez Mansilla, M.; Torres, T. E.; \nFernández Pacheco, R.; Ibarra, M. R.; Goya, G. F .; Zysler, R. D.; Winkler, E. L. \nControlling the Dominant Magnetic Relaxation Mechanisms for Magnetic \nHyperthermia in Bimagnetic Core -Shell Nanoparticles. Nanoscale  2019 , 11 (7), 3164 –\n3172. https://doi.org/10.1039/c8nr07834c.  \n(35)  Fabris, F.; Lohr, J.; Li ma, E.; de Almeida, A. A.; Troiani, H. E.; Rodríguez, L. M.; \nVásquez Mansilla, M.; Aguirre, M. H.; Goya, G. F.; Rinaldi, D.; Ghirri, A.; Peddis, D.; \nFiorani, D.; Zysler, R. D.; De Biasi, E.; Winkler, E. L. Adjusting the Néel Relaxation \nTime of Fe 3 O 4 /Zn  x Co 1− x Fe 2 O 4 Core/Shell Nanoparticles for Optimal Heat \nGeneration in Magnetic Hyperthermia. Nanotechnology  2021 , 32 (6), 065703. \nhttps://doi.org/10.1088/1361 -6528/abc386.  \n(36)  Fabris, F.; Lima, E.; Quinteros, C.; Neñer, L.; Granada, M.; Sirena, M.;  Zysler, R. D.; \nTroiani, H. E.; Leborán, V.; Rivadulla, F.; Winkler, E. L. Tunnel Magnetoresistance in  32 Self-Assemblies of Exchange -Coupled Core/Shell Nanoparticles. Phys. Rev. Appl.  \n2019 , 11 (5), 054089. https://doi.org/10.1103/PhysRevApplied.11.054089.  \n(37)  Jiang, C.; Chan, P. H.; Leung, C. W.; Pong, P. W. T. CoFe2O4Nanoparticle -Integrated \nSpin-Valve Thin Films Prepared by Interfacial Self -Assembly. J. Phys. Chem. C  2017 , \n121 (40), 22508 –22516. https://doi.org/10.1021/acs.jpcc.7b07242.  \n(38)  Anil Kumar, P .; Ray, S.; Chakraverty, S.; Sarma, D. D. Engineered Spin -Valve Type \nMagnetoresistance in Fe3O 4 -CoFe2O4 Core -Shell Nanoparticles. Appl. Phys. Lett.  \n2013 , 103 (10). https://doi.org/10.1063/1.4819956.  \n(39)  Datt, G.; Kotnana, G.; Maddu, R.; Vallin, Ö.; Josh i, D. C.; Peddis, D.; Barucca, G.; \nKamalakar, M. V.; Sarkar, T. Combined Bottom -Up and Top -Down Approach for \nHighly Ordered One -Dimensional Composite Nanostructures for Spin Insulatronics. \nACS Appl. Mater. Interfaces  2021 , 13 (31), 37500 –37509. \nhttps://doi .org/10.1021/acsami.1c09582.  \n(40)  Zhou, B. H.; Rinehart, J. D. Pseudo Spin Valve Behavior in Colloidally Prepared \nNanoparticle Films. ACS Appl. Electron. Mater.  2019 , 1 (7), 1065 –1069. \nhttps://doi.org/10.1021/acsaelm.9b00196.  \n(41)  Jiang, C.; Ng, S. M.; L eung, C. W.; Pong, P. W. T. Magnetically Assembled Iron \nOxide Nanoparticle Coatings and Their Integration with Pseudo -Spin-Valve Thin \nFilms. J. Mater. Chem. C  2017 , 5 (2), 252 –263. https://doi.org/10.1039/C6TC03918A.  \n(42)  Fabris, F.; Lima, E.; De Biasi, E .; Troiani, H. E.; Vásquez Mansilla, M.; Torres, T. E.; \nFernández Pacheco, R.; Ibarra, M. R.; Goya, G. F.; Zysler, R. D.; Winkler, E. L. \nControlling the Dominant Magnetic Relaxation Mechanisms for Magnetic \nHyperthermia in Bimagnetic Core –Shell Nanoparticle s. Nanoscale  2019 , 11 (7), 3164 –\n3172. https://doi.org/10.1039/C8NR07834C.  \n(43)  Lee, J. H.; Jang, J. T.; Choi, J. S.; Moon, S. H.; Noh, S. H.; Kim, J. W.; Kim, J. G.;  33 Kim, I. S.; Park, K. I.; Cheon, J. Exchange -Coupled Magnetic Nanoparticles for \nEfficient Heat Induction. Nat. Nanotechnol.  2011 , 6 (7), 418 –422. \nhttps://doi.org/10.1038/nnano.2011.95.  \n(44)  Sartori, K.; Choueikani, F.; Gloter, A.; Begin -Colin, S.; Taverna,  D.; Pichon, B. P. \nRoom Temperature Blocked Magnetic Nanoparticles Based on Ferrite Promoted by a \nThree -Step Thermal Decomposition Process. J. Am. Chem. Soc.  2019 , 141 (25), 9783 –\n9787. https://doi.org/10.1021/jacs.9b03965.  \n(45)  Krycka, K. L.; Borchers, J.  A.; Laver, M.; Salazar -Alvarez, G.; López -Ortega, A.; \nEstrader, M.; Suriñach, S.; Baró, M. D.; Sort, J.; Nogoués, J. Correlating Material -\nSpecific Layers and Magnetic Distributions within Onion -like Fe3O4/MnO/γ Mn2O3 \nCore/Shell Nanoparticles. J. Appl. Phy s. 2013 , 113 (17), 5 –8. \nhttps://doi.org/10.1063/1.4801423.  \n(46)  Salazar -Alvarez, G.; Lidbaum, H.; López -Ortega, A.; Estrader, M.; Leifer, K.; Sort, J.; \nSuriñach, S.; Baró, M. D.; Nogués, J. Two -, Three -, and Four -Component Magnetic \nMultilayer Onion Nanopa rticles Based on Iron Oxides and Manganese Oxides. J. Am. \nChem. Soc.  2011 , 133 (42), 16738 –16741. https://doi.org/10.1021/ja205810t.  \n(47)  Hettler, S.; Bencok, P.; Sartori, K.; Musat, A.; Choueikani, F.; Grene, J.; Begin -colin, \nS.; Steadman, P.; Arenal, R. ; Pichon, B. P. A Detailed Investigation of the Onion \nStructure of Exchanged Coupled Magnetic Fe 3 −. 2021 . \nhttps://doi.org/10.1021/acsami.0c18310.  \n(48)  Gavrilov -Isaac, V.; Neveu, S.; Dupuis, V.; Taverna, D.; Gloter, A.; Cabuil, V. \nSynthesis of Trimagneti c Multishell MnFe 2 O 4 @CoFe 2 O 4 @NiFe 2 O 4 \nNanoparticles. Small  2015 , 11 (22), 2614 –2618. \nhttps://doi.org/10.1002/smll.201402845.  \n(49)  Sun, S.; Zeng, H. Size -Controlled Synthesis of Magnetite Nanoparticles. 2002 , No. 31,  34 8204 –8205.  \n(50)  Zhang, Z.; L u, X.; Yan, Y.; Lu, J.; Li, Z.; Liu, Q.; Zhu, F.; Cao, J.; Wang, Y.; Huang, \nZ.; Zhai, Y.; Li, Y.; Ruan, X.; He, L.; Wu, J.; Du, J.; Zhang, R.; Xu, Y. Direct \nObservation of Spin Polarization in Epitaxial Fe 3 O 4 (001)/MgO Thin Films Grown \nby Magnetron Sput tering. Appl. Phys. Lett.  2022 , 120 (18), 182403. \nhttps://doi.org/10.1063/5.0091241.  \n(51)  Yamashita, S.; Kikkawa, J.; Yanagisawa, K.; Nagai, T.; Ishizuka, K.; Kimoto, K. \nAtomic Number Dependence of Z Contrast in Scanning Transmission Electron \nMicroscopy. Sci. Rep.  2018 , 8 (1), 1 –7. https://doi.org/10.1038/s41598 -018-30941 -5. \n(52)  Jones, L.; Macarthur, K. E.; Fauske, V. T.; Van Helvoort, A. T. J.; Nellist, P. D. Rapid \nEstimation of Catalyst Nanoparticle Morphology and Atomic -Coordination by High -\nResolution  Z-Contrast Electron Microscopy. Nano Lett.  2014 , 14 (11), 6336 –6341. \nhttps://doi.org/10.1021/nl502762m.  \n(53)  Resende, P. M.; Gutiérrez -Fernández, E.; Aguirre, M. H.; Nogales, A.; Martín -\nGonzález, M. Polyethylene Three -Dimensional Nano -Networks: How Later al Chains \nAffect Metamaterial Formation. Polymer (Guildf).  2021 , 212 (June 2020). \nhttps://doi.org/10.1016/j.polymer.2020.123145.  \n(54)  Ewels, P.; Sikora, T.; Serin, V.; Ewels, C. P.; Lajaunie, L. A Complete Overhaul of the \nElectron Energy -Loss Spectroscopy and X -Ray Absorption Spectroscopy Database: \nEelsdb.Eu. Microsc. Microanal.  2016 , 22 (3), 717 –724. \nhttps://doi.org/10.1017/S14319276160 00179.  \n(55)  Torruella, P.; Arenal, R.; De La Peña, F.; Saghi, Z.; Yedra, L.; Eljarrat, A.; López -\nConesa, L.; Estrader, M.; López -Ortega, A.; Salazar -Alvarez, G.; Nogués, J.; Ducati, \nC.; Midgley, P. A.; Peiró, F.; Estradé, S. 3D Visualization of the Iron O xidation State \nin FeO/Fe3O4 Core -Shell Nanocubes from Electron Energy Loss Tomography. Nano  35 Lett. 2016 , 16 (8), 5068 –5073. https://doi.org/10.1021/acs.nanolett.6b01922.  \n(56)  Garnero, C.; Lepesant, M.; Garcia -Marcelot, C.; Shin, Y.; Meny, C.; Farger, P.; W arot-\nFonrose, B.; Arenal, R.; Viau, G.; Soulantica, K.; Fau, P.; Poveda, P.; Lacroix, L. M.; \nChaudret, B. Chemical Ordering in Bimetallic FeCo Nanoparticles: From a Direct \nChemical Synthesis to Application as Efficient High -Frequency Magnetic Material. \nNano Lett.  2019 , 19 (2), 1379 –1386. https://doi.org/10.1021/acs.nanolett.8b05083.  \n(57)  Bertoni, G.; Verbeeck, J. Accuracy and Precision in Model Based EELS \nQuantification. Ultramicroscopy  2008 , 108 (8), 782 –790. \nhttps://doi.org/10.1016/j.ultramic.2008.01.004 . \n(58)  Francombe, M.; Hoffman, R. W. Physics of Thin Films. Advances in Research and \nDevelopment ; 1971; Vol. 6.  \n(59)  Dormann, J. L.; Fiorani, D.; Tronc, E. Advances in Chemical Physics ; Prigogine, I., \nStuart, A. R., Eds.; JOHN WILEY & SONS, INC., 1997; Vol. XCVIII.  \n(60)  W. H. Meiklejohn and C. P. Bean. New Magnetic Anisotropy. Phys. Rev. Lett.  1957 , \n105 (5), 904 –913. https://doi.org/10.1103/PhysRev.105.904.  \n(61)  Lavorato, G.; Winkler, E.; Ghirri, A.; Lima, E.; Peddis, D.; Troiani, H. E.; Fiorani, D.; \nAgostinelli, E.; Rinaldi, D.; Zysler, R. D. Exchange Bias and Surface Effects in \nBimagnetic CoO -Core/Co0.5Ni0.5Fe2O4 -Shell Nanoparticles. Phys. Rev. B  2016 , 94 \n(5), 054432. https://doi.org/10.1103/PhysRevB.94.054432.  \n(62)  Peddis, D.; Cannas, C.; Piccaluga,  G.; Agostinelli, E.; Fiorani, D. Spin -Glass -like \nFreezing and Enhanced Magnetization in Ultra -Small CoFe2O4 Nanoparticles. \nNanotechnology  2010 , 21 (12), 125705.  \n(63)  Martínez, B.; Obradors, X.; Balcells, L.; Rouanet, A.; Monty, C. Low Temperature \nSurface  Spin-Glass Transition in γ -Fe2O3 Nanoparticles. Phys. Rev. Lett.  1998 , 80 (1), \n181–184. https://doi.org/10.1103/PhysRevLett.80.181.   36 (64)  Winkler, E.; Zysler, R. D.; Vasquez Mansilla, M.; Fiorani, D.; Rinaldi, D.; Vasilakaki, \nM.; Trohidou, K. N. Surface Spin -Glass Freezing in Interacting Core -Shell NiO \nNanoparticles. Nanotechnology  2008 , 19, 185702. https://doi.org/10.1088/0957 -\n4484/19/18/18 5702.  \n(65)  Rinaldi -Montes, N.; Gorria, P.; Fuertes, A. B.; Martínez -Blanco, D.; Amghouz, Z.; \nPuente -Orench, I.; Olivi, L.; Herrero -Martín, J.; Fernandez -Garcia, M. P.; Alonso, J.; \nPhan, M. -H.; Srikanth, H.; Marti, X.; Blanco, J. A. Entangled Core/Shell Ma gnetic \nStructure Driven by Surface Magnetic Symmetry -Breaking in Cr 2 O 3 Nanoparticles. \nJ. Mater. Chem. C  2022 , 10 (5), 1798 –1807. https://doi.org/10.1039/D1TC04947J.  \n(66)  Zhan, X.; Mao, Z.; Chen, X. Exchange Bias and Coercivity for Ferromagnets Coupled \nto the Domain State and Spin Glass State. J. Phys. D. Appl. Phys.  185002 , 185002. \nhttps://doi.org/10.1088/0022 -3727/49/18/185002.  \n(67)  Lima Jr, E.; Vargas, J. M.; Zysler, R. D.; Rechenberg, H. R.; Cohen, R.; Arbiol, J.; \nGoya, G. F.; Ibarra, A.; Ibarra, M.  R. Single -Step Chemical Synthesis of Ferrite \nHollow Nanospheres. Nanotechnology  2009 , 20 (4), 045606. \nhttps://doi.org/10.1088/0957 -4484/20/4/045606.  \n(68)  De Biasi, E.; Lima, E.; Vargas, J. M.; Zysler, R. D.; Arbiol, J.; Ibarra, A.; Goya, G. F.; \nIbarra, M . R. Exchange Bias in Ferrite Hollow Nanoparticles Originated by Complex \nInternal Magnetic Structure. Mater. Res. Express  2015 , 2 (10). \nhttps://doi.org/10.1088/2053 -1591/2/10/105001.  \n(69)  Khurshid, H.; Chandra, S.; Li, W.; Phan, M. H.; Hadjipanayis, G. C. ; Mukherjee, P.; \nSrikanth, H. Synthesis and Magnetic Properties of Core/Shell FeO/Fe 3 O 4 Nano -\nOctopods. J. Appl. Phys.  2013 , 113 (17), 17B508. https://doi.org/10.1063/1.4794978.  \n(70)  VERWEY, E. J. W. Electronic Conduction of Magnetite (Fe3O4) and Its Tr ansition \nPoint at Low Temperatures. Nature  1939 , 144 (3642), 327 –328.  37 https://doi.org/10.1038/144327b0.  \n(71)  Lima, E.; E. S. Brito, G.; Cavelius, C.; Sivakov, V.; Shen, H.; Mathur, S.; F. Goya, G. \nInfluence of the Substrate and Precursor on the Magnetic a nd Magneto -Transport \nProperties in Magnetite Films. Curr. Nanosci.  2012 , 8 (5), 659 –668. \nhttps://doi.org/10.2174/157341312802884544.  \n(72)  Lavorato, G. C.; Rubert, A. A.; Xing, Y.; Das, R.; Robles, J.; Litterst, F. J.; Baggio -\nSaitovitch, E.; Phan, M.; Srik anth, H.; Vericat, C.; Fonticelli, M. H. Shell -Mediated \nControl of Surface Chemistry of Highly Stoichiometric Magnetite Nanoparticles. \nNanoscale  2020 , 12 (25), 13626 –13636. https://doi.org/10.1039/D0NR02069A.  \n(73)  Lee, J.; Kwon, S. G.; Park, J. G.; Hyeon,  T. Size Dependence of Metal -Insulator \nTransition in Stoichiometric Fe3O4 Nanocrystals. Nano Lett.  2015 , 15 (7), 4337 –4342. \nhttps://doi.org/10.1021/acs.nanolett.5b00331.  \n(74)  Santoyo Salazar, J.; Perez, L.; De Abril, O.; Truong Phuoc, L.; Ihiawakrim, D.; \nVazquez, M.; Greneche, J. M.; Begin -Colin, S.; Pourroy, G. Magnetic Iron Oxide \nNanoparticles in 10 -40 Nm Range: Composition in Terms of Magnetite/Maghemite \nRatio and Effect on the Magnetic Properties. Chem. Mater.  2011 , 23 (6), 1379 –1386. \nhttps://doi.org/10.1021/cm103188a.  \n(75)  Salamon, M. B. The Spin -Glass Transition in Three Dimensions: Is It Understood? J. \nAppl. Phys.  1987 , 61 (8), 4228 –4231. https://doi.org/10.1063/1.338483 . \n(76)  Paulsen, C.; Hamida, J. A.; Williamson, S. J.; Maletta, H. Threshold Field for the de \nAlmeida –Thouless Transition Line in Eu 0.4 Sr 0.6 S Spin Glass. J. Appl. Phys.  1984 , \n55 (6), 1652 –1654. https://doi.org/10.1063/1.333431.  \n(77)  Brown, W. F. Therm al Fluctuations of a Single -Domain Particle. Phys. Rev.  1963 , 130 \n(5), 1677 –1686. https://doi.org/10.1103/PhysRev.130.1677.  \n(78)  Dormann, J. L.; Fiorani, D.; El Yamani, M. Field Dependence of the Blocking  38 Temperature in the Superparamagnetic Model: Coinci dence. Phys. Lett. A  1987 , 120 \n(2), 95 –99. https://doi.org/10.1016/0375 -9601(87)90085 -5. \n(79)  Garc, P.; Gonz, M. A.; Prieto, Á. A.; Garitaonandia, J. S.; Piñeiro, Y.; Rivas, J. \nSignificant Surface Spin Effects and Exchange Bias in Iron Oxide -Based Hollow \nMagnetic Nanoparticles. 2022 . \n(80)  Khurshid, H.; Lampen -Kelley, P.; Iglesias, Ò.; Alonso, J.; Phan, M. -H.; Sun, C.; \nSaboungi, M.; Srikanth, H. Spin -Glass -like Freezing of Inner and Outer Surface \nLayers in Hollow γ -Fe2O3 Nanoparticles. Sci. Rep.  2015 , 5 (1), 15054. \nhttps://doi.org/10.1038/srep15054.  \n(81)  Khurshid, H.; Li, W.; Phan, M. -H.; Mukherjee, P.; Hadjipanayis, G. C.; Srikanth, H. \nSurface Spin Disorder and Exchange -Bias in Hollow Maghemite Nanoparticles. Appl. \nPhys. Lett.  2012 , 101 (2), 022403. https ://doi.org/10.1063/1.4733621.  \n(82)  Rinaldi -Montes, N.; Gorria, P.; Martínez -Blanco, D.; Fuertes, A. B.; Barquín, L. F.; \nPuente -Orench, I.; Blanco, J. A. Scrutinizing the Role of Size Reduction on the \nExchange Bias and Dynamic Magnetic Behavior in NiO Nano particles. \nNanotechnology  2015 , 26 (30), 305705. https://doi.org/10.1088/0957 -\n4484/26/30/305705.  \n(83)  Peddis, D.; Cannas, C.; Piccaluga, G.; Agostinelli, E.; Fiorani, D. Spin -Glass -like \nFreezing and Enhanced Magnetization in Ultra -Small CoFe2O4 Nanopartic les. \nNanotechnology  2010 , 21 (12). https://doi.org/10.1088/0957 -4484/21/12/125705.  \n(84)  Zysler, R. D.; Winkler, E.; Vasquez Mansilla, M.; Fiorani, D. Surface Effect in the \nMagnetic Order of Antiferromagnetic Nanoparticles. Phys. B Condens. Matter  2006 , \n384 (1–2), 277 –281. https://doi.org/10.1016/j.physb.2006.06.010.  \n(85)  Süllow, S.; Nieuwenhuys, G. J.; Menovsky, A. A.; Mydosh, J. A.; Mentink, S. A. M.; \nMason, T. E.; Buyers, W. J. L. Spin Glass Behavior in URh2Ge2. Phys. Rev. Lett.   39 1997 , 78 (2), 354 –357. https://doi.org/10.1103/PhysRevLett.78.354.  \n(86)  Bhowmik, R. N.; Poddar, A.; Ranganathan, R.; Mazumdar, C. Magnetism of \nCrystalline and Amorphous La0.67 Ca0.33 MnO3 Nanoparticles. J. Appl. Phys.  2009 , \n105 (11), 0 –11. https://doi.org/10.1063/1.3138814.  \n(87)  Winkler, E.; Zysler, R. D.; Vasquez Mansilla, M.; Fiorani, D.; Rinaldi, D.; Vasilakaki, \nM.; Trohidou, K. N. Surface Spin -Glass Freezing in Interacting Core -Shell NiO \nNanoparticles. Nanotechnology  2008 , 19 (18), 185702. https://doi.org/10.1088/0957 -\n4484 /19/18/185702.  \n(88)  Liao, X.; Ulusoy, S.; Huang, R.; Wetterskog, E.; Gunnarsson, K.; Wang, Y.; Liang, H.; \nZeng, Y. J.; Salazar -Alvarez, G.; Svedlindh, P. Low -Field -Induced Spin -Glass \nBehavior and Controllable Anisotropy in Nanoparticle Assemblies at a Liq uid-Air \nInterface. Sci. China Mater.  2022 , 65 (1), 193 –200. https://doi.org/10.1007/s40843 -\n021-1720 -7. \n \n   40 Table of Contents Entry  \n \n \n \nNanoparticles with onion -like architecture offer a unique opportunity to modulate the \ncoupling between magnetic phases by introducing spacers in the same structure. \nFe3O4/MgO/CoFe 2O4 shows enhanced coercivity due to the coupling between the FiM phases \nand exchange bias field originates from the freezing of the surface spins below the freezing \ntemperature .  \n \n \n"    },    {        "title": "1103.2939v1.Oxygen_hyperstoichiometric_hexagonal_ferrite_CaBaFe4O7_δ_δ__approx_0_14____coexistence_of_ferrimagnetism_and_spin_glass_behavior.pdf",        "content": "1/23  \n \n \nOxygen hyperstoichiometric  hexagonal ferrite CaBaFe 4O7+ (  0.14)  : \ncoexistence of ferrimagnetism and spin glass behaviour  \n \n \nTapati Sarkar *, V. Duffort, V. Pralong, V. Caignaert and B. Raveau  \n \nLaboratoire CRISMAT, UMR 6508 CNRS ENSICAEN,  \n6 bd Maréchal Juin, 14050 CAEN, France  \nAbstract  \n \n An oxygen hyperstoichiometric ferrite CaBaFe 4O7+ (  0.14) has been \nsynthesized using “soft” reduction of CaBaFe 4O8. Like the oxygen stoichiometric \nferrimagnet CaBaFe 4O7, this oxide also keeps the hexagonal symmetry (space group: \nP63mc), and exhibits the same high Curie temperature of 270 K. However, the \nintroduction of extra oxygen into the system weakens the ferrimagnetic interaction \nsignificantly at the cost of increased magnetic frustration at low tempera ture. Moreover, \nthis canonical spin glass (T g ~ 166 K) exhibits an intriguing cross -over from de Almeida -\nThouless type to Gabay -Toulouse type critical line in the field temperature plane above a \ncertain field strength, which can be identified as the anisot ropy field. Domain wall \npinning is also observed below 110 K. These results are interpreted on the basis of \ncationic disordering on the iron sites.  \n \n \n \n \n \n \n \nPACS number: 75.47.Lx  \n \nKeywords  : “114” ferrites, ferrimagnetism and magnetic frustration, spin glass  Ising -\nHeisenberg competition, magnetic anisotropy, domain wall pinning.  \n \n * Corresponding author: Tapati Sarkar  \ne-mail: tapati.sarkar @ensicaen.fr  2/23  Introduction  \n \nThe recent discovery of the new series of “114” oxides, (the cobaltites – \n(Ln,Ca) 1BaCo 4O7 [1 – 8] and the ferrites – (Ln,Ca) 1BaFe 4O7 [9 – 11]) have opened up a \nnew field for the investigation of strongly correlated electron systems. These oxides \nconsist of CoO 4 (or FeO 4) tetrahedra sitting in alternating layers of kagomé and triangular \narrays [10].  The structure can also be described as the stacking of close -packed [BaO 3] \nand [O 4] layers whose tetrahedral cavities are occupied by Co2+/Co3+ (or Fe2+/Fe3+) \nspecies, forming triangular and kagomé layers of CoO 4 (or FeO 4) tetrahedra. This \nstructure has  been primarily responsible for the wide variety of magnetic states that has \nbeen observed in this group of oxides, ranging from a spin glass for cubic LnBaFe 4O7 [9, \n10] to a ferrimagnet for orthorhombic CaBaCo 4O7 [5] and hexagonal CaBaFe 4O7 [9] \noxides.  \nRecent studies of the “114” cobaltites [12 – 17] have revealed the existence of \nclosely related structures with various crystallographic symmetries, and possibility of \noxygen non -stoichiometry in the range “O 7” to “O 8.5” in those systems. This change of \noxygen stoichiometry, which induces the variation of Co2+:Co3+ ratio in the system, is \nexpected to influence the physical properties of these compounds considerably. This is \nthe case of the oxygen rich “114” cobaltites YBaCo 4O8.1 [15] and YbBaCo 4O7.2 [17], \nwhich were shown to be magnetically frustrated rather than magnetically ordered at low \ntemperatures.  \nIn contrast to the cobalt oxides, no report of oxygen hyperstoichiometric “114” \nferrites exists till date, probably due to the fact that Fe2+ gets too easily  oxidized into Fe3+, \nthereby destabilizing the “114” structure at the benefit of pure “Fe3+” oxides. We have, \nthus, investigated the possibility to stabilize the mixed valence Fe2+/Fe3+ in the “114” \noxygen hyperstoichiometric CaBaFe 4O7+ ferrite by reducin g the fully oxidized \ncompound CaBaFe 4O8 [18] at low temperature in an argon -hydrogen atmosphere.  We \nreport herein on the magnetic properties of the “114” oxygen hyperstoichiometric \nCaBaFe 4O7.14 hexagonal ferrite. We show that, like the stoichiometric phas e CaBaFe 4O7, \nthis oxide also exhibits ferrimagnetism with a T C of 270 K, but that the competition \nbetween ferrimagnetism and magnetic frustration is much more pronounced than for the \nstoichiometric phase, as seen from the decrease of the magnetization . Mor e importantly, \nwe observe that CaBaFe 4O7.14 is characterized by a canonical spin glass behaviour with 3/23 Tg  166 K, and an intriguing cross -over from an Ising to a Heisenberg spin glass type \nbehaviour in the external magnetic field at low temperature. Beside s this competition \nbetween ferrimagnetism and spin glass  behaviour , one also observes domain wall pinning \nbelow 110 K. This very different magnetic behaviour of CaBaFe 4O7.14 is explained in \nterms of cationic deficiency and disordering on the iron sites, th e “barium -oxygen” \nhexagonal close packing remaining  untouched.  \n \nExperimental  \n \nThe precursor CaBaFe 4O8 [18] was prepared by the sol gel method. Stoichiometric \namounts of calcium carbonate (Prolabo, 99%) and barium carbonate (Alfa Aesar, 99%) \nwere dissolved in a large excess of melted citric acid monohydrate at ~ 200°C. Iron \ncitrate  (Alfa Aesar, 20% of Fe)  was separately dissolved in hot water leading to a dark \nbrown solution which was poured on the citrate mixture. The water was then evaporated \nfollowed by d ecomposition of the gel. The gel was calcined at 450 °C under air to obtain \nan amorphous precursor, which was then pressed into pellets before firing at 1200 °C to \nobtain CaBaFe 4O8.  \nThe oxygen hyperstoichiometric “114” ferrite, CaBaFe 4O7+ was then obtain ed by \nreducing CaBaFe 4O8 under an Ar/H 2 10% mix at 610 °C for 24  hrs. \nThe oxygen content of the sample was determined by redox titration. The sample \nwas dissolved in hot HCl (3M) flushed with argon to remove the dissolved oxygen. After \ncooling down the sol ution, Fe2+ cations were titrated using 2  10-2 M cerium(IV) sulfate \n(Riedel -de Haën) and 1.10 -phenantroline iron(II) sulfate (Alfa Aesar) as an indica tor \nunder constant argon flow . We obtained  = 0.14.  \nThe X -ray diffraction patterns were registered wit h a Panalytical X’Pert Pro \ndiffractometer under a continuous scanning mode in the 2  range 10° - 120° and step size \n2=0.017°. The d.c. magnetization measurements were performed using a \nsuperconducting quantum interference device (SQUID) magnetometer with  variable \ntemperature cryostat (Quantum Design, San Diego, USA). The a.c. susceptibility, ac(T) \nwas measured with a Physical Property Measurement System ( PPMS ) from Quantum \nDesign with the frequency ranging from 10 Hz to 10 kHz (H dc = 0 Oe and H ac = 10 Oe ). \nAll the magnetic properties were registered on dense ceramic bars of dimensions ~ 4  2  \n2 mm3. \n 4/23  \nResults and discussion  \n \nStructural Characterization  \n \nThe X -ray diffraction pattern (Fig. 1) revealed that CaBaFe 4O7.14 stabilized in the \nsame hexagonal sy mmetry (space group: P63mc) as the “O 7” phase [9]. The Rietveld \nanalysis from the XRD data was done using the FULLPROF refinement program [19]. \nThe fit is also shown in Fig. 1 (red curve). The bottom blue curve corresponds to the \ndifference between the obs erved and calculated diffraction patterns. Satisfactory \nmatching of the experimental  data with the calculated profile of the XRD pattern and the \ncorresponding reliability factors RF = 3.88 % and RBragg = 5.01 % confirm that the fit \nobtained is reasonably a ccurate. The extracted lattice parameters ( a = 6.355 Å, c = 10.372 \nÅ) show a very marginal increase over the “O 7” phase – a increases by ~ 0.11 % while c \nremains virtually unchanged. The refinements of the atomic coordinates, thus, lead to \nresults similar to those previously obtained for CaBaFe 4O7 [9]. The low  value and the \nlow scattering factor of oxygen do not allow any oxygen excess or cationic deficiency to \nbe detected from X -ray powder diffraction data. A very careful neutron diffraction study \nmight perhaps allow the issue to be sorted out, but will really be at the limit of accuracy, \nand consequently, is not within the scope of this paper.  \n \nD. C. magnetization study  \n \nIn Fig. 2, we show the Zero Field Cooled (ZFC) and Field Cooled (FC) \nmagnetization o f CaBaFe 4O7+ recorded under a magnetizing field of 0.3 T. The sample \nshows the same increase in magnetization below ~ 270 K as the oxygen stoichiometric \noxide indicating a similar transition to an ordered magnetic state below 270 K. However, \na careful loo k at the magnetization values reached at the lowermost measured \ntemperature (5 K) immediately reveals a striking difference in the magnetic behaviour of \nCaBaFe 4O7.14 vis – à – vis that of CaBaFe 4O7. While the F.C. magnetization of the \noxygen stoichiometric  compound reaches a value of more than 2.5 µ B/f.u. at T = 5 K, the \nmaximum magnetization value of our oxygen rich sample is only 0.93 µ B/f.u., which is \nless by more than a factor of ½.  \nThis large difference in the magnetization value at low temperature be tween the \ntwo samples (  = 0 and  > 0) prompted us to record the hysteresis curve of our oxygen 5/23 rich sample at low temperature (T = 5 K) and compare it with that of the oxygen \nstoichiometric sample. This is shown in Fig. 3. The magnetization value obtaine d at the \nhighest measuring field of 5 T (2.5 µ B/f.u.) is again different from the oxygen \nstoichiometric sample (3.1 µ B/f.u.), as expected. More importantly, a rather striking \ndifference is seen in the shape of the hysteresis loop. The coercive field (H C) and \nremanent magnetization (M r) of our sample at T = 5 K are 0.77 T and 0.63 µ B/f.u. \nrespectively. While the value of the coercive field compares well with that of the oxygen \nstoichiometric sample, the value of the remanent magnetization is much lower than that \nobtained for CaBaFe 4O7 (M r ~ 1.8 µ B/f.u.). This results in the overall shape of the \nhysteresis loop of our sample (Fig. 3) to be very different from that of the oxygen \nstoichiometric sample (inset of Fig. 3). The degree of magnetic saturation in a sam ple can \nbe roughly quantified from the M -H loop by calculating \n5\nrM H T\nM . While the \noxygen stoichiometric sample had  = 1.7, our oxygen rich sample yields  = 4.0. This \nhigher value of  for the oxygen rich sample indicates an increased lack  of magnetic \nsaturation in the sample, or in other words, a weakening of long range order.  \nAnother important difference with the oxygen stoichiometric sample is in the \nvirgin curve of the M(H) loop. While the virgin curve of the  = 0 sample lies entirely \nwithin the main loop, our oxygen rich sample shows an unusual magnetic behaviour \nwhere a major portion of the virgin curve lies outside the hysteresis loop and meets the \nmain loop only at very high fields.  \n \nA. C. magnetic susceptibility study  \n \nThe tempera ture dependence of the a.c. susceptibility of CaBaFe 4O7.14 in the \ntemperature range 20 K – 280 K and at 4 measuring frequencies ranging from 10 Hz to \n10 kHz is shown in Fig. 4. The sample shows several interesting features which we will \nnow proceed to disc uss separately:  \n(a) At T = 272 K, one can see a sharp peak which is frequency independent i.e. the \nposition of the peak maximum does not shift with a change in the measuring \nfrequency. This peak corresponds to the paramagnetic to ferrimagnetic (PM -FM) \ntransiti on occurring in the sample as it is cooled below 272 K. We note here that \nthe oxygen stoichiometric sample also showed a similar peak at around the same 6/23 temperature. However, in the latter sample, the peak corresponding to the PM -FM \ntransition was the stro ngest (maximum amplitude) compared to the other peaks. In \nour sample, this peak is much smaller in magnitude which corresponds to a \nsignificant weakening of the magnetic ordering (or a smaller volume fraction of \nferrimagnetic domains) which we had mentione d earlier in connection with the \nM(H) loop.  \n(b) The oxide CaBaFe 4O7.14 shows a broader peak at lower temperature (~ 166 K) \nwhich shows pronounced frequency dependence. The peak temperature shifts from \n166 K (for a measuring frequency of 10 Hz) to 176 K (for a  measuring frequency \nof 10 kHz). This corresponds to a peak shift of 0.02 per decade of frequency shift \n(\nlogf\nfT\nTpf\n = 0.02). This value of the parameter p lies within the range for \ncanonical spin glasses, which indicates that this peak is a sig nature of the sample \nundergoing a spin glass transition. We confirm this by analyzing the frequency \ndependence of this peak using the power law form \n0z\nf SG\nSGTT\nT\n\n , where, 0 is \nthe shortest relaxation time available to the system, TSG is the unde rlying spin -\nglass transition temperature determined by the interactions in the system, z is the \ndynamic critical exponent and  is the critical exponent of the correlation length. \nThe actual fittings were done using the equivalent form of the power law: \n\n\n\n\nSGSG f\nTT Tzln ln ln0\n. The fit parameters ( 0 = 7.3  10-10 sec, z = 5.01 and \nTSG = 162.2 K) give a good linear fit (as can be seen in the inset of Fig. 4), and \nconfirms that this peak does correspond to a spin glass transition in the sample. \nWhether the magnetic order disappears in the spin glass phase is not clear at the \nmoment. Our data shows that the spin glass transition occurs within the \nferrimagnetically ordered phase. Whether this transition is accompanied by the \ndestruction of ferrimagnetic long r ange order is an open issue as of now. The \npossibility of coexistence of ferrimagnetic and spin glass orders cannot, however, \nbe ruled out.  7/23 (c) At a lower temperature of ~ 110 K a very broad peak is seen (which broadens out \nto almost kind of a shoulder at lowe r measuring frequency). We will come back to \nthe nature of this feature in the following section.  \n \nMagnetic field dependence of the spin glass freezing temperature  \n \nIn Fig. 5, a.c. susceptibility at 10 kHz driving frequency is plotted as a function of \ntemp erature for different external magnetic fields H dc ranging from 0 to 0.3 T. As can be \nseen from the figure, χ' is suppressed by the magnetic field. First, we focus our discussion \non the evolution of the spin glass freezing temperature (marked by a black ar row in the \nfigure), which occurs at ~ 176 K at the lowest applied field. This peak temperature shows \na continual shift towards lower temperature as the external magnetic field is increased, \nand reaches a value of 155 K at an external magnetic field of 0.3 T. Concomitantly, the \npeak amplitude keeps decreasing as the external magnetic field is increased from 0 to 0.3 \nT. A further increase of the external magnetic field should eventually suppress the spin \nglass transition completely.  \n The purpose of exploring  how the freezing temperature responds to external \nmagnetic field is to check the stability of the spin glass system. This is done by \nexamining the field versus temperature phase diagram obtained from the a.c. \nsusceptibility measurement as shown in Fig. 6.  As was mentioned above, the spin glass \nfreezing temperature is suppressed by increasing the external magnetic field.  \n From a theoretical perspective, de Almeida and Thouless [20] studied the Ising \nspin glass system, and predicted that the spin freezing te mperature ( Tg) depends on H. In \nthe low H range, Tg follows the so -called de Almeida -Thouless (AT) line, expressed as  \n\n23\n001\n\n\n\n\n\ngg\nTHTH H\n. In addition, Gabay and Toulouse [21] investigated the H \ndependence of the spin freezing temperature for the Heise nberg spin glass system. This \nled to the so -called Gabay -Toulouse (GT) line, expressed as  \n\n21\n001\n\n\n\n\n\ngg\nTHTH H . The \nAT line and the GT line are the two critical lines predicted in the presence of field on the \nH-T plane, which mark the phase transition. The first one occurs for an anisotropic Ising \nspin glass while the second is valid for an isotropic Heisenberg spin glass.  8/23 Our sample shows a very interesting behaviour. At low field values (H dc < 0.15 T), \nTg follows the AT line. This can be seen in Fig. 6, where the red line denotes the AT line. \nSince the AT line predicts that \n32H Tg , so we have plotted H2/3 in the H -T phase \ndiagram. However, with an increase in the field (H > 0.15 T), we find deviation from the \nAT line. Remarkably, it is  found that at high field, the variation of Tg(H) agrees with the \nGT line. This can be seen in the inset of Fig. 6, where the blue line denotes the GT line. \nSince the GT line predicts that \n2H Tg , so the H -T phase diagram in the inset is p lotted \nwith H2 in the y -axis.  \nThese experimental results can be explained using the theoretical calculation by \nKotliar and Sompolinsky [22], who have predicted that in the presence of random \nanisotropy, the critical behaviour for a spin glass in fields lo wer than the anisotropy field \nis close to Ising type following the AT line, and crosses over to Heisenberg behaviour in \nhigh fields. The fact that we see a crossover in critical lines on the H -T plane for our \nsample indicates the existence of magnetic anis otropy in the system. At higher applied \nfields, the system behaves like a Heisenberg spin glass, where the spins can freeze along \nany direction with respect to the applied magnetic field. However, when the applied field \nis lower than the anisotropy field, the spins are forced to be aligned along the local \nanisotropy axis. The preference of the spin alignment adds an Ising character to the \nassociated spin cluster.  \n \nDomain wall pinning at lower temperature  \n \nIn this section, we discuss the third feature seen i n the χ'(T) curve – the broad peak \nat ~ 110 K (Fig. 4). This peak at 110 K does not shift (i.e. the peak maximum occurs at \nthe same temperature) with a change in the external magnetic field H dc (see the red line in \nFig. 5). Based on this behaviour, we attr ibute the origin of the feature seen at ~ 110 K to \nenhanced domain wall pinning. The signature of this domain wall pinning can also be \nseen in Fig. 7, where we plot the variation of the coercivity (H C) with temperature. As is \nclear from the figure, the coe rcivity is majorly enhanced below 110 K, which occurs due \nto the domain wall pinning. A close look at the high temperature region, which is \nenlarged and shown in the inset of Fig. 7, reveals that the coercivity also shows an \nenhancement below the paramagne tic to ferrimagnetic phase transition temperature 9/23 (shown by a black arrow), and another enhancement below the spin glass freezing \ntemperature (shown by a blue arrow), as expected.  \n At this stage, we need to go back to our earlier observation of an unusual initial \nmagnetization curve in the M(H) loop measured at low temperature (Fig. 3). Such \nunusual magnetic hysteresis behaviour, with the virgin curve lying outside the main \nhysteresis loop, was earlier associated with irreversible domain wall motion in spin el \noxides [23]. Thus, this unusual magnetization curve is an additional confirmation of the \ndomain wall pinning at ~ 110 K that we had mentioned earlier. In fact, we find that the \nvirgin curve lies outside the main M(H) loop for temperatures below 110 K, b ut above \n110 K, it lies completely inside the main hysteresis loop. This is shown in Fig. 8, where \nwe plot the M(H) loops at temperatures slightly below (Fig. 8 (a)), and slightly above \n(Fig. 8 (b)) 110 K. In the figures, the virgin curves are shown in red  for the sake of \nclarity.  \n \nOrigin of the competition between ferrimagnetism and spin glass behaviour  \n \n In order to understand the different magnetic behaviour of CaBaFe 4O7.14 with \nrespect to CaBaFe 4O7, we must keep in mind that the oxygen excess in the for mer \ninduces an increase of the Fe3+ content in the structure i.e., the Fe3+:Fe2+ ratio increases \nfrom 1 in the stoichiometric phase to 1.32 in the oxygen hyperstoichiometric phase. As a \nconsequence, the Fe3+-Fe3+ antiferromagnetic interactions increase in the oxygen rich \nphase, and may decrease the ferrimagnetism in the structure.  Bearing in mind the model \npreviously proposed by Chapon et. al. [4] to explain the competition between 1D \nferromagnetism and 2D magnetic frustration in the cobaltite YBaCo 4O7 which has the \nsame hexagonal structure, we must consider the iron framework of our compound. The \nlatter consists of corner -sharing [Fe 5] bipyramids running along “ c” interconnected \nthrough “Fe 3” triangles (Fig. 9). In other words, in both oxides, CaBaFe 4O7 and \nCaBaFe 4O7.14, we can expect, similarly to the hexagonal cobalt oxides LnBaCo 4O7, that \nthe system exhibits an unidimensional magnetic order in the bipyramidal rows along “ c”, \nwhereas the triangular geometry of the iron lattice in the (001) plane induces magnetic \nfrustration as soon as the iron species are coupled antiferromagnetically. Such a model \ncan account for the competition between 1D ferrimagnetism and 2D magnetic frustration \nin both oxides, CaBaFe 4O7 and CaBaFe 4O7.14, and explain that the magnetic  frustration 10/23 may be larger in the latter owing to the appearance of larger short range \nantiferromagnetic interactions in the (001) plane . \n Nevertheless, the valency effect alone is not sufficient to explain the appearance of \nthe spin glass behaviour.   Two hypotheses  can be considered to explain this particular \nbehaviour. The first scenario deals with the fact that CaBaFe 4O7.14 contains interstitial \noxygen in spite of the apparent close packed character of the structure, leading to a local \npuckering of the “ O4” and “BaO 3” layers. As a result, the distribution of iron in the \ncationic sites would be locally disordered, leading to a spin glass behaviour. This local \ndistortion would also change the crystal field and would be responsible for the domain \nwall pinnin g. The second scenario deals with the fact that the “barium oxygen” \nframework remains close packed, but that the compound exhibits a  cationic deficiency \naccording to the formula Ca 0.98(Ba 0.98O0.02)Fe 3.93O7. Such an effect would be similar to \nthat observed for “oxidized” spinels -Fe2O3 and Co 3-xO4, which do not contain \ninterstitial oxygen, but were found to be iron or cobalt deficient [24, 25]. This second \nscenario would explain the magnetic behaviour of this phase, which is close to that \nobserved for CaBaF e4-xLixO7 [26]. In both the systems, the doping of the Fe sites with \nlithium or vacancies respectively introduces disordering on the Fe sites, which is in turn,  \nat the origin of the appearance of spin glass behaviour at lower temperature. Thus, the \ncompeti tion between 1D ferrimagnetism and spin glass behaviour appears normal. \nSubsequently, the competition between anisotropic (Ising) and isotropic (Heisenberg) \nspin glass can be understood from the peculiar geometry of the [Fe 4] lattice. Finally, the \niron va cancies would change the nature of the crystal field in the structure, playing the \nrole of pinning centres. This explains both, the broad peak at 110 K and the enhanced \ncoercivity below this temperature, which are the signatures of domain wall pinning.   \n The small deviation from the stoichiometry does not allow to distinguish the \npossibility of interstitial oxygen vis à vis that of cationic deficiency from a structural \nstudy. Attempts are being  made to synthesize similar hexagonal ferrites with larger \noxyge n excess in order to answer this question.  \n \n \n \n \n \n 11/23 Conclusion s \n \n This study illustrates the extraordinarily rich physics of the “114” CaBaFe 4O7+ \nferrite, in connection with its ability to accommodate oxygen excess, similar to what is \nobserved for the spine l family, Fe 3O4 – -Fe2O3. The remarkable feature of this “114” \noxide deals with the competition between ferrimagnetism and spin glass behaviour that \ncan be induced by varying the oxygen content, without changing the hexagonal symmetry \nof the structure. Su ch a behaviour can be explained, like for the “114” cobaltites, as due \nto the competition between 1D magnetic ordering along “ c” and 2D magnetic frustration \nin the triangular (001) lattice. Nevertheless, CaBaFe 4O7 differs significantly from \nCaBaCo 4O7, the latter’s ferrimagnetism originating mainly from a lifting of its 2D \ngeometrical frustration through a strong orthorhombic distortion of its initial hexagonal \nlattice. We believe that the scenario of cation disordering  on iron sites  is the key for \nunderstan ding the magnetism of these materials. Further investigations, especially using \nneutron diffraction and X -ray synchrotron have to be performed in order to further \nunderstand this phenomenon.  \n \nAcknowledgement s \n \nThe authors acknowledge the CNRS and the Conse il Regional of Basse Normandie \nfor financial support in the frame of Emergence Program. V. P. acknowledges support by \nthe ANR -09-JCJC -0017 -01 (Ref: JC09_442369).  \n \n \n \n \n \n 12/23 References  \n \n      [1]     Martin Valldor and Magnus Andersson, Solid State Sciences , 2002, 4, 923  \n      [2]     Martin Valldor, J. Phys.: Condens. Matter ., 2004 , 16, 9209  \n      [3]     L. C. Chapon, P. G. Radaelli, H. Zheng and J. F. Mitchell, Phys. Rev. B , 2006 , 74,  \n               172401  \n      [4]     P. Manuel, L. C. Chapon, P. G. Radaell i, H. Zheng a,d J. F. Mitchell, Phys. Rev.  \n               Lett., 2009 , 103, 037202  \n      [5]    V. Caignaert, V. Pralong, V. Hardy, C. Ritter and B. Raveau, Phys. Rev. B , 2010 , 81,  \n               094417  \n      [6]     E. A. Juarez -Arellano, A. Friedrich, D. J. Wilson, L. Wiehl, W. Morgenroth, B.  \n                Winkler, M. Avdeev, R. B. Macquart and C. D. Ling, Phys. Rev. B , 2009 , 79, 064109   \n      [7]     N. Hollmann, Z. Hu, M. Valldor, A. Maignan, A. Tanaka, H. H. Hsieh, H. -J. Lin, C.     \n                T. Chen and L. H. Tjeng, Phys. Rev. B , 2009 , 80, 085111  \n      [8]     D. D. Khalyavin, L. C. Chapon, P. G. Radaelli, H. Zheng and J. F. Mitchell, Phys.  \n                 Rev. B , 2009 , 80, 144107  \n      [9]     B. Raveau, V. Caignaert, V. Pralong, D. Pello quin and A. Maignan, Chem. Mater .,  \n               2008 , 20, 6295  \n      [10]    V. Caignaert, A. M. Abakumov, D. Pelloquin, V. Pralong, A. Maignan, G. Van  \n               Tendeloo and B. Raveau, Chem. Mater ., 2009 , 21, 1116  \n      [11]    V. Pralong, V. Cai gnaert, A. Maignan and B. Raveau, J. Mater. Chem ., 2009 , 19,  \n               8335  \n      [12]    M. Karppinen, H. Yamauchi, S. Otani, T. Fujita, T. Motohashi, Y. -H. Huang, M.  \n               Valkeapää and H. Fjellvåg, Chem. Mater ., 2006, 18, 490  \n      [13]   E. V. Tsipis, D. D. Khalyavin, S. V. Shiryaev, K. S. Redkina and P. Núñez,  \n               Materials Chemistry and Physics , 2005 , 92, 33 \n      [14]   E. V. Tsipis, V. V. Kharton, J. R. Frade and P. Núñez, J. Solid State Electrochem ,  \n                2005 , 9, 547  \n      [15]   O. Chmaissem, H. Zheng, A. Huq, P. W. Stephens and J. F. Mitchell, J. Solid State  \n               Chemistry , 2008 , 181, 664  \n      [16]   A. Maignan, V. Caignaert, D. Pelloquin, S. Hébert, V. Pralong, J. Hejtmanek and D.  \n                Khomskii, Phys. Rev. B , 2006 , 74, 165110  \n      [17]   A. Huq, J. F. Mitchell, H. Zheng, L. C. Chapon, P. G. Radaelli, K. S. Knight and P.  \n                W. Stephens, J. Solid State Chem ., 2006 , 179, 1136  \n      [18]    D. Herrmann and M. Bacmann, Mat. R es. Bull ., 1971 , 6, 725  \n      [19]    J. Rodriguez -Carvajal, An Introduction to the Program FULLPROF 2000; Laboratoire  13/23                 Léon Brillouin, CEA -CNRS: Saclay, France (2001)  \n      [20]   J. R. L. de Almeida and D. J. Thouless, J. Phys. A , 1978 , 11, 983  \n      [21]   M. Gabay and G. Toulouse, Phys. Rev. Lett ., 1981 , 47, 201 (1981)  \n      [22]   G. Kotliar and H. Sompolinsky, Phys. Rev. Lett ., 1984 , 53, 1751 (1984)  \n      [23]   P. A. Joy and S. K. Date, J. Magn. Magn. Mater ., 2000 , 210, 31 (2000)  \n      [24]   J.-E. Jørgensen, L. Mosegaard, L. E. Thomsen, T. R. Jensen and J. C. Hanson, J.  \n               Solid State Chem ., 2007 , 180, 180  \n      [25]   F. Kh. Chibirova, Physics of the Solid State , 2001 , 43, 1291  \n      [26]   K. Vijayanandhini, Ch. Simon,  V. Pralong, V. Caignaert and B. Raveau , Phys. Rev.  \n                B, 2009, 79, 224407  \n \n 14/23 Figure Captions  \n \nFig. 1 X-ray diffraction pattern along with the fit for CaBaFe 4O7+. \nFig. 2 MZFC (T) and M FC (T) curves of CaBaFe 4O7+ measured at H = 0.3 T.  \nFig. 3 M(H) curve of CaBaFe 4O7+ measured at T = 5 K. The virgin curve is shown in red    \n          circles, while the rest of the hysteresis loop is shown in black triangles. The inset  \n          shows the M(H) curve of the oxygen stoichiometric sample (CaBaFe 4O7) measured  \n          at T = 5 K.  \nFig. 4 The real (in -phase) component of a.c. susceptibility for CaBaFe 4O7+ as a function  \n           of temperature in the frequency range f = 10 Hz – 10 kHz, at zero static magnetic  \n           field (H dc) and at a dr iving ac field (H ac) of 10 Oe. The inset shows the plot of ln   \n           vs \n\n\n\n\nSGSG f\nTTTln  for the peak at 166 K.  \nFig. 5 The real (in -phase) component of a.c. susceptibility for CaBaFe 4O7+ as a function  \n          of temperature. The driving f requency was fixed at f = 10 kHz and h ac = 10 Oe.  \n         Each curve was obtained under different applied static magnetic field (H dc) ranging  \n         from 0 T to 0.3 T.  \nFig. 6 Field vs temperature phase diagram of CaBaFe 4O7+. In order to show the AT l ine,  \n          we have plotted H2/3 vs Tg. The inset shows H2 vs Tg and the GT line.  \nFig. 7  Temperature dependence of coercive field for CaBaFe 4O7+. The inset is an  \n           enlarged version of the high temperature region.  \nFig.  8 M(H) loops of CaBa Fe4O7+ at (a) T = 75 K and (b) T = 135 K.  \nFig.  9 Schematic representation of the [Fe 4] tetrahedral framework of hexagonal  \n           CaBaFe 4O7+ showing the Fe 5 bipyramids sharing corners with Fe 3 triangular  \n           groups (adapted from Ref. 11).  \n \n \n \n \n \n \n 15/23 \n20 40 60 80 1000.02.0x1034.0x1036.0x1038.0x1031.0x104P63mc\na=6.3546(2) Å\nc=10.3721(4) Å\n2 = 1.94\nRBragg = 5.01 %\nRF = 3.88 %\n  Intensity (arb. units)\n2 (degree) \nFig. 1 . X-ray diffraction pattern along with the fit for CaBaFe 4O7+. \n \n 16/23  \n0 100 200 300 4000.00.20.40.60.81.0\nH = 0.3 T ZFC\n FCMagnetization ( B/f.u.)\nTemperature (K)\n  \n \nFig. 2 . MZFC (T) and M FC (T) curves of CaBaFe 4O7+ measured at H = 0.3 T.  \n 17/23  \n \n-4 -2 0 2 4-2-1012\n-4 -2 0 2 4-3-2-10123CaBaFe4O7Magnetization ( B/f.u.)\nMagnetic field (T)\n \nT = 5 KMagnetization ( B/f.u.)\nMagnetic field (T)\n \n \nFig. 3.  M(H) curve of CaBaFe 4O7+ measured at T = 5 K. The virgin curve is shown in  \nred ci rcles, while the rest of the hysteresis loop is shown in black triangles. The  inset \nshows the M(H) curve of the oxygen stoichiometric sample (CaBaFe 4O7) measured at T \n= 5 K.  \n 18/23 \n50 100 150 200 2504.0x10-36.0x10-38.0x10-31.0x10-2\n110 K166 K\n272 K\n-3.6 -3.3 -3.0 -2.7 -2.4-9-8-7-6-5-4-3-20 = (7.3 ± 0.1) X 10-10 sec\nTSG = 162.2 K\nz = 5.01 ± 0.01ln \nln{(Tf-TSG)/TSG}\n  Hac = 10 Oe\nHdc = 0 10 Hz\n 80 Hz\n 1 kHz\n 10 kHz' (emu/gm)\nTemperature (K)\n  \n \nFig. 4 . The real (in -phase) component of a.c. susceptibility for CaBaFe 4O7+ as a function             \nof temperature in the frequency range f = 10 Hz – 10 kHz, at zero static magnetic            \nfield (H dc) and at a driving ac fie ld (H ac) of 10 Oe. The inset shows the plot of ln             \nvs \n\n\n\n\nSGSG f\nTTTln  for the peak at 166 K.  \n \n \n \n \n \n \n \n \n \n 19/23  \n \n50 100 150 200 250 3002.0x10-34.0x10-36.0x10-38.0x10-31.0x10-2\n 0.2 T\n 0.225 T\n 0.25 T\n 0.275 T\n 0.3 T 0 T\n 0.025 T\n 0.05 T\n 0.075 T\n 0.1 T\n 0.125 T\n 0.15 T\n 0.175 T\nTemperature (K)' (emu/gm)\n  \n \n \nFig. 5 . The real (in -phase) component of a.c. susceptibility for CaBaFe 4O7+ as a function            \nof temperature. The driving frequency was fixed at f = 10 kHz and h ac = 10 Oe.          \nEach curve was obtained under different applied static magnetic field (H dc) ranging          \nfrom 0 T to 0.3 T.  \n \n \n \n \n \n \n \n \n 20/23  \n155 160 165 170 175 1800.0750.1500.2250.3000.3750.450\n155 160 165 170 1750.000.020.040.060.080.10\nGT line H2 (T2)\nT (K)\nAT lineFM\nSpin glass\n  H2/3 (T2/3)\nT (K)\n \n \nFig. 6 . Field vs temperature phase diagram of CaBaFe 4O7+. In order to show the AT line,           \nwe have plotted H2/3 vs Tg. The inset shows H2 vs Tg and the GT line.  \n \n \n \n \n \n \n \n \n 21/23 \n0 50 100 150 200 250 3000.00.10.20.30.40.50.60.70.8\n120 150 180 210 240 270 3000.020.040.060.080.10\n T (K)HC (T)\n113 K\nTemperature (K)\n  HC (T) \n \nFig. 7 . Temperature dependence of coercive field for CaB aFe 4O7+. The inset is an            \nenlarged version of the high temperature region.  \n \n \n \n \n \n \n \n \n \n \n \n \n 22/23 \n-5 -4 -3 -2 -1 0 1 2 3 4 5-2-1012-2-1012\n(b)Magnetization ( B/f.u.)\nMagnetic field (T)T = 135 KT = 75 K(a)\n   \n  \n \nFig. 8 . M(H) loops of CaBaFe 4O7+ at (a) T = 75 K and (b) T = 135 K.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n 23/23  \n \n \n \nFig. 9 . Schematic representation of the  [Fe 4] tetrahedral framework of hexagonal            \nCaBaFe 4O7+ showing the Fe 5 bipyramids sharing corners with Fe 3 triangular            \ngroups (adapted from Ref. 11).  \n \n \n \n \n \n \n \n "    },    {        "title": "1203.2944v1.Room_temperature_ferromagnetism_and_giant_permittivity_in_chemical_routed_Co1_5Fe1_5O4_ferrite_particles_and_their_composite_with_NaNO3.pdf",        "content": " \n1 \n Room temperature ferromagnetism and giant permittiv ity in chemical routed \nCo 1.5 Fe 1.5 O4 ferrite particles and their composite with NaNO 3  \nR.N. Bhowmik *, P. Lokeswara Rao, and J. Udaya Bhanu  \nDepartment of Physics, Pondicherry University, R. Venkataraman Nagar, Ka lapet, Pondicherry-\n60014, India.  \n*Author for correspondence (RNB): Tel.:+91-9944064547; Fax: +91- 4132655734.                                                                  \n                           E-mail: rnbhowmik.phy@pondiuni.edu.in  \nAbstract \nWe report structural, magnetic and dielectric properties of Co 1.5 Fe 1.5 O4 nanoparticles and their \ncomposites with non-magnetic NaNO 3. The samples were derived from metal nitrates solution at \ndifferent pH values. The chemical routed sample was air heated at  200 0C and 500 0C. Heating of \nthe material showed unusual decrease of crystallite size, but c ubic spinel structure is seen in all \nsamples. The samples of Co 1.5 Fe 1.5 O4 showed substantially large room temperature \nferromagnetic moment, electrical conductivity, dielectric const ant, and low dielectric loss. The \nsamples are soft ferromagnet and electrically highly polariz ed. The interfaces of grains and grain \nboundaries are actively participating to determine the magnetic and dielectric properties of the \nferrite grains. The effects of interfacial contribution are be tter realized using the ferrite and \nNaNO 3 composite samples. We have examined different scopes of modifyin g the magnetic and \ndielectric parameters using same material in pure and composite form. \nKey words: A. magnetic materials , B. chemical synthesis , C. electrical characterisation , D. \ndielectric properties .  \n2 \n  \n1. INTRODUCTION \nMagnetic nanocomposite [1, 2] is one of the exciting topics in pres ent generation research. This \nis due to the flexibility of modifying magnetic, electric, diel ectric and optical properties. In \nmagnetic composites, the magnetic particles are usually adde d either in an insulating or \nconductive matrix [3]. Among the different types of magnetic part icles, spinel ferrites are well \nstabilized in different non-magnetic environment and highly promisi ng for the applications in \nmagnetic data storage, magnetic resonance imaging, magnetic ally guided drug delivery, etc [4, \n5]. Spinel ferrites can also be used in microwave devices due to the  exhibition of high electrical \nresistivity and low dielectric loss [6, 7]. Among the spinel ferr ites, Co xFe 3-xO4 series (0 ≤ x ≤ 3) \nis promising candidate for producing multifunctional materials by va rying synthesis condition, \ncobalt content, and particle size and shape dependent parameters (mag netic moment, coercivity, \nmagnetic blocking temperature, conductivity and dielectric constant ) [8-10]. CoFe 2O4 is widely \nstudied as a well–known hard magnetic material with large coerc ivity and magnetization [4, 11, \n12]. However, experimental work on Co rich compositions of this serie s is limited, despite \nindicating improved magnetic and microwave properties [13], and useful applications in \nchemical sensors [14], catalytic activity [15], photo-conductive devices [16, 17].  \nIn this work we focus on the Co 1.5 Fe 1.5 O4 ferrite. The ferrite nanoparticles were synthesized by \nco-precipitation of metal nitrates solution at different pH values.  The as prepared sample was \nheated up to 500 0C to study the properties of the material with low annealing temperature side, \nand study of low temperature annealed samples is few due to the f act that chemical heterogeneity \nmay exist at the microscopic scale of crystal structure.  We  also prepared a simple magnetic  \n3 \n composite of Co 1.5 Fe 1.5 O4 particles with NaNO 3. The novelty of this magnetic composite is that \nNaNO 3 was naturally formed as the bye-product and coexisting with ferrite partic les.  \n2. EXPERIMENTAL \nA. Sample preparation \nFig. 1 shows the schematic presentation of the material synthesis. Stoichiom etric amounts \nof high pure (> 99.999%) Co(NO 3)2.6H 2O and Fe(NO 3)3.9H 2O salts were taken to synthesize \nCo 1.5 Fe 1.5 O4. The salts were mixed in distilled water and stirred to prepar e a stock solution (S 0) \nof pH value ∼ 0.5. The S 0 solution was divided into three parts. NaOH solution with pH ∼ 13.7 \nwas added separately as precipitating agent in the different pa rts of the S 0 solution in stirring \ncondition and final pH values of the mixed solution were maintained at 12, 11 and 9.5, \nrespectively. Each solution was then heated at 100-110°C with continuous sti rring for 2 hours, \nfollowed by the heating of the solution at 140-150°C for nearly 1 hour. We observed a black \ncoloured gel at the centre of the beaker and white powder on the wa ll. X-ray diffraction (XRD) \npattern identified this white powder as NaNO 3. Each of these dried powders at 140-150°C was \ndivided into two parts (P series and S series). To get pure form of ferrite particles (P series), the \nbye-product (white coloured NaNO 3 powder) was carefully removed from the wall and \nremaining black coloured gel was washed with distilled water and he ated at 110°C. The cleaning \nprocess was repeated for several times until there was no more white pow der formed on the inner \nsurface of the beaker. Pure form of the black coloured Co 1.5 Fe 1.5 O4 samples (P series) obtained \nfrom the solutions with pH values 12, 11 and 9.5 were denoted as P1, P2 and P3, r espectively. \nTo get the composite material (S series), we did not wash out the white powder from the mixed \ncomposite. The mixture of gel and white powder was dried and finally, cooled to room \ntemperature. The mixed powder was ground for 2 hours to make it more homogene ous. The  \n4 \n magnetic composite (Co 1.5 Fe 1.5 O4 mixed with NaNO 3) samples (S batches) obtained from pH \nvalues 12, 11 and 9.5 were denoted as S1, S2 and S3, respectively. The samples of P and S \nbatches were then heated at 200 0C for 2 hours and corresponding samples were denoted as \nP1_200, P2_200, P3_200 for P series and S1_200, S2_200, S3_200 for S series, respectively . \nThe 200 0C samples of P and S series were heated at 500 0C for 2 hours  and corresponding \nsamples were denoted as P1_500, P2_500, P3_500 for P series, and S1_500, S2_500, S3_500 for \nS series, respectively. The rate of heating/cooling was maintai ned at 5 0C per minute. The \nheating of the as prepared samples at higher temperature was per formed in order to study the \nthermal effects on crystal structure and physical properties.  \nB. Sample characterization and measurements \nThe samples were characterized and measured at room temperatur e. XRD pattern of the \nsamples was recorded using Cu-K α radiation (λ = 1.54056 Å, 2 θ range 20 0 to 80 0 with step size \n0.02 0 and time/step 2s). Dc magnetization was measured at magnetic  field range ± 15 kOe using \nvibrating sample magnetometer (Lake Shore 7404) and some measurement was carried out using \nPPMS (Quantum Design, USA). Dielectric properties of the pelle t shaped (12 mm diameter, 2-3 \nmm thickness) samples were measured at 1 Volt ac signal with frequency range 1 Hz to 0.1 MHz \nusing broadband dielectric spectrometer (Novocontrol Techchnology, Germa ny). The pellets \nwere sandwiched between two gold plated electrodes and measured in a closed sam ple chamber.  \n3. RESULTS AND DISCUSSION \nA. Structure and morphology \nFig. 2 shows the profile fit of XRD pattern using FULLPROF program. The profiles \nconfirmed the cubic spinel structure with space group Fd3m. Lattice parameters (8.27-8.28 Å) of \nthe pure form of Co 1.5 Fe 1.5 O4 samples are in between the lattice parameters of  CoFe 2O4 (~ 8.38Å  \n5 \n [11]) and Co 2FeO 4 (~ 8.24 Å [13]) particles. Table 1 shows that lattice parameter of the 200 0C \nsamples have increased with the increase of pH value in chemical  reaction, where as the lattice \nparameter of the 500 0C samples has shown decreasing trend with the increase of pH va lue. \nGrain/crystallite size has been estimated using the infor mation of prominent XRD peaks (220, \n311, 400, 511 and 440) in Debye-Scherrer formula: . Here, θc = X c/2 \nand X c is the peak center in 2 θ scale, λ = wavelength of X-ray radiation (1.54056 Å), ω is the \nFull width at half maximum of the peak counts. Table 1 shows that c hange of the crystallite size \nin pure samples is small during the increase of heating temperat ure from 200 °C to 500 °C. This \nmay be due to less heating time (2 hours). Generally, crystall ite size increases with heating \ntemperature, although grain growth process may be slow at low heat ing temperature [18], due to \nthermal activated re-crystallization at disordered grain boundary atoms. Interestingly, there is an \nunusual decrease of crystallite size in pure samples on increasi ng heating temperature from 200 \n0C to 500 0C. It shows the crystallites or grain boundary structure of the f errite nanoparticles is \nnot chemically in proper equilibrium at low temperature heating. T he decrease of crystallite size \nwith increasing heating temperature was earlier reported in f ew materials, which accompanied a \nlot of surface defects [17] and some cases it indicated a str ong magnetic lattice coupling [19]. \nUnfortunately, most of the reports have studied the nano-structured fer rites with well crystalline \nstructure, which were prepared by chemical routes and heated at hi gher temperatures to avoid \nsurface defects and structural heterogeneity of the particles .  However, properties of the surface \ndefective materials are remarkably advanced from application point of view [20-22]. The \ncrystallite size of the pure samples also shows a non-monotonic inc rease with increasing pH \nvalue, irrespective of heating at 200 °C/500 °C. The samples of P2 (pH value 11) batches \nshowed some exception whose crystallite size is larger than P1 (pH values  12) and P3 (pH values  \n6 \n 9.5) batches. Our results of lattice parameter and crystallit e size for the samples at different pH \nvalues are slightly different in comparison with a monotonic increas ing trend with increasing pH \nvalues in CoFe 2O4 [23]. In case of composites, the XRD pattern confirmed the coexiste nce of \nferrite and NaNO 3. Fig. 3 shows the XRD pattern of S1_200 sample, consisting of P1_200 \n(ferrite) and NaNO 3. XRD data (not shown for all composites) showed the increase of XRD  peak \ncounts of NaNO 3 component in composite samples with the increase of pH values. XRD pr ofile \nof NaNO 3 is fitted into rhombohedral structure with space group R3C. The novelty o f this \nmagnetic composite is that it is naturally formed during the co-precipitated synthesis of ferrites \nand there is no need to add magnetic ferrite nanoparticles in NaN O 3. Such magnetic composite \nalso provide some advantages for studying comparative physical pr operties, which is one of the \nobjectives of the present work.  \nB. Magnetic properties \nField (H) dependent magnetization (M) of the pure samples at 200 °C i s shown in Fig. 4. \nThe M(H) curves (first quadrant only) for 500 °C samples are show n in the inset-a of Fig. 4. All \nsamples in pure form exhibited hysteresis loop, as inset-b of Fig. 4 shows for 200 °C samples. \nP3_200 sample only showed very small loop, where superparamagnetic fea tures of the particles \nlargely dominate at room temperature. Since crystallite size of all pure samples is below 10 nm, \nthe synthesized samples are consisting of single magnetic doma ins and smaller size of the lowest \npH samples belongs to the superparamagnetic regime [1]. Depending on the strength of the \ninteractions among magnetic domains and magnetic domain structure, P1 and P2 series exhibited \nstrong ferromagnetism at room temperature. Fig. 5 shows a signifi cant decrease of magnetization \nin the composite samples in comparison with pure samples. Although composite sample s showed \nnon-linear increase of M(H) curve and resembling to ferromagnet ic feature, Arrot plot (in the  \n7 \n inset-a of Fig. 5) using first quadrant of M(H) data does not show a ny positive intercept of the \nlinear extrapolation of M 2 vs. H/M curve from higher field side to the M 2 axis only for S3 _200 \nsample. This confirms superparamagnetic behaviour of the ferrite particles in low pH valued \nsamples at room temperature. Rest of the composite samples inter cepted the positive side of M 2 \naxis (shown for S3 _500 sample in the inset-a of Fig. 5) and showed finite spontaneous \nferromagnetic moment. Coercive field (H C) and remanent magnetization (M R) of the samples \nwere calculated from the ferromagnetic loop, as shown in the inset -b of Fig. 5 for S2 _500 \nsample. Table 2 shows the room temperature values of magnetization of  each sample at 15 kOe \n(M 15 kOe ) and magnetic parameters (H C and M R). M 15 kOe  of the pure samples has increased with \nheating temperature, irrespective of pH value. However, variation of t he M 15 kOe  with pH is non-\nmonotonic. For example, M 15 kOe  for P2_200 sample is larger in comparison with P1_200 and \nP3_200 samples. In 500 °C series, M 15 kOe  is remarkably large for P3_500 in comparison with \nP1_500 and P2_500 samples. M R of the 200 °C samples has decreased with the decrease of pH \nvalue, irrespective of the pure and composite samples. In contrast, M R of the 500 °C pure \nsamples showed significant increase on reducing the pH value in pure sample with minimum \nvalue of M R for P2_500 sample. In composite samples M R increased with decreasing pH value \nwith a maximum M R for S2_500 sample. At the same time, the higher pH samples (P1_200 and \nP1_500) showed larger coercivity (H C), irrespective of the heating temperatures. The result of \ncoercivity at different pH values is different from the report ed behavior of CoFe 2O4 particles \n[23]. Interestingly, lower pH samples have increased their H C by heating the sample, unlike the \ndecrease of coercivity in higher pH samples. We found that the room t emperature magnetization \nand coercivity of Co 1.5 Fe 1.5 O4 ferrite are smaller or comparable to the reported data of CoF e 2O4  \n8 \n particles [11, 18, 20]. The CoFe 2O4 is a hard ferromagnet [24-25], but the present composition \nCo 1.5 Fe 1.5 O4 shows the properties of a good soft ferromagnet at room temperature.  \nC. Dielectric Properties \nWe examined certain dielectric parameters (ac conductivity ( σ), dielectric constant ( ε), \ndielectric loss (tan δ) and electrical contribution from grains ( σg) and grain boundaries ( σgb )) of \nthe samples. Fig. 6(a) shows that stock solution (S 0) with pH value 0.5 is highly conductive with \nconductivity ∼ 8x10 -3 S/cm at frequency 10 Hz. The conductivity, mostly due to conductive i ons, \nrapidly increased with frequency (f) to attain the value ∼ 2x10 -2 S/cm at f = 10 kHz. The \nfrequency activated conductivity ( σ(f)) of the stock solution (S 0) then saturated above 10 kHz, \nwhich indicated leveling of ionic contributions at higher frequencies a nd electrical transport \nbetween two electrodes may be due to free motions of the ions. σ(f) has significantly decreased \nin the pure form of ferrite particles in comparison with stock sol ution (S 0). The ferrite samples \nalso showed relatively slow σ(f) in 200 0C (Fig. 6(a)) and 500 0C (Fig. 6(b))  samples. σ(f) of the \nsample P3_500 is very weak up to 1 kHz, which is followed by a sharp incr ease of conductivity. \nOver all conductivity of the 200 0C samples is higher than the 500 0C samples. The general trend \nis that conductivity of the material has increased with the incr ease of pH value. The σ(f) of the \ncomposite samples at 200 0C (Fig. 6(c)) and at 500 0C (Fig. 6(d)) is slow and magnitude wise \nsmall in comparison with pure samples. We understand that electric al conductivity of the \ncomposite samples at grain boundaries is strongly affected by the  coexistence of relatively poor \nionic conductor (dc conductivity ~10 -9 S/cm estimated from Fig. 6(c)) NaNO 3 in the composites. \nThe basic property of increasing conductivity with increasing pH va lue or the decrease of  \nconductivity by increasing the heating temperature from 200 0C to 500 0C of the as prepared \nsamples are also retained in composite samples. The conductivity val ues at 1 Hz ( σ1 Hz ) of all  \n9 \n ferrite samples are shown in Table 3. We noted that pure form of the  ferrite samples are \nsufficiently conductive at room temperature (> 10 -4 S/cm) and could be the potential candidate \nfor solid state fuel applications [26]. As shown in Fig. 6, σ(f) of ferrite samples are fitted with \nJonscher power law: σ(f) ∼ fn with at least two exponent (n 1 and n 2) values. The exponent values \nof pure and composite samples at lower frequency regime (n 1) and higher frequency regime (n 2) \nare always less than 0.4, except n 2 ∼ 0.70 for P3_500 sample. This indicated a multiple hopping, \nmixed with long range hopping, of electronic charge carriers (polarons)  at the grains and grain \nboundaries [27-28]. The n 1 values (0.18-0.19) are nearly same for P1_200, P2_200 and P3_200 \nsamples, where as n 2 value decreases from 0.33 to 0.20 on decreasing the pH value from 12 to  \n9.5. This means short ranged hopping of polarons or electrons inside the grai ns are more \nfavoured for the samples with high pH value. For 500 0C samples, n 1 value decreases from 0.33 \nto 0.05 with the decrease of pH value. This indicated slowing down of the  dynamics of bound \ncharge carriers (polarons) as an effect of reduced surface def ects in heated samples. On the other \nhand, increase of n 2 values at 500 0C from 0.19 to 0.70 on decreasing the pH value suggests that \nelectronic charge carriers become more localized at the surfa ce of grains and forming short \nranged polarons at the interfaces of grains and grain boundaries. The values of n 1 and n 2 obtained \nfrom 500 0C composite samples are significantly small in comparison with pure samples. This is \ndue to coexistence of mobile ions (Na +, NO 3-) from ionic conductor NaNO 3 at the surfaces of \ngrains and grain boundaries. It is interesting to note that n 1 of the composite samples are \nsignificantly higher than n 2, unlike a different trend observed in pure samples. This shows that \nNaNO 3 is affecting in the formation of localized polarons at the grai n boundaries of the \ncomposite samples. In the composites, grains are consisting of highly conducting Co 1.5 Fe 1.5 O4 \nparticles (domains). It is believed that grain boundaries of ferrit es are more active at lower  \n10 \n frequencies. As the frequency increases the grains become more active and short ranged hopping \nof electrons between Fe 2+  ↔ Fe 3+  and holes between Co 2+  ↔ Co 3+  ions in the octahedral sites of \nthe cubic spinel structure is activated [28-29]. The hopping of electrons  between Fe 2+  ↔ Fe 3+  in \nthe octahedral sites is suppressed in the composite samples. As  the frequency is increased, the \nelectrons do not follow the frequencies of applied ac electric fie ld. This leads to weakening of \nthe frequency activated conductivity at higher frequencies with small values  of n 2.  \nThe Cole-Cole plots (-Z// vs. Z /) of complex impedance spectrum (Fig. 7(a)) showed no \nclear signature of a semi-circle at the lower frequency side, i.e., higher values of Z /. This reveals \na perturbed impedance contribution from grain boundary or defective surfa ce of ferrite particles \nof 200 0C samples. In the absence of any straight line in Cole-Cole plot  of complex impedance, \nwe suggest that the curved line is not due to a typical electr ode effect. Rather, the concaved \nupward curve shows the interfacial effect of the complex microst ructure at the grain boundaries \n[28, 30]. A small semi-circle at higher frequency side, i.e., at smaller values of Z /, suggests a \nwell defined impedance contribution mainly from grains. Fig. 7(b) s hows that interfacial effect \nstill dominates in 500 0C pure (P1_500 and P2_500) samples. The appearance of two coexisting \nsemi-circles in P3_500 (low pH) sample gives the indication of the s eparation of grain boundary \nimpedance (R gb ) at low frequencies from the contribution of grains (R g) at high frequencies. \nThere is a dramatic increase of the R g in the composite samples at 200 0C (Fig. 7(c)) and 500 0C \n(Fig. 7(d)) in addition to a strong perturbation in the grain boundary contri bution. The \nmagnitudes of grain ( ρg) and grain boundary ( ρgb ) resistivity were obtained from R g and R gb  of \nthe samples using fitted data of Cole-Cole plot. As in Table 3, the  trend of resistivity (inverse of \nconductivity) is well consistent to the features observed from ac conductivity at  1 Hz.  \n11 \n Fig. 8 indicated the signature of giant relative permittivity/di electric constant ( ε) in pure \nand composite form of the samples, as well as in the stock soluti on (S 0). The stock solution (S 0) \nis highly polarized under the application of ac field and typical ε at 1 Hz is ∼ 1.616x10 9. When \nthe ions of the stock solution (S 0) become more localized in the cubic spinel structure, the ε value \nsignificantly decreases and can be understood from the relativel y lower value of ε ∼10 6-10 8 at 1 \nHz in pure samples. The dielectric constant is further decreased in composite samples due to the \ncoexistence of weakly polarized molecules of NaNO 3 whose permittivity is nearly 3 orders less \nin comparison with pure ferrite samples. Typical magnitude of ε at 1 Hz is shown in Table 3 for \nall samples. It may be noted that magnitude of ε gradually decreases with the increase of \nfrequency and exhibited a typical value ∼ 102-10 5 at 100 kHz. Such huge values of ε over a large \nfrequency regime show highly polarized nature of the samples [ 31]. Electrical polarization in the \npresent ferrite material aroused due to the short ranged displac ements of B sites cations (Fe 3+ , \nFe 2+ , Co 2+ , Co 3+ ) or hopping of charge carriers among the cations (electron hopping: Fe 2+  ↔ \nFe 3+ , hole hopping: Co 3+  ↔ Co 2+ ). The effects of site exchange of cations (Fe 3+ , Co 2+ ) among A \nand B sites of the spinel structure may be expected, but this is g enerally observed for the samples \nheated at high temperatures ( ≤ 800 0C). However, one can expect a large amount of electrical \npolarization from the heterogeneous electronic microstructure at the grain boundaries [28, 30]. \nAs the frequency of the ac field increased, the forward and backw ard motions of the electronic \ncharge carries stored at the interfaces of grains lag behind t he driving frequency (f) of ac field. \nThis reduces interfacial polarization of the samples at higher f requencies, but polarization from \ninternal dynamics of the ferrite samples (e.g., short rang ed displacements of B sites cations, \nhopping of charge carriers among the cations, etc) maintains the la rge dielectric constant ( ε) up \nto higher frequency. Table 3 shows that ε depend on pH and heating temperature of the samples  \n12 \n in pure and composite form. The general tendency is that ε decreased with decreasing pH values, \nirrespective of heating temperature. Heating of the samples from 200 0C to 500 0C has decreased \nthe magnitude of ε up to 5-10 times depending on the pure and composite form of materials. W e \nattribute the decrease of ε in 500 0C samples to the reduction of polarization originated from \nheterogeneous electronic microstructure of samples at 200 0C. Fig. 9 (a-d) shows that tan δ of the \nstock solution (S 0) is very small (0.2-2.5) and the value has increased to 1-9 and 1-11 for pur e \nand composite form of samples, respectively. This means tan δ of the ferrite particles in pure \nsamples has not changed significantly in composites. This is due t o the fact that tan δ of the ionic \nconductor NaNO 3 (∼0.03-2 in (Fig. 9(c)) is not adding much contribution in composite samples. \nLow dielectric loss of the samples below 100 Hz indirectly sugges ts that huge dielectric constant \nis not an artifact of the electrode effects, it may be the intrinsic nature  of the samples. \nIt is interesting to note that pure and composite form of the sampl es exhibited a tan δ peak \nat finite frequency (f P), which can be close to the hopping frequency of electrical charge carriers \nbetween two successive ionic sites of the cations (Fe 2+  ↔ Fe 3+  and Co 3+  ↔ Co 2+ ). The tan δ peak \nat higher frequencies suggests an appreciable contribution of the orientation of electrical dipoles \nto the dielectric relaxation process mainly at grains. These di poles originated due to electron \ndensity modulation of the multi-valence cation pairs (Fe 2+  (more electron density) ↔ Fe 3+  (less \nelectron density) and Co 3+  (less electron density) ↔ Co 2+ (more electron density)) [32-33]. On \nincreasing the pH, the peak frequency (f P) shifts to lower value in P series of 200 0C samples \n(Fig. 9(a)), whereas f P shifts to higher values for 500 0C samples (Fig. 9(b)). Sufficiently large \nvalue (10 -3-10 -4s) of the relaxation time/hopping time ( τm = 1/f p) of the dipoles shows strong \ninteractions among the electronic charge carriers (polarons). T he origin of strong interactions \nmay not be electrostatic alone; rather magnetic interactions  between B site magnetic spins of the  \n13 \n grains are also affecting the dielectric relaxation process . Table 3 shows that τm for the pure form \nof 500 0C samples increases with the decrease of pH values, unlike a d ecreasing trend of τm in \n200 0C samples. τm of the composites at 500 0C also decreased with the decrease of pH values, \nbut value is relatively small in comparison with pure counter part s. The fast relaxation process in \ncomposite samples supports the effect of magnetic interactions  in dielectric relaxation process, \nbecause non-magnetic NaNO 3 helped to reduce the magnetic interactions among ferromagnetic \ngrains of composite samples. The reduced magnetic interactions made the hoppi ng mechanism of \ncharge carriers short ranged type in composite samples, where as variable long range hopping of \nthe charge carriers are dominating the relaxation dynamics of pure samples .   \nWe understand the properties of the samples annealed at lower temper atures by a \nschematic model in Fig. 10. We used nitrate salts and NaOH in co -precipitation route, where \ndifferent types of positive (Fe 3+  + Co 2+  +H ++ Na +) and negative (NO 3- + OH -) ions coexisted in \nthe precursor solution (see Fig. 1). The number of reagent ions (Na + and NO 3-) is more for the \nsolution at higher pH, because of higher amount of NaOH in a fixed vol ume of nitrate solution. \nThe reagent ions (or compound NaNO 3) were sitting at the surfaces of grains or grain boundaries \nduring the growth of ferrite particles. Fig. 10(a) suggests t hat magnetic spins and bye-products \n(ions or salts) form an inhomogeneous defective layer surrounding t he ferromagnetic domains. \nThe effects of such layers are prominent for the samples at hig her pH value. When the chemical \nrouted sample is heated the chemical surfactants (bye-products) t hat retained at the surfaces \n(grain boundaries) are removed from the particles. The removal of sit ting ions introduces crystal \ndefects/porosity at the sitting sites of the defective layer s (Fig. 10(b)). There is a possibility that \nlarge number of surface spins can be pinned at the defective sites of surfaces. Applied thermal \nenergy during heating of the as prepared samples is spent mainly  to reduce the volume of the  \n14 \n surfactants induced crystal defects at outer layers (grain boundar ies) of the nano-sized crystals, \nleaving a little (or nearly zero) energy that can activate c rystal growth process. Hence, crystallite \nsize of the samples heated at low temperature range 200 0C to 500 0C is effectively reduced due \nto decrease of surface defects volume (Fig. 10(c)). In the absenc e of less number of defect sites \nat 500 0C samples, we suggest that less number of surface spins is pinned ( Fig. 10(c)). This \nresults in increasing magnetization with reduced coercivity in 500 0C samples of the P1 and P2 \nseries. The defective surface layer is magnetically more  active due to additional surface stress \n[21, 34] created by the sitting ions. The pinning of magnetic domains a t the heterogeneous grain \nboundaries/surfaces increased coercivity, and showed better room temperature  ferromagnetism in \nthe samples with higher pH value. The creation of magnetic na noparticles with surface spin \npinning could be an alternative technique for overcoming the superparam agnetic fluctuation in \nnano-sized magnetic particles [35]. The samples with less pH val ue (e.g., P3_200, S3_200) are \nlargely superparamagnetic in nature. Since superparamagnetism i s a typical character where \nmagnetic exchange interactions inside the single domains are ove rcome by the thermal activated \nrandom motion of the domains, we suggest that surface spins are magne tically less active for the \nsamples with less pH value. In this case, surface spins are easily allowed for the random freezing \non the less defective surfaces. This results in the decrease of  ferromagnetic moment and inter-\nparticles interactions. The decrease of magnetic moment in low  pH samples is different from the \nobservations in composite samples. The coexistence of non-magnetic N aNO 3 reduces effective \nmagnetic volume and inter-particles magnetic interactions in com posite samples. There is a \nprobability that electronic charge carriers are highly mobile in the defective surface layers of the \nsamples. This concept is matching to the higher values of electri cal conductivity, dielectric \nconstant and relaxation time of the samples prepared at higher pH va lue and heated at lower  \n15 \n temperature (200 0C). The presence of poor conductor NaNO 3 reduced the effective conductivity \nof the ferrite particles in the composite samples. But, the fundame ntal property of higher \nconductivity in samples with higher pH is unchanged in the composite s amples also and this \nvalidates our assumptions in the proposed schematic diagram.  \nD. Conclusions \nThis experimental work highlighted the magnetic and dielectric pr operties of nano-structured \nCo 1.5 Fe 1.5 O4 ferrite, which was synthesized in chemical co-precipitation and subsequent heating \nat low temperature regime. Crystallite size of the samples  is in single domain range. An unusual \ndecrease of crystallite size by heating the co-precipita ted sample is attributed to the reduction of \ndefective surface volume. Magnetic and dielectric properties of the  pure and composite form of \nCo 1.5 Fe 1.5 O4 nanoparticles strongly depend on the pH value during coprecipitation and pinni ng of \nsurface spins at defective sites. Ferromagnetic moment in compos ite samples is decreased due to \nthe coexistence of non-magnetic NaNO 3. Superparamagnetic features dominate in the samples \nobtained at lower pH value, irrespective of pure or composite form of C o 1.5 Fe 1.5 O4 nanoparticles. \nThe samples obtained at higher pH value are highly soft ferromag netic with large moment, as \nwell as highly conductive and exhibited large dielectric constant . The results promise a wide \nscope of varying magnetic and dielectric properties by engineer ing pH dependent surface defects \nin pure and composite form of Co 1.5 Fe 1.5O4 particles. This is useful for room temperature \napplications of ferrite nanoparticles. \nAcknowledgment \nWe thank to CIF, Pondicherry University for providing experimental fa cilities and also to Dr. A. \nBanerjee of UGC-DAE CSR, Indore, for doing magnetic measurement of some  samples.   \n16 \n REFERENCES \n[1] Y.-wook Jun, J.-wook Seo, and J. Cheon, Accounts of Chem. Res. 41 (2008) 179 .  \n[2] S. Li, M.M. Lin, M.S. Toprak, D.K. Kim, and M. Muhammed, Nano Reviews 1 (2010) 5214.  \n[3] S.-H. Yu, and M. Yoshimura, Adv. Funct. Mater 1 (2002) 9. \n[4] R. Skomski, J. Phys.: Condens. Matter 15 (2003) R841. \n[5] A. Sandhu, H. Handa, and M. Abe, Nanotechnology 21 (2010) 442001. \n[6] B.K. Kuanr, V.Veerakumar, K. Lingam, S. R. Mishra, A.V. Kuanr, R .E. Camley, and Z. Celinski, J. \nAppl. Phys. 105 (2009) 07B522. \n[7] V.G. Harris, A. Geiler, Y. Chen, S. D. Yoon, M. Wu, A. Yang, Z. Chen, P. He, P. V. Parimi, X. Zuo, \nC.E. Patton, M. Abe, O. Acher, and C. Vittoria, J. Magn. Magn. Mater. 321 (2009) 2035.  \n[8] A.R. West, H. Kawai, H. Kageyam, M. Tabuchi, M. Nagata, and H. Tukamoto, J. Ma ter. Chem. 11  \n(2001) 1662. \n[9] A. C. C. Tseung, and J. R. Goldstein, J. Material Science 7 (1972) 1383. \n[10] M.T. Klem, M. Young, and T. Douglas, Materials Today 8 (2005) 28.  \n[11] Z. Zi, Y. Sun, X. Zhu, Z.Yang, J. Dai, W. Song, J.Magn.Magn. Mater. 321 (2009) 1251.  \n[12] V. Pallai, and D.O. Shah, J. Magn. Magn. Mater. 163 (1996) 243. \n[13] I. P. Muthuselvam, and R.N. Bhowmik, Solid State Sci. 11 (2009) 719. \n[14] X. S. Niu, W. P. Du, and W. M. Du, Sens. Actuators B 99 (2004) 405. \n[15] L.F. Liotta, and G. D. Carlo, et al., Appl. Catal. B 70 (2007) 314. \n[16] A. K. Giri, E. M. Kirkpatrick, P. Moongkhamklang, S. A. Majetich, and V.G. Harr is, Appl. Phys. \nLett. 80 (2002) 2341. \n[17] Z. Zhu, X. Li, Q. Zhao, Y. Shi, H. Li, and G. Chen, J. Nanopart. Res. 13 (2011) 2147. \n[18] Vinod Kumar, M. S. Yadav, and R. P. Pant, J. Magn. Magn. Mater. 320 (2008) 1729. \n[19] X. G. Zheng, H. Kubozono, H. Yamada, K. Kato, Y. Ishiwata, and C. N. Xu, Nature Nanotec hnology \n3 (2008) 724. \n  \n17 \n [20] K. E. Mooney, J. A. Nelson, and M. J. Wagner, Chem. Mater. 16 (2004) 3155. \n[21] F. Casoli, L. Nasi, F. Albertini, S. Fabbrici, C. Bocchi, F. Germini, P. Luches , A. Rota, and S. Valeri, \nJ. Appl. Phys. 103 (2008) 043912. \n[22] X.P. Zhong, G.H. Wang, and H.L. Luo, J. Magn. Magn. Mater. 120 (1993) 190. \n[23] V. Kumar, A. Rana, N. Kumar, and R.P. Pant, Int. J. Appl. Ceram. Technol. 8 (2011) 120. \n[24] Y. Ceden˜o-Mattei, and O.Perales-Pe´rez, Microelectronics Journal  40 (2009) 673. \n[25] Y. Qu, H. Yang, N. Yang, Y. Fan, H. Zhu, and G. Zou, Mater. Lett. 60 (2006) 3548. \n[26] W.Z. Zhu, and S.C. Deevi, Mater. Sci. Eng. A 362 (2003) 228. \n[27] I. P. Muthuselvam, and R.N. Bhowmik, J. Phys. D: Appl. Phys. 43 (2010) 465002. \n[28] M. George, S.S. Nair, K.A. Malini, P.A. Joy, and M.R, Anantharaman, J. Phys. D: App l. Phys. 40  \n(2007) 1593. \n[29] A.M.M. Farea, S. Kumar, K.M. Batoo, A. Yousef, and Alimuddin, Physica B: Condensed Matter 403 \n(2008) 684. \n[30] R. Mart´ınez, A. Kumar, R. Palai, J.F. Scott, and R.S. Katiyar, J. Phys. D: Appl . Phys. 44 (2011) \n105302. \n[31] M. Viviani, M. Bassoli, V. Buscaglia, M.T. Buscaglia, and P. Nanni, J. P hys. D: Appl. Phys. 42  \n(2009) 175407. \n[32] M.A. Subramanian, T. He, J. Chen, N.S. Rogado, T.G. Calvarese, and A.W. Sleight , Adv. Mater. 18 \n(2006) 1737. \n[33] R.N. Bhowmik, R. Ranganathan, B. Ghosh, S. Kumar, and S. Chattopadhyay, J. Alloys Compd. 456   \n(2008) 348. \n[34] R. N. Bhowmik, R. Ranganathan, R. Nagarajan, B. Ghosh, and S. Kumar, Phy s. Rev. B 72 (2005) \n094405. \n[35]  V. Skumryev, S. Stoyanov, Y. Zhang, G. Hadjipanayis, D. Givord, and J. Nogués,  Nature 423 (2003) \n850. \n   \n18 \n Table 1. Lattice parameter (a), Crystallite size (d), cell volume (V ) of pure samples and NaNO 3. \nSample Lattice constant,  \na (Å) Cell volume , \na3 (10 -30  m3) Crystallite size  \n<d >311  (nm) Crystallite size, \n<d> avg  (nm) for 6 \nprominent peaks \nP1_200 8.293 ± 0.002 570.34 ± 0.20 9.46 8.64 \nP2_200 8.276 ± 0.002 566.84 ± 0.25 10.1 9.08 \nP3_200 8.249 ± 0.003 561.39 ± 0.37 8.6 7.95 \nP1_500 8.257 ± 0.001 562.95 ± 0.06 9.26 8.36 \nP2_500 8.272 ± 0.002 566.02 ± 0.19 9.8 8.71 \nP3_500 8.278 ± 0.002 567.25 ± 0.25 7.94 6.57 \nNaNO 3 a=b=5.07663± 0.00096 \nc=16.85566 ± 0.00366 376.21 ± 0.13 62.2  \n \n \n \n \n \n \n \n \n \n \n \n \n  \n19 \n Table 2. List of M  at 15 kOe, M R, H C for samples measured at 300K with different pH values and \nannealing temperatures. \nSample M at 15 kOe (emu/g) M R (emu/g)  H C (Oe) \nP1_200 16.39 1.29 77.51 \nP2_200 23.69 0.93 32.86 \nP3_200 14.58 0.05 5.05 \nP1_500 29.47 1.31 35.71 \nP2_500 28.19 0.56 12.59 \nP3_500 34.05 3.15 9.42 \nS1_200 8.23 0.36 37.26 \nS3_200 4.03 0.0 0.0 \nS1_500 10.32 0.25 19.26 \nS2_500 8.91 0.58 58.56 \nS3_500 6.41 0.13 25.56 \n \n \n \n \n \n \n \n \n \n  \n20 \n Table 3. List of σ1Hz , ε1Hz , resistivity ρ, relaxation time τm for samples of different pH values and \nannealing temperatures. \nSample σ1Hz   \n(10 -6S/cm)  n1 n 2 ρg  \n(Ω-cm) ρgb   \n(Ω-cm) ε1Hz  (10 6) τm (10 -4 \nsec) \nP1_200 534.07 0.19 0.33 670  -- 960 8.33 \nP2_200 106.26 0.19 0.24 1516 --- 191 3.87  \nP3_200 185.57 0.18 0.20 1562 -- 334 3.87  \nP1_500 62.38 0.33 0.19 395 -- 112 5.15  \nP2_500 35.39 0.28 0.23 3250 -- 64 19.00 \nP3_500 17.21 0.05 0.70 32722 144.4M 31 208.00 \nS1_200 80.30  0.22 0.07 3482 -- 144  --- \nS3_200 2.70 0.07 0.03 185105 5.52x10 5 5 1.97  \nS1_500 89.34 0.38 0.14 3810 -- 49 14.22 \nS2_500 4.71 0.28 0.08 26682 6.02 x10 5 8 11.24 \nS3_500 3.68 0.13 0.05 89802 5.48x10 5 7 1.16  \nNaNO 3 1.81×10 -3 0.08 0.94 ---- 2.14x10 8  3.26×10 -3 333.33 \n \n \n \n \n \n  \n21 \n         \n \n                             20 30 40 50 60 70 80 20 30 40 50 60 70 80   \n(440) (511) (400) (220) \n(311) (a) P1_200 \n  \n Experimental data \n Fitted data \n Difference \n Bragg's Position \n \n  \n(b) P2_200 Intensity (arb. units) \n  \n(c) P3_200 \n2θθ θθ (deg) \n \n \n  \n(d) P1_500  \n (e) P2_500 \n   \nFig. 2 (Color online) XRD profile fit of pure sampl es synthesized at different pH values. \nThe as prepared samples were annealed at 200 0C (a-c) and 500 0C (d-f), respectively. \n  \n(f) P3_500 \n2θθ θθ (deg) \n  \n22 \n                            0200 400 600 \n0200 400 600 \n28 30 32 34 36 38 40 0200 400 600 (a) S1_200 \n(N 113) (N 104) \n(N 006) \n(N 110) (S 220) \n(S 311) \n  \n(b) P1_200 \n(S 311) (S 220) \n  Counts/s \nFig. 3 XRD pattern of S1_200 (a), P1_200 (b), and N aNO 3 (c) samples. XRD patterns of the samples \nhave been plotted in the limited range of (x-y) sca les for clarity. (c) NaNO 3\n(N 113) (N 110) (N 006) (N 104) \n  \n2θ (deg) \n \n                -15000 -10000 -5000 0 5000 10000 15000 -20 -10 010 20 30 \n-100 0 100 -2 -1 0120 5000 10000 15000 020 T=300K \nFig. 4 (Color online) M(H) loops at 300 K for pure samples at 200 0C. Inset-a shows the M(H) data at first \nquadrant for 500 0C heated pure samples. Inset-b shows the loop of 20 0 0C samples at lower magnetic field. \n  M (emu/g) \nH (Oe)  P1_200 \n P2_200 \n P3_200 \nInset-b \n  M (emu/g) \nH (Oe) Inset-a \n  M(emu/g) \nH(Oe)  P1_500 \n P2_500 \n P3_500 \n  \n23 \n                          -15000 -10000 -5000 0 5000 10000 15000 -10 -5 0510 \n-100 -50 0 50 100 -0.5 0.0 0.5 0 2000 4000 0100 T=300K \nS3_500 S2_500 S1_500 \nS3_200 S1_200 \nFig. 5 (Color online) M(H) loops of composite sampl es at 300 K. Inset-a shows the Arrot plot for visua lizing the \nspontaneous magnetization. Inset-b shows the low fi eld loops which are used to calculate M R and H C.\n  M (emu/g) \nH (Oe) Inset-b MR\nHC\n   M (emu/g) \nH (Oe) Inset-a \nS3_500 S2_500 S1_500 \nS3_200 S1_200 \n  M2 (emu/g) 2\nH/M \n  \n                                      10 010 110 210 310 410 5 10 -5 10 -4 10 -3 \n10 010 110 210 310 410 5 10 -6 1x10 -5 1x10 -4 10 -3 10 010 110 210 310 410 510 -4 10 -3 10 -2 \n10 010 110 210 310 410 510 -8 10 -7 10 -6 1x10 -5 1x10 -4 \nn2n1n2\nn1(b)  P1_500 \n P2_500 \n P3_500 \n  σ (S/cm) \nFrequency (Hz) \nFig. 6 (Colour online) Frequency dependent ac condu ctivity of different samples. \nThe lines guide to the linear fit of the conductivi ty data in log-log scale according \nto Jonscher power law with exponents (n 1 and n 2). n2\nn1(d)  S1_500 \n S2_500 \n S3_500 \n  σ S/cm) \n(Frequency (Hz) n = 0.8 \nn2\nn1n1n2(a)  P1_200 \n P2_200 \n P3_200 \n  σ (S/cm) \n(C)  S1_200 \n S3_200 \n NaNO 3 \n σ S/cm \n  \n24 \n           0 200 400 050 100 \n0 1000 2000 3000 0500 1000 0.0 2.0x10 44.0x10 46.0x10 48.0x10 401x10 42x10 4\n0.0 5.0x10 31.0x10 41.5x10 42.0x10 40.0 5.0x10 31.0x10 4interfacial effect (a) \n  -Z'' (ohm) \nZ' (ohm) P1_200 \nP2_200 \nP3_200 \n(d) (C) \nFig. 7. (Color online) (log-log scale) Cole-Cole pl ots for different pH values Pure samples at 200 0C (a) and \nat 500 0C (b), composite samples at 200 0 C (C) and at 500 0C (d). The lines are fit curves of data to semi-cir cles.   -Z'' (ohm) \nZ' (ohm)  P1_500 \n P2_500 \n P3_500 (b) \n  -Z'' (ohm) \nZ (ohm)  S3_200 \n  -Z'' (ohm) \nZ' (ohm)  S2_500 \n S3_500 \n \n                         10 010 110 210 310 410 510 410 510 610 710 8\n10 010 110 210 310 410 5 10 210 310 410 510 610 710 010 110 210 310 410 5 10 410 510 610 710 810 9\n10 010 110 210 310 410 510 110 210 310 410 510 610 710 8\n P1_500 \n P2_500 \n P3_500 \n             (b) \n  ε (log scale) \nFrequency (Hz) (log scale) \nFig. 8 (Colour online) Frequency dependent dielectr ic constant for sol (S 0) and pure \nsamples at 200 0C (a), at 500 0C (b), and composite samples at 200 0C, at 500 0C (d).  S1_500 \n S2_500 \n S3_500 \n           (d) \n  \nFrequency (Hz) (log scale)  P1_200 \n P2_200 \n P3_200 \n sol (S 0)\n          (a) \n  ε (log scale)  S1_200 \n S3_200 \n NaNO 3\n            (C) \n  \n  \n25 \n                     10 010 110 210 310 410 5110 \n10 010 110 210 310 410 5110 10 010 110 210 310 410 50.1 110 \n10 010 110 210 310 410 50.1 1\n(b) \n  tan δ\nFrequency (Hz)  P1_500 \n P2_500 \n P3_500 (d) \n  \nFrequency (Hz)  S1_500 \n S2_500 \n S3_500 (C) \n  \n S1_200 \n S3_200 \n NaNO 3\nFig. 9. (Color online) (log-log scale) Frequency de pendent dielectric loss (tan δ) \nfor stock solution and Pure samples at 200 0C (a), Pure samples at 500 0C (b), \ncomposite samples at 200 0C (C) and composite samples at 500 0C (d). (a) \n  tan δ\n P1_200 \n P2_200 \n P3_200 \n Solution (S 0)\n   \n26 \n               \n                              \n          "    },    {        "title": "1504.03792v3.Acoustic_study_for_dynamical_molecular_spin_state_without_undergoing_magnetic_phase_transition_in_spin_frustrated_ZnFe__2_O__4_.pdf",        "content": "arXiv:1504.03792v3  [cond-mat.str-el]  16 Oct 2015Acoustic study of dynamical molecular-spin state without u ndergoing magnetic phase\ntransition in spin-frustrated ZnFe 2O4\nTadataka Watanabe1,∗Shota Takita1, Keisuke Tomiyasu2, and Kazuya Kamazawa3\n1Department of Physics, College of Science and Technology (C ST),\nNihon University, Chiyoda, Tokyo 101-8308, Japan\n2Department of Physics, Tohoku University, Sendai, Miyagi 9 80-8577, Japan and\n3Comprehensive Research Organization for Science and Socie ty (CROSS), Tokai, Ibaraki 319-1106, Japan\n(Dated: January 23, 2018)\nUltrasound velocity measurements were performed on a singl e crystal of spin-frustrated ferrite\nspinel ZnFe 2O4from 300 K down to 2 K. In this cubic crystal, all the symmetric ally-independent\nelastic moduli exhibit softening with a characteristic min imum with decreasing temperature be-\nlow∼100 K. This elastic anomaly suggests a coupling between dyna mical lattice deformations and\nmolecular-spin excitations. In contrast, the elastic anom alies, normally driven by the magnetostruc-\ntural phase transition and its precursor, are absent in ZnFe 2O4, suggesting that the spin-lattice\ncoupling cannot play a role in relieving frustration within this compound. The present study infers\nthat, for ZnFe 2O4, the dynamical molecular-spin state evolves at low tempera tures without un-\ndergoing precursor spin-lattice fluctuations and spin-lat tice ordering. It is expected that ZnFe 2O4\nprovides the unique dynamical spin-lattice liquid-like sy stem, where not only the spin molecules but\nalso the cubic lattice fluctuate spatially and temporally.\nPACS numbers: 72.55.+s, 75.20.-g, 75.40.Gb, 75.50.Xx\nI. INTRODUCTION\nCubic spinels AB2O4with magnetic Bions have at-\ntracted considerable interest in light of the geometri-\ncal frustration which is inherent in the B-site sublat-\ntice of corner-sharing tetrahedra (pyrochlore lattice).1\nOne of the most extensively studied spinel systems is\nchromite spinels ACr2O4withA= Mg and Zn, for\nwhich the magnetic properties are fully dominated by\nthe Jahn-Teller (JT)-inactive Cr3+with spin S= 3/2\n(Fig. 1(a)) residing on the pyrochlore network.2ACr2O4\nwith Weiss temperature Θ W≃ −390 K undergoes an\nantiferromagnetic (AF) ordering at TN≃13 K along\nwith a cubic-to-tetragonal structural distortion.3–5Fer-\nrite spinels AFe2O4withA= Zn and Cd are another\nJT-inactive spinel system with Fe3+showing a high spin\nofS= 5/2 (Fig. 1(b)).6ForAFe2O4with Θ W≃120 K\n(A= Zn) and ≃ −50 K (A= Cd), neutron scattering\nexperiments in the high-purity single crystals observed\nneither long-range magnetic ordering nor a structural\ntransition down to low temperature (1.5 K) although an\nAF-transition-like anomaly occurs in the magnetic sus-\nceptibility at T∗≃13 K (Fig. 1(c)).7,8Additionally, it\nis noted that the magnetic susceptibility of ZnFe 2O4ex-\nhibits a deviation from the Curie-Weiss law below ∼100\nK (Fig. 1(d)),7which implies the enhancement of the AF\ninteractions at low temperatures.9Thus, the frustrated\nmagnetism of AFe2O4should be different in nature from\nthat ofACr2O4.\nForACr2O4, the phase transition to spin-lattice or-\ndering is explained by the spin-JT mechanism via spin-\nlattice coupling, where local distortions of the tetra-\nhedra release the frustration in the nearest-neighbor\nAF interactions.10–12In the frustrated paramagnetic\n(PM) phase of ACr2O4, inelastic neutron scatter-ing (INS) experiments provided evidence of quasielas-\ntic magnetic scattering, indicating the presence of\nstrongspinfluctuationsbecauseofspinfrustration.3,13–15\nThis quasielastic mode involved the fluctuations of AF\nhexagonal spin molecules (AF hexamers) in the py-\nrochlore lattice (Fig. 1(e)).13,15Further, ultrasound ve-\nlocity measurements of ACr2O4suggested the coexis-\ntence/crossover of the precursor spin-lattice fluctuations\ntowards a phase transition (spin-JT fluctuations) and\nthe gapped molecular-spin excitations also coupled with\nthe lattice,16,17which is compatible with the recent ob-\nservation of finite-energy molecular-spin excitations in\ntime-of-flight INS experiments in the PM phase of this\ncompound.18\nForAFe2O4, whereas spin-lattice ordering is absent\ndown to low temperature, the INS experiments observed\nmagnetic diffuse scattering and its very soft dispersion\nrelation in the energy range below ∼2 meV, arising pos-\nsibly from the dynamical molecular-spin state.7,8Thus,\nin the absence of the spin-JT effect, the frustrated mag-\nnetism in AFe2O4is expected to be mainly governed by\nthe dynamical molecular-spin state. For ZnFe 2O4, the\nobserved diffuse scattering was attributed to the fluctua-\ntions of AF twelve-membered spin molecules (AF dode-\ncamers illustrated in Fig. 1(f)).19The formation of the\ndifferenttypesofspinmoleculesinbetweenZnFe 2O4(the\nAF dodecamers) and ACr2O4(the AF hexamers) is con-\nsidered to arise from the difference in the dominant ex-\nchange paths, specifically, the third-neighbor AF interac-\ntionsJ3with additional nearest-neighbor ferromagnetic\n(FM)J1forZnFe 2O4,7,19butAFJ1forACr2O4,13,15, re-\nspectively. For CdFe 2O4, the INS experiments produced\nscattering patterns, which resembles that of ACr2O4, in-\ndicative of the dominant AF J1.8\nInterestingly,thediffuse-neutron-scatteringpatternsof2\nH = 1000 Oe T* 0.5\n0.4\n0.3\n0.2M/H  (emu/mol Oe)\n T (K)50403020100(c) \nZnFe 2O4\nH || [001] \n(e) Cr 3+ AF hexamer Cr 3+\n(f) Fe 3+ AF dodecamer Fe 3+(a) Cr 3+ (3d 3 )eg\nt2g \n(b) Fe 3+ (3d 5 )eg\nt2g \n3002001000 50 150 250 \n T (K)40\n30\n20\n10\n0H/M  (mol Oe/emu)\nH = 1000 Oe ZnFe 2O4\nH || [001] (d) \nFIG. 1: (Color online) (a) and (b) show the spin states of\nCr3+(3d3) and high-spin Fe3+(3d5) in the octahedral crystal\nfield, respectively. (c) and (d) depict respectively the mag -\nnetic susceptibility and the inversed magnetic susceptibi lity\nof single-crystalline ZnFe 2O4as functions of temperature. (e)\nand (f) illustrate respectively a Cr3+AF hexamer and a Fe3+\nAF dodecamer in the pyrochlore lattice. The dotted cube in\n(e) and (f) depicts a unit cell of the cubic spinel structure.\nZnFe2O4vary with temperature,7while those of ACr2O4\nand CdFe 2O4are independent of temperature.8,13,15\nThis temperature dependence in ZnFe 2O4was explained\nby the competition between the third-neighbor AF J3\nand the temperature-dependent nearest-neighbor FM\nJ1, where the nearest-neighbor FM J1are weakened\nwith decreasing temperature due to the temperature-\ndependent bond angle of the nearest-neighbor Fe3+-O-\nFe3+.7,9The neutron scattering experiments in ZnFe 2O4\nsuggested that the deviation from the Curie-Weiss law\nbelow∼100 K in the magnetic susceptibility of this\ncompound (Fig. 1(d)) arises from the AF component,\nwhereas the FM component leads to the Curie-Weiss be-\nhavior with Θ W≃120 K at high temperatures.7And\nit is considered that, for ZnFe 2O4, the formation of the\nspin molecules (the AF dodecamers) is realized at low\ntemperatures, where the AF component generates the\nfrustration.19\nNotably, molecular-spin excitations were observed in\ntheINSexperimentsinthefrustratedmagnetsofnotonly\nACr2O4andAFe2O4but also HgCr 2O4,20GeCo2O4,21\nLiV2O4,22and Tb 2Ti2O7,23where the number of mag-\nnetic ions, shape, and symmetry of spin molecules are\nconsideredto varyfrom compound to compound depend-\ning on the dominant exchange path. These observationsimply that the dynamical molecular-spin state can uni-\nversally emerge in the frustrated magnets. Thus a com-\nparative study among the spinel magnets using a variety\nof experimental probes must provide a root for under-\nstanding the nature of dynamical molecular-spin state.\nIn this paper, we present an analysis of ultra-\nsound velocity measurements for the zinc ferrite spinel\nZnFe2O4. The sound velocity or the elastic modulus\nis a useful probe enabling symmetry-resolved thermo-\ndynamic information to be extracted from frustrated\nmagnets.16,17,24–32As mentioned earlier, the observed\nelasticanomaliesin the chromitespinels ACr2O4inferred\nthe coexistence of spin-JT fluctuations and molecular-\nspin excitations in the PM phase.16,17The present study\nfinds elastic anomalies in ZnFe 2O4that suggest the\nevolution of a dynamical molecular-spin state at low\ntemperatures without undergoing precursor spin-lattice\nfluctuations and spin-lattice ordering, which is a be-\nhavior uniquely different from another spin-frustrated\nmolecular-spinsystem ACr2O4. Moreover,ourstudyalso\nsuggests that, for ZnFe 2O4, the molecular-spin excita-\ntions consist of multiple gapped modes and sensitively\ncouple to the trigonal lattice deformations, which is a\nbehavior similar to ACr2O4although the details are dif-\nferent in between ZnFe 2O4andACr2O4.\nII. EXPERIMENTAL\nThe ultrasoundvelocitymeasurementswereperformed\non a high-purity single crystal of ZnFe 2O4grown by the\nflux method.7Figure 1(c) and (d) plots respectively the\ntemperature dependence of the magnetic susceptibility\nand the inversed magnetic susceptibility of the ZnFe 2O4\nsingle crystal used in the present study, where the AF-\ntransition-like anomaly at T∗∼13 K and the deviation\nfrom the Curie-Weiss law below ∼100 K occur.7The\nultrasound velocities were measured using the phase-\ncomparison technique with longitudinal and transverse\nsound waves at a frequency of 30 MHz. The ultrasonic\nwaves were generated and detected by LiNbO 3transduc-\ners glued to the parallel mirror surfaces of the crystal.\nThe measurements were performed at temperatures from\n300 K to 2 K for all the symmetrically-independent elas-\ntic moduli in the cubic crystal, specifically, compression\nmodulus C11, tetragonal shear modulusC11−C12\n2≡Ct,\nand trigonal shear modulus C44. The respective mea-\nsurements of C11,Ct, andC44were performed using lon-\ngitudinal sound waves with propagation k/bardbl[001] and po-\nlarization u/bardbl[001], transverse sound waves with k/bardbl[110]\nandu/bardbl[1¯10], and transverse sound waves with k/bardbl[110]\nandu/bardbl[001]. The sound velocities of ZnFe 2O4measured\nat room temperature (300 K) are 6480 m/s for C11, 2930\nm/s forCt, and 3740 m/s for C44.3\nIII. RESULTS AND DISCUSSION\nFigure 2(a)-(c) presents the temperature dependence\nof the elastic moduli, C11(T),Ct(T), andC44(T) in\nZnFe2O4. On cooling from room temperature (300 K)\nto∼100 K, all the elastic moduli exhibit ordinary hard-\nening consistent with the background C0\nΓ(T) taken from\nan empirical evaluation of the experimental CΓ(T) in 100\nK< T <300 K (dotted curves in Fig. 2(a)-(c))33. Here,\nthe background values at T= 0 K,C0\n11(0)≃233.8 GPa,\nC0\nt(0)≃46.7 GPa, and C0\n44(0)≃75.9 GPa give the re-\nspective sound velocities of v0\n11≃6620 m/s, v0\nt≃2960\nm/s, and v0\n44≃3770m/s, which are ∼2%,∼1%, and ∼\n0.8% largerthan the measuredsoundvelocitiesat300K,\nrespectively. The values of v0\n11,v0\nt, andv0\n44give the aver-\naged sound velocity ¯ v∼3700 m/s,34which is compatible\nwith the Debye temperature Θ D∼250 K for ZnGa 2O4,\na nonmagnetic reference compound for ZnFe 2O4, giving\nthe averaged sound velocity ¯ v∼3500 m/s.35\nIn Fig. 2(a)-(c), below ∼100 K, all the elastic mod-\nuli of ZnFe 2O4exhibit an anomalous temperature vari-\nation, specifically, the deviation from the ordinal hard-\nening indicated as the dotted curves in Fig. 2(a)-(c).\nC11(T) exhibits softening with decreasing temperature\nbelow∼50 K but turns to hardening below ∼6 K. Sim-\nilarly,Ct(T) andC44(T) exhibit softening with decreas-\ning temperature below ∼80 K, which turn to harden-\ning below ∼6 K and ∼4 K, respectively. Taking into\naccount the absence of orbital degeneracy in the B-site\nhigh-spin Fe3+in ZnFe 2O4(Fig. 1(b)), the anomaly in\nCΓ(T) should have a magnetic origin where the spin de-\ngrees of freedom play a significant role.6Note that the\nelasticanomaliesemergeat temperatureswherethe mag-\nnetic susceptibility exhibits the deviationfrom the Curie-\nWeiss law (Fig. 1(d)). This correspondence implies that\nthe elastic anomalies are driven by the generation of\nfrustration below ∼100 K, which is compatible with the\ntemperature-dependent J1/J3suggested from the neu-\ntron scattering experiments.7\nThe elastic anomalies in the JT-inactive magnets like\nZnFe2O4are attributed to magnetoelastic coupling act-\ning on the exchange interactions. In this mechanism, the\nexchange striction arises from a modulation of the ex-\nchange interactions by ultrasonic waves.34Both the lon-\ngitudinal and transverse sound waves couple to the spin\nsystem via the exchange striction mechanism, which de-\npends on the directions of both polarization uand prop-\nagationkof sound waves relative to the exchange path.\nSimilar to ZnFe 2O4, the softening-with-minimum elas-\ntic anomaly in CΓ(T) is also observed in other frustrated\nmagnets of ACr2O4,16,17SrCu2(BO3)2,25,26GeCo2O4,29\nand MgV 2O4,32the origin of which is considered to be\nthe coupling of the lattice to the gapped magnetic ex-\ncitations via the exchange striction mechanism. Recall-\ning that molecular-spin excitations, i.e., the excitations\nof AF dodecamers, were observed in the INS experi-\nments for ZnFe 2O4,7,19the softening-with-minimum ex-\nhibited in CΓ(T) for ZnFe 2O4arises from the coupling(e) Ct\n40 %\nMgCr2O4ZnFe 2O4\nTN\nΔCt / Ct\n(f) C44 \n4 %MgCr2O4\nTNZnFe 2O4\nΔC44 / C44 (d) C11 \nZnFe 2O4\nMgCr2O410 %TNΔC11 / C11 T*\n3002001000\nT (K)ZnFe 2O4(a) C11 \n232\n228\n224~1.8 %C11  (GPa)\n76 \n75 \n74 \nT (K)C44  (GPa)(c) C44 ZnFe 2O4 ~1.3 %\n30025020015010050046.6\n46.2\n45.8Ct (GPa)ZnFe 2O4(b) Ct\n~0.9 %k||u||[001] \nAF Dodecamer \nk||[110] u||[110] -\nk||[110] u||[001] T*\nT*\nFIG. 2: (Color online) (a)-(c) Elastic moduli of ZnFe 2O4as\nfunctions of temperature. (a) C11(T), (b)Ct(T), and (c)\nC44(T). The dotted curves in (a)-(c) indicate the background\nC0\nΓ(T) in each modulus taken from an empirical evaluation\nof the experimental CΓ(T) in 100 K < T < 300 K.33The\ninsets to (a)-(c) illustrate single AF dodecamers in the Fe3+\npyrochlore lattice with the propagation kand polarization u\nof sound waves in the respective elastic modes. (d)-(f) The\ndependence on temperature of the elastic moduli of ZnFe 2O4\n[from Fig. 2(a)-(c)] and MgCr 2O4.17(d)C11(T), (e)Ct(T),\nand (f)C44(T). The curves are vertically shifted for clarity.\nT∗andTNin (d)-(f) indicate the temperature at which the\nAF-transition-like anomaly occurs in the magnetic suscept i-\nbility for ZnFe 2O4seen in Fig. 1(c), and the AF ordering\ntemperature for MgCr 2O4, respectively.\nof the lattice to the molecular-spin excitations, which\nis similar to the softening-with-minimum observed in\nCΓ(T) ofACr2O4.16,17The insets to Fig. 2(a)-(c) il-\nlustrate single AF dodecamers in the Fe3+pyrochlore\nlattice with the propagation kand polarization uof\nsound waves in the respective elastic modes. From the\nsymmetry point of view, the AF-dodecamer excitations\nshould couple more sensitively to the trigonal lattice de-\nformations generated by sound waves with k/bardbl[110] and\nu/bardbl[001] (the inset to Fig. 2(c)). For ZnFe 2O4, as shown\nin Fig. 2(a)-(c), the magnitude of the softening in CΓ(T)4\nis indeed largest in the trigonal shear modulus C44(T),\nspecifically, ∆ C11/C11∼0.4 %, ∆Ct/Ct∼1.8 %, and\n∆C44/C44∼2.8%, whichiscompatiblewiththe trigonal\nsymmetry of the AF dodecamer.\nFigure 2(d)-(f) compares the relative shifts of C11(T),\nCt(T), andC44(T), respectively, in between ZnFe 2O4\n[from Fig. 2(a)-(c)] and MgCr 2O4.17Note here that\nCΓ(T) for MgCr 2O4in the PM phase ( T > T N) ex-\nhibits not only softening-with-minimum in C44(T) from\nmolecular-spin excitations but also a huge Curie-type\n−1/Tsoftening in C11(T) andCt(T), being a precursor\nto the spin-JT transition.17This coexistence of twotypes\nof elastic anomalies in MgCr 2O4infers the coexistence of\nmolecular-spin excitations and spin-JT fluctuations. For\nZnFe2O4, in contrast, CΓ(T) exhibits solely softening-\nwith-minimum, as is clearly seen in the expanded view\nofCΓ(T) (Fig. 3(a)-(c) [open circles, from Fig. 2(a)-(c)]),\nwhich infers the presence of molecular-spin excitations\nbut the absence of spin-JT fluctuations.\nWe also note here that, whereas CΓ(T) for MgCr 2O4\nexhibits a discontinuity at TN(Fig. 2(d)-(f)), CΓ(T) for\nZnFe2O4exhibits no discontinuity at T∗(Figs. 2(d)-\n(f) and 3(a)-(c)). Thus, the experimental CΓ(T) for\nZnFe2O4indicates that the AF-transition-like anomaly\natT∗in the magnetic susceptibility seen in Fig. 1(c)\nis not a phase transition. This inference is compati-\nble with the absence of long-range magnetic ordering at\nleast down to 1.5 K as revealed by the neutron scattering\nexperiments.7Regarding CΓ(T) for ZnFe 2O4, the conti-\nnuity in elasticity at T∗(the absence of a phase transi-\ntion) is compatiblewith the absenceofCurie-typesoften-\ning (the absence of a precursorfor the magnetostructural\ntransition), indicating that the spin-lattice coupling can-\nnot produce the spin-JT transition because the strength\nof the exchange interactions is not large enough to over-\ncome the cost in elastic energy involved in the static\nlong-range lattice deformation. As a result, it is consid-\nered that, for ZnFe 2O4, solely the dynamical molecular-\nspin state emerges without undergoing spin-lattice fluc-\ntuations and spin-lattice ordering, which is different from\nthecoexistenceofthedynamicalmolecular-spinstateand\nthe spin JT effect in ACr2O4. However, the precise na-\nture of the magnetic state of ZnFe 2O4belowT∗remains\ntobediscovered. Freezingofthespinmoleculesisapossi-\nbility that might occur at T∗in ZnFe 2O4. Furthermore,\nalthough the spin-lattice coupling in ZnFe 2O4is much\nweaker than that in ACr2O4as indicated in Fig. 2(d)-\n(f), there remains a possibility of spin-JT transition at\nlowT <1.5 K for ZnFe 2O4.\nAs is clear from a comparison between CΓ(T) for\nZnFe2O4(Fig. 2(a)-(c)) and C44(T) for MgCr 2O4\n(Fig. 2(f)), the softening in CΓ(T) begins to occur be-\nlow∼50 K or ∼80 K in ZnFe 2O4but above 300 K in\nMgCr2O4. The softening occurring at lower tempera-\ntures for ZnFe 2O4indicates the evolution of the dynam-\nical molecular-spin state at lower temperatures, which is\ndriven by the generation of frustration below ∼100 K be-\ncauseofthetemperature-dependent J1/J3. Furthermore,the magnitude of the softening in CΓ(T) for ZnFe 2O4is\nsmaller than that in C44(T) for MgCr 2O4. As discussed\nlater in conjunction with Eq. (1) and Table I, the reason\nfor the smaller magnitude of the softening for ZnFe 2O4\nrelativetoMgCr 2O4isbecausethe couplingisweakerbe-\ntween the dynamical lattice deformations and molecular-\nspin excitations. Additionally, as is also clear from a\ncomparison between CΓ(T) of ZnFe 2O4(Fig. 3(a)-(c))\nandC44(T) of MgCr 2O4(Fig. 2(f)), the former exhibits\nits minimum at ∼5 K, which is lower than the minimum\npoint of ∼50 K in the latter. As also discussed later in\nconjunction with Eq. (1) and Table I, the lower temper-\nature at which the minimum point occurs for ZnFe 2O4\nrelative to MgCr 2O4is due to the smaller gap associated\nwith its molecular-spin excitations.\nSoftening-with-minimum in CΓ(T) driven by the\nmolecular-spin excitations is generally explained as the\npresence of a finite gap for the excitations, which is sen-\nsitive to strain.17In the mean-field approximation, the\nelastic modulus CΓ(T) of the molecular-spin system is\nwritten as17:\nCΓ(T) =C0\nΓ(T)−G2\n1,ΓNχΓ(T)\n{1−KΓχΓ(T)},(1)\nwhereC0\nΓ(T) is the background elastic constant, Nthe\ndensity of spin molecules, G1,Γ=|∂∆1/∂ǫΓ|the coupling\nconstant for a single spin molecule measuring the strain\n(ǫΓ) dependence of the excitation gap ∆ 1,KΓthe inter-\nspin-molecule interaction, and χΓ(T) the strain suscepti-\nbility of a single spin molecule. From Eq. (1), the mini-\nmum in CΓ(T) appears when this elastic mode strongly\ncouples to the excited state at ∆ 1; on cooling, CΓ(T) ex-\nhibits softening roughly down to T∼∆1, but recovery\nof the elasticity (hardening) roughly below T∼∆1.\nAs explained above, the softening-with-minimum\nanomaly in CΓ(T) for ZnFe 2O4should arise from a gap\nin the molecular-spin excitations that is sensitive to the\nstrain. This interpretation helps to understand the INS\nresults for ZnFe 2O4.7The broad magnetic scattering\nspectrum should observe gapped molecular-spin excita-\ntions that are considerably smeared. The smeared INS\nspectra at 1.5 K, only one-third of the minimum po-\nsition of ∼5 K inCΓ(T), are probably due to strong\nspin frustration as well as some kind of quantum ef-\nfect in the molecular-spin system. Recall that, for\nother frustrated magnets of ACr2O4and SrCu 2(BO3)2,\nobservations have been reported of the softening-with-\nminimum in CΓ(T) and the T-dependent observation\nof the gapped magnetic excitations in the INS spectra.\nForACr2O4, whereas CΓ(T) exhibited the minimum at\n∼50 K [Fig. 2(f)],17the INS experiments observed broad\nquasielastic magnetic scattering spectrum at tempera-\ntures down to TN≃13 K but observed distinct ∼4-meV\ngapped excitations below TN.3,13,15For the dimer-spin\nsystem SrCu 2(BO3)2, softening-with-minimum in CΓ(T)\nwas observed,25,26whereas the INS experiments demon-\nstrated∼3-meVgapped excitations at temperatures only\nbelow∼10 K.36For ZnFe 2O4, it is expected that the5\nZnFe 2O4(b) Ct\nT*46.6\n46.4\n46.2\n46.046.8 Ct (GPa) AF Dodecamer \nN = 1.73x10 27  m -3 \nEq. (1) ( Δ1 and Δ2)Eq. (1) ( Δ1)AF Dodecamer \nN = 1.73x10 27  m -3 \nEq. (1) ( Δ1 and Δ2)Eq. (1) ( Δ1)ZnFe 2O4(a) C11 \nT*233.6\n233.4\n233.2\n233.0233.8C11  (GPa)\nZnFe 2O4(c) C44 \nT*\n50403020100\n T (K)75.5\n75.0\n74.5\n74.076.0 C44  (GPa)AF Dodecamer \nN = 1.73x10 27  m -3 \nEq. (1) ( Δ1 and Δ2)Eq. (1) ( Δ1)\nFIG. 3: (Color online) Expanded view of CΓ(T) below 50 K\nin ZnFe 2O4[open circles, from Fig. 2(a)-(c)]. (a) C11(T), (b)\nCt(T), and (c) C44(T).T∗in (a)-(c) indicates the temper-\nature at which the AF-transition-like anomaly occurs in the\nmagnetic susceptibility for ZnFe 2O4seen in Fig. 1(c). The\nsolid curves (dotted curves) in (a)-(c) are fits of the exper-\nimental CΓ(T) to Eq. (1) with two singlet-triplet gaps ∆ 1\nand ∆ 2(single singlet-triplet gap ∆ 1) for the AF-dodecamer\nexcitations.19\nINS experiments at low T <1.5 K show clear gapped\nmolecular-spin excitations.\nWe now give a quantitative analysis of the experi-\nmentalCΓ(T) in ZnFe 2O4using Eq. (1) assuming ex-\ncitations of the AF dodecamers in the Fe3+pyrochlore\nlattice [Fig. 1(f)].19Here, the value of the density of\nAF dodecamers, Nin Eq. (1), is assumed to be N=\n1.73×1027m−3, which is one-twelfth of the density of\nFe3+ions in ZnFe 2O4.19We fit Eq. (1) to the experi-\nmentaldata CΓ(T)below50K.Althoughthebackground\nC0\nΓ(T) in Eq. (1) generally exhibits hardening with de-\ncreasing temperature,33we here assume that C0\nΓ(T) is\nconstant because, for ZnFe 2O4, the hardening of the\nbackground below ∼50 K is negligibly small compared\nwith the softening-with-minimum in CΓ(T), as indicated\nin Fig. 2(a)-(c).\nFor ZnFe 2O4, taking into account the vanishing total\nspinStot= 0inthegroundstateoftheAFdodecamers,19\n∆1in Eq. (1) is assumed to be singlet-multiplet excita-TABLE I: Values of the fitting parameters in Eq. (1) with two\nsinglet-triplet gaps ∆ 1and ∆ 2for the experimental CΓ(T) of\nZnFe2O4[from Fig. 3(a)-(c)] (upper column) and ACr2O4(A\n= Mg and Zn) (lower column).17For ZnFe 2O4(upper col-\numn), values of the fitting parameters in Eq. (1) with singlet -\ntriplet ∆ 1and singlet-nonet ∆ 2are also shown in parentheses.\n∆1(K)G1,Γ(K) ∆ 2(K)G2,Γ(K)KΓ(K)\nZnFe2O4C11 890 2630 -6\n[Dodec.] (1190) (3180) (-18)\nCt5 980 15 2910 -10\n(5) (1230) (15) (3470) (-23)\nC44 1350 3570 -6\n(2038) (4370) (-27)\nMgCr 2O4C4439 3600 136 10200 -19\nZnCr2O4C4434 3160 111 9290 -19\n[Hex.]\ntions of the single AF dodecamers. We note that, to\nreproduce the softening in the experimental CΓ(T) for\nZnFe2O4using Eq. (1), we must assume the coupling\nof the lattice to not only the lowest excitations ∆ 1but\nalso the higher excitations ∆ i(i= 2, 3, 4, ...). Dot-\nted curves in Fig. 3(a)-(c) are examples of the fits us-\ning Eq. (1) with the single singlet-triplet gap ∆ 1= 5\nK, where we assume the inner-AF-dodecamer excitations\nfrom the ground state with Stot= 0 to the excited state\nwithStot= 1; if we include only ∆ 1in Eq. (1), the soft-\nening in the experimental CΓ(T) for ZnFe 2O4cannot be\nreproduced. The gradient of the softening in CΓ(T) pro-\nduced by Eq. (1) becomes steeper at low temperatures\nand more gentle at high temperatures than the experi-\nmentaldata. Hence the experimental CΓ(T) forZnFe 2O4\nsuggests that the molecular-spin excitations consist of\nmultiple gapped modes.\nThe level scheme of the AF-dodecamer excitations are\nnotclarifiedsofar,whichshouldincludeinner-andouter-\nAF-dodecamer excitations. However, by assuming the\ncoupling of the lattice to not only the lowest excita-\ntions ∆ 1but also the higher excitations ∆ i(i= 2, 3,\n4,...), Eq. (1) reproduces well the experimental CΓ(T)\nfor ZnFe 2O4. Solid curves in Fig. 3(a)-(c) are examples\nof the fits using Eq. (1) with the lowest singlet-triplet\nexcitations ∆ 1, and the next higher singlet-triplet exci-\ntations ∆ 2. This assumption is similar to that applied to\nthe AF-hexamer excitations in ACr2O4.17Given the val-\nuesofthefitting parameterslisted inthe uppercolumnof\nTable I, the fits to Eq. (1) arein excellent agreementwith\nthe experimental data of ZnFe 2O4(Fig. 3(a)-(c)), repro-\nducing the softening-with-minimum in CΓ(T). We note\nhere that the fitted curves obtained by assuming ∆ 2to\nbe the singlet-quintet, -septet, and -nonet gaps, respec-\ntively, also give excellent agreement with the experimen-\ntal data of ZnFe 2O4(the fitted curves are not shown in\nFig. 3(a)-(c)). Thus, although the present study reveals\nthe coupling of the lattice to the multiple AF-dodecamer\nexcitations for ZnFe 2O4, the nature of the excitations ∆ 2\ncannot be identified so far.6\nIn the fitting of Eq. (1) to the experimental data of\nZnFe2O4, we find that the magnitudes of G1,Γ,G2,Γ, and\n|KΓ|increase with increasing the degree of ∆ 2degener-\nacy. This is exemplified by the values of the fitting pa-\nrameters with the singlet-nonet ∆ 2shown in parentheses\nin the upper column of Table I. On the other hand, we\nalso find three qualitative features of G1,Γ,G2,Γ, andKΓ,\nwhich are common regardless of the degree of ∆ 2degen-\neracy and thus should be intrinsic features for ZnFe 2O4.\nFirst, the KΓvalues are negative for all the elastic\nmodes, indicating that the inter-AF-dodecamer interac-\ntion is antiferrodistortive. Second, the coupling constant\nG2,Γ=|∂∆2/∂ǫΓ|is larger than G1,Γ=|∂∆1/∂ǫΓ|, indi-\ncating that the higher excitations ∆ 2couple to the dy-\nnamical lattice deformations more strongly than the low-\nest excitations ∆ 1. The larger value of G2,ΓthanG1,Γ\nmight suggest the coupling of the lattice to the higher\nmultiple excitations ∆ i(i= 2, 3, 4, ...). Third, both\nthe coupling constants G1,ΓandG2,Γexhibit the largest\nvalues for the trigonal shear modulus C44(T) of the three\nelastic moduli, and hence are compatible with the trigo-\nnal symmetry of the AF dodecamer.\nIn the lower column of Table I, the values of the\nfit parameters in Eq. (1) for the experimental C44(T)\nofACr2O4(A= Mg and Zn) are also listed for\ncomparison.17ForACr2O4, the value of Nin Eq. (1)\nis assumed to be N= 3.45×1027m−3(one-sixth of the\ndensityofCr3+ionsinACr2O4), wherethespin molecule\nis assumedto be the Cr3+AF hexamer(Fig. 1(e)).13,15,17\nAs described before in conjunction with Fig. 2(a)-(c) and\nFig. 2(f), the magnitude of the softening in CΓ(T) for\nZnFe2O4is smaller than that in C44(T) for MgCr 2O4. In\naccordance with Eq. (1), this difference in the magnitude\nbetween ZnFe 2O4andACr2O4arises from the difference\nin the coupling strength between the dynamical lattice\ndeformations and molecular-spin excitations. From Ta-\nble I, the coupling constants G1,ΓandG2,ΓforC44(T) of\nZnFe2O4aresmallerthanthoseof ACr2O4. Additionally,\nalong with Figs. 3(a)-(c) and 2(f), CΓ(T) for ZnFe 2O4\nexhibits a minimum at ∼5 K, which is lower than the\nminimum point of ∼50 K inC44(T) for MgCr 2O4. From\nEq. (1), this difference in the minimum point between\nZnFe2O4andACr2O4arises from the difference in the\nmagnitudes of the gaps ∆ 1and ∆ 2in the molecular-spin\nexcitations.\nFor ZnFe 2O4, the magnitudes of the inter-spin-\nmolecule interactions |KΓ|listed in Table I are com-\nparable to those of ∆ 1and ∆ 2, which is in contrast\nto the weaker magnitudes of |KΓ|than ∆ 1and ∆ 2for\nACr2O4. The comparable magnitudes of |KΓ|, ∆1, and\n∆2for ZnFe 2O4imply that the inter-spin-molecule in-teractions are not completely negligible, which is com-\npatible with the presence of a very weak dispersive fea-\nture of the molecular-spin excitations in the INS spectra\nof ZnFe 2O4, suggesting the presence of the inter-spin-\nmolecule correlations.7Taking into account the smaller\nvalues of ∆ 1and ∆ 2for ZnFe 2O4than for ACr2O4,\nthe very weak dispersion observed in the INS spectra of\nZnFe2O4might be a result of frustration occurring in the\neffectively weaker exchange interactions.\nWe finally note that the recent time-of-flight INS ex-\nperiments in the PM phase of MgCr 2O4revealed the\npresence of multiple modes associated with finite-energy\nmolecular-spin excitations, where it is suggested that not\nonly the ground state but also the excited states are\nhighly frustrated in this compound.18Hence, although\nthe assumption oftwo gaps∆ 1and ∆ 2givesfrom Eq. (1)\na successful agreement with experimental data for CΓ(T)\nof both ZnFe 2O4andACr2O4, it is expected that the\nlevel schemes of the spin molecules in these compounds\nconsist of not only the excited levels of ∆ 1and ∆ 2but\nalsohigherexcitedlevels. SimilartoMgCr 2O4,thefuture\ntime-of-flight INS experiments in ZnFe 2O4are expected\nto reveal complex and exotic molecular-spin excitations.\nIV. SUMMARY\nIn summary, ultrasound velocity measurements of\nZnFe2O4revealed the elastic anomalies, which strongly\nsuggest the evolution of the molecular-spin excitations at\nlow temperatures. Additionally, the present study also\nrevealed that the elastic anomalies driven by the magne-\ntostructural phase transition and its precursorare absent\nin ZnFe 2O4, suggesting that the spin-JT mechanism can-\nnot play a role in releasing frustration within this com-\npound. The present study infers that, for ZnFe 2O4, the\ndynamical molecular-spin state evolves at low temper-\natures without undergoing precursor spin-lattice fluctu-\nations and spin-lattice ordering. Further experimental\nand theoretical studies are indispensable if the dynami-\ncal molecular-spin state in ZnFe 2O4, which is expected\nto govern the magnetic properties, is to be understood.\nV. ACKNOWLEDGMENTS\nThis work was partly supported by a Grant-in-Aid\nfor Scientific Research (C) (Grant No. 25400348) from\nMEXT of Japan, and by Nihon University College of Sci-\nence and TechnologyGrants-in-Aidfor ProjectResearch.\n∗tadataka@phys.cst.nihon-u.ac.jp\n1S. H. Lee, H. Takagi, D. Louca, M. Matsuda, S. Ji, H.\nUeda, Y. Ueda, T. Katsufuji, J. H. Chung, S. Park, S. W.\nCheong, and C. Broholm, J. Phys. Soc. Jpn. 79, 011004(2010).\n2H. Ueda, H. Mitamura, T. Goto, and Y. Ueda, Prog.\nTheor. Phys. 159, 256 (2005).\n3S. H. Lee, C. Broholm, T. H. Kim, W. Ratcliff II, and S.7\nW. Cheong, Phys. Rev. Lett. 84, 3718 (2000).\n4L. Ortega-San-Mart´ ın, A. J. Williams, C. D. Gordon, S.\nKlemme, and J. P. Attfield, J. Phys.: Condens. Matter 20,\n104238 (2008).\n5J. -H. Chung, M. Matsuda, S. -H. Lee, K. Kakurai, H.\nUeda, T. J. Sato, H. Takagi, K. -P. Hong, and S. Park,\nPhys. Rev. Lett. 95, 247204 (2005).\n6W. Schiessl, W. Potzel, H. Karzel, M. Steiner, G. M.\nKalvius, A. Martin, M. K. Krause, I. Halevy, J. Gal, W.\nSch¨afer, G. Will, M. Hillberg, and R. W¨ appling, Phys.\nRev. B53, 9143 (1996).\n7K. Kamazawa, Y. Tsunoda, H. Kadowaki, and K. Kohn,\nPhys. Rev. B 68, 024412 (2003).\n8K. Kamazawa, S. Park, S. H. Lee, T. J. Sato, and Y. Tsun-\noda, Phys. Rev. B 70, 024418 (2004).\n9Y. Yamada, K. Kamazawa, and Y. Tsunoda, Phys. Rev.\nB66, 064401 (2002).\n10Y. Yamashita and K. Ueda, Phys. Rev. Lett. 85, 4960\n(2000).\n11O. Tchernyshyov, R. Moessner, and S. L. Sondhi, Phys.\nRev. Lett. 88, 067203 (2002).\n12S. Ji, S. -H. Lee, C. Broholm, T. Y. Koo, W. Ratcliff, S.\n-W. Cheong, and P. Zschack, Phys. Rev. Lett. 103, 037201\n(2009).\n13S. H. Lee, C. Broholm, W. Ratcliff II, G. Gasparovic, Q.\nHuang, T. H. Kim, and S. W. Cheong, Nature (London)\n418, 856 (2002).\n14H. Suzuki and Y. Tsunoda, J. Phys. Chem. Solids 68, 2060\n(2007).\n15K. Tomiyasu, H. Suzuki, M. Toki, S. Itoh, M. Matsuura,\nN. Aso, and K. Yamada, Phys. Rev. Lett. 101, 177401\n(2008).\n16Y. Kino and B. L¨ uthi, Solid State Commun. 9, 805 (1971).\n17T. Watanabe, S. Ishikawa, H. Suzuki, Y. Kousaka, and K.\nTomiyasu, Phys. Rev. B 86, 144413 (2012).\n18K. Tomiyasu, T. Yokobori, Y. Kousaka, R. I. Bewley, T.\nGuidi, T. Watanabe, J. Akimitsu, and K. Yamada, Phys.\nRev. Lett. 110, 077205 (2013).\n19K. Tomiyasu and K. Kamazawa, J. Phys. Soc. Jpn. 80,\nSB024 (2011).\n20K. Tomiyasu, H. Ueda, M. Matsuda, M. Yokoyama, K.\nIwasa, and K. Yamada, Phys. Rev. B 84, 035115 (2011).\n21K.Tomiyasu, M.K.Crawford, D.T.Adroja, P.Manuel, A.Tominaga, S. Hara, H. Sato, T. Watanabe, S. I. Ikeda,J.\nW. Lynn, K. Iwasa, and K. Yamada, Phys. Rev. B 84,\n054405 (2011).\n22K. Tomiyasu, K. Iwasa, H. Ueda, S. Niitaka, H. Takagi, S.\nOhira-Kawamura, T. Kikuchi, Y. Inamura, K. Nakajima,\nand K. Yamada, Phys. Rev. Lett. 113, 236402 (2014).\n23Y. Yasui, M. Kanada, M. Ito, H. Harashina, M. Sato, H.\nOkumura, K. Kakurai, and H. Kadowaki, J. Phys. Soc.\nJpn.71, 599 (2002).\n24Y. Kino, L¨ uthi, and M. E. Mullen, J. Phys. Soc. Jpn. 33,\n687 (1972); Solid State Commun. 12, 275 (1973).\n25S. Zherlitsyn, S. Schmidt, B. Wolf, H. Schwenk, B. L¨ uthi,\nH. Kageyama, K. Onizuka, Y. Ueda, and K. Ueda, Phys.\nRev. B62, R6097 (2000).\n26B. Wolf, S. Zherlitsyn, S.Schmidt, B. L¨ uthi, H. Kageyama,\nand Y. Ueda, Phys. Rev. Lett. 86, 4847 (2001).\n27T. Watanabe, S. Hara, and S. Ikeda, Phys. Rev. B 78,\n094420 (2008).\n28S. Bhattacharjee, S. Zherlitsyn, O. Chiatti, A. Sytcheva, J .\nWosnitza, R. Moessner, M. E. Zhitomirsky, P. Lemmens,\nV. Tsurkan, and A. Loidl, Phys. Rev. B 83, 184421 (2011).\n29T. Watanabe, S. Hara, S. Ikeda, and K. Tomiyasu, Phys.\nRev. B84, 020409(R) (2011).\n30V. Felea, S. Yasin, A. G¨ unther, J. Deisenhofer, H.-A. Krug\nvonNidda, S.Zherlitsyn, V.Tsurkan, P.Lemmens, J.Wos-\nnitza, and A. Loidl, Phys. Rev. B 86, 104420 (2012).\n31Y. Nii, N. Abe, and T. Arima, Phys. Rev. B 87, 085111\n(2013).\n32T. Watanabe, T. Ishikawa, S. Hara, A. T. M. N. Islam,\nE. M. Wheeler, and B. Lake, Phys. Rev. B 90, 100407(R)\n(2014).\n33Y. P. Varshni, Phys. Rev. B 2, 3952 (1970).\n34B. L¨uthi,Physical Acoustics in the Solid State (Springer,\n2005).\n35H. Martinho, N. O. Moreno, J. A. Sanjurjo, C. Rettori, A.\nJ. Garc´ıa-Adeva, D. L. Huber, S. B. Oseroff, W. Ratcliff\nII, S.-W. Cheong, P. G. Pagliuso, J. L. Sarrao, and G. B.\nMartins, Phys. Rev. B 64, 024408 (2001).\n36H. Kageyama, M. Nishi, N. Aso, K. Onizuka, T. Yosihama,\nK. Nukui, K. Kodama, K. Kakurai, and Y. Ueda, Phys.\nRev. Lett. 84, 5876 (2000)."    },    {        "title": "1703.06385v1.Magnetic_properties_of_Sn_substituted_Ni_Zn_ferrite_synthesized_from_nano_sized_powders_of_NiO__ZnO__Fe2O3_and_SnO2.pdf",        "content": "Magnetic p roperties of Sn-substituted Ni -Zn ferrite :synthesized from \nnano -sized powders of NiO, ZnO, Fe2O3 and SnO 2 \nM.A. Ali1, M.M. Uddin1,*, M.N. I. Khan2, F.-U.-Z.Chowdhury1, S.M. H oque2, S.I. Liba2 \n \n1Department of Physics, Chittagong University of Engineering and Technology (CUE T), \nChittagong4349, Bangladesh  \n2Materials Science Division, Atomic Energy  Center, Dhaka1000, Bangladesh  \n \nAbstract:  \nA series of Ni0.6-x/2Zn0.4-x/2SnxFe2O4 (x = 0.0, 0.05, 0.1, 0.15, 0.2 and 0.3) (NZSFO) ferrite \ncomposites  have been synthesized from nano powders using standard solid  state reaction \ntechnique. The s pinel  cubic structure of the investigated samples has been observ ed by the \nX-ray diffraction  (XRD).  The magnetic  properties  such as saturation  magnetization  (Ms), \nremanen t magnetization  (Mr), coercive field (Hc) and Bohr magneton  (µB) are calculated  from  \nthe hysteresis  loops . The value of Ms is found to decrease with increasing Sn content in the \nsamples. This change has been  successfully explained by the variation of A-B interaction \nstrength due to Sn substitution  in different sites. T he compositional stability and quality of  the \nprepared  ferrite  composite s have also been endorsed by the fairly constant initial permeability \n(µ/) over a wide range  of frequency region . The decreasing trend of µ/ with increasing  Sn \ncontent ha s been observed. Curie temperature  (TC) has found to increase with the increas e in Sn \ncontent. Wide spread frequency utility zone indicate s that the NZSFO can be considered as a \ngood candidate for use in broadband pulse transformer  and wide band read -write heads for \nvideo recording . The abnormal behavior for x = 0.05 has been explained  with existing theory .  \nKeywords:  Magnetic properties, Saturation magnetization, Permeability, Curie temperature.  \nPACS:  75; 07.55. -w; 75.50.Gg;  75.60.Ej;  75.50.Ss  \n* Corresponding author: ( M.M. Uddin ): Email: mohi@cuet.ac.bd  \n 1. Introduction  \nOver the last few decades, scientific community has paid significant attention to the spinel \nferrites due to their fascinating properties to meet the requirements in various applications. No \nother magnetic materials can replac e the ferrites due to their low price, availability, stability \nand have a n extensive use of technological application in transformer, high quality filters, high \nand very high frequency circuits and operating devices.  The Ni -Zn ferrites became an \nimportant candidate  to us e it in the  high frequency applications due to the ir high electrical \nresistivity, high permeability, compositional stability and low eddy current losses [ 1-6]. The \nuniqueness of Ni-Zn ferrites  is motivating numerous researche rs to look forward that they can \nopen the way for commercial applications of these materials and new types of ferrites are \nunveiling  with excellent properties for practical application . The properties of Ni -Zn ferrites \ncan be  tailored  by altering chemical compos ition, preparation methods, sintering temperature \n(Ts) and impurity element or levels  and the reports regarding th ese issue s are available in the \nliteratures  [5-28]. Recently, many researchers reported the structural, magnetic and electrical \nproperties of Ni-Zn ferrite and/or substituted Ni -Zn ferrites in bulk [ 6, 12, 13, 19 -21, 26 -28] \nand nano forms [ 16, 22-24]. \nThe properties of Ni-Zn ferrites  can be changed remarkably by  substitution of tetravalent ions \nsuch as Ti4+, Sn4+. Investigations on the substitution  of Sn4+ have been  reported  by many \nresearchers  [6, 9-11]. We have reported the structural, morphological and electrical properties \nof Sn-substituted  Ni-Zn ferrites  [6]. Das et al  reported the variation of lattice parameter,  \nsaturation magnetization and Curie tem perature with Ti4+, Zr4+ substitution, and Sn4+ in Ni‐Zn \nferrite compositions synthesized by chemical method [ 9]. The Sn4+ substituted Ni 1-yZnyFe2O4 \n(y = 0.3, 0.4)  ferrite samples were prep ared in an oxidizing atmosphere using the solution \ntechnique  and studies on Mössbauer and magnetization  properties have been investigated by \nKhan et al [10]. The magnetic hysteresis and the thermal variation of magnetic parameters in \nSn4+ doped Ni -Zn ferrite s prepared by standard ceramic technique have also been reported by Maskar et al [11]. We have synthesized the Sn4+ substituted Ni -Zn ferrites using nano powders \n(which  is different from Maskar et al  work [11]) by standard ceramic technique. Another \nsignificant dissimilarity is that they have doped Sn in the Ni -Zn ferrites , where  as we have \nsimultaneously substituted Sn for both Ni and Zn. The characterization and the frequency \ndependence of magnetic properties of Ni -Sn-Zn ferrites provide the way to classify the ferrites \nfor particular applications. The information would be very noteworthy for the scientific \ncommunity in this regard.  \nTo the best of our knowledge, such type of study of Ni -Zn ferrites prepared fro m nano powders \nhas not been reported yet.  Here , we report  the magnetic properties of Sn -substituted \nNi0.6Zn0.4Fe2O4 ferrites  prepared from nano -sized raw materials by the solid state reaction \ntechnique . \n2. Materials and methods  \nSolid state reaction route was followed to synthesize Sn -substituted Ni -Zn ferrite,  \nNi0.6-x/2Zn0.4-x/2SnxFe2O4 (0.0 ≤ x ≤ 0.30 ) (NZSFO).  High purity (99.5%) (US  Research \nNanomaterials, Inc.)  oxides of nano powders were used as raw materials . The particle size of  \nnickel oxide (NiO), zinc oxide (ZnO), iron oxide (Fe 2O3) and tin oxide (SnO 2) are 20 -40, \n15-35, 35 -45 and 35 -55 nm, respectively. The detail of preparation technique has been \ndescribed elsewhere [ 5, 6]. The phase formation and surface morphology of the synthesized \nsamples were  carried out by the X-ray diffraction (XRD) using Philips X’pert P RO X-ray \ndiffractometer (PW3040) with CuK α radiation (λ = 1.5405 Å) and s canning electron \nmicroscope (SEM), respectively . The magnetic properties ( M-H curve, s aturation \nmagnetization, Ms; coercive  field, Hc; and Bohr magneton ; μB) have been elucidated by the \nvibrating sample magnetometer (VSM) ( Micro Sen se EV9) with a maximum applied field of \n10 kOe.  Frequency and temperature dependent permeability were investigated by using Wayne Kerr precision impedance analyzer (6500B). An applied voltage of 0.5 V with a low \ninductive coil  was used to measure permeability . \n3. Results and discussion  \n3.1. XRD analysis  \nThe X-ray diffraction ( XRD ) pattern of Sn -substitut ed Ni -Zn ferrites with the chemical \ncomposition of Ni0.6-x/2Zn0.4-x/2SnxFe2O4 (NZSFO) are  shown  in Fig. 1.  The XRD spectra  were \nindexed and fcc cubic  phase was identified . The structural parameters are calculated from the \nXRD data and have been discussed in Ali et al [6]. The lattice constants are calculated from the \nXRD data and represented in  Table 1.  \n \n \n \n \n \n \n \nFig.1 : The X -ray diffraction pattern of the NZSFO (x = 0.0, 0.05, 0.1, 0.15, 0.2 , 0.3 and 0.4) \nferrites samples  [6]. \nThe distances between the magnetic ions at tetrahedral ( A) and octahedral ( B) sites have been \ncalculated using the equation: 𝐿𝐴=𝑎 3\n4and 𝐿𝐵=𝑎 3\n2. The values are also depicted in Table \n1. The hopping lengths of LA and LB decrease with incre asing Sn concentration might be cause of \nlattice parameters of the Ni -Zn ferrites decrease with increasing Sn4+ concentration.  \n20 30 40 50 60 70x=0.30\nx=0.20\nx=0.15\nx=0.10\nx=0.05\n  Intensity (a. u. )\n2 (deg.)x=0.00(111) (220)(311)\n(222) (400) (422) (511)(440) \n \n3.2 Magnetic p roperties  \nThe plots of applied magnetic field  H (up to 1 0 kOe)  dependent magnetization at room \ntemperature, of Ni0.6-x/2Zn0.4-x/2SnxFe2O4 (x = 0.0, 0.05, 0.1, 0.15, 0.2, and 0.3) ceramics \nsintered at 1300 °C , are shown in Fig. 2.  \n \n \n \n \n \n \n \nFig. 2:(a) M–H loops of the NZSFO  ferrite samples , (b) m agnification of upper saturated part \nof the M-H loops.  \nThe value of magnetization increases  with increasing applied magnetic field  up to a certain \nfield above which the sample becomes saturated . The saturation magnetization ( Ms), coercive \nfield ( Hc), remanent magnetization, Mr, and Bohr magneton , μB, are also calculated  from the \nmeasured magnetic hysteresis loop  and are presented in Table 1. It is seen that the values of Hc \nof the Sn-substituted  samples  (NZSFO)  are larger than that of the parent (NZFO) and it could \nbe inferred that the prepared ferrites are not reasonably  soft in nature.   \n0 2 4 6 8 104050607080\n x = 0.00\n x = 0.05  x = 0.20\n x = 0.30 x = 0.15\n x = 0.10\n  \n  \nApplied field (kOe)M (emu/gm)(b)\n-9 -6 -3 0 3 6 9-90-60-300306090\n(a)\n  M (emu/gm)\nApplied field (kOe) x = 0.00\n x = 0.05\n x = 0.10\n x = 0.15\n x = 0.20\n x = 0.30The variation of saturation magnetization ( Ms) with S n content of the NZSFO is shown in \nTable 1 . The value of Ms shows decreasing trend with increasing x except x = 0.05 where the Ms \nincreases slightly. This characteristic can be understood in terms of exchange interactions of \ncations  in the samples. However, the AB interactions are generally dominant  in the ferrites , AA \nand BB interactions can no longer be ignored. The magnetic moment  of the Ni  ion is affected \nby the modified strength of Ni2+↔O2-↔Ni2+ interactions due to the  presence of non-magnetic \nions Sn and Zn in the samples . \nTable 1: The lattice constants ( aexpt), average grain size ( Dg), magnetic cation hopping length \n(LA and L B), saturation magnetization ( Ms), coercive field  (Hc), remanent magnetization  (Mr) \nand Bohr magneton ( nB) of NZSFO for different x. \nComposition  \nx aexpt \n(Å) Dg \n(μm)  LA \n(Å) LB \n(Å) Ms \n(emu/gm)  Hc \n(Oe)  Mr \n(emu/gm)  μB \n \n0.00 8.39311  07.8 3.6343  7.2686  72.73  \n60.0 [ 9] \n96.0 [ 11] 1.26 0.16 3.09 \n0.05 8.38996  10.1 3.6329  7.2659  80.82  67.25 5.00 3.48 \n0.10 8.37546  18.8 3.6266  7.2533  70.23  62.41  2.07 3.07 \n0.15 8.38137  21.0 3.6292  7.2584  68.09  71.82 4.55 3.02 \n0.20 8.37665  30.1 3.6271  7.2543  68.07  78.10  5.16 3.06 \n0.30 8.34531  34.8 3.6136  7.2272  64.47  94.47  6.40 2.99 \n \nIt is assumed that the Sn ions occupy tetrahedral (A) sites initially at lower Sn concentrations  \nhowever , it reside s in B-sites at higher Sn concentrations  leading the reduction of A-A \ninteractions. Consequently, the value of net magnetic moment , 𝑀 =𝑀 𝐵−𝑀 𝐴, increases  in the samples . On further increase of substituting Sn ions , they enter into B-sites and pushing some  \nFe3+ ions into A-sites resulting  the magnetic  ion density in the B sub-lattice  decreases . The \nconcentration of Fe3+ ions decreases in  the B sub-lattice while it increases for A sub-lattice \nthereby  the net ma gnetic moment of the ferrite diminishes . Our calcul ated values of Ms shown \nin Table 1 are compared  with the reported values  [9, 11 ]. Das et al [9] have reported the value \nof Ms ~ 60 emu/gm for x = 0.0 and observes the Ms decreases with increasing Sn concentration \nup to 5 wt% in the Ni -Zn ferrites. Maskar  et al [11] have also observed that the value of Ms ~ 96 \nemu/gm for x=0.0 and notice d the lower Ms value for further substitut ion in Ni -Zn ferrites. We \nhave found t he value of Ms~ 72.2 emu/gm, and a decreasing trend with increasing Sn content \nup to 40 wt% is also observed, except for x = 0.05. As mentioned in Table 1, the M s for x = 0.0 \nis found to differ from the reported values of other researchers (ref. [9] and [11]). This \ndiscrepancy in M s value might be due to dissimilarity  in sample preparation techniques and \nconditions employed . \nThe Sn content  dependence of the coercive fiel d of NZSFO is depicted in Table 1. It shows that \nthe Hc value increases with increasing Sn content  that can be elucidated by the Brown’s \nrelation : Hc = 2K1/0Ms, where K1 is the anisotropy constant and µ0 is the permeability of free \nspace.  As per relation, the value of Hc is found to increase  with the decrease in  the value of Ms. \nFurthermore, Stoner –Wohlfarth single -domain theory proved that the Hc increases with the \nincrease of grain size [ 29]. The grain sizes of the prepared samples (NZFO and NZSFO) are \nalso found to increase with Sn contents [6]. Therefore, it is expected to increase the value of Hc \nwith the increase of x in the prepared samples. It could be noted that the values of Hc for the \nSn-substituted samples are comparatively large. The large value of Hc for the Sn -substituted \nsamples can be explained by the following equations. 𝐻𝑐=𝜋𝑟\n𝑀𝑠 𝐾1𝐴  12 \n, where A is the \nexchange stiffness constant, K1 is the anisotropy  constant and r is the radius of the spherical pores  [30]. In general , Hc varies directly with porosity and anisotropy ; and inversely with grain \nsize [ 30]. Thus , the Hc appears to be influenced by saturation magnetization and K1, in addition \nto the microstructure.  \nThe porosity of NZSFO increases almost linearly with Sn concentration ( ~27-34%) while the \nporosity for NZFO is around 19% [6]. The grain size of the prepared samples (Table 1 ) is found \nto increase with Sn contents from 10 to 34 μm for (0.05  x  0.3) while the grain size of  \nNZFO is only 7.8 μm.  In addition, the increase in Tc, suggests that the value of K1 is also \nincreased with Sn contents. It can be recalled that the value of Ms decreases with Sn content. As \na result, the value of Hc is much larger for Sn-substituted samples (NZSFO).  The values of Mr \nand μB as a function of Sn concentration are also presented in Table 1 . The mechanism for the \nvariation of μB and Mr is closely related to the Ms and Hc, respectively.  \nFig. 3  represents the real part of initial  permeability ( µ/) and imaginary part  of the initial  \npermeability (µ//) over the frequency range from 1 kHz to 1 00 MHz for the NZSFO for \ndifferent Sn concentration . The µ/ and µ// of the  µ* have been  calculated using the following \nrelations:  µ/=Ls/L0 and µ//µ/.tanδ, where Ls is the self -inductance of the sample core \nand 𝐿0=𝜇0𝑁2𝑆\n𝜋𝑑  can be  derived geometrically , where L0 is the inductance of the winding coil \nwithout the sample core, N is the number of turns of the coil ( N = 5), S is the area of \ncross -section of the toroidal sample as given below:  𝑆=𝑑×ℎ and 𝑑=𝑑2−𝑑1\n2, here d1 = inner \ndiameter, d2 = outer diameter and  h=height and also 𝑑  is the mean diameter of the toroidal \nsample (𝑑 =𝑑2+𝑑1\n2). The real part of permeability µ/ decreases with the frequency and the \nimaginary part of permeability µ// exhibits a peak, which is related to the relaxation \nphenomena.  It is seen that the µ/ remains almost constant until the frequency is raised to a \ncertain value and then drops to very low  values at higher frequencies. The fairly constant µ/ \nvalues with a wide range frequency region is known as the zone of  utility of the ferrite  that demonstrate the compositional stability and quality of ferrites prepared by conventional double \nsintering route . This characteristic s is anticipated for various applications such as broadband \npulse transformer and wide band read -write heads for video reco rding [ 31]. The value of µ// \ngradually increases with the frequency and become  maximum at a certain frequency, where  µ/ \nrapidly decreases. This feature is well known as the  ferromagnetic resonance [ 32]. At higher \ndoping concentration, the permeability value  is lower and the frequency of the ons et of \nferromagnetic resonance  is higher that is in good agreement with Snoek’s limit 𝑓𝑟𝜇/=\nconstant , where fr is the resonance frequency of domain wall  motion, above which µ/ decreases  \n[33].  \nVariation of µ/with Sn concentration at 1 MHz frequency  is shown in Fig. 4(a). The decrease  in \nthe initial  permeability  of the Ni –Zn ferrites  can be explained  using  the following  equation  \n𝜇/=𝑀𝑠2𝐷\n 𝐾1, where µ/ is the  initial  permeability, Ms the saturation  magnetization, D the average  \ngrain  size and K 1 the magneto -crystalline  anisotropy constant.  As µ/ is proportional to the \nsquare of the saturation magnetization and saturation magnetization is decreased with the \nincrease in Sn concentration, the value of µ/ is expected to be decreased. Tetravalent  Sn4+ ions \nhave a strong  octahedral -site preference,  and the saturation  magnetization  decreased  with the \nincreasing  Sn4+ substitution  due to the  weaker  A–O–B super -exchange  interaction  results the \nvalue of µ/ decrea ses [34]. Fig. 4(b) shows the relative quality factor NZSFO. The peak \ncorresponding to maxima in Q -factor shifts to a higher  frequency range as Sn content increases. \nQ-factor has the maximum value of 5.2×103at f = 20 MHz for the x =0.05 sample. The Q-value  \ndepends on the ferrite microstructure, e.g. pore, grain size , etc. \n \n \n \n  \n \n \n \n \n \n \n \nFig. 3: The frequency dependence of permeability (a) real part (b) imaginary part  of the \nNZSFO for different Sn concentration.  \n \n \n \n \n \n \nFig. 4: Variation of (a) μ/ with Sn concentration at 1 MHz frequency, (b) variation of Q -factor \nwith frequency for different Sn concentration  in the NZSFO ferrites.  \nCurie temperature ( Tc) is the transition temperature above which the ferrite material loses its \nmagnetic properties. Temperature dependence of initial permeability, µ/ of the toroid shaped \nsample of NZSFO  at constant frequency 1 MHz of an AC signal is shown in Fig. 5 (a) . The \ninitial permeability increases rapidly with increasing temperature and then drops o ff sharply \n103104105106107108123 x=0.15\n x=0.2 0 \n x=0.3 0  \n (102)\nFrequency, f (Hz) x=0.0 0\n x=0.05\n x=0.1 0(a)\n1031041051061071080123(b)\n  (103)\nFrequency, f (Hz) x=0.0 0\n x=0.05\n x=0.1 0\n x=0.15\n x=0.2 0\n x=0.3 0\n1031041051061071080246\n  Q factor (103)\nFrequency, f (Hz) x=0.00\n x=0.05\n x=0.10\n x=0.15\n x=0.20\n x=0.30(b)\n0.0 0.1 0.2 0.30.51.01.52.02.53.0\n  \n  \nSn concentration, x (102)f =1 MHz (a)near the transition temperature  known as Tc  showing the Hopkinson effect  [35]. A significant \npeak is obtained near the Tc where t he value of K1 becomes almost negligible.  At the Tc, \ncomplete spin disorder take s place, i.e., a ferromagnetic  material  converts to a paramagnetic \nmaterial . The Tc gradually increases with increasing Sn concentration excluding x = 0.05 where \nit is decreased moderately as shown in Fig. 5 (b).  \n \n \n \n \n  \n \n \n \nFig. 5 : (a) Temperature dependent initial permeability ( μ/) for different Sn concentration, (b) \nvariation of the Curie temperature ( Tc) as a function of Sn concentration in the NZSFO ferrites.  \n \nIt can be explained as follows; i nitially the dopant cations are  assumed to occupy tetrahedral \n(A) sites and it is entered into B sites due to further increasing of dopant cations thereby  \npushing some  Fe3+ ions to A-sites resulting the magnetic  ion density  decreases  in the B \nsub-lattice  [9]. The increase in the magnetic ions in the A sites increases the A-B interaction, \nconsequently increasing the Tc (Fig. 5 (b)). However, the mechanism of the Tc decreasing in \nparticular poin t has not been understood yet.  \nFinally, from the Table 1, it is evident that the sample with x = 0.05 shows unusual results. \nMoreover, the T c values are fairly linear with Sn content except for x = 0.05. This unusual \nbehavior might be explained assuming that initially at lower Sn concentrations (0  x  0.1) Sn \n0.0 0.1 0.2 0.32.02.42.83.23.6\n  Tc (C 102)\nConcentration, x(b)\n0 1 2 3 4 50123\n x=0.2 0\n x=0.3 0 x=0.1 0\n x=0.15\n   (102)\nT (C 102) x=0.0 0\n x=0.05(a)ions occupy tetrahedral ( A) sites whilst these ions reside in octahedral ( B) sites at higher Sn \nconcentrations [9]. However, this can be confirmed by other investigations like, neutron \ndiffraction, but unfortunately we are unable to perform such investigation and left this issue to \nother researchers for further study .  \n4. Conclusion s \nSn-substituted polycrystalline ferrites, NZSFO ( x = 0.0, 0.05, 0.1, 0.15, 0.2  and 0.3) sintered at \n1300  °C, have been successfully synthesized using standard ceramic technique. The single \nphase spinel structure of the samples has been confirmed from the XRD patterns. The grain \nsize increases from 7.8 to 34.8 µm with increasing Sn content . The saturation magnetization is \nfound to be decreased with increasing Sn concentration while the coercivity is i ncrease d. The \ninitial permeability is fairly constant up to 10 MHz  i.e., wide range of operating frequency or \nstability region has been achieved for the samples. The Curie temperatures rise gradually with \nincreasing Sn content , except  for x = 0.05, which is fruitfully explained  by the variation of A-B \ninteraction strength due to dopant cations entering in different sites. A reasonably low Hc for x \n= 0.0, implies that this material might be a  promising candidate for transformer core and \ninductor applications.   \nAcknowledgements: The authors are grateful to the Directorate of Research and Extension, \nChittagong University of Engineering and Technology (CUE T), Chittagong -4349, \nBangladesh for arranging the f inancial support for this work.  \nReferences  \n[1] Chen Q, Du P, Huang W, Jin L, Weng W and Han G 2007 Appl. Phys. Lett. 90 132907  \n[2] Sugimoto M 1999 Ceram. J. Am. Soc. 82 269 \n[3] Smit J and Wijn HPG 1959 Ferrites 136  \n[4] Eerenstein W, Mathur N D and Scott J F 2006 Nature 442 759 \n[5] Ali M A, Khan M N I, Chowdhury F -U.-Z, Akhter S and Uddin M M 2015 J. Sci. Res. \n7 65 [6] Ali M A, Uddin M M, Khan M N I, Chowdhury F -U.-Z and Haque S M 2017 J. Magn. \nMagn. Mater. 424 148 \n[7] Khan D C, Misra M and Das A R 1982 J. Appl. Phys. 53 2722  \n[8] Khan D C and Misra M 1985 Bull. Mater. Sci. 7 253 \n[9] Das A R, Ananthan V S and Khan D C 1985 J. Appl. Phys. 57 4189  \n[10] Khan D C, Srivastava R C and Das A R 1992 J. Phys.: Condens. Matter 4 1379  \n[11] Maskar P K, Kakatkar S V, Patil R S, Jadhav V A, Chaudhari N D, Sankpal A M  and \nSawant S R 1995 Mater. Chem. Phys. 41 154. \n[12] Mundada O G, Jadhav K M and Bichile G K 1997 J. Mater. Sci. Lett. 16 432 \n[13] Prasad M S R, Prasad B B V S V, Rajesh B, Rao K H and Ramesh K V 2011 J. Magn. \nMagn. Mater. 323 2115  \n[14] Kaiser M 2012 Physica B 407 606 \n[15] Kaur B, Arora M, Shankar A, Srivastava A K a nd Pant R P 2012 Adv. Mat. Lett. 3 399 \n[16] Hashim M, Alimuddin, Kumar S, Ali S, Koo B H, Chung H and Kumar R 2012 J. \nAlloy. Compd. 511 107 \n[17] Mandal A, Ghosh D, Malas A, Pal P and Das C K 2013 J. Engg. Art. ID 391083  \n[18] Yoo B S, Chae Y G, Kwon Y M, Kim D H, Lee B W and Liu C 2013 J. Magn. 18 230 \n[19] JanČárik V, UŠák E, Šoka M, UŠáková M 2014 Acta Physica Pol. A 126 90 \n[20] Kwon  Y M, Lee M -Y, Mustaqima  M, Liu C and Lee B W 2014  J. Magn. 19 64 \n[21] Ateia E E, Ahmed M A, Salah L M and El -Gamal A A 2014 Physica B 445 60 \n[22] Köseoğlu Y 2015 Ceram. Int. 41 (Part A) 6417  \n[23] Kumar R, Kumar H, Kumar M, Singh R R and Barman P B 2015 J. Super. Nov . Magn. \n28 3557  \n[24] Hedayati K 2015 J. Nanostructure 5 13 \n[25] Kumar R, Kumar H, Singh R R and Barman P B 2015 AIP Conf. Proc. 1675  030003  \n[26] Wang S F, Hsu Y F, Chou K M and Tsai J T 2015 J. Magn. Magn. Mater. 374 402 \n[27] Ashtar M, Maqsood A and Anis -ur-Rehman M 2016 J. Nanomater. Mol. Nanotechnol. \n5 3 \n[28] Ishaque M, Khan M A, A li I, Athair M, Khan H M, Iqbal M A, Islam M U and Warsi M \nF 2016 Mater. Sci. Semi. Proc. 41508  \n[29] Stoner E C and Wohlfarth E P 1991 IEEE Trans. Magn. 27 3475  \n[30] Baha P D (1965) J. Am. Ceram. Soc. 48 305 \n[31] Zabotto F L, Gualdi A J, Eiras J A, de Oliveira A J A  and Garcia D 2012 Mater. Res.  15 \n428 [32] Brockman F G, Dowling P H and Steneck W G 1950 Phys. Rev. 77 85 \n[33] Snoek J L 1948 Physica 14 207 \n[34] Sun K 2008 J. Magn. Magn. Mater. 320 1180  \n[35] Overshott K J 1981 IEEE Trans. Magn. 17 2698  \n "    },    {        "title": "1604.07052v2.Optomagnonics_in_Magnetic_Solids.pdf",        "content": "arXiv:1604.07052v2  [cond-mat.mes-hall]  29 Jul 2016Optomagnonics in Magnetic Solids\nTianyu Liu,1Xufeng Zhang,2Hong X. Tang,2and Michael E. Flatt´ e1\n1Optical Science and Technology Center and Department of Phy sics and Astronomy,\nUniversity of Iowa, Iowa City, Iowa 52242, USA\n2Department of Electrical Engineering, Yale University, Ne w Haven, CT 06520, USA\nCoherent conversion of photons to magnons, and back, provid es a natural mechanism for rapid\ncontrol of interactions between stationary spins with long coherence times and high-speed photons.\nDespite the large frequency difference between optical phot ons and magnons, coherent conversion\ncan be achieved through a three-particle interaction betwe en one magnon and two photons whose\nfrequency difference is resonant with the magnon frequency, as in optomechanics with two photons\nand a phonon. The large spin density of a transparent ferroma gnetic insulator (such as the ferrite\nyttrium iron garnet) in an optical cavity provides an intrin sic photon-magnon coupling strength\nthat we calculate to exceed reported optomechanical coupli ngs. A large cavity photon number\nand properly selected cavity detuning produce a predicted e ffective coupling strength sufficient for\nobserving electromagnetically induced transparency and t he Purcell effect, and even to reach the\nultra-strong coupling regime.\nCavity optomechanics, the optical control of mechan-\nical excitations, has formed the framework for demon-\nstrations of slow light [1] and squeezed light [2], and\nproposals for quantum memory [3]. In cavity optome-\nchanics, radiation pressure couples the photons in opti-\ncal or microwave cavities to the phonons of mechanical\nresonators. In addition to clarifying the fundamental na-\nture of quantum interactions and noise, such studies can\nbe applied to systems in which each excitation provides\nadvantages; e.g., in quantum memory the photons serve\nas broad-band long distance information carriers and the\nphononsaslong-timeinformationstorage. Spin waves,as\nelastic waves, are collective excitations and interact with\nlight. Spin waves, however, are more easily decoupled\nfrom the environment than elastic waves, and can also\nbe efficiently manipulated magnetically (in addition to\nelectrically). These advantages suggest a new field, spin\noptodynamics, or “optomagnonics,” in which optical or\nmicrowave fields are paired with these collective spin ex-\ncitations, whosequantaareknownasmagnons. Magnons\nhave been shown to efficiently replace radio-frequency\n(rf) phonons in microwave cavities, in which strong and\nultrastrongcouplingsofmagnonsandmicrowavephotons\nhave been achieved via the interaction between magnons\nand the oscillating magnetic fields of the microwave pho-\ntons[4–8]. Recentrealizationsofweakopticalwhispering\ngallery mode coupling to magnetostatic spin waves in a\nyttrium iron garnet (YIG) sphere are perhaps the first\nexamples of cavity optomagnonics [9–12].\nHere, we describe a theoretical framework for op-\ntomagnonics, which takes place through the magnon-\nphoton interaction in an optical cavity containing a mag-\nnetic slab, as shown in Fig. 1. As in cavity optomechan-\nics[13–16], inwhichthepresenceofelasticwavesmodifies\nthe lighttransmission, herelight transmissionis modified\nby the magnetic media and the presence of magnons. In\na microwave cavity a magnon couples to the magnetic\ncomponent of the rf fields, and a microwave photon con-verts directly into a magnon, or vice versa, through a\ntwo-particle interaction. For the optomagnonic configu-\nration a three-particle interaction couples a magnon and\nthe electric component of the optical fields within the op-\ntical cavity. From the electron-radiation interaction, we\ncalculate the intrinsic magnon-photon coupling strength\n(g0) in YIG and find that it can be made comparable\nto or larger than the intrinsic phonon-photon coupling\nstrength in cavity optomechanics. By virtue of detun-\ning and a large photon number, g0can be enhanced\nto reach the strong coupling regime where an effective\ncoupling geffexceeds either the cavity linewidth or the\nmagnon linewidth, and in these regimes electromagnet-\nically induced transparency [1, 5, 17] and a Purcell en-\nhancement [5, 18–20] can be achieved. We find even the\nultra-strong regime in which geffexceeds both is feasible.\nThesedevelopmentsinoptomagnonicsmayalsoassistthe\nlow-dissipation propagation of magnons in spintronic de-\nvices. For example, an optomagnonic arrangement may\nformthebasisforahigh-efficiency,low-dissipationhybrid\nspintronic interconnect that transmits spin information\nin opticalform. Developmentsin understandingcoherent\nconversion between magnons and photons may therefore\nassist in connecting spintronic devices to a network for\nquantum communication. Furthermore, the nonrecipro-\ncal nature of the magnetic system allows for an isolating,\ndiodelike character of the switching from one mode to\nanother; that is, a first mode can be switched into a sec-\nond, whereas the second mode does not switch into the\nfirst.\nIntrinsic photon-magnon interactions. Photons inter-\nact with magnonsthroughlinear andquadraticmagneto-\noptical coupling,\nHI=1\n8ˆ\ndVǫ0/angbracketleftBigg/summationdisplay\nα,βǫαβ\nr(M)Eα∗\n1Eβ\n2+h.c./angbracketrightBigg\ntime,(1)\nwhereǫαβ\nr(M) (α,β=x,y,z) is the relative dielectric2\nFigure 1. (a) Schematic illustration of cavity optomagnoni cs.\nThe yellow slab sandwiched by two mirrors is the cavity for\nmagnons and for optical photons. (b) ωℓ,ωp, andω0denote\nthe frequencies of the control light, the probe light, and th e\noptical cavity mode, respectively. The yellow wave package\nshows the linewidth of the probe light. (c) geffsplits two\npolariton states with different control lights and probe lig ht\nphoton numbers. (d) Due to the three-particle interaction b e-\ntween magnons and photons, the transmission spectra can be\ntuned by the control light to produce a transparency window\naround the frequency of the magnon modes.\ntensor as a function of the magnetization (which includes\nthe effect of magnons). The time average ensures energy\nconservation. The subscripts “1” and “2” denote two\nlight beams that interact with the magnetization,\nEα\ni=iE0i/summationdisplay\nqi,meα\ni,m(ξ,ζ)a†\ni,me−iqiη+iωit,(2)\nwherei= 1,2,E0i= (2/planckover2pi1ωi/ǫ0n2\n0V)1/2withn0the re-\nfractive index of YIG, and η,ξ, andζare the coordinates\nalong the length, width, and thickness, respectively. We\nconsider ω1≈ω2= (2πc0)/(n0λ0), withc0the speed of\nlight in vacuum, as the excited magnons have much less\nenergy than the photons. eα\ni,m(ξ,ζ) are the normalized\nfieldfunctions fordifferentopticalcavitymodes, and a†\ni,m\nis the creation operator for cavity mode m. Here,mis\na simplified notation for different modes, including dis-\ntinguishing transverse electric (TE) and magnetic (TM).\nAlthough each field is written as a propagating wave,\nthe summation with its Hermitian conjugate yields the\nappropriate cavity standing wave. YIG is almost trans-\nparent, so we consider only the Hermitian part of the\ndielectric tensor. For crystals with cubic symmetry and\nassuming the saturation magnetization is along the [001]\ndirection, we have, up to linear order in MxandMy,\nǫr(M) =\n0 0ǫxz\nr\n0 0ǫyz\nr\nǫzx\nrǫzy\nr0\n, (3)\nwithǫxz\nr=−iKMy+ 2G44MxM0,ǫyz\nr=iKMx+\n2G44MyM0,ǫzx\nr= (ǫxz\nr)∗, andǫzy\nr= (ǫyz\nr)∗, whereM0∝bardblˆzis the saturation magnetization [21, 22]. Kand\nG44can be obtained from measurements [21, 22] of the\nmagnetic circular birefringence,\nΦMCB=πM0K\nλ0n0fork∝bardblM0, (4)\nand the magnetic linear birefringence,\nΦMLB=2πM2\n0G44\nλ0n0forM0∝bardbl[111]⊥k,(5)\nwithλ0the wavelength of the incident light. Applying\nthe Holstein-Primakoff transformation [23] to the mag-\nnetization, we find\nM+(r) =/parenleftbigg2/planckover2pi1γM0\nV/parenrightbigg1\n2/summationdisplay\nn,kbkeikηφn(ξ,ζ),(6)\nM−(r) =/parenleftbigg2/planckover2pi1γM0\nV/parenrightbigg1\n2/summationdisplay\nn,kb†\nke−ikηφn(ξ,ζ),(7)\nwhereγis the gyromagnetic ratio and φn(ξ,ζ) are the\nnormalized functions for different magnon modes. We\nassume the cavity is subject to pinned magnetic bound-\nary conditions on the edges of its cross section, that is,\nφn(ξ,ζ) = cos/parenleftbiggnπξ\n2w/parenrightbigg\n, (8)\nwheren= 1,3,5,...andwis the half width of the cavity.\nAs the magnon modes we consider have frequencies of\nseveral GHz, and the dimension along the thickness di-\nrection is small compared with the magnon wavelength,\nwe regard the magnon wave function as homogeneous\nalong the direction of the slab thickness and so it is in-\ndependent of ζ. The photon-magnon interaction then\nsimplifies to\nHI=/summationdisplay\nm,m′,kn/bracketleftBig\n/planckover2pi1g(+)\nmm′nama†\nm′bknδ(qm−qm′+kn)\n+/planckover2pi1g(−)\nmm′nama†\nm′b†\nknδ(qm−qm′−kn)/bracketrightBig\n,(9)\nwith\ng(±)\nmm′n=/parenleftbigg2/planckover2pi1γ\nM0V/parenrightbigg1\n2c0\nn2\n0\n×[ΦMLBG(±)\n44,mm′n±ΦMCBK(±)\nmm′n],(10)\nwhere\nG(±)\n44,mm′n=1\nSˆw\n−wdξˆd\n−ddζ/parenleftbig\ne∗\n1m,ze2m′,x∓ie∗\n1m,ze2m′,y\n+e∗\n1m,xe2m′,z∓ie∗\n1m,ye2m′,z/parenrightbig\nφn(ξ,ζ) (11)\nK(±)\nmm′n=1\nSˆw\n−wdξˆd\n−ddζ/parenleftbig\ne∗\n1m,ze2m′,x∓ie∗\n1m,ze2m′,y\n−e∗\n1m,xe2m′,z±ie∗\n1m,ye2m′,z/parenrightbig\nφn(ξ,ζ),(12)3\nandS= 4wdis the area of the cavity cross section. The\nanti-Stokes and Stokes processes have different coupling\nratesg(±)\nmm′n, andg(+)\nmm′n=g(−)∗\nm′mndue toG(±)∗\n44,mm′n=\nG(∓)\n44,m′mnandK(±)∗\nmm′n=−K(∓)\nm′mn. This asymmetry has\nrecently been observed in the coupling between whisper-\ning gallery modes and magnon modes [11]. Here, we have\nexplicitly written down the dependence of the intrinsic\ncoupling rate g(±)\nmm′non cavity and magnon mode num-\nbers. For given mode numbers, we will use g(±)\n0for sim-\nplicity instead of g(±)\nmm′n. ΦMCB≈ΦMLB= 6.1 rad/cm\nfor YIG [22, 24], so we obtain g(−)\n0≈2π×27 Hz for\nthe Stokes process (TE 00→TM31+φ3withφ3then= 3\nmagnonmode) of1 .55-µmincident light. Aselection rule\nrestricts transitions to those between different polariza-\ntions if Φ MCB= ΦMLB. Changing the ratio of Φ MCBto\nΦMLBallows TE to TE and TM to TM transitions but\nthe resulting rates are still much smaller than the TE\nto TM transitions. The nonreciprocal behavior of tran-\nsitions from one mode to another is unique to the opto-\nmagnonic system, for time-reversal symmetry is broken.\nIn the strongcouplingregime discussedlater, this feature\nand electromagnetically induced transparency produces\nan opticaldiode, in which the probe light ofthe TEmode\nis totally reflected into the TM mode, but is absorbed by\nthecavityfortheothermodes(includingTMtoTE).The\nnatureofthe controllight interactionallowsthe direction\nof this optical diode to be switched with the frequency of\nthe control light: Red detuning allows TM →TE but pre-\nvents TE →TM, whereas blue detuning allows TE →TM\nbut prevents TM →TE.\nThe coupling rate also depends on the mode numbers.\nAlong the thickness direction, the two lowest optical\nmodes, together with the homogeneous magnon mode,\nyield the largest modal overlap. For the width direction,\nthe coupling rates of the opposite-parity TE to TM tran-\nsitions of other mode numbers differ from that value by\nless than 1%. The parity requirement ensures the inte-\ngrand in Eqs. (11) and (12) is an even function along the\nwidth of the cavity.\nThe intrinsic photon-magnon coupling strengths in\nYIG exceed the reported photon-phonon coupling\nstrength (2 π×2.7 Hz) in a cavity that supports strong\noptomechanicalcoupling[13], suggestingthepotentialfor\ncavityoptomagnonics. ComparingtheinteractionHamil-\ntonian in the electro-optical, optomechanical, and opto-\nmagnonic systems using the same effective Hamiltonian,\nHI= (/planckover2pi1ϕ/τ)a†a(b+b†), withϕ(τ) the optical phase\nshift(time)ofasingleroundtrip,theinteractionstrength\nand quality factor Qmfor the three systems are reported\nin Table I with uniform parameters where possible and\ntypical values for the electro-optical and optomechanical\nsystems [25]. Table I shows that, within the same opti-\ncal cavity, the optomagnonic coupling is ten times larger\nthan the optomechanical coupling, as is the correspond-\ning quality factor. Although the electro-optical couplingis even stronger, the poor quality factor ofthe fundamen-\ntal frequency makes strong coupling in an electro-optical\nsystemmuchmoredifficultthanintheothertwosystems.\nTable I. Comparison of the coupling rates in electro-\noptical [26], optomechanical [13] and optomagnonic system s.\nElectro-optical Optomechanical Optomagnonic\nϕ\nω0τn2\n0r\n2d/radicalBig\n/planckover2pi1ωm\n2C1\nl/radicalBig\n/planckover2pi1\n2mωmK\n2n2\n0/radicalBig\n/planckover2pi1γM0\nV\nvalues 1 .2×10−113.1×10−143.1×10−13\nQm 500 104105\nSpin optodynamics in cold atoms (87Rb with a D2\ntransition)[27–29]hasbeenproposed,sowealsocompare\nthe cold atom g0following our three-particle definition\n(differing from the convention in Ref. [27]) to YIG. The\nlinear magneto-optical coupling in the dielectric tensor\n(KǫαβτMτ, whereǫαβτis the Levi-Civita tensor) has the\nsame form for both YIG and the vector ac-Stark effect\nin cold atoms. For cold atoms K= (d2v)/(ǫ0/planckover2pi12∆caγ)\nfor87Rb with dthe electric dipole of the D2transi-\ntion [30], vthe vector shift, ǫ0the vacuum permittivity,\n∆cathe detuning between the cavity resonance and the\nD2transition frequency, and γthe gyromagnetic ratio.\nAlthough K(87Rb)/K(YIG)∼107, the spin density ra-\ntio is so small that M0(87Rb)/M0(YIG)∼10−11. As\ng0∝K√M0,g0(87Rb) is of similar order as g0(YIG).\nStrong coupling regimes . In analogy to cavity optome-\nchanics, we consider control light acting on the cavity as\nshown in Fig. 1(a) to enhance the photon-magnon inter-\naction by a factor of√Nℓ(withNℓthe number of control\nlightphotonswithfrequency ωℓ). Thiscanbeunderstood\nin a frame rotating with ωℓ, whereqdenotes the cavity\nresonance mode. Considering the cavity modes qand\nq′with specific transverse mode numbers mandm′, we\nwill drop the subscripts of mandm′for simplicity. The\nsystem is then described by\nH=/summationdisplay\nq/planckover2pi1∆qa†\nqaq+/summationdisplay\nn,k/planckover2pi1ωnkb†\nkbk\n+/summationdisplay\nn,q,q′,k/bracketleftBig\n/planckover2pi1g(+)\nqq′naqa†\nq′bkδ(q−q′+k)\n+/planckover2pi1g(−)\nqq′naqa†\nq′b†\nkδ(q−q′−k)/bracketrightBig\n, (13)\nwhere ∆ q≡ωℓ−ωqis the detuning of a control light at\nfrequency ωℓfrom the cavity resonance frequency ωq≡\nω0, andaq(bk) are the annihilation operators for the\noptical cavity modes (magnon of frequency ωk).\nWe derive the equations of motion for bkandaqfrom\nthe Heisenberg equation, and find\n˙bk=−(iωk+γm\n2)bk−i/summationdisplay\nn,qg(−)\nq,q−k,naqa†\nq−k,(14)\n˙aq=−(i∆q+κq\n2)aq4\n−i/summationdisplay\nn,k′/bracketleftBig\ng(−)\nq+k′,q,naq+k′b†\nk′+g(+)\nq−k′,q,naq−k′bk′/bracketrightBig\n−(κe,q/2)1/2ain,q(t)−κ′1/2\nqai,q(t), (15)\nwithγm=ωm/Qmthe magnon damping rate, κe,qthe\noptical damping rate for cavity mode q,κ′\nqthe parasitic\noptical damping rate into all other channels that are un-\ndetected (representing a loss of information), and κqthe\ntotal optical damping rate of mode q(κq=κe,q/2+κ′\nq).\nSources of κ′\nqinclude homogeneous broadening due to a\nlarge linewidth of the cavity resonance allowing a direct\nconversion of the control laser into the cavity resonance\nmode, or an inhomogeneous broadening due to absorp-\ntion by the mirrors of the cavity.\nIntroducing fluctuations ( δaqandδbk) to the steady\nstates (¯aqand¯bk) of the optical modes [ aq(t) = ¯aq+\nδaq(ω)e−iωt] and the magnon mode [ bk(t) =¯bk+\nδbk(ω)e−iωt], we solve the linear Heisenberg-Langevin\nequations for the fluctuations in the frequency space, and\nobtain the cavity mode spectra,\nδaq(ω) =−(κe,q/2)1/2δain,q(ω)−κ′1/2\nqai,q(ω)\ni(∆q−ω)+κq/2−κ(−)(16)\nandδa†\nq(ω) = [δaq(−ω)]∗. For the lower sideband of the\nprobe light ( ω≡ωp−ωℓ<0 withωpthe frequency ofthe\nprobe light), δaq(ω) andδa†\nq(ω) are resonant when the\ncontrol light is red detuned (∆ q=ω) and blue detuned\n(∆q=−ω), respectively. The input-output boundary\nconditions δaout,q(ω) =δain,q(ω)+(κe,q/2)1/2δaq(ω) and\nδa†\nout,q(ω) =δa†\nin,q(ω) + (κe,q/2)1/2δa†\nq(ω) yield the re-\nflection amplitudes\nr(−)\nq(ω) = 1−κe,q/2\ni(∆q−ω)+κq/2−κ(−)(17)\nfor red detuning, and\nr(+)\nq(ω) = 1−κe,q/2\n−i(∆q+ω)+κq/2−κ(+)(18)\nfor blue detuning, where\nκ(−)(ω)\n=/summationdisplay\nn\n−/vextendsingle/vextendsingle/vextendsingleg(−)\nq,q−k,n/vextendsingle/vextendsingle/vextendsingle2\nNℓ,q−k\ni(ωk−ω)+γm/2+/vextendsingle/vextendsingle/vextendsingleg(−)\nq+k,q,n/vextendsingle/vextendsingle/vextendsingle2\nNℓ,q+k\n−i(ωk+ω)+γm/2\n(19)\nandκ(+)(ω) =/bracketleftbig\nκ(−)(−ω)/bracketrightbig∗, withNℓ,q±k=|¯aq±k|2the\nphoton number of control light with frequency ωl,q±k.\nThe imaginary (real) part of κ(±)yields a correction to\nthe resonance frequency (the line width) of the cavity\nmode due to the photon-magnon interaction. The in-\nteraction strength is enhanced by/radicalbigNℓ,q±k, as shown in\nEq. (19). Thus\ngeff\nq,q−k,n=g(−)\nq,q−k,n/radicalbig\nNℓ,q−k, (20)so even though the intrinsic coupling rate g(−)\nq,q−k,nis in-\nversely proportional to√\nV,geff\nq,q−k,nis proportional to\nthe control light power and is limited by the maximum\nallowable photon density.\nWith the control light red detuned from the cavity res-\nonance, we plot the transmission (density plot) and re-\nflection spectra of the anti-Stokes process as shown in\nFig. 2. When γm< geff< κq, one can obtain electro-\nmagnetically induced transparency (EIT), as shown in\nFigs. 2(a) and 2(b). The asymptotic lines on the density\nplot denote the resonances with the cavity and with the\nmagnon modes, respectively. The applied magnetic field\nis swept to tune the magnon mode frequency. When ωk\nis adjusted to be in resonance with the detuned control\nlight, a transparency window is opened in the reflection\nspectra and its width is determined by geff.\nThe EIT properties can be determined by translating\nEq. (13) to the Tavis-Cummings model for the fluctua-\ntions with the control light red detuned,\nH=/summationdisplay\nq/planckover2pi1∆qδa†\nqδaq+/summationdisplay\nn,k/planckover2pi1ωnkδb†\nkδbk\n+/summationdisplay\nn,q,k/bracketleftBig\n/planckover2pi1geff\nq,q−k,nδaqδb†\nk+h.c./bracketrightBig\n,(21)\nwhich yields two types of polaritons formed by cavity\nmodes dressed by magnon modes. The energy state of\nthe system can be labeled with the polariton number,\nEM,N=/planckover2pi1ω+(N+ 1/2) +/planckover2pi1ω−(M+ 1/2) with ω±=\n(1/2)[(∆q+ωk)±/radicalBig\n(∆q−ωk)+4|geff\nq,q−k,n|2], whose en-\nergy level diagram is shown in Fig. 1(c). ωℓis on reso-\nnance for the |M,N−1∝angbracketright → |M,N∝angbracketrighttransition whereas ωp\nis detuned by ωfrom the |M−1,N∝angbracketright → |M,N∝angbracketrighttransi-\ntion. Thecoexistenceofthecontrolandprobelightforms\na dark state that makes the probe light less absorbed.\nIn another regime, for κq< geff< γm, magnons are\ndamped so fast that there are no stable polariton states.\nOn resonance with the magnon modes, the energy of a\ncavityphotonistransferredtoamagnonandcontrolpho-\nton and then dissipated to the environment. The yellow\ncurve in Fig. 2(d) shows the reflection spectrum of the\nprobe light for the off-resonant case, and the blue one\nfor the resonant case. The reflection is strongly reduced\nwhen the probe light, interacting with the control light,\nis resonant with the magnon modes.\nFor blue-detuned control light, the change in the re-\nflection spectra with increasing control power is shown\nin Fig. 3. The monotonic decrease of the linewidth as\nthe control light power increases [Fig. 3(d)] indicates en-\nergy is transferred from the control light to the probe\nlight. The reflection can even exceed one when the\ngain compensates the energy loss due to the cavity res-\nonance. Figure 3(e) shows that there exists a critical\npower at which the reflection vanishes. Furthermore,\nthe power is limited according to Eqs. (18) and (19),5\nTrans.Reflection\nn=3\nq\n3.402860 Oe\n3.453.503.553.60\nTrans.\n|rq|2|rq|2(a) (b)\n(c) (d)\n2860 Oe\n2600 OeReflection2845 2860 2875\nFigure 2. Transmission (density plot) and reflection spectr a.\n(a) and (b) Electromagnetically induced transparency (EIT )\nwithκq= 35 MHz, κe,q= 14 MHz, γm= 0.1 MHz,geff= 10\nMHz, and ∆ q= 3.5 GHz. (c) and (d) Purcell enhancement\nwithκq= 2 MHz, κe,q= 0.8 MHz,γm= 35 MHz, geff= 10\nMHz, and ∆ q= 3.5 GHz. The frequency ( ω) is the sideband\nshift of the probe ωpfrom the cavity resonance frequency ωℓ,\nω=ωp−ωℓ.\nabove which κ(+)=geff/(γm/2) cancels the cavity damp-\ning rate κqand the reflection diverges, leading to a\nself-oscillation regime. Increasing the intrinsic optical\ndamping rate moves the system from the undercoupled\nregime [η=κe,q/(2κq)<0.25] to the overcoupled one\n(0.25< η≤0.5), and the critical power decreases so that\nthe reflection becomes divergent more gradually, yielding\nmore ability to control the effect experimentally [31].\nTo see the direction of power flow in the cavity, we\nplot the magnon linewidth as a function of detuning for\na given control power in Figs. 3(f) and 3(g), considering\nthe case with ω >0 only, which corresponds to Stokes\n(anti-Stokes) process for blue (red) detuning. Figure 3\nshows that, for blue detuning, the linewidth decreases as\nthe detuning approaches the resonance with the magnon\nmode, which indicates that power flows from the control\nlight to magnons, and that even parametric pumping of\nmagnons can be achieved within the shaded range of the\ndetuning. In contrast, for red detuning the linewidth in-\ncreases as the detuning approaches the resonance with\nthe magnon mode, which indicates that magnons can de-\ncay into the optical modes and thus the spin system can\nbe cooled by detuning the control light. For a given γm\nandκq, increasing the control power (and thus geff) will\nlead to the ultrastrong limit ( geff> γm,κq). We found\nthat the correspondingmagnonlinewidth will not change\nqualitatively, but its magnitude will increase by orders of\nmagnitude since it is proportional to ( geff)2.\nTo conclude, we have studied the photon-magnon in-0.81.4Reflection\nFrequency (GHz)3.4 3.5 3.6(a)\n(c)(b)\n1.0\n0.7\n0.40.61.0\n0.2(d)\n(e)\n(f) (g)\nDetuning q (GHz) -3.55 -3.35 3.35 3.55Cooling Amplifi on\nMagnon LW     (MHz)0.10.50.2 0.3 0.4 0.5 η=\n+++\nPower (mW)0.5 1.5 2.5\nLinewidth   (kHz).02.06\n-2\n   Gain(100 dB)2\nFigure 3. (a)-(e) Reflection of the lower side band probe with\nblue-detuned control at resonance with the magnon mode.\n(a)-(c) Reflection spectra for different control power [from top\nto bottom, 0 .78, 2.01, and 2 .26 mW, which have been labeled\nwith “+” in (d)]. The frequency ( ω) is the sideband shift of\nthe probe ωpfrom the control light ωℓ,ω=ωp−ωℓ. (d)\nThe linewidth of the optomagnonic resonance as a function\nof the control power. (e) Gain at resonance as a function of\nthe control power with varying η=κe,q/(2κq) for a given κq.\nThe shaded area indicates the instable regime. (f) and (g)\nThe linewidth of the magnon mode as a function of detuning\nfor a given control power (11 mW). The red (blue) curve is\nobtained under the control light of red (blue) detuning. The\nshaded area indicates the parametric oscillation regime wh ere\nthe linewidth becomes negative. Parameters associated wit h\nthe plots are κq= 35 MHz, γm= 0.1 MHz, and ∆ q=−3.5\nGHz.ηis fixed to be 0.2 in the figures other than (e). ωk=\n3.45 GHz in (f) and (g).\nteraction in an optical cavity made of a magnetic solid.\nThe interaction is intrinsically greater than for optome-\nchanics, and differs in characterfromthe photon-magnon\ninteraction in an microwave cavity. With control light\nand detuning of the probe light from the cavity reso-\nnance, this system can accomplish coherent conversion\nbetween a cavity mode and a magnon mode, or nonre-\nciprocal conversion between two optical modes. As a ba-\nsis for further studies of quantum dynamics, two classic\ncoherent situations (electromagnetically induced trans-\nparency and the Purcell effect) have been simulated.\nWe note that different aspects of optomagnonic sys-\ntems have been investigated in a related work done si-\nmultaneously in Ref. [32]. We acknowledge support of\nthe Center for Emergent Materials, a NSF MRSEC un-\nder Award No. DMR-1420451 and DARPA MESO.\n[1] A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichen-\nfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and\nO. Painter, Nature (London) 472, 69 (2011).\n[2] T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel,\nand C. A. Regal, Phys. Rev. X 3, 031012 (2013).6\n[3] K. Stannigel, P. Komar, S. J. M. Habraken, S. D.\nBennett, M. D. Lukin, P. Zoller, and P. Rabl,\nPhys. Rev. Lett. 109, 013603 (2012).\n[4] H.Huebl, C. W.Zollitsch, J. Lotze, F.Hocke, M. Greifen-\nstein, A. Marx, R. Gross, and S. T. B. Goennenwein,\nPhys. Rev. Lett. 111, 127003 (2013).\n[5] X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang,\nPhys. Rev. Lett. 113, 156401 (2014).\n[6] Y. Tabuchi, S. Ishino, T. Ishikawa, R. Ya-\nmazaki, K. Usami, and Y. Nakamura,\nPhys. Rev. Lett. 113, 083603 (2014).\n[7] J. A. Haigh, N. J. Lambert, A. C. Doherty, and A. J.\nFerguson, Phys. Rev. B 91, 104410 (2015).\n[8] L. Bai, M. Harder, Y. Chen, X. Fan, J. Xiao, and C.-M.\nHu, Phys. Rev. Lett. 114, 227201 (2015).\n[9] J. A. Haigh, S. Langenfeld, N. J. Lambert, J. J. Baum-\nberg, A. J. Ramsay, A. Nunnenkamp, and A. J. Fergu-\nson, Phys. Rev. A 92, 063845 (2015).\n[10] X. Zhang, N. Zhu, C.-L. Zou, and H. X. Tang,\narXiv:1510.03545 (2015).\n[11] A. Osada, R. Hisatomi, A. Noguchi, Y. Tabuchi, R. Ya-\nmazaki, K. Usami, M. Sadgrove, R. Yalla, M. Nomura,\nand Y. Nakamura, Phys. Rev. Lett. 116, 223601 (2016).\n[12] J. Bourhill, N. Kostylev, M. Goryachev, D. L. Creedon,\nand M. E. Tobar, Phys. Rev. B 93, 144420 (2016).\n[13] S. Gr¨ oblacher, K. Hammerer, M. R. Vanner, and M. As-\npelmeyer, Nature (London) 460, 724 (2009).\n[14] J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter,\nNat. Commun. 3, 1196 (2012).\n[15] S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier,\nS. D. Bennett, P. Rabl, J. G. E. Harris, and M. D.\nLukin, Science 335, 1603 (2012).\n[16] C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang,\nScience338, 1609 (2012).\n[17] B. Gouraud, D. Maxein, A. Nicolas, O. Morin, and\nJ. Laurat, Phys. Rev. Lett. 114, 180503 (2015).[18] E. M. Purcell, H. C. Torrey, and R. V. Pound,\nPhys. Rev. 69, 37 (1946).\n[19] C.-H. Su, A. D. Greentree, and L. C. L. Hollenberg,\nOptics Express 16, 6240 (2008).\n[20] L. Li, T. Schr¨ oder, E. H. Chen, M. Walsh, I. Bayn,\nJ. Goldstein, O. Gaathon, M. E. Trusheim, M. Lu,\nJ. Mower, M. Cotlet, M. L. Markham, D. J. Twitchen,\nand D. Englund, Nat Commun 6, 6173 (2015).\n[21] W. Wettling, M. G. Cottam, and J. R. Sandercock,\nJournal of Physics C: Solid State Physics 8, 211 (1975).\n[22] W. Wettling, Appl. Phys. 6, 367 (1975).\n[23] T. Holstein and H. Primakoff,\nPhys. Rev. 58, 1098 (1940).\n[24] D.D.Stancil,IEEE Journal of Quantum Electronics 27, 61 (1991).\n[25] The optical cavity in the three systems is taken to be the\nsame, with l×w×d= 8mm ×400µm×4µm. For the\nelectro-optical system, we use the parameters of lithium\nniobate, with n0= 2.3,r= 308pm /V,ωm= 2π×9GHz,\nandC= 1pF. For the optomechanical system, m=\n145ng, and ωm= 2π×947kHz. For the optomagnonic\nsystem (made of YIG), K= 4.76×10−9m/A,n0= 2.2,\nandM0= 1.39×105A/m.\n[26] M. Tsang, Phys. Rev. A 81, 063837 (2010).\n[27] N. Brahms and D. M. Stamper-Kurn,\nPhys. Rev. A 82, 041804 (2010).\n[28] G. E. Marti, A. MacRae, R. Olf, S. Lourette,\nF. Fang, and D. M. Stamper-Kurn,\nPhys. Rev. Lett. 113, 155302 (2014).\n[29] F. Fang, R. Olf, S. Wu, H. Kadau, and D. M. Stamper-\nKurn, Phys. Rev. Lett. 116, 095301 (2016).\n[30] P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes,\nJ. Phys. B: At. Mol. Opt. Phys. 41, 155004 (2008).\n[31] X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang,\nSci. Adv. 2, e1501286 (2016).\n[32] S. V. Kusminskiy, H. X. Tang, and F. Mar-\nquardt, arXiv:1604.07053 [cond-mat] (2016), arXiv:\n1604.07053."    },    {        "title": "2401.15013v1.Reactive_additive_capillary_stamping_with_double_network_hydrogel_derived_aerogel_stamps_under_solvothermal_conditions.pdf",        "content": "1 \n Reactive additive capillary stamping with double ne twork hydrogel-\nderived aerogel stamps under solvothermal condition s \n \nFatih Alarslan, ‡,§ Martin Frosinn,‡,§ Kevin Ruwisch, $ Jannis Thien, $ Tim Jähnichen, & Louisa \nEckert, & Jonas Klein, § Markus Haase, § Dirk Enke, & Joachim Wollschläger, $ Uwe Beginn, § \nMartin Steinhart *,§ \n \n§ Institut für Chemie neuer Materialien and CellNanO s, Universität Osnabrück, Barbarastr. 7, \n49076 Osnabrück, Germany \n \n$ Department of Physics, Universität Osnabrück, Barb arastr. 7, 49076 Osnabrück, Germany \n \n& Institute of Chemical Technology, Universität Leip zig, Linnéstraße 3, 04103 Leipzig, \nGermany  \n \n‡ F. A. and M. F. contributed equally to this manuscr ipt \n  2 \n Abstract \nIntegration of solvothermal reaction products into complex thin-layer architectures is frequently \nachieved by combinations of layer transfer and subt ractive lithography, whereas direct additive \nsubstrate patterning with solvothermal reaction pro ducts has remained challenging. We report \nreactive additive capillary stamping under solvothe rmal conditions as a parallel contact-\nlithographic access to patterns of solvothermal rea ction products in thin-layer configurations. \nTo this end, corresponding precursor inks are infil trated into mechanically robust mesoporous \naerogel stamps derived from double-network hydrogel s (DNHGs). The stamp is then brought \ninto contact with a substrate to be patterned under  solvothermal reaction conditions inside an \nautoclave. The precursor ink forms liquid bridges b etween the topographic surface pattern of \nthe stamp and the substrate. Evaporation-driven enr ichment of the precursors in these liquid \nbridges along with their liquid-bridge-guided conve rsion into the solvothermal reaction \nproducts yields large-area submicron patterns of th e solvothermal reaction products replicating \nthe stamp topography. As example, we prepared thin hybrid films, which contained ordered \nmonolayers of superparamagnetic submicron nickel fe rrite dots prepared by solvothermal \ncapillary stamping surrounded by nickel electrodepo sited in a second, orthogonal substrate \nfunctionalization step. The submicron nickel ferrit e dots acted as magnetic hardener halving the \nremanence of the ferromagnetic nickel layer. In thi s way, thin-layer electromechanical systems, \ntransformers and positioning systems may be customi zed.    \n \nKeywords      \nDouble-network hydrogels, aerogels, microcontact pr inting, capillary stamping, surface \nmanufacturing, substrate patterning, solvothermal s yntheses, nickel ferrite, magnetic \nnanoparticles.    3 \n Introduction \nSolvothermal syntheses carried out in autoclaves at  temperatures exceeding the boiling point of \nthe used solvents may yield reaction products diffi cult to attain under ambient conditions. 1, 2  \nAlternative syntheses typically require much higher  reaction temperatures or involve high-\ntemperature calcination steps. Thus, metal-organic frameworks, 3 hierarchical nanostructures for \nwater splitting,4 multi-dimensional noble-metal-based catalysts for electrocatalysis,5 \nsemiconductors such as zinc oxide,6 ferrites,7 perovskite oxides,8 LiFePO 4 for Li-ion batteries 9 \nas well as two-dimensional transition metal carbide  and nitride hybrids for catalytic energy \nstorage and conversion 10  were obtained by solvothermal syntheses. The manuf acturing of \nfunctional components containing patterned thin lay ers of solvothermal reaction products has \nremained challenging. It is conceivable to use cont inuous thin films of solvothermal reaction \nproducts 11  as starting material. Potential approaches to gene rate patterned films of solvothermal \nreaction products on receiving substrates then may comprise standard lithography under \nambient conditions,12  combinations of layer transfer by wafer bonding or  ion slicing and \nsubtractive lithography as well as laser-induced fo rward transfer (LIFT).13  It is obvious that the \ndirect lithographic deposition of patterns of solvo thermal reaction products on receiving \nsubstrates would be more efficient. However, additi ve lithographic methods including inkjet \nand aerosol jet printing 14  as well as classical soft lithography 15, 16  and polymer pen \nlithography 17-19  typically only enable the deposition of precursors ; their conversion into the \nsolvothermal reaction products commonly comes along  with the destruction of the \nlithographically generated precursor patterns, for example, because the solvent used for the \nconversion dissolves the precursors.  \n \nFigure 1.  Additive solvothermal capillary stamping. a) A sta mping device ( 1) consists of an upper part ( 1a ) with \nan ink supply hole ( 2) and a lower part ( 1b ). A DNHG-derived aerogel stamp ( 3) with contact elements ( 4) is \nattached to upper part ( 1a) and approached to a substrate ( 5) attached to lower part ( 1b ). b) Stamping device ( 1) is \ninserted into PTFE vessel ( 6). Precursor solution ( 7) deposited on the surface of upper part ( 1a ) flows through hole \n(2) into DNHG-derived aerogel stamp ( 3) and forms liquid bridges ( 8) between contact elements ( 4) and substrate \n(5). c) PTFE vessel ( 6) is then located in a sealed steel autoclave ( 11 ) (not shown, cf. Figure 2). Under solvothermal \nconditions, an ethanol-rich gas phase ( 9) fills PTFE vessel ( 6). The nonvolatile precursors of the solvothermal \nreaction product ( 10) and eventually solvothermal reaction product ( 10) itself enrich in the liquid bridges ( 8). d) \nAfter removal from stamping device ( 1) and detachment of DNHG-derived aerogel stamp ( 3), substrate ( 5) is \nmodified by patterns of solvothermal reaction produ ct (10), here arrays of submicron nickel ferrite dots. \n4 \n The direct deposition of patterns of solvothermal r eaction products may be achieved by the \ncoupling of solvothermal syntheses with in situ  additive substrate patterning. It was shown that \nporous stamps 20-25  are particularly suitable for parallel additive su bstrate patterning even if \ndiluted precursor solutions are used as inks becaus e the pore systems of the stamps act as ink \nreservoirs. Evaporation of the volatile ink compone nts (typically the solvents) drags more and \nmore of the non-volatile ink components, such as pr ecursors of solvothermal reaction products, \ninto the liquid ink bridges formed between the cont act elements of the stamp and the substrate \nto be patterned. The enrichment of the non-volatile  ink components in the liquid bridges is a \ncrucial aspect of additive pattern formation with p orous stamps. 22  However, the porous stamps \nso far available are not compatible with solvotherm al processes; polymeric stamps 20, 21, 23  are \ntoo deformable, whereas silica 22, 24  and phenolic resin stamps 25  are too brittle. In general, \nreactive additive lithography has, so far, predomin antly been conducted with solid stamps under \nambient pressure and temperature. 26  \n \nHere we report the direct contact-lithographic gene ration of thin patterned layers of \nsolvothermal reaction products by additive solvothe rmal capillary stamping with aerogel \nstamps derived from double network hydrogels (DNHGs ) 27, 28  (Figure 1). DNHG-derived \naerogel stamps contain continuous mesopore systems and exhibit excellent mechanical strength \nbecause their scaffold is a combination of a hard b ut brittle network and a soft and ductile \nnetwork. Hence, the DNHG-derived aerogel stamps can  be used for parallel additive contact \nlithography under solvothermal reaction conditions and enable the generation of patterns of \nsolvothermal reaction products by stamp-guided solv othermal conversion of their precursors. \nAs example, we demonstrate the preparation of thin nickel ferrite-nickel (NiFe 2O3-Ni) hybrid \nlayers consisting of a regular monolayer of submicr on nickel ferrite dots embedded in a \ncontinuous nickel film. Nickel ferrite nanostructur es and nanocomposites 29  have, for example, \nattracted significant interest for magnetic hyperth ermia, 30, 31  as well as for catalytic and \npseudocapacitive energy storage.32  Capillary stamping with DNHG-derived aerogel stamp s \ncombined with a solvothermal synthesis based on eth anolic solutions of iron(III)-\nacetylacetonate (Fe(C 5H7O2)3) and nickel(II)-acetylacetonate (C 10 H14 NiO 4)33, 34  yielded arrays \nof submicron nickel ferrite dots on indium tin oxid e (ITO) substrates. Then, the ITO substrates \nfunctionalized with ordered monolayers of submicron  nickel ferrite dots were orthogonally \nfunctionalized 35  with metallic nickel by electrodeposition. The sup erparamagnetic submicron \nnickel ferrite dots embedded into the thin ferromag netic nickel film halved the magnetic \nremanence of the latter, while the saturation value  of the magnetic moment per area remained \nby and large unaffected.  \n 5 \n Materials and Methods \nChemicals and materials  \nAcrylamide (AAm) (>99%) and zirconium(IV)-chloride (>98%) were purchased from Merck. \nPotassium peroxodisulfate (PPS) (>99%) and titanium (IV)-chloride (>99%) were purchased \nfrom Fluka. N,N'-Methylenebis(acrylamide) (MBA) (99%), p-toluenesulfonyl chloride (>98%), \nnickel(II)-acetylacetonate (95%), iron(III)-acetyla cetonate (97%), nickel sulfate, sodium \nchloride, boric acid and potassium dodecyl sulfonat e were purchased from Sigma-Aldrich. \nN,N,N', N'-tetramethylethylenediamine (TMEDA) (99 %) and tet raethoxysilane (98 %) were \npurchased from Alfa Aesar. Ethylene glycol (99.8 %)  was purchased from VWR Chemicals. \nPerfluorodecyltrichlorosilane (FDTS; C 10 H4Cl 3F17 Si) was purchased from abcr GmbH \n(Karlsruhe). Synthetic hectorite Na +0.7 [(Si 8Mg 5.5 Li 0.3 )O 20 (OH) 4]-0.7  (Laponite RD) was \npurchased from GMW (Vilsheim). Macroporous silicon 36, 37  with macropores having a diameter \nof 1 µm and a depth of 730 nm arranged in a hexagon al array with a lattice constant of 1.5 µm \nwas purchased from Smart Membranes (Halle an der Sa ale). Indium tin oxide substrates \n(In 2O3)0.9  • (SnO 2)0.1  (resistance 8-12 Ω sq -1, thickness 1200–1600 Å) were purchased from \nSigma Aldrich. All water used was fully deionized a nd further purified using a Sartorius stedim/ \narium 611 UV device. If not stated otherwise, chemi cals were used as received. \n \nFabrication of DNHG-derived aerogel stamps \nPreparation of synthetic hectorite/zirconylchloride  octahydrate solutions. To prepare  \nsynthetic hectorite solutions, 10 g synthetic hecto rite was dissolved in 1 L deionized water. \nSynthetic hectorite solutions show a complex phase evolution starting with the swelling of \nstacked hectorite platelets, which is followed by e xfoliation and the formation of house-of-cards \nstructures, in which the positive charged sides of the platelets interact with the negative charged \nfaces of surrounding platelets (Figure S1). 38  Therefore, the properties of freshly prepared \nsynthetic hectorite solutions slightly differ from those of aged synthetic hectorite solutions. \nThus, all synthetic hectorite solutions used in thi s work were aged for at least one week. \nZirconylchloride octahydrate was prepared by hydrol yzing zirconium chloride in deionized \nwater, followed by evaporation of excess water unde r reduced pressure until no further mass \nloss was observed. 100 g of zirconylchloride octahy drate was added to the turbid synthetic \nhectorite solutions, which were then stirred for on e week so that transparent synthetic \nhectorite/zirconylchloride octahydrate solutions we re obtained.  \n \nPreparation of tetrakis-(2-hydroxyethoxy)-silane so lutions in ethylene glycol. Ethylene \nglycol (300 g, 4.83 mol), tetraethoxyorthosilane (2 50 g, 1.20 mol) and p-toluenesulfonyl \nchloride (40 mg, 0.21 mmol) were filled into a 1 L round-bottom flask. Vigorous stirring for 60 \nminutes at 70°C under ambient pressure yielded a ho mogenous colorless solution. 200 g of the 6 \n reaction product ethanol was removed from the sol s olution by distillation with a rotary \nevaporator applying a reduced pressure of 300 mbar for two hours and subsequently a reduced \npressure of 90 mbar. Thus, a clear, colorless and m oisture-sensitive solution containing tetrakis-\n(2-hydroxyethoxy)-silane as well as oligomeric or p olymeric silane species derived from \ntetrakis-(2-hydroxyethoxy)-silane in ethylene glyco l was obtained. For characterization by \nNMR spectroscopy, 10 to 15 mg of the solution was m ixed with 0.5 ml deuterized DMSO. \nNMR measurements were performed at 30 °C using a Br uker Avance III spectrometer at 500 \nMHz ( 1H), 125 MHz ( 13 C) or 100 MHz ( 29 Si).  \n1H-NMR (DMSO-d6 δ/ppm) (Figure S2): 1.056 (t, J= 7.0 5, C H3), 1.156 (m, C H3), 3.395 (s, \nCH2), 3.443 (m, C H2), 3.490 (s, br, C H2), 3.749 (s, br. C H2), 4.3960 (s, O H)  \n13 C-NMR (DMSO-d6 δ/ppm) (Figure S3): 18.473 (s, CH3), 56.044 (s, CH2), 61.574 (m, br, \nCH2), 62.797 (s, CH2), 64.854 (s, br, CH2) \n29 Si-NMR (DMSO-d6 δ/ppm) (Figure S4): -108.249 (s, br , Si O2) \n \nPreparation of the sol solution for the DNHG synthe sis. \n8 g tetrakis-(2-hydroxyethoxy)-silane solution was added to 10 g synthetic \nhectorite/zirconylchloride octahydrate solution in a 50 ml round-bottom flask under constant \nstirring. Subsequently, 6 g AAm (84.41 mmol) and 2. 5 mg MBA (0.0162 mmol) were added. \nThe flask was placed in an ice bath after a clear s olution was obtained. A mixture of 2 µl \nTMEDA (1.55 mg, 0.0133 mmol) in 0.5 ml H 2O was added and the flask was closed with a \nseptum cap. A separate flask with a septum containi ng 4 mg PPS (0.0148 mmol) and 1 ml H 2O \nwas placed in the ice bath as well. Both solutions were suffused with nitrogen for 30 minutes. \nUnder exclusion of oxygen, both solutions were comb ined and mixed thoroughly. The \ncombined solutions were subjected to three vacuum-u ltrasonication cycles under cooling to 0°C \nusing ice baths. Each cycle comprised the applicati on of a vacuum for 30 seconds using a \ndiaphragm pump followed by sonication for 30 second s, while the vacuum was maintained. \nThe obtained sol solution was kept at 0°C under nit rogen atmosphere and used within 5 minutes.  \n \nPreparation of DNHG-derived aerogel stamps. The surface of macroporous silicon was \ntreated with oxygen plasma for 10 minutes and then coated with FDTS by chemical vapor \ndeposition at 100 °C for 10 h following procedures reported elsewhere.39  About 15 mL of the \nsol solution was poured onto FDTS-coated macroporou s silicon pieces extending 1 cm 2 located \nin glass vials under exclusion of oxygen under nitr ogen atmosphere. The vials were closed \nairtight and gelation as well as aging was allowed to take place at 25°C for at least one week. \nThe aged cylindrical DNHG monoliths with a diameter  of 24 mm, a height of ~22 mm and a \nmass of ~16 g having a topographically patterned co ntact surface were detached from the \nmacroporous silicon under ambient conditions while still being wet. Then, each aged hydrogel \nmonolith was treated with 500 ml methanol for 120 h , 500 ml THF for 120 h and 500 ml n-7 \n hexane for 120 h in a Soxhlet extractor. This proce dure resulted in shrinkage to 78% of the \ninitial volume of the water-filled DNHG. Evaporatio n of the n-hexane at 20 °C in a vacuum of \n~0.001 mPa did not lead to further shrinkage. Subse quently, the macroporous silicon template \nwas removed from the gel. As a result, DNHG-derived  aerogel stamps ( 3) (cf. Figure 1) were \nobtained, which had contact surfaces extending 1 cm2 topographically patterned with contact \nelements ( 4). The contact elements ( 4) had a diameter of 900 nm and a height of 600 nm. Prior \nto further use, the height of the DNHG-derived aero gel stamps ( 3) was reduced to ~1.3 cm by \nsawing. The remaining surfaces except the topograph ically patterned contact surface with the \ncontact elements ( 4) were ground. \n \nCharacterization of the DNHG-derived aerogel \nNitrogen sorption measurements on DNHG-derived aero gel samples were performed with a \ndevice Autosorb from Quantachrome at 77 K. Before a ny measurement, about 100 mg sample \nmaterial was degassed at 373 K for 10 h in an ultra high vacuum. The specific surface area was \ncalculated using the BET method in a relative press ure range p/p0 = 0.05 - 0.30. The total pore \nvolume was calculated at p/p 0 = 0.995. For the calculation of the pore size dis tribution, the BJH \nmethod was applied to the desorption branch of the isotherm. For the analyses, the program \nASiQwin (Quantachrome Instruments) was used. Mercur y intrusion measurements applied to \ndetermine the porosity of the samples were carried out with a Pascal 440 device (Porotec). \nIntrusion measurements were performed at 297 K up t o 400 MPa. The contact angle of mercury \nwas set to 140° and the surface tension to 0.48 N m−1. Compressive stress tests on 5 DNHG-\nderived aerogel specimens extending ~10 mm * ~10 mm  * ~5 mm were conducted with a PCE-\nMTS 500 test stand equipped with a PCE-DFG N 5K for ce gauge and two parallel steel plates. \nThe compressions of the samples were calculated fro m the rate of compression (0.43 mm/s with \n50 data points per second).  \n  8 \n Figure 2.  Setup for additive solvothermal capillary stamping . a) Stamping device ( 1) consists of an upper part ( 1a ), \non which a DNHG-derived aerogel stamp ( 3) is mounted, and a lower part ( 1b ), on which substrate ( 5) (here: \nFDTS-coated ITO) is placed. Upper part ( 1a ) and lower part ( 1b ) are then connected by pins preventing lateral \ndisplacement. b) Stamping device ( 1) including the DNHG-derived aerogel stamp ( 3) and substrate ( 5) is \ntransferred into PTFE vessel ( 6). c) Upper part ( 1a ) of stamping device ( 1) containing hole ( 2) is covered with \nprecursor solution ( 7) while located in PTFE vessel ( 6). Precursor solution ( 7) flows through hole ( 2) into the \nDNHG-derived aerogel stamp ( 3). d) PTFE vessel ( 6) including stamping device ( 1), DNHG-derived aerogel \nstamp ( 3), substrate ( 5) and precursor solution ( 7) is inserted into steel autoclave ( 11 ). e) Steel autoclave ( 11 ) is \nthen sealed with lid ( 12 ). \n \nAdditive solvothermal capillary stamping  \nThe stamping device ( 1) consisted of an upper part ( 1a ) and a lower part ( 1b ). The upper part \n(1a ) consisted of a stainless-steel cylinder with a di ameter and a height of 2 cm. The steel \ncylinder contained three peripheral holes parallel to the cylinder axis with a diameter of 3 mm \nforming an equilateral triangle with an edge length  of 1.4 cm as well as a central hole ( 2) parallel \nto the cylinder axis with a diameter of 4 mm. A DNH G-derived aerogel stamp ( 3) was glued \nonto the upper part ( 1a ) with double-sided adhesive tape in such a way tha t the contact elements \n(4) of the DNHG-derived aerogel stamp ( 3) pointing away from upper part ( 1a ) where exposed \n(cf. Figure 1). The lower part ( 1b ) of the stamping device ( 1) was an exact copy of the upper \npart ( 1a ) except that it did not contain a central hole ( 2). The ITO substrates ( 5) were coated \nwith FDTS applying the same procedure reported else where 39  as in the case of macroporous \nsilicon. The contact elements ( 4) of the DNHG-derived aerogel stamp ( 3) glued on the upper \npart ( 1a ) were brought into contact with an FDTS-coated ITO  substrate ( 5) placed on the lower \npart ( 1b ) (Figure 1a). The upper part ( 1a ) was then fixed on the lower part ( 1b ) by inserting \npins into the three peripheral holes of upper part ( 1a ) and the corresponding counterpart holes \nin the lower part ( 1b ) (Figure 2a). The pins prevented lateral displacem ent of the upper part ( 1a ) \nand the lower part ( 1b ) with respect to each other. Furthermore, the pins  prevented lateral \n9 \n displacement of the FDTS-coated ITO substrate ( 5), which was not fixated otherwise on the \nlower part ( 1b ). The contact pressure exerted by the DNHG-derived  aerogel stamp ( 3) on the \nFDTS-coated ITO substrate ( 5) amounted to 3.9 kN/m 2 and originated from the mass of the \nupper part ( 1a ) of 40 g. The assembled stamping device ( 1) including the DNHG-derived \naerogel stamp ( 3) and the FDTS-coated ITO substrate ( 5) was then inserted into a cylindrical \nPTFE vessel ( 6) with a height of 12 cm, a diameter of 3.8 cm and a total volume of 40 mL \n(Figure 2b). The upper part ( 1a ) of stamping device ( 1) fitted into PTFE vessel ( 6) in such a \nway that the rim of the upper part ( 1a ) was in close, self-sealing contact with the wall of the \nPTFE vessel ( 6). Nickel ferrite precursor solution ( 7) was prepared by dissolving 54.8 mg (0.2 \nmmol) nickel(II)-acetylacetonate and 150.68 mg (0.4  mmol) iron(III)-acetylacetonate in 50 mL \nethanol. 6 mL of precursor solution ( 7) was deposited on the surface of the upper part ( 1a ) of \nthe stamping device ( 1) located in PTFE vessel ( 6), flowed through the central hole ( 2) in the \nupper part ( 1a ) and infiltrated the DNHG-derived aerogel stamp ( 3) (Figures 1b and 2c). Then, \nthe PTFE vessel ( 6) containing the assembled stamping device ( 1) loaded with precursor \nsolution ( 7) was inserted into a steel autoclave ( 11 ), which was then sealed with a steel lid ( 12 ) \n(Figures 1c and 2d). The solvothermal reaction yiel ding arrays of submicron nickel ferrite dots \n(10) was carried out in a pressure digestion system (B erghof digestec DAB-2) at 413 K (140°C) \nfor 48 hours. After completion of the synthesis and  disassembly of the stamping device ( 1), the \nDNHG-derived aerogel stamp ( 3) was detached from the substrate ( 5) patterned with submicron \nnickel ferrite dots ( 10) (Figure 1d), which was washed with ethanol and dr ied at 40°C for 1 h. \nThe volume of the autoclave ( 11 ) equipped with PTFE vessel ( 6) and stamping device ( 1) \nincluding a DNHG-derived aerogel stamp ( 3) and an ITO substrate ( 5) available to a fluid phase \nin its interior was determined by differential weig hing before and after filling with water and \namounted to ~29.15 mL. \n \nElectrodeposition of Nickel \nFor the electrodeposition of nickel, ITO substrates  ( 5), which were either FDTS-coated or \nfunctionalized with submicron nickel ferrite dots ( 10), were placed in an electrochemical cell. \nWe used an aqueous plating solution containing 1 mo l/L NiSO 4*6H 2O and 0.1 mol/L of the \nother components H 3BO 3, NaCl and NaC 12 H25 SO 4.40  Thus, 0.536 g NiSO 4*6H 2O (0.02 mol), \n0.124 g H 3BO 3 (0.002 mol), 0.117 g NaCl (0.002 mol) and 0.557 g NaC 12 H25 SO 4 (0.002 mol) \ndissolved in 20 ml water were deposited into the el ectrochemical cell. The ITO substrate ( 5) \nacted as working electrode, a platinum wire as coun ter electrode and an Ag/AgCl electrode as \nreference electrode. The electrodeposition was carr ied out at a constant current of 1 mA/cm 2 \nfor 10 min using a potentiostat Interface 1000 (Gam ry). The thickness of the nickel films was \ndetermined by scanning electron microscopy investig ation of a cross-sectional specimen \n(Figure S5). \n 10 \n Contact angle measurements \nContact angles of the nickel ferrite precursor solu tion (0.2 mmol nickel(II)-acetylacetonate and \n0.4 mmol iron(III)-acetylacetonate dissolved in 50 mL ethanol) on FDTS-modified ITO \nsubstrates were measured by the sessile drop method  with a DSA100 drop shape analyzer at \n22°C and a relative humidity of 33 %. Overall 6 mea surements at different positions were \ncarried out. \n \nMicroscopy and energy-dispersive X-ray spectroscopy  \nPrior to scanning electron microscopy (SEM) imaging , the samples were dried overnight at \n40 °C in air and then sputter-coated 2-3 times for 15 s with platinum/iridium alloy using an \nEMITECH K575X sputter coater. SEM images were taken  with a Zeiss Auriga device equipped \nwith a field emission cathode and a Gemini column w ith a working distance of 5 mm applying \nan acceleration voltage of 3 kV . For image detectio n an InLens detector was used. For energy-\ndispersive X-ray (EDX) spectroscopy mappings a X-Ma x 80 mm 2 silicon drift detector (Oxford \nInstruments) was used. The EDX maps extending 1024x 788 pixels were recorded with a pixel \ndwell time of 5000 µs and a frame live time of 1.05  h. Atomic force microscopy (AFM) \ntopography images were recorded with an NTEGRA micr oscope (NT-MDT) in the tapping \nmode using HQ:NSC16/AL BS cantilevers from µmasch w ith a resonance frequency of 170 - \n210 kHz and a force constant of 30 - 70 N/m.  \n \nXPS \nXPS measurements were carried out under ultra-high vacuum using an ESCA system Phi 5000 \nVersaProbe III with a base pressure of 1•10 -9 mbar equipped with a monochromatized aluminum \nanode (Kα = 1486.6 eV) and a 32-channel electrostat ic hemispherical electronic analyzer. An \nion gun and an electron gun were used to prevent sa mple charging. A take-off angle of 45° was \nused. The XP spectra were calibrated using the carb on C 1s peak at 284.5 eV .41  \n \nX-ray diffraction (XRD) of submicron nickel ferrite  dots  \nXRD scans were carried out in theta-theta geometry with Cu Kα radiation using an X’Pert Pro \nMPD diffractometer (PANalytical) equipped with a ro tating sample plate and a PixCel 1D \ndetector. The diffractometer was operated at a volt age of 40 kV and a current of 30 mA. For the \nXRD measurements, ~2 mg submicron nickel ferrite do ts ( 10) were carefully scraped off from \nseveral ITO substrates ( 5) with scalpels. \n \nMagnetometry \nMagnetization curves of ITO substrates ( 5) with an area of 1 cm 2 functionalized with arrays of \nsubmicron nickel ferrite dots ( 10), continuous nickel layers with a thickness of ~10 0 nm or \nnickel ferrite-nickel hybrid films ( 13 ) (cf. Figure 7 below) were measured at 300 K by va rying 11 \n the magnetic field from -1 T to 1 T using a vibrati ng sample magnetometer (LakeShore, Model \n7404). Magnetization loops were corrected by subtra cting the diamagnetic contribution from \nthe substrate.  \n \n  12 \n  \nFigure 3.  Overview of the general synthesis procedure of DNH Gs. a), b) Conversion of tetrakis-(2-hydroxy-\nethoxy)-silane to a hard SiO 2 particle network a) Hydrolysis of tetrakis-(2-hydr oxy-ethoxy)-silane yielding \nhydroxysilane species, which b) form a SiO 2 particle network by polycondensation. c), d) Gener ation of the soft \npolyacrylamide network. c) Generation of initiation  sites (pink stars in c4) for d) the free radical p olymerization \n(FRP) of polyacrylamide on synthetic hectorite plat elets. The formed polyacrylamide chains (blue) are crosslinked \nby the synthetic hectorite platelets, methylene-bis -acrylamide (green) and zirconium hydroxide polycat ions (brown) \n(panel c5). e) Resulting DNHG structure . \n13 \n Results and discussion \nSynthesis of DNHGs  \nThe general procedure for the DNHG synthesis involv es two orthogonal polymerizations \nsimultaneously carried out in the same flask (Figur e 3). The first polymerization is a \npolycondensation reaction yielding a hard silica ne twork (Figure 3a,b). The second \npolymerization is a free radical polymerization (FR P) yielding a soft polyacrylamide network \n(Figure 3c,d). Two additional components, zirconyl chloride octahydrate and synthetic hectorite \nplatelets (Figure S1), are active in both reactions ,42, 43  as detailed below.  \n \nThe starting point for the formation of the hard si lica network is the preparation of a solution \nof tetrakis-(2-hydroxyethoxy)-silane in ethylene gl ycol (Figure 3a1). This silane, which can \nonly be synthesized directly in the solvent and rea ctant ethylene glycol, cannot be isolated from \nthe reaction mixture. The removal of excess ethylen e glycol would shift the reaction equilibrium \nto higher degrees of polymerization and crosslinkin g because tetrakis-(2-hydroxyethoxy)-silane \nmolecules may condense under release of an ethylene  glycol molecule. Even in the presence of \nexcess ethylene glycol, tetrakis-(2-hydroxyethoxy)- silane forms to some extent oligomers or \npolymers, as apparent from the 1H (Figure S2), 13 C (Figure S3), and 29 Si (Figure S4) NMR \nspectra of the reaction mixture. Apart from 1H signals at 3.394 ppm and 4.396 ppm as well as \nthe 13 C signal at 62.797 ppm originating from ethylene gl ycol, the NMR spectra contain only \nbroad signals with widths characteristic of oligome rs and polymers. Diffusion-ordered NMR \nspectroscopy (DOSY) (Figure S6) confirmed that the narrow signals ascribed to ethylene glycol \nare associated with large diffusion coefficients, w hereas the broad signals ascribed to tetrakis-\n(2-hydroxyethoxy)-silane condensation products are associated with a broad distribution of \nlower diffusion coefficients. When the tetrakis-(2- hydroxyethoxy)-silane/ethylene glycol \nmixture is brought into contact with water, hydroly sis of the silane species produces metastable \nhydroxysilane species (Figure 3a2), which further o ligomerize and polymerize by condensation \nreactions (Figure 3b1). After formation of a viscou s sol presumably composed of small silica \nparticles and branched polymeric silica structures (Figure 3b2), gelation proceeds by further \ncondensation reactions. Zirconylchloride is strongl y acidic and thereby catalyzes hydrolysis and \ncondensation of the silicon dioxide network. The re sulting clear, colorless, stiff and brittle silica \nnetwork consists of a rigid network of covalently b ond silica particles with diameters of a few \nnm (Figure 3b3).44  \n \nThe formation of the soft polyacrylamide network is  initiated by the redox initiator system \npotassium peroxodisulfate/tetramethylethylenediamin e (PPS/TMEDA) (Figure 3c1). 45  \nMethylene-bis-acrylamide (MBA) crosslinks polyacryl amide chains covalently, while \nzirconium hydroxide polycations formed by the hydro lysis of zirconyl chloride octahydrate \nnoncovalently crosslink polyacrylamide chains.46  As a result, stretchable polyacrylamide 14 \n networks are obtained. To understand the impact of the crosslinking components in the \nsynthesis of the soft polyacrylamide networks of th e DNHGs, we measured the tensile strengths \nand the elongations at break of polyacrylamide hydr ogels obtained by systematically varying \nthe contents of either MBA or zirconyl chloride oct ahydrate in the reaction mixtures used for \ntheir syntheses (Supporting Text 1 and Figure S7).  The tensile strength of the polyacrylamide \nhydrogels at first increases with increasing amount s of MBA, passes a maximum and decreases \nagain for high MBA contents (Figure S8), likely bec ause of increasing degrees of \ninhomogeneity related to the hydrophobic nature of MBA. 47  The elongation at break decreases \nwith increasing amounts of MBA and, therefore, incr easing degrees of crosslinking (Figure S9). \nThe tensile strength of the polyacrylamide gels inc reases (Figure S10) and the elongation at \nbreak decreases (Figure S11) with increasing amount s of zirconyl chloride octahydrate in the \nreaction mixtures related to the increasing degree of non-covalent crosslinking of the \npolyacrylamide chains by zirconium hydroxide polyca tions. \n \nSynthetic hectorite platelets are known to interact  with the PPS/TMEDA initiator system.43  \nNamely, the N,N’-tetramethyethylenediammonium radic al formed by this initiator system \n(Figure 3c2) adsorbs to the negatively charged surf ace of the synthetic hectorite platelets \n(Figure 3c3) and generates sites for the initiation  of polyacrylamide chain growth on the \nsurfaces of synthetic hectorite platelets (Figure 3 c4). Starting from these sites, acrylamide and \nMBA (Figure 3d1) are copolymerized by FRP. As menti oned above, zirconyl chloride \noctahydrate (Figure 3d2) undergoes hydrolysis to fo rm zirconium hydroxide polycations \n(Figure 3d3), which crosslink polyacrylamide chains  (Figure 3d4).46  Crosslinking by MBA as \nwell as radical recombination of the active ends of  growing polyacrylamide chains having their \nstarting points adsorbed on synthetic hectorite pla telets are further crosslinking modes (Figure \n3d5). Preliminary experiments revealed that the add ition of synthetic hectorite increases both \nthe tensile strength (Figure S8) and the elongation  at break (Figure S9) of polyacrylamide \nhydrogels, indicating that the synthetic hectorite reduces the amount of free polymer chain \nends 43  and contributes crosslinking points only at the st arting points of the polyacrylamide \nchains. \n \nThe hard silica network and the soft polyacrylamide  network eventually form a DNHG without \napparent macroscopic phase separation (Figure 3e). Preliminary experiments revealed that \nincreasing the amount of  tetrakis-(2-hydroxyethoxy)-silane in reaction mixtu res used to \nsynthesize DNHGs results at first in an increase in  the tensile strength and the elongation at \nbreak until maximum values are reached. Further inc reases in the amount of tetrakis-(2-\nhydroxyethoxy)-silane result in decreases in the te nsile strength and the elongation at break \n(Figures S12 and S13). This outcome can be rational ized by the assumption that, as long as the \nhard and brittle network has a sufficiently lower m ass fraction then the soft and ductile network, 15 \n upon deformation the brittle network may break into  smaller clusters, which act as sliding \ncrosslinks dissipating energy. 28  The DNHG formulation used here is optimized so as to convert \nthe resulting DNHG into an aerogel with high mechan ical robustness. An important structural \nfeature of the obtained DNHG is the inter-crosslink ing between the polyacrylamide and silica \nnetworks by the zirconium-containing species and th e synthetic hectorite. Zirconium forms \nmineral zirconium(IV)silicate with silicon, while a ttractive interactions exist between \nzirconium ions and (poly)acrylamide. 46  Co-condensation of the synthetic hectorite platele ts \nwith the silica species and synthetic hectorite-zir conium ion interactions further strengthen the \ninteractions between the polyacrylamide and silica networks. The obtained colorless DNHG \nshows high mechanical strength and is and transpare nt to slightly opaque. \n \n  16 \n  \na) \n \nb) \n \nc) \nFigure 4.  SEM images of the contact surfaces of DNHG-derived  aerogel stamps ( 3) with contact elements ( 4). a) \nAs-prepared DNHG-derived aerogel stamp. b), c) DNHG -derived aerogel stamp after infiltration with prec ursor \nsolution ( 7), solvothermal capillary stamping, disassembly of stamping device ( 1) and detachment from ITO \nsubstrate ( 5). b) Top view and c) cross-section. \n \nDNHG-derived aerogel stamps \nThe DNHGs (Figure 3e) were converted to DNHG-derive d aerogels by a two-step solvent \nexchange procedure from water to methanol to n-hexane followed by subcritical drying under \nambient conditions. The first solvent exchange from  water to methanol also results in the \nremoval of residual reactants such as ethylene glyc ol and of unreacted acrylamide. The \n17 \n polyacrylamide network tends to minimize its surfac e area exposed to the non-solvent \nmethanol 48  so that the polyacrylamide precipitates onto the s ilica network. It is reasonable to \nassume that the polyacrylamide preferentially agglo merates in the joints between neighboring \nsilica particles. Hence, a tough shell of polyacryl amide encapsulates the brittle silica network. \nWhile the tough polyacrylamide network reinforces t he stiff silica network, the stiff silica \nnetwork fixates the tough polyacrylamide network. T he second solvent exchange involves the \nreplacement of methanol by n-hexane. The lower surface tension of n-hexane further reduces \nthe Laplace pressure across the menisci that form i n the mesopores during subcritical \nevaporation of the n-hexane under ambient conditions. The DNHG resists the stress occurring \nduring evaporation and undergoes only minor shrinka ge, while the structural features of the \nDNHG are conserved. The DNHG-derived aerogel obtain ed in this way is a variation of class I \nhybrid composite aerogels,49  since the reinforcing polyacrylamide network and t he silica \nnetwork are physically entangled. Even though the s ilica network and the polyacrylamide \nnetwork are not covalently connected with each othe r, they cannot be separated without \ncleavage of covalent bounds. The DNHG-derived aerog el has a mean pore diameter of 18 nm \nas well as a total pore volume of 34 cm 3/g (Figures S14 and S15) and combines a low density  \nof 0.5 g * cm −3 with an excellent compressive strength of 53.57 MP a ± 7.71 MPa (average of \nfive measurements on different specimens) (Figure S 16).  \n \nDNHG-derived aerogel stamps with topographically pa tterned contact surfaces can easily be \nobtained by carrying out the DNHG synthesis in cont act with any kind of mold. The mechanical \nrobustness of the DNHG-derived aerogels should allo w the realization of even filigree arbitrary \nsurface structures. For the stamping of ink, the co ntact surfaces of the topographic stamp \nfeatures contacting the receiving substrate should exhibit sufficient surface porosity for ink \ntransfer. Considering the spongy pore morphology of  the DNHG-derived aerogel stamps used \nhere and their mean pore diameter of 18 nm, we esti mate the minimum printable feature size to \n~100 nm. Here we used macroporous silicon 36, 37  containing macropores with a diameter of 1 \nµm and a depth of 730 nm arranged in hexagonal arra ys with a pore-center-to-pore-center \ndistance of 1.5 µm as mold. The macroporous silicon  was selected because it is commercially \navailable and because its feature sizes match those  of 2D photonic crystals with bandgaps in \nthe infrared range. 50  The DNHG-derived aerogel stamps obtained in this w ay consisted of a \nmonolithic body, which had a height of 13 mm and a topographically patterned contact surface \nextending 1 cm 2. The topographic patterns of the contact surfaces consisted of arrays of rod-\nlike contact elements with a height of ~600 nm and a diameter of 900 nm arranged in a \nhexagonal lattice with a lattice constant of 1.5 µm  (Figure 4a). The shrinkage in the course of \nthe transition from a DNHG in contact with a macrop orous silicon mold to a DNHG-derived \naerogel stamp does not affect the lattice constant of the arrays of the contact elements because \ntheir positions are fixed by the positions of the m acropores of the macroporous silicon molds.  18 \n  \nArrays of submicron nickel ferrite dots by solvothe rmal capillary stamping \nSolvothermal capillary stamping (Figures 1 and 2) w as carried out using a specifically \nconstructed stamping device that consisted of two s teel cylinders; an upper part and a lower \npart. The DNHG-derived aerogel stamps were glued on  the upper part. Indium tin oxide (ITO) \nsubstrates surface-modified with the silane perfluo rodecyltrichlorosilane (FDTS) were placed \non the lower part. The upper part and the lower par t of the stamping device were assembled in \nsuch a way that the contact elements of the DNHG-de rived aerogel stamps contacted the FDTS-\ncoated ITO substrates with a contact pressure of 3. 9 kN/m 2 (Figures 1a and 2a). The assembled \nstamping device was inserted into a cylindrical PTF E vessel (Figure 2b). An ethanolic precursor \nsolution containing nickel(II)-acetylacetonate and iron(III)-acetylacetonate was deposited \nthrough the opening of the PTFE vessel and the cent ral hole in the surface of the upper part of \nthe stamping device onto the DNHG-derived aerogel s tamp (Figures 1b and 2c). The precursor \nsolution invaded the DNHG-derived aerogel stamp and  filled its mesopore network up to the \ntips of contact elements. The filling level of the DNHG-derived aerogel stamps could be \nassessed with the naked eye owing to the brown colo r of the precursor solution. Figure S17a \nshows a photograph of a cross-section of a colorles s as-prepared DNHG-derived aerogel stamp, \nwhereas Figure S17b shows a photograph of a cross-s ection of a DNHG-derived aerogel stamp \nafter infiltration with precursor solution. It is o bvious that the precursor solution infiltrated the \nentire volume of ~1.3 cm 3 of the DNHG-derived aerogel stamp.  \n \nThe contact angle of the ethanolic precursor soluti on on the FDTS-coated rough and grainy ITO \nsubstrates under ambient conditions amounted to 52. 4° ± 1.5°. Therefore, the precursor solution \ndid not spread on the FDTS-coated ITO substrates. I nstead, liquid bridges of the precursor \nsolution connecting the tips of the contact element s of the DNHG-derived aerogel stamps and \nthe surface of the FDTS-coated ITO substrates forme d (cf. Figure 1b). The PTFE vessel \ncontaining the stamping device including the DNHG-d erived aerogel stamp, the FDTS-coated \nITO substrate and the precursor solution was insert ed into a steel autoclave (Figure 2d,e) with \na free volume of ~29.15 mL available to the fluid p hases. The solvothermal conversion yielding \nnickel ferrite was carried out at 413 K for 48 h. W e approximated the solvothermal reaction \nconditions by considering the phase behavior of pur e ethanol, which we estimated by the van \nder Waals equation of state using van der Waals par ameters a =12.18 L 2 bar/mol 2 and b = \n0.08407 L/mol.51  Assuming that 6 mL (~0.1 mol) liquid ethanol is ap plied to the stamping \ndevice with a free volume of 29.15 mL, at 293.15 K the ethanol forms coexisting liquid and \ngaseous phases at a pressure of 4.3 bar. The mole f raction of the liquid phase amounts to 98 % \nand that of the gas phase to 2 %. At the reaction t emperature of 413 K, liquid and vapor phases \ncoexist at a pressure of 24.6 bar. The mole fractio ns of the liquid and vapor phases amount to \n84 % and 16 %. Thus, under the solvothermal reactio n conditions applied here precursor 19 \n solution and an ethanol-rich vapor phase coexist. H owever, prior to the supply of precursor \nsolution, no ethanol at all is present in the volum e between upper part and lower part of the \nstamping device. Hence, the ethanol-rich vapor phas e is solely obtained by evaporation of \nethanol, which can, in principle, occur at the meso pore openings of the DNHG-derived aerogel \nstamp or at the liquid bridges between the contact elements of the DNHG-derived aerogel stamp \nand the ITO substrate. However, the concave menisci  and the negative Laplace pressure of the \nprecursor solution at the mesopore openings impedes  transfer of solvent molecules from the \nliquid phase to the vapor phase. The liquid bridges  do not only have a large exposed liquid \nsurface. Their concave curvature normal to ITO subs trate is smaller than the concave curvatures \nof the menisci at the mesopore openings and impedes  evaporation to lesser extent. On the other \nhand, the curvature of the liquid bridges parallel to the ITO substrate is convex. This convex \ncurvature component will also enhance evaporation, considering that the vapor pressure \nresulting from liquid surfaces with convex curvatur e is enhanced as compared to that resulting \nfrom plane surfaces, as quantified by the Kelvin eq uation. 52  Therefore, it is reasonable to \nassume that the ethanol preferentially evaporates f rom the liquid bridges into the volume \nbetween the upper part and the lower part of the st amping device.  \n \nThe applied volume of the precursor solution exceed s the volume of the DNHG-derived aerogel \nstamp by a factor of more than 5 so that the DNHG-d erived aerogel stamp is always in contact \nwith a bulk reservoir of the precursor solution loc ated above the upper part of the stamping \ndevice. Evaporation drags new precursor solution fr om the interior of the DNHG-derived \naerogel stamp into the liquid bridges. The interior  of the DNHG-derived aerogel stamp is in \nturn refilled from the above-mentioned bulk reservo ir of the precursor solution. The nonvolatile \nnickel ferrite precursors thus enrich in the liquid  bridges and are then converted to the \nsolvothermal reaction product nickel ferrite (Figur e 1c). We assume that this precursor \nenrichment mechanism is the main reason for the for mation of three-dimensional submicron \nnickel ferrite dots in place of the liquid bridges.  After completion of the solvothermal capillary \nstamping procedure, removal of the stamping device from the autoclave and the PTFE vessel, \ndisassembly of the stamping device and detachment f rom the ITO substrate, the DNHG-derived \naerogel stamps did not show any damage. While the D NHG-derived aerogel stamps are \napparently partially filled with the reaction produ ct nickel ferrite, the contact elements at their \ncontact surface remained intact (Figure 4b,c). The DNHG-derived aerogel stamps could be \nreused after ultrasonication in ethanol for 30 minu tes. \n 20 \n   \na)                                    b) \n   0 1 2 3 4 5020 40 60 80 100 120 140 160 Height [nm] \nDistance [ m]  \n c)                                          d)    \nFigure 5.  Arrays of submicron NiFe 2O4 dots on ITO substrates. a) Large-field SEM top-vie w image. b) SEM top \nview image at higher magnification. c) AFM topograp hy image (the image field extends 5 x 5 µm 2) and d) \ntopographic height profile along the red line in pa nel c). \n \nProperties of submicron nickel ferrite dot arrays  \nSolvothermal capillary stamping yielded ITO substra tes patterned with ordered monolayers of \nsubmicron nickel ferrite dots (cf. Figure 1d) typic ally extending 1 cm 2 – corresponding to the \narea of the contact surface of the DNHG-derived aer ogel stamps. The nearest-neighbor distance \nbetween the submicron nickel ferrite dots amounted to 1.5 µm and corresponds to the nearest-\nneighbor distance between the contact elements of t he DNHG-derived aerogel stamps. The \nsubmicron nickel ferrite dots had a diameter of ~70 0 nm (Figure 5a,b) and a height of ~150 nm \n(Figure 5c,d). X-ray photoelectron spectroscopy (XP S) was deployed to evaluate whether the \nFDTS coating on the ITO substrates was still intact  after the solvothermal synthesis (Figure \nS18). An XP spectrum of an FDTS-coated ITO substrat e shows the fluorine 1s peak at 686.43 \neV indicating the presence of FDTS. However, after the solvothermal synthesis fluorine was no \nlonger found. Moreover, after the solvothermal synt hesis the precursor solution spread on the \nITO substrates. These observations corroborate the notion that the solvothermal treatment \nresulted in the destruction of the FDTS coating. \n \nX-ray powder diffractometry confirmed that any mate rial that could be scraped off from the \n21 \n ITO substrates consisted of nickel ferrite. The dif fractogram obtained in this way (Figure 6a) \nexhibited the characteristic reflections of cubic N iFe 2O4 showing inverse spinel structure (space \ngroup Fd-3m), such as the (220) reflection at 2θ = 30.295°, the (311) reflection at 2θ = 35.686°, \nthe (511) reflection at 2θ = 57.377° and the (440) reflection at 2θ = 63.015°. We measured the \nmagnetic moment of an array of submicron nickel fer rite dots on an ITO substrate as function \nof the external magnetic field by vibrating sample magnetometry (VSM) at 300 K. While bulk \nnickel ferrite shows ferrimagnetic behavior, the su bmicron nickel ferrite dots are \nsuperparamagnetic with vanishing magnetization hyst eresis and vanishing remnant \nmagnetization. The magnetic moment per sample area approached its saturation value of \n1.1•10 −3 emu/cm 2 at an external magnetic field of ± 10000 G (Figure  6b). Rescaling the \nmagnetic moment per sample area to the nickel ferri te volume yielded a saturation \nmagnetization of 290 emu/cm 3, which is somewhat lower than the saturation magne tization of \nbulk nickel ferrite amounting to 330 emu/cm 3.53  To approximate the total nickel ferrite volume, \nwe assumed that the submicron nickel ferrite dots w ere cuboids having bottom square faces \nwith edge lengths of 700 nm and heights of 150 nm, which are arranged in a hexagonal lattice \nwith a lattice constant of 1.5 µm. In this way, we estimated the effective nickel ferrite layer \nthickness to 38 nm.  \n \n 20 30 40 50 60 70 \n(622) (533) (620) (440) (511) (422) (400) (222) (311) (220) (111) \n2 Intensity  \n-10000 -5000 0 5000 10000 -1.5 -1.0 -0.5 0.0 0.5 1.0 x10 -3 Magnetic moment [emu/cm 2]\nMagnetic field [G]  \na)                                       b) \nFigure 6.  Characterization of submicron nickel ferrite dots obtained by solvothermal capillary stamping. a) XRD  \npattern of a powder of submicron nickel ferrite dot s scrapped off from ITO substrates. The red lines i ndicate \ncharacteristic reflections of cubic NiFe 2O454  according to PDF cart 01-074-2081 (Inorganic Cryst al Structure \nDatabase). b) Magnetic moment per sample area of su bmicron nickel ferrite dots on an ITO substrate ext ending \n1 cm 2 as function of an external magnetic field measured  by VSM at 300 K. \n \nWe used ordered monolayers of submicron nickel ferr ite dots on ITO substrates to demonstrate \nthe preparation of thin NiFe 2O3-Ni hybrid films by orthogonal substrate functional ization. Thus, \nwe additionally electrodeposited ~100 nm thick nick el layers on ITO substrates modified with \nsubmicron nickel ferrite dots. The nickel was depos ited onto the exposed ITO areas surrounding 22 \n the submicron nickel ferrite dots (Figure 7a,b). In  this way, NiFe 2O3-Ni hybrid films consisting \nof an ordered monolayer of submicron nickel ferrite  dots surrounded by a continuous nickel \nfilm with a thickness of ~100 nm were obtained (Fig ure 7c). We further probed the elemental \ndistribution in NiFe 2O3-Ni hybrid films by energy-dispersive X-ray (EDX) s pectroscopy. It is \nchallenging to map peaks representing the elements exclusively present in the nickel ferrite dots; \noxygen is also contained in the ITO substrates, and  the iron peaks were overlapped by much \nstronger nickel peaks. However, the number of nicke l atoms per volume in the nickel ferrite \ndots is lower than in the surrounding pure nickel f ilms. Therefore, in maps of the intensity of \nthe Ni Lα 1,2  peak the positions of the nickel ferrite dots are apparent as areas in which nickel is \ndepleted (Figure 7d). The dependence of the magneti c moment per sample area of the NiFe 2O3-\nNi hybrid film and the pure nickel film on an exter nal magnetic field measured by VSM is \ndisplayed in Figure 7e. The saturation values of th e magnetic moment per sample area lying in \nthe range from 3.3 x10 −3 emu/cm 2 to 3.4x10 −3 emu/cm 2 were similar for the NiFe 2O3-Ni hybrid \nfilm and the pure nickel film. Rescaling the magnet ic moment per sample area to the \napproximated sample volumes yielded saturation magn etizations of 350 emu/cm 3 for the pure \nnickel film and of 290 emu/cm 3 for the NiFe 2O3-Ni hybrid film. The volume of the latter was \nestimated by adding the effective nickel ferrite la yer thickness of 38 nm obtained as described \nabove to the effective thickness of the nickel laye r amounting to 75 nm. The effective thickness \nof the nickel layer was approximated by assuming th at a 100 nm thick nickel layer was \nelectrodeposited onto the exposed areas of the ITO substrate not covered by nickel ferrite dots. \nThe VSM curve of the NiFe 2O3-Ni hybrid film showed a more pronounced magnetizat ion \nhysteresis than the VSM curve of the pure nickel fi lm. While the pure nickel film reached the \nsaturation magnetization already at external magnet ic field strengths of ±200 G, the NiFe 2O3-\nNi hybrid film approached the saturation magnetizat ion only at external field strengths of ±1300 \nG. The coercive field strengths increased from ±30 G for the pure nickel film to ±90 G for the \nNiFe 2O3-Ni hybrid film. The remnant magnetic moment per sa mple area decreased from \n3.1*10 −3 emu/cm 2 for the pure nickel film to 1.5x10 −3 emu/cm 2 for the NiFe 2O3-Ni hybrid film. \nRescaling to the estimated sample volumes yielded r emnant magnetizations of 310 emu/cm 3 \nfor the pure nickel film and of 133 emu/cm 3 for the NiFe 2O3-Ni hybrid film. The squareness \nMR/MS of the magnetization hysteresis loops (ratio of th e remnant magnetization MR and the \nsaturation magnetization MS) amounted to ~0.91 for the pure nickel film and to  ~0.45 for the \nNiFe 2O3-Ni hybrid film. Hence, the incorporation of ordere d monolayers of nickel ferrite dots \ninto a thin ferromagnetic nickel layers results in magnetic hardening of the latter.   \n \n \n 23 \n            \na)                             b) \n \nc)  d)  \n \ne) -1500 -1000 -500 0 500 1000 1500 -4 -2 024\nMagnetic field [G] Magnetic moment [emu/cm 2]x10 -3 \n                                         \nFigure 7.  Thin NiFe 2O3-Ni hybrid films. a) An ITO substrate ( 5) functionalized with an ordered monolayer of \nsubmicron nickel ferrite dots ( 10 ) is b) subjected to orthogonal functionalization b y electrodeposition of nickel. \nThus, NiFe 2O3-Ni hybrid films ( 13 ) consisting of ordered monolayers of submicron nic kel ferrite dots ( 10) \nsurrounded by ~100 nm thick electrodeposited nickel  films are obtained on ITO substrates ( 5). c) SEM image of a \nNiFe 2O3-Ni hybrid film ( 13 ). d) EDX map of the Ni Lα 1,2  peak at 0.85 eV of a NiFe 2O3-Ni hybrid film ( 13 ). Nickel \nferrite dots ( 10 ) are located in areas where the nickel is depleted . e) Magnetic moments per sample area of a \nNiFe 2O3-Ni hybrid film ( 13 ) (red) on an ITO substrate ( 5) and a ~100 nm thick continuous nickel film \nelectrodeposited on an FDTS-coated ITO substrate ( 5) (blue) as function of an external magnetic field measured \nby VSM. The samples extended 1 cm 2. The magnetization measurements were carried out a t 300 K. \n \nConclusions \nSo far, solvothermal syntheses and state-of-the-art  lithography have by and large remained \nincompatible. Thus, the preparation of patterned th in films consisting of solvothermal synthesis \nproducts has remained challenging. We have demonstr ated capillary stamping in autoclaves \nunder solvothermal conditions enabling stamp-guided  conversion of precursors into \nsolvothermal reaction products. The aerogel stamps used for this purpose were derived from a \n24 \n double-network hydrogel by solvent exchange and dry ing under subcritical ambient conditions. \nPrecursor solutions imbibe the DNHG-derived aerogel  stamps. Thus, liquid bridges form \nbetween the stamps’ contact elements and the substr ates to be patterned. Preferential \nevaporation of the solvent from the liquid bridges drags more precursor solution into the liquid \nbridges, where the precursors are enriched. Liquid- bridge guided solvothermal syntheses \neventually yield submicron dots of the solvothermal  reaction products in place of the liquid \nbridges. Therefore, solvothermal capillary stamping  may yield device components comprising \ncomplex thin-layer architectures of solvothermal re action products formed on functional \nsubstrates. Problems related to alternative sol-gel  routes (high-temperature calcination steps) \nand direct serial ballistic deposition of the targe t materials (insufficient adhesion) are overcome. \nAs example, we generated arrays of submicron nickel  ferrite dots having heights of ~150 nm \non ITO substrates. Subsequent orthogonal substrate functionalization by electrodeposition of \nnickel onto the exposed substrate areas surrounding  the submicron nickel ferrite dots yielded \nthin nickel ferrite-nickel hybrid films consisting of a monolayer of submicron nickel ferrite dots \nsurrounded by a continuous nickel layer. The submic ron nickel ferrite dots halved the \nremanence of the ferromagnetic nickel film, while t he saturation value of the magnetic moment \nper area remained by and large constant. Remanence engineering of thin ferromagnetic layers \nmay help customize miniaturized transformers, posit ioning systems and electromechanical \nsystems such as nanorelays. Solvothermal capillary stamping may pave the way for complex \nfunctional thin-film configurations so far predomin antly accessible by combinations of layer \ntransfer techniques, such as wafer bonding or ion s licing, and subtractive lithography. \nOrthogonal functionalization of substrates patterne d by solvothermal capillary stamping may \nyield functional hybrid layers, in which the proper ties of the solvothermal reaction product and \nthe second component are either synergistic or comp lementary.  \n \nASSOCIATED CONTENT  \nSupporting Information . NMR characterization of Si(OC 2H4OH) 4; cross-sectional SEM \nimage of an electrodeposited Ni layer; mechanical c haracterization of polyacrylamide \nhydrogels and DNHGs; characterization of DNHG-deriv ed aerogels by nitrogen sorption \nmeasurements, SEM and stress-strain measurements; p hotographs of non-infiltrated and \ninfiltrated DNHG-derived stamps; XPS characterizati on of substrate surfaces. This material is \navailable free of charge via the Internet at http:/ /pubs.acs.org.”  \n \nAUTHOR INFORMATION \nCorresponding Author \n* Martin Steinhart, Institut für Chemie neuer Mater ialien and CellNanOs, Universität \nOsnabrück, Barbarastr. 7, 49076 Osnabrück, Germany;  https://orcid.org/0000-0002-5241-\n8498; Email: martin.steinhart@uos.de 25 \n  \nAuthor Contributions \nThe manuscript was written through contributions of  all authors. / All authors have given \napproval to the final version of the manuscript. \n‡ These authors contributed equally. \n \nFunding Sources \nThe authors thank the European Research Council (ER C-CoG-2014, Project 646742 INCANA) \nfor funding.  \n \nNotes \nThe authors declare no competing financial interest . \n \nREFERENCES \n(1) Rabenau, A. The Role of Hydrothermal Synthesis in Preparative Chemistry. Angew. Chem. \nInt. Ed. 1985 , 24 , 1026-1040. \n(2) Demazeau, G. Solvothermal Reactions: An Origina l Route for the Synthesis of Novel \nMaterials. J. Mater. Sci. 2008 , 43 , 2104-2114. \n(3) Al Amery, N.; Abid, H. R.; Al-Saadi, S.; Wang, S.; Liu, S. Facile Directions for Synthesis, \nModification and Activation of Mofs. Mater. Today Chem. 2020 , 17 , 100343. \n(4) Fang, M.; Dong, G. F.; Wei, R. J.; Ho, J. C. Hi erarchical Nanostructures: Design for Sustainable \nWater Splitting. Adv. Energy Mater. 2017 , 7, 1700559. \n(5) Gao, F.; Zhang, Y . P .; Wu, Z. Y .; You, H. M.; D u, Y . K. Universal Strategies to Multi-Dimensional \nNoble-Metal-Based Catalysts for Electrocatalysis. Coord. Chem. Rev. 2021 , 436 , 213825. \n(6) Ehrentraut, D.; Fujii, K.; Riegler, J.; Byrappa , K.; Nikl, M.; Fukuda, T. Functional One, Two, \nand Three-Dimensional Zno Structures by Solvotherma l Processing. Prog. Cryst. Growth \nCharact. Mater. 2012 , 58 , 51-59. \n(7) Diodati, S.; Walton, R. I.; Mascotto, S.; Gross , S. Low-Temperature Wet Chemistry Synthetic \nApproaches Towards Ferrites. Inorg. Chem. Front. 2020 , 7, 3282-3314. \n(8) Walton, R. I. Perovskite Oxides Prepared by Hyd rothermal and Solvothermal Synthesis: A \nReview of Crystallisation, Chemistry, and Compositi ons. Chem. Eur. J. 2020 , 26 , 9041-9069. \n(9) Li, Z. J.; Yang, J. X.; Guang, T. J.; Fan, B. B .; Zhu, K. J.; Wang, X. H. Controlled \nHydrothermal/Solvothermal Synthesis of High-Perform ance Lifepo4 for Li-Ion Batteries. Small \nMethods 2021 , 5,  \n(10) Lim, K. R. G.; Handoko, A. D.; Nemani, S. K.; Wyatt, B.; Jiang, H. Y .; Tang, J. W.; Anasori, B.; \nSeh, Z. W. Rational Design of Two-Dimensional Trans ition Metal Carbide/Nitride (Mxene) \nHybrids and Nanocomposites for Catalytic Energy Sto rage and Conversion. ACS Nano 2020 , 14 , \n10834-10864. \n(11) Lange, F. F. Chemical Solution Routes to Singl e-Crystal Thin Films. Science 1996 , 273 , 903-\n909. \n(12) Andeen, D.; Kim, J. H.; Lange, F. F.; Goh, G. K. L.; Tripathy, S. Lateral Epitaxial Overgrowth \nof Zno in Water at 90 Degrees C. Adv. Funct. Mater. 2006 , 16 , 799-804. 26 \n (13) Serra, P .; Pique, A. Laser-Induced Forward Tra nsfer: Fundamentals and Applications. Adv. \nMater. Technol. 2019 , 4, 1800099. \n(14) Mondal, K.; McMurtrey, M. D. Present Status of  the Functional Advanced Micro-, Nano-\nPrintings - a Mini Review. Mater. Today Chem. 2020 , 17 , 100328. \n(15) Xia, Y .; Whitesides, G. M. Soft Lithography. Annu. Rev. Mater. Sci. 1998 , 28 , 153-184. \n(16) Qin, D.; Xia, Y .; Whitesides, G. M. Soft Litho graphy for Micro- and Nanoscale Patterning. \nNat. Protoc. 2010 , 5, 491-502. \n(17) Huo, F.; Zheng, Z.; Zheng, G.; Giam, L. R.; Zh ang, H.; Mirkin, C. A. Polymer Pen Lithography. \nScience 2008 , 321 , 1658-1660. \n(18) Carbonell, C.; Valles, D. J.; Wong, A. M.; Tsu i, M. W.; Niang, M.; Braunschweig, A. B. \nMassively Multiplexed Tip-Based Photochemical Litho graphy under Continuous Capillary Flow. \nChem 2018 , 4, 857-867. \n(19) Liu, G. Q.; Petrosko, S. H.; Zheng, Z. J.; Mir kin, C. A. Evolution of Dip-Pen Nanolithography \n(Dpn): From Molecular Patterning to Materials Disco very. Chem. Rev. 2020 , 120 , 6009-6047. \n(20) Xu, H.; Ling, X. Y .; van Bennekom, J.; Duan, X .; Ludden, M. J. W.; Reinhoudt, D. N.; Wessling, \nM.; Lammertink, R. G. H.; Huskens, J. Microcontact Printing of Dendrimers, Proteins, and \nNanoparticles by Porous Stamps. J. Am. Chem. Soc. 2009 , 131 , 797-803. \n(21) Han, W.; Hou, P .; Sadaf, S.; Schäfer, H.; Wald er, L.; Steinhart, M. Ordered Topographically \nPatterned Silicon by Insect-Inspired Capillary Subm icron Stamping. ACS Appl. Mater. Interfaces \n2018 , 10 , 7451-7458. \n(22) Schmidt, M.; Philippi, M.; Münzner, M.; Stangl , J. M.; Wieczorek, R.; Harneit, W.; Müller-\nBuschbaum, K.; Enke, D.; Steinhart, M. Capillary Na nostamping with Spongy Mesoporous Silica \nStamps. Adv. Funct. Mater. 2018 , 28 , 1800700. \n(23) Hou, P .; Kumar, R.; Oberleiter, B.; Kohns, R.;  Enke, D.; Beginn, U.; Fuchs, H.; Hirtz, M.; \nSteinhart, M. Scanner-Based Capillary Stamping. Adv. Funct. Mater. 2020 , 30 , 2001531. \n(24) Runge, M.; Hübner, H.; Grimm, A.; Manoharan, G .; Wieczorek, R.; Philippi, M.; Harneit, W.; \nMeyer, C.; Enke, D.; Gallei, M.; Steinhart, M. Capi llary Stamping of Functional Materials: \nParallel Additive Substrate Patterning without Ink Depletion. Adv. Mater. Interfaces 2021 , 8, \n2001911. \n(25) Guo, L. M.; Klein, J.; Thien, J.; Philippi, M. ; Haase, M.; Wollschläger, J.; Steinhart, M. \nPhenolic Resin Dual-Use Stamps for Capillary Stampi ng and Decal Transfer Printing. ACS Appl. \nMater. Interfaces 2021 , 13 , 49567-49579. \n(26) Carbonell, C.; Braunschweig, A. B. Toward 4d N anoprinting with Tip-Induced Organic \nSurface Reactions. Acc. Chem. Res. 2017 , 50 , 190-198. \n(27) Gong, J. P .; Katsuyama, Y .; Kurokawa, T.; Osad a, Y . Double-Network Hydrogels with \nExtremely High Mechanical Strength. Adv. Mater. 2003 , 15 , 1155-1158. \n(28) Gong, J. P . Why Are Double Network Hydrogels S o Tough? Soft Matter 2010 , 6, 2583-2590. \n(29) Etemadi, H.; Plieger, P . G. Synthesis and Char acterisation of Mxfe 3-Xo 4 (M = Fe, Mn, Zn) \nSpinel Nanoferrites through a Solvothermal Route. J. Mater. Sci. 2021 , 56 , 17568-17583. \n(30) Koli, R. R.; Deshpande, N. G.; Kim, D. S.; She lke, A. R.; Fulari, A. V.; Fulari, V. J.; Cho, H. K . \nTailoring the Magnetic Hyperthermia Performances of  Gram-Bean-Extract-Mediated Highly \nDisperse Mfe2o4 (M = Fe, Ni, Mn) Nanoferrites. Ceram. Int. 2020 , 46 , 24290-24301. \n(31) Etemadi, H.; Plieger, P . G. Magnetic Fluid Hyp erthermia Based on Magnetic Nanoparticles: 27 \n Physical Characteristics, Historical Perspective, C linical Trials, Technological Challenges, and \nRecent Advances. Adv. Ther. 2020 , 3,  \n(32) Ortiz-Quinonez, J. L.; Das, S.; Pal, U. Cataly tic and Pseudocapacitive Energy Storage \nPerformance of Metal (Co, Ni, Cu and Mn) Ferrite Na nostructures and Nanocomposites. Prog. \nMater. Sci. 2022 , 130 ,  \n(33) Yanez-Vilar, S.; Sanchez-Andujar, M.; Gomez-Ag uirre, C.; Mira, J.; Senaris-Rodriguez, M. A.; \nCastro-Garcia, S. A Simple Solvothermal Synthesis o f Mfe 2o4 (M = Mn, Co and Ni) Nanoparticles. \nJ. Solid State Chem. 2009 , 182 , 2685-2690. \n(34) Huo, J. Z.; Wei, M. Z. Characterization and Ma gnetic Properties of Nanocrystalline Nickel \nFerrite Synthesized by Hydrothermal Method. Mater. Lett. 2009 , 63 , 1183-1184. \n(35) Alarslan, F.; Vittadello, L.; Klein, J.; Khan,  Q. A.; Kijatkin, C.; Haase, M.; Schäfer, H.; Imlau , \nM.; Steinhart, M. Thin Patterned Lithium Niobate Fi lms by Parallel Additive Capillary Stamping \nof Aqueous Precursor Solutions. Adv. Eng. Mater. 2022 , 24 , 2101159. \n(36) Lehmann, V.; Föll, H. Formation Mechanism and Properties of Electrochemically Etched \nTrenches in N-Type Silicon. J. Electrochem. Soc. 1990 , 137 , 653-659. \n(37) Birner, A.; Grüning, U.; Ottow, S.; Schneider,  A.; Müller, F.; Lehmann, V.; Föll, H.; Gösele, U. \nMacroporous Silicon: A Two-Dimensional Photonic Ban dgap Material Suitable for the near-\nInfrared Spectral Range. Phys. Status Solidi A 1998 , 165 , 111-117. \n(38) Ruzicka, B.; Zaccarelli, E. A Fresh Look at th e Laponite Phase Diagram. Soft Matter 2011 , \n7, 1268–1286. \n(39) Fadeev, A. Y .; McCarthy, T. J. Self-Assembly I s Not the Only Reaction Possible between \nAlkyltrichlorosilanes and Surfaces: Monomolecular and Oligomeric Covalently Attached Layers \nof Dichloro- and Trichloroalkylsilanes on Silicon. Langmuir 2000 , 16 , 7268-7274. \n(40) Ren, Z.; Li, Y .; Yu, J. A Flexible Supercapaci tor with High True Performance. iScience 2018 , \n9, 138-148. \n(41) Kundu, S.; Wang, Y .; Xia, W.; Muhler, M. Therm al Stability and Reducibility of Oxygen-\nContaining Functional Groups on Multiwalled Carbon Nanotube Surfaces: A Quantitative High-\nResolution Xps and Tpd/Tpr Study. J. Phys. Chem. C 2008 , 112 , 16869-16878. \n(42) Yang, C. H.; Wang, M. X.; Haider, H.; Yang, J.  H.; Sun, J.-Y .; Chen, Y . M.; Zhou, J.; Suo, Z. \nStrengthening Alginate/Polyacrylamide Hydrogels Usi ng Various Multivalent Cations. ACS Appl. \nMater. Interfaces 2013 , 5, 10418–10422. \n(43) Strachota, B.; Matějka, L.; Zhigunov, A.; Kone fał, R.; Spěváček, J.; Dybal, J.; Puffr, R. Poly(N-\nIsopropylacrylamide)-Clay Based Hydrogels Controlle d by the Initiating Conditions: Evolution \nof Structure and Gel Formation. Soft Matter 2015 , 11 , 9291–9306. \n(44) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-G el \nProcessing ; Acad. Press, Boston, 2010. \n(45) Feng, X. d.; Guo, X. Q.; Qiu, K. Y . Study of t he Initiation Mechanism of the Vinyl \nPolymerization with the System Persulfate/ N,N,Nʹ, Nʹ-Tetramethylethylenediamine. Makromol. \nChem. 1988 , 189 , 77–83. \n(46) Michael, F. M.; Fathima, A.; AlYemni, E.; Jin,  H.; Almohsin, A.; Alsharaeh, E. H. Enhanced \nPolyacrylamide Polymer Gels Using Zirconium Hydroxi de Nanoparticles for Water Shutoff at \nHigh Temperatures: Thermal and Rheological Investig ations. Ind. Eng. Chem. Res. 2018 , 57 , \n16347–16357. 28 \n (47) Orakdogen, N.; Okay, O. Influence of the Initi ator System on the Spatial Inhomogeneity in \nAcrylamide-Based Hydrogels. J. Appl. Polym. Sci. 2007 , 103 , 3228-3237. \n(48) Seidel, A.; Peterca, M.; Mark, H. F. Encyclopedia of Polymer Science and Technology ; Wiley, \nHoboken, NJ, 2014. \n(49) Maleki, H.; Durães, L.; Portugal, A. An Overvi ew on Silica Aerogels Synthesis and Different \nMechanical Reinforcing Strategies. J. Non-Cryst. Solids 2014 , 385 , 55–74. \n(50) Birner, A.; Wehrspohn, R. B.; Gösele, U. M.; B usch, K. Silicon-Based Photonic Crystals. Adv. \nMater. 2001 , 13 , 377-388. \n(51) Weast, R. C. Handbook of Chemistry and Physics ; Chemical Rubber Company, Cleveland, \n1972. \n(52) Butt, H. J.; Golovko, D. S.; Bonaccurso, E. On  the Derivation of Young's Equation for Sessile \nDrops: Nonequilibrium Effects Due to Evaporation. J. Phys. Chem. B 2007 , 111 , 5277-5283. \n(53) Coey, J. M. D. Magnetism and Magnetic Materials ; Cambridge University Press, Cambridge, \n2010. \n(54) Subramanyam, K. N. Neutron and X-Ray Diffracti on Studies of Certain Doped Nickel \nFerrites. J. Phys. C Solid State Phys. 1971 , 4, 2266–2268. \n \n "    },    {        "title": "1506.00659v1.Calculating_the_3D_magnetic_field_of_ITER_for_European_TBM_studies.pdf",        "content": "Calculating the 3D magnetic field of ITER for European TBM studies\nSimppa ¨Ak¨aslompoloa,\u0003, Otto Asuntaa, Thijs Bergmansa, Mario Gagliardib, Jose Galabertb, Eero Hirvijokia, Taina Kurki-Suonioa,\nSeppo Sipil ¨aa, Antti Snickera, Konsta S ¨arkim ¨akia\naDepartment of Applied Physics, Aalto University, FI-00076 AALTO, FINLAND\nbFusion for Energy, Barcelona, Spain\nAbstract\nThe magnetic perturbation due to the ferromagnetic test blanket modules (TBMs) may deteriorate fast ion confinement in ITER.\nThis e \u000bect must be quantified by numerical studies in 3D. We have implemented a combined finite element method (FEM) –\nBiot-Savart law integrator method (BSLIM) to calculate the ITER 3D magnetic field and vector potential in detail. Unavoidable\ngeometry simplifications changed the mass of the TBMs and ferritic inserts (FIs) up to 26%. This has been compensated for by\nmodifying the nonlinear ferromagnetic material properties accordingly. Despite the simplifications, the computation geometry and\nthe calculated fields are highly detailed. The combination of careful FEM mesh design and using BSLIM enables the use of the\nfields unsmoothed for particle orbit-following simulations. The magnetic field was found to agree with earlier calculations and\nrevealed finer details. The vector potential is intended to serve as input for plasma shielding calculations.\nKeywords: ITER, Test Blanket Module, Magnetization, Ferritic Insert\n1. Introduction\nThe goal of the fusion reactor ITER is to demonstrate the tech-\nnological and scientific feasibility of fusion energy. The fol-\nlowing reactor, DEMO, has a mission to demonstrate the large-\nscale production of electrical power and tritium fuel self-suf-\nficiency. One of the tasks of ITER is to be a testbed for DEMO\ncomponents. ITER Test Blanket Modules (TBMs) will test the\ntechnology of tritium breeding modules for DEMO. Three of\nthe eighteen ITER equatorial ports are reserved for these mod-\nules. The material chosen for DEMO is ferritic steel [1]. There-\nfore, the ITER TBMs will be made of ferromagnetic material\nthat will get magnetized by the tokamak magnetic fields. The\nresulting local perturbation in the magnetic fields can deterio-\nrate the confinement of the plasma. Especially, the weakly col-\nlisional fast ions may find a local “hole” in the magnetic bottle\nand thus cause a hot spot on the first wall [2].\nThe TBM designs are checked for such threats by perform-\ning simulations of fast ions [3, 4]. The key ingredient for the\nsimulations is a 3D magnetic field that includes the fields due\nto the magnetized components. This paper describes a method\nfor calculating the field due to ferromagnetic ITER components.\nThe used geometry describes the ferritic inserts and test blanket\nmodules in detail. We also calculate another useful quantity:\nthe magnetic vector potential – an important input for related\nplasma response calculations.\nInput data. The key “raw” data we use to calculate the 3D\nfield consists of the geometry and electric current in toroidal\n\u0003Corresponding author\nEmail address: simppa.akaslompolo@alumni.aalto.fi (Simppa\n¨Ak¨aslompolo)field (TF) and poloidal field (PF) coils (including the central\nsolenoid), the plasma equilibrium, and the geometry and mate-\nrial parameters of the ferromagnetic components. Two sets of\ncomponents are considered: the TBMs and the ferritic inserts\n(FI) that are in place to reduce the variation of the toroidal field\ncaused by having only 18 discrete TF coils.\nMethods. Our main tool is the commercial COMSOL Multi-\nphysics finite element method (FEM) platform (ver. 4.4.0.195)\nand its AC /DC Module. For geometry simplifications we also\nused the SpaceClaim Engineer 3D direct modeler. In addition,\nMATLAB routines were used to prepare and deliver informa-\ntion to COMSOL as well as to build the COMSOL model.\nNo FEM calculation can match the precision of a direct\nBiot-Savart law integration for magnetic fields from known coil\ngeometry. To capitalise on this, we utilise a two-step COM-\nSOL calculation: First we perform a magnetization calculation .\nThen a follow-up permanent magnet COMSOL calculation ex-\ntracts the field due to the magnetization from the results of the\nmagnetization calculation. The permanent magnet results from\nCOMSOL are finally superimposed on the Biot-Savart law in-\ntegrated fields. These fields are produced with the recently ex-\ntended BioSaw code [5].\nIn the magnetization calculation, the magnetic fields (mf)\ninterface of the AC /DC module in COMSOL solves the vector\npotential Aand the divergence control variable  from\n8>>><>>>:r\u0002H(jBj)=Je+r \nr\u0002A=B\nr\u0001(A+r )=0: (1)\nSymbol Bdenotes magnetic flux density and Jeis the current\ndensity in coils or plasma. The nonlinear magnetic proper-\nties are described by the function H(jBj). At the boundaries\nPreprint submitted to Fusion Engineering and Design, http: // dx. doi. org/ 10. 1016/ j. fusengdes. 2015. 05. 038 June 3, 2015arXiv:1506.00659v1  [physics.plasm-ph]  1 Jun 2015of the computational domain, the boundary condition is set to\nn\u0002A=0;where nis the boundary’s normal vector. How-\never, the boundaries are e \u000bectively several kilometres from the\ntokamak, as will be explained in the context of equation 2.\nThe permanent magnet model can be considered a reduced\nversion of the above problem. We removed all coil and plasma\ncurrents and changed the constitutive relation inside the ferro-\nmagnetic components to B=\u00160(H+M), where Mis the mag-\nnetization vector. COMSOL extracts the magnetization from\nthe solution of the first step and e \u000bectively turns the ferromag-\nnetic components into permanent magnets. The divergence con-\ndition variable is used for the permanent magnet model only\nwhen the vector potential needs to be evaluated.\n2. Geometry\nIn this section we describe each major component present in the\nFEM model. The description justifies and explains all simplifi-\ncations made to the geometry before importing it to COMSOL.\nThe 18 ITER toroidal field coils are D-shaped supercon-\nducting coils enclosing the plasma. We reconstructed the 3D\ngeometry by sweeping the coil cross section [6] over the oper-\nating temperature spine curve [7]. However, the curve was not\nperfectly smooth and continuous after it was drawn according\nto the specifications. Therefore a 2nddegree B ´ezier curve [8]\nwas fitted to a dense sampling of the CAD curve. The numer-\nically smooth final curve is in a format natively supported by\nCOMSOL.\nThe poloidal field (PF) coils, the central solenoid (CS) and\nthe plasma are assumed to be toroidally symmetric. We re-\nceived the geometry information in EQDISK format, a quasi-\nstandard in fusion community. ITER has 6 CS coils and 6 PF\ncoils. The only change to this input was the elimination of a 5\ncm wide gap between the stacked CS coils by symmetrically\nstretching each coil vertically until they touched each other.\nIncluding this gap would have required small elements in the\nspace between the coils without contributing significantly to the\ncalculation. The current density was reduced to compensate for\nthe increased cross-sectional area of the CS coils. The geome-\ntry is shown in Fig. 1.\nThe plasma cross-section was covered with a rectangular\nmesh (which was later swept toroidally) with the goal of ex-\ntending the mesh up to the plasma-facing components (Fig.\n1(b)). The mesh nodes were carefully fitted to coincide with\nthe grid used in the EQDISK calculation, though the pitch was\na multiple of the EQDISK grid pitch. This grid setting aligned\nthe element edges to cylindrical coordinates. This was useful,\nas the current densities were now always parallel to an element.\nFurthermore, the calculated fields would later be exported in the\nsame coordinate system.\nThe FI geometry we received represented the “configuration\nmodel” of the components, including the special elements at the\nNBI ports. This is a simplified description primarily intended\nfor checking that no two components in the vast ITER CAD\nmodel collide. Therefore small details such as bolt holes had\nalready been removed. Nevertheless, the CAD data was still(a)\n (b)\nFigure 1: (a) A single 20 degree sector including all the current-carrying do-\nmains. The calculation was performed in the complete 360 degree geometry.\n(b) The cross-sectional mesh of the toroidal current-carrying domains. The\nthick round curve is the plasma separatrix.\n(a) (b) (c) (d) (e) (f)\nFigure 2: Various 3D models for the ferromagnetic components. (a) a simple\nFI geometry for fast testing. (b) and (c) are the FI models used for calculations\n(no di \u000berence in results). (d) the original FI configuration model consisting of\nstacks of 40mm thick plates, which were merged in (c). The TBM geometry\nbefore (e) and after (f) simplification.\nfar too detailed for finite element analysis (FEA) as a part of a\nmodel encompassing the whole ITER torus.\nWe made several simplified FI models starting from the\nconfiguration model, that are shown in Fig. 2(a-d). The first\nsimplification was to remove radial gaps. The FIs are made of\nstacks of 40 mm thick steel plates with 4 mm gaps between the\nplates. To expedite the calculations, several toroidal gaps less\nthan 10 mm wide were removed and a few somewhat wider gaps\nwere extended by 10 mm. Modifying the gaps did not change\nthe final results. Many small surface details, such as bevels,\nwere also removed to simplify the final model.\nThree equatorial ports of ITER are dedicated to TBMs, with\nroom for two TBMs in each port. In our study, we placed\na model of the European helium-cooled pebble bed (HCPB)\nTBM into all six TBM slots. In reality the di \u000berent ITER part-\nners will have their own test blanket module implementations\nin their slots.\nThe CAD model for the HCPB is very complex, but we re-\nceived a model which had cooling ducts and many other smaller\nfeatures already removed. We further simplified the model by,\ne.g., removing piping, merging thin plates together and remov-\ning air gaps. Figures 2(e-f) show the geometry before and after\nsimplification.\nThe whole torus, including the coils, was enclosed inside a\n2so called “finite sphere” with a radius of 14 meters. This radius\nallowed us to fit the components inside the sphere with a mar-\ngin of several meters in most cases, but only about one meter\nnear a PF coil. The same structure was also implemented in the\npermanent magnet model albeit with all the coils absent. The\nfinite sphere was enclosed inside a spherical shell, dubbed the\n“infinite shell”. The name comes from the COMSOL feature\nwe used to remap the radial coordinate %2=R2+z2inside the\ninfinite shell in order to use boundary conditions at infinity:\n%0=%0\u0001%\n%0+ \u0001%\u0000%; (2)\nwhere%0is the inner radius of the infinite shell and \u0001%is the\nthickness of the shell. In our model the outer surface of the shell\nwas mapped to a distance of several kilometers.\n3. Current densities and material properties for the Finite\nElement Analysis\nWe included the following free currents in our model: the toroidal\nand poloidal field coils (including the central solenoid) and the\ntoroidal plasma current. The magnitude of the current density\nwas assumed to be uniform in each coil. For the circular PF\nand CS coils, the current direction is trivial to calculate, but for\nthe D-shaped TF coil we assumed the direction to be parallel to\nthe spine curve described in section 2. COMSOL has the func-\ntionality to create a curvilinear coordinate system within the TF\ncoil, but as this seemed to cause numerical problems in our ge-\nometry, we chose another route: a MATLAB routine returning\na unit vector parallel to the spine curve of the TF coil was cre-\nated. The magnitude of the toroidal plasma current density was\ncalculated with a MATLAB routine from the current flux func-\ntion fand the pressure flux function pread from the EQDISK\nfile using equation 3.3.6 in [9]. (Note: there is a typo in that\nequation;\u00160should be in the denominator.)\nAll domains were assumed to have the same electrical prop-\nerties: relative permittivity \"r=1 and conductivity \u001b=1 S/m.\nThe current density was fixed in A /m2. Most domains had linear\nmagnetic response with relative magnetic permeability \u0016r=1,\nwhile for the ferromagnetic components we set the magnetiza-\ntionMas a function of magnetizing field Hby defining the H-B\ncurve, or H(B).\nThe FIs will be made of SS430 stainless steel, for which\ntheB-Hcurve was the mean curve of the B-Hcurves in the ta-\nble 4-1 of [10]. The magnetic properties data for the EUROFER\nsteel [11] of the TBMs is temperature dependent, but we made a\nconservative assumption of uniform 350\u000eC. A two-piece linear\nmodel for the H-Bcurve was constructed from the three avail-\nable parameters. The first linear segment was assumed to pass\nthrough the origin, and the slope was calculated from the ra-\ntio of the coercive field Hcand the remanent magnetization Mr.\nThe slope of the high field segment was vacuum permeability\n\u00160, and the knee point was calculated by solving the location\nwhere the first segment passes through saturation magnetiza-\ntionMs.Removing small details changed the metal volumes of the\nTBMs and FIs. To compensate for this, we modified the mag-\nnetic response of the materials, i.e., the H(jBj) function. We\nrequired that the simplifications would not change the magnetic\nmomentM=R\nMdVof the objects at the uniform magnetic\nfield limit. This resulted in the formula for a new H-Bcurve\nH\u0003(B), where the di \u000berence in metal volume is accounted for:\nH\u0003(B)=H(B+f1\u0000cgfB\u0000\u00160H(B)g): (3)\nHere the volume ratio cis defined as c=Voriginal=Vsimplified , and\nit varies between 0 :7355 and 0:738 for the di \u000berent kinds of FI\nsectors and is 1 :001 for the TBMs.\n4. Results\nThe COMSOL calculation produced 3D magnetic flux density\nBand vector potential Afor various ITER scenarios. Figure\n3 shows these fields for the 15 MA plasma current H-mode\nscenario during flat top phase. We then combined the COM-\nSOL results with Biot-Savart law integrated background fields\nand analysed the field. Figure 4 shows a toroidal field rip-\nple map (a measure of FI performance), the homoclinic tangle\nnear the X-point, and Poincar ´e plots showing the structure in-\nside the plasma separatrix. Finally, the field was decomposed\ninto toroidal Fourier components, which are shown in Figure 5.\nThese form the input for spectral plasma response codes. The\nmagnetic fields were verified against earlier work [12] and were\nfound to agree quantitatively. Please check the supplementary\nmaterial (available electronically) for illustration.\n5. Summary and Future work\nWe have devised a method for calculating the magnetization of\nITER ferromagnetic components using the finite element method,\nand combined the resulting magnetic flux density Band mag-\nnetic vector potential Ato Biot-Savart law integrated fields. The\nformer can be used for studying, e.g., fast ion behaviour in the\nrealistic ITER 3D field, while the latter provides the input for\ncalculating the plasma response to the external perturbation.\nFuture work. We are using the calculated fields in the ASCOT [13]\nsuite of codes in order to simulate fast ion wall loads due to fu-\nsion alphas and heating neutral beams.\nThe simulations are in progress, and we already reported\nthat the detail level at which the FIs are modeled in the field cal-\nculation does not appear to play a significant role for fusion al-\npha wall loads at least in the 15 MA H-mode case [14, 15]. The\n3D fields will also be delivered to our collaborators so that the\nplasma response to the external perturbations can be included in\nfuture wall load simulations. At the time of writing this article,\nwe have not discovered strong changes in the wall loads due the\nEuropean TBMs. Only a couple of ITER scenarios have so far\nbeen addressed.\n3BΦBB\nR BzR = 14 m\nAzAA\nR AΦR = 14 m\nBΦBB\nR BzR = 14 m\nAzAA\nR AΦR = 14 mFigure 3: The magnetic flux density B(T) and the total magnetic vector poten-\ntialA(T/m) as calculated by COMSOL. The total field is shown on the top row\nand the field due to the ferromagnetic components on the lower row. All im-\nages show three orthogonal cut planes displaying three orthogonal components\nof the field, as indicated in the figure. The thin black lines indicate component\nand domain boundaries in the model. There are harmless numerical artifacts\nvisible in Ain the “infinite shell”, caused by remapping of the spatial coordi-\nnates.\n(a)\n (b)\n(c)\n0.010.010.05\n0.05 0.050.050.050.05\n0.1\n0.1\n0.10.10.10.1 0.10.5 0.5\n0.5\n0.5\n0.5\n0.50.51 1\n1\n1\n1\n1 12\n2222225\n5\n5\n55\n555\n55\nR (m)z (m)100 × [ max(Bφ) − min(Bφ) ] /\n  [ max(Bφ) + min(Bφ) ]\n4 6 8−505 (d)\nFigure 4: (a) Poloidal and (b) toroidal Poincar ´e plot showing the induced island\nstructure within the plasma, (c) toroidal field ripple map, (d) the homoclinic\ntangle near X-point.(a)\n4 6 8−505Absolute value of Bφ, k=5\nR (m)z (m)\n  \nT\n00.10.20.30.4 (b)\n4 6 8−505Complex phase of Bφ, k=5\nR (m)z (m)\n  \ndegrees\n−1000100\n09274563−1000100\nFourier mode kPoloidal angle (deg)Bφ Toroidal Fourier components\n  \nlog10( | B[T] | )\n−14−12−10−8−6−4−2 (c)\n(d)\n4 6 8−505Absolute value of Aφ, k=5\nR (m)z (m)\n  \nA/m\n00.10.20.30.4 (e)\n4 6 8−505Complex phase of Aφ, k=5\nR (m)z (m)\n  \ndegrees\n−1000100\n09274563−1000100\nFourier mode kPoloidal angle (deg)Aφ Toroidal Fourier components\n  \nlog10( | A [A/m] | )\n−12−10−8−6−4−2 (f)\nFigure 5: Toroidal Fourier decomposition of the toroidal components of Band\nAfields. A single component on a poloidal plane is shown in figures (a), (b),\n(d) and (e). Figures (c) and (f) show the amplitude of the first 65 modes along\nthe separatrix (black line).\nAcknowledgements\nThe authors would like to thank Nicol `o Marconato and Pablo\nVallejos for their help on using COMSOL.\nThis project has received funding from Fusion For Energy\n(grant F4E-GRT-379), the Academy of Finland (project No.\n259675), Tekes – Finnish Funding Agency for Technology and\nInnovation. We acknowledge the computational resources from\nAalto Science-IT project, CSC - IT center for science and the\nInternational Fusion Energy Research Centre.\nReferences\nReferences\n[1] L. Boccaccini, A. Aiello, O. Bede, F. Cismondi, L. Kosek, T. Ilkei, J.-\nF. Salavy, P. Sardain, L. Sedano, Present status of the conceptual design\nof the eu test blanket systems, Fusion Engineering and Design 86 (6-8)\n(2011) 478–483. doi:10.1016/j.fusengdes.2011.02.036 .\n[2] G. Kramer, B. Budny, R. Ellis, M. Gorelenkova, W. Heidbrink, T. Kurki-\nSuonio, R. Nazikian, A. Salmi, M. Scha \u000ber, K. Shinohara, J. Snipes,\nD. Spong, T. Koskela, M. V . Zeeland, Fast-ion e \u000bects during test blanket\nmodule simulation experiments in DIII-D, Nuclear Fusion 51 (10) (2011)\n103029. doi:10.1088/0029-5515/51/10/103029 .\nURL http://stacks.iop.org/0029-5515/51/i=10/a=103029\n[3] T. Kurki-Suonio, O. Asunta, T. Hellsten, V . Hyn ¨onen, T. Johnson,\nT. Koskela, J. L ¨onnroth, V . Parail, M. Roccella, G. Saibene, A. Salmi,\nS. Sipil ¨a, ASCOT simulations of fast ion power loads to the plasma-\nfacing components in ITER, Nuclear Fusion 49 (9) (2009) 095001. doi:\n10.1088/0029-5515/49/9/095001 .\nURL http://stacks.iop.org/0029-5515/49/i=9/a=095001\n[4] K. Shinohara, T. Kurki-Suonio, D. Spong, O. Asunta, K. Tani, E. Strum-\nberger, S. Briguglio, T. Koskela, G. Vlad, S. G ¨unter, G. Kramer, S. Putvin-\nski, K. Hamamatsu, I. T. G. on Energetic Particles, E \u000bects of complex\nsymmetry-breakings on alpha particle power loads on first wall struc-\ntures and equilibrium in ITER, Nuclear Fusion 51 (6) (2011) 063028.\ndoi:10.1088/0029-5515/51/6/063028 .\nURL http://stacks.iop.org/0029-5515/51/i=6/a=063028\n[5] T. Koskela, O. Asunta, E. Hirvijoki, T. Kurki-Suonio, S. ¨Ak¨aslompolo,\nITER edge-localized modes control coils: the e \u000bect on fast ion losses\nand edge confinement properties, Plasma Physics and Controlled Fusion\n54 (10) (2012) 105008. doi:10.1088/0741-3335/54/10/105008 .\nURL http://stacks.iop.org/0741-3335/54/i=10/a=105008\n4[6] ITER Organization, Desing Description Document 11-2: TF Coils and\nStructures, Tech. rep., ITER Organization, ITER D2MVZNX v2.2 page\n17, F4E D25QXAR v1.0.\nURL https://user.iter.org/?uid=2MVZNX\n[7] ITER Organization, TFW RADIAL PLATE, ITER D28HP9H F,\nF4E D25W2CJ v1.0 (2009).\nURL https://user.iter.org/?uid=28HP9H_F\n[8] G. E. Farin (Ed.), Curves and surfaces for computer aided geometric de-\nsign : a practical guide, 4th Edition, Academic Press Limited, 1997.\n[9] J. Wesson, Tokamaks, 2nd Edition, V ol. 48 of The Oxford Engineering\nScience Series, Clarendon Press, 1997.\n[10] C. Hamlyn-Harris, IWS Ferritic Material Magnetic Curves, Tech.\nrep., ITER Organization, F4E D25NUFN v1.0, ITER D3MBTJ7 v1.1\n(2011).\nURL https://user.iter.org/?uid=3MBTJ7\n[11] F. Tavassoli, Fusion Demo Interim Structural Design Criteria (DISDC),\nAppendix A: Material Design Limit Data: A3.S18E Eurofer Steel, Tech.\nRep. CEA /DMN /DIR/NT/2005-01, Department of Materials for Nuclear,\nF4E D22H6RK v1.0 (December 2005).\nURL https://idm.f4e.europa.eu/?uid=22H6RK\n[12] V . Amoskov, A. Belov, E. Gapionok, E. Lamzin, S. Sytchevsky, Database\nof magnetic field produced by tf coils, ferromagnetic inserts, and test\nblanket modules magnetized in toroidal and poloidal magnetic fields\n(15ma dt scenario at burn), Tech. Rep. ITER D64D8GV v. 1.2, Saint\nPetersburg Company Energopul LTD (November 2011).\nURL https://user.iter.org/?uid=64D8GV\n[13] E. Hirvijoki, O. Asunta, T. Koskela, T. Kurki-Suonio, J. Miettunen,\nS. Sipil ¨a, A. Snicker, S. ¨Ak¨aslompolo, ASCOT: Solving the kinetic equa-\ntion of minority particle species in tokamak plasmas, Computer Physics\nCommunications 185 (4) (2014) 1310–1321. arXiv:1308.1904 ,\ndoi:10.1016/j.cpc.2014.01.014 .\nURL http://www.sciencedirect.com/science/article/pii/\nS0010465514000277\n[14] T. Kurki-Suonio, S. ¨Ak¨aslompolo, K. S ¨arkim ¨aki, S. Sipil ¨a, A. Snicker,\nE. Hirvijoki, O. Asunta, T. Koskela, M. Gagliardi, Iter fusion alpha par-\nticle confinement in the presence of the european tbms and elm coils,\nin: 41st EPS Conference on Plasma Physics, Europhysics conference ab-\nstracts, European Physical Society, 2014, p. P5.017.\nURL http://ocs.ciemat.es/EPS2014PAP/pdf/P5.017.pdf\n[15] T. Kurki-Suonio, S. ¨Ak¨aslompolo, K. S ¨arkim ¨aki, S. Sipil ¨a, A. Snicker,\nE. Hirvijoki, O. Asunta, T. Koskela, M. Gagliardi, ITER energetic particle\nconfinement in the presence of ELM control coils and european tbms, in:\n25th Fusion Energy Conference (FEC 2014) Saint Petersburg, Russia 13\n-18 October 2014, IAEA, 2014, pp. TH /P3–P30.\n5"    },    {        "title": "1110.4905v1.Exchange_spring_behavior_in_bimagnetic_CoFe2O4_CoFe2_nanocomposite.pdf",        "content": "1 Exchange-spring behavior in bimagnetic \nCoFe 2O4/CoFe 2 nanocomposite \nLeite, G. C. P.1, Chagas, E. F. 1, Pereira, R. 1, Prado, R. J. 1, Terezo, A. J. 2 , \nAlzamora, M. 3, and Baggio-Saitovitch, E. 3 \n1Instituto de Física , Universidade Federal de Mato Grosso, 78060-900, Cuiabá-\nMT, Brazil 2Departamento de Química, Universidade Federal do Ma to Grosso, 78060-900, \nCuiabá-MT, Brazil \n3Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 Urca. Rio de \nJaneiro, Brazil. \nPhone number: 55 65 3615 8747 \nFax: 55 65 3615 8730 \nEmail address: efchagas@fisica.ufmt.br  \n \nAbstract \nIn this work we report a study of the magnetic beha vior of ferrimagnetic oxide CoFe 2O4 and \nferrimagnetic oxide/ferromagnetic metal CoFe 2O4/CoFe 2 nanocomposites. The latter compound is \na good system to study hard ferrimagnet/soft ferrom agnet exchange coupling. Two steps were used \nto synthesize the bimagnetic CoFe 2O4/CoFe 2 nanocomposites: (i) first preparation of CoFe 2O4 \nnanoparticles using the a simple hydrothermal metho d and (ii) second reduction reaction of cobalt \nferrite nanoparticles using activated charcoal in i nert atmosphere and high temperature. The phase \nstructures, particle sizes, morphology, and magneti c properties of CoFe 2O4 nanoparticles have \nbeen investigated by X-Ray diffraction (XRD), Mossb auer spectroscopy (MS), transmission \nelectron microscopy (TEM), and vibrating sample mag netometer (VSM) with applied field up to \n3.0 kOe at room temperature and 50K. The mean diame ter of CoFe 2O4 particles is about 16 nm. \nMossbauer spectra reveal two sites for Fe3+. One si te is related to Fe in an octahedral coordination \nand the other one to the Fe3+ in a tetrahedral coor dination, as expected for a spinel crystal \nstructure of CoFe 2O4. TEM measurements of nanocomposite show the format ion of a thin shell of \nCoFe 2 on the cobalt ferrite and indicate that the nanopa rticles increase to about 100 nm. The \nmagnetization of nanocomposite showed hysteresis lo op that is characteristic of the exchange \nspring systems. A maximum energy product (BH) max  of 1.22 MGOe was achieved at room \ntemperature for CoFe 2O4/CoFe 2 nanocomposites, which is about 115% higher than th e value \nobtained for CoFe 2O4 precursor.  The exchange-spring interaction and th e enhancement of product \n(BH) max  in nanocomposite CoFe 2O4/CoFe 2 have been discussed. \nKeywords: Exchange-Spring, Ferrite, Nanocomposite, (BH) max product, \nCoercivity 2 Introduction  \n \nThe figure of merit for a permanent magnet material , the quantity ( BH )max  to the ideal hard \nmaterial (rectangular hysteresis loop) is given by /g4666/g1828/g1834 /g4667/g3040/g3028/g3051 /g3404/g4666/uni0032/g2024/g1839/g3020/g4667/g2870. For materials with high \ncoercivity ( HC) the magnetic energy product is limited by the sat uration magnetization ( MS). \nAiming to overpass this limitation, and in order to  obtain a material with high ( BH)max  product, \nKneller and Hawig (1991) [1] proposed a nanocomposi te formed by both hard (high HC) and soft \n(high MS) magnetic materials exchange coupled. These materi als, called exchange spring or \nexchange-hardened magnets, combine the high coercit ivity of the hard material with the high \nsaturation magnetization of the soft material, maki ng possible the increase of the ( BH )max  product \nof the nanocomposite when compared with any individ ual phase that form the nanocomposite. [1-\n6]. \nThe increase of the MS is caused by the exchange coupling between grains of nanometer size. \nKneller and Hawig [1] derived a relationship that p redicts how to reach a significant remanence \nenhancement using the microstructural and magnetic properties of this new kind of material, as the \ndistribution of soft and hard magnetic phases and t he fraction of soft magnetic phase, indicating \nthe possibility of developing nanostructured perman ent magnetic materials. \nAccording to the exchange spring model of Kneller a nd Hawig, the critical dimension ( bcm ) for the \nm-phase (soft material) depends on the magnetic cou pling strength of the soft phase Am and the \nmagnetic anisotropy of the hard phase Kh, according to the following equation: \n/g1854/g3030/g3040 /g3404/g2024/g4672/g3002/g3288\n/g2870/g3012/g3283/g4673/g2869/g2870/g3415\n   equation (1).  \nTo obtain a sufficiently strong exchange coupling, the grain size of the soft phase must be smaller \nthan 2 bcm . In a general way, a good magnetic coupling of the  hard and soft components is achieved \nin materials with grain sizes of about 10–20 nm [7] , the approximate value of the domain wall \nwidth in the hard magnetic materials. \nCobalt ferrite, CoFe 2O4, is a hard ferrimagnetic material that has interes ting properties like high HC \n[8, 9] moderate MS [10, 11], high chemical stability, wear resistance , electrical insulation and \nthermal chemical reduction [12, 13]. The latter pro perty allows the transformation of CoFe 2O4 in \nCoFe 2 (a soft ferromagnetic material with high MS value of about 230 emu/g  [14]) in \nmoderate/high temperature. This property was used b y Cabral et. al.  [13] to obtain the \nnanocomposite CoFe 2O4/CoFe 2 and by Scheffe et al.  to hydrogen production [12]. Also, the \nCoFe 2O4/CoFe 2 nanostrutured bimagnetic material was formerly stu died as layered thin films by \nJurca et. al.  [15] and Viart et. al.  [16]. \nIn this work we describe an original process of che mical reduction used for the synthesis of the \nCoFe 2O4/CoFe 2 nanocomposite materials, as well as the magnetic an d structural characterization \nof both precursor and nanocomposite materials. Fina lly, the enhancement obtained for the (BH) max  \nproduct of the CoFe 2O4/CoFe 2 nanocomposite compared with that of the CoFe 2O4 precursor is \nreported.  3 Experimental procedure \nSynthesis of CoFe 2O4 \nThe hydrothermal method was used to synthesize coba lt ferrite. This method provides different \nclasses of nanostructurated inorganic materials fro m aqueous solutions, by means of small Teflon \nautoclaves and has a lot of benefits such as: clean  product with high degree of crystallinity at a \nrelative low reaction temperature (up to 200ºC). Al l the reagents used in this synthesis are \ncommercially available and were used as received wi thout further purification. An appropriate \namount of analytical-grade ammonium ferrous sulfate  ((NH 4)2(Fe)(SO 4)2·6H 2O (0.5 g, 1.28 mmol) \nand sodium citrate Na 3C6H5O7 (0.86 g, 4.72 mmol)  was dissolved in 20 ml of ultra pure water and \nstirred together for 30 min at room temperature, th en stoichiometric CoCl 2.6H 2O (0.15 g, 0.64 \nmmol) was added and dissolved, followed by the addi tion of an aqueous solution of 5M NaOH. \nThe molar ratio of Co (II) to Fe (II) in the above system was 1:2. The mixtures were transferred \ninto an autoclave, maintained at 120 °C for 24 h an d then cooled to room temperature naturally. A \nblackish precipitate was separated and several time s washed with ultra pure water and ethanol.  \n \nSynthesis  CoFe 2O4/CoFe 2 Nanocomposite \n \nTo obtain the nanocomposite we mixed the nanopartic les of cobalt ferrite with activated charcoal \n(carbon) and subjected the mixture to heat treatmen t at 900 °C for 3 hours in inert atmosphere \n(Ar), promoting the following chemical reduction: \n/g1829/g1867/g1832/g1857 /g2870/g1841/g2872/g3397/uni0032/g1829\n/uni2206/g1372/g1829/g1867/g1832/g1857/g2870/g3397/uni0032/g1829/g1841 /g2870 \nThe symbol ∆ indicates that thermal energy is necessary in the process. \nThe similar process was used by Cabral et. al . [13] to obtain the same nanocomposite and by \nScheffe  et. al . to produce hydrogen[12]. \nTheoretically, varying the molar ratio between acti vated carbon and cobalt ferrite we can control \nthe formation of CoFe 2 phase in the nanocomposite. However, the process i s difficult to control \ndue the residual oxygen in the inert atmosphere. \nTwo samples were prepared using the process describ ed here: a full and another partially reduced. \nThe molar ratio between activated charcoal and coba lt ferrite was 2:1 and 10:1, to the partially and \nfully reduced samples respectively. \n \nStructural and magnetic measurements \n \nThe crystalline phases of the calcined particles we re identified by the powder X-ray diffraction \n(XRD) patterns of the magnetic nanoparticles were o btained on a Siemens D5005 X-ray \ndiffractometer using Cu-K radiation (0.154178 nm).  \nMagnetic measurements were carried out using a VSM (VersaLab Quantum Design) at room \ntemperature and 50K. 57 Fe Mossbauer spectroscopy experiments were performe d in two \ntemperatures, 4.2 and 300 K to CoFe 2O4 samples. 4 The morphology and particle size distribution of th e samples were examined by direct observation \nvia transmission electron microscopy (TEM) (model J EOL-2100, Japan). \nResults and Discussion \nThe XRD analysis of the synthesized powder after ca lcination (figure 1) shows that the final \nproduct is CoFe 2O4 with the expected inverse spinel structure (JCPDS No. 00-022-1086), \npresenting the Fd3m spatial group with a lattice pa rameter a = 8.403Å ± 0.0082 Å. Value close to \nthat is expected for the bulk CoFe 2O4 (a = 8.39570) [17]. The XRD pattern also reveals trace s of \nCo and Co 7Fe 3 crystalline phases (indicated in figure 1). \nFigure 2 shows the diffraction profile obtained for  the sample completely reduced. The XRD \nprofile is similar to that to the CoFe 2 (JCPDS No. 03-065-4131), indicating the expected c hemical \nreduction occurred. Due the small quantity of the s ample partially reduced obtained we could not \nperform XRD measurements. \nTo analyze the cation distribution of the precursor  compound (CoFe 2O4), Mossbauer spectroscopy \nexperiments at room temperature and 4.2 K were perf ormed, as shown in the figure 3. The \nMossbauer measurements at 4.2 K reveals two sites f or Fe 3+  related to both octahedral and \ntetrahedral coordination, respectively, as expected  for the spinel crystal structure of CoFe 2O4 [18]. \nThe morphology and dimension of nanoparticles were analyzed by TEM measurements. The \nmeasurement of the cobalt ferrite sample (precursor  material) shows formation of aggregates. This \nresult is expected to samples prepared by hydrother mal method [19, 20]. Figure 4 shows a TEM \nimage of cobalt ferrite particles. The TEM measurem ent reveals that the CoFe 2O4 nanoparticles \nform a polidisperse system with approximately spher ical nanoparticles. The of particle size \ndistribution indicates that ferrite cobalt particle s have mean diameter of 16 nm and the standard \ndeviation of about 4.9 nm. The particle size histog ram obtained by TEM measurements of the \ncobalt ferrite sample is shown in figure 5. \nThe TEM measurements of the nanocomposite (CoFe 2O4/CoFe 2) are shown in figures 6 and 7. In \nfigure 6a one can see there is roughness at the sur face of the nanoparticle. Note that similar \nroughness was not observed at the surface of the pr ecursor material (figure 4). In addition, figure \n6b shows that the superficial material connects the  nanoparticles and the most part of this material \nis in the interface of the nanoparticles. In figure  7a one can see that the nanoparticle is composed \nof two parts a big core and a thin shell (thickness  about 1.5 nm). Similar pictures are observed to \nother nanoparticles (not shown). As previously ment ioned, the shell does not cover each \nnanoparticle but the aggregates of nanoparticles. W e attribute the core to the CoFe 2O4 (hard \nmaterial) and the shell to the CoFe 2 (soft material). Thus the nanocomposite obtained i s constituted \nof spheres of magnetically hard material in a soft matrix. \nThe inserts in figures 7a and 7b show details of th e interplanar distance of both core and shell, \nrespectively. The interplanar distance observed to the core is about 0.49 nm (insert of figure 7a). \nThis value is the same obtained by Chen et. al  [21] to the (111) plane of CoFe 2O4. The insert in \nfigure 7b shows an interplanar distance of about 0. 3 nm, obtained to the shell. But due the small \nthickness of the shell we consider necessary measur ements of high-resolution TEM (HRTEM) to \nmore precise results. 5 TEM analysis indicates that the nanoparticles of na nocomposite are larger than the originals \nnanoparticles, indicating the reduction process inc reases the mean size (diameter) of the \nnanoparticles to about 100 nm. Also, TEM measuremen ts showed that the dimension of the soft \nphase (CoFe 2) is larger than the critical size obtained by equa tion 1 (see figure 6b). Using the \nmagnetic parameters available for CoFe 2O4 and CoFe 2 (Am ~ 1.7 × 10 −11  J/m [22, 23], Kh ~ 2.23 × \n10 5 J/m 3)[24], the calculated critical grain size bcm  for the soft CoFe 2 phase is about 20 nm. \nThe cobalt ferrite sample studied in this work has shown coercivity about 1.69 kOe, at room \ntemperature. This result is higher than the coerciv ity obtained by Cabral et. al.  (1.32 kOe) [13] but \nlower than those reported by Ding et. al.  [8] and Liu et. al. [9] to samples treated by thermal \nmagnetic annealing and mechanical milling, respecti vely.  \nThe hysteresis loop at 50K shows a strong increase of coercivity (8.8 kOe) compared with the \nvalue obtained at room temperature (see the figure 8). Similar behavior of coercivity was observed \nby Maaz et. al.  [25] and Gopalan et. al.  [26]. Another effect observed by theses authors an d also \nobserved in this work is the increase of the remane nce ratio (M r/M S). The saturation magnetization \n(MS) and remanent magnetization ( Mr) obtained here were, respectively, 445 emu/cm 3 (82 emu/g) \nand 181 emu/cm 3 (33 emu/g) at room temperature, while at 50 K were  477 and 323 emu/cm 3 (88 \nand 60 emu/g). These values indicate an increase fo r remanence ratio (M r/M S), from  0.42 to 0.68 , \nwhen the temperature is decreased from 300 K to 50 K. In these results there are two important \nfacts: first the increase of M r/M S value; and second, the M r/M S value obtained at room temperature \nis close to the theoretical value expected (0.5) to  non interacting single domain particles with \nuniaxial anisotropy [27] even the cobalt ferrite ha s a cubic structure. Kodama [28] attribute the \nexistence of an effective uniaxial anisotropy in ma gnetic nanoparticles to the surface effect. The \nstrong anisotropy that produces a high coercivity c an also caused by surface effect [28]. Golapan \net. al.  [26] suggest that the increase in the value of the  Mr/M S ratio is associated with an enhanced \nof cubic anisotropy contribution at lower temperatu re. \nFigure 9 shows the hysteresis loop of the sample pa rtially reduced (CoFe 2O4/CoFe 2) at room \ntemperature and 50K. The hysteresis curves of the n anocomposite can be described by a single-\nshaped loop (no steps in the loop) similar to that of a single phase indicating that magnetization of \nboth phases reverses cooperatively. \nThe same behavior observed to coercivity for the co balt ferrite was also seen for the \nnanocomposite. The coercivity increased from 1.34 k Oe  (at 300K) to 6.0 kOe  (at 50K). This \nenormous increase of coercivity deserves more inves tigation. \nThe MS obtained at room temperature was about 146 emu/g , a value is higher than the MS obtained \nfor precursor material and lower than the expected for pure CoFe 2 (230 emu/g ) [14].  \nThe CoFe 2O4/CoFe 2 nanocomposites demonstrate inter-phase exchange co upling between the \nmagnetic hard phase and the magnetic soft phase, wh ich lead to magnets with improved energy \nproducts. We obtained an energy product (BH) max  of 1.22 MGOe to the nanocomposite. This value \nis about 115% higher than the value obtained for Co Fe 2O4. To room temperature we obtained \n0.568 MGOe to the product (BH) max , assuming the theoretical density for CoFe 2O4 [29]. The value \nof (BH) max  to the nanocomposite is higher than the best value  obtained by Cabral et. al.  (0.63 \nMGOe) to same nanocomposite (but with different mol ar ratio). Also, the precursor sample 6 prepared in this work showed higher coercivity and saturation magnetization than the precursor \nsample of Cabral et. al .. This observation suggest that the (BH) max  product depends of the \nmagnetic properties of precursor material. \nConsidering the nanocomposite formed only by the mi xture of CoFe 2O4 and CoFe 2, we expect that \nthe value of M S is the sum of individual saturation magnetization of these two compounds.  \nUsing  the values of M S = 230 emu/g  to CoFe 2 [14] and 82 emu/g  to cobalt ferrite (result of this \nwork), the saturation magnetization of the nanocomp osite (146 emu/g ) suggests that content of \nCoFe 2 in the nanocomposite is about 40% and that of CoFe 2O4 60 %.  \nTo better visualization the improvement obtained in  magnetic properties, figure 10 show both of \nhysteresis curve of the nanocomposite CoFe 2O4/CoFe 2 and cobalt ferrite at room temperature. The \nsmall decrease of coercivity and the increase of Mr and MS are expected. These behaviors can be \nqualitatively explained by the simple one-dimension al model proposed by Kneller and Hawig. \nConclusion \nWe synthesize nanocomposite of hard ferrimagnetic C oFe 2O4 and soft ferromagnetic CoFe 2 with \nexchange spring behavior at room temperature. This assertion is confirmed by the hysteresis curve \nof the nanocomposite, which do not show steps in th e loop. The thermal treatment at 900 °C used \nin the synthesis method increases the mean size of nanoparticles to about 100 nm (indicated by \nTEM measurements). However the thermogravimetric an alysis (not shown) indicates that the \nsimilar treatment can be used at temperature about 600°C, increasing the time.  \nThe chemical reduction process described in this wo rk is a good pathway to obtain CoFe 2O4/CoFe 2 \nwith exchange spring behavior, but the residual oxy gen in the argon commercial gas makes \ndifficult the control the CoFe 2 molar ratio in the nanocomposite. \nThe magnetic energy product was greatly improved in  the nanocomposite when compared with the \nferrite precursor. However, other studies show that  the coercivity of this precursor material can be \nincreased by thermal annealing, thermal and magneti c annealing or mechanical milling. This \nincrease of coercivity may also improve the magneti c energy product of the nanocomposite, but \nthis assumption deserves more investigation. \nAcknowledgments \nThis work has been supported by Brazilian funding a gency CAPES (PROCAD-NF 2233/2008). \nThe authors would like to thank the LME/LNLS for te chnical support during electron microscopy \nwork. 7  \nFigure 1 – XRD diffraction patterns of the CoFe 2O4. Rietveld fits (solid line) are displayed. \n \nFigure 2 - XRD diffraction patterns of the CoFe 2 produced by reduction reaction of cobalt ferrite \nnanoparticles blended with activated charcoal in th e molar ratio 1:10. \n8  \nFigure 3 – Mossbauer spectra of CoFe 2O4 at room temperature (RT) and 4,2 K (He).  \n \nFigure 4 - Transmission electron microscopy of as-p repared CoFe 2O4 by hydrothermal method. \n9  \nFigure 5– Histogram of the particle size distributi on, fitted by a log normal distribution (solid line) . \nParticles have mean diameters of 16 nm. \n \nFigure 6 – Transmission electron microscopy of nano composite CoFe 2O4/CoFe 2. View of a) one \nnanoparticle and b) two nanoparticles. \na b 10  \nFigure 7– TEM measurements of nanocomposite CoFe 2O4/CoFe 2. (A) Show the an interplanar \ndistance of  CoFe 2O4 the insert show details of marked area. (B) Show t he an interplanar distance \nof  CoFe 2 the insert show details of marked area.  \n \n0.3  nm  11 Figure 8 – Hysteresis loops CoFe 2O4 nanoparticles at room temperature (300 K) and 50 K  at \nmaximum applied field of 30kOe. \n \nFigure 9 - Hysteresis loops for CoFe 2O4/CoFe 2 nanocomposites at room temperature (300 K) and \n50 K at maximum applied field of 20 kOe \n \nFigure 10 – Hysteresis loops to CoFe 2O4/CoFe 2 and CoFe 2O4 nanocomposites both at room \ntemperature (300 K). \n \nReference \n \n[1] E.F. Kneller, R. Hawig, The Exchange-Spring Mag net: A New Material Principle for \nPermanent Magnets, Journal of Magnetism and Magneti c Materials, 27 (1991). \n[2] L. Withanawasam, A.S. Murphy, G.C. Hadjipanayis , R.F. Krause, Nanocomposite \nR2Fe14B/Fe exchange coupled magnets, J. Appl. Phys,  76 (1994) 7065-7067. \n12 [3] T. Schrefl, J. Fidler, H. Kronmüller, Remanence  and coercivity in isotropic nanocrystalline \npermanent magnets, Phys. Rev. B, 49 (1994) 6100-611 0. \n[4] R. Skomski, J.M.D. Coey, Giant energy product i n nanostructured two phase magnets, Phys. \nRev. B, 48 (1993) 15812-15816. \n[5] H. Zeng, S. Sun, J. Li, Z.L. Wang, J.P. Liu, Ta iloring magnetic properties of core/shell \nnanoparticles, Appl. Phys. Lett., 85 (2004) 792-794 . \n[6] E.E. Fullerton, J.S. Jiang, S.D. Bader, Hard/so ft magnetic heterostructures: model exchange-\nspring magnets, Journal of Magnetism and Magnetic M aterials, 200 (1999) 392-404. \n[7] A. Hernando, J.M. González, Soft and hard nanos tructured magnetic materials, Hyperfine \nInteractions, 130 (2000) 221-240. \n[8] J. Ding, P.C. McCormick, R. Street, Magnetic Pr operties of Mechanically Alloyed CoFe204, \nSolid State Communications, 95 (1995) 31-33. \n[9] B.H. Liu, J. Ding, Strain-induced high coercivi ty in CoFe2O4 powders, Appl. Phys. Lett., 88 \n(2006) 042506-042508. \n[10] T.L. Templeton, A.S. Arrott, A.E. Curzon, M.A.  Gee, X.Z. Li, Y. Yoshida, P.J. Schurer, J.L. \nLaCombe, Magnetic properties of CoxFe3−xO4 during c onversion from normal to inverse spinel \nparticles, J. Appl. Phys, 73 (1993) 6728-6730. \n[11] M. Rajendran, R.C. Pullar, A.K. Bhattacharya, D. Das, S.N. Chintalapudi, C.K. Majumdar, \nMagnetic properties of nanocrystalline CoFe2O4 powd ers prepared at room temperature: variation \nwith crystallite size, J. Magn. Magn. Mater., 232 ( 2001) 71-83. \n[12] J.R. Scheffe, M.D. Allendorf, E.N. Coker, B.W.  Jacobs, A.H. McDaniel, A.W. Weimer, \nHydrogen Production via Chemical Looping Redox Cycl es Using Atomic Layer Deposition-\nSynthesized Iron Oxide and Cobalt Ferrites, Chem. M ater. , 23 (2011) 2030-2038. \n[13] F.A.O. Cabral, F.L.A. Machado, J.H. Araújo, J. M. Soares, A.R. Rodrigues, A. Araújo, \nPreparation and Magnetic Study of the CoFe2O4 – CoF e2 Nanocomposite Powders, IEEE \nTransactions on Magnetics, 44 (2008) 4235-4238. \n[14] M. Mohan, V. Chandra, S.S. Manoharan, A New Na no CoFe2 Alloy Precursor for Cobalt \nFerrite Prodution Via Sonoreduction Process, Curren t Science, 94 (2008) 473-476. \n[15] I.S. Jurca, N. Viart, C. Mény, C. Ulhaq-Bouill et, P. Panissod, G. Pourroy, Structural Study of \nCoFe2O4/CoFe2 Multilayers, Surface Science, 529 (20 04) 215-222. \n[16] N. Viart, R.S. Hassan, J.L. Loison, G. Versini , F. Huber, P. Panissod, C. Mény, G.d. Pourroy, \nExchange Coupling in CoFe2O4/CoFe2 Bilayers Elabora ted by Pulsed Laser Deposition, Journal \nof Magnetism and Magnetic Materials, 279 (2004) 21- 26. \n[17] G. Bate, E.B. Wohlfarth, Ferromagnetic Materia ls, North-Holland, Amsterdam, 1980. \n[18] H.H. Hamdeh, W.M. Hikal, S.M. Taher, J.C. Ho, N.P. Thuy, O.K. Quy, N. Hanh, Mössbauer \nevaluation of cobalt ferrite nanoparticles synthesi zed by forced hydrolysis, Journal of Applied \nPhysics, 97 (2005) 064310-064310-064304. \n[19] M.G. Naseri, E.B. Saion, H.A. Ahangar, A.H. Sh aari, M. Hashim, Simple Synthesis and \nCharacterization of Cobalt Ferrite Nanoparticles by  a Thermal Treatment Method, J. Nanomat., \n2010 (2010 ) 1-8. 13 [20] S.C. Goh, C.H. Chia, S. Zakaria, M. Yusoff, C. Y. Haw, S. Ahmadi, N.M. Huang, H.N. Lim, \nHydrothermal preparation of high saturation magneti zation and coercivity cobalt ferrite \nnanocrystals without subsequent calcination, Mater.  Chem. and Phys., 120 (2010) 31-35. \n[21] Z. Chen, L. Gao, Synthesis and magnetic proper ties of CoFe2O4 nanoparticles by using PEG \nas surfactant additive, Material Science & Enginner ing B, 141 (2007) 82-86. \n[22] X. Liu, A. Morisako, Soft magnetic properties of FeCo films with high saturation \nmagnetization, J. Appl. Phys, 103 (2008) 07E726-707 E728. \n[23] M.A. Willard, D.E. Laughlin, M.E. McHenry, Rec ent advances in the development of \n(Fe,Co)88M7B4Cu1 magnets, J. Appl. Phys. , 87 (2000 ) 7091-7096. \n[24] A.J. Rondione, A.C.S. Samia, Z.J. Zhang, Chara cterizing the magnetic anisotropy constant of \nspinel cobalt ferrite nanoparticles, Appl. Phys. Le tt., 76 (2000). \n[25] K. Maaz, A. Mumtaz, S.K. Hasanain, A. Ceylan, Synthesis and magnetic properties of cobalt \nferrite (CoFe2O4) nanoparticles prepared by wet che mical route, Journal of Magnetism and \nMagnetic Materials, 308 (2007) 289-295. \n[26] E.V. Gopalan, I.A. Al-Omari, D.S. Kumar, Y. Yo shida, P.A. Joy, M.R. Anantharaman, \nInverse magnetocaloric effect in sol–gel derived na nosized cobalt ferrite, Applied Phisics A, 99 \n(2010) 497-503. \n[27] T. Ibusuki, S. Kojima, O. Kitakami, Y. Shimada , Magnetic Anisotropy and Behaviors of Fe \nNanoparticles, IEEE Transactions on Magnetics, 37 ( 2001) 2223-2225. \n[28] R.H. Kodama, Magnetic nanoparticles, Journal o f Magnetism and Magnetic Materials, 200 \n(1999) 359-372. \n[29] A. Rafferty, T. Prescott, D. Brabazon, Sinteri ng behavior of cobalt ferrite ceramic, Ceram Int, \n34 (2008) 15-21. \n \n "    },    {        "title": "2306.14513v1.Microscopic_conductivity_of_passive_films_on_ferritic_stainless_steel_for_hydrogen_fuel_cells.pdf",        "content": "Microscopic conductivity of passive films\non ferritic stainless steel for hydrogen fuel cells\nTaemin Ahn and Tae-Hwan Kim∗\nDepartment of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, South Korea\nHydrogen fuel cells offer a clean and sustainable energy conversion solution. The bipolar sepa-\nrator plate, a critical component in fuel cells, plays a vital role in preventing reactant gas cross-\ncontamination and facilitating efficient ion transport in a fuel cell. High chromium ferritic stainless\nsteel with an artificially formed thin chromium oxide passive film has recently gained attention due\nto its superior electrical conductivity and corrosion resistance, making it a suitable material for\nseparators. In this study, we investigate the microscopic electrical conductivity of the intrinsic pas-\nsive oxide film on such ferritic stainless steel. Through advanced surface characterization techniques\nsuch as current sensing atomic force microscopy and scanning tunneling microscopy/spectroscopy, we\ndiscover highly conductive regions within the film that vary depending on location. These findings\nprovide valuable insights into the behavior of the passive oxide film in fuel cells. By understanding\nthe microscopic electrical properties, we can enhance the design and performance of separator ma-\nterials in hydrogen fuel cells. Ultimately, this research contributes to a broader understanding of\nseparator materials and supports the wider application of hydrogen fuel cells.\nKeywords: scanning tunneling microscopy, current sensing atomic force microscopy, hydrogen fuel cells,\nferritic stainless steel, passive film, microscopic conductivity\nI. INTRODUCTION\nHydrogen fuel cells are progressively becoming an ap-\npealing and sustainable technology, offering several ben-\nefits conducive to a transition towards a clean energy\nfuture [1, 2]. One key component of these cells is the\nbipolar separator plates. These plates play an integral\nrole in proton exchange membrane fuel cells, necessitat-\ning features like corrosion resistance, durability, and low\ncontact resistance within the fuel cell stack [3]. Although\ngraphite and carbon composite materials are commonly\nused, stainless steel bipolar plates present a compact and\npotentially economical alternative, especially for portable\nand transport applications [4, 5].\nStainless steel bipolar plates have advantageous prop-\nerties such as low interfacial contact resistance, excellent\ncorrosion resistance, high thermal conductivity, and low\ngas permeability [6, 7]. Moreover, stainless steel offers de-\nsirable mechanical strength and formability, especially as\na thin plate. However, these stainless steel plates pose a\nsignificant challenge due to the increased interfacial con-\ntact resistance between the stainless steel surface and the\nmembrane electrode assembly layer [5, 8, 9]. This chal-\nlenge is largely attributed to the semiconducting charac-\nteristics of the passive oxide film formed on the stainless\nsteel surface under the fuel cell’s typical operating con-\nditions, usually a highly acidic environment [10–12].\nTo circumvent this challenge, a ferritic stainless steel\nhas been developed featuring low interfacial contact resis-\ntance ( <5 mΩ·cm2) and high corrosion resistance (corro-\nsion current density <0.1µA·cm−2) through a pickling\nprocess followed by sophisticated passivation [13]. This\n∗Electronic address: taehwan@postech.ac.krstainless steel variant, which features a conducting Cr ox-\nide passive film, shows high electrical conductivity, ren-\ndering it a promising material for bipolar plates [3, 14].\nHowever, oxide films on complex alloys such as stain-\nless steel are typically non-uniform. This non-uniformity\nresults in microscopic differences in electrical conductiv-\nity, which can hinder the overall performance. Hence,\nexamining the microscopic conductivity traits becomes\ncritically important from a practical application perspec-\ntive. By understanding the relationship between the non-\nuniform conductivity and the other features of the oxide\nfilm, we could identify ways to enhance regions of the ox-\nide film that demonstrate high electrical conductivity. In\nturn, this would enable us to achieve the higher electrical\nconductivity necessary for bipolar plates.\nIn this study, we aim to investigate the microscopic\nelectrical conductivity of the chromium oxide passive film\non the ferritic stainless steel bipolar plates. We have\nemployed advanced microscopic characterization tech-\nniques such as current sensing atomic force microscopy\n(CSAFM) [15–17] and scanning tunneling microscopy\n(STM) [18–20] to unravel the underlying microscopic\ncharacteristics of the conducting passive film. Our find-\nings have the potential to optimize the electrical perfor-\nmance of stainless steel bipolar plates, thereby facilitat-\ning their broader application in fuel cell technology.\nII. EXPERIMENTAL DETAILS\nPoss470FC, a commercially available variant of fer-\nritic stainless steel, exhibits outstanding corrosion resis-\ntance and high electrical conductivity [13]. After a spe-\ncialized chemical treatment, the resulting thin Cr oxide\nwithin a few nanometers from the surface significantly\nenhances Poss470FC’s corrosion resistance and electricalarXiv:2306.14513v1  [cond-mat.mtrl-sci]  26 Jun 20232\nconductivity, meeting the 2020 Department of Energy\ntargets [21]. To investigate the intrinsic properties of\nthe passive film on the stainless steel, it is necessary to\npreserve the characteristic passive film under commer-\ncial conditions. This work employed thin Poss470FC\nsheets cut into small samples, which were ultrasonically\ncleaned with ethanol to prevent surface contamination.\nThis methodology guaranteed the relevance and validity\nof the findings regarding the inherent traits of the artifi-\ncially formed Cr oxide on Poss470FC.\n(a) (b)\nIn air (or N2) In vacuumLaserPhoto \ndetector\nItIPt tipPt-Ir tip\nVVFeedback Feedback\nSSPassive filmIZ-scannerZ-scanner\nFig. 1: (a) Schematic representation of current sensing\natomic force microscopy (CSAFM) measurement of the pas-\nsive film in air or a dry N 2atmosphere. (b) Schematic repre-\nsentation of scanning tunneling microscopy (STM) measure-\nment in an ultrahigh vacuum (UHV) environment.\nIn order to investigate the local conductivity of our\nsamples, we employed a combination of CSAFM and\nSTM (refer to the appendix for more details). In-\ncorporating current measurements with contact mode\nAFM imaging [Fig. 1(a)], the CSAFM method, instru-\nmental in exploring microscopic conductivity variations\nwithin resistive samples, was conducted using a com-\nmercial AFM (XE-100, Park Systems) equipped with\nsolid Pt probe tips (25Pt300B, Rocky Mountain Nan-\notechnology). These tips were chosen for their ability\nto resist the degradation often associated with metal-\ncoated probe tips [22–24]. Despite its effectiveness,\nCSAFM comes with limitations like potential tip wear\nand unavoidable disruptive influence on the sample sur-\nface [22, 25–31]. To mitigate these limitations, we com-\nplemented our approach with STM measurements, which\nwere performed under ultra-high vacuum (UHV) condi-\ntions ( P < 1.0×10−10Torr) at room temperature using\na home-built STM with an electrochemically etched Pt-Ir\ntip [32]. STM, which involves positioning an atomically\nsharp metallic tip approximately 1 nm from the sample\nsurface [Fig. 1(b)], provides comprehensive atomic-scale\ntopographic and electronic information without causing\nany damage to the samples.III. RESULTS AND DISCUSSION\nBias (V)Current (nA)\nCurrent (µA)\nBias (mV)\n-1.0\n-0.2 -0.1 0.0 0.1 0.20.0\n-0.51.0\n0.55\n-5\n-10 0.0 100(c)\n(d)50 nN\n100 nN\n150 nN\n200 nN\n250 nN\n300 nN\n350 nN\n400 nN750 nN\n800 nN\n1400 nN\n450 nN500 nN\n550 nN\n600 nN\n650 nN\n700 nN\nNormal force (nN)Resistance (kΩ)\n1.0106109\n103\n1000 100\n170 nm 100 nA 0 nm 0 nA(a) (b)\n750 nN\n800 nN\n1400 nN750 nN\n800 nN\n1400 nN\nFig. 2: (a) Contact mode CSAFM topographic image of the\nferritic stainless steel and (b) its corresponding current map\nwith a sample bias of +0 .5 V and a tip normal force of 400 nN\nin air. The scale bar is 10 µm. (c) I(V) curves obtained with\nvarying tip normal force in the regions where higher current\nwas obtained in the current map. The inset better visual-\nizes the 750, 800, 1400 nN data. (d) Estimated resistances\nderived from the linear regression of the reciprocal slopes of\nthe measured I(V) curves in the bias range of ±0.1 V. For\ncomparison, the red dashed line in the inset represents the\nresistance (650 kΩ) obtained in a dry N 2atmosphere with a\nnormal force of 10 nN.\nTo investigate the microscopic electrical conductivity\nof the passive film on ferritic stainless steel, CSAFM mea-\nsurements were performed in ambient environments. Fig-3\nures 2(a) and 2(b) depict the representative CSAFM to-\npographic image and its corresponding current map of\nthe ferritic stainless steel with a sample bias of +0 .5 V,\nrespectively. The topographic image reveals typical fea-\ntures derived from the manufacturing process of the fer-\nritic stainless steel. Interestingly, the simultaneously ob-\ntained current map does not exhibit features correlated\nwith topography, which suggests that the formation of\nthe conductive passive film is not considerably affected\nby surface roughness. Moreover, the current map uncov-\ners the existence of two distinct regions. These regions\nare differentiated by the measured current values, with\nareas of higher current predominantly surpassing those\nwith lower current. The prevalence of these higher cur-\nrent regions aligns well with the reported high electrical\nconductivity of the passive film on the ferritic stainless\nsteel.\nTo definitively ascertain the ideal normal force for our\nambient experiments, we systematically increased the\nnormal force until we attained a stable I(V) curve. We\nobtained local I(V) curves from a region with elevated\nconductivity within the current map by adjusting the\nnormal force from 50 nN to 1400 nN [Fig. 2(c)]. The\nestimated resistance of the passive film, as a function of\nnormal forces, was determined by calculating the recip-\nrocal slope of the I(V) curves within ±0.1 V, as shown\nin Fig. 2(d). In contrast to previous studies on passive\nfilms of other austenitic and ferritic phases [33–35], our\nfindings highlight the significantly enhanced conductiv-\nity (by at least a factor of 100) of the passive film on\nthe ferritic stainless steel under comparable normal forces\n(∼400 nN). This also lends credence to its superior elec-\ntric conductivity compared to other stainless steel vari-\nants. In general, the estimated resistance decreases with\nincreasing normal force, which could be attributed to the\ninevitable water layer between the tip and sample under\nambient conditions (refer to the appendix for more de-\ntails) [22, 36]. However, it is important to acknowledge\nthe potential risk of passive film fracture under excessive\nnormal force, as the estimated resistance was extraordi-\nnarily low above 800 nN.\nTo avoid the potential risk of passive film fracture asso-\nciated with excessive normal forces and current fluctua-\ntions induced by the presence of a water layer in ambient\nconditions, we carried out supplementary CSAFM mea-\nsurements in a dry N 2atmosphere [22, 28]. In contrast\nto the ambient conditions, we could successfully acquire\nreliable CSAFM current maps and I(V) curves with the\nconsiderably reduced normal force in the dry atmosphere.\nFigure 3 shows the CSAFM results of the ferritic stain-\nless steel obtained with a normal force of only 10 nN\n(compared to 400–800 nN under the ambient conditions)\nand a sample bias of +0 .1 V in the dry atmosphere. Our\nfindings were largely consistent with those observed un-\nder ambient conditions, except for the much lower normal\nforce. The current map also reveals the presence of two\ndistinct conducting regions similar to those under the\nambient conditions [Fig. 3(b)].\n130 nm\n1.0 µA0 nm\n0 µACurrent (nA)\nBias (V)Bias (mV)\n-15\n-3.0 -1.5 3.0 0 1.550 5 -5 10 -10\n0\n-5\n-101015(a)\n(b)\n(c)\nFerrite SS\nSS 304\nFig. 3: (a) Contact mode CSAFM topographic image of the\nferritic stainless steel and (b) its corresponding current map\nwith a sample bias of +0 .1 V and a normal force of 10 nN\nin a dry N 2atmosphere. The scale bar is 1 µm. (c) Typical\nI(V) curves obtained on the ferritic stainless steel (red dots)\nand stainless steel 304 (SS304, black dots) in the same dry N 2\natmosphere with a normal force of 10 nN.\nFor a direct comparison, we repeated the I(V) mea-\nsurement under the identical measurement conditions us-\ning a popular austenitic stainless steel variant (SS304).\nFigure 3(c) exhibits the ohmic behavior with low resis-\ntance of the passive film on the ferritic stainless steel, in4\n(a)\n(b)\n(c)\ndI/dV(nS)\nCurrent (pA)\nBias (V)\nBias (V)-300\n0 0.2 -0.230\n0 0.5 1.0 -0.5 -1.02.0\n1.5\n1.0\n0.5\n0.0\n55 nm\n0 nm\n280 pS\n0 pS\nFig. 4: (a) STM topographic image of the ferritic stain-\nless steel and (b) its corresponding differential conductance\n(dI/dV ) mapping image at a sample bias of +1 .0 V. Imaging\ncondition: Vb= +1 .0 V,It= 50 pA. The scale bar is 400 nm.\n(c)dI/dV (V) and I(V) curves (inset) obtained on the regions\nmarked with different colored dots in (b).\ncontrast to the insulating characteristics of SS304. To\nachieve a similar current range ( ±10 nA), the I(V) curve\nwas captured within a sample bias range of merely ±0.1 V\non the passive film of the ferritic stainless steel, whereas\nthe curve on SS304 was obtained within ±3 V. The es-\ntimated resistance was 650 kΩ on the passive film of the\nferritic stainless steel, which is comparable to the resis-tance at a normal force of 750 nN in the ambient atmo-\nsphere [refer to the red dashed line in Fig. 2(d)].\nWhile we can prevent the passive film fracture in a dry\natmosphere using a small normal force, we cannot over-\nlook the mandatory contact resistance between the tip\nand sample. This is due to the fact that the measured\nresistance invariably incorporates this contact resistance.\nIn response to this limitation of CSAFM, we further in-\nvestigated the electronic properties of the passive film\nwith STM under UHV conditions. The quantum tunnel-\ning phenomenon between the tip and sample allows STM\nto provide local density of states (DOS) information and\ntopography without mechanical contact, unlike CSAFM\nmeasurements [Fig. 1(b)].\nThe ferritic stainless steel samples were transferred to\nour custom UHV STM chamber after being evacuated in\nthe load-lock chamber overnight. During this transition\nto the STM chamber, the sample was not subjected to\nany thermal treatment or annealing, ensuring to retain\nthe intrinsic properties of the passive film. Before the\nSTM measurements, a metallic PtIr tip was routinely\nverified on an atomically clean Cu(100) surface.\nFigures 4(a) and (b) show the STM topography\nand its corresponding differential tunneling conductance\n(dI/dV ) map, obtained at a sample bias of +1 .0 V and a\ntunneling current of 50 pA. The STM image reveals more\nintricate but similar topographic features [Fig. 4(a)],\nwhereas the dI/dV map shows three or more regions with\ndifferent tunneling conductance intensities [Fig. 4(b)].\nThedI/dV contrast represents local DOS differences of\nthe oxide film surface obtained at 1.0 eV above the Fermi\nlevel.\nFurthermore, we measured point scanning tunneling\nspectroscopy (STS) spectra on the regions showing dis-\ntinct tunneling conductance [Fig. 4(c)]. Three such\nregions are marked by red, green, and black dots in\nFig. 4(b). Given that the local DOS is roughly pro-\nportional to the differential tunneling conductance in\nmeasured STS spectra [20], we inferred that the darker\n(brighter) region in the dI/dV map [Fig. 4(b)] presents\nhigher (lower) local DOS at the Fermi energy ( Vb= 0 V)\n[Fig. 4(c)]. These local DOS variations are likely due to\nsubtle differences in the chemical composition of the ox-\nide film. Despite the spatially nonuniform tunneling con-\nductance, we confirmed that the entire surface displays\nthe metallic behavior without any electronic bandgap,\nthus reaffirming the superior electrical conductivity of\nthe passive film.\nIn sharp contrast to the CSAFM measurements, we\nobserved a location dependence in the dI/dV map and\nSTS spectra in Fig. 4. This surprising discrepancy be-\ntween the CSAFM and STM measurements could be at-\ntributed to the extreme sensitivity of STM measurements\nto the topmost surface, while CSAFM measurements en-\ncompass the entire thickness of the passive film. Further\ninvestigation is required to gain a deeper understanding\nof this discrepancy between these complementary tech-\nniques.5\nIV. SUMMARY\nIn conclusion, our study offers a comprehensive mi-\ncroscopic investigation of the electrical conductivity of\nthe chromium oxide passive film on the commercially\navailable ferritic stainless steel, which has shown great\npromise for bipolar plate application in hydrogen fuel\ncells. Through the utilization of advanced surface char-\nacterization techniques such as CSAFM and STM/STS,\nwe were able to distinctly identify both the remarkably\nhigh conductivity and the location-dependent conduc-\ntance within the passive film. These discoveries not only\nclarify the exceptional electrical conductivity of the ma-\nterial but also offer crucial insights that could be instru-\nmental in enhancing the electrical performance of fer-\nritic stainless steel bipolar plates. Although these find-\nings mark significant progress, more research is needed\nto fully understand the location-dependent conductance\nand its implications for practical applications. Future\nwork could explore this aspect further and investigate\nother potential materials for bipolar plate application.\nUltimately, our research aids in the design and advance-\nment of efficient separator materials for hydrogen fuel\ncells, thereby promoting the broader application of this\nsustainable energy technology in diverse fields.\nV. APPENDIX\nA. Current sensing atomic force microscopy\n(CSAFM)\nTo explore the local conductivity of our ferritic stain-\nless steel samples, we utilize CSAFM, which combines\ncurrent measurements with contact mode AFM imaging.\nIn general, CSAFM operates under the standard AFM\ncontact mode, using cantilevers coated with a conductive\nfilm [16, 17]. By integrating current measurements with\ncontact mode AFM imaging, CSAFM serves as a pow-\nerful and effective method for investigating microscopic\nconductivity variations within resistive samples. When\na bias voltage is applied between the sample and the\nconducting cantilever, a current is induced [Fig. 1(a)],\nenabling us to obtain a spatially resolved conductivity\nimage. CSAFM provides concurrent information on the\nspatial distribution of current and the sample topography\nwith a constant cantilever load and bias voltage. Further-\nmore, the measured current can be adjusted by varying\nthe bias voltage and/or cantilever load.\nFor our specific experiments, we employ a commer-\ncial AFM (XE-100, Park Systems) with solid platinum\n(Pt) probe tips (25Pt300B, Rocky Mountain Nanotech-\nnology), chosen for their ability to resist the degradation\nfrequently encountered with metal-coated probe tips [22–\n24]. These probes, featuring a force constant of 18 N/m\nand a typical radius of less than 20 nm, allow for precise\nmicroscopic conductivity measurements.\nWe frequently encountered issues with unreliable cur-rent maps when using low normal forces. This phe-\nnomenon can be attributed to the inevitable presence\nof a water layer between the metal probe tip and sample\nin ambient conditions. The water layer results in the re-\nduced electric field confinement near the tip-sample junc-\ntion, causing an unstable current flow during the mea-\nsurement process [22, 36]. To achieve stable current in\nCSAFM measurements under ambient conditions, it is\nimperative to apply a higher contact force to break the\nwater layer [22]. In our study, we utilized a relatively\nhigh normal force of 400 nN in ambient conditions to\nguarantee highly reliable electrical contacts between the\nconducting tip and the sample during the process of cur-\nrent mapping [37].\nCrucially, CSAFM allows for the simultaneous visual-\nization of topography and current distribution, offering\ninvaluable insights into the conductive characteristics of\nthe passive film across different regions of the sample.\nHowever, as with any experimental method, CSAFM has\nlimitations, such as the potential for tip wear and degra-\ndation, and possible disruptive influence on the sample\nsurface [22, 25–31]. These factors can result in inconsis-\ntent or inaccurate measurements over time. To minimize\nthese effects, we conducted our experiments under con-\ntrolled humidity conditions, maintaining a relative hu-\nmidity of less than 30%. Additionally, we utilized N 2gas\nflow to further decrease the humidity ( <9%) [28].\nFor a more in-depth analysis, we measured representa-\ntive current-voltage I(V) curves in regions of the passive\nfilm exhibiting higher conductivity in the concurrently\nobtained current map and topographic image. Each\npoint I(V) curve was derived from an average of more\nthan ten individual measurements taken at a fixed posi-\ntion. This approach ensured the reproducibility and con-\nsistency of the observed I(V) characteristics, enhancing\nthe reliability of our findings.\nB. Scanning tunneling microscopy (STM)\nTo further enhance the analysis of our ferritic stainless\nsteel samples, we expanded our methodology to include\nSTM [19]. This advanced technique provides atomic-\nlevel surface scrutiny, mitigating the limitations associ-\nated with CSAFM. STM involves bringing an atomically\nsharp metallic tip into close proximity with the sample\nsurface (approximately 1 nm) [Fig. 1(b)]. When a bias\nvoltage is applied between the tip and the sample, elec-\ntrons tunnel through the vacuum barrier, generating a\ntunneling current that depends on the tip-sample dis-\ntance, applied bias voltage, and the local DOS of the\nsample. We performed STM measurements in the con-\nstant current mode using an electrochemically etched\nPt-Ir tip in a home-built STM under UHV conditions\n(P < 1.0×10−10Torr) at room temperature [32].\nTo refine our analysis, we STS, an advanced technique\nof STM [20, 38]. STS records the tunneling current re-\nsponse to varied bias voltages while maintaining a con-6\nstant sample-tip distance. This non-invasive method en-\nables us to obtain the local DOS of the sample, inves-\ntigating its intrinsic electronic properties with atomic\nprecision—an advantage over CSAFM. Combined with\nSTM scanning mode, STS produces spatially resolved lo-\ncal DOS maps, providing detailed insights into the lo-\ncal electronic properties of the sample. In this study,\nwe obtained differential tunneling conductance ( dI/dV )\nspectra using a lock-in amplifier that modulated the bias\nvoltage by 30 mV at a frequency of 997 Hz.\nWhile STM requires atomically clean and stable sur-\nfaces, strong vibration isolation, and high-performanceelectronics, it offers extraordinary spatial precision and\nunmatched atomic-level insights in terms of precision and\ndetail. The combined use of STM and STS is instrumen-\ntal in our investigation of the local conductivity of our\nferritic stainless steel samples.\nACKNOWLEDGMENTS\nThis work was supported by POSCO Steel & Green\nScience (2019Y081).\n[1] A. Sch¨ afer, J. B. Heywood, and M. A. Weiss, Energy 31,\n2064 (2006).\n[2] Z. Xu, D. Qiu, P. Yi, L. Peng, and X. Lai, Prog. Nat.\nSci. Mater. Int. 30, 815 (2020).\n[3] Q. Liu, F. Lan, C. Zeng, J. Chen, and J. Wang, J. Power\nSources 538, 231543 (2022).\n[4] P. Yi, X. Li, L. Yao, F. Fan, L. Peng, and X. Lai, Energy\nConvers. Manag. 183, 65 (2019).\n[5] A. Kraytsberg, M. Auinat, and Y. Ein-Eli, J. Power\nSources 164, 697 (2007).\n[6] Y. Leng, P. Ming, D. Yang, and C. Zhang, J. Power\nSources 451, 227783 (2020).\n[7] S. Karimi, N. Fraser, B. Roberts, and F. R. Foulkes, Adv.\nMater. Sci. Eng. 2012 , 828070 (2012).\n[8] R. A. Antunes, M. C. L. Oliveira, G. Ett, and V. Ett,\nInt. J. Hydrog. Energy 35, 3632 (2010).\n[9] C. Turan, ¨O. N. Cora, and M. Ko¸ c, Int. J. Hydrog. En-\nergy36, 12370 (2011).\n[10] N. Shaigan, X.-Z. Yuan, F. Girard, K. Fatih, and\nM. Robertson, J. Power Sources 482, 228972 (2021).\n[11] C. O. A. Olsson and D. Landolt, Electrochim. Acta 48,\n1093 (2003).\n[12] N. De Cristofaro, M. Piantini, and N. Zacchetti, Corros.\nSci.39, 2181 (1997).\n[13] J. Kim, K. Jo, Y. Kim, J. Lee, Y. Lee, J. Kim, and\nJ. Seok, U.S. Patent 11047029 B2 (2021).\n[14] Y. Leng, D. Yang, P. Ming, B. Li, and C. Zhang, World\nElectr. Veh. J. 12, 101 (2021).\n[15] F. J. Giessibl, Rev. Mod. Phys. 75, 949 (2003).\n[16] F. Houz´ e, R. Meyer, O. Schneegans, and L. Boyer, Appl.\nPhys. Lett. 69, 1975 (1996).\n[17] F. Hui and M. Lanza, Nat. Electron. 2, 221 (2019).\n[18] G. Binnig and H. Rohrer, Rev. Mod. Phys. 59, 615\n(1987).\n[19] P. K. Hansma and J. Tersoff, J. Appl. Phys. 61, R1\n(1987).\n[20] R. M. Feenstra, Surf. Sci. 299–300 , 965 (1994).\n[21] DOE, U.S., Hydrogen and fuel cell technologies office\nmulti-year research, development, and demonstrationplan (2014).\n[22] L. Jiang, J. Weber, F. M. Puglisi, P. Pavan, L. Larcher,\nW. Frammelsberger, G. Benstetter, and M. Lanza, Ma-\nterials 12, 459 (2019).\n[23] J. Weber, Y. Yuan, F. K¨ uhnel, C. Metzke, J. Sch¨ atz,\nW. Frammelsberger, G. Benstetter, and M. Lanza, ACS\nAppl. Mater. Interfaces 15, 21602 (2023).\n[24] M. A. Lantz, S. J. O’Shea, and M. E. Welland, Rev. Sci.\nInstrum. 69, 1757 (1998).\n[25] X. Ji, J. Oh, A. Keith Dunker, and K. W. Hipps, Ultra-\nmicroscopy 72, 165 (1998).\n[26] O. Stukalov, C. A. Murray, A. Jacina, and J. R. Dutcher,\nRev. Sci. Instrum. 77, 033704 (2006).\n[27] L. Zitzler, S. Herminghaus, and F. Mugele, Phys. Rev. B\n66, 155436 (2002).\n[28] Y. Ji, F. Hui, Y. Shi, T. Han, X. Song, C. Pan, and\nM. Lanza, Rev. Sci. Instrum. 86, 106105 (2015).\n[29] D.-Z. Guo, S.-M. Hou, G.-M. Zhang, and Z.-Q. Xue,\nAppl. Surf. Sci. 252, 5149 (2006).\n[30] T. D. B. Jacobs and A. Martini, Appl. Mech. Rev. 69,\n060802 (2017).\n[31] S. A. Sumaiya, A. Martini, and M. Z. Baykara, Nano\nExpress 1, 030023 (2020).\n[32] T. Ahn, S. Song, U. Ham, and T.-H. Kim, Rev. Sci. In-\nstrum. 94, 063702 (2023).\n[33] T. Souier and M. Chiesa, J. Mater. Res. 27, 1580 (2012).\n[34] M. C. Lin, G. Wang, L. Q. Guo, L. J. Qiao, and A. A.\nVolinsky, Appl. Phys. Lett. 103, 143118 (2013).\n[35] L. Q. Guo, M. C. Lin, L. J. Qiao, and A. A. Volinsky,\nCorros. Sci. 78, 55 (2014).\n[36] S. Kremmer, S. Peissl, C. Teichert, F. Kuchar, and\nH. Hofer, Mater. Sci. Eng. B 102, 88 (2003).\n[37] A. Bietsch, M. A. Schneider, M. E. Welland, and\nB. Michel, J. Vac. Sci. Technol. B 18, 1160 (2000).\n[38] B. Voigtl¨ ander, Scanning probe microscopy: Atomic\nforce microscopy and scanning tunneling microscopy\n(Springer, 2015)."    },    {        "title": "1204.2973v1.Spin_Glass_like_Phase_below___210_K_in_Magnetoelectric_Gallium_Ferrite.pdf",        "content": " 1Spin Glass-like Phase below ~ 210 K in Magnetoelectric Gallium Ferrite 1 \n 2 \nSomdutta Mukherjee1, Ashish Garg2 and Rajeev Gupta1,3, ∗  3 \n1Department of Physics 4 \n2Department of Materials Science and Engineering  5 \n3Materials Science Programme 6 \nIndian Institute of Technology Kanpur, Kanpur 208016, India 7 \n 8 \nAbstract: 9 \nIn this letter we show the presence of a spin-glass like phase in single crystals of 10 \nmagnetoelectric gallium ferrite (GaFeO 3) below ~210 K via temperature dependent ac and dc 11 \nmagnetization studies. Analysis of frequency dispersion of the susceptibility peak at ~210 K 12 \nusing the critical slowing down model and Vogel-Fulcher law strongly suggests the existence 13 \nof a classical spin-glass like phase. This classical spin glass behavior of GaFeO 3 is 14 \nunderstood in terms of an outcome of geometrica l frustration arising from the inherent site 15 \ndisorder among the antiferromagnetically coupled  Fe ions located at octahedral Ga and Fe 16 \nsites. 17 \n 18 \n 19 \n  20 \n 21 \n22 \n                                                 \n∗ Corresponding author; FAX: +91-512-2590914; guptaraj@iitk.ac.in    2Simultaneous presence of more than one order parameters in single phase magnetoelectric 1 \n(ME) and/or multiferroic (MF) materials leads to conceptualization of many exciting devices 2 \nsuch as multi-state memories, sensors etc.1,2 Applicability of these materials for such device 3 \napplications requires a good understanding of the coupling behavior among magnetic, 4 \nelectrical and structural order parameters si nce such couplings trigger many interesting 5 \nphenomena in the above materials when studied over temperature,3 composition4 and length 6 \nscales.5  For instance, materials such as SrMnO 36 and EuTiO 37 undergo strain induced 7 \nferromagnetic-ferroelectric phase transition below a critical temperature owing to their large 8 \nmagneto-structural coupling. More recently, our work on another magnetoelectric oxide, 9 \nGaFeO 3 (GFO), which is particularly attractive due to tunability of its magnetic transition 10 \ntemperature, has shown the presence of substantial magneto-structural coupling8 below room 11 \ntemperature (RT).  Our results indicated a sudden change in the strength of the interaction 12 \nacross ~ 200 K strongly suggestive of a spin reorie ntation in this material. Despite scarcity of 13 \nsuch observations of spin reorie ntation particularly associated with spin frustration (very few 14 \nexceptions e.g. BiFeO 33 and YMnO 39), there is a growing interest in examining spin 15 \ndynamics in ME and MF materials since it ha s been proposed that magnetic frustration in 16 \nsome MF systems can result in spiral ma gnetic ordering inducing ferroelectricity.10 These 17 \naspects make it essential to examine the magnetic behavior of such materials to understand 18 \nthe spin interactions from a practical pers pective of material and device design. 19 \nGFO simultaneously exhibits ferrimagneti sm and piezoelectricity and its magnetic 20 \ntransition can be tuned above RT by manipulati ng the material’s composition i.e. Ga to Fe 21 \nratio.11 Noncentrosymmetric orthorhombic structure ( Pc2 1n) of GFO has eight formula units 22 \nper unit-cell with four inequivalent cationic si tes: Ga1 ions occupying tetrahedral sites and 23 \nGa2, Fe1 and Fe2 ions occupying all the octahedral sites. Ideally GFO is expected to be an 24 \nantiferromagnet,12,13 however finite temperature magnetic measurements show it as a 25  3ferrimagnet.12,14 Latter is believed to be an outcome of  cationic site disorder due to very small 1 \ndifferences in the sizes of Ga3+ and Fe3+ ions. Detailed structural characterization using X- 2 \nray8,12 and Neutron diffraction12 rules out any structural phase transition in the ferrimagnetic 3 \nstate.  However, our Raman spectroscopic stud y, as mentioned above, clearly indicates a 4 \nsubtle change in the spin orientation across ~200 K. Occurrence of these two contrasting 5 \nevents is indeed quite intriguing and requires a careful investigation of the spin dynamics. In 6 \nthis letter we report the results of temperature dependent ac susceptibility and dc 7 \nmagnetization measurements to further elucidat e hitherto observed spin reorientation near 8 \n200 K in GFO. Our results clearly demonstrate the existence of a spin-glass phase in GFO 9 \nand we show that this is a manifestation of ge ometrical frustration emanating from cation site 10 \ndisorder.  11 \nSingle crystals of GFO were flux grown from high purity precursor oxides Ga 2O3 and 12 \nFe2O3 using Bi 2O3 as flux8,11 yielding dark brown needle shaped crystals with [110]- 13 \norientation. Details of structural ch aracterization can be found elsewhere.8 Further, samples 14 \nwere subjected to temperature dependent ac  and dc magnetization measurements using 15 \nSQUID magnetometer. The measurements were performed under both Field Cooled (FC) and 16 \nZero Field Cooled (ZFC) conditions over a temperature range, 2 K to 330 K. In all the 17 \nmeasurements, external dc field and the probing ac field were applied along the c-axis of the 18 \ncrystals.  19 \nTemperature dependent dc magnetization data of GFO, at fields: 100 Oe and 500 Oe, 20 \nare shown in Fig. 1(a). On cooling, magnetization increases sharply below T c ~290 K 21 \nmarking the transition from the paramagnetic (PM) phase to ferrimagnetic (fM) phase, a well 22 \nestablished transition. Cooling the sample below T c results in splitting of FC and ZFC curves. 23 \nThis splitting marks the onset of magnetic irreve rsibility at a certain temperature, defined as 24 \nTir below which bifurcation between FC and ZFC curves starts occurring. Further lowering of 25  4temperature leads to the formation of a cusp in ZFC plot at a temperature defined as T p. 1 \nBifurcation of ZFC and FC curves is more pronounced at lower field strength where T p and 2 \nTir remained well separated and shifted toward higher temperature. A cusp in the ZFC plot 3 \nand the distinctive separation of FC and ZFC data at T ir are typical features of spin- 4 \nglasses.3,4,9 This is usually explained in terms of spin freezing or change in the spin-ordering 5 \nleading to a spin-glass like phase formation at low temperatures.  However, the splitting of 6 \nthe FC and ZFC curves is not a sufficient evidence to conclude spin-glass nature15 and it is 7 \nalso often observed in the ferromagnetic regions in many systems, attributed to the pinning of 8 \nthe domain walls.4  9 \nIn materials showing a spin glass behavior, spin interactions lead to a highly 10 \nirreversible yet metastable state and can be well analyzed by ac magnetization studies.3,4  11 \nThere is, in fact, preliminary evidence of magnetic frustration provided by ac susceptibility 12 \nmeasurements on polycrystalline GFO.16 However, a narrow frequency range of 4 kHz – 10 13 \nkHz used in the experiments does not conclusively prove spin-glass nature of GFO. This 14 \nwarrants a detailed investigation using ac susceptibility over a reasonably wide temperature 15 \nand frequency domain. In this context, we first examine the temperature dependence of ac 16 \nsusceptibility in the frequency range of 0.1 to 1000 Hz as shown in Fig. 1 (b) and (c). Upon 17 \ncooling from 330 K to 2 K, both the χ′ and χ′′ display sharp peaks at ~T c. These frequency 18 \nindependent peaks termed as Hopkinson peaks are typical feature in many ferromagnetic 19 \nmaterials.17 With further lowering of temperature,  another set of weak and broad peaks 20 \n(corresponding to spin freezing temperature Tf ~ 210 K) appear in both χ′ and χ′′ plots (Fig. 21 \n1(b) and (c)). The peak positions shift to high er temperatures with increasing frequency and 22 \nalso their magnitudes depend strongly on frequency. Frequency dispersion of these low 23 \ntemperature susceptibility peaks has also been observed for a variety of other oxides 24 \nexhibiting spin glass behavior such as BiFeO 3,3 LuFe 2O4+δ18 and CaBaFe 4O719 and as well as 25  5in dilute magnetic alloys20 and has been explained as an indication of presence of short range 1 \nspin interactions.  2 \nIn the spin glass state, the slower spin dynamics with decreasing temperature implies 3 \nthat spins take longer time to relax to a relatively stable state i.e. relaxation time increases 4 \nwith decreasing temperature. Dynamic susceptibility measurements can thus be used to 5 \ndistinguish whether GFO is a classical spin glass or a superparamagnet by comparing the 6 \ninitial frequency dependence of Tf (ω) using the expression ( Δp = ΔTf/(TfΔlogω)).3,20 Our 7 \nmeasurements show that Tf  varies from ~212 K (0.1 Hz) to ~216 K (103 Hz) in χ′ plot while 8 \nit varies from 210 K (0.1 Hz) to ~212 K (103 Hz) in χ″. The calculated peak shift ( Δp) per 9 \ndecade of frequency shift has a value of about 0.005 and 0.003 for χ′ and χ′′, respectively 10 \nwhich are an order of magnitude lower than those observed for super-paramagnetic systems 11 \n(10-1–10-2) while their values match well with those for classical spin glasses,20,21 suggesting 12 \nthat GFO undergoes spin glass transition below the freezing temperature. Above can further 13 \nbe substantiated by analyzing the frequency dependence of the peaks in χ' using the 14 \nconventional critical slowing down model of spin dynamics,22 i.e. 15 \n0()                                                               (1)z\nfs\nsTT\nTνω τ\nτ−−⎛⎞=⎜⎟\n⎝⎠ 16 \nwhere, Ts is spin glass transition temperature determined by the system interactions (at ω → 17 \n0, Tf (ω) → Ts), z  is dynamic critical exponent, ν is the critical exponent of the correlation 18 \nlength and τo is the shortest relaxation time available to the system.22 Fig. 2 (a) shows the best 19 \nfit to the data in the frequency range, 0.1 to 1000 Hz, suggesting that the spin glass behavior 20 \nin GFO can be well described using critica l slowing down model and the fitting yielded 21 \nfollowing parameters: Ts = 211 ± 0.5 K, z ν = 5.5 ± 1.5 and τo ~ 10-13 s. These values are in 22 \ngood agreement with those reported for well known spin glass and cluster glass systems. The 23 \nvalue of z ν for most classical as well as cluster glass systems lie between 5-10 such as for 24  6Ising spin glass Fe 0.5Mn 0.5TiO 3,23 geometrically frustrated system LuFe 2O4+δ18 and cluster 1 \nglass U 2CuSi 3.24 Thus z ν alone cannot be used as a decisive parameter to differentiate 2 \nbetween the type of spin glasses.   3 \n The other criterion to distinguish different kinds of spin glasses is based on the 4 \nVogel25- Fulcher26 law relating the relaxation in a spin glass system to the driving frequency 5 \nand subsequently estimating the activation energy using the expression:  6 \n0\n0exp                                                                 (2)()a\nBfE\nkT Tωω⎡⎤−=⎢⎥−⎢⎥⎣⎦ 7 \nHere, T 0 is the Vogel-Fulcher temperature and kB is the Boltzmann constant. Taking ω0 = 1013 8 \nHz as calculated earlier, a linear variation of Tf versus 1/ln( ω0/ω) is obtained and the best fit 9 \nof the experimental data to the eq. 2 (solid line in Fig. 2(b)) yields T 0 = 202.9 K and Ea = 1.66  10 \nkBTs. This activation energy, Ea is a measure of the energy barrier separating different 11 \nmetastable states accessible to the system . For a canonical spin glass such as Cu-Mn20 as well 12 \nas for a geometrically frustrated system CaBaFe 4O7,19 ω0 has been reported to be ~1013 Hz. 13 \nHowever, for cluster glass Li doped CaBaFe 4-xLixO7 (x = 0.1 to x = 0.4),19 U2CuSi 324 and 14 \nLa0.5Sr0.5CoO 327 the reported values of  ω0 range between 1012-1016 Hz. The observed scatter 15 \nin ω0 for different systems with similar characte ristics thus, does not allow us to draw any 16 \nmeaningful conclusions. On the other hand the value of activation energy, Ea, appears to 17 \nexhibit a trend. For instance, the value of Ea is ~2 kBTs for a canonical spin-glass Cu-Mn20 18 \n(Mn ~ 3.3-8 at.%) and Ea ~1.25 kBTs for geometrically  frustrated CaBaFe 4O7 19.  In contrast, 19 \nEa is quite large for cluster glass systems: ~12 kBTs for Li-doped CaBaFe 4-xLixO7 (x=0.4)19, ~ 20 \n3.1kBTs for U 2CuSi 3 24\n and ~ 7 kBTs for La 0.5Sr0.5CoO 3.27 From this, we can infer that GFO is 21 \nclose to being a classical spin-glass with E a ~ 1.66  kBTs  which can further be substantiated by 22 \ndc field dependence of ac susceptibility data that can differentiate between a classical spin 23 \nglass from the assemblies of magnetic cluste rs based on the temperature shift of the 24  7susceptibility peak as a function of applied dc field.28,29 For a classical spin glass, Tf usually 1 \nshifts toward lower temperatures with increasing applied dc field while for cluster glass, it 2 \nmoves to higher temperature due to  the growth of the clusters.28,29  3 \nFig. 3 depicts the in-phase component of temperature dependent ac susceptibility 4 \nwhere an ac magnetic field of magnitude 4 Oe and a driving frequency of 100 Hz were 5 \napplied with superimposed different dc fields of 0 to 10 kOe. A first glance, the susceptibility 6 \n(χ') vs. temperature plot shows the presence of tw o peaks: a strong peak in the vicinity of 280 7 \nK corresponding to fM-PM transition and a low temperature peak at ~210 K corresponds to 8 \nthe spin-glass phase. Fig. 3 clearly shows that with increasing dc field, the low temperature 9 \npeak shifts to low temperatures (from ~ 207  K at zero field to ~ 185 K at 500 Oe) 10 \naccompanied by decreasing peak amplitude. The peak eventually disappears at ~ 1 T 11 \nsuggesting complete suppression of spin-glass be havior at higher external fields. Such peak 12 \nshift (of Tf) towards lower temperatures with increasing dc field is observed in many classical 13 \nspin glasses and can be quantitatively describe d using de Almeida-Thouless (AT) line for an 14 \nanisotropic Ising spin glass system30 as expressed by  15 \n3\n2\n0()1                                                                      (3)(0)fTHHHT⎛⎞=−⎜⎟⎝⎠ 16 \nwhere, H is the external applied dc magnetic field, T f (H) is the field dependent freezing 17 \ntemperature, and H o determines the boundary of the applied dc magnetic field up to which the 18 \nspin glass phase can exist. Eq. 3 suggests that a plot of H2/3 vs. freezing temperature ( Tf) 19 \nwould yield the values of H o and T(0). The plot is shown in inset of Fig. 3 and we obtain H o = 20 \n1.2 T and T(0) = 209 K. The above value of field is close to the experimental observations i.e. 21 \nsusceptibility peak disappearing at ~ 1T. A low value of goodness of fit to the AT line in the 22 \nplot points towards the Ising nature of the spin glass and the spin freezing in GFO is quite 23  8similar to that of conventional spin glass systems. Moreover, the ratio of T c to Ts ~ 1.4:1, also 1 \nsupports Ising nature of the present system as postulated by Campbell et al.31 2 \nUsually, a necessary condition to achieve a spin glass state is magnetic frustration 3 \nwhich may or may not be associated with disorder. In case of magnetic oxides, there have 4 \nbeen a large number of studies on geometrical spin frustration on compounds such as 5 \npyrochlores,19 spinels18 and garnets32 where spin glass behavior is an outcome of the 6 \nformation of a triangular framework of the antiferromagnetically coupled magnetic ions 7 \nresulting in spin frustration. In order to analyze the origin of the observed spin glass behavior 8 \nwe propose a physical model of geometrically frustrated network of antiferroimagnetically 9 \narranged cations in GFO. GFO has an inherent si te disorder where some of the Ga sites are 10 \noccupied by Fe ions and vice-versa. While A- type antiferromagentic spin ordering ensures 11 \nthat Fe (at Fe1 and Fe2 sites) ions are antiferromagentically aligned with respect to each 12 \nother.13 Site disordering renders some of the Fe ions to occupy Ga sites (primarily Ga2 sites 13 \nas the occupancy of Fe at Ga1 site is negligible).12 This leads to the formation of zigzag chain 14 \nof corner sharing tetrahedral spin network among Fe1, Fe2 and Fe (at Ga2 site) ions leading 15 \nto spin frustration in the lattice as shown in Fig. 4. Although similar may also happen at Ga1 16 \nsites, theoretical calculations and experimental12,13 data predict it as quite unlikely. It is likely 17 \nthat such spin frustration affects the antiferromagentic spin ordering in GFO leading to a 18 \nconcomitant co-existence of a spin-glass phase.  19 \n In summary, using detailed temperature a nd frequency dependent dc and ac magnetic 20 \nmeasurements, we clearly demonstrate the existe nce of a spin-glass like transition at ~ 210 K 21 \nin single crystalline gallium ferrite (GFO), in addition to the previously reported 22 \nparamagnetic to ferrimagnetic transition at ~290 K. We observe that low temperature peak of 23 \nac susceptibility shows strong frequency dispersion and analysis of this frequency dispersion 24 \nusing the critical slowing down model and the Vogel-Fulcher law strongly supports the 25  9formation of a classical spin-glass like phase. These results are consistent with a recent 1 \nreport8 on changes in the magneto-structural coupling coefficient of GFO across ~200 K. We 2 \nargue that the disorder driven geometrically fr ustrated corner sharing tetrahedral network of 3 \nFe ions gives rise to the observed spin glass phase in GFO. 4 \nAuthors thank Prof. S. Ramakrishnan for permit ting the use of SQUID facility at Tata 5 \nInstitute of Fundamental Research, Mumb ai and Mr. G.S. Jangam for conducting the 6 \nmeasurements. Authors acknowledge the financial support from the Department of Science 7 \nand Technology and Council for Scientif ic and Industrial Research, India. 8 \n 9 \nReferences: 10 \n1 J. F. Scott, Nature Mater 6, 256 (2007). 11 \n2 G. A. Prinz, Science 282, 1660 (1998). 12 \n3 M. K. Singh, W. Prellier, M. P. Singh, R. S. Katiyar, and J. F. Scott, Phys. Rev. B 77, 13 \n144403 (2008). 14 \n4 J. Dho, W. S. Kim, and N. H. Hur, Phys. Rev. Lett. 89, 027202 (2002). 15 \n5 R. Mazumder, P. Mondal, D. Bhattacharya, S. Dasgupta, N. Das, A. Sen, A. K. Tyagi, 16 \nM. Sivakumar, T. Takami, and H. Ikuta, J. Appl. Phys. 100, 033908 (2006). 17 \n6 J. H. Lee, and K. M. Rabe, Phys. Rev. Lett. 104, 207204 (2009). 18 \n7 C. J. Fennie and K. M. Rabe, Phys. Rev. Lett. 97, 267602 (2006). 19 \n8 S. Mukherjee, A. Garg, and R. Gupta, J. Phys.: Condens. Matter 23, 445403 (2011). 20 \n9 W. R. Chen, F. C. Zhang, J. Miao, B. Xu, S. Dong, L. X. Cao, X. G. Qiu, B. R. Zhao, 21 \nand P. Dai, Appl. Phys. Lett. 87, 042508 (2005). 22 \n10 D. Khomskii, Physics 2, 20 (2009). 23 \n11 J. P. Remeika, J. Appl. Phys. 31, S263 (1960). 24  1012 T. Arima, D. Higashiyama, Y. Kaneko, J. P.  He, T. Goto, S. Miyasaka, T. Kimura, K. 1 \nOikawa, T. Kamiyama, R. Kumai, and Y. Tokura, Phys. Rev. B 70, 064426 (2004). 2 \n13 A. Roy, S. Mukherjee, R. Gupta, S. Auluck, R. Prasad, and A. Garg, J. Phys.: 3 \nCondens. Matter 23, 325902 (2011). 4 \n14 R. B. Frankel, N. A. Blum, S. Foner, A. J. Freeman, and M. Schieber, Phys. Rev. Lett. 5 \n15, 958 (1965). 6 \n15 S. R. Shinde, S. B. Ogale, J. S. Higgins, H. Zheng, A. J. Millis, V. N. Kulkarni, R. 7 \nRamesh, R. L. Greene, and T. Venkatesan, Phys. Rev. Lett. 92, 166601 (2004). 8 \n16 N. Wang, F. S. Wen, L. Li, Y. F. Lü, S. C. Liu, Y. F. Lu, Z. Y. Liu, B. Xu, J. L. He, 9 \nD. L. Yu, and Y. J. Tian, J. Magn. Magn. Mater. 322, 3595 (2010). 10 \n17 J. Nogué and K. V. Rao, J. Magn. Magn. Mater. 135, L11 (1994). 11 \n18 F. Wang, J. Kim, Y.-J. Kim, and G. D. Gu, Phys. Rev. B 80, 024419 (2009). 12 \n19 K. Vijayanandhini, C. Simon, V. Pralong, V. Caignaert, and B. Raveau, Phys.  Rev. B 13 \n79, 224407 (2009). 14 \n20 C. A. M. Mulder, A. J. van Duyneveldt, and J. A. Mydosh, Phys. Rev. B 23, 1384 15 \n(1981). 16 \n21 J. A. Mydosh, Spin Glass: An Experimental Introduction  (Taylor & Francis, London, 17 \n1993). 18 \n22 P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977). 19 \n23 K. Gunnarsson, P. Svedlindh, P. Nordblad, L. Lundgren, H. Aruga, and A. Ito, Phys. 20 \nRev. Lett. 61, 754 (1988). 21 \n24 D. Li, S. Nimori, T. Yamamura, and Y. Shiokawa, J. Appl. Phys. 103, 07B715 22 \n(2008). 23 \n25 H. Vogel, Phys. Z. 22, 645 (1921). 24 \n26 G. S. Fulcher, J. Am. Ceram. Soc. 8, 339 (1925). 25  1127 S. Mukherjee, R. Ranganathan, P. S. Anilkumar, and P. A. Joy, Phys. Rev. B 54, 9267 1 \n(1996). 2 \n28 F. Rivadulla, M. A. López-Quintela, and J. Rivas, Phys. Rev. Lett. 93, 167206 (2004). 3 \n29 R. Ang, Y. P. Sun, X. Luo, C. Y. Hao, X. B. Zhu, and W. H. Song, Appl. Phys. Lett. 4 \n92, 162508 (2008). 5 \n30 J. R. L. de Almeida and D. J. Thouless, J. Phys. A 11, 983 (1978). 6 \n31 I. A. Campbell, Phys. Rev. B 33, 3587 (1986). 7 \n32 P. Schiffer, A. P. Ramirez, D. A. Huse, P. L. Gammel, U. Yaron, D. J. Bishop, and A. 8 \nJ. Valentino, Phys. Rev. Lett. 74, 2379 (1995). 9 \n 10 \n 11 \n 12 \n 13 \n 14 \n15  12List of figures: 1 \nFig. 1 (color online) (a) ZFC and FC dc ma gnetization vs. temperature plots at 100 Oe 2 \n(filled symbols) and 500 Oe (open symbols). T ir represents the temperature at which 3 \nbifurcation between FC and ZFC curves occurs and the cusp in ZFC plots is marked as T p. 4 \nTemperature dependent (b) real ( χ′) and (c) imaginary ( χ′′) parts of ac susceptibility data 5 \nmeasured at several frequencies. Inset of 1 (b) shows the magnified view of the low 6 \ntemperature peak in χ′ plot.  7 \n 8 \nFig. 2 (color online) (a) Plot of time constant ( τ) vs. dynamic spin freezing temperature ( Tf) of 9 \nGFO with solid line representing the best fit to equation 1. (b) Plot of 1/ln( ω0/ω) vs. dynamic 10 \nspin freezing temperature ( Tf) with solid line representing the best fit to equation 2. 11 \n 12 \nFig. 3 (color online) Plot of temperature dependence of χ′ measured at several applied dc 13 \nfields H. The figure also shows that at sufficient ly large applied dc fields (e.g. H=1T), the low 14 \ntemperature peak corresponding to the spin gl ass transition disappears completely. Inset 15 \nshows the plot of dynamic spin freezing temperature ( Tf) vs. H2/3 with the solid line being the 16 \nbest fit to equation 3. 17 \n 18 \nFig. 4. (color online) Schematic diagram illus trating geometrical spin frustration in corner 19 \nsharing tetrahedral network of Fe ions in GFO unit cell. The frustration (marked as ‘?’) arises 20 \ndue to cationic site disorder driving Fe ions to  occupy some of the Ga2 sites. For Clarity Ga1 21 \nions which have negligible Fe occupancy are removed. 22 \n  23 \n 24 "    },    {        "title": "1407.3734v1.Bismuth_ferrite_as_low_loss_switchable_material_for_plasmonic_waveguide_modulator.pdf",        "content": "Bismuth ferrite as low-loss switchable material for   \nplasmonic waveguide modulator \nViktoriia E. Babicheva 1,2,*, Sergei V. Zhukovsky 1,2 , and Andrei V. Lavrinenko 1 \n1DTU Fotonik, Technical University of Denmark, Oerst eds Plads 343,2800 Kgs. Lyngby, Denmark  \n2 ITMO University, Kronverkskiy, 49, St. Petersburg 197101, Russia \n* E-mail:  baviev@gmail.com \nAbstract . We propose new designs of plasmonic modulators, w hich can be utilized for dynamic signal switching i n \nphotonic integrated circuits. We study performance of plasmonic waveguide modulator with bismuth ferri te as an \nactive material. The bismuth ferrite core is sandwi ched between metal plates (metal-insulator-metal co nfiguration), \nwhich also serve as electrodes so that the core cha nges its refractive index under applied voltage by means of partial \nin-plane to out-of-plane reorientation of ferroelec tric domains in bismuth ferrite. This domain switch  results in \nchanging of propagation constant and absorption coe fficient, and thus either phase or amplitude contro l can be \nimplemented. Efficient modulation performance is ac hieved because of high field confinement between th e metal \nlayers, as well as the existence of mode cut-offs f or particular values of the core thickness, making it possible to \ncontrol the signal with superior modulation depth. For the phase control scheme, π phase shift is provided by 0.8- µm \nlength device having propagation losses 0.29 dB/ µm. For the amplitude control, we predict up to 38 d B/ µm \nextinction ratio with 1.2 dB/ µm propagation loss. In contrast to previously propo sed active materials, bismuth ferrite \nhas nearly zero material losses, so bismuth ferrite  based modulators do not bring about additional dec ay of the \npropagating signal. \n1. Introduction \nPlasmonic structures were shown to provide advantag es for waveguiding and enhanced light-matter intera ction, as \nutilizing surface plasmon waves at metal-dielectric  interface allows efficient manipulation of light o n the \nsubwavelength scale [1-4]. A metal-insulator-metal (MIM) waveguide provides the most compact configura tion due \nto high mode localization within the dielectric cor e, and consequently efficient interaction between f ield of the mode \nand active material if it is placed between metal l ayers [5-7]. Although detailed characterization of the devices \nencounters issues because of the small mode size an d high insertion losses, it has been shown recently  that the \nefficient coupling from a photonic waveguide to an MIM structure can be realized to launch the signal [8]. \nMoreover, different approaches have been proposed, for example confining light either by thick metal l ayers or by \nmore specifically designed metamaterials, for insta nce hyperbolic metamaterials [9,10]. \nPlasmonic waveguide modulators and switches are of major interest for ultra-compact photonic integrate d circuits \nand have been widely studied last several years [11 ,12]. Several promising designs have been proposed including \ninvestigation of various active materials, such as silicon [13-16], transparent conductive oxides (TCO s) [7,17-21], \ngraphene [22], nonlinear polymers [23], thermo-opti c polymers [24,25], gallium nitride [26,27], and va nadium \ndioxide [28-32]. Some of them were shown to outperf orm conventional photonic-waveguide-based designs i n terms \nof compactness [19,33]. \nIn general, one can distinguish two classes of acti ve materials according to physical mechanisms under lying in \nrefractive index control: carrier concentration cha nge (e.g. TCOs, silicon, and graphene) and nanoscal e structural \ntransformations (e.g. gallium and vanadium dioxide) . For example, TCOs provide a large change of refra ctive \nindexes and can be utilized for fast signal modulat ion on the order of several terahertz [7,17-21,34-3 6]. However, \nthey possess high losses, consequently the modal pr opagation length is fairly small [17,18]. For loss mitigation, one \ncan implement gain materials and directly control t he absorption coefficient [37,38], but such active materials can \nsignificantly increase the noise level. \nIn contrast to carrier concentration change, struct ural transformations cannot provide such high bit r ate, and \nmegahertz operation is expected due to microsecond timescales of the transformations. Yet, refractive index changes \nthat accompany nanoscale material transformations a re much higher than those caused by carrier concent ration \nchange. In particular, extinction ratio up to 2.4 d B/ µm was demonstrated for a hybrid plasmonic modulator  based on \nmetal – insulator phase transition in vanadium diox ide [31]. \nFerroelectric materials, such as bismuth ferrite (B iFeO 3, BFO) or barium titanate (BaTiO 3, BTO), possess \npromising features for optical modulation [39-47]. Under applied voltage, the ferroelectric domains ca n be partially \nreoriented from the in-plane orientation (with an o rdinary refractive index no) to the out-of-plane orientation (with \nextraordinary index ne) [48,49]. Thus, the refractive index for a field p olarized along one axis can be changed, and \ncontrol of propagating signal is achieved. Variatio n of the applied voltage provides a varying degree of domain \nswitching, and thus the required level of propagati ng signal modulation can be realized. BTO was shown  to provide \n \n high performance for photonic thin film modulators [39-42], as well as electro-optic properties in pla smonic \ninterferometer-based [43] and waveguide-based [45] modulators. However, BFO has higher birefringence w ith \nrefractive index difference ∆n = 0.18 nearly three times higher than in BTO. Rece ntly a strong change of refractive \nindex in BFO was demonstrated [44] and proposed for  electro-optic modulation [46-47].  \nHere for the first time, we propose an implementati on of BFO as the active materials for plasmonic wav eguide \nmodulators. We analyze different modulator designs based on MIM waveguide, and compare the performance  of \nthese modulators. Because of the low losses of BFO at telecom wavelength, one can achieve large phase shifts and \nhigh extinction ratio on a sub-micron length. Speci fically, we predict a π phase shift in low-loss phase modulator \nonly 0.8 µm in length, and up to 38 dB/ µm extinction ratio in a high-contrast absorption mo dulator. In Section 2, we \nanalyze dispersion properties of an MIM waveguide w ith BFO core. In Section 3, phase and absorption mo dulation \nis studied in more detail. Section 4 follows with s ummary and conclusions. \n2. Eigenmodes of the waveguide with BFO core \nSchematic view of the MIM waveguide with BFO is sho wn in Fig. 1a. We are interested in modulation at t he \ntelecom wavelength, λ0 = 1.55 µm, so the metal permittivity is fixed at εm = –128.7 + 3.44 i (silver, [50]). Plasmonic \nmodes are defined by the equation [51]: \n1\ntanh( ) m zz \nmkεqd qε±  = −   \n    (1) \nwhere “±” corresponds to symmetric and antisymmetri c modes, respectively; d is the core thickness; εxx  and εzz  are \ncomponents of the permittivity tensor of the core; 2 2 \n0 0 ( / ) zz xx zz qε ε β ε k = − ; 2 2 \n0 0 m m kβ ε k = − ; k0 = 2π/λ0 is the \nwave number in vacuum; β0 = β + iα is the complex propagation constant to be determin ed. We consider no = 2.83 \nand ne = 2.65 [44] and solve the dispersion equation of a  three-layer structure. We consider two options for  the \ndevice off-state: with εxx  = no2 and εzz  = ne2 (“x-ordinary”, denoted “ox”) and with εxx  = ne2 and εzz  = no2 (“z-ordinary”, \ndenoted “oz”); we assume that the imaginary part of  εij  is very small at 1.55 µm. Under applied voltage, the domains \nare reoriented, and both off-states switch to the s ame on-state (labeled “e”) with tensor components e qual to \nεxx  = εzz  = ne2 (Fig. 1b).  \n \nFig. 1. (a) Schematic view of plasmonic modulator b ased on metal-insulator-metal waveguide with BFO co re as \nactive material. (b) Illustration of BFO switching in the “ x-ordinary” and “ z-ordinary” scenario. (c) Schematics of \nBFO-based plasmonic switches based on phase or abso rption modulation principles. \n \nWe solve the dispersion equation (1) numerically fo r different core thickness d = 50…400 nm. As seen in Fig. 2, \nthe structure supports three modes in the considere d parameter range: two symmetric (denoted “s 1” and “s 2”) and one \nantisymmetric (denoted “as”). The results show a si gnificant change of propagation constant β and absorption \ncoefficient α for all the three modes during switching between e ither of the two off-states [(ox) and (oz)] and the  on-\nstate (e), when the refractive index along one of t he axes changes from no to ne. \nSuch difference in the mode indexes can allow effic ient operation of the device. We see that the mode “s 1” \nprovides the maximum change of β between the off-state “ox” and the on-state (Fig. 2a), as well as the lowest losses \nnearly uniform across the range of core thickness v ariation (Fig. 2b). Thus, this configuration is par ticularly \nfavourable for a phase modulator in an interferomet er-type setup (see Fig. 1c, top). On the other hand , the two \nremaining modes (“s 2” and “as”) feature an abrupt step in the dependenc e α(d) near the cut-off values of the core \nthickness, occurring at different d for on- vs. off-state (Fig. 2b). These modes are t herefore particularly suitable for \ndirect amplitude modulation in a waveguide-type dev ice (Fig. 1c, bottom), especially when the off-stat e “oz” is used. \nIn the following section, we perform a more detaile d analysis of these regimes.  \nFig. 2. Propagation constants (a) and absorption co efficients (b) for different modes of MIM waveguide : two \nsymmetric (s 1 and s 2) and antisymmetric (as). Notations (ox), (oz), and  (e) correspond to two off-states ( x-ordinary \nand z-ordinary) and the on-state, respectively (see Fig.  1b). Legend is the same on both plots. \n \n3. Modulator designs and performance characterizati on \n3.1. Phase-modulation operation \nThe first symmetric mode “s 1” possesses the highest β, which varies in a range 11…14 µm-1 and corresponds to \nthe effective index neff  = 2.7…3.5. Absorption coefficient of this mode is the smallest and has almost no difference \nbetween the off- and on-states. Thus this mode is s uitable for signal phase control (Fig. 1c, top) \nWe calculated the length required to achieve π phase shift π o e Lπ β β = − . It shows value around 4 µm in a broad \nrange of d and decreases with the decrease of core thickness d (Fig. 3a). The propagation losses are \n0.08…0.3 dB/ µm and thus a short length remains relatively high t ransmission ( TdB  = 10lg(T 0/T)  = 8.68 αLπ, Fig. 3b). \nThus, the phase control can be put into practice vi a the Mach-Zehnder interferometer with the device l ength down \nto 4 µm. The operation bandwidth is large since the effec t of mode index change is essentially non-resonant (near-\nflat lines in Fig. 3a) and since the BFO refractive  index only slightly varies with the wavelength [44 ]. \n \nFig. 3. (a) Device length L π needed to achieve π phase difference between on- and off-state. (b) Lo ss in the device \nwith length L π. The labels (ox) and (oz) correspond to the switch ing scenarios from the x- and z-ordinary off-state to \nthe on-state (see Fig. 1b). \n \nOn the other hand, when the core thickness varies, the second symmetric “s 2” and antisymmetric “as” modes \npossess a much more abrupt change. They have very l ow β and high α for some particular thicknesses, which \ncorresponds to the modes exhibiting cut-off (Fig. 2 ). We can define the mode as propagating when it sa tisfies the \ncondition Q = β/α > 1.Thus “s 2” has cut-off at: d(s 2,e) = 272 nm, d(s 2,ox) = 272 nm, and d(s 2,oz) = 253 nm. Because \nof the fast pronounced change near the cut-off thic knesses, the range d = 253…272 nm corresponds to the largest \ndifference between β(s 2,e) and β(s 2,oz). The length required for π phase shift is down to 800 nm (see Fig. 3a) and th e \nmode losses are even lower than for “s 1” (see Fig. 3b). Similar properties are shown by mo de “as” in a range of thicknesses 116…125 nm. Propagation losses of these  two modes are 0.29 and 0.6 dB/ µm. Thus, adopting BFO a \nlow-loss  ultra-compact plasmonic modulator can be realized. \n \n3.2. Absorption-modulation operation \nAnother way to implement a plasmonic switch is the direct manipulation of absorption coefficient α. Because of \nthe mode cut-off discussed previously, both modes “ s2” and “as” provide such a possibility (see Fig. 2b) . One can \ndefine the figure of merit (FoM) of the device as () FoM e o o α α α = − . Both modes have high FoMs in the cut-off \nregion, where there is an abrupt α change (Fig. 4a).  \nWe see that for the symmetric mode “s 2”, the FoM value of 67 is reached. At this point, t he extinction ratio \nER = αe – αo =  20 dB/ µm, and consequently 3 dB switch can be realized on 150 nm. Corresponding propagation \nlength z = 1/(2 αo) is 12 µm (Fig. 4b). For the asymmetric mode “as”, the devi ce characteristics are also prominent: \nFoM up to 29, extinction ratio of 28 dB/ µm (allowing a 3 dB switch on 107 nm), and propagati on length z = 3.5 µm \n(Fig. 4b). \nFor all the considered designs, modes are strongly localized within the core and efficient coupling fr om photonic \nwaveguide [8] can be realized to launch symmetric m ode. In case of special requirements from the desig n, launching \nof antisymmetric mode can be accomplished by coupli ng of another plasmonic waveguide with asymmetric m ode. \n \n \nFig. 4. (a) FoM and (b) propagation length z for th e second symmetric “s 2” and asymmetric “as” modes. Triangular \nmarks on (b) correspond to maximum FoM on (a). \n \n4. Conclusion \nIn summary, we studied properties of the MIM plasmo nic waveguide with the BFO core aiming to utilize s uch a \nwaveguide as a building block for an efficient plas monic modulator. The proposed designs give the foll owing three \nadvantages.  \ni) From the material point of view, low losses of B FO (nearly zero for λ > 1400 nm [44]) do not cause additional \nattenuation from waveguide core, and thus do not in crease insertion loss of the whole device, in contr ast to TCO or \nvanadium dioxide.  \nii) From the design point of view, MIM configuratio n allows cut-off of the propagating mode and thus m akes it \npossible to modulate propagation signal by switchin g it on and off through metal layers serving as ele ctrodes.  \niii) MIM configuration provides high confinement of  the mode, and the field does not expand outside th e \nwaveguide. \nThe device can be realized in two ways (Fig. 1c). O n the one hand, signal phase control can be impleme nted in \nMach-Zehnder interferometer and device length 0.8…4  µm is required. Such a compact structure indicates t he high \npotential of BFO-based devices. Operation with the first symmetric waveguide mode can be broadband as BFO \nrefractive index is only slightly varying at wavele ngths close to the telecom range, and mode characte ristics do not \nhave pronounced change when the core thickness vari es. On the other hand, effective signal amplitude c ontrol by \ndirect change of absorption can be realized. In thi s case a BFO plasmonic modulator can have FoM up to  67, which \nis comparable with recently reported values for mod ulators based on dielectric-loaded plasmonic wavegu ide with \ngraphene [22], and is much higher than FoMs of prev iously reported devices based on indium tin oxide, vanadium \ndioxide, or InGaAsP active layers [18,29,37,38].  \nAcknowledgments  \nV.E.B. acknowledges financial support from SPIE Opt ics and Photonics Education Scholarship and Kaj og Hermilla \nOstenfeld foundation. S.V.Z. acknowledges partial f inancial support from the People Programme (Marie C urie \nActions) of the European Union’s 7 th  Framework Programme FP7-PEOPLE-2011-IIF under REA grant agreement \nNo. 302009 (Project HyPHONE). \n \nReferences \n1. A.V. Zayats, I.I. Smolyaninov, and A.A. Maradudi n, “Nano-optics of surface plasmon polaritons,” Phy sics Reports 408, 131-\n314 (2005). \n2. J.A. Schuller, E.S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extr eme light \nconcentration and manipulation,” Nature Materials 9 , 193 (2010).  \n3. Dmitri K. Gramotnev and Sergey I. Bozhevolnyi, “P lasmonics beyond the diffraction limit,” Nature Pho tonics 4, 83-91 \n(2010). \n4. V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang , “Toward integrated plasmonic circuits,” MRS Bull. 3 7(08), 728–738 \n(2012). \n5. J.A. Dionne, L.A. Sweatlock, H.A. Atwater, and A . Polman, “Plasmon slot waveguides: Towards chip-sc ale propagation with \nsubwavelength-scale localization,” Phys. Rev. B 73 , 035407 (2006).  \n6. Y. Kurokawa and H.T. Miyazaki, “Metal-insulator- metal plasmon nanocavities: Analysis of optical pro perties,” Phys. Rev. B \n75 , 035411 (2007). \n7. A.V. Krasavin and A.V. Zayats, “Photonic signal processing on electronic scales: electro-optical fi eld-effect nanoplasmonic \nmodulator,” Physical Review Letters 109 , 053901 (2012). \n8. A. Emboras, R. M. Briggs, A. Najar, S. Nambiar, C. Delacour, P. Grosse, E. Augendre, J. M. Fedeli, B. d e Salvo, H. A. \nAtwater, and R. Espiau de Lamaestre, “Efficient coup ler between silicon photonic and metal-insulator-si licon-metal plasmonic \nwaveguides,” Appl. Phys. Lett.101(25), 251117 (2012 ). \n9. S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Bo ltasseva, and A. V. Kildishev, \"Plasmonic waveguide s cladded by \nhyperbolic metamaterials,\" Optics Letters 19, xxx ( 2014). \n10. V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, \"Multilayer claddin g with anisotropic \nhyperbolic dispersion for plasmonic waveguide,\" in preparation \n11. K. F. MacDonald and N. I. Zheludev, “Active pla smonics: current status,” Laser Photon. Rev. 4(4), 5 62–567 (2010). \n12. W. Cai, J. S. White, and M. L. Brongersma, “Compac t, high-speed and power-efficient electrooptic plas monic modulators,” \nNano Lett. 9(12), 4403–4411 (2009). \n13. J. A. Dionne, K. Diest, L. A. Sweatlock, and H.  A. Atwater, “PlasMOStor: a metal-oxide-Si field ef fect plasmonic \nmodulator,” Nano Lett. 9(2), 897–902 (2009). \n14. Shiyang Zhu, G. Q. Lo, and D. L. Kwong, “Theore tical investigation of silicon MOS-type plasmonic s lot waveguide based \nMZI modulators,” Optics Express 18 , 27802 (2010). \n15. S. Zhu, G. Q. Lo, and D. L. Kwong, “Electro-abs orption modulation in horizontal metal-insulator-si licon-insulator-metal \nnanoplasmonic slot waveguides,” Appl. Phys. Lett. 9 9, 151114 (2011). \n16. R. Thomas, Z. Ikonic, and R.W. Kelsall, “Electro- optic metal–insulator–semiconductor–insulator–metal  Mach-Zehnder \nplasmonic modulator,” Photon. Nanostructures 10 , 183 (2012). \n17. A. Melikyan, N. Lindenmann, S. Walheim, P. M. L eufke, S. Ulrich, J. Ye, P. Vincze, H. Hahn, T. Sch immel, C. Koos, W. \nFreude, and J. Leuthold, “Surface plasmon polariton  absorption modulator,” Opt. Express19(9), 8855–886 9 (2011). \n18. V.E. Babicheva and A.V. Lavrinenko, “Plasmonic m odulator optimized by patterning of active layer an d tuning \npermittivity,” Opt. Commun. 285 , 5500 (2012).  \n19. V. J. Sorger, N. D. Lanzillotti-Kimura, R.-M. Ma , and X. Zhang, “Ultra-compact silicon nanophotonic  modulator with \nbroadband response,” Nanophotonics1(1), 1–6 (2012).  \n20. V.E. Babicheva, N. Kinsey, G. V. Naik, M. Ferrer a, A. V. Lavrinenko, V. M. Shalaev, and A. Boltassev a, \"Towards CMOS-\ncompatible nanophotonics: Ultra-compact modulators using alternative plasmonic materials,\" Opt. Expres s 21, 27326-27337 \n(2013) \n21. H. W. H. Lee, S. P. Burgos, G. Papadakis, and H.  A. Atwater, \"Nanoscale conducting oxide plasmonic slot waveguide \nmodulator,\" in Frontiers in Optics 2013, I. Kang, D . Reitze, N. Alic, and D. Hagan, eds., OSA Technical  Digest (online) (Optical \nSociety of America, 2013), paper FTu4E.3. \n22. J. Gosciniak and D.T.H. Tan, “Graphene-based wa veguide integrated dielectric-loaded plasmonic elec tro-absorption \nmodulators,” Nanotechnology 24, 185202 (2013). \n23. A. Melikyan, L. Alloatti, A. Muslija, D. Hiller kuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van \nThourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Koh l, W. Freude, and J. Leuthold, \"High-speed plasmoni c phase \nmodulators,\" Nature Photonics 8, 229–233 (2014). 24. J. Gosciniak, S.I. Bozhevolnyi, \"Performance of thermo-optic components based on dielectric-loaded surface plasmon \npolariton waveguides,\" Scientific Reports 3, 1803 (2 013). \n25. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A . Dereux, “Thermo-\noptic control of dielectric-loaded plasmonic wavegu ide components,” Opt. Express18(2), 1207–1216 (2010 ). \n26. A. V. Krasavin, A. V. Zayats, and N. I. Zhelude v, \"Active control of surface plasmon–polariton wav es,\" J. Opt. A: Pure \nAppl. Opt. 7, S85–S89 (2005). \n27. Wangshi Zhao and Zhaolin Lu, ''Nanoplasmonic op tical switch based on Ga-Si3N4-Ga waveguide,'' Opti cal Engineering 50 , \n074002 (2011). \n28. Luke A. Sweatlock and Kenneth Diest, \"Vanadium dioxide based plasmonic modulators,\" Opt. Express 20 , 8700-8709 \n(2012) \n29. B. A. Kruger, A. Joushaghani, and J.K. S. Poon, \"Design of electrically driven hybrid vanadium diox ide (VO 2) plasmonic \nswitches,\" Opt. Express 20 , 23598-23609 (2012) \n30. Kelvin J.A. Ooi , Ping Bai, Hong Son Chu and Lay Kee Ang, \"Ultracompact vanadium dioxide dual-mode p lasmonic \nwaveguide electroabsorption modulator,\" Nanophotoni cs 2(1), 13–19 (2013). \n31. A. Joushaghani, B. A. Kruger, S. Paradis, D. Ala in, J. S. Aitchison and J. K. S. Poon, “Sub-volt br oadband hybrid plasmonic-\nvanadium dioxide switches,” Appl. Phys. Lett. 102 , 061101 (2013). \n32. Jin Tae Kim, \"CMOS-compatible hybrid plasmonic m odulator based on vanadium dioxide insulator-metal phase transition,\" \nOpt. Lett. 39, 3997-4000 (2014) \n33. H.M.G. Wassel, Daoxin Dai, M. Tiwari, J.K. Vala mehr, L. Theogarajan, J. Dionne, F.T. Chong, and T. Sherwood, \n“Opportunities and Challenges of Using Plasmonic Comp onents in Nanophotonic Architectures,” IEEE Journal  on Emerging and \nSelected Topics in Circuits and Systems 2, 154-168 ( 2012). \n34. E. Feigenbaum, K. Diest, and H. A. Atwater, “Un ity-order index change in transparent conducting ox ides at visible \nfrequencies,” Nano Lett.10(6), 2111–2116 (2010). \n35. A. P. Vasudev, Ju-Hyung Kang, Junghyun Park, Xi aoge Liu, and M. L. Brongersma, \"Electro-optical mod ulation of a silicon \nwaveguide with an “epsilon-near-zero” material,\" Op t. Express 21 , 26387-26397 (2013). \n36. Z. Lu, W. Zhao, and K. Shi, “Ultracompact elect roabsorption modulators based on tunable epsilon-ne ar-zero-slot \nwaveguides,” IEEE Photon. J. 4(3), 735–740 (2012). \n37. V. E. Babicheva, I. V. Kulkova, R. Malureanu, K. Yvind, and A. V. Lavrinenko, “Plasmonic modulator b ased on gain-\nassisted metal–semiconductor–metal waveguide,” Phot on. Nanostructures 10(4), 389–399 (2012). \n38. V.E. Babicheva, R. Malureanu, and A.V. Lavrinenko , “Plasmonic finite-thickness metal-semiconductor-m etal waveguide as \nultra-compact modulator,” Photon. Nanostructures 11 (4), 323–334 (2013). \n39. A. Petraru, J. Schubert, M. Schmid, C. Buchal, “F erroelectric BaTiO3 thin-film optical waveguide modu lators,” Appl. Phys. \nLett. 81 , 1375 (2002). \n40. P. Tang, D.J. Towner, T. Hamano, A.L. Meier, B.W . Wessels, “Electrooptic modulation up to 40 GHz in  a barium titanate \nthin film waveguide modulator,” Opt. Express 12 , 5962 (2004). \n41. P. Tang, D.J. Towner, A.L. Meier, B.W. Wessels, “Low-voltage, polarization-insensitive, electro-opt ic modulator based on a \npolydomain barium titanate thin film,” Appl. Phys. Lett. 85 , 4615 (2004). \n42. Pingsheng Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, \"BaTiO3 thin-film waveguide modulator with a low voltage-\nlength product at near-infrared wavelengths of 0.98  and 1.55 µm,\" Opt. Lett. 30, 254-256 (2005). \n43. M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Elect rooptic modulation in thin \nfilm barium titanate plasmonic interferometers,” Na no Lett. 8, 4048 (2008). \n44. S. G. Choi, H. T. Yi, S.W. Cheong, J. N. Hilfiker , R. France, and A. G. Norman, “Optical anisotropy a nd charge-transfer \ntransition energies in BiFeO3 from 1.0 to 5.5 eV,” P hys. Rev. B. 83, 100101–100104(R) (2010). \n45. V.E. Babicheva, A.V. Lavrinenko, “Plasmonic modu lator based on metal-insulator-metal waveguide with  barium titanate \ncore”, Photonics Letters of Poland 5, 57-59 (2013).  \n46. S.H. Chu, D.J. Singh, J. Wang, E.-P. Li, K.P. On g, \"High optical performance and practicality of ac tive plasmonic devices \nbased on rhombohedral BiFeO3,\" Laser & Photonics Revi ews 6(5), 684–689 (2012) \n47. T. Qu, Y. Song, K. Yang, Y. Huang, S. Wu, Z. Ta n, and X. Long, \"High performance electro-optic mod ulator employing a \nthin BiFeO3 film on Au with absorption resonance,\" i n Optical Interference Coatings, M. Tilsch and D. Ris tau, eds., OSA \nTechnical Digest (online) (Optical Society of Ameri ca, 2013), paper MB.6. \n48. I.D. Kim, Y. Avrahami, H.L. Tuller, Y.B. Park, M .J. Dicken, H.A. Atwater, “Study of orientation eff ect on nanoscale \npolarization in BaTiO3 thin films using piezoresponse  force microscopy,” Appl. Phys. Lett. 86 , 192907 (2005). \n49. M.J. Dicken, K. Diest, Y.B. Park, H.A. Atwater, “Growth and optical property characterization of te xtured barium titanate \nthin films for photonic applications,” J. Cryst. Gro wth 300 , 330 (2007). \n50. P.B. Johnson and R.W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370 (1972). \n51. I.D. Rukhlenko, M. Premaratne, and G.P. Agrawal,  “Guided plasmonic modes of anisotropic slot wavegu ides,” \nNanotechnology 23 , 444006 (2012). "    },    {        "title": "0909.4920v1.Space_time_symmetry_violation_of_the_fields_in_quasi_2D_ferrite_particles_with_magnetic_dipolar_mode_oscillations.pdf",        "content": "Space-time symmetry violation of the fi elds in quasi-2D ferrite particles  \nwith magnetic-dipolar -mode oscillations \n  \nE.O. Kamenetskii  \n \nDepartment of Electrical and Computer Engineering, \nBen Gurion University of the Negev, Beer Sheva, 84105, ISRAEL \n \n September 27, 2009 \n \nAbstract \n \nIn magnetic systems with reduced dimensionality , the effects of dipolar interactions allow the \nexistence of long-range ordered phases. Long-range magnetic-dipolar interactions are at the heart of the explanation of many peculiar phenomena observed in nuclear magnetic resonance, ferromagnetic \nresonance, and Bose-Einstein-condensate structures. In this paper we show that magnetic-dipolar-\nmodes (MDMs) in quasi-2D ferrite disks are characterized by symmetry breaking effects. Our \nanalysis is based on postulates about a physical meaning of the magnetostatic-potential function \n),(tr as a complex scalar wave function, which presumes the long-range phase correlations. An \nimportant feature of the MDM oscillations in a ferrite disk concerns the fact that a structure with \nsymmetric parameters and symmetric basic equations goes into eigenstates that are not space-time \nsymmetric. The proper solutions are found based on an analysis of magnetostatic-wave propagation \nin a helical coordinate system. For a ferrite disk, we show that while a composition of two helical \nwaves may acquire a geometrical phase over-running of 2during a period, every separate helical \nwave has a dynamical phase over-running of  and so behaves as a double-valued function. We \ndemonstrate that unique topological structures of the fields in a ferrite disk are intimately related to \nthe symmetry breaking properties of MDM oscillations. The solutions give the MDM power-flow-\ndensity vortices with cores at the disk center and azimuthally running waves of magnetization. One can expect that the proposed models of long-range ordered phases and space-time violation \nproperties of magnetic-dipolar interactions can be used in other magnetic structures, different from \nthe ferromagnetic-resonance system with reduced dimensionality.  \nPACS: 76.50.+g; 68.65.-k; 11.30.Er \n   \n \n \n \n   \n \n   2 \n \n1. Introduction    \n \nSymmetry violation effects are considered as powerful concepts for many developments in \nmagnetism. In particular, unique magnetoelect ric (ME) properties – the coupling between the \nmagnetization and polarization vectors – in some magnetic crystals, arise from dynamical symmetry breakings [1 – 3]. There are also the symmetry violation effects closely related to the vortex states in \nconfined magnetic structures. Different characteristic scales in magnetic dynamics – the scales of the \nspin (exchange interaction) fields, the magnetosta tic (dipole-dipole interaction) fields, and the \nelectromagnetic fields – may define different vortex states in confined magnetic structures [4]. In a \nview of recent studies of the magnetic-dipolar-mode (MDM) oscillations in quas i-2D ferrite disks [5 \n– 12], dynamical symmetry breaking effects in such structures can be a subject of a special interest. An important feature of the MDM oscillations in a ferrite disk concerns the fact that a structure with \nsymmetric parameters and symmetric basic equations goes into eigenstates that are not space-time \nsymmetric.      The dynamical symmetry breaking effects and vortex solutions in MDM [or magnetostatic (MS)] \noscillations are strongly  connected with understanding ph ysics of magnetic dipole-dipole \ninteractions in low-dimensional magnetic systems.  The dipolar interactions, normally weak enough \nto be ignored in bulk magnetic materials, play an  essential role in stabilizing long-range magnetic \norder in quasi-2D systems. Such interactions represent a topical problem in a condensed matter \ntheory. The long-range phase correlations among different parts of a confined magnetic structure are at the heart of the explanation of many peculiar phenomena observed in nuclear magnetic resonance \n(NMR), ferromagnetic resonance (FMR), and Bose-Einstein-condensate (BEC) structures. In spite \nof the fact that nature of these magnetic structures is very different, certain similarities in physical models of magnetic-dipolar interactions can be found. There can be both classical and quantum \nmodels. A number of existing classical models describing the dynamics behavior of the long-range magnetic dipole interaction do not give a comprehensive solution of the problem since cannot \nexplain the reason for the large-scale magnetic ordering and so leaves open the question of long-range phase correlations [13]. To explain such long-range phase correlations, some quantum models \nhave been used. In these models, the role of quantum entanglement in the magnetic-dipolar \ninteractions arises as an important factor. In confined magnetic structures, macroscopic entanglement of a quantum many-spin system [14] can be considered to be caused by the geometric \nphases [15, 16].  \n     Recent studies of magnetic-dipolar interactions in a quasi-2D ferrite disk revealed unique properties of eigenmode oscillations. The MDMs ar e characterized by energy eigenstates [5, 6], \ngauge electric fluxes and eigen electric (anapole) moments [7]. Special vortex characteristics of \nMDMs in thin-film ferrite disks were found numeri cally and analytically [8, 9]. The obtained results \ngive a deep insight into an explanation of the experimental multiresonance absorption spectra shown \nboth in well known previous [17, 18] and new [10 – 12] studies. In a view of these unique spectral \nproperties, a detailed analysis of the dynamical symmetry breaking effects in MDM oscillations appears as a very important subject. In this paper, we show that the MDM oscillations in a ferrite \ndisk are macroscopically entangled states associated with geometric phases. To come to such a \nconclusion, we make analytical studies of the MDM spectra in cylindrical and helical coordinate systems.  We demonstrate that unique topological structures of the fields in a ferrite disk are \nintimately related to the symmetry breaki ng properties of the MDM oscillations.   3    The paper is organized as follows. The paper begins with Section 2 giving an analysis of the \nknown models for long-range magnetic-dipolar interactions in confined magnetic structures. Section \n3 is devoted to spectral characteristics of magnet ic-dipolar modes in a normally magnetized quasi-\n2D ferrite disk analyzed in cylindrical and helical coordinate systems. Based on such spectral characteristics, unique topological properties of th e MDM fields are shown in Section 4. In Section \n5 we discuss the symmetry breaking effects of the MDM oscillations in a ferrite disk. The paper will \nbe concluded by a summary in Section 6.  \n2. The models of long-range magnetic-dipolar interactions in confined magnetic structures \n \n2.1 Classical models \n  \n    It is clear that classically, distant magnetic dipolar fields can be modeled as a sum of the fields produced by the magnetic dipoles. Let us consider  localized classical magnetic dipoles. Such a \ndipole placed in point j and having a magnetic moment \njM\n creates in point j a magnetic field \n \n                                                       \n3 5 3\njjj\njjjj jj j\nrM\nrrr MH\n  \n\n,                                                      (1) \n \nwhere jjr is a radius-vector connecting points  j and j. If in a point j, another dipole having a \nmagnetic moment jM\n is placed,  it is affected by a torque  \n                                                        \n                                                                   H MTj\n .                                                             (2) \n \nInteraction energy for these two magnetic dipoles is  \n \n                                        \n3 5 3\njjj j\njjjj j jj j\nj jjrM M\nrr Mr MH M\n\n \n  \n\n .                             (3)  \n \nOne can find energy of magnetic interactions for all the magnetic moments in a sample as  \n                                                                \n \njjjj\njMW 21.                                                    (4)             \n \nThis classical interpretation of interaction between magnetic dipoles cannot explain, however, the reason for magnetic ordering [13] and so leaves open the question of long-range phase correlations  \nfor magnetic-dipolar interactions in a confined magnetic structure. \n    A classical model described by Eqs. (1) – (4) can be analyzed numerically. The simplest possible numerical model of dipolar interactions involves a discrete lattice of classical spins and direct \nsummation of their magnetic fields. In Ref. [19], authors used the discrete dipole approximation – a \nnumerical approach based on a model involving N discrete classical magnetic dipoles. The approach \n– viewed as a discrete version of the Landau-Lif shitz equation – involves a solution of the coupled  4Larmor equations of the individual magnetic dipo les with all the fields (dipole, exchange, and \nmagnetic-anisotropy) acting on them. In this approximation, the dipole fields are considered as \n\"pure\" magnetostatic fields. The problem is reduced to solving a system of linear equations. One \nobtains the eigenfrequencies of the resonant modes and the eigenvectors are the relative amplitudes of excitation of the individual dipoles. Similar micromagnetic strategies are used in Refs. [20], \nwhere the solutions are obtained for the spatiall y nonhomogeneous dipolar field in nonellipsoidal \nmagnetic samples. In the models, used both in Refs. [19] and [20], the concept of phenomenological magnetization is introduced. The boundary conditio ns for the dipolar-mode fields are imposed on \nthe magnetization and it is supposed that there exist the long-range  magnetization wave \npropagation . One has to note, however, that in neglect of the exchange interaction (when the system \ndoes not show the space dispersion properties), the Landau-Lifshitz equation contains only the time \nderivative of magnetization and so there is evident inconsistency in solutions of the dipolar-mode \nspectral problem obtained with use of the boundary  conditions for magnetization. Certainly, from a \nspectral theory it is known that in a formulation of the boundary-value problem, the form of \nhomogeneous boundary conditions should be in correspondence with to the form of a self-conjugate \ndifferential operator (see e. g. [21]). It is also well known that the amplitude of the dynamic magnetization is not fully specified at the boundaries of a magnetic system by usual electrodynamic \nboundary conditions [22]. \n    Another classical approach in analyzing a long-range mechanism of the dipole-dipole interaction is based on consideration of a magnetic medium as a continuum. Contrary to an exchange spin \nwave, in magnetic-dipolar waves the local fluctuation of magnetization does not propagate due to \ninteraction between the neighboring spins. When  field differences across the sample become \ncomparable to the bulk demagnetizing fields the lo cal-oscillator approximation is no longer valid, \nand indeed under certain circumstances, entirely new spin dynamics behavior in a magnetic medium \ncan be observed. This dynamics behavior in a ma gnetic sample is the following. Precession of \nmagnetization about a vector of a bias magnetic  field produces a small oscillating magnetization \nm \nand a resulting dynamic demagnetizing field H\n, which reacts back on the precession, raising the \nresonant frequency. In the continuum approximation, vectors H\n and m are coupled by the \ndifferential relation: \n \n                                                                m H\n  4 ,                                                      (5)                               \n \nwhere  \n \n                                                                    H\n                                                               (6) \n \nand  is a MS potential. This, together with the Landau-Lifshitz equation, leads to complicated \nintegro-differential equations for the mode solutions in a lossless magnetic sample.  \n    For calculation, the formulation based on the MS-Green-function integral problem for \nmagnetization m was suggested and used in Refs. [23 – 25]. In this case one solves \"pure static\" \nMS equations for a dipolar field. It is supposed that the sources of a MS field are both volume \n\"magnetic charges\", arising from m , and surface \"magnetic charges\", arising from discontinuity \nof the normal component of m on the surface of a ferrite sample. The MS potential  is defined \nbased on integration of the MS Poisson equation \n  5                                                                     m 42 ,                                                         (7) \n \nwhere \n                                                                      mm\n .                                                          (8)                  \n      \nFor the edge and volume sources one obtains [22]:  \n                                                \ndSrrrmndVrrrm\nS Vr )( )( \n\n ,                                     (9) \n \nwhere n is the outwardly directed normal.  \n    Such a theoretical analysis of the RF magnetization eigenvalue problem encounters a significant \ndifficulty due to the absence of exact information of the boundary conditions for RF magnetization \nm since, as we discussed above, in classical electrodynamics the boundary conditions are imposed \non the normal components of the magnetic induction and the tangential component of the magnetic \nfields, but not on the components of magnetization. So the dynamic magnetization at the boundary \nof a magnetic element is undefined from classical electrodynamics. To solve a problem, approximate boundary conditions were derived recently by Guslienko and Slavin [26]. These \neffective boundary conditions, applicable within a macroscopic approach, are generalized from the \nexchange boundary conditions of Rado and Weertman n [27]. They are useful when the regions of \nspatial inhomogeneity in the magnetization are confined near the boundaries of an otherwise uniformly magnetized sample. It becomes evident that the MS spectral problem for long-range \ndipolar-mode fields, being analyzed based on such boundary conditions, is not the self-conjugate problem. In frames of the above continuum-medium classical approach, the question of long-range \nphase correlations for magnetic-dipol ar interactions remains still open. \n    The question on the magnetic-dipolar long-range phase correlations arises not only in ferromagnetic bodies. It appears also in the nuclear-magnetic-resonance (NMR) confined structures. \nIn spite of the fact that nature of NMR and FMR structures is very different, the physical models of \nmagnetic-dipolar interactions in such magnetic systems with reduced dimensionality, allowing the existence of long-range ordered phases, can be quite similar. It was pointed out that classical dipolar \nfields can play a prominent role in NMR of highly magnetized samples at low temperatures. The \nsimplest numerical model of dipolar interactions in NMR structures involves a discrete lattice of \nspins and direct summation of their magnetic fields [28]. A combined effect of spatial inhomogeneities in the dipolar field with corresponding inhomogeneities in magnetization shows the \nexistence of discrete NMR spectra (so called spectral clustering). The analysis predicts the existence \nof a set of MS modes which depend upon sample shape and field gradients [29].       From the above analyzed FMR and NMR problems, one can conclude that for a confined \nmagnetic structure with homogeneous material parameters, the MDMs will appear only if (a) \nexchange interaction takes place and/or (b) an internal DC magnetic field is non-homogeneous. Nevertheless, in 1956, White and Solt showed experimentally that in \"big\" (when the exchange \nfluctuations are neglected) spherical ferrite samples, having homogeneous internal DC magnetic \nfield, the MDMs occur [30]. Walker obtained analytical solutions for such MDMs in ferrite spheroids [31]. To solve the problem, Walker used the continuum approximation based on the \nknown [from the linearized local (non-exchange-interaction) Landau -Lifshitz equation] permeability  6tensor  [13]. The egenvalue problem was formulated based on the differential-operator equation \nfor a \"fictitious\"  MS-potential wave  function (H\n): \n \n                                                                  0) (\n.                                                       (10) \n \nThe boundary conditions were imposed on the MS-potential field and not on the RF magnetization. \nIn such a spectral problem, there are MS-potential propagating fields which cause and govern propagation of magnetization fluctuations. In other words, space-time magnetization fluctuations are corollaries of the propagating MS-potential fields, but there is no the magnetization-wave spectral \nproblem. Similar MS-wave approach was used in studies of absorption spectra in NMR samples \n[32]. An analysis of the MDM boundary-value problem based on the second-order differential equation (10) does not have evident contradictions since the boundary conditions for the MS-\npotential wave function are in correspondence with to the form of a differential operator. \nNevertheless, the physical meaning of the MS-potential wave function \n),(tr  (which presumes the \nfact of the long-range phase correlations) in confined magnetic structures is unclear from classical \nelectrodynamics models. \n \n2.2. Long-range phase correlation and macroscopic quantum entanglement  \n  \n    Generally, in classical electromagnetic problems for time-varying fields, there are no differences between the methods of solutions: based on the field representation or based on the potential \nrepresentation of the Maxwell equations. For the wave processes, in the field representation we \nsolve a system of first-order partial differential equations (for the electric and magnetic vector fields), while in the potential re presentation we have a smaller number of second-order differential \nequations (for the scalar electric or vector magnetic potentials). The potentials are introduced as \nformal quantities for a more convenient way to solve the problem and a set of equations for potentials are equivalent in all respects to th e Maxwell equations for fields [22]. The situation \nbecomes completely different, however, if one supposes to solve a boundary-value problem for \nelectromagnetic wave processes in small samples of a strongly temporally dispersive magnetic medium [33]. In this case one has MS waves. There are the magnetic-dipole oscillations [13]. The \nfact that in the MS-wave processe s one has negligibly small variati on of the electric energy [33] \nraises the questions about the nature of the RF electromagnetic fields in small ferrite samples. In particular, the physical meaning of the electromagnetic power flow (the Poynting vector) becomes \nunclear since for MS-wave processes there are no real mechanisms of transformation of the curl \nelectric field to the MS-potential magnetic field. For magnetic samples with the MS resonance behaviors in microwaves, the spectral problem cannot be formally reduced to the complete-set \nMaxwell-equation representation. A \"fictitious\" MS-potential wave function \n, which describes \nMS waves in small ferrite samples,  does not have a proper justification in classical electromagnetic \nproblems.          \n    The fact that proper classical interpretation of interaction between magnetic dipoles in a confined \nmagnetic structure cannot explain the reason for magnetic ordering, leaves open the question of \nlong-range phase correlations described by MS-potential wave function ),(tr . At the same time, \nsuch a wave function is not properly related to exchange-interaction spin waves. It is well known \nthat magnetostatic ferromagnetism has a character essentially different from exchange ferromagnetism [13, 20, 34]. The MDM spectral pr operties shown in Refs. [5 – 7] are based on  7postulates about a physical meaning of MS-potential functions ),(tr as complex scalar wave \nfunctions with energy-eigenstate orthogonality conditions. The model [5 – 7], in which a static \ninternal magnetic field is regarded as a potential well  for MS-potential wave functions, gives an \nimportant insight into the essence of the MDM localization. With the Hilbert-space spectral \nproperties of scalar wave functions ),(tr , one can explain experimentally observed discrete \nenergy states and eigen electric moments of oscillating MDMs [10 – 12, 17, 18].  \n    From a quantum point of view, it is evident that a ferrite sample is a many-spin system with \nstrong quantum fluctuations. An important goal is  to understand the dynamics of such a many-body \nmacroscopic system. In a view of discussed difficultie s in classical explanations of long-range phase \ncorrelations for dipole-dipole interactions in co nfined magnetic structures, the problem founds \nunexpected solution in recent studies of macr oscopic quantum entanglements in a many-spin \nsystem. Entanglement is a striking feature of quantum mechanics revealing the existence of nonlocal \ncorrelations among different parts of a quantum system. It appears that when long-range phase correlations for dipole-dipole interactions in a quasi-2D ferrite disk take place, one has certain \nentangle states for precessing spins. The entangled many-body states of a \"big\" (when sizes of a \nsample are much larger than characteristic sizes of the exchange-interaction properties) confined magnetic system may suggest new types of magnetic-dipolar collective phenomena. When an \nintense homogeneous DC magnetic field aligns all the spins of a ferromagnet along its direction, a \nferromagnetic sample is characterized by an unen tangled (or product) state. When, however, a spin-\nchain system with a long-range dipole-dipole interaction is placed into a nonhomogeneous DC \nmagnetic field, the entanglement can occur [35]. Another situation of spin entanglement can be \ncaused by the geometric phases. It was shown that the concurrence for the entanglement of two distinguishable spins can be formulated in terms of the Berry phase acquired by the spins when each \nspin is rotated about the quantization axis [15, 16, 36].  \n    For our studies of long-range phase correlations, the most interesting model is a model of spin entanglement due to geometric phases. In a quasi-2D ferrite disk, the MDMs are characterized by \ndiscrete energies of macroscopically distinct stat es. Entanglement of interacting spins is strongly \ncorrelated with macroscopic properties of these distinct states and the many-spin systems are \nregarded as systems which are arranged on topological structures. The fact of macroscopic quantum \nentanglement for long-range magnetic-dipolar inte ractions in a quasi-2D  ferrite disk becomes \nevident from an analysis of the MDM spectral problems.   \n3. Magnetic-dipolar modes in a normally magnetized quasi-2D ferrite disk  \n A phenomenological theory can provide an important guidance in understanding the macroscopic \nproperties of a many-body system. Our phenomenological theory is based on an analysis of spectral \nproperties of MS-potential wave functions in quasi-2D ferrite disks. In such an analysis, one becomes faced, however, with nonintegrability (path dependence) of the problem. Such \nnonintegrability appears because of a special phase factor on a lateral border of a normally \nmagnetized ferrite disk.      In an initial formal assumption of separation of variables for MS-potential wave functions in a \nquasi-2D ferrite disk, a spectral problem in cylindrical coordinates \n,,rz  is formulated with respect \nto membrane MS functions (described by coordinates ,r) with amplitudes dependable on z \ncoordinate. For a dimensionless membrane MS-potential wave function ~, the boundary condition \nof continuity of a radial component of the magnetic flux density on a lateral surface of a ferrite disk \nof radius  is expressed as [6, 7]:   8 \n                                                 \n    \n\n\n\n\n\n\n\n\n\n\nra\nr rir r   ~ ~ ~\n,                              (11) \n \nwhere  and a are, respectively, diagonal and off-diagonal components of the permeability tensor \n. The term in the right-hand side (RHS) of Eq. (11) has the off-diagonal component of the \npermeability tensor, a, in the first degree. There is also the first-order derivative of function ~ \nwith respect to the azimuth coordinate. It means that for the MS-potential wave solutions one can \ndistinguish the time direction (given by the direct ion of the magnetization precession and correlated \nwith a sign of a) and the azimuth rotation direction (given by a sign of ~). For a given sign \nof a parameter a, there are different MS-potential wave functions, )(~ and )(~, corresponding to \nthe positive and negative directions of the phase va riations with respect to  a given direction of \nazimuth coordinates, when 2 0 . Let, for a given direction of a bias magnetic field, a certain \nazimuthally running magnetostatic wave acquires a phase 1 after rotation around a disk. For an \nopposite direction of a bias magnetic field such a phase will be 2. It is evident that 2 1  \nand there should be n 22 1   or  n . Quantities n are odd integers. This follows from \nthe time-reversal symmetry breaking effect. A system  comes back to its initial state after a full 2 \nrotation. But this 2rotation can be reached if both partial rotating processes, with phases 1 and \n2, are involved. So minimal 1n  and, generally, quantities n are odd integers. From the above \nconsideration, one may come to conclusion that for a given direction of a bias magnetic field, a \nmembrane function ~ behaves as a double-valued function.  \n    To make the MS-potential wave functions single-valued and so to make the MDM spectral \nproblem analytically integrable, two approaches were suggested. These approaches, distinguishing \nby differential operators and boundary conditions used for solving the spectral problem, give two \ntypes of the MDM oscillation spec tra in a quasi-2D ferrite disk. \n \n3.1. G- and L-mode magnetic-dipolar oscillations in a ferrite disk: A cylindrical coordinate \nsystem \n \nIn frames of the first approach, we describe the spectral problem by the second-order differential-\noperator equation [5 – 7]  \n \n                                                            0~ )(ˆ 2  G ,                                                           (12)                            \n \nwhere  \n                                                                  2 ˆ\n  G ,                                                               (13)                             \n \n2\n is the two-dimensional (with respect to in-plane coordinates) Laplace operator, ),(~r is a \ndimensionless membrane MS-potential wave function within the domain of definition of operator \nGˆ, and  is a propagation constant along z axis )  ~( zie . Operator Gˆ is positive definite for \nnegative quantities . Outside a ferrite region Eq. (12) becomes the Laplace equation ( 1 ).  9Double integration by parts on square S – an in-plane cross-section of a disk structure – of the \nintegral \nSdS G*~ )~ˆ(  gives the boundary conditions for self-adjointess of operator Gˆ. The \ncorresponding boundary conditions for a disk of a radius  are: \n     \n                                                          0~ ~\n \n\n\n\n\n\n\n   r r r r  .                                           (14) \n \nFunctions )(~r , being single-valued functions, are described by the Bessel functions of integer \norders. An orthogonal spectrum of oscillations in a ferrite disk is obtained when one solves the \ncharacteristic equation for MS waves in an axially magnetized ferrite rod [arising from Eq. (14)]:  \n  \n                                                                \n0 )(21\n\n\nKK\nJJ,                                                   (15) \n \nwhere  K KJJ    and , , ,  are the values of the Bessel functions of an order  and their derivatives \n(with respect to the argument) on  a lateral cylindrical surface ( r ),  together with the \ncharacteristic equation for MS waves in a normally magnetized ferrite slab: \n                                                                  2tan  1d,                                                (16) \n \nwhere d is a disk thickness. Solutions for membrane MS-potential wave function ),(~r, satisfying \nthe second-order differential equation (12) with operator Gˆ, we will conventionally call as G-mode \nmagnetic-dipolar oscillations. The G-mode oscillations are characterized by the orthogonality \nrelations with energy eigenstates  [5]. The boundary condition (14) is a so-called essential boundary \ncondition [6]. It is very importan t to note, however, that this bo undary condition does not satisfy the \ncondition of continuity of the magnetic flux density on a lateral surface of a disk [see Eq. (11)]. To \nsettle the problem, one should impose a certain boundary phase factor  which is described by \nsingular edge wave functions. On a lateral border of a ferrite disk one has the following \ncorrespondence between a double-valued functions ~ and a single-valued functions ~[7]:  \n \n                                                                     r r ~ ~,                                               (17) \n \nwhere  \n        \n                                                                      \niqef                                                          (18) \n \nis a double-valued function. The azimuth number q is equal to 21 and for amplitudes we have \n f f  and f = 1. Function  changes its sign when  is rotated by 2 so that 12 iqe .  10As a result, one has the energy-eigenstate spectr um of MDM oscillations with topological phases \naccumulated by the boundary wave function . The topological effects become apparent through \nthe integral fluxes of the pseudo-electric fields [7 ]. There should be the positive and negative fluxes \ncorresponding to the counterclockwise and clockwis e edge-function chiral rotations. The different-\nsign fluxes are inequivalent to avoid cancellation. Ev ery MDM in a thin ferrite disk is characterized \nby a certain energy eigenstate and different-sign quantized fluxes of the pseudo-electric fields which are energetically degenerate. The spectral theory, developed based on orthogonal singlevalued \nmembrane functions \n~ and topological magnetic currents, shows the magnetoelectric effect from a \nviewpoint of the Berry phase connection. From the theory of G-modes, it follows that a \nmacroscopic-size ferrite disk may behave as a single quantum-like particle with the observable \nenergy eigenstates and eigen electric moment properties of oscillating modes [5 – 7, 10 – 12]. It is \nvery important to note that for the  G-MDMs, the energy orthogonality relations one has only for \nspectra with respect to the DC bias magnetic field and at a constant oscillating frequency [6].    \n    In the second approach, we formulate th e spectral problem for MS-wave function with the \nboundary condition using continuity of the magnetic flux density on a lateral surface of a disk. There is a so-called natural boundary condition [6]. In th is case, one may suppose that there will not be \nsingular edge wave functions. The spectral problem is described by a differential-matrix-operator equation [5 – 7]    \n \n                                                                \n 0~~\n ˆ ˆ \n\n\n\nBRi L\n,                                                   (19) \n \nwhere ~ is a dimensionless membrane MS-potential wave function (different from membrane \nfunctions ~), B~\n is a dimensionless membrane function of a magnetic flux density. In Eq. (19), Lˆ \nis a differential-matrix operator: \n \n                                                               \n\n\n\n\n\n\n\n0ˆ1\nL ,                                                    (20) \n \n(subscript  means correspondence with the in-plane, ,r, coordinates),  is the MS-wave \npropagation constant along z axis )  ~\n  ,  ~(  zi zieBB e   \n, and Rˆ is a matrix: \n \n                                                                 \n\n\n\n00ˆ\nzz\neeR\n,                                                         (21) \n                                                            \nwhere ze is a unit vector along z axis. Continuity of functions ~ and B~\n on a lateral surface of a \nferrite disk give self-adjointess of operator Lˆ. Solutions satisfying the firs t-order differential-matrix \noperator Lˆ we will conventionally call as L-mode magnetic-dipolar oscillations . There is an open \nquestion, however, about singlevaluedness of MS-potential wave functions for the L-mode solutions. \n    The spectral problem described by Eq. (19) pr esumes the possibility of separation of variables. In \nframes of such a presumption, the L-MDMs are normalized to the density of the power flow along z  11axis in an axially magnetized ferrite rod [5]. This mode normalization is not physically well \njustified, however. It is evident that for the MS-wave process in an axially magnetized ferrite rod \ndescribed by functions ~ and B~\n, one has the longitudinal phase variations along z axis (defined by \nthe propagation constant ) together with azimuth phase variation [defined by the RHS term in Eq. \n(11)]. This results in appearan ce of helical waves with a combined effect of longitudinal and \nazimuth power flows. Proper integrable solutions for L-mode functions ~ should be obtained based \non an analysis of the MDM propagation in a helical coordinate system. Such an analysis will give us \nevidence for the symmetry breaking effects of MDMs in a ferrite disk.  \n \n3.2. MDMs in a helical coordinate system \n The helices are topologically nontrivial structures and the phase relationships for waves propagating \nin such structures could be very special. Unlike the Cartesian or cylindrical coordinate systems, in the helical system, two different types of solutions are admitted, one right-handed and one left-\nhanded. Since the helical coordinates are nonorthogonal and curvilinear, different types of helical \ncoordinate systems can be suggested. In our analysis we will use the Waldron coordinate system [37]. As an alternative helical coordinate system, we can point out, for example, the system \nproposed by Lin-Chung and Rajagopal [38]. Waldron showed [37] that the solution of the Helmholtz equation in a helical coordinate system can be reduced to the solution of the Bessel \nequation. With use of the Waldron coordinate system, Overfelt had got analytic exact solutions of \nthe Laplace equation in a helical coordinate system with a reference to the helical Bessel functions \nand helical harmonics for static fields [39].  \n    In the Waldron coordinate system, the pitch of the helix is fixed but the pitch angle is allowed to \nvary as a function of the radius. In cylindrical coordinates \nzr,, , the reference surfaces, which are \northogonal, are given, respectively, by constr ,  const , and constz . In the Waldron helical \nsystem ,,r , we retain the family of cylinders const r  with meaning unchanged, but instead of \nthe parallel planes const z , we use a family of helical surfaces given by 2p constz  , \nwhere p is the pitch. Fig. 1 shows the helical reference surfaces 2pz  for the right-handed (a) \nand left-handed (b) helical coordinates. Coordinate  is measured parallel to coordinate z from the \nreference surface 2pz . The third coordinate surfaces is the set of planes const . We, \nhowever, use the azimuth coordinate  instead of . Coordinate  is numerically equal to \ncoordinate , but whereas  is measured in a plane constz ,  is measured in a helical surface \nconst . Contrary to a cylindrical coordinate system, the helical coordinate system is not \northogonal.       \n    Let us consider a wave process in a helical structure with a constant pitch  p. Geometrically, a \ncertain phase of the wave can reach a point pzr,,  from the point zr,,  in two independent \nways. In the first way, due to translation in the  direction at const r  and const , and, in \nthe second way, due to translation in  at constr  and const . In other words, for any point A \nwith coordinates ),,(r , the point B, being distant with a period of a helix , is characterized by \ncoordinates ) ,,( p r  or by coordinates ),2,( r . The regions between the surfaces \np n np )1( and    , for all integer numbers n, are continuous in a multiply connected space.  \n    To analyze symmetry properties of magnetic-dipolar spin modes we consider now the MS-wave \npropagation in the Waldron right-handed and left-handed helical coordinate systems. For the first  12time, such studies we carried out in Refs. 40, 41. It was supposed [40, 41] that since in the Landau-\nLifshitz equation there are opposite  signs for vector products with respect to the right-handed and \nleft-handed helical coordinate systems, the off-diagonal components of the permeability tensor \nshould have different signs for the right-handed and left-handed helical MS waves. At the present stage of studies, such a statement in Refs. 40, 41 cast,  however, certain doubts. It is clear that in the \nlaboratory frame, the short-range local loop of the electron precession should be completely non-\ncorrelated with a character of the long-range helical MS-wave process in an entire ferrite sample. So one, certainly, can assume that in a helical coordinate system describing MS waves in a sample, the \nquantities of diagonal and off-diagonal components of the permeability tensor remain the same as in \na cylindrical coordinate system and that signs of the off-diagonal components do not have any connection with the type of the helix. It means that the direction of the azimuth phase variation of \nthe entire-sample helical wave and the direction of the local magnetization precession should be \nconsidered as separate notions. Since the direction of the magnetization precession is correlated with the direction of time, the above statement just shows that for a separate MS-potential helical wave \nthe coordinate phase variation is independent on the time phase variation. \n    Let us suppose formally that there exist MS-wave helical solutions in a system characterized by a certain pitch p. For a DC magnetic field directed along z-axis, for both types of helices (right-handed \nor left-handed), one has the permeability tensor:    \n \n                                                           \n\n\n\n\n\n10 000\naa\nii\n,                                                      (22) \n    \nwhere the components  and a can be found from Ref. 13. The signs of the tensor components \nare the same for both right-hand and left-hand helices, but with respect to the frequency and bias-\nfield regions, the quantities of  and a may be positive or negative. For helical MS modes in an \ninfinite axially magnetized ferrite rod, the components of the magnetic flux density are expressed by \nmeans of the components of the magnetic field in the Waldron helical coordinate system ,,r  \n[37, 40] as: \n \n                                            \n\n     , tan sin 1,\ncos, cos\n),(\n0),(\n0),(\n0),(\n0\nLR\nr aLRr LRarLR\na r\nHi H H BH i H BH Hi B\n     \n   \n  \n                   (23) \n \nwhere superscripts R and L mean, respectively, right-handed and left-handed helical coordinate \nsystems. The pitch angles are defined from the relations: \n \n                            rpR0)(\n0 tan tan        and      rpL0)(\n0 tan tan   ,                (24) \n \nwhere 2pp . The quantities 0 tan and p are assumed to be positive.   13    With representation of magnetic field as H\n and with use of transformations in helical \ncoordinates [37, 40], we rewrite Eqs. (23) as: \n                        \n\n\n  . tan111\n2sin2tan, tan1\ncos1, tan1\n).(\n0 ).(\n0),(\n0).(\n0 ).(\n0).(\n0\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nrir rBrirBrirB\naLR\nLRLRaLR\nLRLR\na r\n\n\n\n\n     (25)                    \n \n    Based on Waldron's equation for the divergence [37], we have  \n \n                                          0cos 10   B B\nrrBrrBr\n.                                        (26)  \n \nAfter some transformations we obtain the Walker equation [42] in helical coordinates: \n \n                         0 tan12 tan1 1 12\n).(\n0 22\n02\n22\n2 22\n\n\n\n\n\n  LR\nr rrr r.         (27)     \n \nOutside a ferrite region (where 1 ) Eq. (27) reduces to the Laplace equation in helical \ncoordinates [37, 39]. Following Overfelt's approach [39], we assume that solutions of the Laplace \nand Walker equations are found as \n \n                                                          ZPrR r,, ,                                                  (28) \n \nwhere  \n \n                                                              \n   . exp~, exp~\n  \ni Ziw P\n                                                      (29) \n \nHere the quantities of wavenumbers w and  are assumed to be real and positive. For a chosen \ndirection of z axis, there are four solutions for the MS-potential wave function inside and outside a \nferrite rod: \n \n                                                                \n.  ~, ~, ~, ~\n)4()3()2()1(\n\n\ni iwi iwi iwi iw\neeeeeeee\n\n                                                        (30)                            \n  14    We assume that the helical wave )1(is the forward (propagating in a ferrite rod along the z axis) \nright-hand-helix (FR) MS wave. For this wave we will take  rpR0)(\n0 tan tan   .  Other types \nof helical waves  )4( )3( )2(, ,  will be considered with respect to the wave )1(. It is evident that \nthe wave )2( is the forward left-hand-helix (FL) wave, the wave )3( is the backward (propagating \nin a ferrite rod oppositely to the direction of the z axis) right-hand-helix (BR) wave, and the wave \n)4( is the backward left-hand-helix (BL) wave. For the BR wave ()3(), there is \n rpR0)(\n0 tan tan   , and for the FL wave ()2() and BL wave ()4() there is \n rpL0)(\n0 tan tan   . As an example, Figs. 1 (a) and (b) illustrate, respectively, propagation \nof the FR helical wave )1( and the FL helical wave )2( in helical coordinate systems. \n        For helical waves in a ferrite rod of radius , we have from Eq. (27): \n  \n                                          01 1 2\n22\n22\n\nr pwr rr\nr rr                               (31) \n \ninside a ferrite rod r  and \n \n                                           01 1 2\n22\n22\n\nr pwr rr\nr rr                                (32) \n \noutside a ferrite rod r . Physically acceptable solutions for Eqs. (31) and (32) are possible only \nfor negative quantities . Inside a ferrite region ( r ) the solutions are in the form: \n \n                                                 \n\n\n .   ,   ,   ,   \n21\n4)4(21\n3)3(21\n2)2(21\n1)1(\n\n\n\n\n\n    \ni iw\npwi iw\npwi iw\npwi iw\npw\neer Jaeer Jaeer Jaeer Ja\n\n\n\n\n\n    \n                                      (33) \n \nFor an outside region ( r ) one has: \n \n                                                       \n\n\n .   ,   ,   ,   \n4)4(3)3(2)2(1)1(\n\n\n\n\n\n    \ni iw\npwi iw\npwi iw\npwi iw\npw\neer Kbeer Kbeer Kbeer Kb\n\n\n\n\n\n\n                                           (34)  \n                                                     \nHere J and K are Bessel functions of real and imaginary arguments, respectively. Coefficients \n4,3,2,1 4,3,2,1  and b a  are amplitude coefficients.  15    Now we can obtain proper equations for magnetic flux density components of helical waves. For \nthe FR and BR waves there are  \n \n                  \n . tan111\n2sin2tan, tan1\ncos1, tan1\n0\n00)3,1(0\n0)3,1(0)3,1(\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nrir rBrirBrirB\naaa r\n\n\n\n                 (35) \n \nand for the FL and BL waves we have \n \n                  \n . tan111\n2sin2tan, tan1\ncos1, tan1\n0\n00)4,2(0\n0)4,2(0)4,2(\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nrir rBrirBrirB\naaa r\n\n\n\n                 (36) \n           \n    The above four helical waves should be considered as components of the MS-potential function \nand components of the magnetic flux density. So we have the following four-component functions: \n \n                    \n\n\n\n\n )4()3()2()1(\n][\n\n ,      \n\n\n\n\n )4()3()2()1(\n][\nrrrr\nr\nBBBB\nB ,      \n\n\n\n\n\n)4()3()2()1(\n][\n\n\nBBBB\nB ,      \n\n\n\n\n\n)4()3()2()1(\n][\n\n\nBBBB\nB .                   (37) \n \n     \nSince 0 sinB B Bz  [37], one has from Eqs. (35) and (36) after some algebraic \ntransformations: \n \n                                                 .)4,3,2,1( )4,3,2,1(\n)4,3,2,1(\nzBz\n                                         (38) \n   \nOne can rewrite this equation as: \n  16                                                              \n\n\n\n\n\n\n)4(\n||)3(\n||)2(\n||)1(\n||\n ][\n\nzB .                                                        (39)       \n \n    On a cylindrical surface of a ferrite rod of radius  we have the boundary conditions: \n \n                                       r r          and             rr rr B B .                             (40) \n \nIn a general form, the boundary condition for radial  components of the magnetic flux density [see \nEqs. (35) and (36)] can be written as   \n                                        \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nr rarp ir\n\n 1 .                           (41) \n \n    Based on the above Bessel equations and boundary conditions one obtains, as a result, \ncharacteristic equations for helical MS waves in a ferrite rod. For helical modes )1( and )4( there \nis a characteristic equation in a form:  \n \n                                            \n\n0 21\n\n\n\n\n\n\n pw\nKK\nJJa\npwpw\npwpw.                                    (42) \n \nFor helical modes )2( and )3( one has: \n \n                                            \n\n0 21\n\n\n\n\n\n\n pw\nKK\nJJa\npwpw\npwpw.                                   (43) \n \nIn these equations, the prime denotes differentiation with respect to the argument.  \n    As we discussed above, for any point A with coordinates ),,(r , the point B, being distant with \na period of a helix, is characterized by coordinates ) ,,( p r  or by coordinates ),2,( r . It \nmeans that for any separate  helical wave there is a trivial relation: pw . For this relation, Eqs. \n(42) and (43) are reduced to the equation \n \n                                                            0\n00\n00 21KK\nJJ .                                                       (44) \n \nThis equation has singlevalued solutions, but does not have any sense for our studies. It is evident \nthat in a cylindrical coordinate system, Eq. ( 44) does not reflect the azimuth phase variation \nappearing due to the boundary conditions for the magnetic flux density.      In an analysis of the MDM oscillation resonances  any separate helix is of no interest to us, while \ncombination of two helices may have a physical meaning. From the characteristic equation (42), it  17becomes clear that we have the same quantities of pw  for helical modes )1(and )4(. It means \nthat phases of these two helical waves (propagating in opposite directions of z-axis, but at the same \ndirection of azimuth rotation) are reciprocally correlated and may be linked together. Two \nconstituting objects, )1(and )4(, with non-local connection are considered as entangled helical \nwaves. A similar phase correlation (entanglement) for helical waves )2( and )3(one has from Eq. \n(43). At the same time, waves )1( and )3( as well as waves )2( and )4(  are not linked together \n(not entangled). One can see that at a given radius r for certain phase correlations between helical \nwaves )1(and )4( (as well as for helical waves )2(and )3(), there is the possibility to obtain \ninterference along z-axis. So for certain phase correlations between helical-mode MS-potential wave \nfunctions, there could be nodes and bulges in some points along z-axis. It is necessary to note, \nhowever, that it is not a \"classical\" example of a standing wave. The possible nodes and bulges for the MS-potential wave function along z-axis are due to the entanglement. \n    For reciprocally correlated (entangled) waves, having the same quantities of \npw ,  one can \nconsider the closed-loop phase run of the double-helix  resonance. For waves )1( and )4(, the \nclosed-loop phase way has two parts: the forw ard part of the way is along the FR wave )1( and the \nbackward part of the way – along the BL wave )4(. To have such a closed-loop phase way, we may \nassume that \n \n                                      )4( )1(w w ,   )4( )1( ,   and   )4( )1(p p .                                         (45) \n \nSimilarly, we may have the closed-loop phase way for waves )2( and )3( if we assume that \n \n                                      )3( )2(w w ,   )3( )2( ,   and   )3( )2(p p .                                       (46) \n \nEqs. (45) and (46) describe, in fact, the resonance conditions. One resonance state is due to the \n)4( )1(  phase correlation and another resonance state is due to the )3( )2(  phase \ncorrelation. The resonance )4( )1( , being characterized by the ri ght-hand rotation (with respect \nto a bias magnetic field directed along z-axis) of a composition of heli ces, we will conventionally \ncall as the (+) resonance, while the resonance )3( )2(  with the left-hand rotation of a helix \ncomposition we will conventionally call as the (–) resonance. In a case of the (+) double-helix \nresonance, the azimuth phase over-running of the MS-potential wave functions is in a correspondence with the right-hand resonance rota tion of magnetization in a ferrite magnetized \nalong z-axis by a DC magnetic field [13]. \n    The solutions for the (+) and (–) resona nces can be represented, respectively, as \n \n                                         \n\n\n\n\n)4()1(\n)(] [\n        and       \n\n\n\n)3()2(\n)(] [\n                                       (47)    \n \nIt is also necessary to note that from Eqs. (35) and (36) one has \n \n                                                        )4( )1(\nr rB B      and         )3( )2(\nr r B B .                                   (48)     18 \nAt the same time,  \n \n                                       ,)2( )1( )2( )1(\n  B B B Br r         and            ,)4( )3( )4( )3(\n  B B B Br r   .              (49) \n \n    It is evident that for a smooth infinite ferrite rod, no concrete pitch parameter exists and so all the \nabove analysis of the helical mode propagation bears a formal character and does not have a \nphysical meaning. The problem, however, acquires a real physical meaning in a case of a restricted \nferrite-rod waveguide section – a ferrite disk. In a disk, the quantity of pitch p is determined by the \nvirtual \"reflection\" planes – the planes perpendicular to z-axis, where the nodes or bulges of helical \nMS-potential wave functions can be located. We  introduce now an effective disk thickness effd, so \nthat the planes 2effd z  and 2effdz  are virtual \"reflection\" planes. It is necessary to note that \nthe helical wave )4( is not a really reflected wave with respect to the wave )1( and, vice versa, the \nwave )1( is not a result of reflection of the incident wave )4(. The same assertion one has to \nexpress with respect to helical waves )2(and )3(. The resonant states are the states of the phase \ncorrelated (entangled) helices. Since for the entangled states )4( )1(  and  )3( )2(  there are \ndifferent pitches [see Eqs. (45) and (46)], we have to  consider different quantities (1 4)\neffd and (2 3)\neffd \nfor the (+) and (–) resonances, respectively. For the entangled (double-helix)  states, )4( )1(  or  \n)3( )2( , there should be phase over-running for the azimuth coordinate, but no phase over-\nrunning for the MS-potential wave function along z-axis.  \n    Let us consider the case of for the (+) double-helix resonance, )4( )1( , when the closed loop \nappears in a ferrite-rod section with (1 4)\neffd equal to 2)(p . This resonance state is illustrated in Fig. \n2. For every separate helical wa ve, the phase shift between points a and b (see. Fig. 2) is equal to . \nWe suppose now that along z-axis a mutual phase shift between the waves )1( and )4( is also  \nso that the MS potential 0)4( )1(  in points a and b. The planes 2effd z  and 2effdz  \ncan be characterized as the \"magnetic walls\". At the same time, the waves )1( and )4(are in phase \nwith respect to the azimuth coordinate. One has, as  a result, the condition that all the composition of \nwaves )1( and )4( is running azimuthally counterclockwise without any phase over-running along \nz-axis. Since in the Waldron helical coordinate system we retain the family of cylinders const r  \nwith meaning unchanged with respect to the cylindrical coordinate system, radial variations in a disk \ndescribed by a composition of two helical waves ca n be expressed in cylind rical coordinates with \nreplacing the Bessel function order )4,1()4,1( )4,1(p w  in Eq. (42) by a certain quantity )(. In such \na case, we can introduce a notion of an equivalent membrane function (EMF). For the case shown in \nFig. 2, the azimuth phase over-running for the EMF is characterized by the azimuth wave number \n1)( . It is worth noting that )( shows the geometrical phase variation, while )4,1(w  \ncharacterizes the dynamical phase variation. When a composition of waves )4( )1(  acquires a \ngeometrical phase over-running of 2during a period, every separate wave, )1( or )4(, has a \ndynamical phase over-running of  and so behaves as a double-valued function. There can be \ndifferent combinations of the )1( and )4( double-valued-function branches. Fig. 3 illustrates the  19(+) double-helix resonance, )4( )1( , when (1 4)\neffd is equal to )(p. The MS potential \n0)4( )1(  in points a, b, and c. In this case, as well, we have the geometrical phase \nvariation with the EMF characterized by the azimuth wave number 1)( . One can easily picture \nthe situation of 2)( . In this case, in a disk plane one will see two double-helix loops \ngeometrically shifted to 90. Based on the above consideration for the (+) double-helix resonance, \nwe can rewrite Eq. (42) in a form:  \n \n                                                 0)()(\n21\n)()(\n)()(\n\n\n\n\n\n\n\n\n \n\n\n\n a\nr rKK\nJJ,                             (50) \n \nwhere ,...3 ,2 ,1)(  and )4( )1( )( . This is an equation for the EMF radius variations.  \n    A similar analysis one can make for the (–) double-helix resonance, )3( )2( . Fig. 4 shows \nsuch a resonant state for (2 3) ( )2effdp  . Different combinations of the )2( and )3( double-\nvalued-function branches are possible in a case of the (–) resonance like, for example, to those \ndiscussed above for the (+) resonance. In the (–) double-helix resonance one can also introduce a \nnotion of the EMF and so rewrite Eq. (43) as   \n                                                \n 0)()(\n21\n)()(\n)()(\n\n\n\n\n\n\n\n\n \n\n\n\n a\nr rKK\nJJ,                             (51) \n \nwhere ,... 3 ,2 ,1)(  is the azimuth wave number for EMFs at the (–) resonance and \n)3( )2( )( . \n    It becomes evident, however, that an introduction of the notion of the EMF (and so the possibility \nto reduce a problem to description in cylindrical coordinates) has a physical meaning only for the (+) \ndouble-helix resonance, but not for the (–) double-helix resonance. When one substitutes the \nsolution in the form  \n \n                                                               \n)(\n)( ~)(\n)(\n\n\n\n\n\n\njerJ                                           (52)   \n \ninto Eq. (11), one obtains Eq. (50). It means that solution in a form of Eq. (52) is described by the integer-order Bessel function in cylindrical coordinates. This is the singlevalued solution which \nreflects the azimuth phase variation appearing because of the boundary conditions for the magnetic \nflux density. As a result, we have possibility for separation of variables. The problem becomes \nintegrable. Regarding Eq. (51), it is evident that there are no proper EMF solutions correlated with \nthe boundary conditions for the magnetic flux density. \n    A real ferrite disk is an open thin-film struct ure with a small thickness/diameter ratio. For a real \nthin-film ferrite disk one has a small thickness \nd, so that () () ( 14 )\neff dd  . It means that the virtual \n\"reflection\" planes for helical modes can be found in free space regions far above and below a real \ndisk. These \"reflection\" planes are, in fact, the ma pping planes. Fig. 5 illustrates the (+) resonance in  20a real thin-film disk for the case when (1 4) ( )2effdp   and 1)( .  Fig. 6 shows the (+) resonance \nin a real thin-film disk for the case when (1 4) ( )\neffdp   and ()1.  For an open thin-film structure, \nin a case of the (+) resonance, one can use the method of separation of variables as well. This \nbecomes evident from the following arguments: (a) the possibility to introduce the EMFs inside a \nferrite disk and (b) the fact that the boundary conditions on the planes 2d z , demanding \ncontinuity of  and zB, are the same for every type of a helical wave. For helical waves )1( and \n)4(, the boundary conditions on plane surfaces of  a ferrite disk are the following:    \n \n                                          )1(\n2)1(\n2 \n dzdz ,            )1(\n2)1(\n2 \n dzzdzz B B ,                                 (53a) \n \n                                          )4(\n2)4(\n2 \n dzdz ,           )4(\n2)4(\n2 \n dzzdzz B B .                                  (53b) \n \nFrom Eq. (38) it evidently foll ows that for both helical waves, )1( and )4(, there are the same \nconditions for continuity of  zB.   \n    In an assumption of separation of variables, there are exponentially descending solutions along z \naxis for MS-potential functions in regions above and below a disk. For 2   ,2 dz d z  , and \nr  we describe the MS-potential function by the Bessel equation:  \n \n                                        01 )(\n22)(2)()(\n2)( 2\n\n\n\n\n\n  \n \nrr rr\nr rr ,                       (54) \n \nwhere )( is a real quantity. The solutions are  \n \n                                                           )\n21( )(\n1)()()( dzie e f                                           (55)                            \n \nfor 2dz  and  \n \n                                                            )\n21()(\n2)()()( dzie e f  .                                         (56) \n \nfor 2d z . Coefficients 2 1  and f f  are the amplitude coefficients. Similarly to the method used in \nRefs. [5, 6] one obtains, as a result, a system of two equations. There are the ferrite-rod equation \n(50) and the ferrite-slab equation (see Refs. [5, 6]): \n \n                                                              \n12tan)(d .                                                  (57) \n \nEq. (57) for L-modes is similar to Eq. (16) used for G-modes.  214. The vortex structures and azimuthally running waves of magnetization for L-MDMs  \n \nThe above analysis of the MDM propagation in a helical coordinate system gives a proper \njustification for the L-mode membrane functions ~ and gives possibility to obtain integrable \nsolutions for L-modes in a cylindrical coordinate system. While G-modes are orthogonal ones and \nfor these modes one has the quantum-like soluti ons with energy eige nstates [5 – 7], the L-modes are \nnon-orthogonal modes and solutions for these modes are classical-like. For L-modes one can \nobserve the field structures in any local point of a ferrite disk [8, 9].  \n    Because of separation of variables in a cylindrical coordinate system, the MS-potential wave \nfunction for L-mode can be written as \n \n                                                            ) ,(~)(, , ,)( )( )(    r z Cq q q   ,                                       (58)  \n \nwhere ) ,(~\n,)(rq  is a dimensionless effective membrane function defined as a solution of Eq. (50), \n)(,)(zq  is an amplitude factor defined as a solution of Eq. (57), and C is a dimensional \ncoefficient, ,...3 ,2 ,1)(  is the Bessel-function order, and ,...3 ,2 ,1q  is the number of zeros of \nthe Bessel functions corresponding to different radial variations of the EMF. In cylindrical \ncoordinates, the azimuth and z-axis variations of the wave function are not mutually correlated and \none can impose the boundary conditions independently for the longitudinal z and the in-plane ,r \ncoordinates. In our studies we will consider the case of (1 4)\neffd = 2)(p  and 1)( . Inside a ferrite \ndisk ( 2 2   , dz d r  ) one represents the MS-potential function as \n \n                             tiieez zrCJtzr )( )()(\n1  sin1 cos ,,,\n\n  \n\n\n\n\n\n\n\n\n .                  (59)                            \n \nOutside a ferrite disk, for 2 2   and  dz d r  , one has  \n \n                             tiieez z r CKtzr )( )( )(\n1  sin1 cos  ,,,\n     \n\n\n\n\n  .                    (60)  \n \nThese solutions show the  azimuthally-propagating-wave  behavior for EMFs. There are rotationally \nnon-symmetric  waves. \n    The normalized \"thickness\" functions )(z  for the 1st (q = 1) and 2nd (q = 2) MDMs are shown in \nFig. 7. Fig. 8 illustrates the effective membrane functions ~ for the 1st (q = 1) MDM at different \ntime phases. The calculations were made for a ferri te disk with the following material parameters: \nthe saturation magnetization is  1880  4sM G and the linewidth is Oe 8.0H . The disk \ndiameter is 3D mm and the thickness 05.0t mm. The disk is normally magnetized by the bias \nmagnetic field  49000H Oe. Generally, these data correspond to the sample parameters used in \nmicrowave experiments [10 – 12]. The MDM resonance frequencies, obtained from solutions of \nEqs. (50) and (57), are: f = 8.548 GHz for the 1st MDM and f = 8.667 GHz for the 2nd MDM.   22    Based the known MS-potential function, one defines the magnetic field \nH  for every L-\nmode. One can obtain also components of the magnetization m as \n \n                                                                     m ,                                                         (61) \n \nwhere \n                \n                                                             \n\n\n\n\n\n00 000\naa\nii\n                                                     (62) \n \nis the magnetic susceptibility tensor, and components of the magnetic flux density as   \n                                                                      \n\nB ,                                                        (67) \n \nwhere the permeability tensor is defined by Eq. (22). Parameters of tensors  and  are found \nfrom Ref. [13]. \n    Helical wavefronts of MS-potential wavefunctions presume an azimuth component of the power \nflow density. This azimuth component can be found from an analysis of the power flow density for \nL-modes. In a general representation, for monochr omatic MS-wave processes with time variation \n~tie , the power flow density for a certain magnetic-dipolar mode n (in Gaussian units) is expressed \nas [8]:  \n \n                                                            * *\n16qq qq q B Bip   .                                               (68) \n \nIt was shown [8] that there exist only an azimut h component of the power flow density for EMF. \nFor 1)( , taking into account that )(~)(~ ~n q q r , where i\nq e~)(~, one obtains \n \n                                \n\n  rr\nrr z Crzrpq\na q qq\nq)(~\n)(~)(  8)(~\n),(2 2 \n.                         (69) \n \nThis is a non-zero circulation quantity around a circle r2 . An amplitude of a MS-potential function \nis equal to zero at 0r . For a scalar wave function, this presumes the Nye and Berry phase \nsingularity [43]. Circulating quantities ),(zrpq  are the MDM power-flow-density vortices with \ncores at the disk center. At a vortex center amplitude of qp is equal to zero. As an example, in \nFig. 9 one can see the picture of the power flow density distribution for the 1st (q = 1) L-MDM \ncalculated based on Eq. (69).     In a ferrite sample with MDM oscillations, one has non-homogeneous precession of \nmagnetization. The azimuthally-propagating-wave behavior for the MS-potential EMFs in a quasi-\n2D ferrite disk necessarily presumes the azimuth waves for magnetization \nm. Figs. 10 and 11 show \ngalleries of magnetization m at different time phases for the 1st (q = 1) and 2nd (q = 2) MDMs,  23respectively. It is evident that for a given radius r there is the phase-running variation of \nmagnetization with respect to azimuth angle . At the same time, for a given azimuth angle , the \nmagnetization vectors are in phase or 180 out of phase in the radial direction. Figs. 12 and 13 \nillustrates this statement more explicitly for the 1st (q = 1) and 2nd (q = 2) MDMs, respectively. \nCyclic evolution of magnetization gives the geometric phase. For MDMs in a ferrite disk, one can \nsee the precession dynamics in correlation w ith the cyclic geometrical phase evolution of \nmagnetization m. At a given time phase tq\nres)( , where )(q\nres is the resonance frequency of the q-th \nMDM, the precessing magnetization vector have different phases (with respect to the unit azimuth \nvector e) in different parts of a sample. When (for a given radius inside a disk and a given time \nphase ()q\nrest ) an azimuth angle  varies from 0 to 2, the magnetization vector accomplishes the \n2 geometric-phase rotation. Because of magnetic ordering in a ferrite, the collective states of \ndipolar interacting precessing spins are characterized by strong spin correlations. Due to dipolar \ninteractions, the precessing spins may exhibit macroscopic quantum coherence behavior allowing the existence of long-range ordered phases. This phase ordering assumes that different spin states in \nthe whole-structure MDM share the same spatial long-range MS-potential wave function. The \nmacroscopic magnetization \nm in a given point inside a quasi-2D ferrite disk is a macroscopically \ndistinct state and because of a superposition of such macroscopically distinct states, every MDM can \nbe considered as a macroscopically entangled quantum state. Solid-state spin systems have been \nproposed as possible candidates for large scale realizations of quantum entanglement [14]. There is increasing interest in combined phenomena of the geometric phase and the entanglement of a system \n[15, 16, 36]. The geometrical phase evolution of magnetization \nm in a quasi-2D ferrite disk is the \nBerry phase implemented by a rotating magnetic field of a MDM. Such a rotating magnetic field is \nan attribute of MDM oscillations in a disk [8, 9]. \n    The observed azimuthally running waves of magnetization are rotating states with lack of inversion symmetry dependent on the spin rotational symmetry. The antisymmetric dipole-dipole \ninteraction between two magnetic moments results in the magnon modes which display chirality. \nBoth contributions – the precession dynamics and the geometrical phase evolution – of the magnetization field cannot be measured separately. This differs from the known magnetic system \nwhere in the crystal lattice with lack of inversion symmetry the chiral effects are independent of the \nspin rotational symmetry [44]. The hallmark of chirality is that it is exhibited by systems existing in two distinct states that are time-invariant and interconverted by space inversion. In our case, the \nchiral states are not time-invariant. Evidence for chirality is given by the double-helix behavior of \nMDM oscillations in a thin-film ferrite disk. For ti me reversal (which means an opposite direction of \na bias magnetic field) the double-helix resonance will take place with another set of helical waves. Concerning the above statement on chirality of the MDMs, one can argue that in a usual Faraday \neffect in an unbounded ferrite medium there are also two rotating waves with the forward-back \npropagation which can be considered as waves with lack of inversion symmetry. The main aspect, however, is that these waves are not helical modes since no concrete pitch is determined. \n    It is evident that in a disk center, the magnetization of a MDM has a maximum. So one does not \nhave magnetization vortices for MDM oscillations (see e.g. Ref. [4]). The azimuthally running \nwaves of magnetization are, in fact, circulating magnetization currents. It becomes evident that such \ncirculating magnetization currents with the invers ion symmetry violation s hould be accompanied by \nelectric fluxes piercing the magnetic current rings. Such electric fluxes studied recently in Ref. [7], give a new insight into physics of interactions between MDM ferrite disks [45].  \n  245. The spectra and symmetry breaking effects for MDM oscillations  \n \nAs we noted above, for a bias magnetic field directed along z axis, only for the (+) double-helix \nresonance, )4( )1( , one can introduce the EMFs and consider spectral properties of L-MDMs in \na cylindrical coordinate system. No solutions in a cylindrical coordinate system can be obtained for \nthe (–) double-helix resonance, )3( )2( . Nevertheless, such a resonance exists. A proper \nsolution for this resonance can be obtained only in a helical coordinate system.  \n    When a bias magnetic field is directed contrarily to z axis, Eq. (50) describes the (+) double-helix \nresonance, which is now due to the )3( )2(  phase correlated (entangled) helices. In this case \n,...3 ,2 ,1)(  as well, but )3( )2( )( . Eq. (50) is now an equation for the EMF radius \nvariations in a cylindrical coordinate system for the )3( )2( double-helix resonance. At the same \ntime, Eq. (51) corresponds to the (–) double-helix resonance due to the )4( )1( interference. In \nthis equation, one has ,... 3 ,2 ,1)(  and )4( )1( )( . No solutions in a cylindrical coordinate \nsystem are presumes for the (–) double-helix resonance, )4( )1( , and a proper analysis can be \nmade only in a helical coordinate system. For a bias magnetic field directed contrarily to z axis, one \nobtains the L-MDM spectral characteristics based on soluti on of a system of two equations: Eq. (50) \nand Eq. (57) with )3( )2( )( . Since )4( )1( )3( )2(  , one can suppose that the \nabsorption peak positions for the (+) resonances ( L-MDMs) are different for the cases of a bias \nmagnetic field directed along and contrarily to z axis. This fact should give an evidence for the \nsymmetry breakings for MDM oscilla tions in a quasi-2D ferrite di sk. However, the question about \nexperimental verification of the shift of the L-MDM absorption peaks for reversed directions of a \nbias magnetic field (along or contrarily to z axis) is still open. A thickness d of a real ferrite disk is \nvery small compared to both (1 4)\neffd and (2 3)\neffd. It can be presumed also that there is a very small \ndifference between wavenumbers )4( )1(  and )3( )2( . All this may give negligibly small the \nbias-direction shift of the absorption spectra and very precise experiments should be made to verify \nthis effect. To the best of ou r knowledge, no such experiments were realized till now.    \n    There is, however, an experimental evidence for symmetry breakings of MDM oscillations for a \ngiven direction of a bias magnetic field following from experiments made about 50 years ago by Dillon [17]. In his experiments, Dillon used very well polished YIG-monocrystall disk. When such a \nnormally magnetized disk was placed in a cavity in a region of a homogeneous microwave magnetic \nfield, a multiresonance sharp-peak absorption spectrum was observed [17]. A similar experiment with a well polished YIG-monocrystall disk was repeated by Yukakawa and Abe [18]. One can \nsuppose that these experimental spectra, both in Ref. [17] and in Ref. [18], are the spectra of the (+) \nresonant states: In these resonant states, magnetization precession coincides with direction of the field azimuth rotation and so such spectra should be more easily excited. When, however, Dillon used a well polished ferrite disk, but with a small ra dial flaw, the spectral peaks became split. This \npeak splitting is more evident for high-order modes. Similar peak splitting was observed in \nexperimental spectra in Ref. [10]. In experiments [10], the authors used disks cut from an epitaxy-grown YIG-film wafer. Lateral surfaces of these disks were not specially polished and so had some \nimperfections. The peak splitting experimentally observed in Refs. [10, 17, 18], can be explained as \nfollows. Due to a small radial flaw or small imperf ections on a lateral surface, some transformation \nof one azimuthally rotating MDM to another one can occur in a ferrite disk. As a result, one has \ncoupling between two double-helix-resonance modes, \n)4( )1(  and )3( )2( , which gives  25evident peak splitting. The fact of the presence of two double-helix resonances, )4( )1(  and \n)3( )2( , for a given direction of a bias magnetic field is an indirect evidence for symmetry \nbreakings of MDM oscillations.  \n \n6. Conclusion \n Long-range magnetic-dipolar interactions in confined magnetic structures are not in a scope of classical electromagnetic problems and, at the same time, have properties essentially different from the effects of exchange ferromagnetism. The MDM spectral properties in confined magnetic \nstructures are based on postulates about a physical meaning of the MS-potential function ) ,(\ntr  as \na complex scalar wave function, which presumes the long-range phase correlations.  \n    An important feature of the MDM oscillations in a ferrite disk concerns the fact that a structure \nwith symmetric parameters and symmetric basic equations goes into eigenstates that are not space-time symmetric. In an analysis of spectral properties of MS-potential wave functions in quasi-2D \nferrite disks one becomes faced with nonintegrability (path dependence) of the problem. This \nnonintegrability appears because of a special phase factor on a lateral border of a normally magnetized ferrite disk. One has a system withou t rotational and translational invariance and so \nwithout possibility for separation of variables in the wave equation. To make the MDM spectral \nproblem analytically integrable, two approaches were suggested. These approaches, distinguishing \nby differential operators and boundary conditions for the MS-potential wave function, give two types of the MDM oscillation spectr a. Solutions satisfying the second -order differentia l equation are \nconventionally called as \nG-mode  magnetic-dipolar oscillations. These MDMs are characterized by \nthe orthogonality relations with energy eigenstates and topological magnetic currents. Solutions satisfying the first-order differential-matrix operator we conventionally call as \nL-mode  magnetic-\ndipolar oscillations . Proper integrable solutions for L-mode MS-potential functions can be obtained \nfrom an analysis of the MDM propagation in a helical coordinate system. This analysis discovers unique symmetry properties of MDM oscillations. \n    For helical waves, one has a combined effect  of longitudinal and azimuth power flows. In our \nstudies of MS helical waves, we use Waldron's helical coordinate system. In the Waldron coordinate system, the pitch of the helix is fixed but the pitch angle is allowed to vary as a function of the \nradius. Contrary to a cylindrical coordinate system, the helical coordinate system is not orthogonal. \nInside a ferrite region, the MS-poten tial wave function is described by  the Walker equation in helical \ncoordinates. Outside a ferrite, one has the Laplac e equation in helical coordinates. For a given \nquantity of a pitch, one obtains solutions for four MS helical waves. An analysis shows that there \ncan be two pairs of reciprocally correlated (entangled) helical waves. For every of these pairs one can consider the closed-loop phase run of the double-h elix resonance. In a disk, the quantity of pitch \nis determined by the virtual \"reflection\" planes, where the nodes or bulges of helical MS-potential \nwave functions can be located. For the entangled (double-helix)\n states there should be phase over-\nrunning for the azimuth coordinate, but no phase over-running for the MS-potential wave function \nalong the disk axis. As a result, the helical-wave problem can be reduced to  an integrable problem \nfor effective membrane functions in a cylindrical coordinate system. The solutions give the MDM \npower-flow-density vortices with cores at the disk center and azimuthally running waves of \nmagnetization. \n    The spectral properties of MDM oscillations analyzed in the paper give evidence for symmetry breaking effects. The solutions for MS-potential wave functions show non-time-invariant chiral \nstates of magnetic structures. The theory presente d in the paper clearly explains the experimentally  26observed splitting of the spectral peaks as a result of coupling between two double-helix-resonance \nmodes. The presence of such splitting is an indirect evidence for symmetry breakings of MDM \noscillations.  \n \nAcknowledgement  \n The author is thankful to Michael Sigalov for productive discussions and help in preparation of the paper. \n \nReferences \n [1] V. G. Bar'yakhtar, V. A. L'vov, and D.  A. Yablonskii, Pis'ma Zh. Eksp. Teor. Fiz. \n37, 565  \n       (1983). [2] A. M. Kadomtseva, A. K. Zvezdin, Yu. F. Popo v1, A. P. Pyatakov1, and G. P. Vorob’ev, JETP \nLett. \n79, 571 (2004). \n[3] M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006). \n[4] Electromagnetic, magnetostatic, and exchange-interaction vortices in confined magnetic \nstructures ,  Edited by E.O. Kamenetskii (Research Signpost Publisher, Kerala, India, 2008).  \n[5] E.O. Kamenetskii, Phys. Rev. E, 63, 066612 (2001). \n[6] E.O. Kamenetskii, M. Sigalov, and R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005). \n[7] E.O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007). \n[8] M. Sigalov, E.O. Kamenetskii, and R. Shavit, J. Phys.: Condens. Matter 21, 016003 (2009).  \n[9] E.O. Kamenetskii, M. Sigalov, and R. Shavit, J. Appl, Phys. 105, 013537 (2009). \n[10] E. O. Kamenetskii, A.K. Saha, and I. Awai, Phys. Lett. A 332, 303 (2004). \n[11] M. Sigalov, E.O. Kamenetskii, and R. Shavit, Appl. Phys. B 93, 339 (2008). \n[12] M. Sigalov, E. O. Kamenetskii, and R. Shavit, J. Appl. Phys. 104, 053901 (2008). \n[13] A. Gurevich and G. Melkov, Magnetic Oscillations and Waves  (CRC Press, New York, 1996). \n[14] T. Morimae, A. Sugita, and A. Shimizu, Phys. Rev. A 71, 032317 (2005).  \n[15] E. Sjöqvist, Phys. Rev. A 62, 022109 (2000). \n[16] B. Basu and P. Bandyopadhyay, J. Phys. A: Math. Theor. 41, 055301 (2008). \n[17] J. F. Dillon Jr., J. Appl. Phys. 31, 1605 (1960).  \n[18] T. Yukawa and K. Abe, J. Appl. Phys. 45, 3146 (1974). \n[19] K. Rivkin, A, Heifetz, P. R. Sievert, and J. B. Ketterson, Phys. Rev. B 70, 184410 (2004). \n[20] H. Puszkarski, M. Krawczyk, and  J.-C. S. Levy, Phys. Rev. B 71, 014421 (2005); M. \nKrawczyk and H. Puszkarski, J. Appl. Phys. 104, 113920 (2008).    \n[21] M. A. Naimark, Linear Differential Operators , Vol. 1 (Frederick Unger Publ. Co., New York, \n1968); S. G. Mikhlin, Variational Methods in Mathematical Physics (McMillan, New York, \n1964). \n[22] J.D. Jackson, Classical Electrodynamics , 2nd ed. (Wiley, New York, 1975). \n[23] P.H. Bryant, J. F. Smyth, S. Sc hultz, and D. R. Fredkin, Phys. Rev. B 47, 11255 (1993). \n[24] K.Yu. Guslienko, S. O. Demokritov and B. Hillebrands, and  A. N. Slavin, Phys. Rev. B  66, \n132402 (2002). \n[25] C.E. Zaspel, B. A. Ivanov, J. P. Park and P. A. Crowell, Phys. Rev. B 72, 024427 (2005).  \n[26] K. Yu. Guslienko and A. H. Slavin, Phys. Rev. B 72, 014463 (2005). \n[27] G. T. Rado and J. R. Weertmann, J. Chem. Phys. Solids 11, 315 (1959). \n[28] J. Jeener, Phys. Rev. Lett. 82, 1772 (1999).  27[29] K. L. Sauer, F. Marion, P. J. Nacher, and G. Tastevin, Phys. Rev. B 63, 184427 (2001). \n[30] R. L. White and I. H. Solt, Jr., Phys. Rev. 104, 56 (1956). \n[31] L. R. Walker, Phys. Rev. 105, 390 (1957). \n[32] D.D. Osheroff and M.C. Cross, Phys. Rev. Lett. 59, 94 (1987). \n[33] L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media , 2nd ed. (Pergamon,  \n       Oxford, 1984). \n[34] J. M. Luttinger and L. Tisza, Phys. Rev. 70, 954 (1946). \n[35] D. I. Kamenev, G. P. Berman, and V. I. Tsifrinovich, Phys. Rev. A 73, 062336 (2006).  \n[36] R. A. Bertlmann, K. Durstberger, Y. Hasegawa, and B. C. Hiesmayr, Phys. Rev. A 69, 032112 \n(2004). \n[37] R.A. Waldron, Quarterly J. Mech. Appl. Math. 11, 438 (1958). \n[38] P. J. Lin-Chung and A. K. Rajagopal, Phys. Rev. E 52, 901 (1995). \n[39] P.L. Overfelt, Phys. Rev. E 64, 036603 (2001). \n[40] E. O. Kamenetskii, J. Magn. Magn. Mater. 302, 137 (2006). \n[41] E. O. Kamenetskii,  arXiv:cond-mat/0505717. \n[42] L. R. Walker, Phys. Rev. 105, 390 (1957). \n[43] J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).  \n[44] D. Belitz, T. R. Kirpatrick, and A.  Rosch, Phys. Rev. B 73, 054431 (2006). \n[45] E. O. Kamenetskii, J. Appl. Phys. 105, 093913 (2009). \n \n \n  \n \n  \nFigure captions: \n \nFig. 1. The right-handed (a) and left-handed (b) Waldron's helical coordinate systems. Coordinate  \nis measured parallel to coordinate z from the reference surface 2pz . Arrows illustrate, as an \nexample, the propagation directions of helical waves: (a) the forward right-hand-helix MS wave (the \nwave )1() and (b) the forward left-hand-helix MS wave (the wave )2().  \n \nFig. 2. The (+) resonance caused by the )4( )1(  phase correlation for (1 4)\neffd equal to 2)(p .  \nThe MS potential 0)4( )1(  in points a and b. The azimuth phase over-running for the \nEMF is characterized by the azimuth wave number 1)( . Arrows show directions of propagation \nfor helical MS modes and a direction of rotation of  a composition of helices. When a composition of \nwaves )4( )1(  acquires a geometrical phase over-running of 2during a period, every separate \nwave, )1( or )4(, has a dynamical phase over-running of  and so behaves as a double-valued \nfunction inside a disk. \n \nFig. 3. The (+) resonance caused by the )4( )1(  phase correlation for (1 4)\neffd equal to )(p. The \nMS potential 0)4( )1(  in points a, b, and c.  The azimuth phase over-running for the EMF  28is characterized by the azimuth wave number 1)( . Arrows show directions of propagation for \nhelical MS modes and a direction of rotation of a composition of helices. \n \nFig. 4. The (–) resonance caused by the (2) (3)  phase correlation for (2 3)\neffd equal to ()2 p.  \nThe MS potential (2) (3)0   in points a and b. Arrows show directions of propagation for \nhelical MS modes and a direction of rotation of a composition of helices. \n \nFig. 5. Illustration of the (+) resonance in a real thin-film disk for the case when (1 4) ( )2effdp   and \n1)( . A real ferrite disk is an open thin-film structure with () () ( 14 )\neff dd  . The virtual \n\"reflection\" planes for helical modes are found in free space regions above and below a disk.  \n \nFig. 6. Illustration of the (+) resonance in  a real thin-film disk for the case when (1 4) ( )\neffdp   and \n()1. A real ferrite disk is an open thin-film structure with () () ( 14 )\neff dd  . The virtual \n\"reflection\" planes for helical modes are found in free space regions above and below a disk.  \n \nFig. 7. The normalized \"thickness\" functions )(z  for the 1st (q = 1) and 2nd (q = 2) MDMs.  \n \nFig. 8. The effective membrane functions ~ for the 1st (q = 1) MDM at different time phases. \n \nFig. 9. The power flow density distribution for the 1st (q = 1) L-MDM calculated based on Eq. (69). \n \nFig. 10. Gallery of magnetization m at different time phases for the 1st (q = 1) MDM (arbitrary \nunits). \n \nFig. 11. Gallery of magnetization m at different time phases for the 2nd (q = 2) MDM (arbitrary \nunits).  \n \nFig. 12. Explicit illustration of cyc lic evolution of magnetization for the 1st (q = 1) MDM. When (for \na given radius inside a disk and a given time phase t) an azimuth angle  varies from 0 to 2, \nthe magnetization vector accomplishes the 2 geometric-phase rotation. For a given azimuth angle \n, the magnetization vectors are in phase in the radial direction. \n \nFig. 13. Explicit illustration of cyclic evolution of magnetization for the 2nd (q = 2) MDM. When \n(for a given radius inside a disk and a given time phase t) an azimuth angle  varies from 0 to \n2, the magnetization vector accomplishes the 2geometric-phase rotation. For a given azimuth \nangle , the magnetization vectors are in phase or 180 out of phase in the radial direction. \n \n \n  \n \n  29\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n \n \n \n \n \n \n \n                         \n                     ( a)                                                                                        ( b) \n \n \nFig. 1. The right-handed (a) and left-handed (b) Waldron's helical coordinate systems. Coordinate  \nis measured parallel to coordinate z from the reference surface 2pz . Arrows illustrate, as an \nexample, the propagation directions of helical waves: (a) the forward right-hand-helix MS wave (the \nwave )1() and (b) the forward left-hand-helix MS wave (the wave )2().  \n \n  \n \n  \n \n  \n \n  \n \n  \n \n  30\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n  \n \n  \n \n \n \n \nFig. 2. The (+) resonance caused by the )4( )1(  phase correlation for (1 4)\neffd equal to 2)(p .  \nThe MS potential 0)4( )1(  in points a and b. The azimuth phase over-running for the \nEMF is characterized by the azimuth wave number 1)( . Arrows show directions of propagation \nfor helical MS modes and a direction of rotation of a composition of heli ces. When a composition of \nwaves )4( )1(  acquires a geometrical phase over-running of 2during a period, every separate \nwave, )1( or )4(, has a dynamical phase over-running of  and so behaves as a double-valued \nfunction inside a disk. \n  \n \n   \n(1 4)\neffd 0H\n  31\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n  \n \n \n \n \nFig. 3. The (+) resonance caused by the )4( )1(  phase correlation for (1 4)\neffd equal to )(p. The \nMS potential 0)4( )1(  in points a, b, and c.  The azimuth phase over-running for the EMF \nis characterized by the azimuth wave number 1)( . Arrows show directions of propagation for \nhelical MS modes and a direction of rotation of a composition of helices. \n \n \n   \n \n   \n(1 4)\neffd 0H\n \nc \nb  32\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n  \n \n  \n \n \n  \nFig. 4. The (–) resonance caused by the \n(2) (3)  phase correlation for (2 3)\neffd equal to ()2 p.  \nThe MS potential (2) (3)0   in points a and b. Arrows show directions of propagation for \nhelical MS modes and a direction of rotation of a composition of helices. \n \n  \n \n   \n \n  \n  33\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n  \n \n  \n \n \n  \n \nFig. 5. Illustration of the (+) resonance in  a real thin-film disk  for the case when \n(1 4) ( )2effdp   and \n1)( . A real ferrite disk is an open thin-film structure with () () ( 14 )\neff dd  . The virtual \n\"reflection\" planes for helical modes are found in free space regions above and below a disk.  \n \n    (1 4)\neffd 0H\n  34\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n \n \n \n \n  \nFig. 6. Illustration of the (+) resonance in  a real thin-film disk for the case when \n(1 4) ( )\neffdp   and \n()1. A real ferrite disk is an open thin-film structure with () () ( 14 )\neff dd  . The virtual \n\"reflection\" planes for helical modes are found in free space regions above and below a disk.  \n \n \n  \n \n  \n  (1 4)\neffd 0H\n \nb  35\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n \n \n \n \nFig. 7. The normalized \"thickness\" functions )(z  for the 1st (q = 1) and 2nd (q = 2) MDMs.  \n \n \n     \n \nFig. 8. The effective membrane functions ~ for the 1st (q = 1) MDM at different time phases.  36\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n  \n   \n \n \n     \nFig. 9. The power flow density distribution for the 1\nst (q = 1) L-MDM calculated based on Eq. (69). \n \n  \n  \n \n  \n \n  \n \n  \n \n   37\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n  \n \n  \n \n \n \nFig. 10. Gallery of magnetization m at different time phases for the 1st (q = 1) MDM.  \n \n \n \n   \n \n  38\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n \n \n \n \n \n \nFig. 11. Gallery of magnetization m at different time phases for the 2nd (q = 2) MDM.  \n \n \n \n \n \n    39\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n \n \n \n \n \n \n \n \n \n  \n \n \n \n \n   \n \n \n \n \n \n \n \nFig. 12. Explicit illustration of cyc lic evolution of magnetization for the 1st (q = 1) MDM. When (for \na given radius inside a disk and a given time phase t) an azimuth angle  varies from 0 to 2, \nthe magnetization vector accomplishes the 2geometric-phase rotation. For a given azimuth angle \n, the magnetization vectors are in phase in the radial direction. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  40\"Space-time symmetry violation of the fields in quasi-2D ferrite particles with magnetic-dipolar-\nmode oscillations\", by E.O. Kamenetskii  \n------------------------------------------------------------------------------------------------------------------------- \n \n \n \n \n \n \nFig. 13. Explicit illustration of cyclic evolution of magnetization for the 2nd (q = 2) MDM. When \n(for a given radius inside a disk and a given time phase t) an azimuth angle  varies from 0 to \n2, the magnetization vector accomplishes the 2geometric-phase rotation. For a given azimuth \nangle , the magnetization vectors are in phase or 180 out of phase in the radial direction. \n "    },    {        "title": "1703.07545v1.Coexistence_of_Interfacial_Stress_and_Charge_Transfer_in_Graphene_Oxide_based_Magnetic_Nanocomposites.pdf",        "content": "  \n1 \n Coexistence of Interfacial Stress and Charge Transfer in Graphene Oxide  \nbased Magnetic Nanocomposites  \nAmodini Mishra1, Vikash  Kumar  Singh2 and  Tanuja Mohanty1* \n1School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India, 110067  \n2Solid State Physics Laboratory, Timarpur, New Delhi, India , 110054  \n \nAbstract  In this paper , we establish  the existence of both compressive  stress  and charge transfer \nprocess in  hydrothermally synthesized cobalt ferrite -graphene oxide  (CoFe 2O4/GO)  \nnanocomposite s. Transmission electron microscopy (TEM) results reveal the decoration  of  \nCoFe 2O4  nanoparticles on GO sheets.  Magnetic response of nanocomposite s was confirme  from \nsuperconducting quantum interference device (SQUID) magnetometer measurement . Optical \nproperties of these nanocomposite s were investigated by Raman spectroscopy . Interfacial \ncompressive stress involved in this system is evaluated from observed blue shift of characteristic \nG peak of graphene oxide. Increase in full width half -maximum ( FWHM)  as well as up shift in  \nD and G peaks are clear indicator of involvement of charge transfer process between GO sheets \nand dispersed magnetic nanoparticles.  The effect of charge transfer process is quantified  in \nterms of shifting  of Fermi level of these n anocomposite s. This is evaluated from variation in \ncontact surface potential difference (CPD)  using Scanning Kelvin probe microscopy  (SKPM).   \nXRD spectra of CoFe 2O4/GO confirm the poly crystal line nature o f  CoFe 2O4  nanoparticles .  \nLattice strain estimated from XRD peaks are correlated  to the observed Raman  shift.  \n \nKeywords : Graphene Oxide , Stress , Raman spectra, charge transfer and Fermi level . \n \n \n \n \n   \n2 \n Introduction  \n      Graphene oxide (GO), a derivative of graphene, is an excellent  two dimensional  (2D) flat \nsheet of hexagonally bonded sp2 hybrid carbon atoms on which oxygen functional groups (such \nas hydroxyl, epoxide, carboxyl and carbonyl and hydroxyl groups)  are covalently linked on their \nbasal planes . 1-6 These function al groups attached to the negatively charged GO sheets can act as \nhost for the positively charged ions of nanoparticles  (NPs)  leading to formation of \nnanocomposites. These nanocomposites exhibit unique properties as compared to individual \ncomponents and th erefore find a wide  range of applications in surface -enhanced  Raman \nscattering, sensors, catalysis and optoelectronic devices.7-10 Nanocomposites synthesized by \nhydrothermal route are found to be in the form of dispersion of nucleated nanoparticles on GO \nsheets. It is a well known fact that, magnetic nanoparticles (MNPs) have potential applications in \nthe field of energy storage devices, MRI and magnetic field driven  drug delivery.11-12 \nParticularly, Cobalt ferrite (CoFe 2O4)  NPs have found lots of applicat ions in the field of \ncatalysis and magnetism based nano devices  due to their remarkable chemical and mechanical \nstability, magnetic behavior, low toxicity and biocompatibility in physiological environments.  \n13-15    However, pristine CoFe 2O4 NPs suffers from irreversible aggregation and settling due to \nstrong dipole -dipole interaction which can  be overcome  by employing viscoelastic carrier or \nsurfactant. Particularly two dimensional ( 2D) planar structures like GO sheets are expected to \nsolve this  sedimentation problem by acting as a carrier  which enhances the properties of \nCoFe 2O4 NPs in nanocomposites  forms  and expands its application possibilities. These  \nCoFe 2O4/GO nanocomposite  are considered  as one of the most promising electrode materials due  \nto its high abundance, strong magnetic properties, low toxicity as well as cost effectiveness .16-20 \nIn past few years, although a lot of interest has been developed by different scientific \ngroups on the magnetic properties and applications of t he CoFe 2O4/GO nanocomposite materials, \nyet, studies on surface electronic , interfacial stress  and charge transfer phenomenon  of these \nmaterials are still unexplored. This research report emphasizes on the existence  of charge transfer \nas well as compressive  stress in  CoFe 2O4/GO magnetic nanocomposite which are confirmed \nfrom  Raman spectroscopy, XRD and scann ing Kelvin probe  measurement . The surface  \nelectronic property, particularly shifting of Fermi surface is monitored using scanning Kelvin \nprobe microscopy, wh ere, it is measured in terms of variation in the contact surface potential \ndifference (CPD). The morphology and structure of nanocomposite were examined using   \n3 \n scanning electron microscopy and transmission electron microscopy. Their magnetic  response \nwas studied  using SQUID . \n \nExperimental Methods  \n    Materials  \n      Graphite flakes (99.8 %, 325 mesh) was purchased from Alfa Aesar.Hydrazine hydrate \n(N2H4) and sulfuric acid (H 2SO 4, 95%) are procurred from Sigma –Aldrich.Potassium \npermanganate (KMnO 4), sodium nitrate, (NaNO 3) hydrogen peroxide (H 2O2), ethanol, \nhydrochloric acid (HCl), Cobalt(II) nitrate hexahydrate [Co(NO 3)2·6H 2O], Iron(III) nitrate \nnonahydrate [Fe(NO 3)3·9H 2O], ammonium hydroxide (NH 4OH) and double distilled water were \npurchased from Merck. All  the chemicals are used for experiment without further purification.  \nSynthesis of graphene oxide sheets  \nGraphene oxide (GO) was synthe sized from graphite flakes using modified Hu mmers’ method.21  \n \nSynthesis of CoFe 2O4/GO nanocomposite  \nIn the first step,  graphene oxide (GO) was synthe sized from graphite flakes using modified \nHummers’ method.21  Graphene oxide based cobalt ferrite nanocomposite (CoFe 2O4/GO) was \nprepared by the hydrothermal method using Cobalt(II) nitrate hexahydrate [Co(NO 3)2·6H 2O], \nIron(III) nitrate nonahydrate [Fe(NO 3)3·9H 2O].16 For this purpose, firstly 0.25 g of graphene \noxide powder was added in 80 mL of ethanol and completely dispersed by ultrasonication for 60 \nmin. In the second step, 0.3 g of Co(NO 3)2·6H 2O and 0.9 g of Fe(NO 3)3·9H 2O were dissolved in \n50 mL of ethanol followed by stirring for 3h. The solution was mixed dropwise into the GO \nsuspension with continuous stirring for 5 h. After that, 4.3 g of sodium acetate (CH 3COONa) was \nadded into the mixture under continuous stirr ing. After agitation for 8 h, the mixture solution was \ntransferred to a Teflon -line autoclave. The autoclave was heated under oven at 200 °C for 24 h \nand then cooled down to room temperature. The solid product was separated by centrifugation \nand washed tho roughly with water and absolute ethanol to remove impurities. Finally, the \nproduct was dried in an oven at 50 °C for a full night. The final product was labeled as graphene \noxide based cobalt ferrite nanocomposite (CoFe 2O4/GO). The steps involved during sy nthesis \nprocess of CoFe 2O4/GO nanocomposite are sche matically illustrated in Fig. 1.    \n4 \n  \nFigure 1   Schematic representation of steps involved in the synthesis  of CoFe 2O4/GO. \nnanocomposite.  \nCharacterization   \nThe surface morphology of GO and CoFe 2O4/GO   was investigated  by scanning electron \nmicroscopy (SEM) (Care -Zeiss EVO -40, working voltage 20 kV, Germany) . The elemental \nidentification of CoFe 2O4/GO nanocomposite was confirmed  from energy dispersive X -ray \nanalysis (EDAX).  EDAX measurement was carried out u sing a (Zeiss EVO ED15) microscope \ncoupled with an ( Oxford -X-MaxN) EDX detector. The magnetic properties of this  \nnanocomposite were  investigated at room temperature using a Quantum Design MPMS -7 \nSQUID magnetometer.  From the magnetization versus applied field plot  (M-H), the saturation \nmagnetization (M s), coercivity (H c) and remanence magnetization (M r) was measured. For \nstructural analysis, transmission electron microscopy study was carried out by 200 kV TEM, \nJEOL 2 100F, Japan . X-ray diffraction (XRD) spectra of CoFe 2O4/GO nanocomposite samples \n  \n5 \n were recorded using an X -ray diffractometer (Panal ytical 2550 -PCX -raydiffracto meter). XRD \ndata were collected using Cu -Kα (λ = 0.154 nm) radiation with  2θ  ranging from 10°to  70° at  \nscanning ra te 3° min-1. Optical properties of GO and CoFe 2O4/GO nanocomposite were \ninvestigated using Raman spectroscopy (HORIBA Xplora) having green  laser (λ= 514 nm) \nexcitation with a laser spot size 1 μm. The effect of CoFe 2O4 nanoparticles decoration on the \nFerm i energy level of GO sheets is  monitored  by scanning Kelvin probe microscopy (SKPM, \nKP Technology,  UK).  \nResults and discussion  \nSEM and EDAX Studies  \n SEM image and EDAX spectra analysis of GO and CoFe 2O4/GO nanocomposite thin film was \ncarried out for observation of the surface morphology and identification of the elements present \nin the GO and CoFe 2O4/GO nanocomposite as shown  in Fig.  2. In the SEM image of GO , \ncrumpled sheets like structures are observed , while in the case of CoFe 2O4/GO nanocomposite, \nclustering of CoFe 2O4 nanoparticles on GO sheet is found . \nEDAX spectrum of GO sheets confirms the presence of C, O and Si elements  and that of \nCoFe 2O4/GO nanocomposite indicates the prominent presence of C, O, Co, Fe, and Si elements. \nAdditional Si peak arising in both the cases are from the silicon  substrate. The peaks in the \nEDAX pattern were perfectly assigned  to the elements present in CoFe 2O4/GO composites \nEDAX spectra of GO and CoFe 2O4/GO nanocomposite clearly signify the high purity in \nchemical composition of CoFe 2O4/GO nanocomposite.    \n6 \n  \nFigure 2  SEM image and EDAX spectrum of GO and CoFe 2O4/GO nanocomposite.  \nSQUID Measurement  \n        Magnetic properties of this nanocomposite were investigated using a SQUID. The M -H \nloop for the CoFe 2O4/GO nanocomposite at 300 K (room temperature) is shown   in Fig.  3 (a). At \nroom temperature, the value of saturation magnetization ‘M s’ comes out to be 75.37 emu/g \nwhich is lower than that of corresponding pure bulk CoFe 2O4 (94 emu/g). The remanence \nmagnitude ‘M r’ extracted from the hysteresis loop at the intersections of the loop (shown in the \ninset) with the vertical magnetization axis is found to be 20.05 emu/g. The coercivity Hc obtained \nfrom hysteresis loop is 0.41 kOe for CoFe 2O4/GO nanocomposite22,23 which is quite low thus \nindicating its soft magnetic nature. These CoFe 2O4/GO nanocomposite exhibit a ferromagnetic \nbehavior having small remnant magnetization and coercivity, whi ch is desirable for many \npractical applications that required strong magnetic signals at small applied magnetic fields.  \n  \n7 \n  \nFigure 3  (a) Hysteresis loop(M -H) of CoFe 2O4/GO nanocomposite at room temperature 300 K \n(Inset: Zoom M -H loop of CoFe 2O4/GO nanocompos ite at 300 K). (b) The plot of χ vs. T of \nzero-field-cooling (ZFC) and field-cooling  (FC) for CoFe 2O4/GO nanocomposites.  \n      The presence of superparamagnetic particles was examined using zero -field-cooling (ZFC) \nand field-cooling  (FC) measurements with an applied magnetic field of 100 Oe. The magnetic \nsusceptibility (χ) vs. temperature plot for CoFe 2O4/GO nanocomposite is shown  in Fig.  3 (b). For \nthe zero -field-cooled (ZFC) case, the sample was cooled from 300 K to 2 K and then a magnetic \nfield H = 100 Oe was turned on for magnetization (M) measurements with increasing \ntemperature after ensuring stabilization at each temperature. Upon reaching 300 K, the data were \nsimilarly collected  with decreasing temperature (FC mode) keeping the same applied field. It i s \nclear that FC and ZFC curves show divergence at around 300 K which can be considered as the \nblocking temperature (T b). Below this temperature the material shows ferromagnetic behavior \nabove which it is superparamagnetic in nature.  Above the blocking tem perature, the fine \nnanoparticles lose their hysteresis property as evident from M –H loops.24,25  The magnetic \nmoments follow the direction of the applied magnetic field resulting in low remanence and low \ncoercivity which is the characteristic feature of superparamagnetism.   \nTEM Studies  \n       Microstructure analysis of these composites were carried o ut using TEM, for which in the \nfirst step, ethanol -based  solutions of GO and CoFe 2O4/GO were placed  on carbon -coated  copper \n  \n8 \n grids followed by drying  at room temperature before use. TEM image of GO and CoFe 2O4/GO \nnanocomposite are shown  in Fig. 4 (a) and Fi g. 4 (b) respectively.  \nFig. 4 (a) corresponds to t he appearance  of thin and wrinkled transparent GO sheets. It is \nconsistent with our observati on from the SEM analysis. Fig.  4 (b) exhibits the dispersion of \nCoFe 2O4 NPs on GO sheets. The sheet -like corrugated morphology of GO is also well preserved \nin CoFe 2O4/GO nanocomposite,  and CoFe 2O4 NPs are dispersed  on GO sheet. This type of \nnucleation of magnetic nanoparticles on GO sheets is expected from hydrothermal synthe sis. The \naverage particles size of CoFe 2O4 nanoparticles in CoFe 2O4/GO nanocomposite is about 18 ± 2  \nnm. The line spacing is found to be 0 .24 nm as shown in Fig . 4 (c) The selected area diffraction \n(SAD) pattern of CoFe 2O4/GO nanocomposite is shown in Fig . 4 (d)  where we observe the \ndiffraction rings corresponding to the plane (111), (220) and (311) of CoFe 2O4 as well as a \ndiffraction pattern corresponding to hexagonally arranged carbon atoms in GO sheets.  \n \n \nFigure 4  TEM images of (a) GO sheets, (b) CoFe 2O4/GO nanocomposite. (c) High -resolution \nTEM image of CoFe 2O4/GO nanocomposite and (d) selected area diffraction pattern of \nCoFe 2O4/GO nanocomposite.  \n \n \n  \n9 \n XRD measurement  \n       CoFe 2O4/GO nanocomposite t hin fil m were chara cterized  by X RD (Panal ytical 2550 -PC X -\nray diffracto meter) se t up using Cu Kα radiation (λ=0.154 nm). The data were collec ted betw een \nscattering angle (2θ) f rom 10° to 70° at scanning ra te 3° min-1. The c rystalline n ature of \nCoFe 2O4/GO nanocomposite was iden tified by ana lyzing its X-ray di ffraction (XR D) spectra as \nshown in Fig.  5 (a).  \nXRD spect rum of CoFe 2O4/GO nanocomposite exhibits the polycrystal line nature o f CoFe 2O4 \nNPs having a characteristic peak at 2θ = 35.6° in addition to other peaks of CoFe 2O4 appearing at \n2θ = 18.7° (111), 30.1° (220), 35.6° (311), 43.2° (400), 54.1° (422), 57.3° (511) and 62.9° (440) \n(matched with JCPDS No. 75 -0033 ). X-ray peak broadening analysis was used to calculate the \ncrystalline sizes and lattice strain by the Williamson -Hall (W -H) analysis assuming peak widths \nas a function of 2θ.  \nThe strain induced in powders due to crystal imperfection and distortion is calculated using the \nformula  \n                                                 Δ =  \n                                     (1) \nWhere β is full width half maximum (FWHM) of diffraction peak (in radian) and θ is Bragg’s  \ndiffraction  angle (in degree)  and Δ is lattice strain. The crystallite size was calculated from \nthe X -ray diffraction spectra  using Scherrer's formula where, the crystallite size is inversely \nrelated to   Cos  Considering the fact that  particle size and strain are independent of  each other \nhaving a Cauchy -like form, which in combination are related to FWHM by W -H equation as \nfollows ,                \n                                                  Cos  =   \n  +   \n  Sin                                                                                      (2) \nWhere, th e term Kλ /D represents the Scherrer's particle size distribution. 26,27  Fig. 5 (b) shows \nthe W -H plot for CoFe 2O4/GO nanocomposite . A linear least square fitting  (5% error)  to \nCosvs. Sindata plot yields the value of average crystallite size  (D), and lattice strain  (Δ) \nto be 17 nm and 0.003  respectively. The crystallite size is the good agreement with the observed \nsize of crystallites from TEM measurement and lattice  strain is expected to be compressive  type \nwhich will be discussed in forthcomi ng section.      \n10 \n  \nFigure 5  (a) XRD spectrum (inset Figure for GO) and (b) Williamson -Hall plot (linearly fitted  \ncos vs Sindata) for CoFe 2O4/GO nanocomposite.  \nRaman Studies  \n        The Raman spectra of GO sheets and CoFe 2O4/GO nanocomposite are shown  in Fig . 6. The \nmain features in the Raman spectra of graphene oxide sheets are D and G peaks located at 1345 \ncm−1 and 1587  cm−1 respectively. G band is attributed  to the Brillouin -zone -centered LO and iTO \nphonon mode. D band is attributed  to the double resonance excitation of phonons close  to \nthe K point scattering due to defected on iTO (E2g) phonon in the Brillouin zone.25,26 Spectra \ntaken from the  CoFe 2O4/GO nanocomposite shows a distinct broadening  of the D and G peaks of \nGO sheets from a full width of half-maximum  (FWHM ) of 122 cm−1 to 165 cm−1 and 69 cm−1 to \n77 cm−1 respectively  which  may be due to lattice  strain  stemming  from  the interaction  between  \nGO sheets and CoFe 2O4 magnetic  nanoparticles.28,29 Raman spectra of CoFe 2O4/GO \nnanocomposite show a up shift in Raman peaks position of D and G peaks about  GO sheets. \nThe D peak is shifted from 1345  cm−1 to 1354  cm−1 while the  G peak is shifted  from \n1587  cm−1 to 1595  cm−1 (Fig. 6). This is unlike to the reported observation of red shift in case of \ngraphene oxide based polymer nanocomposites.30   \n \n  \n11 \n  \nFigure 6   Raman spectra of GO sheets and CoFe 2O4/GO nanocomposite.  \n \nThe observed shift in Raman spectrum of graphene oxide is similar to that found in grap hene \nwhen subjected to lattice strain.  Strain can be due to stretch in carbon -carbon bond or symmetry \nbreaking or anisotropy in the lattice .31,32 The direction of shift in Raman G peak is dependent on \nthe nature of strain. It is reported  that blue shift in G peak can be assigned  to interfacial  \ncompressive  strain.  The local strain can be explained in terms of a schematic/model to \nunderstand the observed blue shift of the Raman D and G peaks in CoFe 2O4/GO (Fig. 7). The \nschematics below is a depiction of TEM images where nanocomposite of CoFe 2O4/GO are in the \nform of  decoration of CoFe 2O4 MNPs on GO sheets  Fig.7 . Lattice mismatch and disorder are \nexpected to produce compressive  stress on few layers of graphene oxide resulting in close \npackin g of surface atoms which could have led to scattering at higher vibrational wave number.  \n  \n12 \n  \nFigure  7   Schematic illustration of interfacial  compressive  stress involved in CoF 2O4/GO \nnanocomposite.  \nIn Raman spectra, significant blue shift observed in D and G peaks may be attributed to \nsimultaneous contribution from interfacial  stress as well as from charge transfer process. \nCompressive strain involved in these v ander -Waal systems could have arisen fr om lattice \nmismatch between CoFe 2O4 nanocrystallites and GO flakes resulting in up  shift in G peak. The \nrole of defects introduced during synthesis of CoF 2O4/GO nanocomposite  also cannot be ruled \nout. The existence of strain  is also confirmed by XRD studies as shown in Figure 5(b).In our \nprevious result, similar type of blue shift in Raman E 2g phonon is observed in case of Fe 3O4/GO \nnano composites. 33 \nFor a h exagonal system like graphene oxide, the strain can be expressed in term of interfacial  \nstress (σ) as, 34 \n                                  ωσ - ω0 = ασ                                                                              (3)  \n \n where, α = A (S 11+S12)/ω 0 is the stress coefficient for Raman Shift and σ is the compressive \nstress.  A is a constant, S 11 and S 12 are graphite elastic constants having values as A = -1.44 x10-7 \ncm-2, S11 = 0.98 x10-12 Pa-1 , S12 = -0.16 x10-12 Pa-1 respectively.  34  ωσ and ω 0 are frequencies of \nRaman E 2g phonon under stressed and unstressed conditions respectively. Using these constants,   \n  \n13 \n in equation (3), Raman shift of  8 cm-1 in G peak of CoFe 2O4/GO corresponds to the  stress \ncoefficient ( α) and  compressive stress (σ) to be  7.46 cm-1 and 1.07 GPa respectively.  We suggest \nthat this stress might have arisen due to lattice mismatch as well as increase in defect \nconcentration. The amount of defects present in the sample can be quantified by measuring the \nratio (I D/IG) of the D and G bands. The value of  ID/IG for GO sheets and CoFe 2O4/GO \nnanocomposite are found to be 1.11 to 1.30 respectively. The increased value of ID/IG for \nCoFe 2O4/GO nanocomposite as compared with GO sheets  indicates the increase in disorder in \nGO sheets resulting from the incorporati on of CoFe 2O4 magnetic  nanoparticles. The i nter \ndistance (LD) between Raman active defects is estimated using Tuinstra - Koenig relation.35,36. \n  \n       \n   \nWhere C (λ) = (2.4 × 10−10 nm−3), λ4 is a constant and in this case λ = 514 nm i.e  the excitation \nwave length.  The inter defect distance of GO and C oFe 2O4/GO nanocomposite are calculated to \nbe 15nm and 13 nm respectively. With L D >10 nm, one can expect the variation in I D/IG ratio is \ndue to scattered Raman active defects only. The defec t density 'nD' is calculated using the \nrelation37 \nnD (cm-1) = 1014/ πL2\nD \nand is found to be 1.88x1025 /cm2  for nanocomposites thus indicating a 30% increase in point \ndefects in GO due to  nucleation of CoFe 2O4 nanocrystallites on it.  \nThe observed blue shift in the D and G Raman peaks and increase in FWHM confirm the \noccurrence of charge transfer between the GO sheets and CoFe 2O4 NPs. The study of charge -\ntransfer interactions of graphene with various electron donors and acceptors are reported  in the \nliterature . Charge  transfer studies in CoFe 2O4/GO and particularly its correlation with surface \nelectronic behavior  has not been reported  till date. In this report, observed blue shift in G peak of \nGO is attributed  to the situation where an electro n donor molecule gets adsorbed .  The increase  \nof FWHM of G  for nanocomposite  band confirms the interaction with these molecules. The \neffect of charge transfer is quantified from shifting of Fermi surface measured by scanning \nKelvin probe studies.   \n \n \n   \n14 \n SKP Studies  \n         In graphene oxide, Fermi level lies at Dirac point similar to that in graphene. But, in the \ncase of CoFe 2O4/GO nanocomposite where MNPs are spread  over GO sheets the Fermi level of \nGO is expected to be changed noticeably by the charge tran sfer between GO and CoFe 2O4 NPs. \nFermi level energy of any material is related to its work function (WF) by the equation .  \n \nΦsample  = χs + (E C - EF)                     (3)  \nWhere s is the electron affinity of the sample, and E C and E F are the conduction band energy and \nFermi energy of the material respectively.38  The estimation of Fermi level shifting is carried out \nin terms of work function using scanning Kelvin probe microsco py (SKPM) setup as shown in \nFig. 8. The WF value of the GO sheets is measured in terms of surface potential or contact \npotential difference (CPD) between GO and the reference Au tip (WF=5.1 eV).  Average value of \nCPD is given by  \n \n 1\nCPD tip SampleVe  \n   (4) \nWhere Φ tip and Φ sample  are the work function of tip and sample surface respectively and ‘e’ is the \nelementary charge on an electron .39,40 \nThe measured average CPD value of GO sheet is found to be 514 mV which corresponds to WF \nof 4.6 eV. In the case of CoFe 2O4/GO nanocomposite , obtained average CPD is -610 mV. For \nsimplicity in plotting, the absolute  value of CPD has been taken into account as  shown in Fig. 8 \n(b). The change in contact surface potential must have emancipated from charge transfer between \nGO and CoFe 2O4.Using equation 4 , the average work function of CoFe 2O4/ GO nanocomposite is \nfound to be 5.7 eV. The significant change in the work function value of GO after decoration of \nCoFe 2O4 nanoparticles confirms the shifting of Fermi energy level toward s valence band as \nshown in Fig. 8 (c). This shifting may be due to electron transfer from GO to CoFe 2O4 which is \nalso envisaged from changes in Raman spectra.    \n   \n15 \n  \nFigure 8  CPD mapping of (a) GO and (b) CoFe 2O4/GO and (c) shifting of Fermi level.  \n \nConclusion  \nDispersion of  CoFe 2O4 nanoparticles on GO sheets involves interfaical compressive stress as \nwell as charge transfer between host GO sheets and CoFe 2O4 magnetic nanoparticles. The \nsuperparamagnetic  behavior of these nanocomposite is confirmed from its high value of \nmagne tic saturation with Ms (75.37 emu/g) and low coercivity value with H c (0.41 kOe), thus \nindicating soft magnetic nature of CoFe 2O4/GO nanocomposite. Charge transfer process induces \na blue shift in E 2g phonon as well as an increase in FWHM of Raman spectra o f GO sheets. \nCompressive strain calculated from XRD peak is related to the observed blue shift in Raman \npeak. Point defects generated in these nanocomposites are of the order of 1025 per cc which play \nan important role for generation of interfacial compres sive stress as well as charge transfer \nprocess.  The effect of charge transfer is quantified in terms of  changes in surface potential of \nGO, leading to a shift in Fermi surface towards valence band.  \n \n  \n16 \n Acknowledgments  \nThe authors are thankful to AIRF, JNU,  New Delhi for providing XRD, SEM, characterization. \nAmodini Mishra is thankful to UGC for providing fellowship.  \n \nReferences  \n[1] Geim A K, Novoselov K S (2008)  The Rise of Graphene. Nat Mater   6:183-191. \n[2]  Geim A  K (2009)  Graphene: Status and Prospects.  Sci. 324 :1530 -1534.  \n[3]  Lv W , Sun F Tang , D-M Fang, H -T Liu, C  Yang, Q  -H Cheng (2011)  A S andwich Structure \nof Graphene and Nickel Oxide with Excellent Supercapacitive Performance. J. Mater.Chem.  \n21:9014 -9019.  \n[4] Dreyer D  R, Park S , Bielawski  C W, Ruoff  R D (201)  The Chemistry of Graphene Oxide.  \nChem. Soc. Rev.  39:228-240.  \n[5] Zhu B.Y, Mura li S,  Cai W , Li X , Suk  J.W, Potts  J R,(201)  Graphene and  Graphene Oxide: \nSynthesis, Properties, and Applications.  Adv. M ater. 22: 3906 -3924.   \n[6] Rodier  B J, Mosher  E P, Burton  S T, Matthews  R,  Pentzer  E (2016)  Polythioether Particles \nArmored with Modifiable Graphene Oxide Nanosheets.  Macromol. Rapid Commun.  37:894-899.  \n[7] Cao J, Wang   Y, Zhou  Y, Ouyang  J-H, Guo D J L (2013)  High Voltage asymmetric    \nSupercapacitor based on MnO and Graphene Electrodes, J. Electro. Chem.  689: 201–  206. \n[8] Zhou   K, Zhu  Y, Yang  X, Li C (2011)  Preparation and Application of Mediator -Free H 2O2 \nBiosensors of Graphene -Fe3O4 Composites. Electro. 23.4 : 862 – 869. \n[9] Liu B J, Bai  H, Wan g Y, Liu  Z, Zhang X, Sun D D (2010)  Self-Assembling TiO 2 Nanorods  \non Large Graphene  Oxide Sheets at a Two -Phase Interface and Their  Anti -Recombination in   \nPhotocatalytic Applications. Adv. Funct. Mater.  20:4175 -4181.  \n [10] Chen  D, Feng  H, Li J (2012)  Graphene Oxide: Preparation, Functionalization, and  \nElectrochemical Applications.  Chem. Rev.  112:6027−6053.  \n[11] Wiedwald  U, Ziemann P (2010)  Preparation, Properties and Applications of Magnetic  N. \nBeilstein  J. Nanotechnol.   1:21–23. \n[12] Hola  K, Markova  Z, Zoppellaro  G, Tucek J, Zboril R (2015)  Tailored Functionalization of   \nIron Oxide Nanoparticles for MRI, Drug Delivery, Magnetic Separation and Immobilization of \nBiosubstances. Biotech. Adv . 33:1162 –1176.    \n17 \n [13] Erdem D, Bingham N S, Heiligtag F  J, Pilet  N, Warnicke  P, Heyderman L J,  Niederberger \nM (2016)  CoFe 2O4 and CoFe 2O4-SiO 2 Nanoparticle Thin Films with Perpendicular      Magnetic \nAnisotropy for Magnetic and Magneto -Optical Applications. Adv. Funct. Mat er.  26: 1954 –1963.  \n[14] Mansori  F, Amiri  G, Fatemi  M (2016)  Synthesis and Tissue D istribution of CoFe 2O4  \nNanoparticles Coated with DMSA in rats liver. Nanomed icin. J . 3:196-201. \n(15) Yuan  H, Jiao  Q, Zhang  Y, Zhang  J, Wu  Q, Zhao  Y, Neerunjun  S, Li H (2016)  Magnetic  \nCoFe 2O4 Nanoparticles Supported Basic Poly(Ionic Liquid) Catalysts: Preparation and  Catalytic \nPerformance Comparison in Transesterification and Knoevenagel Condensation. Catal. Lett.  \n146:951–959. \n[16] Ma  S, Zhan S , Jia Y, Zhou Q (2015))  Highly Efficient Antibacterial and Pb(II) Removal \nEffects of AgCoFe 2O4-GO Nanocomposite. ACS Appl. Mater. Interfaces . 7: 10576−10586.  \n[17] Fu Y, Chen  H, Sun X , Wanga  X (2012)  Combination of Cobalt Ferrite and Graphene: Hig h \nPerformance and Recyclable Visi ble-light Photocatalysis. Appl. Cat. B: Environ . 280:111–112.  \n[18]  Li  X, Feng  J, Du Y , Bai  J, Fan H , Zhang  H, Peng Y , Li F(2015)  One-Pot Synthesis of \nCoFe 2O4/graphene Oxide Hybrids and their Conversion into FeCo/graphene Hybrids for  \nlightweight and High ly Microwave Absorber. J. Mater. Chem.  A  3:5535 –5546.  \n[19] Kumar P R,  Kollu   P, Santosh  C, Rao K E V,  Kim  D K, Grace A N (2014)  Enhanced  \nProperties of Porous CoFe 2O4–Reduced Graphene Oxide Composites with Alginate Binders for \nLi-ion Battery Applications.  New J. Che m 38: 3654 -3661.  \n[20]  Ramachandran R, Mani V, Chen S -M,  Saraswathi  R, Lou B -S (2013)  Recent Trends in  \nGraphene based Electrode Materials for Energy Storage Devices and Sensors Applications . Int. \nJ. Electrochem. Sci.  8:11680 - 11694.  \n[21]  Mishra A , Mohnaty  T (2016) Structural and Morphological Study of  Magnetic \nFe3O4/reduced  Graphene Oxi de. Mat. Today. Proced.  3:1576 -1581.  \n[22]  Turtelli   R S, Duong  G V, Nunes  W, Grossinger  R, Knobel M  (2008)  Magnetic Properties \nof N anocrystalline CoFe 2O4 Synthesized by Modified Citrate -gel Method . J. Mag. Mag. Mater.  \n320:e339 -e342.  \n[23] Wang  G, Ma Y , Dong X, Tong  Y, Zhang  L, Mu J, Bai Y, Hou  J Y, Che  H, Zhang  X (2015) \nMonodisperse Polyvinylpyrrolidone -Coated CoFe 2O4 Nanoparticles: Synthesis, Characterization \nand Cytotoxicity Study. Appl. Surf. Sci  357:2131 -2135.    \n18 \n [24] Dutta  P, Seehra  M, Thota  S, Kuma r J (2007)  A Comparative Study of the Magnetic \nProperties of Bulk and Nanocrystalline Co 3O4. J. Phys.  Cond.  Matt   20: 015218 -015228.  \n[25] Ragasudha  M, Ravinder  D, Veerasomaiah  P (2016)  Investigation of Superparamagnetism in \nPure a nd Chromium Substituted Cobalt N ano Ferrite . J. Mag. Mag. Matt.  420:45-50. \n[26] Williamson G K, Hall W  H (1953)  X-ray  Line Broadening from Field Aluminium and \nWolfram.  Acta. Metallurgica  1:22-31. \n[27] Mishra  A, Choudhary  S N, Choudhary  R N P,  Murthy  V R K,  Prasad  K (2012)  Dielectric \nrelaxation in complex perovskite  Ba(Bi 1/2Ta1/2)O3. J. Mater. Sci: Mater Electron 23:185–192. \n [28] Ferrari A C, Meyer J C, Scardai  V, Casiraghi  C, Lazzeri  M, Mauri  F,  Piscanes S , Jiang  D, \nNovoselov K S,  Roth  S, Geim A K  (2006)  Raman Spectrum of Graphene and Graphene Layers. \nPhys. Rev. Lett  97:187401 -187404.  \n[29] Ferrari A C, Robertson  J (2000)  Interpretation of Raman spectra of disordered and \namorphous carbon. Phys. Rev. B  61:14 095 - 14 107.  \n[30] Li Z, Young, R J, KInloch  I. A(2013) Interfacial Stress Transfer in Graphene Oxide   \nNanocomposites.  ACS Appl. Mater. Interfaces  5: 456-463.   \n[31] Zheng X, Chen W, Wang  G, Yu Y, Qin S, Fang  J, Wang  F, Zhang X -A (2015)  The Raman \nRed shift of graphene impacted by gold nanoparticles. AIP Adv  5:057133 -6. \n[32] Rohrl J , Hundhausen  M, Emstev  K V, Seyller T , Graupner  R, Ley L (2008)  Raman spectra \nof epitaxial graphene on SiC(0001) . Appl. Phys. Lett  92: 201918 -201921.  \n[33] Mishra  A, Mohanty  T (2016)  Analysis of Surface Potential and Magnetic Properties of \nFe3O4/Graphene Oxide Nanocomposites. AIP Conf. Proceed  050010 :1731.  \n[34] Ni Z H,  Wang H  M,  Ma Y, Kasim  J, Wu Y H, Shen   Z X (2008)  Tunable Stress and \nControlled Thickness Modification in Graphene by Annealing.   ACS. Nano  5:1033 -1039.    \n[35] Tuinstra  F, Koenig J L (1970)  Raman Spectrum of Graphite. J. Chem. Phys  53: 1126−1130.  \n[36] Mishra  M, Meinerzhagen F, Schleberger  M, Kanjilal  D, Mohanty T (2015)  Swift Heavy Ion \nInduced Optical and Electronic Modifications of Graphene−TiO 2 Nanocomposites . J. Phys. \nChem. C  119:21270−21277.  \n[37] Cancado  L G, Jorio  A,  Ferrira  E H M, Stavale  F, Achete C A, Capaz R B, Moutinho M V \nO, Lombardo  A, Kulmala T S,  Ferrari  A C (2011)   Quantifying Defects in Graphene via Raman \nSpectroscopy at Different Excitation Energies . Nano . Lett 11:3190 -3196.    \n19 \n  [38] Kumar  A, Mohanty  T (2014)  Electro -optic modulation induced enhancement in \nphotocatalytic activity of N -doped TiO 2 thin films.  The J. Phy. Chem C  118:7130 -7138.  \n[39]Sadewasser  S, Leendertz C , Streicher F , Lux -Steiner M C (2009)  The influence of surface \ntopography on Kelvin probe force microscopy . Nanotechnology  20, 505503 -505513.  \n[40] Cheran L -E, Thompson M, Liess  H -D (1999)  Scanning Kelvin microprobe in the tandem  \nanalysis of surface topography and chemistry . Analyst 124: 961-970. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n "    },    {        "title": "2201.04384v1.Magnetic_domain_wall_pinning_in_cobalt_ferrite_microstructures.pdf",        "content": "Graphical Abstract\nMagnetic domain wall pinning in cobalt ferrite microstructures\nSandra Ruiz-G ´omez, Anna Mandziak, Laura Mart ´ın-Garc ´ıa, Jos ´e Emilio Prieto, Pilar Prieto, Carmen Munuera, Michael Foerster,\nAdri ´an Quesada, Luc ´ıa Aballe, Juan de la Figuera\narXiv:2201.04384v1  [cond-mat.mtrl-sci]  12 Jan 2022Highlights\nMagnetic domain wall pinning in cobalt ferrite microstructures\nSandra Ruiz-G ´omez, Anna Mandziak, Laura Mart ´ın-Garc ´ıa, Jos ´e Emilio Prieto, Pilar Prieto, Carmen Munuera, Michael Foerster,\nAdri ´an Quesada, Luc ´ıa Aballe, Juan de la Figuera\nHighly crystalline non-stoichiometric cobalt ferrites have\nbeen grown by MBE on Ru(0001).\nCorrelative structural, magnetic and chemical analysis\nof the crystals have been performed by XMCD-PEEM\nmicroscopy, LEEM microscopy, and atomic force mi-\ncroscopy.\nThe source of domain walls pinning has been studied find-\ning a 18%, 30% and 45% of the DWs pinned in chemical\ndefects, AFM features and substrate steps, respectively.\nThe role of substrate steps in pinning magnetic domains\nis expected to be widespread in magnetic oxide spinels\ngrown on metal substrates.Magnetic domain wall pinning in cobalt ferrite microstructures\nSandra Ruiz-G ´omeza, Anna Mandziakb, Laura Mart ´ın-Garc ´ıac, Jos´e Emilio Prietoc, Pilar Prietod, Carmen Munuerae, Michael\nFoersterf, Adri ´an Quesadag, Luc ´ıa Aballef, Juan de la Figuerac\naMax-Planck-Institut fr Chemische Physik fester Sto \u000be 01187 Dresden Germany\nbSolaris National Synchrotron Radiation Centre Krakow 30-392 Poland\ncInstituto de Qumica Fsica “Rocasolano” CSIC Madrid 28006 Spain\ndDpto. de Fsica Aplicada Universidad Autnoma de Madrid Madrid 28049 Spain\neInstituto de Ciencia de Materiales de Madrid CSIC Madrid 28049 Spain\nfAlba Synchrotron Light Facility Cerdanyola del Valles 08290 Spain\ngInstituto de Cermica y Vidrio CSIC Madrid E-28049 Spain\nAbstract\nA detailed correlative structural, magnetic and chemical analysis of non-stoichiometric cobalt ferrite micrometric crystals was\nperformed by x-ray magnetic circular dichroism combined with photoemission microscopy, low energy electron microscopy, and\natomic force microscopy. The vector magnetization at the nanoscale is obtained from magnetic images at di \u000berent x-ray inci-\ndence angles and compared with micromagnetic simulations, revealing the presence of defects which pin the magnetic domain\nwalls. A comparison of di \u000berent types of defects and the domain walls location suggests that the main source of pinning in these\nmicrocrystals are linear structural defects induced in the spinel by the substrate steps underneath the islands.\nKeywords: Correlative Microscopy, Cobalt ferrites, Domain wall pinning\n1. Introduction\nCobalt ferrite is a ferrimagnetic oxide, which at the stoi-\nchiometric composition CoFe 2O4presents a high magnetocrys-\ntalline anisotropy compared with other cubic (spinel-based)\nferrites[1]. This property, combined with its high Curie tem-\nperature and insulating character has made cobalt ferrite (CFO)\npopular for spin filtering[2, 3, 4, 5, 6, 7]. CFO thin films,\nthe form required by applications, have been grown by many\nmethods that provide epitaxial layers, among them magnetron\nsputtering[2, 5], pulsed laser deposition [3, 7] or molecular\nbeam epitaxy [4].\nOther members of the same family of cubic ferrites with the\nspinel structure such as magnetite Fe 3O4and NiFe 2O4have\nalso attracted much interest in spintronics. A particular fea-\nture of cobalt ferrite is that it can accept a wide range of Fe /Co\nratios, which strongly influence its magnetic and electronic\nproperties[8, 9, 10, 11]. In Fe-rich compositions[10, 11], di-\nvalent Co cations occupy preferentially octahedral sites while\niron cations occupy both octahedral and tetrahedral sites, and\ndepending on the Fe /Co ratio, can present both divalent and\ntrivalent oxidation states.\nThe detailed magnetic structure of the CFO thin films is\nhighly relevant for their magnetic properties, and are often very\ndi\u000berent from those of bulk single crystals. This is true even\nfor nominally epitaxial layers of high structural quality. One\nreason is that films posess a variety of defects that are not\npresent in the bulk material, or at least not in the same den-\nsities. For example, many spinel films present high densities of\nso-called antiphase boundaries (APBs)[12]. Antiphase bound-\naries appear when films grow epitaxially on substrates that pro-vide nucleation centers for the spinel phase at distances that\nare not integer multiples of the spinel unit cell. A classic case\nis films of spinel oxides grown on MgO, which has a smaller\nunit cell. In this case, the anion lattice might be continuous\nthroughout the film but antiphase boundaries appear between\nregions that originate from di \u000berent nuclei. Many of the unex-\npected magnetic properties of films of spinel ferrites in general\n[12] and cobalt ferrite in particular [13] have been attributed\nto their presence[14]. The e \u000bect of APB’s on the magnetic do-\nmains has been recently observed directly by transmission elec-\ntron microscopy[15], their structure determined at the atomic\nlevel[16] and their magnetic interactions determined through\natomistic spin dynamics[17]. Since APBs are di \u000ecult to re-\nmove after growth[18], deposition methods that avoid their ap-\npearance are being sought. One method applied with some suc-\ncess is to employ special substrates[19, 20, 21] with an isostruc-\ntural spinel unit cell and a very small lattice mismatch. How-\never, this limits the substrates to a few particular oxide spinels,\nsuch as CoGa 2O4or MgGa 2O4. Another approach is to induce\nfilm growth from a single nucleus. Although a continuous film\nis di\u000ecult to grow in such way, we have shown that using high-\ntemperature oxygen assisted molecular beam epitaxy individual\nislands with sizes of up to tens of micrometers can be obtained,\nboth for magnetite [22, 23, 24], nickel ferrite [25] or cobalt fer-\nrite [26, 27]. Such microcrystals, each grown from a single\nnucleus, present magnetic domains in remanence that are or-\nders of magnitude larger that those of films deposited by more\nstandard methods, a finding that was ascribed to the absence of\nantiphase boundaries.\nHowever, even if the magnetic domains are very large, not\nPreprint submitted to Applied Surface Science January 13, 2022all of them can be explained without invoking the presence of\ndefects acting as pinning sites. In this work we consider in de-\ntail the possible defects which could cause the observed mag-\nnetization domain distribution. We believe our results can be\napplicable to other oxide spinels thin films.\n2. Experimental Methods\nThe growth of the cobalt ferrite crystals and the subse-\nquent x-ray absorption experiments have been performed at the\nCIRCE experimental station of the Alba synchrotron[28]. It\nis equipped with a low-energy electron microscope than can\nalso be used to image the distribution of photoemitted electrons\nupon x-ray illumination, i.e. as a photoemission microscope. In\nthis mode, it can provide images of the energy-filtered distribu-\ntion of photoelectrons with a spatial resolution down to 20 nm\nand an energy resolution down to 0.2 eV .\nThe x-ray beam hits the sample at an angle of 16\u000efrom the\nsurface plane, while the azimuthal angle of the sample can be\nchanged in order to probe di \u000berent components of the magne-\ntization. Both for x-ray absorption spectro-microscopy (XAS-\nPEEM) and for x-ray magnetic circular dichroism microscopy\n(XMCD-PEEM), we use photoelectrons from the secondary\nelectron background to form the images, i.e., electrons pho-\ntoemitted from the sample at very low kinetic energies (typi-\ncally 2 eV). Dichroic images are obtained from the pixel-by-\npixel asymmetry between images acquired with opposite x-ray\nhelicities at the resonant x-ray absorption energies of the mag-\nnetic elements[29]. A single image for a given x-ray beam in-\ncidence angle relative to the sample gives only the component\nof the magnetization along the beam direction. By changing\nthe azimuthal angle between the sample and the x-ray beam,\nthe magnetization can be measured along di \u000berent directions.\nAll components of the magnetization can be obtained if at least\nthree non-coplanar directions are measured[24]. In our exper-\nimental setup the polar angle is fixed to 16\u000ebetween the x-ray\nbeam and the surface plane. Thus, the setup is more sensitive to\nthe in-plane magnetization components, although out-of-plane\nmagnetization components can also be detected.\nThe substrate is a Ru(0001) single crystal cleaned by cycles\nof annealing in oxygen at 1200 K in 10\u00006mbar of molecu-\nlar oxygen, followed by flashing to 1800 K in vacuum. The\ngrowth of the mixed cobalt-iron oxides is performed keeping\nthe substrate at high temperature (typically 1100 K) while de-\npositing Co and Fe in a molecular oxygen background pressure\nof 10\u00006mbar. Fe and Co are deposited using home-made dosers\ncontaining a rod of each material heated by electron bombard-\nment and surrounded by a water cooling jacket.\nThe micromagnetic simulations were performed with the\nMuMax3 software[30] using a low-end graphic GPU (2Gb\nGeForce GTX760). We used the bulk materials constants for\nstoichiometric CFO: saturation magnetization, exchange sti \u000b-\nness and first order magnetocrystalline cubic anisotropy were\nMs=3\u0002105A m\u00001,Aex=2:64\u000210\u000011J m\u00001, and\nKc1=12:5\u0002104J m\u00003, respectively. The cubic anisotropy axis\nwere assigned considering that the islands are (111) terminated,\nand that the island sides run along the h110idirections. Eachmagnetic configuration was relaxed in order to minimize first\nthe energy and then the total torque using a Bogacki-Shampine\nsolver[30]. The mesh size was 904 \u0002765\u00021 cells and each cell\nis 8.46 nm\u00028.46 nm\u00023 nm (di \u000berent values of the height\nbetween 3 and 10 nm were employed without any significant\ndi\u000berence in the results). The lateral size of the cell was chosen\nto coincide with the experimental resolution of the images.\n3. Results and discussion\n0º \n 60º \n -60º \na) \nb) \n0 90 \n180 \n270 \n0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0 \n0 25 50 75 100 125 150 175 0.0 0.2 0.4 0.6 0.8 1.0 \nAzimuthal angle (º) Polar angle (º) Normalized Frequency d) c) \nFigure 1: a) XMCD images of the same island acquired with a photon energy\ncorresponding to the Fe L 3edge, and with azimuthal angles of the x-ray beam\nrelative to the sample of respectively 0, 60 and -60\u000e. The scale bar is 2 \u0016m. b)\nArrow representation of the magnetization vector obtained from the previous\nimages. The color of each arrow indicates the in-plane orientation according\nto the color wheel shown on the right side and the saturation the out-of-plane\ncomponent, from fully pointing towards the substrate (black) to fully pointing\ntowards the surface (white). c) In-plane micromagnetism relaxed configuration,\nusing a random initial configuration and the material parameters described in\nthe experimental section. The color codes are the same as used in b). The shape\nand thickness of the islands are taken from the experimentally measured ones.\nd) Histogram of the magnetization as a function of the in-plane azimuthal angle\n(where 0\u000eindicates magnetization pointing to the right) and of the polar angle\n(where 90\u000eindicates in-plane). The pixel size is 8.46 nm both in the simulation\nand the experimental image. The continuous lines correspond to the experi-\nmental data, and the dashed ones to the relaxed micromagnetic simulation.\nThe growth of the spinel islands has been described in de-\ntail before[26, 27], and thus here we will just summarize the\nmost relevant aspects. The growth of mixed iron-rich Co-Fe\noxides[31, 27] starts with the nucleation of islands composed of\na divalent mixed oxide with the rock salt structure (Fe xCo1\u0000xO).\nSuch islands then grow and coalesce to form a complete layer\n2wetting the substrate, typically two atomic layers thick (de-\npending on flux, substrate temperature and oxygen pressure).\nUpon continuing the deposition, three dimensional islands with\nthe spinel structure nucleate on top of the wetting layer. At high\ntemperature such islands can grow up to hundred nanometers in\nthickness, and they are typically well separated from each other.\nWe note that due to the high di \u000busivity at elevated temperatures,\nthe composition of both wetting layer and spinel islands evolves\nwith time, as shown by chemical maps acquired during growth\nby photoemission microscopy[27].\nAfter growth, the sample is brought to room temperature\nin an oxygen background pressure in order to avoid reduc-\ntion. The islands composition, determined by XAS-PEEM\nand their structure, measured by microspot low energy elec-\ntron di \u000braction, reveal that they are iron-rich cobalt ferrite\n(Co 0:5Fe2:5O4[26]). Magnetic mapping is done by means of\nXMCD-PEEM. Three non-coplanar x-ray incidence angles are\nmeasured, as shown in Figure 1a for respectively 0, 60 and -\n60\u000eazimuthal angle for a representative island of about 10 nm\nthickness. In our geometry, the white regions correspond to ar-\neas with their local magnetization along the x-ray beam, black\nones to areas where the local magnetization is in the opposite\ndirection, and gray regions to areas where there is either no lo-\ncal magnetization or the magnetization is orthogonal to the light\ndirection[29, 26]. No contrast is detected in the wetting layer,\nas expected at room temperature. In Figure 1b the obtained\nmagnetization vector is presented. The magnetization is repre-\nsented by arrows whose color indicates the in-plane orientation\nand saturation the out-of-plane component. The magnetic do-\nmains form a rather intricate landscape with a wide distribution\nof sizes, and convoluted domain walls.\nThe first obvious observation is that the magnetization direc-\ntions are clearly not following the island edges. In fact, the\nmagnetization direction is often perpendicular to the nearest is-\nland edge. This observation rules out shape anisotropy as the\nmain factor determining the magnetization direction, in con-\ntrast to what is observed in magnetite islands [24]. The domains\nwalls, like those of magnetite[32], are not chiral. In Figure 1d\nthe histogram of the magnetization as a function of the az-\nimuthal and polar angles through the island is plotted. It is clear\nthat there are several well defined directions in the in-plane ori-\nentation of the magnetization, at 19, 68, 131, 216, 265, and 309\u000e\nwhich correspond roughly to intervals of 60\u000e. From the di \u000brac-\ntion patterns and the geometry of the substrate we know that the\nislands present a (111) surface, and that their edges are oriented\nalong the compact directions of the spinel phase, i.e. the in-\nplaneh110idirections. Cobalt ferrite in the bulk form presents\ncubic anisotropy[1], with the easy axes along the h100idirec-\ntions. There is no easy axis within the (111) plane, so we con-\nsider instead the projection of the bulk easy axes direction on\nthe (111) plane, which are the in-plane h112idirections. Since\nthe composition of the islands lies between that of stoichiomet-\nric CoFe 2O4and that of magnetite, we must also consider the\neasy axes of pure magnetite at room temperature, which are the\nh111i. However, the projection of the h111idirections on the\n(111) plane also corresponds to the in-plane h112idirections, so\nthe same orientation is expected. In fact, the experimental mag-netization directions roughly correspond to the h112iones, i.e.\nthe bisectrices of the epitaxial triangular islands. This, together\nwith the significant out-of-plane component present, leads to\nthe conclusion that magnetocrystalline anisotropy is the main\nresponsible for the experimentally observed magnetization di-\nrections.\nIn order to better understand the origin of the magnetic\ndomain distribution observed in our cobalt ferrite islands,\nwe performed micromagnetic simulations using the MuMax3\ncode[30] on islands with the experimental geometry. Relax-\ning from a random configuration gives rise to a magnetization\ndistribution quite di \u000berent from the experimental one that can\nbe seen in Figure 1c. A comparison of experimental and cal-\nculated magnetization directions is shown in Figure 1d in the\nform of continuous histograms and dashed lines, respectively.\nWhile the domain distribution cannot be reproduced by the sim-\nulation, the orientation of the domains is in reasonable agree-\nment with the micromagnetic simulations, as expected if mag-\nnetocristalline anisotropy is driving the orientation of the mag-\nnetization within each domain. However, it is clear that assum-\ning a structurally perfect island, as done in the micromagnetic\nsimulations, does not correctly reproduce the experimental do-\nmain distribution.\nA straightforward explanation for the observed domain dis-\ntribution (see Figure 2a) could be that the magnetic domain\nwalls get pinned on linear defects. The spinel islands might\npresent di \u000berent types of linear defects such as (i) steps at the\nisland surface, (ii) boundaries between regions with di \u000berent\ncomposition, (iii) steps at the substrate-island interface, and\nboundaries (iv) of stacking faults, (v) between antiphase do-\nmains, or (vi) between twin domains. We start by locating each\nof them in order to discriminate which ones are responsible for\nthe pining of domain walls.\nSteps at the island surface were unambiguosly located by ex-\nsitu AFM on the very same areas observed by PEEM (see Fig-\nure 2a). The island is resting on a region with wavy substrate\nsteps running mostly along the x-axis. The location of sub-\nstrate steps can be determined through the Co xFe1\u0000xO wetting\nbilayer[33]. The island has nucleated close to a small hexago-\nnal protrusion, which is covered with Co xFe1\u0000xO but not by the\nspinel island. The top of the spinel island is remarkably flat,\nwith only some steps of around 0.4 nm height at the north-west\ncorner. This is the expected height for atomic steps of a spinel\nphase along theh111idirection. In addition, the area around\nthe south corner is about 1 nm lower than the rest of the is-\nland, and presents additional steps. Otherwise, the island has\nan atomically flat top surface, and therefore a cross-sectional\nwedge shape, with 12 nm thickness at the south part, and 8 nm\nnear the northern side.\nTo correlate possible changes in composition with the loca-\ntion of the domain walls, images with chemical contrast can\nbe obtained by averaging the two XAS-PEEM images acquired\nwith opposite circular polarization. We note that the intensity\nof the XAS signal has been integrated beyond the white line,\nin order to avoid any leakage from the magnetic signal. No\nchemical contrast whatsoever is observed at either the images\nat the Fe or Co absorption edges (not show). Nevertheless, at\n3Figure 2: (a) AFM image acquired ex-situ in the same island. (b) Chemical contrast image at the O K absorption edge. (c) Representative LEEM image acquired in\nthe same island at 23 eV to enhance the contrast of the Ru steps. Bottom row show the draws of the features observed in the images.\nthe post-O K edge (shown in Figure 2b), some regions with dif-\nferent contrast are visible. The change in contrast is 5%. A\npossible source for some of the observed di \u000berent gray levels is\nthat they arise from di \u000berences in the total height of the island,\nas some coincide with surface or substrate steps.\nIn low-energy electron microscopy mode, an elastically scat-\ntered electron beam of a selected energy is used to form an\nimage of the surface (see Figure 2c). Varying the electron\nenergy and the focusing conditions can provide contrast due\nto thickness or to several types of buried defects. A classic\nexample is the observation of interface steps. The substrate\nsteps underneath Ag islands on Si(111)[34] were observed us-\ning slightly out-of-focus conditions. The observation was ex-\nplained in terms of the long range strain fields associated with\nthe interface steps, visible in islands several nanometers thick.\nIn the uniform gray areas of the island (see Figure 2c), faint\nlines can be distinguished to follow the paths of the substrate\nsteps coming from outside the island. It is reasonable to pre-\nsume that they continue below the island giving rise to the ob-\nserved lines in the LEEM image of the island.\nAnother type of defects that can be detected by LEEM imag-\ning through the islands are stacking faults. For example, it has\nbeen shown that regions with di \u000berent stacking sequence in Co\nislands on Ru(0001)[35] present di \u000berent electron reflectivities\nat a given energy. There are several regions on the LEEM image\nof the island that show di \u000berent gray level contrast at several\nenergies (see Figure 2c). While a distinction between di \u000berent\nstacking fault types cannot be done without additional informa-\ntion, we believe it is reasonable to interpret the borders between\nsuch regions as extended defects, which in a spinel structure can\ncorrespond to several types of stacking faults that can be con-\nsidered to consist of combinations of three basic types, called I,II and III in Ref. [[36]].\nFigure 3 shows the comparison of magnetic domains (im-\nage) together with the topographic AFM contrast (blue lines),\nchemical contrast (yellow lines), LEEM reflectivity contrast\n(red lines), and substrate steps (green lines). Evaluating the %\nof domain wall length that correspond to a change in contrast in\nthe di \u000berent images we observe the following: 18% of the total\nDW length correspond to boundaries in the chemical contrast\nimage (yellow lines), 30% are located in features observed in\nthe AFM image (blue lines) and coincide with boundaries ob-\nserved in the LEEM image (red lines) and 45% are located over\nsubstrate steps (see yellow arrows in Figure 3), although there\nare many more steps than magnetic domain walls.\nWe thus find that most magnetic domain walls are located\nover substrate steps. We analyze now the reasons why substrate\nsteps might strongly pin magnetic domain walls. Again we re-\nmark that we lack a detailed atomic information of the matching\nof the spinel island to the steps of the Ru substrate. However,\nwe can discuss the general structure of the island and the sub-\nstrate. The Ru(0001) substrate has an hcp stacking sequence\nwith an interplanar distance of 0.214 nm, which is the height\nof the monoatomic steps at the surface. Spinel islands along a\nh111idirection can be considered to have an fcc stacking se-\nquence of units, each one composed of a cation layer and a\nclose-packed oxygen layer and with a height close to 0.242 nm.\nThere are two di \u000berent types of such units which alternate along\nthe vertical direction and di \u000ber in the composition and struc-\nture of the cation layer, which can be either a mixed tetragonal-\noctahedral cation layer or a kagom ´e octahedral cation layer[36].\nThus there is a 13% di \u000berence in height between a Ru layer\nand a spinel unit. On the other hand, two such units, one of\neach type, are required to form what can be considered the ele-\n4Figure 3: Comparison of magnetic domains (image), topographic AFM contrast (blue lines), chemical contrast (yellow lines), LEEM contrast (red lines), and\nsubstrate steps (green lines). Yellow arrows mark regions in which domain walls are pinned in substrate steps.\nmentary constituent of the spinel structure, so that the presence\nof a substrate step underneath an epitaxial island can give rise\nto adjacent non-equivalent spinel units building either an ex-\ntended defect along a line parallel to the step or stacking faults\nof di\u000berent types[36], including possibly twins. We note that\nfor most substrate steps underneath the spinel island we do not\nfind large extended defects within our experimental resolution.\nHowever, we cannot rule out the presence of narrow ribbons of\nstacking faults around the substrate steps (expected to be a few\nnm wide[37]).\nThe e \u000bect of a monoatomic step underneath an epitax-\nial island can be quantified by the strain field arising from\nthe 13% di \u000berence in height causing magnetostriction in the\nspinel phase. This has been measured for magnetite, where\na typical microcoercivity in the range of mT for bulk dislo-\ncations has been theoretically predicted[38] and experimen-\ntally observed[39]. A detailed prediction of the e \u000bect of the\nstacking faults induced by the substrate steps requires atom-\nistic spin calculations as well as detailed atomistic models, but\nwe can expect e \u000bects comparable to those caused by antiphase\nboundaries on the magnetic properties of spinels. Antiphase\nboundaries in epitaxial (100)-oriented spinel (magnetite) films\nproduce antiferromagnetic 180osuperexchange interactions be-\ntween octahedral cations that oppose their natural ferromag-\nnetic coupling and therefore locally weaken the e \u000bective ex-\nchange sti \u000bness, thus favouring the pinning of the domain wall\nat these defects[40]. Calculations have been performed for an-\ntiphase boundaries in particular geometries[17] and it has been\nreported that they can produce strong pinning of the domain\nwalls. In some of the possible types of stacking faults in (111)-\noriented spinel films, such 180osuperexchange interactions are\nalso present, as in the S-II case[36], where oxygen atoms are\nnormally stacked and the fault a \u000bects only the cation layers.\nFurthermore, they can also appear at the boundaries between\ndi\u000berently stacked regions, particularly if one of these is also\nof type S-II. Thus, we suggest that the main cause for the pin-\nning of domain walls in our epitaxial cobalt ferrite islands on\nRu(0001) is ultimately the coupling mismatch imposed by thesubstrate steps.\n4. Conclusions\nBy experimentally locating the positions of magnetic domain\nwalls in highly perfect non-stoichiometric cobalt ferrite islands,\ncorrelating with the positions of chemical and structural defects\nand comparing with micromagnetic simulations, we find that\nthe magnetic domain walls are pinned at linear structural de-\nfects. 45% of the domain walls are found on top of interface\nsteps, which we thus conclude are the defects ultimately re-\nsponsible for the pinning of domain walls.\nWe suggest that interface steps play a similar role in (111)\noriented spinels grown on hexagonal metal substrates such as\nPt(111) and Ru(0001) to antiphase boundaries found on spinel\ncrystals grown on MgO and other square-symmetric substrates.\nHowever, contrary to the case of antiphase boundaries which\nstem from the coalescence of islands nucleated on the same ter-\nrace, the defects responsible for the pinning of the domain walls\nare the substrate steps. It should be thus possible to obtain struc-\nturally perfect ferrimagnetic crystals with domain sizes limited\nonly by the substrate terrace size.\n5. Acknowledgment\nThis work is supported by the Grants RTI2018-\n095303-B-C51,-A-52, and -B-C53 funded by\nMCIN /AEI/10.13039 /501100011033 and by “ERDF A\nway of making Europe”, and by the Grant S2018-NMT-4321\nfunded by the Comunidad de Madrid and by “ERDF A way\nof making Europe”. These experiments were performed at the\nCIRCE beamline of the ALBA Synchrotron Light Facility.\nReferences\n[1] V . A. M. Brabers, Progress in spinel ferrite research, Handbook of\nmagnetic materials 8 (1995) 189–324. doi: 10.1016/S1567-2719(05)\n80032-0 .\n5[2] M. J. Carey, S. Maat, P. Rice, R. F. C. Farrow, R. F. Marks, A. Kel-\nlock, P. Nguyen, B. A. Gurney, Spin valves using insulating cobalt ferrite\nexchange-spring pinning layers, Applied Physics Letters 81 (2002) 1044–\n1046. doi: 10.1063/1.1494859 .\n[3] M. G. Chapline, S. X. Wang, Room-temperature spin filtering in a\nCoFe 2O4/MgAl 2O4/Fe3O4magnetic tunnel barrier, Physical Review B\n74 (2006) 014418. doi: 10.1103/PhysRevB.74.014418 .\n[4] A. V . Ramos, M.-J. Guittet, J.-B. Moussy, R. Mattana, C. Deranlot,\nF. Petro \u000b, C. Gatel, Room temperature spin filtering in epitaxial cobalt-\nferrite tunnel barriers, Applied Physics Letters 91 (2007) 122107.\ndoi:10.1063/1.2787880 .\n[5] F. Rigato, S. Piano, M. Foerster, F. Giubileo, A. M. Cucolo, J. Fontcu-\nberta, Andreev reflection in ferrimagnetic CoFe 2O4spin filters, Physical\nReview B 81 (2010) 174415. doi: 10.1103/PhysRevB.81.174415 .\n[6] Y . K. Takahashi, S. Kasai, T. Furubayashi, S. Mitani, K. Inomata,\nK. Hono, High spin-filter e \u000eciency in a Co ferrite fabricated by a thermal\noxidation, Applied Physics Letters 96 (2010) 072512. doi: 10.1063/1.\n3318297 .\n[7] E.-J. Guo, A. Herklotz, A. Kehlberger, J. Cramer, G. Jakob, M. Kl ¨aui,\nThermal generation of spin current in epitaxial CoFe 2O4thin films, Ap-\nplied Physics Letters 108 (2016) 022403. doi: 10.1063/1.4939625 .\n[8] M. Takahashi, M. E. Fine, Magnetic behavior of quenched and aged\nCoFe2o4–co3o4 alloys, J. App. Phys. 43 (1972) 4205–4216. doi: 10.\n1063/1.1660897 .\n[9] P. Smith, C. Spencer, R. Stillwell, Co57and Fe57M¨ossbauer studies of\nthe spinels FeCo 2O4and Fe 0:5Co2:5O4, Journal of Physics and Chemistry\nof Solids 39 (1978) 107–111. doi: 10.1016/0022-3697(78)90208-1 .\n[10] J. A. Moyer, C. A. F. Vaz, D. A. Arena, D. Kumah, E. Negusse, V . E.\nHenrich, Magnetic structure of fe-doped CoFe 2o4probed by x-ray mag-\nnetic spectroscopies, Phys. Rev. B 84 (2011) 054447. doi: 10.1103/\nPhysRevB.84.054447 .\n[11] J. A. Moyer, C. A. F. Vaz, E. Negusse, D. A. Arena, V . E. Henrich, Con-\ntrolling the electronic structure of co 1\u0000xfe2+xo4thin films through iron\ndoping, Phys. Rev. B 83 (2011). doi: 10.1103/PhysRevB.83.035121 .\n[12] W. Eerenstein, Spin-dependent transport across anti-phase boundaries in\nmagnetite films, Ph.D. thesis, Rijskuniversisteit, Groningen, 2003.\n[13] J. A. Moyer, C. A. F. Vaz, D. P. Kumah, D. A. Arena, V . E. Henrich, En-\nhanced magnetic moment in ultrathin Fe-doped CoFe 2O4films, Physical\nReview B 86 (2012) 174404. doi: 10.1103/PhysRevB.86.174404 .\n[14] D. T. Margulies, F. T. Parker, M. L. Rudee, F. E. Spada, J. N. Chapman,\nP. R. Aitchison, A. E. Berkowitz, Origin of the anomalous magnetic be-\nhavior in single crystal fe f3gof4gfilms, Phys. Rev. Lett. 79 (1997) 5162.\ndoi:10.1103/PhysRevLett.79.5162 .\n[15] T. Kasama, R. Dunin-Borkowski, W. Eerenstein, O \u000b-axis electron holog-\nraphy observation of magnetic microstructure in a magnetite (001) thin\nfilm containing antiphase domains, Physical Review B 73 (2006) 104432.\ndoi:10.1103/PhysRevB.73.104432 .\n[16] K. P. McKenna, F. Hofer, D. Gilks, V . K. Lazarov, C. Chen, Z. Wang,\nY . Ikuhara, Atomic-scale structure and properties of highly stable an-\ntiphase boundary defects in Fe 3O4, Nature Communications 5 (2014)\n5740. doi: 10.1038/ncomms6740 .\n[17] R. Moreno, S. Jenkins, A. Skeparovski, Z. Nedelkovski, A. Gerber,\nV . Lazarov, R. F. L. Evans, Role of anti-phase boundaries in the for-\nmation of magnetic domains in magnetite thin films, J. Phys. Condens\nMatter (2021). doi: 10.1088/1361-648X/abe26c .\n[18] W. Eerenstein, T. T. M. Palstra, T. Hibma, S. Celotto, Di \u000busive motion\nof antiphase domain boundaries in fe 3o4films, Phys. Rev. B 68 (2003)\n014428. doi: 10.1103/PhysRevB.68.014428 .\n[19] A. V . Singh, B. Khodadadi, J. B. Mohammadi, S. Keshavarz, T. Mewes,\nD. S. Negi, R. Datta, Z. Galazka, R. Uecker, A. Gupta, Bulk single\ncrystal-like structural and magnetic characteristics of epitaxial spinel fer-\nrite thin films with elimination of antiphase boundaries, Adv. Mater. 29\n(2017) 1701222. doi: 10.1002/adma.201701222 .\n[20] A. V . Singh, A. Srivastava, J. B. Mohammadi, S. Regmi, U. Bhat,\nR. Datta, T. Mewes, A. Gupta, Studies of electrical and magnetic proper-\nties across the Verwey transition in epitaxial magnetite thin films, Journal\nof Applied Physics 126 (2019) 093902. doi: 10.1063/1.5088670 .\n[21] A. Srivastava, A. V . Singh, J. B. Mohammadi, C. Mewes, A. Gupta,\nT. Mewes, Ferromagnetic resonance study of the Verwey phase transition\nof magnetite thin film on MgGa2O4(001) substrate, IEEE Transactions\non Magnetics 56 (2020) 6100506. doi: 10.1109/TMAG.2020.3024533 .[22] B. Santos, E. Loginova, A. Mascaraque, A. K. Schmid, K. F. McCarty,\nJ. de la Figuera, Structure and magnetism in ultrathin iron oxides char-\nacterized by low energy electron microscopy, J. Phys. Cond. Matt. 21\n(2009) 314011. doi: 10.1088/0953-8984/21/31/314011 .\n[23] M. Monti, B. Santos, A. Mascaraque, O. Rodr ´ıguez de la Fuente, M. A.\nNi˜no, T. O. Mentes ¸, A. Locatelli, K. F. McCarty, J. F. Marco, J. de la\nFiguera, Magnetism in nanometer-thick magnetite, Phys. Rev. B 85\n(2012) 020404.\n[24] S. Ruiz-Gomez, L. Perez, A. Mascaraque, A. Quesada, P. Prieto, I. Pala-\ncio, L. Martin-Garcia, M. Foerster, L. Aballe, J. de la Figuera, Ge-\nometrically defined spin structures in ultrathin Fe 3O4with bulk like\nmagnetic properties, NAanoscale 10 (2018) 5566–5573. doi: 10.1039/\nc7nr07143d .\n[25] A. Mandziak, J. d. l. Figuera, S. Ruiz-G ´omez, G. D. Soria, L. P ´erez,\nP. Prieto, A. Quesada, M. Foerster, L. Aballe, Structure and magnetism\nof ultrathin nickel-iron oxides grown on Ru(0001) by high-temperature\noxygen-assisted molecular beam epitaxy, Sci. Rep. 8 (2018) 17980.\ndoi:10.1038/s41598-018-36356-6 .\n[26] L. Mart ´ın-Garc ´ıa, A. Quesada, C. Munuera, J. F. Fern ´andez, M. Garc ´ıa-\nHern ´andez, M. Foerster, L. Aballe, J. de la Figuera, Atomically flat\nultrathin cobalt ferrite islands, Adv. Mater. 27 (2015) 5955–5960.\ndoi:10.1002/adma.201502799 .\n[27] S. Ruiz-Gomez, A. Mandziak, J. E. Prieto, M. Aristu, E. M. Trapero,\nG. D. Soria, A. Quesada, M. Foerster, L. Aballe, J. de la Figuera, A real-\ntime XAS PEEM study of the growth of cobalt iron oxide on Ru(0001),\nJ. Chem. Phys. 152 (2020). doi: 10.1063/1.5140886 .\n[28] L. Aballe, M. Foerster, E. Pellegrin, J. Nicolas, S. Ferrer, The\nALBA spectroscopic LEEM-PEEM experimental station: layout and per-\nformance, J Synchrotron Radiat 22 (2015) 745–752. doi: 10.1107/\nS1600577515003537 .\n[29] C. M. Schneider, G. Sch ¨onhense, Investigating surface magnetism by\nmeans of photoexcitation electron emission microscopy, Rep. Prog. Phys.\n65 (2002) 1785–1839.\n[30] A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez,\nB. V . Waeyenberge, The design and verification of MuMax3, AIP Ad-\nvances 4 (2014) 107133. doi: 10.1063/1.4899186 .\n[31] L. Mart ´ın-Garc ´ıa, A. Quesada, L. P ´erez, M. Foerster, L. Aballe, J. de la\nFiguera, Initial stages of the growth of mixed iron-cobalt oxides on\nRu(0001), Phys. Proc. 85 (2016) 12–19. doi: 10.1016/j.phpro.2016.\n11.075 .\n[32] L. Martin-Garcia, G. Chen, Y . Montana, A. Mascaraque, B. M. Pabon,\nA. K. Schmid, J. de la Figuera, Memory e \u000bect and magnetocrystalline\nanisotropy impact on the surface magnetic domains of magnetite(001),\nSci. Rep. 8 (2018) 5991. doi: 10.1038/s41598-018-24160-1 .\n[33] I. Palacio, M. Monti, J. F. Marco, K. F. McCarty, J. d. l. Figuera, Ini-\ntial stages of FeO growth on Ru(0001), J. Phys: Cond. Matt. 25 (2013)\n484001. doi: 10.1088/0953-8984/25/48/484001 .\n[34] R. M. Tromp, A. W. Denier van der Gon, F. K. LeGoues, M. C. Reuter,\nObservation of buried interfaces with low energy electron microscopy,\nPhys. Rev. Lett. 71 (1993) 3299–3302. doi: 10.1103/PhysRevLett.71.\n3299 .\n[35] F. E. Gabaly, J. M. Puerta, C. Klein, A. Saa, A. K. Schmid, K. F. Mc-\nCarty, J. I. Cerda, J. de la Figuera, Structure and morphology of ultrathin\nCo/Ru(0001) films, New. J. Phys. 8 (2007) 80.\n[36] J. Hornstra, Dislocations, stacking faults and twins in the spinel structure,\nJournal of Physics and Chemistry of Solids 15 (1960) 311–323. doi: 10.\n1016/0022-3697(60)90254-7 .\n[37] J. de la Figuera, A. Schmid, N. Bartelt, K. Pohl, R. Hwang, Determi-\nnation of buried dislocation structures by scanning tunneling microscopy,\nPhysical Review B 63 (2001) 165431.\n[38] S. Xu, R. T. Merrill, Microstress and microcoercivity in multidomain\ngrains, Journal of Geophysical Research: Solid Earth 94 (1989) 10627–\n10636. doi: https://doi.org/10.1029/JB094iB08p10627 .\n[39] A. K. Lindquist, J. M. Feinberg, R. J. Harrison, J. C. Loudon, A. J.\nNewell, Domain wall pinning and dislocations: Investigating magnetite\ndeformed under conditions analogous to nature using transmission elec-\ntron microscopy, Journal of Geophysical Research: Solid Earth 120\n(2015) 1415–1430. doi: 10.1002/2014JB011335 , publisher: John Wi-\nley & Sons, Ltd.\n[40] F. C. V oogt, T. T. M. Palstra, L. Niesen, O. C. Rogojanu, M. A. James,\nT. Hibma, Superparamagnetic behavior of structural domains in epitaxial\n6ultrathin magnetite films, Phys. Rev. B 57 (1998) R8107. doi: 10.1103/\nPhysRevB.57.R8107 .\n7"    },    {        "title": "1108.2773v1.First_Principle_Study_of_Magnetism_and_Magneto_structural_Coupling_in_Gallium_Ferrite.pdf",        "content": " 1First Principle Study of Magnetism and Magneto-stru ctural \nCoupling in Gallium Ferrite \n \nAmritendu Roy 1, Rajendra Prasad 2, Sushil Auluck 3, and Ashish Garg 1*  \n \n1Department of Materials Science & Engineering, Indi an Institute of Technology, Kanpur \n- 208016, India \n2 Department of Physics, Indian Institute of Technol ogy, Kanpur - 208016, India \n3 National Physical Laboratory, Dr K S Krishnan Marg , New Delhi-110012, India \n \nABSTRACT \n \nWe report a first-principles study of the magnetic properties, site disorder and magneto-\nstructural coupling in multiferroic gallium ferrite  (GFO) using local spin density \napproximation (LSDA+U) of density functional theory . The calculations of the ground \nstate A-type antiferromagnetic structure predict ma gnetic moments consistent with the \nexperiments whilst consideration of spin-orbit coup ling yields a net orbital moment of ~ \n0.025 µB/Fe site also in good accordance with the experimen ts. We find that though site \ndisorder is not spontaneous in the ground state, in terchange between Fe2 and Ga2 sites is \nmost favored in the disordered state. The results s how that ferrimagnetism in GFO is due \nto Ga-Fe site disordering such that Fe spins at Ga1  and Ga2 sites are \nantiferromagnetically aligned while maintaining fer romagnetic coupling between Fe \nspins at Ga1 and Fe1 sites as well as between Fe sp ins at Ga2 and Fe2 sites. The effect of \nspin configuration on the structural distortion cle arly indicates presence of magneto-\nstructural coupling in GFO. \n \nKey Words:  Gallium Ferrite, Multiferroic, Density functional theory, LSDA+U.   \n \nPACS No.:   71.15.Mb (DFT), 75.47.Lx (Magnetic oxides), 75.50 .Gg (Ferrimagnetics), \n75.80.+q (Magnetomechanical effect, magnetostrictio n),  \n                                                 \n* Corresponding author, Tel: +91-512-2597904; FAX - +91-512-2597505, E-mail: ashishg@iitk.ac.in  2I. INTRODUCTION \n \nIn the recent years, magnetoelectric (ME) and multi ferroic (MF) materials have generated \nimmense research interest owing to their potential in novel device applications such as in \nsensors, transducers and data storage. [1-3] While experiments have been performed on a \nfew selected materials, first principle studies hav e proven useful in prediction of new \nmaterials[4-6] and coupling mechanisms [7, 8].  As various theoretical and experimental \nstudies have shown that magnetism in the ME materia ls, such as antiferromagentic \nBiFeO 3 [9] can be modified by doping [10-12], reducing pa rticle size [13] or by \napplication of epitaxial strain [14, 15]. Moreover,  the ME coupling is shown to be greatly \naffected by epitaxial strain, pointing towards larg e magnetostructural (MS) coupling as it \nhas been predicted that the materials with large MS  coupling can even undergo antiferro-\nferromagnetic transition upon application of suitab le amount of epitaxial strain.[16] MS \ncoupling in another important class of materials, a ntiferromagnetic rare earth manganites \nwith giant ME coupling, over and above ME coupling,  induces additional change in the \nelectric dipole moment resulting in large spontaneo us polarization.[17]  \n \nIn this context, gallium ferrite (GaFeO 3 or GFO) emerges as an interesting \nmaterial simultaneously exhibiting piezoelectricity  and ferrimagnetism at temperatures \nnear room temperature (RT) as its magnetic transiti on temperature can be tuned close to \nor above RT depending upon Ga:Fe ratio [18, 19] and  processing condition.[18-21] GFO \nhas an orthorhombic structure with Pc2 1n symmetry which is retained over a wide \ntemperature range of 4-700 K. [18, 22] First-princi ples studies have shown that GFO is \nan antiferromagnet at 0 K, [23, 24]  but cation sit e disorder driven by almost similar ionic \nsizes of Ga and Fe results in uneven distribution o f magnetic moments in the octahedral \ninterstitial sites and is believed to render GFO as  a ferrimagnetic material with substantial \nmagnetic moment below T c [18]. GFO, reported to possess strong ME coupling [18, 25], \nis also likely to exhibit a cross-linking between t he structural and magnetic order \nparameters. Therefore, a study of magnetic behavior  focusing on the effect of structural \ndistortion on its magnetic behavior would be impera tive to explore this further. Moreover, \nexcept a few reports[18, 24] with rather different emphasis, the studies on the \nfundamental understanding of microscopic magnetic b ehavior of GFO such as effect of \nsite disorder on the magnetic moments and magnetic structure are severely lacking.  \n \nIn this paper, we present a detailed study on the a tomic scale magnetic behavior \nof GFO including the effect of site disorder and po ssible existence of MS coupling in the \nground state. The calculations indicate presence of  MS coupling in GFO. We also find \nthat the magnetism is solely due to cation site dis order in GFO. The calculated magnetic \nmoments of Fe ions in GFO agree well with, albeit s carce, previously reported \nexperimental [18] and theoretical [24] data. Althou gh, there are many reports of magneto-\nstructural coupling in materials, the phenomenon is  not well understood at a microscopic \nlevel. A first principles calculation affords us th is opportunity to explore the origin of MS \ncoupling in GFO. \n \n \n  3II. CALCULATION DETAILS \n \nWe employed first principles density functional the ory [26] based Vienna ab-initio \nsimulation package (VASP) [27] with projector augme nted wave method (PAW) [28] in \nour calculation. Local spin density approximation ( LSDA+U) [29] with Hubbard \nparameter, U = 5 eV, and the exchange interaction, J = 1 eV was used to solve the Kohn-\nSham equation. [30] The value of U was so determine d that the calculated magnetic \nmoments of Fe ions agree well with the experimental ly determined moments. Small \nvariation of U was found not to affect the system’s  stability. Calculations are based on the \nstoichiometric GFO with no partial occupancies of t he cations. We included 3 valence \nelectrons of Ga ( 4s 24p 1), 8 for Fe ( 3d 74s 1) and 6 for O ( 2s 22p 4) ions. The effect of 3d \nsemicore states of Ga ion was found not to affect t he structural and magnetic \ncharacteristics significantly and therefore, ignore d. [23] A plane wave energy cut-off of \n550 eV was used. Conjugate gradient algorithm [31] was used for the structural \noptimization. Structural calculations were performe d at 0 K with Monkhorst-Pack [32] \n7×7×12 mesh while site-disorder and MS coupling stu dy was performed with 4×4×4 \nmesh which hardly made differences with that of 7×7 ×12 mesh calculations. We also \nrepeated some of our calculations using generalized  gradient approximation (GGA+U) \nwith the optimized version of Perdew-Burke-Ernzerho f functional for solids (PBEsol) \n[33] to check the robustness of our LSDA+U calculat ions. Magnetic measurement of the \nexperimentally synthesized sample [23] was done usi ng Lakeshore vibration sample \nmagnetometer. \n \nIII. RESULTS AND DISCUSSION \n \nA. Crystal and Magnetic Structures  \n \nGround state crystal structure, determined in our e arlier study[23], predicted \northorhombic Pc2 1n symmetry with A-type antiferromagnetic spin config uration. \nCalculated ground state lattice parameters, using L SDA+U, are: a = 8.6717 Å, b = 9.3027 \nÅ and c = 5.0403 Å which correspond well with experiments.  Calculated ionic positions, \ncation-oxygen and cation-cations bond lengths are a lso in good agreement with the \nexperiments.[23] \n \nBased on the ground state structural data, [23] (se e Fig. 1) we calculated Fe-O-Fe \nbond angles which can be correlated with the super- exchange interaction between O and \nneighboring Fe 3+  ions. Generally, larger the Fe-O-Fe bond angle, st ronger is the \nantiferromagnetic super-exchange. [34, 35]  From th e structural parameters, obtained \nfrom our first principles calculations and from the  experimental XRD data,[23] we \ncalculated cation-oxygen-cation bond angles as comp iled in Table 1. The maximum value \nof Fe1-O1-Fe2, bond angle is ~168.54 o while other angles are: Fe1-O3-Fe2, 123.13 o and \nFe1-O5-Fe2, 126.23 o , respectively calculated using LSDA+U method as o bserved in \nTable1. As a check, similar values were also obtain ed using GGA+U also. Situated at the \nnext nearest neighbor positions, O4 and O6 also for m wide Fe-O-Fe bonds with angles \nFe1-O4-Fe2, 143.36 o and Fe1-O6-Fe2, 174.46 o. As we show in the following paragraph, \nsuch large Fe-O-Fe bond angles (larger than 90°) le ad to noticeable super-exchange  4interaction between Fe and O ions which is reflecte d in significantly large magnetic \nmoments of O. Maximum bond angle among Fe-O-Ga is o bserved for Fe1-O1-Ga2 \n~166.08 o. Any Fe ion that occupies Ga2 site due to site dis order would therefore form a \nstrong antiferromagnetic spin arrangement with Fe a t Fe1 site through super-exchange \ninteraction. This strongly indicates that Fe at Ga2  site would be ferromagnetically aligned \nwith Fe2 ions. This emphasizes that Fe2 ion is also  antiferromagnetically coupled to Fe at \nGa1 site since the Ga1-O6-Fe2 bond angle, ~124.12 o is significantly larger than 90 o.41, 42  \nIt is therefore, reasonable to state that any Fe io n occupying Ga1 site due to site disorder \nwould align itself antiferromagnetically with Fe2 a nd Fe at Ga2 site and would be \nantiferromagnetically coupled with Fe1 site.  \n \nAs discussed in detail in our previous work (Ref. 2 3), we started our calculation to \ndetermine the ground state structure of GFO with fo ur possible antiferromagnetic spin \nstructures, namely, AFM1 (A-type antiferromagnetic) , AFM-2 (C-type \nantiferromagnetic), AFM-3 (G-type antiferromagnetic ) and AFM-4 and established that \nthe ground state magnetic structure of GFO is A-typ e antiferromagnetic (A-AFM) [23]. \nNow, we calculate the magnetic moments of the const ituent ions in the ground state and \ncompare these with the data reported in the literat ure (see Table 2). Our calculations \nusing LSDA+U method show that Fe1 and Fe2 ions have  magnetic moments of + 4.05 µB \nand - 4.04 µB, respectively whereas GGA+U calculations predict F e magnetic moments \nof + 4.12 µB and -4.12 µB for Fe1 and Fe2, respectively. We find that while the \nmagnitude of moments agrees well with the experimen tal data, the sign, though in \nagreement with the theoretical data shown by Han et al . [24], is opposite to the \nexperimental neutron diffraction results showing -3 .9 µB and + 4.5 µB for Fe1 and Fe2 \nrespectively. The difference in the sign of the mag netic moments with respect to those \nobtained from neutron studies is due to an equivale nt spin structure which is mirror image \nof AFM-1. We calculated the total energy of such a structure and found that the energy \nper unit-cell is identical for either of the two st ructures. As discussed earlier, magnetic \nmoments manifested by oxygen ions are due to super- exchange interactions with the \nsurrounding Fe ions. Table 2 also shows that moment s calculated by Han et al.  [24] using \nLSDA+U (without SOC) yielded somewhat larger values  of magnetic moments than \neither the experimental data or the values shown by  our results.  \n \nFurther, to probe the spin-orbit interaction in the  ground state structure, we \nperformed spin-orbit coupling in conjunction with L SDA+U calculation assuming spin \nmoment directions of Fe1 and Fe2 to be [001], as su ggested by the experiments [36] and \nthe calculations yielded the orbital magnetic momen t of ~ 0.025 µB/Fe site. This value is \nslightly larger than 0.02 µB/Fe site calculated by Han et al [24] and 0.017 µB/Fe site \nmeasured experimentally at 190 K, by Kim et al [36]. Interestingly, while SOC \ncalculations by Han et al [24] reduced the magnetic moment by ~0.75 µB, our SOC \ncalculation did not alter the magnetic moments sign ificantly. Since our LSDA+U \ncalculations without the consideration of spin-orbi t interaction satisfactorily describe the \nmagnetic structure with respect to the experimental  results and a more precise magnetic \nstructure would probably not improve the accuracy o f our further calculations in a \nsignificant way, we ignored spin-orbit interaction in further calculations. \n  5B. Cation Site Disorder and it’s Effect on Magnetic  Behaviour \n \nPrevious experiments suggest that the magnetic stru cture of GFO can be influenced \nsignificantly by cation site-disorder i.e.  mixed occupancies of Ga and Fe on each other’s \nsites. Experiments using both neutron [18] and x-ra y diffraction [22] techniques reveal \nthat structure of GFO exhibits cation site disorder  i.e.  some of the Ga sites are occupied \nby Fe ions. Most previous studies indicate that Fe occupation of Ga1 sites is much \nsmaller than Ga2 sites.[18] Experimental study[18] and our previous discussion in section \nIII (A) show, ferromagnetic coupling of Fe at Fe2 a nd Ga2 sites [18] and thus it is \nbelieved that Fe2 ions mostly occupy Ga2 sites. How ever, there is no concrete evidence \nsupporting this since Fe ions upon getting out of i ts original sites may change its spin \nconfiguration. Since the results shown in the previ ous paragraphs are based upon the \nassumption of full site occupancy, we further inves tigated the cation site disorder in GFO, \nto determine which Fe ions preferentially occupy Ga  sites.   \n \nTo study the effect of cation site disorder on the magnetic structure, we \nselectively interchanged Fe and Ga sites and comput ed total energy of the system. Since, \nGFO unit-cell contains four ions of each type of ca tion, such an interchange would result \nin ¼ th  site occupancy of Fe ions at Ga sites and vice-versa . The change in the energy of \nthe unit-cell with respect to the ground state upon  site interchange is plotted in Fig. 2. The \nfigure shows that at 0 K, partial site occupancy is  not favored in the ground state, also \nobserved previously by Han et al. [24]  Therefore, thermal energy and lattice defects  are \nthe only likely sources to induce the experimentall y observed site disorder in GFO. \nHowever, Fig. 2 also shows that among various possi ble cases of site disorders, Fe2 ions \npreferentially occupy Ga2 sites is most probable si nce ∆E, the energy difference with \nrespect to the ground state in that case is minimum . Although these energy differences \nmay be affected by the computational methodology, i nterestingly, the magnitude of the \navailable thermal energy at room temperature (kT ~25  meV) is of the order of the energy \ndifference for Fe2-Ga2 site disorder indicating tow ards the role of thermally originated \ndefects.  \n  \nAn important implication of the inclusion of cation  site disorder in the calculation \nwould be on the modification of the local magnetic moments. It was observed that upon \ninterchanging Fe1 and Ga1 sites, the average magnet ic moment of Fe ion at Ga1 site  \nbecomes 3.99 µB. While the average magnetic moments of Fe1 ions re main the same, the \nmoments at Fe2 sites are slightly modified with res pect to the perfect structure. On the \nother hand, the magnetic moment of Fe ion at Ga2 si te becomes 4.11 µB when Fe2 and \nGa2 sites are interchanged. Though, earlier Neutron  study [18] shows an increase of \n~4.5% in the magnetic moment of Fe2 ion located at G a2 (4.7 µB) site over the original \nFe2 magnetic moment (4.5 µB), our calculations show only ~ 1.5 % increase of th e \nmoment of Fe ions at Ga2 site with respect to the p arent Fe2 site. Such a small increase in \nthe magnetic moment is probably attributed to the l imitation of local density \napproximation. With Fe2-Ga2 site interchange, the m agnetic moments at Fe1 and Fe2 \nsites are also modified slightly with average momen ts being + 4.05 µB and - 4.06 µB. A \ncloser investigation shows that the Fe1 sites neare st to the occupied Ga2 site have a \nmoment of ~ 4.11 µB while Fe1 site farthest to the Ga2 site has a mome nt of ~ 4.03 µB.   6However, the magnetic moments of the Fe2 sites are almost similar to each other. Further, \nsite interchange between Fe1-Ga2 and Fe2-Ga1 also d emonstrate changes in local \nmagnetic moments similar to the above two most prob able situations of site disorder i.e. , \nFe2-Ga2 and Fe1-Ga1 \n \nAs we have shown earlier, large bond angles for Fe- O-Fe demonstrate \nantiferromagnetic coupling of the spins at Fe1 and Fe2 sites. Further, any Fe at Ga1 site \nwould have ferromagnetic interaction with Fe at Fe1  site while Fe at Ga2 site would \nmake ferromagnetic coupling with Fe at Fe2 site. Ho wever, while the ground state \nstructure showed perfect antiferromagnetism with ne t magnetic moment ~ 0 µB, our VSM \nmeasurements on crushed single crystals of GFO show ed a net magnetic moment of 0.21 \nµB/ Fe site at 120 K. Using the partial site occupanc ies from the Rietveld refinement \ndata[23] and taking the magnetic moments from the p receding paragraph for different \ncation sites, we estimated net magnetic moment of 0 .24 µB/ Fe site which agrees quite \nwell with our experimental results. Therefore, we c onclude that ferrimagnetism in GFO is \nsolely due to site disorder in the structure. As no ted in earlier paragraphs, the Fe ions at \nGa sites would develop different magnetic moments d ue to different crystal environments \nthan their parent sites.  \n \nC. Determination of Magneto-structural (MS) Couplin g \n \nSince GFO is a piezoelectric and antiferromagnetic in the ground state, it is likely to \ndemonstrate piezomagnetism and would possibly have significant MS coupling. To the \nbest of our knowledge, there is no theoretical or e xperiments work in the literature on \nthese features of GFO. As can be expected, MS coupl ing in several magnetic compounds \nresults in structural distortion.[37] Depending upo n the strength of the coupling, this \ndistortion can even cause structural phase transiti on as observed in MnO,[38] CrN [37, \n39] and LaMnO 3 [40], SrMnO 3.[16] In this section, to investigate the presence of MS \ncoupling in GFO, we first look at the effect of spi n ordering which results in significant \nstress in the structure and then we demonstrate tha t structural distortion results in \nvariation in magnetization of the magnetic ions of the system.  \n \nWe keep AFM-1 as the reference magnetic structure a nd change the spin \nconfigurations according to AFM-2, AFM-3 and AFM-4 structures while maintaining the \nlattice parameters and ionic positions of the optim ized AFM-1 structure. On this basis, \nwe calculated the forces on the atoms and stresses along the b-axis and the results are \nlisted in Table 3. Here we observe that the stress,  maximum force and hydrostatic \npressure on AFM-2, AFM-3 and AFM-4 structures are d ifferent indicating that the spin \nconfiguration can influence the structural stabilit y and in turn  suggests towards the \nexistence of MS coupling in GFO. Subsequently, we r elaxed the structures corresponding \nto the above spin configurations such that the forc es on atoms and hydrostatic pressure \nare close to zero and plotted the lattice parameter s and magnetic moment of Fe ion for all \nthe spin configurations, mentioned above, in the re spective optimized structures as shown \nin in Fig. 3 (a) and (b). Here, we see that that no t only significant lattice distortion is \ninvoked upon variation in spin configuration; also the magnetic moments at the two Fe  7sites are affected by the change in the spin config uration. This, therefore, again indicates \ntowards the presence of MS coupling in GFO.  \n \nWojdeł and Íñiguez [15] showed that a quantitative measure of MS coupling can \nbe provided by frozen ion piezomagnetic stress tens or (iij \njuMhδ\nδη −\n= ) and magnetization \nchange driven by atomic displacement (i\npi \npM\nu\nηδζδ= −Ω ), defined at zero external electric \nfield ( M: magnetization, η: strain, u: displacement). However, in a more simplistic \nmanner, one can argue, if the magnetization of a sy stem is affected by application of an \nexternal stress (or vice-versa), the coupling coeff icient (dM \ndτσ= , σ: applied hydrostatic \nstress resulting in volumetric strain in the system ) would be a measure of MS coupling. \nHere, we allow the ions within the unit-cell to com pletely relax in order to accommodate \nthe external stress. In this process, one can combi ne the effects of structural strain and \natomic displacement [15] on the resultant magnetiza tion.  \n \nOn this basis, we sequentially applied hydrostatic stress (pressure) on the structure \nand calculated resultant magnetic moments of Fe1 an d Fe2 ions and results are shown in \nFig. 4. Total energy calculation of the two AFM str uctures, AFM-1 (A-AFM) and AFM-2 \n(C-AFM) (stability wise C-AFM is second most stable  structure after ground state A-\nAFM structure[23]) shows no change in the magnetic structure upon application of \nexternal pressure (see inset of Fig. 4). However, m agnetic moments at Fe1 and Fe2 sites \nas shown in Fig. 4 demonstrate a small change. Line ar fitting of magnetization plotted as \na function of external pressure, yields the coeffic ient of MS coupling ( τ) of the order of ~ \n2×10 -3 µB/GPa. To substantiate the above calculation of τ, we applied the same approach \nto cubic SrMnO 3, a well proven material demonstrating epitaxial st rain driven structural \n(as well as magnetic) phase transition [16] indicat ing the presence of strong MS coupling. \nWe find that similar calculations on SrMnO 3 demonstrate τ ~ 6.5×10 -3 µB/GPa and τ ~ \n2.18×10 -2 µB/GPa in the G-type antiferromagnetic and ferromagne tic states of SrMnO 3 \nrespectively. These values being noticeably larger than that seen in GFO, we can deduce \nthat the MS coupling in GFO is relatively weaker an d therefore may not drive the system \nto any structural transition. This is further suppo rted by the absence of any significant \nstructural anomaly near the magnetic transition tem perature of GFO.[18, 22] While there \nare no experimental results to compare the values o f MS coupling coefficients based on \nabove formalism, possibly pressure dependent neutro n diffraction studies would prove \nuseful in explaining this further. \n \n \nCONCLUSIONS \n \nIn summary, using LSDA+U method as implemented in V ASP, our density functional \ntheory based calculations have explained the magnet ic behavior of GFO vis-à-vis site \ndisorder and subsequent magneto-structural coupling  in multiferroic gallium ferrite. The  8calculated magnetic moments of Fe ions are in reaso nable agreement with the \nexperimental reports.  We find that the cation site  disorder not preferred in the ground \nstate, Fe2-Ga2 site interchange is the most favored  configuration in the disordered states. \nThis appears to be driven by the thermal energy as the energy difference between two \nstates is of the order of k BT. An examination of the role of cation site disord er on \nmagnetic structure of GFO showed modification of th e local magnetic structure and \naltered magnetic moments of Fe ions at Ga site sugg est that ferrimagnetism in GFO is \nsolely due to site disorder. Further, an antiferrom agentic coupling is predicted between Fe \nions at Ga1 and Ga2 sites while Fe ions at Fe1 and Fe2 sites couple ferromagnetically. \nFinally, we find a compelling indication of, albeit  somewhat weaker than compounds like \nSrMnO 3, magneto-structural coupling in GFO as changes in the spin arrangement led to \nsignificant variation in the structural distortion as well as magnetic moments.  \n \nAcknowledgements \n \nAuthors thank Prof. M.K. Harbola and Prof. Rajeev G upta (Physics Department, IIT \nKanpur) for fruitful discussions and suggestions. A uthors thank Ms. Somdutta Mukherjee \nfor her help with the bulk magnetic measurements. A R thanks Ministry of Human \nResources, Government of India for the financial su pport. \n \nReferences: \n \n[1] Prinz G A1998 Science  282 1660 \n[2] Scott J F 2009 Chem. Phys. Chem.  10 1761. \n[3] Scott J F 2007 Nat. Mater. 6 256. \n[4] Baettig P and Spaldin N A 2005 Appl. Phys. Lett.  86  012505. \n[5] Picozzi S, Yamauchi K, Sanyal B, Sergienko I A,  Dagotto E. 2007 Phys. Rev. Lett.  \n99  227201. \n[6] Bhattacharjee S, Bousquet E, Ghosez P 2009 Phys. Rev. Lett.  102 117602. \n[7] Fennie C J 2008 Phys. Rev. Lett. 100 167203. \n[8] Delaney K T, Mostovoy M, Spaldin N A 2009 Phys.  Rev. Lett. 102 157203. \n[9] Sosnowska  I et al . 1982 J. Phys. C: Solid State Phys.  15 4835. \n[10] Khomchenko V A, Kiselev D A, Bdikin I K, Shvar tsman V V, Borisov P, \nKleemann W, Vieira J M, Kholkin A L 2008 Appl. Phys. Lett.  93  262905. \n[11] Das S R, Choudhary R N P, Bhattacharya P, Kati yar R S, Dutta P, Manivannan A, \nSeehra M S 2007 J. Appl. Phys.  101  034104. \n[12] Kadomtseva A M, Popov Y F, Pyatakov A P, Vorob 'ev G P, Zvezdin A K, \nViehland D 2006 Phase Transitions  79 1019. \n[13] Goswami S, Bhattacharya D, Choudhury P 2011 J. Appl. Phys.  109  07D737. \n[14] Wang J, Neaton J B, Zheng H, Nagarajan V, Ogal e S B, Liu B, Viehland D, \nVaithyanathan V, Schlom D G, Waghmare U V, Spaldin N A, Rabe K M, Wuttig M, \nRamesh R 2003 Science  299 1719. \n[15] Wojdeł J C, Íñiguez J. 2009. Phys. Rev. Lett.  103  267205. \n[16] Lee J H, Rabe K M 2010 Phys. Rev. Lett. 104 207204. \n[17] Lueken H. A  2008 Angew. Chem. Int. Edn.  47  8562. \n[18] Arima T et al  2004 Phys. Rev. B  70 064426.  9[19] Remeika J P 1960 J. Appl. Phys.  31 S263. \n[20] Nowlin C H, Jones R V 1963 J. Appl. Phys. 34 1262. \n[21] Kaneko Y, Arima T, He J P, Kumai R, Tokura Y 2 004 J. Magn.Magn.Mater.  272-\n276  555. \n[22] Mukherjee S, Gupta R, Garg A.  2011 arXiv:1103.5541 . \n[23] Roy A, Mukherjee S, Gupta R, Auluck S, Prasad R, Garg A  2011 J. Phys.: \nCondens. Matter  23 325902. \n[24] Han M J, Ozaki T, Yu J 2007 Phys. Rev. B  75 060404. \n[25] Rado G T 1964 Phys. Rev. Lett.  13 335. \n[26] Jones R O and Gunnarsson O 1989 Rev. Mod. Phys.  61 689. \n[27] Kresse G and Furthmüller J  1996 Phys. Rev. B  54 11169. \n[28] Blöchl P E 1994 Phys. Rev. B  50 17953. \n[29] Anisimov V I, Aryasetiawan F, Lichtenstein A I  1997 J. Phys.: Condens. Matter  \n9 767. \n[30] Kohn W and Sham L J 1965 Phys. Rev.  140 A1133. \n[31] Press W H, Flannery B P, Teukolsky S A, Vetter ling W T.  1986 Numerical \nRecipes: The Art of Scientific Computing  (New York: Cambridge University Press). \n[32] Monkhorst H J, Pack J D 1976 Phys. Rev. B   13 5188. \n[33] Perdew J P et al  2008 Phys. Rev. Lett.  100 136406  \n[34] Goodenough J B 1955 Phys. Rev.  100  564.  \n[35] Goodenough  J B 1958 J. Phys. Chem. Solids  6 287. \n[36] Kim J Y, Koo T Y, Park J H 2006 Phys. Rev. Lett.  96 047205. \n[37] Filippetti A, Hill N A 2000 Phys. Rev. Lett.  85 5166. \n[38] Massidda S, Posternak M, Baldereschi A, Resta R 1999 Phys. Rev. Lett.  82  430. \n[39] Corliss L M, Elliott N, Hastings J M 1960 Phys. Rev.  117 929. \n[40] Singh D J, Pickett W E 1998 Phys. Rev. B   57 88. \n \n \n \n \n \n \n \n \n \n  10 List of Tables  \n \nTable 1  Comparison of calculated and experimentally determ ined major bond angles in \ngallium ferrite unit-cell.  \nBond angle (all \ndata are in o) LSDA+U GGA+U Experiment \nFe1-O1-Fe2 168.54 168.33 166.11 \nFe1-O2-Fe2 103.06 103.30 99.33 \nFe1-O3-Fe2 123.13 123.07 121.00 \nFe1-O4-Fe2 143.06 143.90 143.22 \nFe1-O5-Fe2 126.23 126.21 126.20 \nFe1-O6-Fe2 174.46 174.63 173.25 \nFe1-O1-Ga2 166.08 165.81 164.08 \nGa1-O6-Fe2 124.12 124.06 122.57 \n \n \nTable 2  Comparison of the calculated magnetization ( µB) data with previous \ncalculations and experiments. \nIon LSDA+U \nwithout \nSOC * LSDA+U \nwith SOC *  (GGA+U) \nwithout \nSOC * LSDA+U  \n(without \nSOC)  † LSDA+U \n(with SOC)  † Experiment ††  \nGa1 -0.01 -0.01 -0.01 0.01 0.01  \nGa2 0.01 0.01 0.01 0.06 0.03  \nFe1 4.05 4.05 4.12 5.02 4.27 -3.9 \nFe2 -4.04 -4.04 -4.12 -5.11 -4.34 4.5 \nO1 0.06 0.06 0.06 \n-0.03 to \n0.06 -0.07 to 0.06 - O2 0.00 0.00 0.00 \nO3 0.01 0.02 0.01 \nO4 -0.05 -0.05 -0.05 \nO5 0.05 0.06 0.06 \nO6 -0.07 -0.07 -0.07 \n* Present work; † Han et al 21 ; †† Arima et al  1 \n \nTable 3  Calculated stress along crystallographic b-directi on, maximum force on ions in \nthe unit-cell and hydrostatic pressure on the unit- cell upon variation in spin \nconfiguration. \n AFM-1 AFM-2 AFM-3 AFM-4 \nStress (N/m 2) ×10 -4 42.7 45.2 45.2 65.9 \nForce (max.) (eV/Å) 0.0002 0.6400 0.6068 0.6500 \nHydrostatic Pressure \n(kB) -0.27 3.96 10.16 9.37 \n  11 Figure Captions \n \nFigure 1 Schematic crystal structure of GFO. The ar rows indicate the direction of \nmagnetic moment for Fe1 and Fe2 ions. \n \nFigure 2 Change in the energy per unit-cell with re spect to the ground state energy \nupon incorporating cation site disorder.  The calcu lations were carried out \nusing LSDA+U technique.  \n \nFigure 3 Changes in (a) the ground state lattice pa rameters and (b) magnetic \nmoments for different spin configurations. Dashed l ines are only as a \nguide to the eye.  \n \nFigure 4 Variation of magnetic moment as a function  of applied hydrostatic stress \non GFO unit-cell. Inset shows a plot of total energ y for AFM-1 and AFM-\n2 structures versus applied pressure. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  12 Figures  \n \n \n \n \nFig. 1, Roy et al . \n \n \n \n \n \n \n  13 \n \n \nFig. 2, Roy et al .  \n \n \n \n \n \n \n  14 \n \n \nFig. 3 Roy et al . \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  15  \n \n \n \n \n  \n \n \nFig. 4 Roy et al . "    },    {        "title": "2302.05310v1.Laser_induced_magnonic_band_gap_formation_and_control_in_YIG_GaAs_heterostructure.pdf",        "content": "Laser-induced magnonic band gap formation and control in YIG/GaAs heterostructure\nK. Bublikov,1M. Mruczkiewicz,1, 2E.N. Beginin,3M. Tapajna,1D. Gregušová,1M. Ku ˇcera,1\nF. Gucmann,1S. Krylov,1A.I. Stognij,4S. Korchagin,5S.A. Nikitov,3, 6and A.V . Sadovnikov3\n1Institute of Electrical Engineering, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04 Bratislava, Slovakia\n2Centre For Advanced Materials Application CEMEA,\nSlovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava, Slovakia\n3Laboratory \"Magnetic Metamaterials\", Saratov State University, Saratov 410012, Russia\n4Scientific-Practical Materials Research Center of National Academy of Sciences of Belarus, P . Brovki 19, 220072 Minsk, Belarus\n5Financial University under the Government of Russian Federation, 4th Veshnyakovsky pr. 4, 111395 Moscow, Russia\n6Kotel’nikov Institute of Radioengineering and Electronics, RAS, Moscow 125009, Russia\n(*konstantin.bublikov@savba.sk)\n(Dated: February 13, 2023)\nWe demonstrate the laser-induced control over spin-wave (SW) transport in the magnonic crystal (MC)\nwaveguide formed from the semiconductor slab placed on the ferrite film. We considered bilayer MC with\nperiodical grooves performed on the top of the n-type gallium arsenide slab side that oriented to the yttrium iron\ngarnet film. To observe the appearance of magnonic gap induced by laser radiation, the fabricated structure was\nstudied by the use of microwave spectroscopy and Brillouin light-scattering. We perform detailed numerical\nstudies of this structure. We showed that the optical control of the magnonic gaps (frequency width and posi-\ntion) is related to the variation of the charge carriers’ concentration in GaAs. We attribute these to nonreciprocity\nof SW transport in the layered structure. Nonreciprocity was induced by the laser exposure of the GaAs slab\ndue to SWs’ induced electromagnetic field screening by the optically-generated charge carriers. We showed\nthat SW dispersion, nonreciprocity, and magnonic band gap position and width in the ferrite-semiconductor\nmagnonic crystal can be modified in a controlled manner by laser radiation. Our results show the possibility of\nthe integration of magnonics and semiconductor electronics on the base of YIG/GaAs structures.\nI. INTRODUCTION\nCurrently, the intense research in the field of dielectric\nmagnonics [1–7] is focusing on the tasks of signal encoding,\ntransport, and manipulation. This leads to the formation of\nthe solid-state magnonics units, which in contrast with classi-\ncal microelectronics, operate with magnons (quantum of spin\nwave) as information carriers [8, 9]. In analogy to the conven-\ntional complementary metal-oxide-semiconductor (CMOS)-\nbased electronics [10], magnon-base components can act as\nthe independent units in the magnonic networks [11–13] with\nan aim to form functional devices. This is one of the concepts\nthat may allow overcoming the almost achieved physical lim-\nits in CMOS-based electronics. In addition, semiconductor\nmagnonics [14] might play the role of the bridge, allowing\nthe combination of the magnonics and CMOS-based electron-\nics elements. For this purpose, structures based on the bi-\nlayers of semiconductor-insulating magnetic material should\nbe designed. Recently, a problem of incompatibility of the\nsubstrates used in insulating magnonics structures with the\nCMOS- components was investigated [15–18]. The perspec-\ntive bilayers for semiconductor magnonics were grown, such\nas yttrium iron garnet (YIG) / gallium arsenide (GaAs) het-\nerostructure.\nOne of the structures considered to be a magnonic compo-\nnent is the magnonic crystals (MCs) [19, 20]. MCs are formed\nby the artificially created periodicity in the structure in the\ndirection of SWs’ propagation. This leads, due to the pres-\nence of Bragg resonances in such structures, to the formation\nof bandgaps in the spectrum of the propagating waves (also\ncalled magnonic band gaps). MCs are expected to be widely\nused in the magnonic data processing.The lattice of the early-designed MC was often fabricated\nas the periodic defects of the magnetic film surface (e.g.,\ngrooves or holes) or by growing the conductive stripes atop\nthe magnetic layer [19]. Nowadays, an important task for\nmagnonics is to design the reconfigurable MC in which pe-\nriodic spatial variation of media properties will be induced by\nthe physical effects due to external impact. Therefore, meth-\nods of manipulation of the lattice period in time are in de-\nmand. A few types of such MCs and the physical principles\nbehind them will be highlighted next.\nFor instance, using the current flow in the electrode lattice\natop of magnetic film layer allows the creation of a spatial\nvariation of the local magnetic field [21, 22]. MCs can also be\nperformed based on the interaction of the SWs transport with\nthe acoustic waves (which requires the excitation of acoustic\nwaves) [23]. Phenomena of these waves’ interactions are stud-\nied in terms of Straintronics and Magnon Straintronics disci-\nplines [24–27]. More energy-efficient voltage tunable MCs\n(also controlled by the lattice of electrodes) may be created\nbased on the periodic changes of the electric permittivity in\nthe ferroelectric-magnetic insulator bilayers [28] or by the pe-\nriodic variation of anisotropy in the nanoscale-size magnetic\nplanar waveguide [29]. Further, lattices formed in waveg-\nuides by the noncollinear magnetic states, e.g., domain walls\n[30, 31] or skyrmions [32], can be nucleated or annihilated\nby external stimuli. Another interesting approach was pro-\nposed based on the superconductor-insulating magnetic het-\nerostructure, where the periodic lattice of Abrikosov vortices\ninduced a periodic local magnetic field modulation [33]. In\nthe so-called moving MCs, a periodic lattice is formed by the\nstrain-induced propagating acoustic waves [34]. MCs based\non the periodic variation of the magnetization in the magneticarXiv:2302.05310v1  [cond-mat.mes-hall]  10 Feb 20232\nfilm are also possible to realize by the optical means due to\nthe heating of YIG film [35–37].\nThe concept of the dynamic MCs implies that tuning speed\nshould be faster than the time of SWs’ propagation through\nthe structure. Since magnonics working frequencies are in\nthe order of GHz (with possibilities to reach the THz range)\n[38, 39], to obtain a comparable rate of lattice manipulation,\na physical mechanism that induces the lattice should be of\nthe same range. In comparison with the SWs frequencies, the\nheating mechanisms and mechanisms of manipulation by the\nmagnetization states are too inert in time to be applied for dy-\nnamic MCs. This constricts the number of possible methods\nto induce the lattice and thus limits reconfigurability methods\nin magnonics.\nIn this work, we propose to use semiconductor magnon-\nics [18] in order to obtain the optically tunable MC based on\nYIG/GaAs heterostructure. The possibility of optical manipu-\nlation by the SWs’ properties in the magnetic-semiconductor\nbilayers was theoretically and experimentally demonstrated in\nworks [18, 40–47] (e.g., for YIG/GaAs heterostructure), and\nit was proved that this tuning was related to the variation of\nconductivity in the semiconductor layer due to the external\nlight irradiation. The influence of the semiconductor screen-\ning layer conductivity on the propagating SW’ may be com-\npared to the mechanism of screening the SW’s- induced elec-\ntric field by a metal layer which was demonstrated in works\n[48–50], So it also induces the SWs’ nonreciprocity [51] in\nthe semiconductor-magnetic heterostructures [18]. Thus, cre-\nating a periodic variation of conductivity in the semiconductor\nlayer allows obtaining the MCs similar to the one with metal\nstripes lattice. At the same time, the rate of the SWs’ tuning by\nthe mechanism of optical injection of nonequilibrium charge\ncarriers in semiconductor magnonics is limited by injection-\nrecombination processes, which are fast enough to be used in\nthe dynamical magnonics blocks. We point here that in gen-\neral, the definition of the electrodynamic properties of lattices\ncomposed from the periodically arranged semiconductors is a\ncomplex task, and it was considered, e.g., in works [52] with\nthe author of this thesis as a collaborator.\nThe possibility of both manipulation of the SWs’ character-\nistics and inducement of a lattice cell for MCs’ by the optical\nmeans in the insulator magnetic-semiconductor heterostruc-\ntures opens a broad perspective for designing new tunable\nmagnonics devices. The periodic spatial variation of con-\nductivity can be obtained by forming specific semiconductor\npatterns (e.g., deposition of the semiconductor stripes atop\nmagnetic film). In this research, in order to study the phe-\nnomena of the formation of the magnonic band gaps in the\nGaAs/YIG, we have combined the heterostructure of the semi-\nconductor with a grooved surface faced to YIG. Applying an\nexternal laser light irradiation allows us to increase the con-\ntrast of the spatial variation of the charge carriers’ concentra-\ntion in the GaAs layer. Based on the measurements of the\nYIG/GaAs MC sample and their comparison with the results\nof numerical simulations, we demonstrated the processes of\nthe light-induced switching of the magnonic gaps and their\nlight-induced frequency tuning characteristic.II. SAMPLE FABRICATION AND EXPERIMENTAL\nMETHODS\nA. Fabrication of YIG/GaAs magnonic crystals structure\nThe sketch of the fabricated multilayered waveguide struc-\nture is presented in Fig. 1 ( a). As a material for fabrication of\nthe magnetic planar waveguide, we used the commercial ferri-\nmagnetic YIG film [39, 53] grown by high-temperature liquid\nphase epitaxy on the gadolinium gallium garnet ( Gd3Ga5O12\n(111), GGG) substrate. YIG film had the following parame-\nters [39, 53]: thickness 9 mm, permittivity e=9, saturation\nmagnetization MS=139:26 kA/m, gyromagnetic ratio g=\n175:93 rad GHz/T, ferromagnetic resonance (FMR) linewidth\nm0DH=28 GHz/T measured at the frequency 9.7 GHz.\nA waveguide of the width w=1 mm and the length of\n20 mm was etched from the YIG/GGG film with the use of\nthe laser ablation method [54]. The ablation setup was based\non fiber YAG:Nd laser with the high precision 2D scanning\ngalvanometric module (Cambridge Technology 6240H) work-\ning in a pulse mode with a pulse length of 50 ns and a pulse\npower of 5 mJ. This method was adapted for processing with\nYIG films of thickness 0.1 - 10 mm and earlier used in works\n[55, 56].\nThe layered MC was composed by positioning a semicon-\nductor slab atop this YIG waveguide. The slab of width, w=\n1 mm, and of length, L=5 mm, was etched by laser ablation\nfrom the commercial epitaxially grown GaAs film (manufac-\ntured for the components of the CMOS transistors). Accord-\ning to the passport information of the sample, this commercial\nsemiconductor had 1 mm of doped n-type GaAs layer atop of\n500mm thick semi-insulating n GaAs. The expected electron\nconcentration of semi-insulating layer was \u00181010cm\u00003and\nof the highly doped layer \u00181017cm\u00003, which are in agree-\nment with, e.g., [57, 58].\nWe applied laser ablation method to obtain periodic grooves\n(D=200mm period) on one face of the GaAs slab (see inset in\nFig. 1 ( a)). We note here that this spatial periodic modulation\nof the GaAs slab thickness was performed from the highly-\ndoped face of the GaAs slab. Thus, the highly doped layer\nwas split into a lattice of periodic stripes. GaAs slab was fixed\natop the center of the magnetic waveguide with grooves facing\nthe YIG film, perpendicular to the direction of the propagat-\ning waves (see Fig. 1 ( a)). Further we will call this structure\nperiodic GaAs/YIG or YIG/GaAs magnonic crystal.\nThe fabricated YIG/GaAs MC was placed on a holder with\nmicrostrip microwave antennas on its surface. Fixation of\nmultilayer structure on the holder was done in a way that mi-\ncrostrip antennas were in contact with the YIG surface, per-\npendicular to the waveguide direction (see Fig. 1 ( a)). The\nholder design allowed for connecting the microstrip anten-\nnas to a microwave power source through the coaxial cables.\nMicrostrip antennas were used to perform the SWs’ excita-\ntion and detection during microwave measurements (see sec-\ntion \"Microwave spectroscopy\") and the SWs’ excitation dur-\ning BLS measurements (see section \"Brillouin light scattering\nspectroscopy\").\nIn order to induce the carriers in the semiconductor and,3\ntuning-laser\n830 nmzyx\nPin H0Pout\nwYIG\nGGGD\nL\n200 mm\nD\nn-GaAs\nGaAs (n-type)\nPortC1\nlaser\n lightPr\nobing \n0.0001 0.01 11 10\n2\nW (W/cm ) p16 3\nN (10 /cm) e\n0400 1200\nbeam shift  z (μm)010 3\nN (10 /cm) e\n0.1 1 10 (b) (с)0.012\nW=0.552 W/cmp\n800(a)\nFIG. 1. (a)Sketch of the YIG/GaAs periodic structure and draw-\nings of microwave (antennas P inand P out) and BLS (port C 1and\nProbing laser light) experiments. Inset: Optical microscope side-\nview image of the laser-scribed GaAs slab used in the studied struc-\nture. (b)Dependence of the electron concentration on the laser ra-\ndiation power density measured for the GaAs slab from the grooved\nside (doped surface). (c)Dependence of the electron concentration\nversus the laser beam position shift from the Ohmic contacts re-\ngion ( z0) measured for the GaAs slab at the not grooved side (semi-\ninsulating surface). The laser power was fixed at the maximum level\n(Wp=0:552 W/cm2). Obtained data were interpolated by analytic\nfunction (6).\ntherefore, the screening of SWs-induced electric field, we\nused the tuning-laser (see section \"Lasers for optical control\nover GaAs properties\"). The self-constructed stand was used\nto fix together the holder and laser in a way that the beam irra-\ndiated all the surface of GaAs. Because of the sample holder\nconfiguration, the light beam was oriented to the multilayer\nsample from a GGG side (see Fig. 1 ( a)). The photo-induction\nin GaAs was possible since GGG and YIG are optically trans-\nparent materials and the main absorber of optical power, in\nthis case, was the highly doped GaAs layer.\nThe stand which fixed the laser and holder was used to\nplace the holder inside the electromagnetic coil in a way\nthat the multilayer structure was magnetized tangentially (see\nFig. 1 ( a)). It allowed the excitation of the surface spin\nwaves (SSW) type (so-called Damon–Eshbach configuration)\n[59, 60]. The orientation of the external magnetic field\nm0H0=0:09 T was chosen in a way that propagating SSWs\nin the direction from input to output antenna had a maxi-\nmum electromagnetic field localized on the surface faced to\nthe GaAs side [9, 59, 61]. It was necessary for the effectiveinteraction of SSWs with the semiconductor layer.\nB. Lasers for optical control over GaAs properties\nWe used laser irradiation with the aim to vary the charge\ncarriers’ concentration of GaAs by photo injection. Two laser\nsetups were applied for this purpose.\nFirst laser . 632.8 nm wavelength HeNe laser was used to\nstudy the optical effect on the conductivity of the GaAs sam-\nple. This laser setup had a possibility of power control, and the\ncalibrated maximum output power was 1.1 mW. We used the\nfocus lenses system in order to focus this relatively small out-\nput laser beam power in the area of Ohmic contacts. It allowed\nus to obtain the maximum power density Wp=0:552 W/cm2\nin order to experimentally observe the photo impact on the\ncharge carriers’ concentration in the semiconductor sample.\nSecond laser (tuning-laser) . 830 nm wavelength fiber\nlaser was used to irradiate the YIG/GaAs multilayer struc-\nture during the microwave spectroscopy measurements and\nthe Brillouin light scattering measurements (see Fig. 1 ( a)).\nThis laser setup had a possibility of power control, and the\ncalibrated maximum output power was 450 mW. The focus-\ning setup was absent; the laser spot on the sample surface had\nan elliptical shape with the sizes of 9 mm \u00026 mm. Due to the\nelliptical shape of the beam, to decrease the structure heat-\ning and uniformly irradiate the GaAs surface, the laser beam\nwas orientated in a way that the beam ellipse’ major axis was\nparallel to the GaAs slab width, and the beam irradiated full\nsurface of the slab. The maximum of the power density for\nthis beam was equal 1.06 W/cm2.\nC. GaAs slab electron density distribution and other\nparameters\nWe resorted to the Ohmic contacts resistance measurements\nto check the values of the dark electron density on the GaAs\nslab faces and to obtain the optical variation of GaAs elec-\ntron concentration. The details of this process are given in\n\"Appendix\". Based on the measurements, we established that\ndark electron concentrations are Ne=1\u0001109cm\u00003for semi-\ninsulating layer and Ne=1:3\u00011016cm\u00003for highly-doped\nlayer. The corresponding values of electron mobility (also see\n\"Appendix\") are me=8400 cm2=V s for the semi-insulating\nside of GaAs sample and me=4000 cm2=V s for the highly-\ndoped GaAs side. Important to note that further in this work\nwe assume these values of mobility to be constants (e.g., in-\ndependent on light exposure). The electron effective mass for\nthe GaAs we considered to be meff=0:13\u0001meof electron\nmass mesince the sample was highly doped [62, 63]. In ad-\ndition, for the GaAs, we considered permeability m=1, and\ncrystal lattice contribution to the GaAs permittivity eg=12:9\n[58, 62, 63].\nThe electron concentration measurements performed under\nthe laser exposure (\"First laser\", Wp=0:552 W/cm2) gave\nvalues of electron concentration Ne=3:49\u00011010cm\u00003for4\nsemi-insulating layer and Ne=4:54\u00011017cm\u00003for highly-\ndoped layer. This means the variation of the magnitude of\nphoto-induced concentration is around 1.5 order. Based on\nthe results of resistance measurements, the dependencies of\nthe electron concentration vs the optical power density (for\nhighly doped layer, Fig. 1 ( b)) and the diffusion electron con-\ncentration (for semi-insulating layer Fig. 1 ( c)) were obtained.\nThe distance-dependence of the diffusion electron concentra-\ntion for the semi-insulating layer was approximated by the ex-\nponential function (6) and it is plotted together with the mea-\nsured data (see red line in Fig. 1 ( c)). Therefore, the elec-\ntron diffusion length, Ln(distance, at which diffusion con-\ncentration decreases e-times from the maximum value) was\nestimated as: Ln=315mm.\nSummarizing the above results, the electron concentration\nalong the GaAs thickness is estimated as follows. We expect\nthe thickness-uniform distribution in the 1 mmthick highly\ndoped layer with the electron concentration Ne(controlled by\nthe tuning-laser intensity). The electrons in the highly doped\nlayer act as a source of the diffused electrons into the 500 mm\nthick semi-insulating layer. Then, the concentration of dif-\nfused electrons vs. the coordinate along with the thickness\ndecrease exponentially, obeying the relation (6).\nD. Microwave spectroscopy\nTo perform the microwave spectroscopy analysis of the pe-\nriodic GaAs/YIG structure, a pair of 30 mm width microwave\ntransducers for the excitation and detection of the SW was\nattached to the YIG surface. These antennas had 50 Ohm\nimpedance and the level of the input signal on the P intrans-\nducer -10 dBm. The input power of the microwave signal was\n0.1mW in order to avoid the nonlinear effects [61]. Trans-\nmission and dispersion of SSW at different intensities of the\ntuning laser light were experimentally measured using PNA-\nX Keysight Vector Network Analyzer (VNA). Transmission\nresponse were obtained as the frequency dependence of the\nabsolute value of S21coefficient in the case when the excita-\ntion and detection of the signal were performed by microstrip\nantennas. Further in the text by S21we mean the absolute\nvalue of this coefficient.\nE. Brillouin light scattering spectroscopy\nBLS method, which is based on the effect of inelastic light\nscattering on coherently excited magnons [64, 65], was used\nto measure SSWs’ spectra-like signal. The BLS setup was in\nthe quasi-backscattering configuration, so the BLS measured\nsignal was proportional to the squares of the dynamic magne-\ntization components of YIG film surface IBLS\u0018(m2\nx+m2\ny),\nwhere the probing laser beam was focused on. Probing laser\nlight (single-frequency laser EXLSR-532-200-CDRH with a\nwavelength of 532 nm and power of 1 mW) had a 25 mm-\ndiameter spot on the sample surface.\nThe same orientation and value of the external magnetic\nfield as during the microwave spectroscopy measurements\n4.3 4.4 4.5 4.6 4.7 4.8-60-50-40-30-20S (dB)21\nFrequency (GHz)H=900 Oe0(a)\nWavenumber (1/cm)-50-40-30-25\nFrequency (GHz)fg\n4.54.45 4.55fgf0S (dB)21-35\n-45\n1000 2003004.34.44.54.6Frequency (GHz)(b) (с)p/D\nfg\nf00 \n300 200 150\n250P(mW)L fgm\nfgmfgm\nDkb2p/D 0FIG. 2. The results of measured frequency-dependant microwave\ntransmission characteristics of the fabricated structure versus the\npower of the tuning-laser PL(marked in legend). f0marks the\nfrequency of ferromagnetic resonance for in-plane magnetized fer-\nrite film, fg- position of the first magnonic gap in a case of non-\nirradiated structure. (a)Transmission responce S21for the different\nPLvalues. Marked by the yellow fill sector is depicted in an en-\nlarged scale on the panel (b).(c)Dispersion relations of spin waves\nfor cases of different PL.p=Dratio marks the wavenumber value\nof the first Bragg resonance in the periodic structure with period D\nwithout the presence of wave nonreciprocity effect. Dkbmarks the\nvalue of Bragg resonance shift due to the appearance of nonreciproc-\nity in the irradiated structure ( PL=275 mW). The yellow fill region\ncorresponds to the yellow sector from panel (a).\nwere used. The input microwave antenna Pinwas used to ex-\ncite SSW on the specific frequency, and the BLS scanning\nwas performed along the waveguide structure transverse line\n(which can be imagined as a virtual port in Fig. 1 ( a)) with a\n25 nm step. To obtain spectral dependence, the accumulated\nin time signal data was integrated through all the Port C 1mea-\nsured points for each of defined value of excitation frequency.\nIII. RESULTS AND DISCUSSION\nA. Experimental demonstration of the magnonic gap tuning\nAfter preparation of the periodic GaAs/YIG multilayer\nsample and describing its materials properties, microwave5\nspectroscopy measurements were proceeded. Series of\nfrequency-dependant transmission characteristics were ob-\ntained in dependence on the tuning-laser power PL(see\nFig. 2 (a)). FMR frequency (the lowest frequency of the SSW\ntransmission spectra) is marked on the transmission spec-\ntra by the f0label. We can conclude that in the range of\nPL\u0014275 mW it stays constant: f0=4:332 GHz.\nThe dip fg=4:4673 GHz on the transmission characteris-\ntics which corresponds to the first Bragg resonance is almost\nnon-detectable at the low PLpower (see Fig. 2 (a),(b)). How-\never, fgwas possible to identify even at low PLpower due\nto the sensitivity of the small dip to the variation of tuning-\nlaser irradiation. The position of the first Bragg resonance\ndip, as well as the dip width and depth, were growing to-\ngether with the increase of the tuning-laser power PL(see\nthe enlarged scale in Fig. 2 (b)). The maximum frequency\nfgm=4:508 GHz was obtained at PL=275 mW. At the same\nmoment, the growth of PLleads to the decrease of the whole\nS21level, which indicates the increase of the damping.\nThe growth of the dip width and depth under the light irra-\ndiation demonstrates the possibility of the magnonic bandgap\nformation in the GaAs/YIG bilayer by optical means. Tak-\ning into account the measured Nevs.WPcharacteristic of\nthe GaAs sample (see Fig. 1 ( b)) and the periodicity of the\nperformed cavities in the GaAs slab (see Fig. 1 ( a)), we can\nrelate the growth of the dip width and depth to the increase\nof the periodic structure contrast induced by the tuning-laser\nirradiation.\nThe depicted in Fig. 2 ( c) experimentally measured disper-\nsion curves, under the different PL, corresponds to the SSW\npropagating through the studied structure. In the case of the\nnon-irradiated structure, the dispersion curve in the plotted\nrange is smooth and may be fitted by the linear function.\nUnder the tuning-laser exposure, the dispersion curve expe-\nriences a jump that corresponds to the magnonic gap. At the\nsame time, the growth of PLleads to the shift of the dispersion\ncurve to the higher frequencies. In other words, we observe\nnonmonotonic growth of the frequency at the fixed wavenum-\nber or decrease of the wavenumber at the specified frequency.\nThis shift is more pronounced at the low wavenumber (and\nfrequency).\nHere we should describe the connection between the SSW\ndispersion and the magnonics bands in MCs. For MCs, it is\nknown that bandgap formation may be explained by the Bragg\ndiffraction between the propagating SW, k+, and the scattered\nSW (formed due to a periodic lattice presence), k\u0000[19]. The\npresence of leads to the periodicity of the SSWs’ wavevectors\nThe intoduction of the reciprocal k-space and formation of\nBrillouin zones are usually introduced in the consoderation of\nthe periodic lattice [19].\nIn general, when the frequencies of the propagating and\nscattered SSW are equal ( f(k\u0000) =f(k+)), and the wavevec-\ntors obey the so-called Bragg condition [66, 67]:\njk\u0000j+jk+j=m2p\nD; (1)\nformation of the magnonic band occurs. Here mis an integer\nnon negative number, with meaning of the order of the Braggresonance, and Dis the structure period. We point here that\njk\u0000jdoes not need to be equal to jk+j. In other words, the\ninterference of the propagating and scattered waves results in\nthe crossing of the dispersion branches of the propagating and\nscattered waves taking into account the nonreciprocal charac-\nter of surface spin wave.\nIn the case of SSW transport in magnetic film with the same\nboundary conditions at both faces, the SSWs’ dispersion law\nis invariant to the reverse of the kdirection ( f(k) =f(\u0000k)).\nSuch systems are called the reciprocal, and the regular Bragg\ndiffraction condition is satisfied [48]:\nkb=mp\nD; (2)\nwhere kbis the wavelength of the Bragg resonance in the re-\nciprocal system. The property of the Bragg diffraction in the\nreciprocal systems is that the length of the wavevectors of the\npropagating and scattered waves are equal. Thus, eq.(2) uni-\nvocally connects the wavevectors of the magnonic bands to\nthe lattice period, and the SSW’s dispersion law defines the\nfrequency of the magnonic bands. Here we can conclude that\nthe appearance of SSW’s nonreciprocity may be detected by a\ndeviation of thejk\u0000j+jk+jfrom the kbvalue.\nFor the studied structure (see Fig. 1 ( a)), the SSW has\nthe propagation direction from the excitation to the detec-\ntion antenna, and the scattered SSW has the opposite direc-\ntion. As we already mentioned, the orientation of the external\nmagnetic field, H0, provides the condition that propagating\nSSW has the electromagnetic field maximum localized at the\nYIG/GaAs interface, thus the scattered SSW has the electro-\nmagnetic field maximum localized at the YIG/GGG interface.\nSince the boundary conditions are different for the opposite\nsides of the YIG layer, we can expect the nonreciprocity of\nthe propagating and scattered SSW due to the interaction of\nSSW with the semiconductor screening layer [14, 45]. And\nthe nonreciprocity should depend on the electron concentra-\ntion in the GaAs layer. The interaction of the SSW with the\nGaAs screening layer would depend on the penetration depth\nof the SSW- electromagnetic field into the GaAs. Waves with\na longer wavelength should be stronger impacted by the semi-\nconductor screening layer. Further, we will demonstrate the\ncontribution of the semiconductor electron density variation\non the nonreciprocal properties of SSW.\nThe bandgap frequencies fg(observed for the non-\nirradiated structure) and fgm(the maximum observed posi-\ntive shift of bandgap in the structure under the variation of the\nlaser exposure) are pointed in Fig. 2 ( b) according to the dips\non the corresponding S21dependencies. For the non-irradiated\nstructure, the wavelength of the magnonic bandgap (defined\non the measured dispersion characteristic by the fgvalue) is\nequal to the kbwavenumber followed from the eq.(2) at the\nD=200mm,m=1:kb=157:08 cm\u00001. It means that for the\nnon-irradiated structure, SSWs with k<kbare reciprocal, so\nthe GaAs screening layer is not affecting the SSWs of these\nwavelengths.\nVertical dotted line in Fig. 2 ( b) shows the k-position of the\nmagnonic gap in the case of PL=275 mW. The displacement6\n4.304.354.404.454.504.55\n-65-60-55-50-45-40-35-30-25-20-15-10\n0 100 200 300 400\nS (dB)21Frequency (GHz)\nLaser power  P (mW)L\nRegion II\n Region I\nf(P)0 L\nPst\nPth12\nW (W/cm ) p\n0.8 1 0.4 0\nf(P)bg L\nfgm\nfg0.2 0.6\nFIG. 3. The color scale presents the frequency-dependent mi-\ncrowave transmission characteristics vs. the tuning-laser power PL\nmeasured for the studied structure.The power density scale is plotted\nalong the upper axis according to the laser setup description given in\nSection \"Lasers for optical control...\". Dashed-dotted curve f0(PL)\nmarks the FMR frequency dependence vs PL, dotted curve fbg(PL)\nmarks the dependence of first magnonic gap vs tuning-laser power.\nThis gap appears at Pstand reach it maximum at Pth1. \"Region I\" and\n\"Region II\" corresponds to the negligible and well-presented laser-\nirradiation induced heating that impacted the characteristics of the\nstudied microwave transport.\nof this position from the kbisDkb=20:8 cm\u00001. The appear-\nance of Dkbis related to the optically-induced growth of the\nGaAs screening layer influence on the SSW in the fabricated\nstructure. Thus we can conclude that the SSW nonreciproc-\nity was induced by optical means in the GaAs/YIG bilayer (for\nthe waves with wavelengths at least below this magnonic gap),\nand this nonreciprocity manifested itself similarly to works\n[49, 50, 67].\nTo analyze the magnonic gap frequency position depen-\ndence on the tuning-laser power ( fbg(PL)), the series of trans-\nmission characteristics were measured with the PLstep of\n25 mW, and the result is plotted by color map in Fig. 3. The\ndotted curve fbg(PL)is plotted in Fig. 3 with use of inter-\npolation of the obtained at each PLstep bandgap position.\nWe defined the magnonic bandgap appearance threshold at\npower Pst=150 mW as the amplitude depth of the dip on\nthe spectra curve\u00142:5 dB. We note here that fbg(Pst)>fg,\nwhich means that the frequency position of the Bragg reso-\nnance was already displaced due to the laser influence. At the\nsame time, the analysis of the S21dip related to the Bragg res-\nonance at the range below Pstshows, that the dip frequency\nforPL<100mW is almost independent on PL. This means\nthat light control over the Bragg resonance also has a thresh-\nold behavior.\nThe fbgnon-uniformly grows together with PLuntil itsmaximum value: fg(Pth1) = fgm, where Pth1=275 mW.\nThe drop of fbgis observed above Pth1. At the same time,\nf0(PL)stays approximately constant until PL<Pth1and then\nstarts to decrease.\nThe reduction of fbgandf0(PL)in such a system may indi-\ncate the saturation magnetization decrease caused by the heat-\ning. Thus, Pthdivides the power range on the \"Region I\" and\non \"Region II\". Inside the \"Region I\" the fbggrows along\nwith PLand f0(PL)stays approximately constant (the laser-\ninduced heating on the waveguide structure is insignificant).\nAlong the growth of Pthinside the \"Region II\", f0(PL)de-\ncreases and the fbg(PL)also reduces (possible evidence of\nthe YIG layer heating). Below in the text, we will describe the\nsupposed influence of heating on the SSW transport through\nthe studied structure in more detail.\nB. Numerical simulations of the YIG/GaAs bilayer and\nperiodic GaAs/YIG structure\nIn order to explain the experimentally observed results (in\nparticular the fbg(PL)dependence), we used numerical sim-\nulations. The details of the simulation method are described\nin \"Appendix\".\n\"Semi-infinite GaAs/YIG bilayer\" model\nWe started the analysis with the model of the in-plane mag-\nnetized infinite layers of YIG in direct contact with the GaAs\nwith an aim to estimate the contribution of the GaAs- related\nparameters to the SSW characteristics.\nFor this task, we established the following parameters. The\nparameters of the YIG layer used in simulations correspond to\nthe passport values of purchased YIG film (see section \"Fab-\nrication of YIG/GaAs magnonic crystals structure\"). The ori-\nentation and value of the external magnetic field corresponded\nto the experimental one (see Fig. 1 ( a)).\nFor this first simplified model, \"semi-infinite GaAs/YIG\nbilayer\" (see corresponding computation cell in Appendix,\nFig. 11 ( a)), we set GaAs properties equal to one described\nin section \"GaAs slab electron density distribution and other\nparameters\" with the following changes (and mark them as\n\"Default Parameters\"). We set GaAs uniform layer of 3 mm\nthickness in direct contact with the YIG surface. We should\nnote that 3 mm thick GaAs layer was estimated to be enough\n(for the performed variation range of all the parameters) to\nconsider the semiconductor layer as an infinite screening layer\nfor the SSW. The electron concentration, Ne, was considered\nto be uniform within GaAs.\nAt first, for the \"Default Parameters\" and \"semi-infinite\nGaAs/YIG bilayer\" model, we relate the variation of the SSW\nfrequencies with the electron concentration, Ne, in GaAs. We\nperformed simulations for the wavelengths kD=p=0:6 and\nkD=p=1 as these wavelengths belong to the experimentally\nmeasured region. The range of the considered electron con-\ncentration in the GaAs layer ( Ne2[1016cm\u00003; 5\u00011017cm\u00003])\nwas comparable to the one expected for the optically-induced\nelectron concentration in the GaAs slab doped layer.\nThe calculated f(Ne)dependencies are plotted by the7\nkD/π = 0.6\nkD/π = 1100ρ(μm)∞ \n6020\n10 1 016 3\nN (10 /cm) e\n4.6 4.4 4.8\nFrequency (GHz)\nFIG. 4. The numerical simulation results of the SSWs’ frequency\n(dashed lines, right axis) and penetration depth, r¥, (solid lines, left\naxes). Results were obtained for the wavelengths kD=p=0:6 and\nkD=p=1 (see color legend) in dependence of the electron concen-\ntration, Ne, in the structure defined by the \"semi-infinite GaAs/YIG\nbilayer\" model.\ndashed lines in Fig. 4. From these results, we can conclude\nthat the GaAs layer is weakly impacting the frequency of SSW\nwith wavelength kD=p=1 in the region Ne<1\u00011016cm\u00003.\nAt the same time, the frequency growth of the SSW with the\nvalue of wavelength kD=p=0:6 starts to be visible from the\nlower electron concentration: Ne\u00190:3\u00011016cm\u00003. Thus,\nhere we confirm that for the case of the semi-infinite semicon-\nductor screening layer, waves of the longer wavelengths are\nstronger affected by the semiconductor. At the same time, we\ncan conclude that an increase of Newill lead to extend of the\nwavelengths interval (0;kD=p)where the SSW’s frequency is\naffected by GaAs. The further increase of the Neleads to the\nsubstantial growth of the SSW frequency. We note here that\nthe SSWs frequencies limit at Ne!¥is equal to the case of\nYIG film screened by the perfect electric conductor.\nNext, we wanted to relate the influence of the GaAs layer\non the SSWs’ properties with the penetration depth (or skin\ndepth) of the SSW’s electromagnetic field. We defined the\nSSW’s penetration depth, r, as a distance along with the y\naxis, at which SSW’s-induced zcomponent of the electric\nfield, Ez, is reduced e-times, relative to the Ezvalue on the\nYIG- facing GaAs edge. We point here that for the \"semi-\ninfinite GaAs/YIG bilayer\" we mark such penetration depth\nasr¥.\nFor the obtained dependencies of frequency vs. electron\nconcentration depicted in Fig. 4, we also plotted the corre-\nsponding dependencies of r¥(Ne)(continuous lines in Fig. 4).\nWe can conclude that since SSW dependencies of f(Ne)and\nr¥(Ne)are correlated to each other, the semiconductor screen-\ning layer influence the SSW mainly due to the SSW- electric\nfield screening. Further, we will also call the attenuation of\nthe SSW’s- induced electric field due to the semiconductor\nscreening layer as the SSW’s screening.\nHere we want to set the connection between the penetration\ndepth and the SSWs’ wavelengths. First, we can remind that\nfor the structure depicted in Fig 1 ( a), wavevector of propa-\ngating SSW’s is k\u0011kx(since the numerical model considers\nthe structure to be infinite along the zdirection, kz=0). Here-\ninafter k=jkj. The penetration depth of this wave along the\nydirection outside the YIG film, r=1=kS, where kSis theattenuation factor along the ydirection. In a case of pure YIG\nfilm (single magnetic layer in vacuum), kS=kand we mark\nthe corresponding SSWs’ skin depth by r0=1=k. This SSW’s\nattenuation we will call the intrinsic one.\nNext, we can link to the phenomenological model of SSWs\npropagation in the structure magnetic insulator/metal layer,\nwhich was considered in works [50, 68]. In case of the di-\nrect contact of the YIG with the semi-infinite metal layer, the\nSSW’s attenuation factor along the ydirection, kS, can be\nwritten in a form:\nkS(s;k) =s\nk2+2i\nd2¥(f(k);s); (3)\nwhere d¥(f(k);s)is an intrinsic skin depth of a metal, s-\nelectrical conductivity of the metal. 1st term of the eq.(3) is\nresponsible for the impact of the intrinsic SSWs’ attenuation\ninto the attenuation factor of SSWs’ in the semi-infinite metal\nlayer. 2nd term describes the influence of the metal layer\non the SSW’s attenuation along the normal direction to the\nmagnetic film (the SSW’s screening). If this term grows, the\nSSW’s penetration depth reduces. We point here that metal\nlayer with thickness much larger then 1 =kScan be considered\nas semi-infinite layer.\nWorks [50, 68] introduce the analytical form of the\nd¥(f(k);s). However, we do not know the analytical form of\nthe eq.(3) in case of the magnetic layer contact with the semi-\nconductor. Therefore we can not perform quantitative anal-\nysis. Nevertheless, we can extract the influence of the semi-\nconductor layer on the SSW’s screening from the robtained\nby the simulations. In analogy to the d¥for the magnetic\nlayer/semi-infinite metal multilayer, we introduce the r¥, the\nSSWs’ penetration depth in the YIG/semi-infinite GaAs mul-\ntilayer. The r¥would have contributions from the SSW’s in-\ntrinsic decay, r0, and from the intrinsic skin depth of the semi-\ninfinite semiconductor screening layer. Thus, for the \"semi-\ninfinite GaAs/YIG bilayer\" model by comparing the r¥with\nther0it is possible to discuss the role of the GaAs screening\nlayer on the SSWs screenings, which we will do next. Note\nhere, that for the SSW’s transport in the general YIG/GaAs\nmultilayer structures, we have to compare rwith both r0and\nr¥.\n\"Default Parameters\" variation\nAs a second step of the numerical investigations of the SSW\nin the \"semi-infinite GaAs/YIG bilayer\" model (see corre-\nsponding computation cell in Appendix, Fig. 11 ( a)), we were\nfocused on the influence of the \"Default Parameters\" on the\nSSWs’ screening (through analysis of the penetration depth\ndependencies, r). We independently varied (while the other\nparameters were fixed and corresponded to the \"Default Pa-\nrameters\") the electron diffusion length, Ln, the size of the air\ngap between the YIG and GaAs, tg, and the GaAs electron\ncollision frequency, n.\nThe penetration depth dependencies (see Fig. 5) were per-\nformed for the same two wavelengths as above ( kD=p=0:6\nandkD=p=1) and for the particular cases of the electron\nconcentration Ne=7\u000110161=cm3andNe=2\u000110171=cm3.8\n t (μm)g10 1001000\nL (μm)nkD/π = 0.6kD/π = 1\n0 0.4 0.8-12\n 1/n(s∙10)kD/π = 0.6kD/π = 1\n0.2 0.6 1ρ(μm) \n100ρ(μm) \n60 2016 3\nN = 7∙10 (1/cm ) e17 3\nN = 2∙10 (1/cm ) eρρ(μm),  ∞\nt = 0 ( μm) g\n-12\n1/n=0.296 (s∙10)3 (mm) GaAs, uniform Ne \n-12\n1/n=0.296 (s∙10)t = 0 ( μm)  g\n3 (mm) GaAs, uniform Ne(b)\nkD/π = 0.6kD/π = 1\n0 0.4 0.8 0.2 0.6 1-12\n 1/n(s∙10)(e)1 10100kD/π = 0.6kD/π = 1(d)\n t (μm)gL (μm)n10060 20kD/π = 0.6kD/π = 1\n10 1001000(a)\nkD/π = 0.6kD/π = 1\n1 10100(с)10060 201 1\n(f)\nFIG. 5. The dependencies of the SSWs’ penetration depth, r, for the\nwavelengths kD=p=0:6 and kD=p=1, and the GaAs layer elec-\ntron concentration Ne=7\u00011016cm\u00003(left column) and Ne=2\u0001\n1017cm\u00003(right column). Results depicted by solid lines in panels\n(a)-(f) were obtained in dependence on variation of the \"semi-infinite\nGaAs/YIG bilayer\" model parameters. Vertical dashed-dotted lines\nmark the \"Experimental Parameters\" values of the \"experimental\nYIG/GaAs multilayer, and the horizontal dotted lines demonstrate\nSSW’s robtained by this model. ( a)-(b) SSWs’ penetration depth\nwere obtained vs. the electron diffusion length in the GaAs: r(Ln).\nHorizontal dashed lines demonstrate the rof SSW’s screened by the\n1mm thick layer of GaAs with the uniform electron concentration,\nNe. (c)-(d) SSWs’ penetration depth were obtained vs. the air gap\nsize, tgof the YIG/GaAs interface: r(tg). (e)-(f) SSWs’ penetration\ndepth, r¥, were obtained vs. the GaAs mean collision frequency, n:\nr¥(n).\nThese values of the GaAs Necorrespond to the obtained con-\ncentrations of the experimentally-used sample (see Fig. 1 ( b))\nat the weak and high power of the laser light irradiation. Pan-\nels (a-d) in Fig. (5) show that electron diffusion length in the\nGaAs and size of the gap between YIG and GaAs layers in-\nfluence the raccording to the \"S\"-shape dependence with the\nlimits of free YIG film ( r0(k)) and saturation of the parame-\nter impact on the SSW screening ( r¥). At the same time, the\ndependencies of r¥(1=n)have a monotonous decrease from\nthe limit of free YIG film ( r¥(n!¥) =r0). This means\nthat the increase of the electron mean free time increases the\nefficiency of the SSW’s screening by the GaAs layer and thelimit skin depth of the SSW’s in the \"semi-infinite GaAs/YIG\nbilayer\" model is a function of wavenumber, semiconductor\nelectron concentration and semiconductor electron mean free\ntime: r¥(k;Ne;n).\nIn Figs. 5 ( a-b) we present the numerically-obtained de-\npendencies of the SSWs screening, rvs the electron diffusion\nlength, Ln, along the 3 mm thick- GaAs layer. Here we can\nconsider that variation of the Lnleads to the change of the ef-\nfective thickness of the GaAs screening layer. We can split\nthe obtained dependence r(Ln)into three regions (according\nto the Lnrange). If Ln\u001cr¥, the GaAs layer influence on the\nSSW’s is weak and ( r\u0019r0(k)). If Ln\u001dr¥, the GaAs layer\ninfluence on the SSW’s is maximal and Ln\u0019r¥(k;Ne). The\nobserved transition of r(between the SSW’s in the free YIG\nfilm and SSW’s in the YIG/semi-infinite GaAs) happens, then\nLn\u0019r¥. We should point here, that difference between the\nr0(k)andr¥(k;Ne)grows along with Neand wavenumber,\ndefining the left and right limits of dependencies depicted in\nFigs. 5 ( aandb). Thus, the gradient of r(Ln)in the transition\nrange of Lnalso grows along with Neand 1 =k.\nIn addition, we studied the SSW’s screening in the\nYIG/GaAs structure in the case of the GaAs layer of 1 mm\nthickness with the uniform Ne. This case corresponds to tak-\ning into account only the highly doped layer of the GaAs sam-\nple used in the fabricated structure. The dashed horizontal\nlines in Figs. 5 ( a-b) shows that 1 mm layer influence on the\nSSW’s screening is negligible since for the considered Neval-\nues, the obtained r(k)\u0019r0(k). It means that for the con-\nsidered wavelengths and the GaAs electron concentration, the\nrole of the doped layer in the experimentally used GaAs sam-\nple is mainly a source of the diffused electrons to the undoped\nGaAs layer. The main screening of the SSWs’ is by the dif-\nfused electrons to the undoped GaAs layer.\nNext, we investigated the role of the air gap influence be-\ntween the layers of the YIG/GaAs interface. The appearance\nof the air gap, tg, leads to the weakening of the SSW’s screen-\ning by the GaAs layer. The obtained dependencies of r(tg)\ndepicted in Figs. 5 ( c-d) have a similar shape to the r(Ln)de-\npendencies presented in Figs. 5 ( a-b). The r(tg)dependencies\nalso can be split into three regions (according to the tgrange).\nIn the presence of nonzero tg, the eq.(3) is not valid. We would\ncharacterize the r(tg)dependence by comparing the tgwith\nr0. If the tg\u001cr0, the SSW’s screening is similar to the one\nin the structure YIG/semi-infinite GaAs ( r\u0019r¥(Ne;k)). If\nthe air gap between the interfacial layers is big ( tg\u001dr0), the\nSSW’s penetration depth is similar to the one in the YIG film\nwithout any screening layer ( r\u0019r0(k)). The transition be-\ntween this states occurs then tg\u0019r0(k;Ne). Again, due to\ndifference between the r0(k)andr¥(k;Ne)grows along with\nNe, the gradient of r(tg)in the transition range of tggrows\nalong with Ne(see the difference between Figs. 5 ( candd).\nIn the next step, we wanted to study the influence of\nthe electron mean collision frequency (semiconductor media\ndamping), n, on the SSW’s screening by the semiconductor\nlayer. Point here that for these simulations, we varied only n\nparameter in the \"semi-infinite GaAs/YIG bilayer\" model, so\nthe obtained SSWs’ penetration depth was the r¥one. The\nobtained r¥(n)dependencies are depicted in Figs. 5 ( e-f). We9\ncan see that the growth of the semiconductor electrons colli-\nsion frequency, n, leads to the reduction of the SSW’s screen-\ning by the semiconductor layer (value r¥(k;Ne)grows). Thus\nto obtain the reliable result of SSW’s screening by the sim-\nulations, the choice of the nparameter should be related to\nthe range of the expected values valid for the experimental\nsamples. The dependency between nandm(see eq.(7), Ap-\npendix) leads to the dependency of mean collision frequency\non the variation of the semiconductor doping electron concen-\ntration [57] and the semiconductor temperature [58]. Thus,\nwe can expect the ngrowth along with the growth of the laser\nirradiation power, PL.\nAs the result of analyzing the SW penetration depth vs the\n\"Default Parameters\" variation, we can conclude about the im-\nportance of all parameters choice since the role of every pa-\nrameter was found to be significant on the waves screening.\n\"Experimental YIG/GaAs multilayer\" model\nIn order to make the correlation between the presented\nin Figs. 5 ( a-f)rdependencies with the SSW’s screen-\ning expected in the fabricated structure (see Fig. 1 ( a)),\nwe introduced the advanced numerical model \"experimental\nYIG/GaAs multilayer\" with the following \"Experimental Pa-\nrameters\". We established the 1 mmGaAs layer with the de-\nfined concentration Ne(the strongly n-doped layer) attached to\nthe 500 mmthick layer with the diffusion length Ln=315mm\n(semi-insulating layer). We supposed the tg=40mm thick air\ngap in the YIG/GaAs interface in order to take into account the\nroughness of the YIG and GaAs film surfaces. The charge car-\nriers collision frequency was set to be 1 =n=0:296\u000110\u000012s.\nThus, the difference between the \"semi-infinite GaAs/YIG bi-\nlayer\" and the \"experimental YIG/GaAs multilayer\" models\nis in the simultaneous presence of the diffusion length, the air\ngap in the YIG/GaAs interface, and the reduced thickness of\nthe GaAs layer (see corresponding computation cell in Ap-\npendix, Fig. 11 ( a)).\nValues of the \"Experimental Parameters\" parameters ( Ln,\ntg,n) were pointed in the panels of Figs. 5 ( a-f) by the verti-\ncal dashed-dotted lines. The crossing points of rdependen-\ncies with these vertical dashed-dotted lines demonstrate that a\nsmall deviation of every parameter will lead to the change of\nthe resulting r. In other words, for all \"Experimental Param-\neters\" values rdependencies are in the transition between the\nr¥(Ne;k)andr0(k). In conclusion, all the \"Experimental Pa-\nrameters\" would significantly influence the SSWs’ properties\nand their choice in the \"experimental YIG/GaAs multilayer\"\nmodel is important for the correspondence of the simulation\nresults to the experiment. At the same time, simulations of\nthe SSWs skin depth in dependence on a wide range of pa-\nrameters may be useful for designing the waveguide structure\nbased on YIG/GaAs interface.\nWe calculated the values of SSW’s rwith the use of the\n\"experimental YIG/GaAs multilayer\" model for the wave-\nlengths kD=p=0:6 and kD=p=1 and for the electron con-\ncentration Ne=7\u000110161=cm3andNe=2\u000110171=cm3(see\nthe horizontal dotted lines in Fig. 5). We point here that due\nto the impact of the presence of YIG/GaAs air gap and due to\nthe reduction of the GaAs layer effective thickness (500 mm\nthick layer with the diffusion length Ln=315mm), the SSW’sscreening in this simulated structure is weaker than the one\nfor the \"semi-infinite GaAs/YIG bilayer\" with the same value\nofn.\n\"Experimental YIG/GaAs multilayer\" model with peri-\nodic GaAs groves\nIn order to obtain the dispersion characteristics of the\nSSWs’ in the periodic GaAs/YIG structure (see Fig. 1 ( a))\nby numerical simulations, we extended the \"experimental\nYIG/GaAs multilayer\" model by taking into account the peri-\nodic grooves of the GaAs surface that faced the YIG (see cor-\nresponding computation cell in Appendix, Fig. 11 ( b)). Again,\nwe considered the structure to be uniform (infinite) along the\ntransverse direction ( z- axis). The shape of the GaAs layer pe-\nriodic grooves in simulations corresponded to the GaAs slab\nside- image (see insert in Fig. 1 ( a)). In the direction along\nthe propagating SSWs ( x- axis), we considered one period of\nthe periodic GaAs/YIG structure. The computation cell of the\nsimulated structure contained this one period limited from the\nsides by the periodic boundary conditions.\nThe numerically obtained dispersion relations of the SSWs’\nin the periodic GaAs/YIG bilayer are depicted in Fig. 6 by\nthe blue dashed and red dotted curves. We present the dis-\npersion relations for the two electron concentrations: Ne=\n2\u00011016cm\u00003(blue dashed curves) and Ne=2:6\u00011017cm\u00003\n(red dotted curves). These concentrations belong to the ex-\nperimental GaAs slab under the different power of the laser\nexposure (see Fig. 1 ( b),(c)). Due to the periodicity of the\nsimulated structure, the dispersion relations of the SSWs in\nthis structure are also periodic and within the Brillouin zone\ncontain both propagating SSW and scattered SSW. From the\nnumerically-obtained results presented in Fig. 6, we can con-\nclude that scattered SSW is almost not influenced by the vari-\nation of the GaAs Ne. At the same time, we can see that sim-\nulated dispersions of the propagating SSW are influenced by\nNein the same manner as in the experiment (see solid blue\nand red lines in Fig. 6): dispersion curve shifts to the higher\nfrequencies along with the growth of Ne. This confirms the ap-\npearance of the SSWs’ nonreciprocity in the YIG/GaAs struc-\nture along with the growth of the semiconductor electron con-\ncentration, Ne.\nThe position of the crossings of propagating and scattered\nSSW dispersion curves within the Brillouin zone corresponds\nto the first Bragg resonance (see simulation results in Fig. 6).\nThe SSWs’ dispersion relation at the GaAs electron concen-\ntration Ne=2\u00011016cm\u00003(blue dashed curves) demonstrate\nthat propagating SSWs was affected by the semiconductor\nlayer in the wavenumbers range lower then kD=p=1. This\nmeans that Bragg resonance happens between the reciprocal\nSSWs (see eq.(2)). At the same time, SSWs’ dispersion re-\nlation at the Ne=2:6\u00011017cm\u00003of the GaAs (red dotted\ncurves) demonstrate the shift Dkbof the Bragg resonance to\nthe lower wavenumber and higher frequency since the range\nof the propagating SSWs’ wavelengths affected by the GaAs\nload increased along with the Negrowth. For this case,\nBragg resonance happens between the nonreciprocal waves\n(see eq.(1)). At the same time, the threshold behavior over the\nBragg resonance control is in agreement with the experimen-\ntal results (see Fig. 3).10\n2 1 0\nkD/πf0fgm\nfg\nP= 0L\nP= 300 mWL\n17 3\nN = 2.6 ∙10 (1/cm ) e16 3\nN = 2∙10 (1/cm ) eDfconf\nDfconfFrequency (GHz)4.55\n4.50\n4.45\n4.40\n4.35\n4.30Dkb\nFIG. 6. Dispersion relations of SSWs’ in the periodic GaAs/YIG\nstructure (depicted in Fig. 1 ( a)) obtained by microwave spectroscopy\n(PL=0, blue solid curve; PL=275 mW, red solid curve) and by\nFEM ( Ne=2\u00011016cm\u00003, blue dashed curves; Ne=2:6\u00011017cm\u00003,\nred dotted curves). Horizontal lines marks the obtained from\nthe measured S21dependencies: FMR frequency ( f0), measured\nmagnonic gap position for the non-irradiated structure ( fg), and mea-\nsured maximum frequency of the magnonic gap in the irradiated\nstructure ( fgm). The Dfconfmark the frequency difference between\nthe first Bragg resonance (when the SSWs are reciprocal) obtained by\nthe microwave measurements and by numerical simulations, related\nto the experimental sample’s finite size along the zdirection.\nC. Comparison of the numerically and the experimentally\nobtained results\nIn Fig. 6, horizontal lines indicate the experimentally mea-\nsured (see Fig. 2) frequency values of the FMR frequency,\nf0, the magnonic gap for non-irradiated GaAs, fg, and the\nmagnonic gap for the structure under the \"tuning-laser\" Pth1\nexposure, fgm.\nAs we mentioned above, the numerically obtained SSWs’\ndispersion relation at Ne=2\u00011016cm\u00003demonstrates the\nfirst Bragg resonance between the reciprocal waves (see blue\ndashed curves in Fig. 6). At the same time, the frequency of\nthis resonance is higher than the magnonic gap frequency, fg,\nobtained by the microwave measurements of the experimen-\ntal sample without the \"tuning-laser\" exposure (see Dfconf=\n15 MHz above the fgin Fig. 6). We relate this difference\nwith the finite transverse dimension (width) of the fabricated\nsample, which was not taken into account in the numerical\nmodel. According to the first theoretical work focused on the\nSSWs’ transport in the transversely- confined magnetic slabs\n[69], the reduction of the slab width leads to the shift of the\nSSWs’ dispersion to the lower frequency in the range of short\nwavelengths.\nThe GaAs electron concentration value, Ne=2\u00011016cm\u00003,\nwas fitted in a way that numerically obtained SSWs’ disper-\nsion dependency (see red dotted curves in Fig. 6) would corre-\nspond to the Bragg resonance frequency fgm+Dfconf. Thuswe roughly took into account the sample’s width in the numer-\nical model which would correspond to the microwave mea-\nsurements of the magnonic gap in the irradiated sample at\nPth1=275 mW.\nIn addition, we point that the quantitative difference be-\ntween the dispersion curves obtained by microwave spec-\ntroscopy measurements with the numerically obtained dis-\npersion relations depicted in Fig. 6 (for both values of Ne).\nWe relate it to the finite transverse dimension of the fabri-\ncated sample [69]. In particular, for the electron concentra-\ntion value Ne=2:6\u00011017cm\u00003in the numerical model, the\nobtained shift of the Bragg resonance wavelength position,\nDkb=51:8 cm\u00001, is bigger then the one observed in Fig. 2 ( c).\nAlso, the simulated dispersion of the periodic GaAs/YIG bi-\nlayer demonstrates a stronger influence of the GaAs screening\nlayer on the SSW at the long wavelengths. One more manifes-\ntation of the difference between the model and experiment is\nin the lower limit frequency of the waves: for the numerically\n- obtained dispersion dependencies it lies below the experi-\nmentally measured f0.\nThe numerically obtained dispersion relation for the SSWs\nin the layered structure demonstrates the opening near the\ncrossing of the dispersion branches corresponding to the prop-\nagating and scattered waves ( fbgpoint). However, the width\nof this opening is a few orders lower than the experimentally-\nobtained width of the magnonic bandgap dip (see Fig. 2 ( c).\nThe partial differential equation for the eigenvalue problem\nwas defined as f(k). The imaginary part of wavenumber ( k”)\ndescribing the spatially-related damping is not presented in\nthe simulation output. Thus the numerical model is not pro-\nvide the information about all types of losses related to the\nSSW interaction with the periodic semiconductor screening\nlayer and the large bandgap observed in experiments.\nFrom the previous analysis, we can expect that increas-\ning the electron concentration in the GaAs periodic lattice in-\ncreases the magnonic crystal contrast. This should lead to an\nincrease in the interference between the propagating and scat-\ntered SSW, which results in an increase in the width of the\nband gap. So we can use the fbgincrease as the parameter\nevidence of the contrast of periodic screening layer related to\nelectrons concentration, Ne. This is confirmed by the exper-\niment results as the magnonic bandgap forms and increases\nwith the tuning-laser power (see Fig. 2).\nThe series of simulations with the varying of Neallowed to\nplot the fbg(Ne)dependence and compare it with the experi-\nmentally obtained fbg(PL)(see Fig. 7). The juxtaposed of PL\nandNeaxis in Fig. 7 was made, since the Ne(Wp)dependence\ncan be fitted by a linear function (see Fig. 1 ( c)).\nThe tuning-laser irradiation of the studying structure is ex-\npected to induce the heating of the sample. As the GGG and\nYIG are optically transparent materials, the tuning-laser beam\ndirected to the structure from the GGG face should be mainly\nabsorbed by the GaAs layer and thus heat it. However, the mi-\ncrowave SSW transport measurements of the studying multi-\nlayer structure can only indirectly detect the YIG temperature\nincrease. It is due to heat-induced MSdecrease, resulting in\nthe drop of the FMR frequency, f0. According this analysis,11\n0 100 200 300 400\nLaser power  P (mW)LPstPth1Region II\nf(P)0 L\n(from S )21f(P)bg L\n(from S )21fgm\nfg\n4.304.354.404.454.504.55Frequency (GHz)f(N) bg e\n(FEM)\nRegion I0.1 1 0.01 10 10017 3\nN (10 /cm) e\nFIG. 7. Data obtained from the measured S21dependencies (see\nFig. 3): fbg(PL)- the dependence of the first magnonic band gap\nfrequency position versus the variation of the irradiation laser power,\nPstmarks the threshold of the fbg(PL).f0(PL)- the dependence of\nthe FMR frequency versus the variation of the irradiation laser power.\n\"Region I\" and \"Region II\" corresponds to the negligible and well-\npresented impact of the heating (induced by the \"tuning-laser\") on\nthe studied S21dependencies (according to FMR frequency). Data\nobtained by FEM- model: fbg(Ne)- the dependence of the first\nmagnonic gap frequency position versus variation of the GaAs elec-\ntron concentration. Data obtained from BLS measurements: Green\ndots - the dependence of the first magnonic band gap frequency\nposition versus the variation of the irradiation laser power. Green\ncrosses - the dependence of the FMR frequency versus the variation\nof the irradiation laser power. Horizontal lines marks the obtained\nfrom the measured S21dependencies: FMR frequency ( f0), mea-\nsured magnonic gap position for the non-irradiated structure ( fg),\nand measured maximum frequency of the magnonic gap in the irra-\ndiated structure ( fgm).\nthef0(PL)drop is observed only in the \"Region II\" in Fig. (3).\nTherefore, we expect an important contribution from the heat-\ning when the sample is irradiated with laser power exceeding\nthe value P=275 mW.\nWe have to note here that the measurement setup configu-\nration might mask the temperature-induced decrease of FMR\nfrequency, f0. We measure the transport of the SSW be-\ntween two antennas separated by the distance, 9 mm, and the\nheat source (GaAs slab) covers only part of the YIG material\n(5 mm length). Therefore the transport of SSW between the\nantennas will be supported only if their frequency is above the\nthreshold FMR frequency value, f0, in both YIG-heated and\nYIG-non-heated parts. The transmitted signal will be mea-\nsured above the higher frequency of YIG-heated and YIG-\nnon-heated parts. In our case, it is the material’s properties\nthat are close to the antennas (far from the heat source).\nOnce the f0drop becomes pronounced on the transmissionspectra, it means that the heating gradient reaches the anten-\nnas’ region, which distance from the heating source is in the\nmm- range. Considering this range of heat transport, we can\nnot expect that the magnonic gap may be influenced by the\nperiodic temperature gradient in the YIG layer (caused by the\nGaAs periodicity) with thickness ts=9mm since the temper-\nature profile is expected to be flattened in the YIG layer.\nIn the case of the uniform heating of the YIG layer, the\napproximately linear decrease of the dispersion relation fre-\nquencies should be observed, as the MSdecrease uniformly\nin the whole magnetic film. Thus the decrease rate of the fbg\nand of f0should be similar (unlike we see in Fig. 7). There-\nfore, one can expect that the region of YIG under the irradi-\nated GaAs should have a higher temperature. The position of\nthe rejection band fgbis sensitive only to the temperature of\nthe sample covered by the periodic GaAs. On the other hand,\nthe measured f0is sensitive to the area of the sample close to\nthe antennas, as discussed above. Therefore the drop of fgb\nwill be more significant than the drop of frequency of f0as\nthe tuning-laser power increases above P= 275 mW.\nAdditionally, due to the YIG/GaAs air gap in the composed\nstructure and the effective light absorption by the semiconduc-\ntor, the GaAs temperature can be much higher than in YIG\nbelow the GaAs. We can expect that with an increase in tem-\nperature of the GaAs, the electron mobility will decrease, and\nthus, the collision frequency nwill increase [58]. As it was\nshown in Fig. 5 ( e)-(f), the 1 =ndecrease leads to the weaken-\ning of SSW screening by the GaAs and, therefore, contributes\nto further lowering of the fbg.\nThe sample holder configuration did not allow the displace-\nment of the excitation microwave antennas closer to the semi-\nconductor slab edges. In order to study the influence of the\nregions not covered by GaAs on the microwave spectroscopy\nresult (for instance, induced by the non-uniform heating), the\nBLS measurement setup was used instead. The points where\nthe BLS scanning was performed were closest possible to the\nsemiconductor slab edge (see Fig. 1 ( c)). The frequency range\nduring the BLS scanning was chosen to resolve the first Bragg\nresonance and the FMR frequency range. This was done in\norder to study the SSW screening, YIG layer heating, and the\nfbgformation in more detail.\nThe BLS spectra were measured with the mean step of\nPL=50mW in the interval from 0 to 425 mW. The plot-\nted spectra are presented in Fig. 8. Also, the BLS- resolved\nFMR frequency and first Bragg resonance frequencies in de-\npendence on tuning-laser power are depicted in Fig. 7. The\nrelated to FMR dip on the BLS spectra at PL=0mW has\nthe lower frequency value in comparison to obtained by the\nmicrowave spectroscopy f0. This may be linked to the speci-\nficity of the light-resolving of the magnetization dynamics of\nthe multimode SSWs’ transport [70]. In particular, the magne-\ntization dynamics probe by BLS consists of accumulating the\namplitude-frequency characteristics in discrete points along\nthe Port C1line (see Fig. 1 ( a)) and then sum them up. In\ncontrast, detecting the SSW transport by the probing antenna\nmeans obtaining the microwave current induced in the an-\ntenna by the SSW. Thus the resulting signal obtained by these12\nBLS intensity  at port C1 (arb.un.)\n4.2 4.3 4.4 4.5f0fg\n1\n2\n3\n4\n5\n6\n7\n8\n9\nFrequency (GHz)fgm\nFIG. 8. BLS spectra of SW propagating through the periodic\nGaAs/YIG structure. Curves were measured by the variation of the\ntuning-laser PL: 1- 0 mW, 2- 75 mW, 3- 125 mW, 4- 175 mW, 5-\n225 mW, 6- 275 mW, 7- 325 mW, 8- 375 mW, 9- 425 mW. f0,fg, and\nfgmcorrespondingly marks obtained by the microwave spectroscopy\nthe FMR frequency, the position of the first magnonic gap in a case of\nnon-irradiated structure, and the position of the magnonic gap at the\nlaser power PL=275 mW. Red fill marks the BLS-obtained range of\nthe FMR thermal decrease.\ntwo methods will be different if the SSWs spectra contains\nany spatially nonsymmetrical mods with respect to the cen-\ntral waveguide axis. This modes may be especially significant\nnear the FMR frequency since the spectra of long-wavelengths\nSSWs becomes strongly affected by the confinement of the\nstructure [64, 69]. We expect that the difference between the\nFMR frequency obtained by the BLS and microwave spec-troscopy keeps constant for all the measured tuning-laser pow-\ners.\nWe will compare the relative decrease of f0in BLS and\nmicrowave transport measurements. The shift of this FMR-\nrelated dip obtained by the BLS scanning (in the interval\nPL[0 mW\u0000425 mW ]is 0.0344 GHz (compared to 0.02 GHz\nin the same PLinterval at the microwave spectroscopy). Un-\nlike the results obtained by the microwave spectroscopy, this\ndip frequency decrease does not have the threshold Pth1value\nbefore which FMR frequency stays constant (see Fig. 7).\nThis FMR dip behavior may be related to our assumption\nabout the non-uniform heating of the structure along the xdi-\nrection. Thus the scanning closer to the GaAs slab (heating\nsource) edge should better detect this non-uniform heating of\nthe YIG layer. Thus, the comparison of f0(PL)dependen-\ncies obtained by the microwave spectroscopy and by the BLS\nprove the presence of the thermal nonuniformity within the\nYIG layer along the SSW propagation direction.\nFig. 7 demonstrates the good correspondence between the\nband gap frequency dependence on the tuning-laser power ob-\ntained from the microwave spectroscopy (dashed line marked\nbyfbgand from the BLS measurements (green circles). The\nprobed by the BLS technique fbg(PL=0 mW )value is equal\nto one probed by the microwave spectroscopy. The maximum\nfrequency of bandgap obtained by both methods (with the ac-\ncuracy of tining-laser power PLdiscrete step) was achieved\nat at PL=Pth1=275 mW. At the same time, the max-\nimum frequency of bandgap extracted from BLS measure-\nments (4.514 GHz) is slightly bigger than the one extracted\nfrom S21dependencies.\nThe presented BLS spectra demonstrate the formation of\nthe magnonic gap. With the tuning-laser power increase, PL,\nthe dip depth and width of the magnonic gap increase. We can\nnot directly compare the BLS spectra signal intensity with the\nmicrowave spectroscopy one. However, a pronounced dip is\nobserved above Pst=150 mW in both techniques. At the\nsame time, for the high values of PL(curves \"8\" and \"9\" in\nFig. 8), the magnonic gap dip becomes broadened and flattens\nout. We can relate this process to the heating-caused decrease\nin electron mobility [58] leading to the weakening of SSW\nscreening by the GaAs (see Fig. 5 ( e)-(f)).\nD. CONCLUSION\nAs a result of the research conducted on the periodic\nGaAs/YIG magnonic crystal, we can conclude the following.\nWe have confirmed the possibility of changing the magnonic\ncrystal contrast by the optical means in a predictable man-\nner. The degree of this contrast change is enough to form and\nswitch off the rejection band in the spectra of SSW transport in\nthe periodic structure. We unambiguously related the change\nof MC’s contrast with the optically-induced electron density\nvariation in the GaAs.\nWe claim that the critical point of the possibility of opti-\ncal manipulation over the magnonic bandgap formation is the\ndesign of the YIG/GaAs bilayer. This design should allow\nthe working wavelength range to effectively vary the SSW13\nscreening within the possible GaAs electron concentration in\nthe experiment. In our research, we showed that in addition\nto the importance of the semiconductor dark electron con-\ncentration value and the possibility of significantly varying\nthe electron concentration by the photo impact, the important\nrole plays the effective thickness of the semiconductor layer\n(which should be thicker than the skin layer for the working\nrange of wavelengths), and the semiconductor electron means\ncollision frequency.\nThe obtained results will allow the design of new class\nof the optically reconfigurable YIG/semiconductor magnonics\nelements. The spatial limitation for the sizes of the optically-\ninduced lattice will be due to the semiconductor charges dif-\nfusion length and the semiconductor layer thickness enough\nto screen the SW wavelength of the working range.\nE. ACKNOWLEDGMENTS\nThe research has received funding from the Slovak Grant\nAgency APVV (Nos APVV-19-0311(RSWFA), and APVV-\n21-0365), and from VEGA (Project No. 2/0068/21). Fur-\nthermore, this study was performed during the implementa-\ntion of the project Building-up Centre for advanced materials\napplication of the Slovak Academy of Sciences, ITMS project\ncode 313021T081 supported by Research & Innovation Op-\nerational Programme funded by the ERDF (15%). Also, this\nwork was supported by the Ministry of Education and Sci-\nence of the Russian Federation as part of the state assignment\n(Project No. FSRR-2023-0008).\nIV . APPENDIX\nA. Estimation of the semiconductor sample charge carriers’\nconcentration\nIn this section, we are going to describe the sequence of\nsteps we have used to obtain the parameters of the semicon-\nductor sample. The slab of GaAs had fabricated periodic\ngrooves on one of the side surfaces (see Fig. 9) by the laser\nablation method. This was done since this sample was pre-\npared to serve as a periodic load for a multilayered waveguide\nstructure. This shape of the sample defined the procedure that\nneeded to be done to know the GaAs material parameters.\nAccording to the known facts about the GaAs slab we had\n(it was a commercial sample performed for the CMOS tran-\nsistors fabrication), it consisted of the 500 mm thick substrate\n(expected electron concentration around 1010cm\u00003) and 1 mm\nthick strongly doped n-type layer (expected election concen-\ntration around 1017cm\u00003). The grooves were performed on\nthe dopes side of the sample. However, these concentration\nvalues had to be examined in detail. Further, for the purpose\nof the research on the YIG/GaAs multilayer, the optical vari-\nation of GaAs electron concentration had to be checked.\nFor doped semiconductors, the charge transfer is mainly\ndue to one type of charge carrier. Then, for n-type semicon-\nductors, the dependence of the conductance son the sampleelectron concentration Nemay be written in a form [71]:\ns=qNeme; (4)\nwhere qis the electron charge constant and me- electron mo-\nbility.\nThe standard approach to obtain the sample’s electron con-\ncentration experimentally needs 4-Ohmic contacts. Then, the\nelectrons concentration is calculated from Van der Pauw and\nHall measurements that define the electron mobility and con-\nductance [72]. Measured between the contacts, sheet resis-\ntance RSis related to the conductance sthrough the current\nflowed cross-sectional area dbetween the Ohmic contacts:\n1\ns=RSd: (5)\nHowever, fabricated periodic grooves on the doped face of\nthe GaAs slab allowed to perform the deposition of only 2\nOhmic contacts on the stripe between two grooves. On the\nother face of the slab (flat semi-insulating surface), 4 Ohmic\ncontacts were deposited. Fabrication of the contacts con-\nsisted of a few steps. After the evaporation of multilayer\n(Ni(3 nm)/Al 0:88Ge0:12(90 nm)/Ni(27 nm)) atop of GaAs slab,\noptical lithography was used to pattern contacts (two on a\ngrooved side and four on the opposite side). Then the anneal-\ning was done (450°C, 1 min, N 2ambient). Contacts were pat-\nterned on the distance 20 mm from each other (see Fig. 10 ( a)).\nAs a result, for a flat semi-insulating side of the GaAs sam-\nple, it was possible to make both resistance and electron mo-\nbility measurements. For the ribbed side of the highly doped\nside, it was possible to perform only resistance measurements.\nTo obtain the electron concentration for the ribbed side, the\nresults of resistance measurements were compiled with the\nknown results of n-type GaAs room temperature electron mo-\nbility dependence vs. doping concentration [57].\nWe obtained for the semi-insulating side of GaAs sam-\nple the electron mobility me=8400 cm2=V s and the result-\ning dark concentration Ne=1\u0001109cm\u00003. The best matched\npair of mobility (according the [57]) and dark concentration\n100 mm\n1mm500mm\nFIG. 9. Photo-microscope image of the side view of the GaAs slab.\nThe Green dashed line schematically shows the edge of the slab and\nfabricated grooves on its surface. Pink fill schematically shows the\nhighly n-doped GaAs layer (1 mm thickness). Green fill showed the\nsemi-insulator n-doped GaAs substrate (500 mm thickness).14\nR\nR\n(с)(b)\n (a)150 mm\nzyx\nFIG. 10. ( a) SEM image of 4-Ohmic contacts fabricated on a flat\nside of the GaAs slab. ( b), (c) Panels show the experimental resis-\ntance measurements process schemes. The red arrow on panel ( b)\ndemonstrates the laser beam displacement performed for the diffu-\nsion characteristic obtaining (see attached directions of the Cartesian\ncoordinates).\nfor the highly-doped GaAs side is me=4000 cm2=V s and\nNe=1:3\u00011016cm\u00003.\nTo obtain the laser power dependence of the GaAs elec-\ntron concentration for both sides of the sample, we used the\nlaser setup \"First laser\". Due to the technical issues, there was\nno possibility for simultaneous measurement of resistance and\nmobility under the optical irradiation. We measured the re-\nsistance relations vs. the optical power for both sides of the\nsample. At the same time, we had to ignore the mobility de-\npendence on the photo-injected electrons. Moreover, we ne-\nglected the impact of the laser-induced variation of the holes\nconcentration on the measured resistance (due to one-order\nlower holes mobility). Thus, we univocally linked the laser-\nexposure impact on the resistance variation with an optical\ngeneration of pure electrons, and the eq.(4) keeps valid.\nFor the highly-doped side, we were interested in the elec-\ntron concentration variation vs. the laser irradiation’s power\ndensity. For this purpose, the resistance between two Ohmic\ncontacts was measured vs. the power density of the laser\nbeam irradiating the contacts area. Consider the mobility of\nthe highly doped side me=4000 cm2=V s non-depend on thephoto injected electrons, the dependence of electron concen-\ntration Nevs the laser radiation power density was obtained\n(see Fig. 1 ( b)). The maximum obtained electron concentra-\ntion were Ne=4:54\u000110171=cm3(under the maximum avail-\nable laser exposure power density Wp=0:552 W/cm2).\nFor the semi-insulating side, we were interested in the dif-\nfusion of the optically injected electrons. The reason for this is\nthat the main conductance of the sample belongs to the highly-\ndoped layer, which we used as a load for the SW screen-\ning. The thickness-dependence concentration of the diffused\nelectrons from the doped layer to the semi-insulating layer\ncan be approximated by the exponential function defined by\nthe diffusion length, Ln, of the optically-induced electrons of\nthe semi-insulating layer. To obtain it, the resistance mea-\nsurements were done in dependence on the laser beam cen-\nter displacement (beam shift z0) out of the area of the Ohmic\ncontacts. Consider the mobility of the semi-insulating side\nme=8400 cm2=V s non-depend on the photo injected elec-\ntrons, the diffusion dependence of electron concentration Ne\nvs the distancing from the laser beam center z0was obtained\n(see the points in Fig. 1 ( c)). During this measurement, the\npower density of the laser beam was fixed on the maximum\navailable value Wp=0:552 W/cm2. The maximum obtained\nconcentration (when the laser beam was irradiating the Ohmic\ncontacts area) was Ne=3:49\u000110101=cm3. Since we know that\nusually, the spatial distribution of the concentration of diffu-\nsion carriers in semiconductors obeys an exponential law, we\ninterpolated the measured data by function:\nNe=1:7\u00011010e\u00000:003y;y(nm): (6)\nThis function was plotted together with the measured data (see\nred line in Fig. 1 ( c)). Relation (6) allowed us to choose the\ndiffusion length: Ln=315mm, which is typical for the n-\nGaAs samples with similar doping [57, 58].\nIn addition, we should point here that semiconductor elec-\ntron mobility allows to express through the electron effective\nmass, m\u0003, the electron mean collision frequency, n:\nme=q\nm\u0003n: (7)\nThe electron mean collision frequency is an important semi-\nconductor electrodynamic parameter with a meaning of damp-\ning, which in terms of this work is used in the numerical sim-\nulations. Consider for the n- GaAs the table value of the elec-\ntron effective mass m\u0003=0:13meof the electron mass constant\n[62, 63], me, we obtained 1 =n=2:96\u000110\u000013s for the doped\nlayer. We note here that since the electron mean collision\nfrequency depends on the electron mobility, thus it strongly\ndepends on the variation of the semiconductor doping elec-\ntron concentration [57] and on the semiconductor temperature\n[58].\nB. Numerical model and semiconductor describing approach\nThe numerical simulations of the YIG-GaAs periodic struc-\nture was based on the solution of the Helmholtz wave equation15\nfor the electric field vector E[73]:\nÑ\u0002(m\u00001Ñ\u0002E)\u0000(2pf)2\nc2\n0(e\u0000is\n2pfe0)E=0: (8)\nThis equation follows from the Maxwell system and set the\nconformity between the electric field vector Eon the wave\neigenmode frequency wave fand coordinate-dependant ma-\nterial properties: m, the relative permeability, e, the relative\npermittivity, and s, the electrical conductivity. e0is a vacuum\npermittivity, c0is a vacuum light speed constant.\nYIG magnetic permeability tensor\nYIG properties were substituted to eq.(8) as the constant-\nvalue permittivity, e, and gyrotropic frequency dependent per-\nmeability tensor, ˆm.ˆmtensor can be obtained from the lin-\nearized damping-less Landau-Lifshitz equation without ex-\nchange interaction [9, 61]:\nˆm=m02\n4m\u0000ima0\nimam 0\n0 0 13\n5; (9)\nwhere diagonal and non-diagonal components are:\nm=fH(fH+fM)\u0000f2\nf2\nH\u0000f2;ma=fMf\nf2\nH\u0000f2(10)\nand 2 pfH=gm0H0, 2pfM=gm0MS:The approach of de-\nscribing the magnetic properties of solids through the per-\nmeability tensor holds for the samples with quasi-uniform\nmagnetization (e.g., magnetized thin films and layers) with-\nout possible reverse of magnetization [9, 50, 61, 67].\nThus, in our model YIG material properties were fully\ndetermined through the input parameters: gyromagnetic ra-\ntio,g, saturation magnetization, MS, and external magnetic\nfield, H0. This approach was widely used for numerical sim-\nulations of the similar waveguide structures, e.g., in works\n[50, 67, 74, 75].\nGaAs permittivity tensor\nGaAs properties were substituted to eq.(8) as the perme-\nability m=1, and frequency-dependant permittivity tensor, ˆe,\nwhich describes semiconductor gyroelectric properties. Such\napproach to describe the interaction of wave-induced elec-\ntromagnetic field with the charges of semiconductor layer\nthrough the permittivity tensor was raised in [61, 76, 77].\nThe charges motion within the semiconductor may be de-\nscribed by the Boltzmann kinetic equation written in the hy-\ndrodynamic approximation [61]:\n¶V\n¶t+(V\u0001Ñ)V=q\nmeff(E+V\u0002B)\u0000nV; (11)\nwhere B- magnetic field inside semiconductor, E- electric\nfield inside the semiconductor, V- mean charge carriers drift\nspeed, q- elementary charge of charge carrier, meff- charge\neffective mass, n- charges mean collision frequency, followed\nfrom the charges mobility.It is possible to get velocities of charge carriers as the so-\nlution of linearized eq.(11), and current density definition al-\nlows to transform these velocities to the conductivity tensor,\nˆs. We assumed only the electron conductance, and Ne- elec-\ntron concentration, me- electron effective mass, q- electron\ncharge constant, nfollows from the electron mobility defined\nby eq.(7). Introducing the cyclotron and plasma frequencies:\nwc=q\nmem0H0;wp=s\nNeq2\nmee0;\nit is possible to formulate the frequency-dependant permittiv-\nity tensor, ˆe. In case of no macroscopic drift of the electrons\n(external electric field Eis absent), only small oscillations of\nVandEare assumed, and for the Cartesian coordinates and\nexternal magnetic field orientations defined in Fig. 1 ( a),\nˆer=\f\f\f\f\f\feg\u0000a11 a12 0\na21 eg\u0000a22 0\n0 a32 eg+a33\f\f\f\f\f\f; (12)\na33=iw2\np\nw(\u0000iw\u0000w);\na11=a22(f) = (\u0000iw\u0000n)epart;\na12=\u0000a21(f) =wcepart;\nepart=iw2\np\nw(w2+2(\u0000in)w\u0000w2\u0000w2c):\nHere egis a crystal lattice contribution to the semiconductor’s\npermittivity.\nThus, in our model GaAs material properties were fully de-\ntermined through the input parameters: electron concentra-\ntion, Ne, electron effective mass, me, electron collision fre-\nquency, n, crystal lattice contribution to the semiconductor’s\npermittivity, eg, external magnetic field H0. This approach in\ndifferent variations was used to describe the semiconductor\ninfluence on the SW transport, e.g. in works [43, 46, 47, 78–\n81].\nComputation cell\nConsidering the wave processes in waveguide structures\n(e.g., investigated structure, Fig. 1 (a))), equation (8) has coef-\nficients that are constants or periodic functions along the wave\npropagation direction y, (period D), thus the Bloch theorem\ncan be used:\nE(y;z) =E0(y;z)eikxx: (13)\nE0(y;z) =E0(y+a;y+a)- periodic function with period a\nandkx\u0011kas we considering only waves propagating along\nxdirection. To obtain eigenvalues of kfor considered sys-\ntem of equations (13) and (8) supplemented with the YIG and16\nYIGGaAsPEC\nPECPBC\nPBC\n10 µm\n10 mm\n200 µm\nxH0y\nz\nk\n10 µm\n10 mm\n200 µm\nxH0y\nz\nk\n105 µm\n75 µmtg(a) (b)\nt=g  40 µm\nYIGGaAsPEC\nPECPBC\nPBC500 µm\nFIG. 11. The computation cells used in numerical simulations of\nYIG/GaAs multilayers by the finite element method. The boundary\nconditions forming the cells are periodic boundary condition (PBC)\nand perfect electric conditions (PEC). Directions of Cartesian coor-\ndinates, external magnetic field and wavevectors correspond to one\ndepicted in Fig. 1 ( a). The computation cells was used for simula-\ntions of the YIG/GaAs multilayers: ( a) infinite and uniform along x\nandydirections, ( b) infinite and uniform along ydirection and peri-\nodic and infinite along xdirection.\nGaAs material properties parameters mande, they were sup-\nplemented with boundary conditions. It allowed to form the\ncomputation cell (see Fig. 11). We used periodic boundary\nconditions (PBC) along the wave propagation direction ( x\u0000\naxis) and perfect electric conductor (PEC) along the structure\nnormal direction ( y\u0000axis). In the approximation of structure\nto be infinite along the transverse direction ( z\u0000axis) we could\nreduce the numerical task problem to the 2D. The partial dif-ferential equation for the eigenvalue task was formulated from\nthe (8) as f(k). This defined task was solved by use of the\nComsol MULTIPHYSICS commercial software by the finite\nelement method [73].\nPeriodic boundary conditions allowed us to simulate multi-\nlayer infinite and uniform along the SW propagation direction\n(Fig. 11 ( a)) or multilayer infinitely periodic along the SW\npropagation direction (Fig. 11 ( b), one period of structure is\nconsidered, GaAs shape corresponds to the experimental sam-\nple image from Fig. 1 ( a)).\nAfter input of the materials parameters and sizes, for de-\nfined kvalue the certain amount of eigensolutions where ob-\ntained. The result of each solution is the simulated electro-\nmagnetic field spatial distribution within the computation re-\ngion with the corresponding eigenfrequency. This defined\namount of eigensolutions where calculated around defined ini-\ntial frequency value (which was chosen according the surface\nmagnetostatic wave approximation [59]). This gives an effec-\ntive tool for studying the magnonics structures, e.g., it is pos-\nsible to investigate the spatial distribution of the electromag-\nnetic fields within the studied structures, a reflection of elec-\ntromagnetic wave (EM) on its boundaries, standing waves,\nand waves propagating processes. As a result, dispersion rela-\ntions and information about wave attenuation can be obtained.\nWe mention, that computational cell depicted in Fig. 11 ( a)\nwas used for the \"Semi-infinite GaAs/YIG bilayer\" model,\n\"Default Parameters\" variation, and \"Experimental YIG/GaAs\nmultilayer\" model. The computational cell depicted in\nFig. 11 ( b) was used for the \"Experimental YIG/GaAs mul-\ntilayer\" model with periodic GaAs groves. The similar intro-\nduction of the boundary conditions for the system of eq.(8)\nand eq.(13) was used to form computation cell for the waveg-\nuides with gyrotropic materials in works, e.g., [50, 51, 74, 75].\n[1] A. Barman, G. Gubbiotti, S. Ladak, A. O. Adeyeye,\nM. Krawczyk, J. Gräfe, C. Adelmann, S. Cotofana, A. Naeemi,\nV . I. Vasyuchka, et al. , Journal of Physics: Condensed Matter\n(2021).\n[2] S. A. Nikitov, A. R. Safin, D. V . Kalyabin, A. V . Sadovnikov,\nE. N. Beginin, M. V . Logunov, M. A. Morozova, S. A. Odintsov,\nS. A. Osokin, A. Y . Sharaevskaya, Y . P. Sharaevsky, and A. I.\nKirilyuk, Physics-Uspekhi 63, 945 (2020).\n[3] S. A. Nikitov, D. V . Kalyabin, I. V . Lisenkov, A. Slavin, Y . N.\nBarabanenkov, S. A. Osokin, A. V . Sadovnikov, E. N. Beginin,\nM. A. Morozova, Y . A. Filimonov, Y . V . Khivintsev, S. L.\nVysotsky, V . K. Sakharov, and E. S. Pavlov, Physics-Uspekhi\n58, 1002 (2015).\n[4] S. Demokritov and A. Slavin, Magnonics: From Fundamen-\ntals to Applications , Topics in Applied Physics (Springer Berlin\nHeidelberg, 2012).\n[5] B. Lenk, H. Ulrichs, F. Garbs, and M. Münzenberg, Physics\nReports 507, 107 (2011).\n[6] V . Kruglyak, S. Demokritov, and D. Grundler, Journal of\nPhysics D: Applied Physics 43, 264001 (2010).\n[7] G. Gubbiotti, Three-Dimensional Magnonics (Jenny Stanford\nPublishing, 2019).\n[8] S. O. Demokritov, “Magnons,” in Topology in Magnetism ,edited by J. Zang, V . Cros, and A. Hoffmann (Springer In-\nternational Publishing, Cham, 2018) pp. 299–334.\n[9] A. Prabhakar and D. D. Stancil, Spin waves: Theory and appli-\ncations , V ol. 5 (Springer, 2009).\n[10] A. Association et al. , (2015).\n[11] C. S. Davies, A. Francis, A. V . Sadovnikov, S. V . Chertopalov,\nM. T. Bryan, S. V . Grishin, D. A. Allwood, Y . P. Sharaevskii,\nS. A. Nikitov, and V . V . Kruglyak, Phys. Rev. B 92, 020408\n(2015).\n[12] E. Beginin, A. Sadovnikov, A. Y . Sharaevskaya, A. Stognij, and\nS. Nikitov, Applied Physics Letters 112, 122404 (2018).\n[13] A. Sadovnikov, E. Beginin, S. Odincov, S. Sheshukova, Y . P.\nSharaevskii, A. Stognij, and S. Nikitov, Applied Physics Let-\nters108, 172411 (2016).\n[14] A. V . Sadovnikov, E. N. Beginin, S. E. Sheshukova, Y . P.\nSharaevskii, A. I. Stognij, N. N. Novitski, V . K. Sakharov, Y . V .\nKhivintsev, and S. A. Nikitov, Phys. Rev. B 99, 054424 (2019).\n[15] A. Stognij, L. Lutsev, V . Bursian, and N. Novitskii, Journal of\nApplied Physics 118, 023905 (2015).\n[16] A. Stognij, L. Lutsev, N. Novitskii, A. Bespalov, O. Golikova,\nV . Ketsko, R. Gieniusz, and A. Maziewski, Journal of Physics\nD: Applied Physics 48, 485002 (2015).\n[17] L. V . Lutsev, A. I. Stognij, N. N. Novitskii, V . E. Bursian,17\nA. Maziewski, and R. Gieniusz, Journal of Physics D: Applied\nPhysics 51, 355002 (2018).\n[18] A. V . Sadovnikov, E. N. Beginin, S. E. Sheshukova, Y . P.\nSharaevskii, A. I. Stognij, N. N. Novitski, V . K. Sakharov, Y . V .\nKhivintsev, and S. A. Nikitov, Phys. Rev. B 99(2019).\n[19] M. Krawczyk and D. Grundler, Journal of Physics: Condensed\nMatter 26, 123202 (2014).\n[20] A. Chumak, A. Serga, and B. Hillebrands, Journal of Physics\nD: Applied Physics 50, 244001 (2017).\n[21] A. V . Chumak, T. Neumann, A. A. Serga, B. Hillebrands, and\nM. P. Kostylev, Journal of Physics D: Applied Physics 42,\n205005 (2009).\n[22] A. A. Nikitin, A. B. Ustinov, A. A. Semenov, A. V . Chu-\nmak, A. A. Serga, V . I. Vasyuchka, E. Lähderanta, B. A.\nKalinikos, and B. Hillebrands, Applied Physics Letters 106,\n102405 (2015).\n[23] R. Kryshtal and A. Medved, Applied Physics Letters 100,\n192410 (2012).\n[24] A. V . Sadovnikov, A. A. Grachev, A. A. Serdobintsev, S. E.\nSheshukova, S. S. Yankin, and S. A. Nikitov, IEEE Magnetics\nLetters 10, 1 (2019).\n[25] V . Tikhonov, A. Litvinenko, A. Sadovnikov, and S. Nikitov,\nBulletin of the Russian Academy of Sciences: Physics 80, 1242\n(2016).\n[26] A. Litvinenko, R. Khymyn, V . Tyberkevych, V . Tikhonov,\nA. Slavin, and S. Nikitov, Physical Review Applied 15, 034057\n(2021).\n[27] A. N. Litvinenko, S. V . Grishin, Y . P. Sharaevskii, V . V .\nTikhonov, and S. A. Nikitov, Technical Physics Letters 44, 263\n(2018).\n[28] A. B. Ustinov, A. V . Drozdovskii, A. A. Nikitin, A. A. Semenov,\nD. A. Bozhko, A. A. Serga, B. Hillebrands, E. Lähderanta, and\nB. A. Kalinikos, Communications Physics 2, 1 (2019).\n[29] Q. Wang, A. V . Chumak, L. Jin, H. Zhang, B. Hillebrands, and\nZ. Zhong, Phys. Rev. B 95, 134433 (2017).\n[30] Z. xiong Li, X. guang Wang, D. wei Wang, Y . zhuang Nie,\nW. Tang, and G. hua Guo, Journal of Magnetism and Magnetic\nMaterials 388, 10 (2015).\n[31] C. Banerjee, P. Gruszecki, J. W. Klos, O. Hellwig,\nM. Krawczyk, and A. Barman, Phys. Rev. B 96, 024421 (2017).\n[32] F. Ma, Y . Zhou, H.-B. Braun, and W. S. Lew, Nano Letters 15,\n4029 (2015).\n[33] O. Dobrovolskiy, R. Sachser, T. Brächer, T. Böttcher,\nV . Kruglyak, R. V ovk, V . Shklovskij, M. Huth, B. Hillebrands,\nand A. Chumak, Nature Physics 15, 477 (2019).\n[34] A. Chumak, P. Dhagat, A. Jander, A. Serga, and B. Hillebrands,\nPhysical Review B 81, 140404 (2010).\n[35] Y . Fetisov and A. Makovkin, Journal of applied physics 79,\n5721 (1996).\n[36] B. Obry, V . I. Vasyuchka, A. V . Chumak, A. A. Serga, and\nB. Hillebrands, Applied Physics Letters 101, 192406 (2012).\n[37] M. V ogel, A. V . Chumak, E. H. Waller, T. Langner, V . I.\nVasyuchka, B. Hillebrands, and G. V on Freymann, Nature\nPhysics 11, 487 (2015).\n[38] A. Barman, G. Gubbiotti, S. Ladak, A. O. Adeyeye,\nM. Krawczyk, J. Gräfe, C. Adelmann, S. Cotofana, A. Naeemi,\nV . I. Vasyuchka, et al. , Journal of Physics: Condensed Matter\n33, 413001 (2021).\n[39] A. Serga, A. Chumak, and B. Hillebrands, Journal of Physics\nD: Applied Physics 43, 264002 (2010).\n[40] S. Seshadri, Proceedings of the IEEE 58, 506 (1970).\n[41] K. Kawasaki, H. Takagi, and M. Umeno, IEEE Transactions on\nMicrowave Theory and Techniques 22, 918 (1974).\n[42] D. D. Stancil, Journal of applied physics 59, 218 (1986).[43] A. Kindyak, Materials Letters 24, 359 (1995).\n[44] N. Almeida and D. Mills, Physical Review B 53, 12232 (1996).\n[45] Y . Fetisov, A. Makovkin, and V . Studenov, in International\nTopical Meeting on Microwave Photonics. MWP’96 Technical\nDigest. Satellite Workshop (Cat. No. 96TH8153) (IEEE, 1996)\npp. 37–40.\n[46] A. Kindyak, Technical Physics 44, 715 (1999).\n[47] A. S. Kindyak, Journal of communications technology & elec-\ntronics 41(1996).\n[48] E. N. Beginin, Y . A. Filimonov, E. S. Pavlov, S. L. Vysotskii,\nand S. A. Nikitov, Applied Physics Letters 100, 252412 (2012),\nhttps://doi.org/10.1063/1.4730374.\n[49] M. Mruczkiewicz, P. Graczyk, P. Lupo, A. Adeyeye, G. Gub-\nbiotti, and M. Krawczyk, Phys. Rev. B 96, 104411 (2017).\n[50] M. Mruczkiewicz and M. Krawczyk, Journal of Applied\nPhysics 115, 113909 (2014).\n[51] M. Mruczkiewicz, E. Pavlov, S. Vysotsky, M. Krawczyk, Y . A.\nFilimonov, and S. Nikitov, Physical Review B 90, 174416\n(2014).\n[52] S. Korchagin, E. Pleshakova, I. Alexandrova, V . Dolgov, E. Do-\ngadina, D. Serdechnyy, and K. Bublikov, Mathematics 9, 2948\n(2021).\n[53] V . Cherepanov, I. Kolokolov, and V . L’vov, Physics reports 229,\n81 (1993).\n[54] M. Stafe, A. Marcu, and N. N. Puscas, Pulsed laser ablation\nof solids: basics, theory and applications , V ol. 53 (Springer\nScience & Business Media, 2013).\n[55] E. Beginin, A. Sadovnikov, Y . P. Sharaevsky, and S. Nikitov,\nBulletin of the Russian Academy of Sciences: Physics 77, 1429\n(2013).\n[56] E. N. Beginin, A. V . Sadovnikov, Y . P. Sharaevsky, and S. A.\nNikitov, in Solid State Phenomena , V ol. 215 (Trans Tech Publ,\n2014) pp. 389–393.\n[57] M. Sotoodeh, A. Khalid, and A. Rezazadeh, Journal of applied\nphysics 87, 2890 (2000).\n[58] M. L. Lovejoy, M. R. Melloch, and M. S. Lundstrom, Applied\nphysics letters 67, 1101 (1995).\n[59] R. W. Damon and J. Eshbach, Journal of Physics and Chemistry\nof Solids 19, 308 (1961).\n[60] S. Bajpai, Journal of applied physics 58, 910 (1985).\n[61] G. A.G. and M. G.A., Magnetization Oscillations and Waves\n(Taylor & Francis, 1996).\n[62] J. Blakemore, Journal of Applied Physics 53, R123 (1982).\n[63] A. Raymond, J. Robert, and C. Bernard, Journal of Physics C:\nSolid State Physics 12, 2289 (1979).\n[64] S. O. Demokritov, B. Hillebrands, and A. N. Slavin, Physics\nReports 348, 441 (2001).\n[65] V . Demidov, O. Dzyapko, S. Demokritov, G. Melkov, and\nA. Slavin, Physical review letters 100, 047205 (2008).\n[66] P. Yeh, Josa 69, 742 (1979).\n[67] M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y . A.\nFilimonov, D. Kalyabin, I. Lisenkov, and S. Nikitov, New Jour-\nnal of Physics 15, 113023 (2013).\n[68] H. van den Berg, IEEE transactions on magnetics 27, 5480\n(1991).\n[69] T. O’keeffe and R. Patterson, Journal of Applied Physics 49,\n4886 (1978).\n[70] S. O. Demokritov, B. Hillebrands, and A. N. Slavin, Physics\nReports 348, 441 (2001).\n[71] S. M. Sze, Y . Li, and K. K. Ng, Physics of semiconductor de-\nvices (John wiley & sons, 2021).\n[72] O. Pohorelec, M. ˇTapajna, D. Gregušová, F. Gucmann,\nS. Hasenöhrl, Š. Haš ˇcík, R. Stoklas, A. Seifertová, B. Pécz,\nL. Tóth, et al. , Applied Surface Science 528, 146824 (2020).18\n[73] COMSOL Multiphysics and COMSOL Multiphysics Modeling\nGuide, Stockholm, Sweden: COMSOL AB (2017).\n[74] A. Sadovnikov, E. Beginin, K. Bublikov, S. Grishin,\nS. Sheshukova, Y . P. Sharaevskii, and S. Nikitov, Journal of\nApplied Physics 118, 203906 (2015).\n[75] A. V . Sadovnikov, K. Bublikov, E. N. Beginin, S. E.\nSheshukova, Y . P. Sharaevskii, and S. A. Nikitov, JETP letters\n102, 142 (2015).\n[76] A. Gurevich, “Magnetic resonance in ferrites and antiferromag-\nnets,” (1973).\n[77] F. Bass and A. Bulgakov, Kinetic and Electrodynamic Phenom-ena in Classical and Quantum Semiconductor Superlattices\n(Nova Science Publishers, 1997).\n[78] A. Kindyak, A. Boardman, and V . Kindyak, Journal of mag-\nnetism and magnetic materials 253, 8 (2002).\n[79] S. Eliseeva and D. Sementsov, Technical physics 50, 924\n(2005).\n[80] S. Eliseeva, D. Sementsov, and M. Stepanov, Technical Physics\n53, 1319 (2008).\n[81] S. Eliseeva, D. Sannikov, and D. Sementsov, Journal of mag-\nnetism and magnetic materials 322, 3807 (2010)."    },    {        "title": "1602.06015v1.Study_of_Aqueous_Dispersions_of_Magnetic_Nanoparticles_by_Magnetic_and_Rheological_Measurements.pdf",        "content": " 1 Study  of Aqueous  Dispersions of Magnetic Nanoparticles by \nMagnetic and Rheological Measurements   \nShalini  .M \nDepartment of Physics , University  of Mum bai and UM -DAE Centre for Excellence in Basic \nSciences, Mumbai -400098, Indi a \nS. Radha , D. C. Kothari# \nDepart ment of Physics, University of Mumbai, Mumbai – 400098, India  \n#National Centre for Nanosciences and Nanotechnology, University of Mumbai, Mumbai -400098, \nIndia  \nAbstract  \nThe observed magnetic tunability of light transm ission through a ferrofluid can be effec tively \nunderstood in terms of the inter -particle interaction that can be estimated from the magnetic and \nrheological properties of these fluids. The present study reports complementary magnetic and \nrheologi cal measurements of aqueous dispersions o f ferrite  nanoparticles and a  commercial ferrofluid. \nThe room temperature magnetization measured in a SQUID magnetometer up to fields of 1 to 2 Tesla \nshowed superparamagnetic behaviour of the p articles  and the dispersion with the background signal of \nthe liquid showing a diamagnetic behaviour. The room temperature rheological behaviour in zero \nmagnetic field of the fluids w as investigated by measuring the viscosity as a fu nction of shear rate from \n1-100 s-1. The particle size and t he nature of the carrier liquid det ermine the viscosity and is expected to \nhave an effect on the inter -particle interaction.  \nKeywords: ferrofluids, rheology, interparticle interaction , magnetization  \n \nEmail: radhas@ physics.mu .ac.in  \nFax   : +91-22-26529780   2 I. INTRODUCTION  \nMagn etic nanocolloids have many interesting properties which find applications in sealing, printing \ntargeted drug delivery etc. Aqueous dispersions of SPION s (Super Paramagnetic I ron Oxide \nNanoparticles) , specially have been the subject of intense research due to their inherent \nbiocompatibility [1 -3]. Generally , these SPION s are coated with a surfactant to prevent agglomeration  \nthat occur s due to presence of competing Van der Waals forces and the magnetic dipole inter action \nbetween the particles. Among various nano -materials, magnetic nanocrystals have bee n widely used in \nmany applications such as in ferro fluids,  recording media, electronic, optical and biomedical \ndisciplines. In addition, magnetic colloids have been found  to be a n ideal platform to study \nfundamental aspects of magnetism such as magnetic do main formation, models for magnetic structure, \nsuperparamagnetic behavior etc.   \nMagneto -optical effects in ferrofluids have  generated a lot of interest due to the tunability of the \nmedium  by the magnetic field. The studies on variation  of light transmission through a ferrolfluid with \ndifferent geometries of magnetic field and incident light have been wid ely reported  [4-7]. These  effects \nhave been attributed to structures formed inside the medium due to the interaction of the field with the \nparticles.  Recently Shalini et al  [8] have repor ted the observation of simultaneous decrease of forward \ntransmission and back reflection from a ferrofluid comprising of magnetite nanoparticles suspended  in \nkerosen e, in a transverse magnetic field . As the magnetic field is slowly increased, the fluid goe s from \ndisordered  to a partially ordered  state that is modeled to have chain -like structures with superimposed \nrandomness . The interplay of partial order, disorder and dissipation affects the scattering that explains \nthe observed optical behavior . There is  an interes t in further exploring this system by complementary \nstudies of physical properties of the carrier liquid and the collective magnetic response . The present \nwork reports the complementary  rheological and magnetic pr operty measurements  of some ferrofluids . \n  3 II. EXPERIMENTS AND DISCUSSION  \nThe ferrite nanoparticles were prepared by standard  wet chemical route s of co-precipitation of Fe2+ and \nFe3+ ions by NH 4OH at temperatures above 60 \nC and were  later dispersed in double distilled water  to \nform reaso nably stable dispersions . The size of the nanoparticles  as estimated by Scherrer formula from \nXRD measurements was in the range  10-28 nm. A PC based pulsed field hysteresis loop tracer was \nused for observing the hysteresis loops of the powder samples at ro om temperature  [9]. The standard \nsample was a commercial ferrofluid from Ferrolabs Inc. USA  (FLS 300.020) . The magnetization \nmeasurements at room temperature for the fluid samples were carried out on a SQUID  magnetometer \n(Qua ntum Design MPMS X7)  between fields of 1 to 2 Tesla. The liquid sa mples were sealed in a \nmicropipette tip, closed on b oth the sides with Araldit e, since these tips were found suitable  for \nsensitive magnetometers due to their  very l ow background signal .  Viscosity measurements were \ncarried out using a Rotational R heome ter (Haake Mars Rheometer, Therm o Scientific, Germany). The \nmeasurement was done using a Cone/Plate geometry using Cone/35mm/1\n  at room temperature 25  \nC. \nThe samples were tested for a time interval of 600s at a shear rate range of 1-100 s-1. The flow curve \nwas obtained by plotting shear stress vs shear rate.  The data was further fitted with suitable models \nbased on the flow curve using the Haake rheowin software. I n this case, the Oswald De Waale Power \nlaw model  was adopted . This yielded the viscosity curve that shows the variation of viscosity with \nrespect to shear rate.  \nFigure 1(a) shows the variation of magnetization , M vs magnetic field , H for magnetite \nnanoparticles at room temperature, using a loop tracer up to fields of 6kOe. It showed a saturation \nmagnetiz ation of 54.8 emu/g and coercivity of 110 Oe.  The standard sample was diluted to 5% \nconcentration by volume using kerosene. Figure 1(b) shows a representative plot of M -H loop of the \nstandard liquid samples from SQUI D magnetometer. The background signal from the blank liquid (red \ncurve) shows a diamagnetic behaviour  of magnitude much smaller than that of the magnetic fluid (blue  4 curve) (see inset). The magnetic fluid samples showed a saturation magnetization of 20 -22 emu/g and \nHc=12 Oe. However, according to the specifications given by the manufacturers, the saturation \nmagnetization of the stock is about 3 -6 emu/g. This was observed in all the standard samples and \nindicates an increase in saturation magnetization of th e ferrofluid dispersions. A similar effect of \nincreased saturation magnetization of dispersed magnetic nanoparticle s has been earlier observed \n[10,11 ]. The observed M -H curve with large saturation magnetization and low coercivity is a \ncharacteristic of sma ll domain -particles that in the superparamagnetic limit exhibit a  non-saturating \nmagnetization and an  anhysteretic (zero coercivity)  behavior. It is evident that the qualitative nature of \nthe hysteresis curve of the standard sample remains unaltered when d ispersed in fluid except for the \nincreased saturation magnetization. The magnetic measurement on the present batch of synthesized \nnanoparticles in dispersion has not been possible as of date, though earlier measurements on similar \nsystems have indicated an  increase in magnetization [11 ]. The higher coercivity of the synthesized \nnanoparticles compared to the standard one indicates a larger average grain size arising due to the \npolydispersity.  \n The viscosity of liquid samples is estimated as the ratio of the shear stress to shear rate using the \nrelation τ = η γ ’, where γ’ is the shear rate and η is the viscosity. A linear relationship of the shear stress \nwith shear rate is ascribed as Newtonian behavior. A non -linear flow curve indicates a non -Newtonian \nfluid where the viscosity changes with shear rate as against the Newtonian fluid where the viscosity is \nconstant. If the viscosity decreases with increasing shear rate, the sample is said to be showing shear \nthinning behavior whereas if it increases with increas es with increasing shear rate, it is said to show \nshear thickening behavior. Mathematically, this relationship between shear rate and shear stress is \ngiven as τ = K γ ’n using the Ostwald -de Waele model. Here n is the flow index. If n > 1, the fluid is \nsaid to show dilatants or shear thickening behavior while if n<1, it is said to show pseudo -plastic or \nshear -thinning behavior.  K is called the consistency factor that is a measure of the apparent viscosity.   5 The values of viscosity and the flow index arrived at fitting the data of the samples to these models are \ntabulated in Table1.  \n The results of the viscosity  study  of ferrofluid s comprising of magnetite  nanoparti cles dispersed \nin water (FF2) and kerosene (standard; FF1) are show n in Figs. 2  to 4.  Fig 2 (b) shows the viscosity \ncurve of blank liquid - kerosene . It can be seen that the base fluid  show s Newtonian behaviour at room \ntemperature. The viscosity measured a t room  temperature of water is 1.0 cP (m Pa.s) and for Kerosene \nis 1.6 cP (m Pa.s). In figure 3(b), the viscosity of the standard sample FF1 (MNPs dispersed in \nkerosene) is const ant over shear rate throughout, indicating a Newtonian flow behavior. Fig. 4(a) shows \nthe flow curve for the synthesized sample . At low shear rates, the flow curve for the aqueous dispersion \n(MNPs dispersed in water) shows a deviation from linearity. This is reflected in the viscosity curve, \nwhere it shows a sudden increase at lower s hear rates and tends to saturation at higher shear rates. This \neffect is attributed to a non -Newtonian behavior.   \n There have been several studies on ferrofluids to understand the magnetic field dependent \nchanges of viscosity by magnetorheological methods [12,13 ]. These studies correlate the observed \nmagneto -viscous effects  [14] with the formation of chain -like clusters of magnetic nanoparticles under \ncertain external conditions, like the applied field, the size and shape of the particles, the solid content  of \nthe particles in the fluid and the nature of the fluid. Zubarev et al [ 15] have pointed out that the \npolydispersity of the particles also play an important role in the rheological properties of the ferrofluid. \nThe observed difference in viscosity behav ior in our samples presumably arises due to the effect of the \nvarying particle sizes in the synthesized ferrofluids as compared to the commercial one , as is also \nevident from the higher coercivity in the magnetization measurements . The effect of the carrie r fluid is \nnot expected to be as significant since both  water and kerosene , showed comparable viscosity values \nand a Newtonian fluid behavior  at normal shear rates . The theoretical models for  interaction of the \nmagnetic particles in fluids provide an estimate for th e interaction parameter that depends directly on  6 the value of the saturation magnetization [15 ]. Thus it is important to have quantitative magnetization \nmeasurem ents of the magnetic fluids to understand the magneto -rheological behavior.  \n  \n \nII. CONCLUSION  \n The present study  of magnetization and rheology  on a set of ferrofluid samples show interesting \neffects.  However, it  is necessary to carry out further systematic quantitative measurements on these \nfluids to understand the observed enhancement in saturation m agnetization  as well as the variation in \nviscosity .  The nature of the carrier fluid i s to be further investigated by  studying the field dependen t \nrheological properties . This combined study is expected to  provide estimates for the interparticle \ninteractio n that leads to the formation of internal structures in the ferrofluids  under applied fields . \nThese in turn will enable designing magnetic fluids for several desirable applications .  \n \nACKNOWLEDGEMENT  \nThe authors  would like to thank Prof.  A. K. Niga m (TIFR ) and his lab staff for XRD and SQUID \nmeasurements  and Mr Mahesh Samant (ex -CNNUM) for rheology measurements . We also extend our \nthanks to Prof.  Hema Ramachandran ( RRI) for providing the commercial ferrofluid sampl es. Two of \nthe authors (SM and RS) acknowl edge Prof.  R. Nagarajan ( UM-DAE CBS ) for valuable discussion and \nsupport.   7 REFERENCES  \n[1] Technological applications of ferrofluids, J. Popplewell, Physics in Technology  15 150 \n[2] Commercial applications of  ferrofluids, K. Raj, R. Moskowitz , J. Magn. Mag n. Mater. 85 233 \n(1990)  \n[3] Magnetic fluids as  drug carriers:  Targeted transport of drugs  by a magnetic field , E.K. Ruuge, A.N.    \nRusetski , J. Magn. Magn. Mater. 122 335 (1993)  \n[4] Light Scattering in a magnetically polarizable nanoparticles suspension, J.M. Laskar, J. Philip, R.   \nBaldev, Phys. Rev. E 78, 031404 (2008)  \n[5] Experimental evidence of zero forward scattering by magnetic spheres , R.V. Mehta, R. Patel, R.          \nDesai, R.V. Upadhyay, K. Parekh, Phys. Rev. Lett. 96, 127402 (2006)  \n[6] Particle size and magnetic field -induced optical properties of magnetic fluid nanoparticles , G.   \nNarsinga Rao,  Y. D. Yao, Y. L. Chen, K. T. Wu, and J. W. Chen , Phys. Rev.  E 72, 031408 (2005 ) \n[7] Variations in optical transmittance wi th magnetic fields in nanosize d FePt ferrofluid , Kung -Tung  \nWu, Y. D. Yao  and Cheng -Wei Chang , J. App. Phys. 105, 07B505 (2009 ) \n[8] Light scattering from a magnetically tunable dense random medium  with dissipation: ferrofluid , M.   \nShalini, D. Sharma, A. A. Deshpande, D. Mathur, Hema Ramachandran and N. Kumar, Eur. Phys. \nJour. D 66 (2012) 30.  \n[9] PC based pulsed field hysteresis loop tracer , S. D. Likhite, Prachi Likhite and S. Radha , AIP Conf \nProc. 1349  (DAE Solid State Physics Symposium, Manipal ), Dec 2010.  \n[10] Study of Thrombolytic Activity of Enzyme Immobilized Ferrite Nanoparticles, Deepa Jose,            \n       S. Dugal and S. Radha , Proc. DAE Solid State  Physics Symposium, Mumbai, Dec  2008 . \n[11] Synthesis and Characterization of Aqueous Dispersions of Iron Oxide Nanoparticles for \nBiomedical   Applications , Nishant M Tayade, M.Phil. dissertation, 2008, Univ. of Mumbai \n(unpublished)   8 [12] Magnetic and rheological characterization of novel ferrofluids , M. Kroell, M. Pridoehl, G. \nZimmermann, L. Pop, S. Odenbach, A. Hartwig , J.Magn. Magn. Mater. 289 (2005) 21  \n[13] Rheology of FF based on nanodisc cobalt particles, H.  Shahnazian et al., J.Phys. D Appl. Phys. 42 \n(2009) 205004  \n[14] S. Odenbach, Magnetoviscous effects in ferrofluids, Springer, Berlin (2002)  \n[15] Zubarev and Iskakova, Physica A 343  (2004)65   9  \n \nTable 1 Viscosity and Flow behaviour index (n)  for the liquids estimated from var ious models  \nSample                Model           η (Pas) K \n(consistency \nfactor)  n (flow \nindex)  \nWater Newtoni an 0.98 -- 1 \nKerosene  Newtoni an 1.6 -- 1 \nFF 1  \n(MNP+Kerosene)  Ostw ald De \nwaale  1.5 -- 1 \nFF 2 (MNP -Water) Ostw ald De \nwaale (Non \nNewtonian)  -- 0.744  1.175  \n  10  \n \n \nFigure Captions  \nFig. 1(a) M -H loop tracer for magnetite powder  from pulsed field loop tracer  \nFig. 1(b) Room temperature M -H loop of standard FF (5% volume concentration in kerosene) from \nSQUID. The red curve shows the backgr ound signal of carrier liquid. Inset shows the data at lower \nfields.  \n Fig. 2(a) -2(b) Viscosity cur ve and Flow curve for base fluid  Kerosene  \nFig. 3(a) -3(b) Viscosity cur ve and Flow curve of standard sample  (MNP in kerosene)  \nFig. 4(a)  -4(b) Viscosity cur ve and Flow curve of synthesized sample ( MNP in water ) \n \n \n \n \n \n \n \n \n \n  11 \n-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6-60-40-200204060\n  M (emu/g)\nH (T) \nFig. 1(a)  \n-1.0 -0.5 0.0 0.5 1.0-30-20-100102030\n  M (emu/g)\nH(T) standard\n kerosene (Linear Fit)\n-0.4 -0.2 0.2 0.4-0.020.000.02M (emu/g)\nH (T)\n   \nFig. 1(b)   12  \n \nKerosene  \n \n  \n \nFig 2(a) - Flow curve  Fig 2(b)  Viscosity Curve  \n \n \n  \nFig 3(a)  Flow curve  Fig 3(b)  Viscosity C urve \nFF 1 (MNP -kerosene) st andard sample  \n \n  \n \nFig 4(a)  Flow curve  Fig 4(b)  Viscosity Curve  \nFF 2 (MNP -Water) s ample  \n \n \n \n \n \n "    },    {        "title": "1605.03177v1.Engineering_topological_materials_in_microwave_cavity_arrays.pdf",        "content": "Engineering topological materials in microwave cavity arrays\nBrandon M. Anderson, Ruichao Ma, Clai Owens, David I. Schuster, Jonathan Simon\nJames Franck Institute and University of Chicago\nWe present a scalable architecture for the exploration of interacting topological phases of pho-\ntons in arrays of microwave cavities, using established techniques from cavity and circuit quantum\nelectrodynamics. A time-reversal symmetry breaking (non-reciprocal) \rux is induced by coupling\nthe microwave cavities to ferrites, allowing for the production of a variety of topological band struc-\ntures including the \u000b= 1=4 Hofstadter model. E\u000bective photon-photon interactions are included\nby coupling the cavities to superconducting qubits, and are su\u000ecient to produce a \u0017= 1=2 bosonic\nLaughlin puddle. We demonstrate by exact diagonalization that this architecture is robust to exper-\nimentally achievable levels of disorder. These advances provide an exciting opportunity to employ\nthe quantum circuit toolkit for the exploration of strongly interacting topological materials.\nI. INTRODUCTION\nDespite signi\fcant interest in topological physics, the\nexperimental success in realizing strongly correlated topo-\nlogical systems has thus far been limited to the fractional-\nquantum hall (FQH) e\u000bect [1, 2] in two-dimensional elec-\ntron gases. There has recently been signi\fcant theoret-\nical explorations of alternative realizations of FQH sys-\ntems (and related fractional Chern insulators [3, 4]) in\nthe \feld of \\quantum engineering.\" Here a topologically\nnontrivial Hamiltonian is built from the ground up, typ-\nically following a two-ingredient recipe [3, 4]: (1) strong\ninteractions are added to a (2) topologically non-trivial\nsingle particle band structure. This recipe is well mo-\ntivated theoretically, and experimentally there has been\nsuccess in individual implementation of each ingredient.\nFor example, ultracold atomic systems have experimen-\ntally succeeded in the study of both topologically novel\nband structures [5{9], and strongly interacting but topo-\nlogically trivial systems [10, 11]. However, the simultane-\nous implementation of both elements, as is necessary for\ncreating strongly correlated topological states, has thus\nfar remained elusive.\nPhotons are a newly emerging platform for quantum\nengineering. Photonic crystals have successfully simu-\nlated non-interacting band structures in the regime of\nRF [12], microwave [13], or optical [14, 15] domains. In\nall cases, the necessary addition of strong interactions\nto produce strongly correlated states has remained chal-\nlenging. On the other hand, strong photon-photon inter-\nactions are readily achieved in circuit QED experiments\nwhere the exquisite control over few qubit states has al-\nlowed the quantum simulation of, e.g., molecular ener-\ngies [16]. Superconducting circuits have also been ad-\nvanced as a route to strongly correlated photonic lattices\n[17, 18]. Implementing a time-reversal-symmetry break-\ning (TRSB) single particle band stricture is still neces-\nsary to advance towards FQH physics; current proposals\nrequire site-dependent parametric modulation [18, 19],\nwhich remains experimentally di\u000ecult to scale to larger\nsystem sizes. Breaking time reversal symmetry with pas-\nsive circuit elements would therefore be a signi\fcant ad-\nvance in engineering of synthetic quantum materials.Here we propose a new photonic platform to engi-\nneer two-dimensional tight binding models with non-\ntrival band topology, using arrays of three-dimensional\nmicrowave cavities. Such cavities can be easily machined\nfrom metal to work in the few-to-tens of GHz regime,\nand have be shown to provide exceptional coherence at\ncryogenic temperatures with quality factors exceeding\nQ> 108[20]. The cavities can be tunnel-coupled evanes-\ncently by, e.g., directly milling a channel between two\ncavities, or using capacitively coupled transmission lines.\nModern machining techniques allow the creation of scal-\nable lattices with low disorder in on-site energies and\ntunneling energies.\nA key component of our scheme is a new technique\nused to induce the requisite TRSB \rux: this \rux is in-\nduced by the onsite mode structure [21] of the cavity,\nin contrast to previous schemes [12, 15, 17, 22] that in-\nduce a Peierl's phase in the tunnel coupler. The complex\namplitude of the tunnel coupler depends on the local elec-\ntric \feld at the periphery of the cavity. A non-reciprocal\n(TRSB) phase will require an electric \feld with on-site\nangular momentum, which is coupled to the polarization\nof the magnetic \feld through Faraday's law [23]. There-\nfore, by coupling the magnetic \feld to a magnetic dipole,\nsay through use of a ferrimagnetic crystal with a biased\nmagnetic \feld [24, 25], a cavity mode with de\fnite an-\ngular momentum can be energetically isolated. In this\nway, the ferrite transfers the TRSB bias \feld to a TRSB\n\rux of the photonic lattice. This technique is exper-\nimentally advantageous compared to previous schemes\nbecause: (1) It allows for the passive creation of topo-\nlogical band structures, and therefore avoids issues with\nnon-linear mixing with pumping frequency in modulated\ntunnel couplings schemes [18, 19]. (2) The ferrite couples\nto a chiral \\bright\" mode, shifting it in energy, leaving an\nunshifted chiral \\dark\" mode. The frequency of the dark\nmode is \frst-order insensitive to both the ferrite coupling\nstrength, loss, and detuning from cavity resonance [26];\nit is thus ideal for engineering low-disorder time-reversal\nbreaking lattice models.\nThe \fnal ingredient necessary for the study of FQH-\nlike physics is strong photon-photon interactions. These\ncan be incorporated by coupling the microwave cavitiesarXiv:1605.03177v1  [cond-mat.quant-gas]  10 May 20162\nto superconducting qubits [17, 27]. We consider adding\nsuch qubits to each site of the square Hofstdater model\nconstructed from the linear circuit elements. The Hamil-\ntonian describing the e\u000bective model can be simulated\nusing exact diagonalization techniques. We therefore nu-\nmerically explore our system at \fnite size and for few\nphotons. The numerical results demonstrate our archi-\ntecture will have a FQH eigenstate corresponding to a\nbosonic\u0017= 1=2 Laughlin state on a lattice [9, 28].\nIn remainder of this paper we present a scalable archi-\ntecture for study of strongly correlated topological ma-\nterials. The organization of the paper is as follows: In\nSec. II we discuss the general structure of the microwave\ncavities needed for our architecture. We then introduce\non-site coupling elements (Sec. II A) which isolate a de-\nsired eigenmode on each lattice site. When these eigen-\nmodes are tunnel coupled (Sec. II B) an e\u000bective \rux\nemerges when the system is probed in a certain frequency\nrange. This e\u000bective \rux can be understood as an emer-\ngent gauge \feld (Sec. II C) arising from band projection.\nConcluding the discussion of the general non-interacting\ncircuit elements, we show this architecture is su\u000ecient to\nsimulate the Hofstadter model (Sec. II D), and present\nproposals for some other interesting lattice models (Sec.\nII E.) In Sec. III we then consider the e\u000bects of adding\nphoton-photon interactions to each site for the purpose\nof producing fractional Chern insulating states in \fnite-\nsize systems. We use a numerical exact diagonalization\ntechnique to simulate our system, and \fnd that the prop-\nerties of a \u0017= 1=2 bosonic \\Laughlin puddle\" emerge.\nFinally, in Sec. III A we consider the likely forms of dis-\norder in the e\u000bective tight-binding model description of\nour system. We \fnd that the system is insensitive to the\nlargest sources of disorder, whereas the most sensitive\nforms of disorder can be controlled. We conclude that\ncurrent experimental techniques should be su\u000ecient to\nsimulate strongly correlated topological systems.\nII. SINGLE-PARTICLE BUILDING BLOCKS\nWe now describe the single particle building blocks\nfor our microwave architecture. Our goal is to engineer\nan e\u000bective tight-binding Hamiltonian, He\u000b, for photons\nwhose energy is near ~!0. We will use a unique cavity\neigenmode at this characteristic energy to represent the\ntight-binding degree of freedom (and thus restrict our\nwork to \\spinless\" models.) To model He\u000bwe there-\nfore need an isolated eigenmode on every site, whose fre-\nquency is!0, with all other onsite eigenmodes far de-\ntuned energetically.\nThere is signi\fcant freedom in the cavity mode\nstructure. We describe a particular implementa-\ntion employing transverse magnetic (TM) modes of\ncylindrical cavities with non-zero transverse magnetic\n\feld (Bx;By6= 0;Bz= 0) and longitudinal electric \feld\n(Ex;Ey= 0;Ez6= 0). We \frst consider a fundamental\ncavity mode tuned to frequency !0(annihilated by a0).\n+-a.\nb.|| arga.u.\n1.0\n00.5\nrad\np2p\n0FIG. 1. (a) Structure of the electric \feld amplitude and\nphase (with corresponding magnetic \feld polarization) of the\nmodes being considered. The fundamental mode has uniform\nphase everywhere with no nodes in the sole electric \feld com-\nponent,Ez. The two-fold degenerate \frst excited manifold\nmay be spanned by two modes with geometrically orthogo-\nnal linear-nodes in the Ez-\feld (axanday), or equivalently\nby two modes exhibiting a single point-node and \u00062\u0019phase\nwinding around the periphery ( a\u0006). For the modes axand\na+, the polarization of the magnetic \feld at the cavity center\nis presented. The polarization of the magnetic \feld points\nalong the gradient of the phase of Ez. For linear modes the\nmagnetic \feld is oriented perpendicular to the nodal line, with\ndirection oscillating in time. For the chiral modes, this mag-\nnetic \feld polarization precesses in time with frequency !0.\nThe size of the circles does not re\rect the physical dimension\nof the cavities, which is chosen such that the desired mode is\nalways at frequency !0. (b) The geometric phase acquired,\nfor a photon of frequency !0, when tunneling through a cav-\nity in which each of type of mode has been isolated. (left)\nA fundamental mode cavity will induce no tunneling phase\nshift between any two contacts. (center) An isolated linear\nmode (via a diagonal conductor or dielectric) will induce a\ntunneling phase shift of either 0 or \u0019. An isolated circular\nmode (via a ferrite in a magnetic \feld) will produce a phase\nshift equal to the relative angle between the incoming and\noutgoing tunnel-contacts.\nThe electric \feld of the fundamental mode, shown in Fig.\n1(a), is nodeless and has a spatially uniform phase across\nthe cavity. This is true regardless of the cavity geometry.\nWe also consider a di\u000berent cavity where the two-fold de-\ngenerate set of \frst excited modes (for example, TM 210,\nTM120in a Cartesian basis[29]) is tuned to a frequency\n!0. We de\fne the annihilation operators of this mani-\nfold asax(ay), according to a node of the electric \feld\nalong the ^y(^x)-axis (see Fig.1(a)). Using this notation,3\nthe onsite Hamiltonian is H(0)=!0ay\n0a0, for a funda-\nmental mode cavity, and H(1)=!0\u0000\nay\nxax+ay\nyay\u0001\nfor\nthe excited cavity manifold. Here, and in what follows,\nwe drop any constants resulting from zero point motion\nof the electromagnetic \feld, and set ~= 1.\nWhile we have written the Hamiltonian in terms of\n^x/^ymodes, this choice is arbitrary. Analogous to linearly\npolarized light, we may rotate the basis by an angle \u0012:\na\u0012=axcos\u0012+aysin\u0012, anda\u0012+\u0019=2=\u0000axsin\u0012+aycos\u0012.\nAlternatively, we can construct a basis analogous to\ncircularly polarized light: a\u0006= (ax\u0006iay)=p\n2, where\nthe phase changes continuously by 2 \u0019going counter-\nclockwise (clockwise) around the cavity center in the\na+(a\u0000) mode (see Fig. 1(a)). In this basis, the mag-\nnetic \feld has an amplitude maximum at the center of\nthe cavity, and a polarization that lies in-plane and ro-\ntates uniformly in time at frequency !0.\nA. On-site symmetry breaking\nThe on-site degeneracy of H(1)can be broken in a\ntime-reversal preserving or time-reversal breaking man-\nner. The \frst type takes the form of violations of cylin-\ndrical symmetry. For example, by placing a thin bar-\nrier (e.g. a rectangular conductor or dielectric) along\nthe nodal line of the axmode, one adds a perturbation\nV(1)= \u0001 linay\nyayto the Hamiltonian H(1). Theaxmode\nremains (nearly) unperturbed at frequency !0, while the\northogonal aymode will be shifted to higher energy (by\nan amount \u0001 lin). This energetically isolates the axmode\nat an energy !0, and uniquely de\fnes the relative phase\nbetween any two points on the edge of the cavity. (An\nanalogous procedure isolates a\u0012froma\u0012+\u0019=2.) This per-\nturbation only produces a relative phase of 0 or \u0019between\npoints on a cavity edge, and therefore cannot break time-\nreversal symmetry. Manufacturing imprecision gives rise\nto perturbations of this type.\nFor the study of quantum Hall physics, it is necessary\nto break time-reversal symmetry; this does not occur nat-\nurally for light. We consider achieving this by employing\nthe coherent magnon interaction between cavity photons\nand the spins of a ferrimagnetic material [24, 25]: a small\nferrite sphere placed at the center of the cavity with a DC\nbias \feld B= +B0^z. The ferrite acts as a collective spin\nwhich couples to the magnetic \feld of the cavity mode\nand precesses at a frequency !F=\u00160B0. (If the bias \feld\nis reverse the following analysis is valid with a+$a\u0000.)\nThe magnetic \feld of the a\u0006modes has a maximum at\nthe cavity center (at the node of the electric \feld), and\nan in-plane polarization that precesses about \u0006^zat a\nfrequency!0. When the spin precession frequency !F\nis tuned near !0, the polarization of the magnetic \feld\nof thea\u0006mode rotates synchronously with the collec-\ntive spin. The magnetic dipole interaction results in a\nstrong coupling between the a+mode and the ferrite\nmode (denoted aF). The magnetic \feld of the a\u0000mode,\non the other hand, rotates against the collective spin, and\na.\nb.\n-3.0 -1.5 0 1.5 3.0-2-1012\n00.5 1\nAmplitude-2-1012\n-2-1012\n-3.0 -1.5 0 1.5 3.0 0π2π\nPhase-2-10121.0\n00.5\nrad\np2p\n0Transmission |  S12 |\nS21\nS12Port 1\nPort 245 deg= 0\n= 0Ferrite\n++\nNon-recip = arg  (S21) - arg  (S12)FIG. 2. Response of a ferrite-cavity site described by H(F)in\na pump-probe experiment. Here, Sijis the response between\na porti= 1 located at the ^ xaxis, and a second port j= 2\nmeasured 45 degrees away (inset to (b)). In order to account\nfor loss, we introduce a linewidth \u0014and\u0014Ffor the microwave\ncavity and ferrite respectively. For physically relevant values\nof\u0014=gF;\u0014F=gF<10\u00002, this gives a corresponding coopera-\ntivity\u0011= 4g2\nF=\u0014\u0014F>104. (a) Amplitude of the transmission\nresponsejS12j. The chirality of a ferrite in a magnetic \feld\nallows it to couple only to the resonator mode of the same\nhandedness, producing an avoided crossing in the transmis-\nsion spectrum as the ferrite is tuned through resonance with\nthe resonator modes. This avoided crossing appears as two\nmodes which are bright to the ferrite, B+andB\u0000. The dark\nmode, labeled D, does not couple to the ferrite, and is there-\nfore unshifted and insensitive to ferrite loss \u0014F. (b) The non-\nreciprocal phase, \u001eNon\u0000Recip = arg (S21)\u0000arg (S12), re\rects\nthe phase di\u000berence between going in the 0 degree port and\nout the 45 degree port, and the reverse process. This is ide-\nally\u001eNon\u0000Recip = 3\u0019=2 for the dark mode. This time-reversal\nbreak is robust to detuning in either the ferrite or the probe,\nand also loss, with the lowest order correction entering as\n\u001eNon\u0000Recip\u00193\u0019\n2\u00002\u000ep(\u000ep\u00002\u000eF)\ng2\nF\u00002\n\u0011. (c) A slice through the\nnon-reciprocal phase as a function of the probe detuning, for\nthe ferrite tuned to resonance. The non-reciprocal phase of\n\u001eNon\u0000Recip\u00193\u0019=2 is apparent near the dark mode.4\nthus does not couple. This results in strong hibridization\nof thea+mode with the ferrite, producing two bright\nmagnon modes that are pushed away from the dark a\u0000\nmode at frequency !0. Thus, when the system is probed\nnear!0, the isolated dark mode a\u0000sets a unique mag-\nnetic \feld polarization vector, or equivalently a unique\nquantum mechanical phase at the cavity periphery.\nThe coupling of the cavity-ferrite system is de-\nscribed by the Hamiltonian H(F)=H(1)+!Fay\nFaF+\ngF\u0010\nay\n+aF+ay\nFa+\u0011\n, wheregFis the coupling of the fer-\nrite to thea+mode (and must overwhelm \u0001 lin). A more\nsuggestive notation is: H(F)=\u0000\na(F)\u0001yH(F)a(F), where\nwe have de\fned a ferrite-cavity mode vector a(F)=\n(ax;ay;aF)Tand described the cavity-ferrite system with\na coupling matrix:\nH(F)=!0^I+0\n@0 0 gF=p\n2\n0 0 igF=p\n2\ngF=p\n2\u0000igF=p\n2 2\u000eF1\nA;(1)\nwhere 2\u000eFis the detuning of the ferrite from cavity\nresonance ( !F=!0+ 2\u000eF) and ^Iis the identity ma-\ntrix in the cavity-ferrite space. This Hamiltonian has\nan uncoupled dark eigenmode a\u0000that remains at fre-\nquency!0. There are also two hybridized magnon\nmodesB\u0006= (aF\u0006a+)=p\n2 that are frequency shifted\nby!B\u0006\u0000!0=\u000eF\u0006p\n\u000e2\nF+g2\nF. We henceforth assume\nthe experimentally relevant limit where gFis large com-\npared to\u000eF, along with any energy scales appearing in\nHe\u000b.\nKey features of this system are understood by ex-\namining the cavity response using input-output formal-\nism [24, 30]: We consider response at a small detuning\n\u000ep=!\u0000!0, and ferrite detuning 2 \u000eF, from!0, and intro-\nduce a \fnite lifetime of the cavity modes ( \u0014) and ferrite\nmode (\u0014F), with a resulting cooperativity \u0011= 4g2\nF=\u0014\u0014F.\nThe amplitude of the response is shown in Fig. 2(a).\nHere, there are three maxima in the response as \u000epis\nvaried, corresponding to three eigenmodes: the a\u0000mode\nremains at!0for all ferrite detunings, while the a+mode\nmixes with the ferrite mode aFand undergoes an avoided\ncrossing as the ferrite detuning is swept. When probed\nat frequencies near !B\u0006, the bright magnon modes have\nthe TRSB phase winding. Importantly, though only the\nbright mode couples to the ferrite, both the bright and\ndark modes are non-reciprocal. In fact the dark mode is\npreferred because crucially, it is insensitive to loss in the\nferrite and is less sensitive to detuning and linear disor-\nder. When the ferrite is exactly on resonance ( \u000eF= 0),\nthe dark mode has an exact TRSB phase winding of 2 \u0019\nat the periphery of the cavity. At probe frequencies dif-\nferent than !0the phase winding ceases to be uniform.\nHowever, this nonuniformity is quadratically insensitive\nin both the ferrite detuning and the energy of the probe\nphoton. This can be seen from the saddle-point structure\nin Fig. 2(b). Here the non-reciprocal phase response of\nthis system is calculated between two cavity contacts sep-\narated by an angle of \u0019=4 on the cavity periphery (inset);the di\u000berence between forward and backwards phases is\n\u001eNon\u0000Recip\u00193\u0019\n2\u00002\u000ep(\u000ep\u00002\u000eF)\ng2\nF\u00002\n\u0011. This quadratic insen-\nsitivity of the eigenmode structure signi\fcantly decreases\ndisorder inHe\u000barising from disorder in the ferrite, cav-\nity, or bias \feld.\nWe now de\fne our onsite Hamiltonian at a site jwith\nthe notationH(\u000b)\nos;j=\u0010\na(\u000b)\nj\u0011y\nH(\u000b)\nja(\u000b)\njwhere\u000b= 0 cor-\nresponds to a fundamental cavity, \u000b=\u0012de\fnes a site\nisolating a linear mode a\u0012, and\u000b=Fcorresponds to a\nferrite site. The form of the vector of annihilation opera-\ntors on site jdepends on the type of site with a(0)\nj=aj0,\na(\u0012)\nj= (ajx;ajy)T, anda(F)\nj= (ajx;ajy;ajF)Tfor a fun-\ndamental, linear, and ferrite site respectively. The onsite\ncoupling Hamiltonians are H(0)\nj=!0,\nH(\u0012)\nj=\u0012\n!0\u0000\u0001linei\u0012\n\u0000\u0001line\u0000i\u0012!0\u0013\n;\nandH(F)\njis given by Eq. (1). A system of uncoupled cav-\nities is then generically described by the on-site Hamil-\ntonianHos=P\njH(\u000b)\nos;j=P\nj\u0010\na(\u000b)\nj\u0011y\nH(\u000b)\nja(\u000b)\nj, where\neach\u000bjrepresents one of the distinct cavity types.\nB. Tunnel coupling and nontrivial \rux\nCoupling of the cavities is realized by connecting their\nedges with evanescent waveguides. The amplitude of such\na tunnel coupling is determined by the geometry (length\nand cross-section) of the channel. We emphasize that the\ncoupler is only virtually populated { the evanescent wave\n\\propagates\" with a purely imaginary wavevector { so\nthe phase of the photon is spatially uniform throughout\nthe channel, and the channel has no dynamical degree of\nfreedom.\nNow consider a site with an isolated eigenmode (such\nasa\u0012ora\u0006) at frequency !0, that has a nonuniform phase\npro\fle. Attached to this cavity are two or more tunnel\ncontacts to nearby cavities. The nonuniform phase of\nthe mode implies that a photon that tunnels in along\none channel will acquire a geometrical phase shift as it\ntunnels out along a di\u000berent channel; this is the origin of\nthe induced TRSB \rux.\nIn a fundamental mode cavity, both the amplitude and\nphase around the edge are uniform, and therefore no geo-\nmetric phase will be acquired for two tunneling contacts,\nregardless of where they are attached. In contrast, a\nferrite-cavity site with two tunneling channels separated\nby an angle \u001eon the cavity perimeter will experience a\ngeometrical phase shift of \u0006\u001efor an isolated a\u0006mode\n(see Fig. 1(b).)\nOn the other hand, two tunnel contacts on a site with\na modea\u0012will experience a relative phase shift only if\nthe photon crosses a node between the processes of tun-\nneling in and tunneling out (see Fig. 1(b).) For an a\u0012\nmode, the local amplitude at the cavity periphery will be5\nnonuniform and the tunneling magnitude will gain posi-\ntion dependence (see Figs. 1(a).) (An ideal point contact\nat an angle \u001erelative to the ^ xaxis will tunnel with am-\nplitudet\u0018cos (\u0012\u0000\u001e) at frequencies near !0.) This is in\ncontrast to a mode a0ora\u0006, for which the mode magni-\ntude, and thus the tunneling magnitude, is uniform.\nFor an open 1D chain of tunnel-coupled cavities, the\ngeometric phase arising from onsite elements can be elim-\ninated through a gauge transformation. On the other\nhand, closing the loop produces a net phase (\rux) after\ntunneling around a closed loop (plaquette). This \rux\nis analogous to a discrete version of Berry's phase and\ncannot be eliminated through a gauge transformation.\nRather it will, appear on the tunnel coupling terms in\nHe\u000b. In this way, a variety of lattice models can be real-\nized that have nontrivial Peierl's phases.\nC. Band projection and geometric phase\nThe arguments above suggest there is a nontrivial\nBerry's \rux through a plaquette when energy scales are\nrestricted to a small window around !0(and onsite per-\nturbations are su\u000eciently large). At energies away from\n!0the full degrees of freedom must be considered. The\nHamiltonian that describes this general system is given\nbyH0=HT+Hos, whereHT=P\nhiji\u0010\na(\u000bi)\ni\u0011y\nTija(\u000bj)\nj\ntunnel couples the lattice of cavities de\fned by Hosin\nthe previous section. The matrix Tijrepresents the tun-\nneling between two neighboring sites with onsite mode\nstructure\u000biand\u000bj. The speci\fc form depends on the\ntype of tunneling, but we note that an ideal point con-\ntact will have a non-zero overlap for only a single bare\ncavity mode (not a coupled eigenmode) at frequency !0.\nFor fundamental cavities this is naturally a0, whereas in\n\frst excited cavities only one linear combination of ax\nandaywill have a nonzero contribution to Tij. All other\ntunneling terms will vanish.\nThe geometric \rux can now be rigorously calculated\nconsidering a unitary U(\u000b)\njmatrix at every site jthat\nlocally diagonalized H(\u000b)\nj:H(\u000b)\nj=U(\u000b)\nj\u0001(\u000b)\nj\u0010\nU(\u000b)\nj\u0011y\n,\nwhere \u0001(\u000b)\njis a diagonal matrix of onsite energy eigen-\nvalues with a unique mode at frequency !0. Apply-\ning this unitary rotation to every site then transforms\nthe Hamiltonian to Hos=P\nj\u0010\n~a(\u000bj)\nj\u0011y\n\u0001(\u000bj)\nj~a(\u000bj)\nj, and\nHT=P\nhiji\u0010\n~a(\u000bj)\ni\u0011y~Tij~a(\u000bj)\nj, where ~a(\u000bj)\nj=U(\u000bj)\nja(\u000bj)\nj\nand ~Tij=U(\u000bi)\niTij\u0010\nU(\u000bj)\nj\u0011y\n. This transformation has\nthe e\u000bect of locally diagonalizing each onsite Hamilto-\nnian at the cost of transforming the tunneling matrix\nbetween sites.\nThe restriction to the unique mode at frequency !0will\namount to a projection into the onsite modes ^ aj0. Ap-\nplying a projection operator Pj0to eliminate unoccupiedmodes results inHe\u000b;0\u0011P\njPj0H0Pj0=P\nj!0^ay\nj0^aj0+P\nhiji^tij^ay\ni0^aj0, where the e\u000bective tunneling matrix ^tij\ncan contain a nontrivial phase. We emphasize that while\nthis tunneling phase is gauge dependent, the net \rux\nthrough a plaquette naturally remains gauge invariant.\nWe now discuss how the circuit elements described\nabove can result in interesting band structures for a fre-\nquency range around !0. For a plaquette consisting of\nonly fundamental mode cavities, a photon acquires no\nnet phase going around a plaquette (corresponding to\nzero \rux.) An a\u0012mode cavity would contribute a net\n\rux of\u0019to a plaquette if the tunneling contacts cross\nthe nodal line, and 0 otherwise.\nFor plaquettes with ferrite sites, the TRSB \rux is di-\nrectly proportional to the angle between the two tun-\nneling channels attached to the ferrite cavity. Thus, a\nresonator with Nevenly spaced tunneling contacts will\ncontribute a \rux of \u001e= 2\u0019=N to each adjacent plaquette\nconnected by tunnel couplers. This will allow for simu-\nlation of\u000b= 1=NHofstadter models in di\u000berent lattice\ngeometries, such as \u000b= 1=4 in a square geometry and\n\u000b= 1=6 in a triangle. In general, using only the \frst\nexcited modes we are limited to a total \rux of 2 \u0019per in-\nternal ferrite. However, using higher order modes allows\nfor a net \rux of any integer multiple of 2 \u0019per plaquette.\nThe nontrivial e\u000bective \rux is a discrete geometric\n(Berry's) phase; it is a direct lattice analogue to \\syn-\nthetic gauge \felds\" studied in ultracold atomic systems\n[7]. There, Raman \felds are used to couple internal\n(spin) degrees of freedom. The Raman \felds vary slowly\nin space, but also provide a large energetic separation be-\ntween dressed states. After preparing the system in a sin-\ngle dressed state, the dynamics respond analogously to a\nsystem under the in\ruence of a nontrivial external gauge\npotential. Similar to the study of synthetic gauge \felds\nin ultracold atoms, the microwave lattice scheme can also\nbe extended to the regime of synthetic non-Abelian gauge\n\felds, such as spin-orbit coupling [7, 31]; we leave such\nsystems to future work.\nD. Simulating a Hofstadter model\nGiven the circuit elements described above, it is now\nstraightforward to construct an \u000b= 1=4 Hofstadter\nmodel. Of the many equivalent con\fgurations, we\npresent one that requires the minimum number of fer-\nrites per unit cell.\nConsider a square lattice of fundamental resonators,\nwith every fourth fundamental cavity replaced by ferrite\ncavity, such that all plaquettes include one ferrite. This\nresults in a square four-site unit cell. (See shaded area in\nFig. 3(a).) This is consistent with the fact that a Hofs-\ndater model with \rux \u000b=p=qwill have aq-site unit cell.\nWhen the system is probed at frequencies near !0, the\ntime-reversal symmetry breaking mode will contribute a\nphase of\u0019=2 into each of the four neighboring plaque-\nttes. Since each plaquette touches only a single ferrite6\na. b. c.\np/ 2\np/ 3\nFIG. 3. Implementations of topological band structures described in the main text. (a) Hofstadter model with \u000b= 1=4:\na square, four-site, unit cell has one ferrite and three fundamental resonators. In the e\u000becitive model near a frequency !0,\nthe ferrite induces a quarter \rux quantum for each of the four neighboring plaquettes. (b) Triangular Hofstadter model with\n\u000b= 1=6: a triangular lattice with a three site unit cell has a single ferrite. This ferrite touches each of six neighboring\nplaquettes. (c) Haldane model: a hexagonal lattice has a ferrite on each lattice site. By staggering the handedness of the dark\nmodes on A and B sublattices, the net \rux vanishes. Addition of next-nearest-neighbor tunneling terms breaks time-reversal\nsymmetry by inducing a \rux of \u000b=\u0006\u0019=3 in each sublattice.\n9.5-3.0-1.501.53.0\n-3.01.501.53.09.511.0\n-1.0 -0.5 0 0.5 1.0-11.0-9.5-3.01.501.53.0\n C = -2\nC = +1C = +1\n}\nC = 0C = 0}\n}\nFIG. 4. Band structure of the microwave cavity implementa-\ntion of the\u000b= 1=4 Hofstdater model in a strip geometry. The\nunit cell presented in Fig. 3(a) has three fundamental mode\ncavities, along with a single ferrite site, resulting in a total of\nsix bands. When the ferrite energy is tuned large, two bright\nbands (black) are far separated from the four bands (gray)\nbands near !0. These four bands have an edge state and\nChern number structure consistent with the \u000b= 1=4 Hofs-\ntadter model. Here, blue (orange) lines connecting the bulk\nbands represent edge modes localized on the left (right) edge.\nNo edge states connect the dark bands to the bright bands.\nthe total \rux will be uniform \u000b= (\u0019=2)=2\u0019= 1=4.\nWe have veri\fed this system provides the expected\nHofstadter physics in two ways. First, we have explicitly\ncalculated the band projected model for the phase con-vention de\fned above. The net \rux through a plaquette\nis found to be \u0019=2 as expected. Second, we have numeri-\ncally diagonalized the Hamiltonian including all relevant\ndegrees of freedom. We chose the ferrite-cavity coupling\nto be ten times the tunneling energy ( gF= 10t), and con-\nsider a strip geometry. As seen in Fig. 4, the full model\nhas six bands. The top and bottom (black) bands are\ncomposed almost entirely of the bright magnon modes.\nThese bands are only weakly dispersive, as tunneling be-\ntween bright modes must occur o\u000b-resonantly through\nneighboring fundamental cavities, and is therefore sup-\npressed to\u0018t2=gF.\nIn contrast, the middle four (gray) bands are composed\nalmost entirely of dark and fundamental cavity modes.\nThese states form the e\u000bective Hofstadter model, and\nhave all expected properties: The four bands are energet-\nically symmetric around the energy !0; the top and bot-\ntom band are gapped relative to the two middle bands,\nwhich touch at two distinct Dirac points; the band Chern\nnumbers for the continuum model are calculated to be\n(from top to bottom) C= 0;1;\u00002;1;0, consistent with\ntopologically trivial bright bands sandwiching an \u000b= 1=4\nHofstadter model in the dark sector. A \fnite size calcula-\ntion shows chiral edge channels that emerge between the\nHofstadter bands, but not between the dark (Hofstadter)\nand bright bands.\nE. Other lattice models\nThese circuit elements are powerful for implementing\na variety of topological band structures. In passing we\npresent two additional examples. Figure 3(b) is an imple-\nmentation of a triangular Hofstadter model with \u000b= 1=6,\nwhere we use a triangular lattice with a single ferrite\nplaced in each three site unit cell. Using arguments sim-\nilar to above, this introduces a net \rux of \u000b= 1=6 per\nplaquette, as desired.7\nTunnel couplings may additionally cross by, e.g., ma-\nchining channels on both the top and bottom of the sub-\nstrate supporting the cavity array. This allows for im-\nplementation of an even larger class of topologically non-\ntrivial single particle Hamiltonians. In Fig. 3(c) the Hal-\ndane model is constructed from a hexagonal lattice with\nnext-neighbor tunnel couplings added, where a ferrite is\nadded to every site. By alternating the sign of the DC\nbias \feld, and thereby the chirality of the ferrite dark\nmodes, between A and B sites the net \rux per plaquette\nvanishes, while time reversal symmetry is locally broken.\nThis geometry speci\fcally produces the \\ideal\" \rux con-\n\fguration that is gauge equivalent to a \rux quantum per\nplaquette [32].\nIn addition to the examples presented here, other fre-\nquently studied Hamiltonians such as the 2D chiral- \u0019\n[32], or 1D chiral models such as the SSH model may\nalso be directly implemented [33]. The circuit architec-\nture described above is useful for realization of a variety\nof paradigmatic lattice models described in the literature.\nThe possibilities are extensive and we leave elucidation\nof these to future works.\nIII. EXPLORING FRACTIONAL QUANTUM\nHALL PHYSICS\nThe microwave architecture above is linear and should\nbe equally e\u000bective at simulating non-interacting topo-\nlogical structures in both the classical and few-photon\nlimits. On the other hand, to create strongly correlated\ntopological states, strong photon-photon interactions are\nrequired. It is well established that a nonlinear inter-\naction between photons arises through coupling the mi-\ncrowave cavities to Josephson junction qubits [27, 34].\nThe addition of a qubit to each site of the synthetic\n\u000b= 1=4 Hofstadter model proposed above should be suf-\n\fcient to explore bosonic fractional-quantum hall physics\n[9, 28] for microwave photons. We expect that the addi-\ntion of interactions should result in a FQH-like eigenstate\nlying at the edge of the dark bands, and well separated\nfrom the bright bands.\nThese FQH could then be explored in a variety of ways.\nFor example, a pump-probe experiment with low average\nphoton number near the energies of the e\u000bective FQH\nstate will have a small probability of exciting the FQH\nmanifold. Alternatively, a chemical potential for pho-\ntons [35] could be used to drive the system to a steady\nstate with the precise number of photons requisite for\na speci\fc geometry. In \fnite size systems, the desired\nFQH eigenstates will be ones with de\fnite photon num-\nber. We note that these preparation schemes precisely set\nthe photon number, and thus the assumption of de\fnite\nphoton number below is experimentally relevant.\nWe now demonstrate the existence of bosonic FQH\neigenstates in our architecture by numerically explor-\ning the combined single-particle and interacting Hamil-\ntonianHe\u000b;mb=He\u000b;0+He\u000b;Iprojected to describe\n5 10 15 2000.10.2\n5 10 15 2000.030.06\n0 0.25 0.500.10.2\n0 0.05 0.100.10.2\n5 10 15 2000.10.20 0.5 1.0-8.3-8.0-7.7\n0.25max\n0.5\n0.75 1.0\n0.25max\n0.5\n0.75 1.0\n0.1max\n0.2 0.35a. b.\nc. d.\ne. f.FIG. 5. (a) Spectral \row of a of the lowest 30 many-body\neigenstates as a \rux \rx=\ry=\r,\r2[0;2\u0019] is inserted\nintoHe\u000b;mb. Weak disorder is included that visually splits\nthe numerically exact two-fold degeneracy of the ground state\nmanifold in the clean limit. For all \rux, the GSM (orange,\nblue lines) remains gapped relative to the (shaded gray) ex-\ncited states. Provided this gap remains in the presence of\ndisorder, a many-body Chern number can be de\fned. The\ndisorder-averaged minimum value of this gap is denoted \u0016\u0001mb.\nThis is used as a metric to test sensitivity to various types\nof disorder. (b) \u0016\u0001mbas a function of the average interaction\nstrength \u0016Ufor various strengths of interaction disorder \u000eUi.\nThe many-body gap is not signi\fcantly suppressed at large\ninteraction strengths. (c) Same as (b), but all ferrite sites\nare made non-interacting. This comes at the cost a drop of\n\u0016\u0001mbby a factor of about four. (d) E\u000bect of disorder in the\nmagnitude of the tunneling strength j\u000etijj, in a strongly in-\nteracting case ( Ui= 20). (e) E\u000bect of disorder in the \rux\n\u000e\u000bthrough each plaquette. (f) E\u000bect of disorder \u000e!iin the\nfrequency of the onsite eigenmode near !0. All error bars\n(shaded regions) are standard errors of the mean for about\n30 realizations of the disorder; the disorders \u000eUi,j\u000etijj, and\n\u000e!iare uniformly distributed, whereas \u000e\u000bis the half-width\nhalf-max of a Gaussian distribution.\nenergies near !0. Provided the strength of the inter-\nactions is weak compared to the ferrite-cavity coupling,\na projected qubit-mediated interaction Hamiltonian can\nbe used:He\u000b;I=1\n2P\niUi^ni0(^ni0\u00001) whereUiis the ef-\nfective photon-photon interaction for the photon number8\n^ni0of the unique mode near !0at sitei. We will work\nat a \fxed particle number relevant for both numerical\ncalculation and experiments where an exact number of\nphotons can be prepared.\nWe consider a \fnite-size geometry with N=Nx\u0002Ny\nlattice sites and toroidal boundary conditions, producing\na degenerate ground state manifold. Such boundary con-\nditions need not be a purely theoretical construct: They\ncould be implemented explicitly by either machining the\ncavities on a physical torus, or connecting the opposite\nboundaries with waveguides [36]. In order to maintain\na uniform e\u000bective \rux each plaquette must touch ex-\nactly one ferrite. This geometric restriction forces N=4\nto be an integer, and thus that the projected model has\nN\u001e=\u000bN=N=4 \rux quanta. For a system of \fxed\nparticle number Np, a FQH ground state is expected to\nemerge when the \flling factor \u0017=Np=N\u001eis expressible\nas a certain sequence of rational numbers. The most sta-\nble (largest many-body gap) \flling is desirable; this oc-\ncurs at a \flling \u0017= 1=2, which further restricts Np=N=8\nparticles (Ndivisible by eight). It is experimentally ad-\nvantageous to start with few photon states; we thus ex-\nplore small geometries with Nx= 4 andNp= 2;3;4 (and\nthereforeNy= 2Np); all numerical results presented be-\nlow are for Np= 3 andNy= 6. (Interestingly, this\ngeometry produces non-dispersive bands with Ny= 4,\nwhich are only weakly dispersive when Ny= 6;8 [37].)\nAs explored in previous works [3, 4, 37, 38], many prop-\nerties of the FQH are expected to survive in small few-\nparticle geometries. To demonstrate this for our system,\nwe start by exactly diagonalizing He\u000b;mbin the clean\nlimit withUi=U\u001dt. The geometries described above\nresult in a two-fold degeneracy (exact to numerical pre-\ncision) in the many-body ground state manifold (GSM),\nas expected for a \u0017= 1=2 Laughlin state [1, 28]. We\nlabel the states in the GSM as j\t1iandj\t2i; transla-\ntional invariance allows these states to be distinguished\nby their center-of-mass momentum [4]. It will be useful\nto impose twisted boundary condition: \t m(x+Nx;y) =\nei\rx\tm(x;y) and \tm(x;y+Ny) =ei\ry\tm(x;y) for all\neigenstates \t m(x;y), both in the GSM ( m= 1;2) and\nnot in the GSM ( m\u00153). The phases \rx\u0002\ryrepresent an\nAharanov-Bohm \rux \rx;y2[0;2\u0019) adiabatically inserted\nalong the ^x, ^yaxes of the torus (as could be implemented\nwith rf-modulated tunneling [19, 22].)\nFigure 5(a) shows the spectral \row of the lowest 30\neigenstates as a \rux quantum is simultaneously inserted\nalong both axes of the torus. Throughout this process\nthe GSM remains. (Here, we include disorder to visually\nsplit the two ground states; in the clean limit the GSM\nis degenerate to numerical accuracy for all \rux values.)\nFor each \rux \rwe de\fne the spectral gap to the \frst set\nof excited states:\n\u0001mb(\r) = min\nm=2GSMEm(\r)\u0000max\nm2GSMEm(\r);(2)\nand we \fnd that the spectral gap is approximately con-\nstant for all \rux \r= (\rx;\ry)2MBZ, where MBZ isthe many-body Brillouin zone. Since the GSM remains\ngapped through the full \rux insertion process, we can\nde\fne the many-body Chern number [39]:\nCm=1\n4\u0019\u0002\n\r2MBZd2\r[r\r\u0002h\tm(\r)jr\rj\tm(\r)i];\n(3)\nfor a statem2GSM. This Chern number will evaluate\nto an integer and give a quantized hall conductance. For\na clean system, both states in the GSM can be identi-\n\fed by their center-of-mass momentum and Cmcalcu-\nlated independently. In this case we \fnd they each carry\na fractionalized many-body Chern number of C= 1=2,\nconsistent with the thermodynamic limit. This result is\nalso consistent with prior numerical studies of FQH sys-\ntems, and an exact solution for a disorder-free \fnite-size\nHofstadter model [37].\nIn contrast, arbitrarily weak disorder will break trans-\nlational invariance and remove the degeneracy of the\nGSM. (This is a \fnite size e\u000bect, as the degeneracy re-\nmains in the thermodynamic limit.) The states in the\nGSM will remain gapped at all \rux values. The calcu-\nlation ofCmis then de\fned for the m-th energy level.\nWe numerically \fnd that with weak disorder, one state\nin the GSM randomly obtains C= 1, while the other\nhasC= 0, depending on the speci\fc disorder con\fgura-\ntion. As the disorder strength is increased, the spectral\ngap may shrink until the GSM and the \frst excited set\nof states are close enough to strongly mix. In this case,\nthe many-body Chern number may mix with the excited\nstate manifold and destroy the FQH state. (Note that\nlevel repulsion will prevent the gap from ever exactly van-\nishing.) In order to quantify the tolerance to disorder, we\nde\fne the minimum of the many-body gap as\n\u0001mb= min\n\r2MBZ\u0001mb(\r): (4)\nThis quantity will be used to study the stability of our\nscheme in the next section.\nA. Robustness to disorder\nIn any realistic implementation, disorder is present in\nvarious forms. We now study the in\ruence of spatial dis-\norder in (1) interaction strength, (2) tunneling energy,\n(3) \rux through each plaquette, and (4) onsite energy\nupon the interacting Hofstadter model described above.\nFor each disorder type we calculate the minimum many-\nbody gap, and then average over many disorder con\fg-\nurations. This disorder average many-body gap, \u0016\u0001mb,\nwill be used as a heuristic for the disorder tolerance of\nthe FQH state.\nWe expect the FQH state to be robust to disorder in\nthe interaction strength, provided that the average in-\nteraction strength is large compared to the tunneling\nenergy. In this blockaded limit, the two-photon wave-\nfunction overlap is small on any given site, resulting in9\nonly a small energy shift from interaction disorder. (This\nargument also applies to the continuum case where the\nLaughlin wavefunction has minimal overlap between pho-\ntons, and therefore quenches interaction energy.) This\nexpectation is con\frmed through exact diagonalization:\nThe stability of the many-body gap was calculated by\ntaking the smallest gap as a full 2 \u0019\rux was inserted\nthrough the twisted boundary conditions, as in Eq. (4).\nThis calculation was performed for a range of average\ninteraction strengths up to \u0016Ui\u001820t, with a disorder\nstrength\u000eUi=Ui\u0000\u0016Uuniformly distributed in the dif-\nferent ranges of\u0006\u0016U\u0002f1\n4;1\n2;3\n4;1g. The results are shown\nin Fig. 5(b) demonstrating that interaction disorder does\nnot signi\fcantly reduce the many-body gap. We further\nnumerically veri\fed that for all disorder con\fgurations\nthe many-body gap remained open throughout \rux in-\nsertion, and the total many-body Chern number in the\nground state manifold remained C= 1.\nIt is curious that even for the case of the strongest\ninteraction disorder (max ij\u000eUij=\u0016U) when certain lat-\ntice sites can be almost non-interacting, the topological\nstate survives with a many-body gap that does not seem\nto be limited by the smallest Uiin the system. In our\nsystem, we still expect only a small probability for the\noverlap of two photons, and therefore a robustness to\ncompletely removing some number of qubits. Removing\nqubits may provide additional \rexibility to the proposed\nexperimental realization of the interacting lattice, as the\nferrites require a large bias DC magnetic \feld that is\ndetrimental to the operation of superconducting qubits.\nWe therefore repeat the previous calculation, now with\ninteractions turned o\u000b entirely on all ferrite sites (see Fig.\n5(c)). We \fnd the topological ground state is preserved,\nalthough the disorder-averaged many-body gap \u0016\u0001mbis\nreduced by a factor of \u00184.\nFor interaction disorder we considered a wide distribu-\ntion which will realistically arise due to fabrication vari-\nations in qubits. By contrast, tunneling disorder will be\nsmall due to a combination of precision machining tech-\nniques and the quadratic insensitivity of the dark state\non ferrite sites. We still consider small to moderate dis-\norder in both amplitude ( j\u000etijj, uniformly distributed)\nand phase of the tunneling rates; the disorder in phase\ntranslates to a (Gaussian distribution) disordered \rux in\neach plaquette of \u000e\u000b. The resulting many-body gaps are\nplotted in Fig. 5(d)-(e) when the photon-photon inter-\nactions are assumed to be large. We \fnd the many-body\ngap decreases only linearly for both tunneling disorder\ntypes in this regime, suggesting that tunneling disorder\nwill not be a signi\fcant issue in experiment.\nThe system is more sensitive to onsite disorder which\nshifts the onsite mode frequency to !0!!0+\u000e!i. We\nexplore this physics in Fig. 5(f) by adding random onsite\n(uniformly distributed) disorder in the exact diagonal-\nization calculation. The situation is similar to previous\nresults for disordered (fermionic) FQH systems [40, 41]:\nThe total many-body Chern number of the ground state\nmanifold is probabilistically distributed between the low-est lying states for small disorder. At larger disorder a\ncollapse of a mobility gap results in a transition to an in-\nsulating state. We \fnd that for weak disorder, the many-\nbody gap persists, but declines roughly linearly in the\ndisorder strength. Using 3D microwave cavities, onsite\ndisorder is given by variations in the cavity resonances\ndetermined by the cavity dimensions and can precisely\ncontrolled with modern machining techniques. Addition-\nally, the onsite resonance can be made tunable, over a\nrange larger than the tunneling t, by e.g. using a tun-\ning screw or piezo stack to perturb critical dimensions of\nthe cavity [42]. Combined with tomography techniques\n[43, 44] which can map out a tight-binding Hamiltonian,\nonsite disorder can be characterized in the fully coupled\nlattice, and further reduced.\nIV. DISCUSSION\nWe have presented a scalable 3D microwave circuit ar-\nchitecture to explore bosonic FQH models of photons.\nCentral to this approach is a method for implementing\nthe necessary TRSB \rux of the single particle band struc-\nture: the onsite mode structure is used to induce this \rux,\nrather than the tunnel couplers themselves. Speci\fcally,\na ferrite is used to couple a degenerate cavity manifold,\nresulting in an isolated cavity eigenmode at frequency !0\nthat has uniform phase winding around the cavity periph-\nery. As a photon tunnels in and out, it will accumulate\nthe phase di\u000berence between the input and output tunnel\ncontact. This phase is a geometric (Berry's) phase, and\nwill contribute a nontrivial \rux to any connected plaque-\ntte. This allows for exploration of, e.g., an \u000b= 1=4 Hof-\nstadter model on a square lattice. The circuit elements\nare entirely passive, providing a distinct advantage from\ncompeting protocols that require driving of the tunnel\nmatrix elements.\nIn practice, 10GHz microwave resonators may be real-\nized with ferrite-time reversal breaking of order gF=\n400 MHz [45]; this allows a Hofstadter model band-\nwidth of 200 MHz for tunneling energy of J= 50 MHz,\nresonator-to-resonator disorder of order \u00181 MHz, and\nresonator linewidths of \u0014\u001820 Hz for superconducting\ncoaxial resonators [20], and \u0014\u001810 kHz in modest mag-\nnetic \felds. For standard transmon qubits, U= 350 MHz\nis readily achieved [46], providing a many-body gap of\norder (see above) of \u0001 mb\u00188 MHz , which is easily re-\nsolvable. Such states may be spectroscopically populated\n[47], and their average occupation of 1/8 per site veri\fed\nby site-resolved spectroscopy [17].\nThis lattice architecture then forms the basis for the\ninvestigation of topological many-body physics. E\u000bective\nphoton-photon interactions are implemented through the\naddition of superconducting qubits. Consistent with pre-\nvious works, we predict the emergence of a \u0017= 1=2\nbosonic FQH eigenstate, even at a large \rux per pla-\nquette of\u000b= 1=4. We further verify that this phase is\nrelatively robust to experimentally realistic disorder in10\nonsite energy, interactions, tunneling energy, and \rux in\na plaquette. In conjunction with state of the art propos-\nals to implement chemical potentials for photons [35, 48]\nthis work provides a complete roadmap to photonic frac-\ntional quantum hall physics, and a path to spectroscopic\ncreation and manipulation of anyons [49, 50].V. ACKNOWLEDGEMENTS\nThis work was supported by ARO grant W911NF-15-\n1-0397; D.S. acknowledges support from the David and\nLucile Packard Foundation; B.M.A. and R.M. acknowl-\nedge support from the UChicago MRSEC grant NSF-\nDMR-MRSEC 1420709; C.O. is supported by the NSF\nGRFP. The authors thank D. Angelakis, W. DeGottardi,\nM. Hafezi, and M. Levin, for helpful discussions.\n[1] H. L. Stormer, D. C. Tsui, and A. C. Gossard, Rev.\nMod. Phys. 71, S298 (1999).\n[2] A. Stern, Annals of Physics 323, 204 (2008), january\nSpecial Issue 2008.\n[3] E. J. Bergholtz and Z. Liu, International Journal of Mod-\nern Physics B , International Journal of Modern Physics\nB27, 1330017 (2013).\n[4] N. Regnault and B. A. Bernevig, Phys. Rev. X 1, 021014\n(2011).\n[5] M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro,\nB. Paredes, and I. Bloch, Phys. Rev. Lett. 111, 185301\n(2013).\n[6] H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Bur-\nton, and W. Ketterle, Phys. Rev. Lett. 111, 185302\n(2013).\n[7] N. Goldman, G. Juzeli\u0016 unas, P. Ohberg, and I. B. Spiel-\nman, Reports on Progress in Physics 77, 126401 (2014).\n[8] G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat,\nT. Uehlinger, D. Greif, and T. Esslinger, Nature 515,\n237 (2014).\n[9] N. Cooper, Advances in Physics 57, 539 (2008).\n[10] M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and\nI. Bloch, Nature 415, 39 (2002).\n[11] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys.\n80, 885 (2008).\n[12] J. Ningyuan, C. Owens, A. Sommer, D. Schuster, and\nJ. Simon, Phys. Rev. X 5, 021031 (2015).\n[13] Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic,\nNature 461, 772 (2009).\n[14] M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer,\nD. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Sza-\nmeit, Nature 496, 196 (2013).\n[15] HafeziM., MittalS., FanJ., MigdallA., and T. M., Nat\nPhoton 7, 1001 (2013).\n[16] P. J. J. O'Malley, R. Babbush, I. D. Kivlichan,\nJ. Romero, J. R. McClean, R. Barends, J. Kelly,\nP. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen,\nZ. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jef-\nfrey, A. Megrant, J. Y. Mutus, C. Neill, C. Quintana,\nD. Sank, A. Vainsencher, J. Wenner, T. C. White, P. V.\nCoveney, P. J. Love, H. Neven, A. Aspuru-Guzik, and\nJ. M. Martinis, ArXiv e-prints (2015), arXiv:1512.06860\n[quant-ph].\n[17] A. A. Houck, H. E. Tureci, and J. Koch, Nat Phys 8,\n292 (2012).\n[18] J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin,\nPhys. Rev. A 82, 043811 (2010).\n[19] K. Fang, Z. Yu, and S. Fan, Nat Photon 6, 782 (2012).[20] M. Reagor, H. Paik, G. Catelani, L. Sun, C. Ax-\nline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht,\nL. Frunzio, M. H. Devoret, L. Glazman, and\nR. J. Schoelkopf, Applied Physics Letters 102 (2013),\ndx.doi.org/10.1063/1.4807015.\n[21] J. Cho, D. G. Angelakis, and S. Bose, Phys. Rev. Lett.\n101, 246809 (2008).\n[22] L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and\nM. Lipson, Nat Photon 8, 701 (2014).\n[23] J. C. Maxwell, Philosophical Transactions of the Royal\nSociety of London 155, 459 (1865).\n[24] Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Ya-\nmazaki, K. Usami, and Y. Nakamura, ArXiv e-prints\n(2015), arXiv:1508.05290 [quant-ph].\n[25] M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan,\nM. Kostylev, and M. E. Tobar, Phys. Rev. Applied 2,\n054002 (2014).\n[26] K. Le Hur, L. Henriet, A. Petrescu, K. Plekhanov,\nG. Roux, and M. Schir\u0013 o, ArXiv e-prints (2015),\narXiv:1505.00167 [cond-mat.mes-hall].\n[27] M. Reagor, W. Pfa\u000b, C. Axline, R. W. Heeres,\nN. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumo\u000b,\nK. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret,\nL. Jiang, and R. J. Schoelkopf, ArXiv e-prints (2015),\narXiv:1508.05882 [quant-ph].\n[28] M. Hafezi, A. S. S\u001crensen, E. Demler, and M. D. Lukin,\nPhys. Rev. A 76, 023613 (2007).\n[29] D. Pozar, Microwave Engineering, 4th Edition (Wiley,\n2011).\n[30] M. Scully and M. Zubairy, Quantum Optics (Cambridge\nUniversity Press, 1997).\n[31] J. Ruseckas, G. Juzeli\u0016 unas, P. Ohberg, and M. Fleis-\nchhauer, Phys. Rev. Lett. 95, 010404 (2005).\n[32] T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys.\nRev. Lett. 106, 236804 (2011).\n[33] W. P. Su, J. R. Schrie\u000ber, and A. J. Heeger, Phys. Rev.\nLett. 42, 1698 (1979).\n[34] A. Wallra\u000b, D. I. Schuster, A. Blais, L. Frunzio, R. S.\nHuang, J. Majer, S. Kumar, S. M. Girvin, and R. J.\nSchoelkopf, Nature 431, 162 (2004).\n[35] M. Hafezi, P. Adhikari, and J. Taylor, Physical Review\nB92, 174305 (2015).\n[36] J. Ningyuan, C. Owens, A. Sommer, D. Schuster, and\nJ. Simon, Physical Review X 5, 021031 (2015).\n[37] T. Sca\u000edi and S. H. Simon, Phys. Rev. B 90, 115132\n(2014).\n[38] E. Kapit, P. Ginsparg, and E. Mueller, Phys. Rev. Lett.\n108, 066802 (2012).11\n[39] Q. Niu, D. J. Thouless, and Y.-S. Wu, Phys. Rev. B 31,\n3372 (1985).\n[40] D. N. Sheng, X. Wan, E. H. Rezayi, K. Yang, R. N.\nBhatt, and F. D. M. Haldane, Phys. Rev. Lett. 90,\n256802 (2003).\n[41] X. Wan, D. N. Sheng, E. H. Rezayi, K. Yang, R. N.\nBhatt, and F. D. M. Haldane, Phys. Rev. B 72, 075325\n(2005).\n[42] G. Matthaei, L. Young, and E. Jones, Microwave \flters,\nimpedance-matching networks, and coupling structures ,\nArtech House microwave library No. v. 1 (McGraw-Hill,\n1964).\n[43] D. Burgarth, K. Maruyama, and F. Nori, New Journal\nof Physics 13, 013019 (2011).\n[44] R. Ma, J. C. Owens, A. LaChapelle, J. Simon, and\nD. Schuster, \\Hamiltonian tomography of photonic lat-\ntices,\" In Preparation.\n[45] N. Kostylev, M. Goryachev, and M. E. To-\nbar, Applied Physics Letters 108, 062402 (2016),\ndx.doi.org/10.1063/1.4941730.\n[46] H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair,\nG. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor,\nL. Frunzio, L. I. Glazman, S. M. Girvin, M. H. De-\nvoret, and R. J. Schoelkopf, Phys. Rev. Lett. 107, 240501\n(2011).\n[47] P. Schausz, M. Cheneau, M. Endres, T. Fukuhara,\nS. Hild, A. Omran, T. Pohl, C. Gross, S. Kuhr, and\nI. Bloch, Nature 491, 87 (2012).\n[48] M. Hafezi, M. D. Lukin, and J. M. Taylor, New Journal\nof Physics 15, 063001 (2013).\n[49] B. Paredes, P. Fedichev, J. I. Cirac, and P. Zoller, Phys.\nRev. Lett. 87, 010402 (2001).\n[50] R. Umucalilar and I. Carusotto, Physics Letters A 377,\n2074 (2013)."    },    {        "title": "1705.06240v2.High_voltage_charging_system_for_pulsed_power_generators.pdf",        "content": "High voltage charging system for pulsed power generators \n \nM. Evans, B. Foy,  D. Ma ger, R. Shapovalov  and P. -A. Gourdain1 \n \n1Department of Physics and Astronomy, University of Roche ster, Rochester, New York, 14627 , USA  \nA robust and portable power supply  has been developed specifically for charging linear transformer drivers, a modern \nincarnation of fast pulsed power generators.  It is capable of generator +100 kV and -100 kV at 1 mA , while \nwithstanding the large voltage spikes generated when the pulsed -power generator is triggered. The three -stage design \ncombines a zero -voltage switching circuit, a step -up transformer using ferrite cores, and a dual Cockcroft -Walton \nvoltage mu ltiplier . The zero -voltage switching  circuit drives the primary of the transformer in parallel with a capacitor.  \nWith this driver, the tank circuit naturally  remain in  its resonant state, allowing for maximum energy coupling between \nthe zero -voltage switching circ uit and the Cockcroft -Walton voltage multiplier across a wide range of loading \nconditions.  \nI. Introduction:  \nThe High Amperage Driver for Extreme S tates (HADES) 1, will use 1 MA of current to heat and compress \nmillimeter -scale material samples. HADES i s composed of six linear transformer drivers (LTD)  that charge in parallel \nand fire in series to deliver more current than a single LTD.  Each LTD is a 2-meter diameter  casing where 22 high \nvoltage capacitor pairs and 22 spark gap switches2 are arranged symmetrically around a central electrode stack.  The \nspark gap switches are triggered accordingly to a predefined sequence to form the desired current pulse.  This \ntechnology has been proposed in high voltage pulsed accelerators3, Z-pinch drivers4, and compr ession experiments.   \nThe present paper shows a new high voltage supply design that combines a Cockcroft -Walton5 voltage \nmultiplier , which generates hig h voltage DC from  a low voltage DC  source,  using  a step -up transformer, which \ngenerates an AC voltage high enough to limit the number of stages of the voltage multiplier , and a ZVS driver6, which \ngenerates an AC source from a DC supply.  The design presented here has several advantages over existing high  voltage \npower systems. First, the symmetric topology of the voltage multiplier generates  positive and negative high DC \nvoltages without any additional components compared to  a single power supply . Second, the ZVS always drives the \nprimary inductor of the step-up transformer at resonance. The voltage reversal on the inductor switches the gates of \ntransistors inside the ZVS, making it a self -driven circuit. The resonant frequency was chosen to be on the order of 10 \nkHz, the frequency of our ferrite cores, by  adding a capacitor in parallel wi th the inductor. The self -driven  nature of \nthe circuit allows the ZVS to track changes in the resonant frequency, caused by the transformer loading and non -linearities inherent to the ferrite cores. Finally, the input DC v oltage is boosted by the resonant ZVS circuit, allowing \nthe use of benchtop DC supplies to power the whole system.  For a high frequency system  like ours any VAC variations \nare noticeable across the transformer cores , the input would need to be rectified an d regulated to avoid fluctuations.  \nBenchtop  DC power supplies already perform this function.  In this manuscript, we report on the basic design, \nconstruction and characterization of this system and how it is used to charge the capacitors of a 1 GW pulsed -power \nsystem. Minor improvements, like voltage or current regulation of the power su pply, have been discussed in other \nliterature and are not report ed here.  \nII. Principle of operation  \n \nFigure 1: Circuit schematic  of dual high -voltage and frequency charging system  \nFigure 1 shows the circuit schematic  of the dual voltage power supply  together with the peak voltage in the \ndifferent stages of the power supply. In the  first stage of the system , the ZVS driver generates  a high frequency AC \nvoltage from a low voltage DC sourc e. The ZVS operates between 12 to  40 DC input voltage, which allows for control \nof the final output voltage . The ZVS outputs  a 240 VAC peak -to-peak (pk -pk) at 40 Amps which is coupled  to the \nstep-up transformer. It is essential to have a high coupling factor to operate at low power.  The 10-kHz transformer , \nwith a ferrite core , has a 1:250 winding ratio between primary and secondary, r aising the voltage t o a maximum of  60 \nkV AC pk-pk. The frequency is constrained by the ferrite which operates  in a 5 to 20kHz frequency range.  The \ntransformer also adds a layer of electrical insulation between the high and low voltage sides of the supply , and has a \ndesign current limit1 of 10 mA . The AC output is then fe d into the  dual voltage multiplier  to produce ±100 kV DC.  \nWhile coupling a transformer to a voltage multiplier is common practice in high voltage supplies, the novel \nidea presented in this paper is using the ZVS to always drive the  transf ormer at resonance, under a variety of load \nconditions . When the primary coil is driven at resonance the magnetic field of the primary is in phase with magnetic \nfield of the secondary winding . A strongly  coupled  system generates the maximum voltage on the secondary coil due \nto the increase of the mutual flux, reducing resistive losses on the primary coil and heat generation.7 An efficient \nsystem will have a high coupling coeffi cient and less flux leakage .   \n \nIII. Topology and Spice simulation:  \n In the first stage , the ZVS driver  converts DC into  high frequency AC.  A ZVS driver uses two MOSFET s \nthat switch voltage  between them  with minimal loss from O hmic heating . The schematic of a  classical  ZVS circuit is \ndisplayed in figure 2.  \n \n \nFigure 2: Schematic of ZVS driver  \nThe principle of a ZVS works by  exploiting the differences  in physical  electronic components  of the same \ntype and an LC  oscillator6. When power is applied both MOSFETs see voltage on their gates and the MOSFETs begin \nto turn on. In an ideal circuit both MOSFETs would turn on at the exact same time and there would be no oscillation; \nhowever, because no two components are exactly alike , one MOSFET begins to turn on faster than the other. The \ncurrent between gates is no longer identical and the secon d MOSFET begins to turn off. A  capacitor couple s to the \ntransformer coil, forming  an LC circuit, which then oscillates as the MOSFETs successiv ely turn on and off.  \n \nFigure 3: ZVS operating principle .  \nFigure 3 illustrates the voltage at each MOSFET gate and the AC output waveforms. As the voltage across  \nMOSFET 1 begins  to drop, the voltage rises on MOSFET 2. The resulting oscillation can be seen across the secondary \ncoils as an AC voltage. The driver switches between gates  exactly when the voltage across a MOSFET is zero which \nis why it is called zero -voltage switching. This is the time at which the MOSFET is carrying the least amount of power \neliminating the need for large heat sinks.  \n In the second stage,  the step-up transformer  supplies a high voltage  to the dual  voltage multiplier a s well as  \nproviding  isolation between the high and low  voltage  sides . A high turn ratio is required to increase the voltage in the \nsecondary, however to keep the high voltage transformer compact we split the secondary windings between two sides \nof the ferrite .  \nIn the  third stage, a  dual voltage multiplier converts AC  into high voltage  DC via a ladder network of \ncapacitors and diodes. Each “stage” consists of two capacitors and two corresponding diodes . The diodes rectify the \nAC voltage on each side of the ladder  and allow the capacitors to charge in parallel and disch arge in series . The \ncapacitor s block the DC bias from the stage directly below it , allowing each stage to be at a  higher potential.  The \nvoltage multiplier is a common design for generating high voltages at low currents and low costs. However, the system \nhas a high internal impedance which makes it less attractive for high voltages, high  current applications, where \ntransformers are typically required. A schematic diagram of the dual voltage multiplier is shown in figure 4.  \n \nFigure 4: Schematic of dual voltage multiplier  \n Our design u tilizes a four -stage dual  voltage multiplier to produce a ±100 kV  potential difference . The AC \nsignal  from the step -up transformer  passes through the ladder network until it reaches ±100 kV. The higher the \nfrequency the bett er the voltage  amplification  however the frequency is limited by the impedance of the transformer \nand the coupling to the ferrite circuit. The circuit along with the step -up transformer was simulated  with the circuit \nanalysis tool PSpice8. The ZVS circuit was replaced with a VAC signal in this simulation. The AC s ignal input was  a \nsine wave of 20 0V pk-pk at 10 kHz.  The simulation assumes ideal circuit elements. The transforme r inductance was \nchosen based upon  the ferrite  material and calculated to be 10.13  µH. The output voltage with no load is illustrated \nbelow in figure 5.  \n \nFigure 5: PSpice Simulation: Voltage vs time plot of a dual voltage multiplier charging  system  \nThe PSpice  results of the  voltage multiplier show  the v oltage slowly ramping up to max  voltage . The circu it \nreaches a maximum of 11 0 kV measured at each end. The dual voltage multiplier h as a charging time of roughly 30 0 \nms.  \nIV. Design Considerations and Construction:  \n  With the  exception  of the ZVS, the charging system  was constructed from simple components  and displayed \nin figure 6 , an extra capacitor is added to  construct an interlocking pattern  that reduces the distance between the two \nbranches. The extra capacitor is grounded .  \n \nFigure 6: Assembled form . (Step -up transformer and dual  voltage multiplier.)  \n The transformer consists of the primary and secondary windings, copper coated steel welding rod split rings, \nPyrex glass tubing, the ferrite material, and Buna -N O-rings. The core shape allows for the primary and two secondary \nseries windings on the same core. The Pyrex glass tubing, 5.08 cm  diameter and 58.7 cm  in length, provides the \nhousing for the ferrite and the support for the secondary windings. Buna -N O-rings ( #319 ) are placed between the \nferrite and the Py rex tube to  prevent movement and center the ferrite inside the tube . The primary winding is a 12 \nAWG 6 0kV electrical wire  (#2024  from Dielectric Sciences Inc .) at 4 turns. The secondary windings are made of  two \ncores of  30 AWG copper magnetic wire at 500 turns  connected in series  to give 1000 turns . The copper coated rings \nare used as  a mechanical  stress relief and  connect the secondary windings to the voltage multiplier. The MnZn UY32 \nferrite9 has an inductance factor of 5200 nH/N2. It is desi gned to operate between 5 and 20  kHz. Our transformer \ndesign required the core to be 24.6 cm  by 9.20  cm. The ferrite blocks were cut and reassembled to meet these  \ndimensions .  \n The dual  voltage multiplier was assembled using interconnected  brass studs. To construct the positive and \nnegative stages, we use sixteen 2700 pF (30 kV  max)  ceramic Z5T disk capacitors. The capacitors  are complemented \nby sixteen  diodes, (30 kV  max and  200 mA ), attached diagonally  between their respective capacitors.  The voltage \nmultiplier is configured so the positive output is at one end and the negativ e output is at the opposite end, r educing \nthe chance of arcing between output terminals. 150 kV 10 AWG insulation wire  (#2121A Dielectric Sciences Inc. ) is \nattached t o each terminal output. The transformer and voltage multiplier are combined in a support structure made of \nG10 and two fiberglass rods. This provides the system with structural  stabil ity when placed in a PVC housing . The \ncylinder is then filled with STO -50 silicon transformer oil10. The transformer oil acts as an insulator and coolant for \nthe ferrite core when operated in steady state. Transformer oil was chosen over epoxy for easier access to parts for \nmaintenance.  The total weig ht of the power supply is c lose to 100 lbs when filled with transformer oil.  \nV. Results:  \n We measured the ZVS output both unloaded and then  loaded with the step -up transformer  and voltage \nmultiplier . Unloaded the ZVS circuit produces a maximum of 240 V AC pk -pk signal at 15 kHz  at 40 V DC input . The \npower supply loaded with the brick test station produces 200 VAC pk -pk at a frequency of 10 kHz.  \nThe power supply  output voltage is measured using two identical  voltage divider s of 1 G Ω and 1 k Ω, into a \nSIGLENT SHS800 digital oscilloscope with bandwidth of 150 M Hz and sampling rate of 1 GSa/s . The maximum \nvoltage from each voltage output was ±10 0 kV . The current of t he system is determined by  creating a multi -loop \ncircuit and applying  Kirchhoff’s current law . A 100 M Ω resistor is connected between the positive and negative \noutputs where i t creates another current  path.  The potential difference over a  100 M Ω resistor  was 200 kV , producing \n2 mA of current at an output power of 400 Watts. The DC input to the  ZVS was  23 V and 36 A produ cing 828  Watts , \nresulting in an efficiency of 48%.   \nTo measure the charging time and loaded voltage we construct a brick t esting station shown in figure 7 , along \nwith its circuit schematic. The bric k testing station consists of 2x  high vol tage 47 nF capacitors, a spark gap switch, a \nshunt resis tor, 2x 1 GΩ resistors, and 2x  250 M Ω charging resistors.  One capacitor is charged to +90  kV, wh ile the \nother is charged to -90 kV. The spark gap is attached between the capacitors for a total potential difference of 18 0 kV . The spark gap switch was  pressurized  with synthetic  air. The spark gap switch is self -triggered in this configuration . \nThe brick testing station is placed in STO -50 silicon oil to prevent arcing. To measure the voltage on ea ch capacitor a \n1 GΩ voltage monitor  is connected to each electrode.  \n \nFigure 7 : Brick t esting station . (a) P hoto of brick testing station.  Charging resistors are outlined in white boxes.  (b) circuit \nschematic  \n The charging resistors are ma de of TIVAR  Cleanstat11, a conducting plastic, with a  square cross -section of 1 \ncm and length of  30 cm. The high resistive plastic , with resistivity  7.2 GΩ*cm, is used in the packaging industry to \ndissipate electrostatic ch arge build up on conveyor belts.  Since the spark gap are self -breaking , the charging resistors \nare used to slow down t he triggering rate of the brick  by throttling the charge of the capacitor . The 1 GΩ voltage \nmonitors are constructed by connecting four 250 MΩ  resistors  in series. A plot of the chargi ng voltage across the \npositive load capa citor is illustrated in figure 8 .  \n \nFigure 8  Load Capacitor: Voltage vs time  \n \n As seen  in figure 8  the total charging time of our system was  roughly 26  seconds . The max voltage at each \ncapacitor was ±90 kV  at the time of switch breakdown . The spark gap  switch  was self-triggered by controlling the \npressure of dry air between electrodes . At ±90 kV across the capacitors the pressure needed to prevent premature \nbreakdown is 120 psi. Once the capacitor s are fully charged , breakdown occu rs and generates a back electromagnetic \npulse (EMP). The large back EMP caused by the spark gap would require many commercial power supplies t o be \ndisconnected before the breakdown . Or at least they would require additional  protection sin ce they are usually based \non step -up transformer only . However, the proposed power supply can withstand this back EMP, since the voltage \nmultiplier acts as a low impedance , 188 Ω, short to  ground for such pulses. The power supply an d spark gap switch \nwas tested in repetition for reliance and robustness over a thousand times.  \n  \nVI. Conclusion:  \n A dual high voltage and high frequency charging system was designed and construct ed at the eXtreme S tate \nPhysics  Laboratory at the University  of Rochester. The design is a combina tion of three separate systems, a ZVS \ncircuit that supplies high frequency  AC power at resonance, a step -up transformer to increase voltage and dual voltage \nmultiplier to convert medium voltage AC to high voltage DC, w hile protecting the transformer from back EMP. The \nchargi ng system provides ± 10 0 kV at 2  mA for 400 Watts of power  to a 100 M Ω resistor . The self-tuning  ZVS \ncoupled with the high frequency transformer results in fast charge time  for various load conditions . The power supply \ncharges the brick test station  within 26  seconds to voltage of ±90 kV before electrical breakdown. It is c apable of \nfiring thousands of shots through a spark gap switch without failure , making it a reliab le system for future pulsed \npower experiments.   \nAcknowledgments  \nThis work is supported by the Laboratory of Laser Energetics’ Horton Fellowship and  the U.S. Department \nof Energy’s National Nuclear Security Administration under  Award Number  DE-SC0016252.  \n1P-A. Gourdain, HADES: a High Amperage Driver for Extreme States. arXiv:1705.04411  \n2W.A. Stygar, et al., Conceptual designs of two petawatt -class pulsed -power accelerators for high -energy -\ndensity -physics experiments.  Phys. Rev. ST Accel. Beams 18, 110401. 2015 . \n3Mazarakis, M.G., et al., High current, 0.5 -MA, fast, 100 -ns, linear transformer driver experiments.  Phys. Rev. \nST Accel. Beams 12, 050401. 2009.  \n4Mazarakis, M.G., et al., High current linear transformer driver development at Sandia National Laborato ries. \nIEEE Transactions on Plasma Science,Vol. 38, 2010.  \n5E. Everhart and P. Lorrain,  The Cockcroft -Walton voltage multiplying circuit , Rev. Sci. Instru. 24(3)  221 \n(1953).  \n6B. Andreycak, Zero Voltage Switching Resonant Power Conversion , Texas Instruments, 1999.  \n7J. Liu,  L. Sheng, J. Shi, Z. Zhang, and X. He ., IEEE Proceedings of the Twenty -Fourth Annual Applied Power \nElectronics Conference and Exposition, Washington DC., February 2009 (IEEE, 2009), pp.1034 -1038 . \n8http://www.candence.com/Community/CSSharedFiles/forums/storage/27/1306667/demoswitch.pdf  \n9http://www.transformer -assn.org/Standard%20Spec%20for%20Ferrite%20U%20E%20I%20Cores.pdf  \n10http://www.clearcoproducts.com/pdf/dielectric -fluids/MSDS -STO -50-Silicone -TransformerOil.pdf  \n11http://www.quadrantplastics.com/fileadmin/quadrant/documents/QEPP/EU/Product_Data_Sheets_PDF/PE/TI\nVAR_CleanStat_white_PDS_E_07052013.pdf  \n \n \n "    },    {        "title": "1502.06041v1.On_chip_superconducting_microwave_circulator_from_synthetic_rotation.pdf",        "content": "On-chip superconducting microwave circulator from synthetic rotation\nJoseph Kerckhoff,1,\u0003Kevin Lalumière,2Benjamin J. Chapman,1Alexandre Blais,2, 3and K. W. Lehnert1, 4\n1JILA, University of Colorado, Boulder, Colorado 80309, USA\n2Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1\n3Canadian Institute for Advanced Research, Toronto, Canada\n4National Institute of Standards and Technology, Boulder, Colorado 80305, USA\n(Dated: August 24, 2018)\nWe analyze the design of a potential replacement technology for the commercial ferrite circulators that\nare ubiquitous in contemporary quantum superconducting microwave experiments. The lossless, lumped\nelement design is capable of being integrated on chip with other superconducting microwave devices, thus\ncircumventing the many performance-limiting aspects of ferrite circulators. The design is based on the dy-\nnamic modulation of DC superconducting microwave quantum interference devices (SQUIDs) that func-\ntion as nearly linear, tunable inductors. The connection to familiar ferrite-based circulators is a simple\nframe boost in the internal dynamics’ equation of motion. In addition to the general, schematic analysis,\nwe also give an overview of many considerations necessary to achieve a practical design with a tunable cen-\nter frequency in the 4-8 GHz frequency band, a bandwidth of 240 MHz, reflections at the -20 dB level, and a\nmaximum signal power of approximately order 100 microwave photons per inverse bandwidth.\nI. INTRODUCTION\nWith the advent of quantum information processing with\nsuperconducting circuits [1], the ability to route microwave\nsignals without loss or added noise has become critically\nimportant. In particular, the operation of a digital super-\nconducting quantum computer will require numerous ana-\nlog functions, such as signal amplification, feedback, and\ntransduction. Moreover, it is likely that a future quan-\ntum information processor will employ coherent exchange\nof microwave fields among various modular components.\nPreserving quantum information in these propagating mi-\ncrowave fields demands nearly losses and noiseless compo-\nnents.\nAlthough most passive microwave components can be\nreadily fabricated with low-loss superconducting metals\nand integrated with other superconducting circuits, this is\nnot true for non-reciprocal components such as isolators,\ncirculators, and gyrators. Existing technology uses ferri-\nmagnetic materials in intense ( \u00180.1 T) magnetic fields to\ncreate the non-reciprocal behavior required to ensure the\none-way flow of information within the network [2–4]. Such\nmagnetic devices would be quite difficult to integrate with\nsuperconducting circuits, which are disrupted by magnetic\nfields of 0.1 mT or less. Currently, the non-reciprocal el-\nements in quantum information processing networks are\ncommercially available devices connected to the rest of the\nnetwork using meter length coaxial cables. Even if this cum-\nbersome arrangement were tolerable, the loss associated\nwith the transition from planar circuits to coaxial cables and\nthat associated with the ferrimagnetic elements themselves\nis unacceptably large [5–8].\nInstead of achieving non-reciprocity through the use of\nmagnetic materials, one can instead use time-dependent\n\u0003Electronic address: jakerckhoff@hrl.com; Current address: HRL Labora-\ntories, LLC, Malibu, CA 90265, USAreactive elements. Long known as a general method for\ncreating non-reciprocal devices [10–12 ], time varying reac-\ntances have not had much technological impact because\nferrite elements [2]or active transistor [13]devices provide\na less complex source of non-reciprocity for conventional\nelectronics. But with the emergence of superconducting cir-\ncuit based quantum information processing, the idea of cre-\nating non-reciprocal response through time varying reac-\ntances has returned to prominence [14–17 ]because of the\nproblems with ferrite devices and the practical absence of\ntransistor technologies with quantum-limited noise perfor-\nmance [9].\nConveniently, a standard superconducting circuit ele-\nment, the Josephson junction, can be operated as a time-\nvariable reactance. Although the inductance of a Josephson\njunction is intrinsically non-linear, the inductance experi-\nenced by a small electrical signal is effectively linear, loss-\nless, and may be varied by also applying a larger “pump”\ncurrent through the junction [18]. A new type of supercon-\nducting non-reciprocal device exploits this effect, in which\nseveral oscillatory pump tones modulate the inductance\nand therefore the frequency response of several resonant\ncircuits in a cyclic manner [14, 16, 17 ]. Other novel ap-\nproaches to nonreciprocal circuits for superconducting net-\nworks that don’t rely on time-variable reactances are also ac-\ntive areas of research [19, 20 ].\nIn any scheme based on time-variable reactances, it is\nimportant that the pump tones themselves do not inter-\nfere with the operation of other devices in the network [17].\nFurthermore the non-reciprocal device should not mod-\nulate the incoming signal to create sidebands that leave\nthe device. And ideally, large signals should be processed\nlinearly, despite the components’ fundamental nonlinear-\nities. To these ends, we introduce another concept for a\nnon-reciprocal element, a four-port circulator that operates\nby only modulating the coupling rate of four itinerant mi-\ncrowave modes to two resonant circuits in a cyclic manner.\nThis four-port circulator can also be wired as a two-port gy-\nrator [21], and although not explored here, can thus also bearXiv:1502.06041v1  [quant-ph]  21 Feb 20152\nwired as a three-port circulator [2, 20, 22 ]. The symmetry of\nthe circuit ensures that sidebands generated by the dynamic\ncoupling are completely “erased” as they leave the device. In\naddition, the modulating pump tones do not co-propagate\nwith the signal tones and oscillate at a frequency at least a\nfactor of ten less than the signal frequency, and can there-\nfore be easily filtered out of the signal path between devices\noperating at the signal frequency. Finally, the Josephson\njunction elements are arranged into series arrays of junc-\ntions [23], an arrangement that retains the variable induc-\ntance but dilutes the non-linearity to approximate a linear\ntime-variable inductor.\nIn this article, we first analyze the general equations\nof motion of a four port circulator created through time-\ndependent coupling between the ports and the internal res-\nonant modes. We show that this concept is closely analo-\ngous to four-port ferrite circulators (where our time-varying\nreactances create a synthetic magnetic field [15]) and we use\na waveguide ferrite circulator [3]as a pedagogical touch-\nstone. We then introduce and analyze a circuit that re-\nalizes the desired circulator equations of motion. This\nnon-reciprocal circuit uses a modular design comprising\nfour identical subcircuits. These subcircuits are themselves\ncomposed of four tunable inductors arranged in a Wheat-\nstone bridge configuration [11, 24 ], where the tunable in-\nductors are created from flux tunable SQUID arrays. In the\nfinal section, we analyze SQUID arrays and how they form\nflux tunable inductors.\nII. PHENOMENOLOGICAL DESCRIPTION\nOur circulator approach is conceptually related to four-\nport ferrite turnstile circulators [3, 4]. Originally developed\nin the 1950s, these microwave circulators consist of a junc-\ntion of four rectangular waveguides coupled to a cylindrical\nresonator [25], Fig. 1a. As is typical of most practical circu-lators, turnstile circulators are rotationally symmetric and\npreserve the carrier frequencies of signals [4]. Nonreciproc-\nity comes from a ferrite Faraday rotator in the resonator\nthat rotates the polarization of signals in the cylinder. For a\nproperly chosen cylinder length and rotation rate, the junc-\ntion acts as a four port circulator with a finite bandwidth.\nThat is, when matched loads are placed on the four wave\nguide ports, microwave signals within the circulator band-\nwidth are scattered by the junction according to the scatter-\ning matrix\n2\n6664b1,out(t)\nb2,out(t)\nb3,out(t)\nb4,out(t)3\n7775=2\n66640 0 0 1\n1 0 0 0\n0 1 0 0\n0 0 1 03\n77752\n6664b1,in(t)\nb2,in(t)\nb3,in(t)\nb4,in(t)3\n7775(1)\nwhere bi,in(t)and bi,out(t)are, respectively, the complex en-\nvelopes of a traveling wave incident on and scattered by the\njunction at port i.\nThe circulator’s operation is quite modular. If there were\nno coupling between the resonator and the waveguides, the\nscattering between the waveguide ports would be reciprocal\n2\n6664b1,out(t)\nb2,out(t)\nb3,out(t)\nb4,out(t)3\n7775=1\n22\n6664\u00001 1 1 1\n1\u00001 1 1\n1 1\u00001 1\n1 1 1\u000013\n77752\n6664b1,in(t)\nb2,in(t)\nb3,in(t)\nb4,in(t)3\n7775(2)\nwith a relatively large bandwidth. This scattering matrix\nsimply corresponds to the signal transfer between an input\nsource driving three loads in parallel, each with the same\nimpedance as the source [25]. As described in more detail\nin section III, when the resonator is coupled to the waveg-\nuides, the equation of motion for the input, output, and the\ntwo resonant polarization mode envelopes (assuming a sig-\nnal frequency at the resonator center frequency) is approxi-\nmately [9, 27–29 ]\n2\n6666666666664d\nd tax(t)\nd\nd tay(t)\nb1,out(t)\nb2,out(t)\nb3,out(t)\nb4,out(t)3\n7777777777775=2\n6666666666664\u0000\u0014\n2\u0000\np\u0014\n20\u0000p\u0014\n20\n\n\u0000\u0014\n20p\u0014\n20\u0000p\u0014\n2p\u0014\n20\u00001\n21\n21\n21\n2\n0p\u0014\n21\n2\u00001\n21\n21\n2\n\u0000p\u0014\n201\n21\n2\u00001\n21\n2\n0\u0000p\u0014\n21\n21\n21\n2\u00001\n23\n77777777777752\n6666666666664ax(t)\nay(t)\nb1,in(t)\nb2,in(t)\nb3,in(t)\nb4,in(t)3\n7777777777775(3)\nwhere ax,yare the complex envelopes of the resonant polar-\nization modes (with units of (photon number)1=2),\u0014is the\ntotal energy decay rate of a resonator mode into the termi-\nnated waveguides, and \nis the rate of polarization mixing\ndue to the Faraday rotator. Thus, the output signals, bi,out(t)(with units of (photon number /sec)1=2), are a linear com-\nbination of “prompt” scattering from the input signals (as\ndetermined by the lower right matrix block in Eq. (3)) and\nthe resonant modes (lower left matrix block). The resonant\nmodes are governed by inhomogeneous, first order ordinary3\n23 4\n1y xFaraday\nrotatora)\ncap\nattached\nb)\nc)\nSpinning\nresonator\nFIG. 1: a) Schematic of a four-port ferrite turnstile circulator [3, 4]. Arrows represent the electric field polarization of the four waveguide\nand two resonator modes. The electric fields of ports 1 & 3 couple directly to resonator mode x (blue arrows), and the electric fields of\nports 2 & 4 couple directly to resonator mode y (red arrows). b) Depiction of the circulator’s steady state operation: a traveling wave\nsignal incident through waveguide port 1 induces a steady state response in the resonator modes that is rotated by angle  relative to\nthe x-mode. When  =\u0019=4, all of the incident power is emitted out port 2. c) Concept of an alternate realization, based on Eq. (5). The\nferrite Faraday rotator is now removed and reciprocity is now broken by the resonant cylinder mechanically rotating at rate \nrelative to\nthe waveguide junction.\ndifferential equations, determined by the modes’ “internal\ndynamics” (upper left matrix block), and driving from the\ninput signals (upper right matrix block). Note that in the\nabsence of the rotator, \n= 0, the x- and y-polarized res-\nonator modes couple only to waveguides 1 & 3, and 2 & 4,\nrespectively. Thus, orthogonal waveguides (e.g. waveguides\n1 and 2) couple only through the prompt scattering. With\nthe rotator present, excitations are “rotated” between the\npolarization modes, coupling all four waveguides through\nthe resonator as well as through prompt scattering.\nEq. (3) can be solved for the steady state response of the\nresonator modes to input signals. Doing so, one finds that\nthe polarization of the steady state excitation in the res-\nonator is rotated by an angle  =atan(2\n=\u0014), Fig. 1b. When\n =\u0019=4, this steady state excitation couples back to each\nwaveguide with equal magnitude. However, the promptscattering and resonator-mediated paths carrying signals\nfromf1!2, 2!3, 3!4, 4!1ginterfere constructively,\nwhile all other signal path interferences are completely de-\nstructive. Thus, one finds that driving the junction on the\ncavity’s resonance, in steady state, and for  =\u0019=4, the scat-\ntering between inputs and outputs becomes exactly Eq. (1).\nHowever, manipulations of Eq. (3) suggest alternative\nways of realizing the same input-output dynamics. For ex-\nample, we can rewrite these dynamics in terms of a rotating\nbasis of the resonator modes\n\u0014\naq(t)\nap(t)\u0015\n=\u0014\ncos(\nt)sin(\nt)\n\u0000sin(\nt)cos(\nt)\u0015\u0014\nax(t)\nay(t)\u0015\n(4)\nin which case Eq. (3) becomes\n2\n6666666666664d\nd taq(t)\nd\nd tap(t)\nb1,ou t(t)\nb2,ou t(t)\nb3,ou t(t)\nb4,ou t(t)3\n7777777777775=2\n6666666666664\u0000\u0014\n20p\u0014\n2cos(\nt)p\u0014\n2sin(\nt)\u0000p\u0014\n2cos(\nt)\u0000p\u0014\n2sin(\nt)\n0\u0000\u0014\n2\u0000p\u0014\n2sin(\nt)p\u0014\n2cos(\nt)p\u0014\n2sin(\nt)\u0000p\u0014\n2cos(\nt)\np\u0014\n2cos(\nt)\u0000p\u0014\n2sin(\nt)\u00001\n21\n21\n21\n2p\u0014\n2sin(\nt)p\u0014\n2cos(\nt)1\n2\u00001\n21\n21\n2\n\u0000p\u0014\n2cos(\nt)p\u0014\n2sin(\nt)1\n21\n2\u00001\n21\n2\n\u0000p\u0014\n2sin(\nt)\u0000p\u0014\n2cos(\nt)1\n21\n21\n2\u00001\n23\n77777777777752\n6666666666664aq(t)\nap(t)\nb1,i n(t)\nb2,i n(t)\nb3,i n(t)\nb4,i n(t)3\n7777777777775. (5)\nInspection of Eq. (5) suggests an alternate (albeit impracti-\ncal) realization of a turnstile circulator. The Faraday rota-\ntor dynamics are absent (i.e. no explicit polarization mixing\nin the upper left hand matrix block), but the coupling be-tween the waveguides and particular resonator polarization\nmodes “rotates” in time. Thus, one might imagine the same\nturnstile junction, but with the ferrite rod removed and the\ncylinder physically spinning at a rate \n, Fig. 1c.4\n...\n...\n1 3a)\n13\nc)\n13b)... ...d)............ 1 3 2 4\nFIG. 2: a) Electrical schematic of a Wheatstone bridge-based LC resonator that serves as the basic module of our four-port circulator de-\nsign. Analogous to the turnstile-type structure depicted in c, the resonant mode couples to the two transmission lines 1 & 3 (characteristic\nimpedance r) with a magnitude and sign that depends on \u0012. The resonant mode center frequency is \u0012\u0000independent, which is also true\nof c. b) Two such modules placed in parallel, with “orthogonal” bridge unbalancing. d) Four such modules, configured to emulate the\nmechanically-spinning turnstile depicted in Fig. 1c. As mentioned in the text, the inductances in figure d are modulated linearly in section\nII, but the inverse inductances are modulated linearly in section III.\nThe general structure of Eq. (5) deserves comment. In-\ndeed, it has long been recognized that parametrically-\nmodulating components in an electrical network can make\na reciprocal network nonreciprocal [10–12, 14–16 ]. These\nmodulated components create frequency-sidebands on sig-\nnal carriers that serve as extra degrees of freedom to encode\na physical location onto the signal (e.g. a signal’s “port of en-\ntry”). Nonreciprocal networks then also require either reso-\nnant modes or some other means of creating delay between\nthe modulated components. However, networks that don’t\ndemodulate (i.e. coherently “erase”) these sidebands when\nthe signal exits the network suffer either from more compli-\ncated downstream signal processing, or effective loss if the\ninformation in the sidebands is ignored. The network rep-\nresented in Eq. (5) achieves perfect demodulation by lim-\niting the signal modulation to the coupling between reso-\nnant modes (with no internal loss) and the itinerant fields.\nThus, when signals pass through the resonant modes they\nare modulated exactly twice, as they enter and as they exit\nthe resonant modes. In general, only 0thand 2ndorder har-\nmonics of the modulation frequency can appear in the out-\nput signal, and it is easy to design these modulations such\nthe 2ndorder harmonics completely cancel out. In contrast,\nmany other, related proposals modulate the coupling be-\ntween resonant modes or between itinerant fields, or some\ncombination of all three modulation types [10–12, 14–16 ].\nUnfortunately, these types of modulation create sidebands\nat all harmonic orders, which are more difficult to cancel or\nto filter out.\nOur approach emulates the dynamics in Eq. (5), but as\na lumped element, superconducting microwave network\nwith simulated “spinning” of two resonant modes relative\nto four transmission line ports. Our network can be built up\npiecewise, starting with the network depicted in Fig. 2a. In\nthe limit of small inductors (relative to the port impedance)\nthe two transmission lines 1 and 3 are effectively shorted to-\ngether through the bridge of inductors over most frequen-\ncies. However, the bridge also presents a total inductance\noflto the capacitor, forming a resonator with center fre-\nquency 1=p\nl c. For cos(\u0012)6=0, the bridge unbalances, cou-pling the resonant mode to the transmission lines with a\nmagnitude and sign that depends on \u0012[17, 24 ]. The anal-\nogous turnstile-type structure is depicted in Fig. 2c where\na two-port rectangular waveguide couples to a rectangu-\nlar box resonator [25]. Assuming that only one polarization\nmode of the box is near resonant with signals applied at the\nports, the magnitude and phase of the coupling depend on\nthe orientation angle \u0012of the box relative to the waveguide.\nAdding a second bridge resonator in parallel with the first,\nbut now with the inductors imbalanced as \u0006sin(\u0012), Fig. 2b,\nwould be analogous to replacing the rectangular box res-\nonator in Fig. 2c with a rotationally symmetric, cylindrical\nresonator (like that in Fig. 1c). Finally, the full circulator de-\npicted in Fig. 1c is emulated by adding two more transmis-\nsion line ports 2 & 4 that couple to the same two resonant\nmodes, but do so “orthogonally” relative to ports 1 & 3 via\ntwo more bridges. If the unbalancing of the bridges can be\nvaried sinusoidally in time, i.e. make \u0012=\n tas in Fig. 2d,\nthen the two resonant modes couple and uncouple from the\nfour transmission lines in a coordinated fashion that sim-\nulates the mechanical spinning of the cylinder in the four\nport circulator depicted in Fig. 1c and in Eq. (5). The trick, of\ncourse, is to find an experimentally convenient way to both\nrealize dynamically tunable inductors in a superconducting\nmicrowave circuit and tune them naturally in such a highly\ncoordinated fashion.\nOur tunable inductors are dc superconducting quantum\ninterference devices (SQUIDs), which are two Josephson\njunctions connected in parallel [26]. For currents much\nsmaller than the SQUID critical current, the SQUID acts as\nan inductor with inductance\nls='0\nIs,Is=2I0\f\f\f\fcos\u0012\b\n2'0\u0013\f\f\f\f(6)\n(assuming identical junctions and negligible geometric in-\nductance) where Isis the SQUID critical current, I0the\njunction critical current, '0the reduced flux quantum, and\n\bthe magnetic flux threading the SQUID loop. Replac-\ning the four inductors in Fig. 2a with four SQUIDs real-\nizes a bridge of dynamically tunable inductors. Further-5\nFlux control currentBackground\nmagnetic fieldSQUID-based\nrealization\ndc SQUID\nFIG. 3: Schematic of a dc SQUID-based realization of the tunable\nbridge network. In the right hand figure, the wire configuration\n(black lines) is critical as it determines the magnetic flux through\nthe five depicted loops (four SQUID loops, one loop of the bridge\nitself. The four small circles represent unimportant network ter-\nminals.). The total magnetic flux \bthrough each SQUID loop is\nthe sum of the flux from a uniform background field ( \b\u0006) and from\na magnetic flux control current that flows vertically through the\n“twisted” bridge ( \b\u0001). Ideally, the net magnetic flux through the\nbridge loop is always zero.\nmore, twisting the bridge into a figure-eight layout gives\nus a convenient way to achieve the required unbalancing\nof the bridge inductances. We can set the inductance of\neach SQUID appropriately by applying a constant and uni-\nform magnetic field and a smaller, time-dependent, and\ngradiometic magnetic field, as in Fig. 3. Note, too, that this\nconfiguration only induces the desired screening currents\nwithin each SQUID loop. Undesired screening currents\nbetween SQUIDs are not induced (canceling unwanted\nscreening currents in a network like Fig. 2d is also impor-\ntant, but outside the scope of this article). Thus, in princi-\nple, all of the inductive, dynamically unbalanced bridges in\nFig. 2d, could be realized with 16 SQUIDs, a uniform back-\nground magnetic field and two control wires carrying cur-\nrent oscillating as cos (\nt)and sin(\nt). In section IV, we\nwill also address considerations such as increasing the net-\nwork’s saturation power by replacing single SQUIDs with ar-\nrays and the secant- rather than linear-dependence of in-\nductance on magnetic flux.\nIII. CIRCUIT ANALYSIS\nWe now analyze the circuit depicted in Fig. 2d. Analysis\nwill use both the frequency domain, lumped element ap-\nproach common in microwave engineering [25], and a time-domain approach, which shows how Eqs. (5) approximate\nthe circuit’s dynamics.\nThe essential sub-network in this circulator is the two\nport [25]Wheatstone bridge-type [24]network depicted in\nFig. 4a. In contrast to the networks depicted in Fig. 2, in this\nsection we will exclusively consider inductances that vary\nasl(1\u0006d(t,\u0012))\u00001(lsome inductance, and dis a real func-\ntion of time t, and an angle \u0012), as in Fig. 4a. This is a more\nnatural, simplified model for the dependence of SQUID in-\nductances on magnetic flux, Eq. (6). Straightforward circuit\nanalysis [25]gives us the constitutive equations for this net-\nwork\n1\nl\u0014\n1 d(t,\u0012)\nd(t,\u0012) 1\u0015\u0014\n\u001e1(t)\n\u001eq(t)\u0015\n=\u0014\nI1(t)\nIq(t)\u0015\n. (7)\nwhere\u001ei(t)=Rt\n\u00001Vi(\u001c)d\u001cis the time integral of the volt-\nage across port iand is called the “branch flux” across this\nport [30], and Iiis the current entering at port i. Through-\nout this article, we will use the convention that inductance\nis defined as the ratio of the branch flux across and current\nthrough a network branch [18, 26 ](which for time-varying\nor nonlinear inductances is different from the more famil-\niar definition of inductance as the ratio of voltage and the\ntime derivative of current). From Eq. (7), we learn that\nthe unbalancing of the bridge in Fig. 4a gives an output\nreluctance (the current response at one port per flux ap-\nplied at the other; i.e. inverse inductance) proportional to\nd(t,\u0012), but the input reluctance (the current response at\none port per flux applied at the same port) is independent\nofd(t,\u0012). Such clean separation between input and output\nreluctances is highly attractive when d(t,\u0012)is proportional\nto an experimentally-convenient tunable parameter, such\nas the control current in Fig. 3. Our network is designed to\nexploit this separation to realize time-variable coupling be-\ntween resonant modes and itinerant fields without modu-\nlating the intra-resonator dynamics or prompt field scatter-\ning. This bridge is the repeated module that helps us realize\nEq. (5).\nNext, Fig. 4b takes four copies of this bridge, places them\nin a ring, and defines six ports f1, 2, 3, 4, q,pg. Note that\nports 1-4 are each defined between a network node and\nground, while ports qand pare each defined by two net-\nwork nodes. If we let d(t,\u0012)=\u000fcos(\nt+\u0012)(0\u0014\u000f\u00141\n), straightforward circuit analysis then relates port branch\nfluxes and currents:\n1\nl2\n66666642 0 \u000fcos(\nt)\u000fsin(\nt)\u0000\u000fcos(\nt)\u0000\u000fsin(\nt)\n0 2 \u000fsin(\nt)\u0000\u000fcos(\nt)\u0000\u000fsin(\nt)\u000fcos(\nt)\n\u000fcos(\nt)\u000fsin(\nt) 3\u00001\u00001\u00001\n\u000fsin(\nt)\u0000\u000fcos(\nt)\u00001 3 \u00001\u00001\n\u0000\u000fcos(\nt)\u0000\u000fsin(\nt)\u00001\u00001 3 \u00001\n\u0000\u000fsin(\nt)\u000fcos(\nt)\u00001\u00001\u00001 33\n77777752\n6666664\u001eq(t)\n\u001ep(t)\n\u001e1(t)\n\u001e2(t)\n\u001e3(t)\n\u001e4(t)3\n7777775=2\n6666664Iq(t)\nIp(t)\nI1(t)\nI2(t)\nI3(t)\nI4(t)3\n7777775. (8)\nWhile the structure of Eq. (8) is evocative of Eq. (5), they are not equivalent. For example, Eq. (8) contains no reso-6\na)\n+\n-\n+ -\n13 24\n+ + +++\n-\n+-b)\n-\n-\n-\n-\n-\n-1\nFIG. 4: a) The inductance bridge as a network with two ports, 1 & q. b) Four inductance bridges configured as a six port network. Attaching\na capacitor across ports q&pand transmission lines across ports 1-4 realizes the circulator network depicted in Fig. 2d.\nnant dynamics yet and its dynamics are reciprocal [10, 25 ].\nNonetheless, we already have the critical structure that only\nthe couplings between ports 1-4 and ports q&pare vari-\nable in time. Analysis of Eq. (8) simplifies by going into a\n“left-right /even-odd” basis for the port 1-4 variables and a\nrotating, circular basis for the qand pport variables:\n2\n6664\u001el,e(t)\n\u001er,e(t)\n\u001el,o(t)\n\u001er,o(t)3\n7775=1p\n22\n66641 0 1 0\n0 1 0 1\n1 0\u00001 0\n0 1 0\u000013\n77752\n6664\u001e1(t)\n\u001e2(t)\n\u001e3(t)\n\u001e4(t)3\n7775, (9)\n\u0014\n\u001e+(t)\n\u001e\u0000(t)\u0015\n=1p\n2\u0014\nej\nt\u0000j ej\nt\ne\u0000j\ntj e\u0000j\nt\u0015\u0014\n\u001eq(t)\n\u001ep(t)\u0015\n(10)\nand similarly for the current variables ( jbeing the imag-\ninary unit, adopting the electrical engineering conven-\ntion [38]). In these bases, the dynamics of Eq. (8) separate\ninto:\n2\nl\u0014\n1\u00001\n\u00001 1\u0015\u0014\n\u001el,e(t)\n\u001er,e(t)\u0015\n=\u0014\nIl,e(t)\nIr,e(t)\u0015\n, (11)\n1\nl2\n66642 0\u000fj\u000f\n0 2\u000f\u0000j\u000f\n\u000f \u000f 4 0\n\u0000j\u000fj\u000f0 43\n77752\n6664\u001e+(t)\n\u001e\u0000(t)\n\u001el,o(t)\n\u001er,o(t)3\n7775=2\n6664I+(t)\nI\u0000(t)\nIl,o(t)\nIr,o(t)3\n7775. (12)\nThe time-dependent, reciprocal network of Fig. 4b be-\ncomes nonreciprocal when we make modes qand preso-\nnant by placing a capacitor (capacitance c) across each of\nthese ports. Doing so, these ports gain a fixed relation be-\ntween current and branch flux\n\u0000cd2\nd t2\u001eq,p(t) = Iq,p(t), (13)\nor equivalently in the circular basis\n\u0000c\u0012d\nd t\u0007j\n\u00132\n\u001e\u0006(t) = I\u0006(t). (14)\nThe capacitors have no effect on the “even” dynamics in\nEq. (11), but in the following subsection we will show thatthey turn the reciprocal, four-port “odd” network Eq. (12)\ninto a nonreciprocal, two port network.\nA. Frequency-domain analysis\nTaking into account the capacitors and writing the odd\nnetwork dynamics now in the frequency domain, we find:\n1\nl2\n66642\u0000l c(!\u0000\n)20\u000fj\u000f\n0 2\u0000l c(!+\n)2\u000f\u0000j\u000f\n\u000f \u000f 4 0\n\u0000j\u000f j\u000f 0 43\n77752\n6664\u001e+[!]\n\u001e\u0000[!]\n\u001el,o[!]\n\u001er,o[!]3\n7775=\n2\n66640\n0\nIl,o[!]\nIr,o[!]3\n7775(15)\nwhere square brackets [\u0001]indicate a frequency domain vari-\nable. From Eq. (15), one finds that a current applied at ei-\nther the “left” or “right” odd ports (i.e. taking Il,o6=0 or\nIr,o6=0) induces a resonant response in the \u001e\u0006variables\nwhen!=p\n(4\u0000\u000f2)=2l c\u0006\n\u0011!0\u0006\n, respectively. For\n\n= 0, the orthogonal coupling between the odd modes and\nthe resonant modes means that the left and right odd modes\nare uncoupled over all drive frequencies. But, for \n6=0 and\nodd driving at the frequency !0, the\u001e+and\u001e\u0000modes re-\nspond as equal and opposite capacitive and inductive reac-\ntances in parallel, which open a transmission window be-\ntween the left and right odd ports [2]. For instance, elimi-\nnating\u001e\u0006in Eq. (15), setting !=!0, and expanding to first\norder in\nwe find that\nj!016c\n\u000f2\u0014\n0 1\n\u00001 0\u0015\u0014\n\u001el,o[!0]\n\u001er,o[!0]\u0015\n=\u0014\nIl,o[!0]\nIr,o[!0]\u0015\n. (16)\nIn this configuration, signal transfer through the network is\nnonreciprocal: voltage applied at the right odd port will in-\nduce a positive current at the left odd port, but voltage ap-\nplied at the left odd port will induce a negative current at the7\nleft odd port (note that j!0times a branch flux is a voltage).\nA network with the constituent relations given in Eq. (16) is\nknown as a “gyrator,” the most basic building block of non-\nreciprocity in electrical network theory, with “gyration resis-\ntance”\u000f2=16c\n[21].\nFurther analysis is aided by attaching transmission lines\nto ports 1-4. With the capacitors across ports pand q\nand transmission lines across ports 1-4, Fig. 4b becomes\nequivalent to Fig. 2d. The voltages and currents at ports\n1-4 are now decomposed into traveling wave voltages and\ncurrents incident upon (“in”) and scattered by (“out”) the\nnetwork through the transmission lines [25, 27, 29 ]. Our\ngoal is now to relate these input and output waves. While\nsuch input-output analysis is convenient theoretically when\nstudying four-port circulator networks [39], measuring scat-\ntering parameters is also more experimentally convenient\nin microwave networks than direct measurements of port\nvoltages and currents.\nIf the only constraints on the input and output fields are\nthose imposed by our network (e.g. the transmission lines\nare of effectively infinite length) then [9, 25, 27 ]\nIi(t) = Ii,in(t)+Ii,out(t)\nd\nd t\u001ei(t) = Vi,in(t)+Vi,out(t)\nr Ii,in(t) = Vi,in(t)\n\u0000r Ii,out(t) = Vn,out(t) (17)\nwhere the traveling wave variables above are evaluated\nat the port positions and ris the characteristic (real)\nimpedance of each transmission line. Standard network\nanalysis [25]then tells us that if the port branch fluxes and\ncurrents are related by\nj!Yi j[!]\u001ej[!]=Ii[!] (18)\nwhere Yis known as the admittance matrix, it then follows\nthat\nVi,out[!] =\n(1+rY[!])\u00001(1\u0000rY[!])\ni jVj,in[!]\n\u0011Si j[!]Vj,in[!], (19)\nwhere 1is the identity and provided that the matrix inverse\nexists. Sis often referred to as a scattering matrix.\nFor example, using Eq. (16), one finds that when \n=\n 0\u0011\n\u000f2=16c r\n\u0014\nVl,o,out[!0]\nVr,o,out[!0]\u0015\n=\u0014\n0\u00001\n1 0\u0015\u0014\nVl,o,in[!0]\nVr,o,in[!0]\u0015\n. (20)\nIn other words, when the gyrator resistance equals r, the\nodd network is matched: signals are fully transmitted by the\nnetwork, but the transmission is nonreciprocal. A voltagesignal picks up a \u0019phase shift traveling from the right odd\nto left odd port and no phase shift traveling from left odd\nto right odd. Similarly, using the even network relations in\nEq. (11), one finds that to zeroth order in !0l=r\n\u0014\nVl,e,out[!0]\nVr,e,out[!0]\u0015\n=\u0014\n0 1\n1 0\u0015\u0014\nVl,e,in[!0]\nVr,e,in[!0]\u0015\n. (21)\nCombining Eqs. (20) and (21) and putting the input and out-\nput voltage signals back into the port 1-4 basis, we find that\nthis network acts as an ideal, four-port circulator, Eq. (1), for\ninput voltage waves at frequency !0. We also mention that\nas our network is operable as a two port gyrator, it is there-\nfore also operable as a three-port circulator by combining\nports 3 and 4 in Fig. 2d into a single port (i.e. by merging the\ntransmission lines 3 and 4 together) [20, 22 ].\nB. Time-domain analysis\nThis standard scattering matrix approach, though, ob-\nscures the dynamics that guided our intuition: a simulated\n“rotation” of the resonant modes relative to the itinerant\nfields (e.g. Fig. 2c). To that end, we reanalyze the dy-\nnamics of Eq. (11) and Eq. (15) in the time-domain, and\nwithout eliminating the \u001e\u0006dynamics. In quantum optics,\nanalogous models are known as “input-output” (IO) mod-\nels[9, 27–29 ]. Like the scattering matrix models of the pre-\nvious paragraph, IO models relate incident and scattered\nelectromagnetic waves and are thus natural models for res-\nonant microwave networks. But unlike scattering matrix\nmodels, they are time-domain, first order ordinary differ-\nential equations. IO models approximate resonant circuit\ndynamics, but may also be directly compared with, for ex-\nample, optical systems that don’t have lumped element rep-\nresentations. On the other hand, the circuit analysis in the\nprevious section does not require approximations beyond\nthe lump element assumptions, and can be useful in con-\nsidering how IO approximations break down.\nIn this case, our IO model assumes that the network vari-\nables have solutions of the form [9, 27, 28 ]\n\u001ei(t) ='i(t)ej!dt+c.c.\nVi,in(t) =!0pc r v i,in(t)ej!dt+c.c.\nVi,out(t) =!0pc r v i,out(t)ej!dt+c.c.\n!d=!0+\u0001 . (22)\nfor a drive frequency detuned by \u0001from the center fre-\nquency!0. Then, combining Eqs. (11), (15), and (17), mak-\ning a slowly varying envelope approximation and solving to\nlowest order in !0l=r,j\u0001j=! 0, andj\nj=! 0(i.e. assuming\nthat the rate of variation of 'i,vi,in, and vi,outis much less\nthan!d) gives8\n2\n6664d\nd t'+(t)\nd\nd t'\u0000(t)\nvl,o,out(t)\nvr,o,out(t)3\n7775=2\n66664\u0000\nj(\u0001\u0000\n)+\u0014\n2\n0 jp\u0014\n2\u0000p\u0014\n2\n0\u0000\nj(\u0001+\n)+\u0014\n2\njp\u0014\n2p\u0014\n2\n\u0000jp\u0014\n2\u0000jp\u0014\n2\u00001 0\n\u0000p\u0014\n2p\u0014\n20\u000013\n777752\n6664'+(t)\n'\u0000(t)\nvl,o,in(t)\nvr,o,in(t)3\n7775,\u0014\nvl,e,out(t)\nvr,e,out(t)\u0015\n=\u0014\n0 1\n1 0\u0015\u0014\nvl,e,in(t)\nvr,e,in(t)\u0015\n(23)\nwhere we have defined \u0014=\u000f2=8c r. We call Eq. (23) an\nIO model of the network depicted in Fig. 2d. Putting\nthis model back into the f1, 2, 3, 4, q,pgbasis then gives\nus the four port circulator model Eq. (5) with the iden-\ntificationsfaq,ap,b1,(in/out),b2,(in/out),b3,(in/out),b4,(in/out)g=\nf'q,'p,v1,(in/out),v2,(in/out),v3,(in/out),v4,(in/out)g. A natural in-\nterpretation of the IO model Eq. (5) is that while the cen-\nter frequency and total damping of each resonator mode\nare constant in time, the resonant modes couple to (and are\ndamped by) each transmission line in a sinusoidally “rotat-\ning” pattern. While the rotating coupling between resonant\nand port degrees of freedom is apparent in Fig. 2d, the time-\nindependent intra-resonator dynamics are less obvious.\nFinally, we calculate the performance of the circulator\nin this IO representation in order to compare it to the fre-\nquency domain circuit analysis presented in section III A.\nFor linear IO models of the form\nd\nd t~x(t)\n~yout(t)\n=\u0014AB\nCD\u0015\u0014~x(t)\n~yin(t)\u0015\n(24)\nwith time-independent matrices fA,B,C,Dg, a scattering\nmatrix-like representation of the steady state response of\nthe output amplitude vector ~youtto a constant input ampli-\ntude vector~youtis\n~ys s\nout=\nD\u0000CA\u00001B\n~ys s\nin(25)\nin general. However, as is typical for IO models of lossless,\ngain-less, linear systems, Eqs. (23) have a particular form\nwhere B=\u0000C†D,A=\u0000jQ\u00001\n2C†C, and Dis unitary and\nQis Hermitian (†signifying the matrix adjoint) [29]. In this\ncase, in analogy with Eq. (19), it can be shown that [32]\n~ys s\nout=D1=2(1+Yio)\u00001(1\u0000Yio)D1=2~ys s\nin\nYio=2jD1=2\nCQ\u00001C†\u00001D\u00001=2(26)\n(assuming the matrix inverses exist). Using Eq. (26) and the\nfirst Eq. in (23), we find an admittance-like matrix for the IO\nmodel of the odd modes\nYio,odd=\u00002\n\u0014\u0014\nj\u0001\u0000\n\n j\u0001\u0015\n. (27)\nAnd thus, in analogy with Eq. (20), we find for \u0001= 0 and\n\n=\u0014=2 (i.e. for!d=!0and\n=\n 0) this IO acts like an\nideal gyrator\n\nvs s\nl,e,out\nvs s\nr,e,out\n=\u0014\n0\u00001\n1 0\u0015\nvs s\nl,e,in\nvs s\nr,e,in\n. (28)If tuned optimally ( \n=\n 0) and for\u00016=0, the FWHM band-\nwidth of the odd and full circulator network models arep\n2\u0014andp\n2(p\n3\u00001)\u0014, respectively. Thus circulator band-\nwidth is strongly constrained by the modulation amplitude\nof the inductors, \u0014/\u000f2, as will be discussed more in sec-\ntion IV. We also note thatp\n2\u0014=2p\n2\n0, which isp\n2 times\nthe frequency splitting of the internal modes for a matched\nnetwork. A simple proportionality between bandwidth and\nthe frequency splitting of internal modes is typical of many\nnon-reciprocal networks [2].\nC. Simulation\nIt is worth comparing the theoretical scattering response\nof the approximate IO model to the full lumped-element\nscattering matrix (which is exact up to the lumped element\nassumption). In the IO model, the scattering response cor-\nresponds to an ideal four port circulator when \u0001= 0 and\n=\n\u0014=2. Alternatively, one can calculate Sfor the full lumped\nelement network depicted in Fig. 2d, but without the ap-\nproximations made to produce Eqs. (20)-(21). Choosing pa-\nrameters compatible with superconducting microwave cir-\ncuits [5, 23 ]l=1\n2nH, c=2 pF , r=50\n,!=!0=2\u0019\u00026.16\nGHz,\n=\n 0=2\u0019\u000299 MHz, and\u000f=1 we find:\njS11j2=jS22j2=jS33j2=jS44j2=0.002\njS21j2=jS32j2=jS43j2=jS14j2=0.995\njS31j2=jS42j2=jS13j2=jS24j2=0.002\njS41j2=jS12j2=jS23j2=jS34j2=0.000 (29)\nThat is, 99.5% of the incident power at this frequency is\nrouted correctly for these parameters and 0.2% is reflected,\nassuming ideal lumped element components and ideal in-\nductor modulation (section IV will focus on the many con-\nsiderations that go into identifying a practical set of pa-\nrameters). The network’s response to off-resonant drives,\n\u0001 =!d\u0000!06=0, is depicted in Fig. 5 for the various\nmodels. For these parameters, the circulator bandwidth\nisp\n2(p\n3\u00001)\u0014=2\u0019=241 MHz in the IO model response,\nwhich is depicted in Fig. 5a. We see a very similar response\nusing the lumped element circuit model in Fig. 5b. The\ngreatest difference in this response is that that it is no longer\nperfectly symmetric about \u0001= 0, especially outside of the\ncirculator bandwidth.\nThe discrepancy between the lumped element and IO\nmodels appears to be largely due to nonidealities in the\neven network transmission Eq. (21): perfect circulation9\na)c) b)\nFIG. 5: Simulation of the frequency domain response of various models of the circulator, as described in the text. Curves of the other\nscattering parameters are identical to these, with a cyclic permutation of the port indices, confirming proper circulation.\nbreaks down when the even network ceases to look like two\nports shorted together. Thus the ideal even network re-\nsponse occurs in the limit of small !0l=r, and for these pa-\nrameters!0l=r=0.39. If instead we choose the parameters\nl=1 nH, c=1 pF ,\u000f=1=p\n2 (!0=2\u0019\u00026.7 GHz), the cor-\nresponding IO model still has the same !0,\u0014, and\n0, but\nnow!0l=r=0.84. Evaluating the lumped element scatter-\ning parameters for these values now results in a response\nthat deviates further from the ideal IO model, with a 97.8%\nmaximum power transmission, 1% power reflected, and a\nmore asymmetric response about \u0001= 0, Fig. 5c.\nIV. CONSIDERATIONS FOR A SQUID-BASED REALIZATION\nTo better ground the above analysis in the reality of su-\nperconducting microwave circuits, we now outline some\nconsiderations that go into designing dc SQUID networks\nthat approximate linear inductors. Circulator performance\nshould be compared against commercial circulators and the\nneeds of contemporary and future experiments with super-\nconducting quantum microwave circuits. Desirable charac-\nteristics for our circulator include an input-output response\nthat is close to Eq. (1) on resonance, a wide bandwidth, and\nhigh power handling. For example, there is a trade-off in\nthis particular circuit design (Fig. 2d) in that ideal input-\noutput response occurs in the limit of small !0l=r, subsec-\ntion IIIc, but the bandwidth of the network also decreases\nin this same limit ( \u0014=! 0\u0018l!0=r). This trade-off is inde-\npendent of any component nonidealities and arises at the\nschematic level of this particular design. We also note that\ncompetition between bandwidth and the optimal perfor-\nmance at a single frequency appears in any practical circuit\ndesign. The physics of dc SQUIDs also require trade offs in\na good design. Although modifications to this circuit will\nchange the particulars, the considerations outlined below\nappear in any superconducting microwave network based\non dynamically-modulated SQUIDs [6, 23, 26, 31 ].\nWe first address the schematic-level trade-off. One must\nassume that r, the transmission line impedance, is prac-\ntically constrained to 50 \nand that we will target designs\nin which!0=2\u0019, the center frequency of operation, is inthe usual 4-8 GHz band for quantum superconducting mi-\ncrowave networks. In optimizing the ratio !0l=r, this leaves\nonly las the flexible parameter. As described in sub-\nsection IIIc, if network bandwidth is held constant, but\nthis ratio increases, ideal circulator operation will decrease.\nFor example, finite !0l=rproduces back reflections (e.g.\njS11j26=0 in Fig. 5). While it is possible to include addi-\ntional, lossless matching networks at each port to reduce\nback reflections over some frequency range, the Bode-Fano\ncriterion suggests that a nonvanishing !0l=rfundamen-\ntally limits excellent network matching over broad band-\nwidths [25, 33 ]. This further supports the intuition gained\nfrom Fig. 5 that without a radical redesign of the network, a\nlarger ldecreases the performance achievable over a given\nbandwidth of operation.\nTo roughly match the performance of commercial ferrite\ncirculators, we can allow ourselves nonidealities in the sig-\nnal routing at the -20 dB level. We see such performance\nin Fig. 5c, in which l=1 nH. Inductances of this scale\nare achievable in SQUID networks fabricated using optical\nlithography [35, 36 ]. Although the performance depicted in\nFig. 5b is better than in c, the assumed parameters are not\nrealistic. The baseline impedance is a reasonable l=0.5 nH,\nbut Fig. 5b assumes \u000f=1, which implies that the SQUIDs\nperiodically achieve infinite inductance (the feasibility of\n\u000f=1=p\n2 will be discussed below). Infinite inductance is ob-\nviously unphysical, but the actual limitations require some\ndiscussion of SQUID physics.\nA single dc SQUID is formed by two Josephson junctions\nconnected in parallel by superconducting wires, forming\na loop, Fig. 6a. For simplicity, we assume the junctions\nare identical and junction capacitance is negligible, and we\nignore the geometric inductance of the wires for the mo-\nment. Then, Faraday’s law and the Josephson relations al-\nlow us to relate the voltage across ( V1) and current flowing\nbetween ( I1) two leads connected on opposite sides of a\nsingle SQUID loop in the presence of an external magnetic\nfield [26]. Assuming null initial conditions, we identify a sin-\ngle SQUID’s effective inductance L1as the ratio between the\ncurrent and branch flux ( \u001e1(t)=Rt\n\u00001V1(\u001c)d\u001c) in the SQUID\nleads. SQUID inductance is nonlinear, as this ratio depends10\n+\n-\na)\nb)\n...+\n-\nFIG. 6: a) Schematic of a dc SQUID with I0critical current Joseph-\nson junctions, lggeometric inductance in each branch, and a mag-\nnetic flux\b. b) A series array of Nsuch SQUIDs.\nonI1, and we find that to third order in I1=Is\n\u001e1(t) = L1(t)I1(t), with (30)\nL1(t)\u0019ls(t)\u0012\n1+1\n6(I(t)=Is(t))2\u0013\n, (31)\nls(t) ='0\nIs(t)='0\n2I0\f\f\f\fsec\u0012\b(t)\n2'0\u0013\f\f\f\f(32)\nwhere'0=~h=2eis the reduced flux quantum, Isis the\nSQUID critical current (the maximum current flowing be-\ntween these two leads that the junction can support in its\nsuperconducting state), I0is the critical current of a single\njunction, and\b(t)is what the magnetic field flux through\nthe loop would be in the absence of screening currents.\nThus, for small currents, a SQUID acts like a linear induc-\ntor with a magnetic flux-dependent inductance. The rela-\ntive magnitude of the linear and nonlinear inductances, 1 =6,\nis fixed: a larger inductor requires a SQUID that saturates at\nsmaller currents.\nNow consider an array of Nidentical SQUIDs with their\nleads connected in series, Fig. 6b. In this case, the current\nflowing through each, and the voltage across each are iden-\ntical. Thus, the relationship between the branch flux across\nand the current through the entire array is \u001eN=LNIN,\nwhere LN=N L 1. Qualitatively, adding SQUIDs in series al-\nlows us to increase linear inductance without decreasing the\nsaturation current. Quantitatively, to third order in I1=Iawe\nhave that [23, 34 ]\nLN(t)\u0019la(t)\u0012\n1+1\n6N2(I(t)=Ia(t))2\u0013\n, (33)\nla(t) ='0\nIa(t),Ia(t)=Is(t)=N, (34)from which we see that for a fixed linear array inductance la,\nthe nonlinear inductance scales as N\u00002. Less nonlinearity\nmeans higher saturation powers in analog signal process-\ning.\nThe SQUIDs’ nonlinearity limits the circulator’s power\nhandling. As the SQUID inductance increases with cur-\nrent, center frequencies of microwave resonators contain-\ning SQUIDs typically decrease as the power of incident sig-\nnals increase. The approximation of a SQUID as a linear\ninductor tends to break down when this center frequency\nshift is comparable to the resonator bandwidth. In the case\nof high quality resonators, it is convenient to reparameter-\nize the nonlinear inductance in Eqs. (31) and (33) as an ef-\nfective “Kerr constant” that gives this center frequency shift\nper microwave photon stored in the resonator (i.e. stored\nmicrowave energy in units of ~h!0)[23, 34 ]. Up to a factor of\norder unity (depending on the resonator construction) this\nKerr constant is\nK\u0019\u0000~h!2\n0\nI2\nsla/N\u00002, (35)\nwhere the sign of Kindicates the direction of the center fre-\nquency shift. For example, using parameters compatible\nwith Fig. 5c,!0=2\u0019\u00026.16 GHz, la=1 nH, and assuming\nan array of N=20 SQUIDs compatible with junctions pro-\nduced by optical lithography in the NIST NbAlOxNb trilayer\nprocess [35, 36 ],Is=6.6\u0016A, one finds K\u0019\u0000 2\u0019\u0002580 kHz.\nWith this Kerr constant, and assuming the resonator band-\nwidth depicted in Fig. 5c, one would expect the nonlinear\nreactance of the SQUIDs to become noticeable with of or-\nder 100 photons stored in the resonator (because 241 MHz\n=(2\u0019)\u00001jKj\u0002415 photons). A comparable design based on\nsingle SQUIDs would require Is=0.33\u0016A and would ex-\nhibit nonlinearities well below 10 stored photons. For quan-\ntum superconducting microwave experiments, the satura-\ntion power of commercial ferrite circulators is effectively\ninfinite. While experiments involving one or two super-\nconducting qubits often operate at signal powers that do\nnot saturate routers and amplifiers networks with single-\nSQUID-scale saturation currents, higher saturations powers\nare more critical in quantum networks that employ more\nweakly coupled systems (e.g. mechanical oscillators and\nmagnetic spins), applications outside of quantum informa-\ntion (e.g. astrophysical detectors), and in current and future\nquantum networks with more signal multiplexing.\nOptimizing our circuit design according to the prescrip-\ntions thus far, one might conclude that the best strategy is\nto employ SQUID arrays with la\u00191 nH (with no external\nflux bias) as our tunable inductors, and let N!1 ,I0!0\nto minimize nonlinear effects. This is imprudent for several\nreason. One is a larger circuit footprint, which adds stray\ngeometrical inductance throughout the circuit. Other rea-\nsons are due to the geometric inductance of the SQUID loop\nwires themselves, lgin Fig. 6a, which we’ve ignored thus\nfar. This SQUID loop inductance limits both the minimum\nls,min and maximum ls,max achievable through flux tuning\nof a SQUID array. Both constraints worsen as '0=I0lgde-\ncreases [26]. With minimum and maximum array induc-11\ntances in general one finds that\nj\u000fj<\u00112\u00001\n\u00112+1,\u0011=ls,max=ls,min. (36)\nIn practice,\u0011seems to be limited to about 4 in supercon-\nducting microwave circuits with of order 10-100 SQUIDs in\nan array [23], which limitsj\u000fj<0.88. Even longer arrays\nwould be even less tunable. Constraints on the maximum \u000f\nultimately limit circulator bandwidth, which is proportional\nto\u000f2(section IIIB). The simulation depicted in Fig. 5c, with\n\u000f=1=p\n2, is consistent with this tunability constraint, and\nachieves a bandwidth of 241 MHz. Commercial circulators\nused in contemporary superconducting microwave experi-\nments have bandwidth of a few GHz, but the vast majority\nof this bandwidth is unused. Most circuits involved in rout-\ning quantum microwave signals in contemporary experi-\nments operate at bandwidths of order 10 MHz or smaller [5–\n7, 17, 23, 31 ]. Moreover, the center frequency of our network\nmay be tuned broadly by varying the uniform background\nfield, as depicted in Fig. 3. Thus, while not as broadband as\ncommercial options, this network should have an achiev-\nable bandwidth more than sufficient for most applications\nin superconducting microwave networks.\n1. Input-output response with SQUID-like inductance\nmodulation\nWe saw in section III that proper periodic modulation of\nthe inductances according to Fig. 2d causes the network to\nscatter signals without creating any sideband excitations.\nUsing a numerical, time-domain, MATLAB Simscape sim-\nulation of the circuit depicted in Fig. 2d, network perfor-\nmance in this ideal case is depicted in Fig. 7a. Using the\nsame parameters as in Fig. 5c, r=50\n,l=1 nH, c=1 pF ,\n\u000f=1=p\n2,\n=\n 0=2\u0019\u000299 MHz, a continuous-wave, in-\nput current drive at fequency !d=2\u0019\u00026.66 GHz is applied\nto port 1 suddenly at time t=0. The top plot in Fig. 7a de-\npicts the resulting current measured in the output signals\nfor the first 5 ns of the simulation (after separating input\nfrom output signals in the simulation). Initially, the output\ncurrent is equally distributed among the four ports, but af-\nter a few ns nearly all of the output current is measured at\nport 2. The bottom plot gives the normalized output cur-\nrent power spectrum for a 250 ns simulation (i.e. well into\nsteady state). The spectra are sharply peaked at !d, with the\npeak of the I1,out,I3,out, and I4,out signals at least 20 dB below\nthat of I2,out. While the shoulders are slightly fat, there are\nno visible sidebands. Driving the inputs of the other ports\nproduces responses identical to Fig. 7a, up to a cyclical per-\nmutation of the port indices.\nUnfortunately, it is not simple to tune a SQUID’s induc-\ntance exactly as\nl0\ns(t) = l(1\u0006\u000fcos(\nt))\u00001orl0\ns(t)=l(1\u0006\u000fsin(\nt))\u00001, (37)\nas in Fig. 2d. Because the linear inductance of a SQUID\nor array of SQUIDs goes as Eq. (6), applying a simple back-\nground magnetic flux that consists of a static and sinusoidalcomponent yields effective inductances that vary as\nls(t) ='0\n2I0\f\f\fcos\u0010\nF(t)\n2'0\u0011\f\f\f,\n\b(t) = \b\u0006\u0006\b\u0001cos(\nt)or\b(t)=\b\u0006\u0006\b\u0001sin(\nt). (38)\nIt is possible to make lsexactly equal to l0\nsin the limit\n'0=2I0!0,\b\u0006=2'0!\u0019=2. However, this limit corresponds\nto an infinitely flux tunable Josephson inductance, which is\nunphysical. Instead, it is more realistic to set '0=2I0=2l,\nwhere lis the desired lin Eq. (37), and set \b\u0006=2'0=\u0019=3 so\nthat ls=l0\nswhen\b\u0001=0. One then chooses \b\u0001such ls\u0019l0\ns,\ngiven the desired \u000fin Eq. (37).\nWe can now redo the simulation in Fig. 7a, but with a\nvariable inductance model based on Eq. (38) rather than\nthe ideal Eq. (37). Choosing parameter values that closely\nemulate the simulation in Fig. 7a, r=50\n,'0=2I0=2 nH,\n\b\u0006=2'0=\u0019=3,c=1 pF ,\b\u0001=2'0=0.38,\n= 2\u0019\u000290 MHz,\n!d=2\u0019\u00026.63 GHz (parameters found through trial-and-\nerror optimization), produces the analogous plots in Fig. 7b.\nThe time-domain response is nearly identical to the ideal\ncase. The most noticeable difference is that the I3,out re-\nsponse is about the same as I1,out and I4,out. The differences\nbetween the steady state power spectra are more obvious.\nThe output signals now exhibit sidebands, which are caused\nby the slight differences between Eqs. (38) and (37) for these\nparameters. Happily, though, the largest of these sidebands\nare nearly -50 dB cand are the 3rd harmonics of \n(i.e. are at\n!d\u00064\n). The lower harmonics of \nare almost completely\nsuppressed by the symmetry of the circuit, which is remark-\nable considering the significant, \b\u0001=2'0=0.38, modula-\ntions of the SQUID-like inductances.\nA quantitative analysis of the spectrum observed in\nFig. 7b is beyond the scope of this article, but will be con-\nsidered in a companion publication (which will also contain\na quantized model of the circulator) [37]. This is done by\nfirst deriving an Hamiltonian describing the circulator in-\ncluding its input and output ports. In a second step, Yurke’s\napproach to input-output formalism is used to compute the\nscattering properties of the circuit [27]. In contrast to the\nanalysis in section III B, following Yurke allows us to obtain\nexact, time-domain equations of motions for the circuit’s\ndegrees of freedom. Using theses results, the spectrum ob-\nserved in Fig. 7b can be understood quantitatively.\nV. CONCLUSION\nWe have introduced and analyzed a novel design for\na four-port circulator based on time-varying inductances\n(Fig. 2d) that has the potential to replace the lossy and non-\nintegrable commercial ferrite circulators ubiquitous in su-\nperconducting quantum microwave experiments. The ba-\nsic module is a dynamically-unbalanced bridge network\nof four SQUIDs (or SQUID arrays) [24], depicted in Fig. 3.\nThese bridges dynamically modulate the coupling between\nfour transmission lines and two resonant modes, and the\nconstruction ensures that this coupling is the only aspect12\n0 1 2 3 4 5−0.500.51Ideal Inductance Tuning\nTime [ns]Current [arb.]\n0 1 2 3 4 5−1−0.500.51SQUID−like Tuning\nTime [ns]\n6 6.5 7−150−100−500\nFreq. [GHz]Power [dB]\n  \n6 6.5 7−150−100−500\nFreq. [GHz]I2,outI1,outI3,outI4,outa) b)\nFIG. 7: Numerical network simulations. a) Network output response in time and frequency, driving port 1, given parameters from Fig. 5c,\nand the ideal inductance modulation given in Fig. 2d and Eq. (37). b) The same network simulation, but where the linear inductances are\nmodulated in a “SQUID-like” manner, i.e. using Eq. (38), as described in the text.\nof the dynamics that is modulated. The construction also\nensures that when the inductances are tuned perfectly, the\nnetwork’s output signals are not complicated by frequency,\nphase, or amplitude modulation. This critical feature is\ngreatly aided by limiting the dynamic modulation to the\ncoupling between the resonant modes and the transmission\nlines. As a result, the resonant modes act as if they are “spin-\nning” relative to the transmission lines or, equivalently, as if\nthey are coupled by a synthetic magnetic field, Fig. 1.\nThe design has a number of attractive features such as\nmodulation pump tones detuned from the signal by more\nthan a decade, a broadly tunable center frequency, a tun-\nable bandwidth, high saturation power, and a lumped ele-\nment and modular construction. We have given an overview\nof many of the considerations needed to realize a design ca-\npable of achieving a 240 MHz bandwidth and a saturation\npower of order 100 microwave photons per inverse band-\nwidth with superconducting microwave technology. The\ndesign of a practical electromagnetic circulator is a dif-\nficult and important problem and different technologicalconstraints have yielded a wide variety of solutions and\npotential solutions over the decades, of which Refs. [2–\n4, 10–17, 19–21 ]are but a small sample. Because of this\nlong tradition, we analyzed this network from several differ-\nent perspectives, through analogy to familiar, ferrite-based\ncirculator designs, through lumped element circuit analy-\nsis, through approximate input-output models (appropri-\nate for distributed RF or optical systems), in the time and\nfrequency domain, analytically, and numerically. We ex-\npect that the present design will find near-term use context\nof quantum superconducting microwave networks, but we\nalso hope that this diverse analysis will help inspire an even\ngreater diversity of future solutions and perspectives in even\nbroader contexts.\nThis work is supported by the ARO under the contract\nW911NF-14-1-0079. K. Lalumière and A. Blais acknowledge\nsupport from the ARO under grant W911NF-14-1-0078, as\nwell as from NSERC and CIFAR. J. Kerckhoff would like to\nthank John Gough for a useful discussion.\n[1]M. H. Devoret and R. J. Schoelkopf, Superconducting Circuits\nfor Quantum Information: An Outlook , Science 339, 1169\n(2013).\n[2]C. E. Fay and R. L. Comstock, Operation of the Ferrite Junction\nCirculator , IEEE Trans. Microw. Theory Techn. 13, 15 (1965).[3]P . J. Allen, The Turnstile Circulator , IEEE Trans. Microw. The-\nory Techn. 4, 223 (1956).\n[4]B. A. Auld, The Synthesis of Symmetrical Waveguide Circula-\ntors, IEEE Trans. Microw. Theory Techn. 7, 238 (1959).\n[5]F . Mallet, M. A. Castellanos-Beltran, H.-S. Ku, S. Glancy, E.13\nKnill, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehn-\nert, Quantum State Tomography of an Itinerant Squeezed Mi-\ncrowave Field , Phys. Rev. Lett. 106, 220502 (2011).\n[6]K. W. Murch, E. Ginossar, S. J. Weber, R. Vijay, S. M. Girvin, and\nI. Siddiqi, Reduction of the Radiative Decay of Atomic Coher-\nence in Squeezed Vacuum , Nature 499, 62 (2013).\n[7]A. Narla, K. M. Sliwa, M. Hatridge, S. Shankar, L. Frunzio, R.\nJ. Shoelkopf, and M. H. Devoret, Wireless Josephson Amplifer ,\nAppl. Phys. Lett. 104, 232605 (2014).\n[8]N. Roch, M. E. Schwartz, F . Motzoi, C. Macklin, R. Vijay, A.\nW. Eddins, A. N. Korotkov, K. B. Whaley, M. Sarovar, and I.\nSiddiqi, Obersvation of Measurement-Induced Entanglement\nand Quantum Trajectories of Remote Superconducting Qubits ,\nPhys. Rev. Lett. 112, 170501 (2014).\n[9]A. A. Clerk, M. H. Devoret, S. M. Girvin, F . Marquardt, and R.\nJ. Scheolkopf, Introduction to Quantum Noise, Measurement,\nand Amplification , Rev. Mod. Phys. 82, 1155 (2010).\n[10]B. D. O. Anderson and R. W. Newcomb, On Reciprocity and\nTime-Variable Networks , Proc. IEEE 53, 1674 (1965).\n[11]B. D. O. Anderson and R. W. Newcomb, The Time-Variable Lat-\ntice and Nonreciprocal RLC Networks , IEEE Trans. Circuit The-\nory13, 233 (1966).\n[12]N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, Magnetic-free\nnon-reciprocity and isolation based on parametrically modu-\nlated coupled-resonator loops , Nature Phys. 10, 923 (2014).\n[13]S. Tanaka, N. Shimomura, and K. Ohtake, Active Circulators:\nThe Realization of Circulators using Transistors , Proc. IEEE 53,\n260 (1965).\n[14]A. Kamal, J. Clarke, M. H. Devoret, Noiseless Nonreciprocity in\na Parametric Active Device , Nature Phys. 7, 311 (2011).\n[15]K. Fang, Z. Yu, and S. Fan, Realizing Effective Magnetic Field\nfor Photons by Controlling the Phase of Dynamic Modulation ,\nNature Photon. 6, 782 (2012).\n[16]L. Ranzani and J. Aumentado, Graph-based Analysis of Nonre-\nciprocity in Coupled-Mode Systems , arXiv:1406.4922.\n[17]B. Abdo, K. Sliwa, S. Shankar, M. Hatridge, L. Frunzio, R. J.\nSchoelkopf, and M. H. Devoret, Josephson Directional Ampli-\nfier for Quantum Measurement of Superconducting Circuits ,\nPhys. Rev. Lett. 112, 167701 (2014).\n[18]B. Yurke, L. R. Corruccini, P . G. Kaminsky, L. W. Rupp, A. D.\nSmith, A. H. Silver, R. W. Simon, and E. A. Whittaker, Obser-\nvation of Parametric Amplification and Deamplification in a\nJosephson Parametric Amplifier , Phys. Rev. A 39, 2519 (1989).\n[19]J. Koch, A. A. Houck, K. Le Hur, and S. M. Girvin, Time-\nreversal-symmetry breaking in Circuit-QED-Based Photon\nLattices , Phys. Rev. A 82043811 (2010).\n[20]G. Viola and D. P . DiVincenzo, Hall Effect Gyrators and Circu-\nlators , Phys. Rev. X 4, 021019 (2014).\n[21]B. D. H. Tellegen, The Gyrator: A New Electric Network Ele-\nment , Philips Res. Rept. 3, 81 (1948).\n[22]H. J. Carlin, Principles of Gyrator Networks, in Proceedingsof the Symposium on Modern Advances in Microwave Tech-\nniques , edited by J. Fox (Brooklyn Polytechnic Institute, 1955),\npp. 175–203.\n[23]M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale,\nand K. W. Lehnert, Amplification and Squeezing of Quantum\nNoise with a Tunable Josephson Metamaterial , Nature Phys. 4,\n929 (2008).\n[24]N. Bergeal, R. Vijay, V . E. Manucharyan, I. Siddiqi, R. J.\nShoelkopf, S. M. Girvin, and M. H. Devoret, Analog Informa-\ntion Processing at the Quantum Limit with a Josephson Ring\nModulator , Nature Phys. 6296 (2010).\n[25]D. M. Pozar, Microwave Engineering (John Wiley & Sons, Inc.,\nHoboken, NJ, 2011).\n[26]T. Van Duzer and C. W. Turner, Principles of Superconductive\nDevices and Circuits (Prentice Hall, Upper Saddle River, NJ,\n1999).\n[27]B. Yurke and J. S. Denker, Quantum Network Theory , Phys.\nRev. A 29, 1419 (1984).\n[28]C. W. Gardiner and P . Zoller, Quantum Noise (Springer-Verlag,\nBerlin, 2004).\n[29]J. E. Gough, M. R. James, and H. I. Nurdin, Squeezing Compo-\nnents in Linear Quantum Feedback Networks , Phys. Rev. A 81,\n023804 (2010).\n[30]M. H. Devoret, Quantum Fluctuations in Electrical Circuits in\nLes Houches, Session LXIII , edited by Renaud, S., Giacobino,\nE., and Zinn-Justin, J.(Elsevier Science, 1995), pp. 351-386 .\n[31]J. Y. Mutus et al. ,Design and Characterization of a Lumped El-\nement Single-Ended Superconducting Microwave Parametric\nAmplifier with On-Chip Flux Bias Line , Appl. Phys. Lett. 103,\n122602 (2013).\n[32]J. E. Gough, private communication\n[33]R. M. Fano, Theoretical Limitations on the Broad-Band Match-\ning of Arbitrary Impedances , J.Franklin Inst. 249, 57 (1950).\n[34]C. Eichler and A. Wallraff, Controlling the Dynamic Range of a\nJosephson Parametric Amplifier , EPJ Quantum Technology 1,\n2 (2014).\n[35]J. Sauvageau, C. Burroughs, P . Booi, M. Cromar, R. Benz, and\nJ. Koch, Superconducting Integrated Circuit Fabrication with\nLow Temperature ECR-based PECVD SiO 2Dielectric Films ,\nIEEE Trans. Appl. Supercond. 5, 2303 (1995).\n[36]J. A. B. Mates, G. C. Hilton, K. D. Irwin, L. R. Vale, and K.\nW. Lehnert, Demonstration of a Multiplexer of Dissipationless\nsuperconducting Quantum Interference Devices , Appl. Phys.\nLett. 92, 023514 (2008).\n[37]K. Lalumière, J. Kerckhoff, B. J. Chapman, K. W. Lehnert, and\nA. Blais, in preparation (2015).\n[38]In which the Fourier transform of a function is defined as\nF[!]=1p\n2\u0019R1\n\u00001F(t)e\u0000j td t\n[39]This is because an ideal four port network doesn’t always have\nan admittance or impedance matrix representation [2]."    },    {        "title": "1411.1470v1.Giant_magnetodielectric_metamaterial.pdf",        "content": " \nGiant magnetodielectric metamaterial \nKe Bi, Ji Zhou*, Xiaoming Liu \nState Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, \nTsinghua University, Beijing 100084, P.R. China \nCorrespondence and requests for materials should be addressed to J.Z. (email: \nzhouji@mail.tsinghua.edu.cn).  \n \nDielectric materials with tunable permittivity are highly desirable for wireless \ncommunication, radar technology. However, the tunability of dielectric properties in the \nmicrowave frequency range and higher is an im mense challenge for conventional materials. \nHere, we demonstrate a giant magnetodielectric effect in the GHz region in a metamaterial \nbased on ferrite unit cells. The effect is de rived from the coupling of the ferromagnetic \nresonance and the Mie resonance in the ferrite unit cells. Both the simulated and experimental \nresults indicate that the effective permittivity of the metamaterial can be tuned by modifying the applied magnetic field, and a gi ant magnetodielectric effect, [ ε'(H) - ε'(0)]/ε'(0) = 15000 % \nat 11.284 GHz, is obtained. This mechanism offers a promising means of constructing microwave dielectrics with large tunable ranges and considerable potential for tailoring via a \nmetamaterial route.  \n \n 1  \nWith the progressing development of wi reless communication and radar technology, \nmicrowave dielectrics with tunable permittivity are highly desired for use as key materials in \nphase shifters, switches, reconfigurab le antenna, and other tunable devices1. However, it is an \nimmense challenge to obtain dielectric materials with high tunability at microwave \nfrequencies and higher. Electrically tunable ferroelectric dielectrics, such as barium strontium \ntitanate (BST),  are well-studied candidates for this purpose2,3. However, these materials have \ncertain limitations, most notably a low tunabi lity scale of less than  21.3 % and high driving \npower; and for these reason, only the dielectric  thin films are available for potential \napplications2. The magnetodielectric effect (MD) offers another approach to permittivity \ntuning4,5. Chen et al.6 have reported a giant MD effect (∆ε '/ε'=1800 % at 3.5 kOe) and a large \nmagnetic-field-tunable dielectric resonance in sp inel MnZn ferrite. However, the MD effect in \nthose materials appears in very low frequenc y (MHz) region and cannot reach the GHz range. \nCastel and Brosseau7 have reported an MD effect at 4.5 GHz in BaTiO 3–Ni nanocomposites. \nHowever, this MD effect ( ∆ε'/ε'=10 % at 2 kOe) is very small. \nMetamaterials are a class of artificial material s in which subwavelength features , rather \nthan the features of the constituent materials, control the macroscopic electromagnetic \nproperties8; this allows more freedom in tailoring of material properties9-12. Recently, Mie-\nresonance-based dielectric metamaterials with  unusual electromagnetic properties have been \ntheoretically and experimentally studied13-15. The permittivity of a dielectric metamaterial is \ndependent only on its electromagnetic parameters ( ε and μ ), the geometry of the dielectric unit \ncell and the cell’s lattice arrangement16-18. In the work, we demonstr ate a giant MD effect in \nthe GHz region in a dielectric metamaterial ba sed on the coupling of the Mie resonance and \nferromagnetic resonance of ferrite in the unit cells. \nResults \nIn the metamaterial, ferrite rods are used as th e unit cells to generate the Mie resonance, as \nillustrated in Fig. 1. Meanwhile, by interacting with the magnetic field of an electromagnetic wave, ferromagnetic resonance can arise in fe rrite under an applied magnetic field. The  \n 2  \neffective permeability of the ferrite  around th e frequency  area of ferromagnetic resonance \ncan be expressed as follows21: \n                                                    ()ω ω ω ωωμ\nΓ − −− =\niF\n2\nmp22\nmp\n11 ,                                           (1) \nwhere Γ(ω) = [ω2/(ω r+ωm)+ωr+ωm]α; ()m r r mp ω ω ω ω+ = ; γπωs m4M= ; Hγω=r ; α is \nthe damping coefficient of  ferromagnetic precession; γ  is the gyromagnetic ratio; F = ωm/ωr; \nωm and ω r are the characteristic frequency and fe rromagnetic resonance frequency of the \nferrite, respectively; Ms is the saturation magnetization caus ed by the applied magnetic field; \nand H  is the applied magnetic field. According to Eq. (1), the permeability of the ferrite can \nbe tuned by adjusting the applied magnetic field.  Dielectric metamateri al unit cells support an \nelectric and magnetic dipole res ponse attributable to Mie resonances. Proper control of the \nelectromagnetic parameters of the unit cell allows for a modulati on over the effective \npermittivity and permeability of the entire me tamaterial. The effective permittivity of a \nstandard cylindrical dielectric res onator can be expressed as follows19: \n() [ ], 11 1 1 a eff, kr BJ Aε μ ε + ≈                                                  (2) \nwhere ε1 and μ 1 are the permittivity and permeability of the dielectric cylinder, respectively; k \nis the wavenumber; J1 is the Bessel function of order 1; r is the radius of the cylinder;  A and  \nB denote the size factor and the item associa ting with electromagnetic parameters of the \ncylinder, which are defined in Refs. [19] and [ 20]. From Eq. (2), we observe that the effective \npermittivity εeff is influenced by the permeability μ1 and the permittivity ε1 of the dielectric \nrod. For the metamaterial composed of fe rrite unit cells, the effective permittivity εeff can be \nestimated by 19 \n∫≈ da a f) (a eff, effε ε ,                                                    (3) \nwhere f(a) is the cell fraction function,  which can be treated as a probability density \ndistribution function of a unit cell with cell size a. From Eqs. (1) - (3), it can be observed that \n 3  \nthe permittivity of the metamaterial can be affected by the permeability of the ferrite rod, \nwhich can be tuned by adjusting the applied magnetic field. \n Figure 2a shows the simulated scattering spec tra for the unit cell of the metamaterial under \na series of applied magnetic fields H. A transmission dip appears at 11.24 GHz in the absence \nof an applied magnetic field.  When a magnetic field of H = 100 Oe is applied, a transmission \ndip occurs at 11.13 GHz. When H is increased from 100 Oe to 1000 Oe, the resonance \nfrequency of the transmission dip increases to  11.51 GHz and exhibits  magnetically tunable \nbehavior. The effective permittivity of the unit cell of the metamaterial under the same series of applied magnetic fields H was extracted from the simulated scattering parameters using a \nwell-developed retrieval algorithm\n22-24. As shown in Fig. 2b, in all cases, remarkable \nfrequency dispersion occurs in the range of 11-12 GHz. The resonance frequency increases as \nH increases, consistent with the behavior observed in Fig. 2a. In addition, the peak value of \nthe effective permittivity increases until it r eaches a maximum and then decreases as H \nincreases further. Figure 2c shows the dependenc e of the effective permittivity of the unit cell \nof the metamaterial on the magnetic field H at 11.296 GHz. The real part of the effective \npermittivity increases until it reaches a maximum (approximately 229) at H = 500 Oe and \nthen decreases as H increases further. The imaginary part of the effective permittivity exhibits \nsimilar behavior. \nTo clarify the underlying physics of the resonance modes with or without applied magnetic \nfield, we simulated the electromagnetic fiel d distribution for the ferrite rod by using CST \nmicrowave studio. Figure 3a and 3b show  the electric field distribution in yz-plane and \nmagnetic field distribution in xy-plane for the ferrite rod with applied magnetic field H = 0 at \n11.24 GHz, respectively. It can be seen that th e induced circulation of displacement currents \nappears in the ferrite rod (Fig. 3a), whic h leads to a nonzero magnetic dipole momentum, \nresulting in a large magnetic field along x axis (Fig. 3b), demonstrating a magnetic resonance \ncharacteristic. Figure 3c and 3d show  the electric field distribution in yz-plane and magnetic \n 4  \nfield distribution in xy-plane for the ferrite rod with applied magnetic field H  = 500 Oe at \n11.296 GHz, respectively. One can see that th e electromagnetic field distribution for the \nferrite rod with the applied magnetic field is  much different from that without applied \nmagnetic field, which is caused by the magnetizat ion of the ferrite. The linearly polarized \ndisplacement currents are exci ted with a resonant pattern similar to electric dipole \ncharacteristic (Fig. 3c). Concomitantly, the ma gnetic field distributi on in Fig. 3d shows a \nvortical pattern supporting the interpretation of an  electric dipole-relate d resonance. On the \nbasis of this analysis of the el ectromagnetic response of a ferrite rod with the identification of \nthe magnetic and electric Mie-type resonances , we realized that th e electric Mie-type \nresonance instead of magnetic resonance moves to the frequency region of 11 GHz - 12 GHz \nafter the magnetization of the ferrite rod. It is known that resonant permittivity will generally \nlead to a dispersion curve. Therefore, we can obt ain the effective permittivity near the electric \nresonance mode by analyzing the disper sion properties of the ferrite rods. \n \n To confirm the results of the above simulations, experime ntal investigations of the \nelectromagnetic properties of this metamateri al were conducted. The microwave measurement \nsystem and a photograph of the metamaterial ar e shown in Fig. 4a. Figure 4b presents the \nexperimental transmission spectra for the meta material under a series of applied magnetic \nfields H. First, in all cases, a transmission dip oc curs in the transmission spectrum. Second, \nwhen H is increased from 100 Oe to 1000 Oe, the re sonance frequency of the transmission dip \nincreases from 11.07 GHz to 11.52 GHz, simila r to the results presented in Fig. 2a. \n The real parts of the effective permittivitie s retrieved from the experimental scattering \nparameters under the same series of applied magnetic fields H are depicted in Fig. 4c. The \nresults reveal remarkable frequency dispersion in the range of 11-12 GHz in all cases. The \nresonance frequency increases as H increases. In addition, the peak value of the effective \npermittivity increases until it reaches a maximum and then decreases as H increases further; \nthus, magnetically tunable behavior is dem onstrated. The dependence of the effective \n 5  \npermittivity of the metamaterial on the magnetic field H  at a series of frequencies f is \npresented in Fig. 4d. In all cases, the real pa rt of the effective permittivity reaches a maximum \nvalue at a certain H, confirming the results presented in Fig. 2b. At 11.284 GHz, the real part \nof the effective permittivity exhibits a re latively high value (approximately 201) at H = 500 \nOe. From the analysis presented above, it is evid ent that the behavior of the experimental data \nis in good agreement with that of the simulated data. In addition, the metamaterial exhibits a \ngiant MD effect, [ ε'(H) - ε'(0)]/ε'(0) = 15000 % at 11.284 GHz. The inset provides a close-up \nof the plot of the effective permittivity vs. the magnetic field. It is clear that the effective \npermittivity depends strongly on the magnetic fiel d, indicating the high tunability of the \ndielectric properties of this metamaterial. \nDiscussion \nWe experimentally and numerically demonstrat ed a giant MD effect in a metamaterial \nbased on ferrite rods in the GHz  region attributable to the coupling of the Mie resonance and \nthe ferromagnetic resonance, in which the eff ective permittivity derived from Mie resonance \nin ferrite unit cells is st rongly dependent on th e applied magnetic field, because a \nferromagnetic resonance take place and dramatica lly change the effective permeability of the \ncell. The giant MD effect makes this metamaterial promising in key devices for wireless \ncommunication and radar technology. \nMaterials and Methods \nSample fabrication. The ferrite material chosen for this work was yttrium iron garnet (YIG) \nferrite. Commercial YIG rods were cut to dimensions of 4 × 4 × 10.8 mm3. The saturation \nmagnetization 4 πMs, linewidth ΔH, and relative permittivity εr of the YIG rods were 1950 Gs, \n10 Oe, and 15, respectively, and the same values  were used in the simulations. The sample \nwas fabricated by inserting the ferrite rods into  a Teflon substrate. The distances between the \nrods in the x direction and z direction were 5 mm a nd 11.8 mm, respectively. \n 6  \nSimulations.  The dimensions of the unit cell were 5 × 5 × 11.8 mm3. The YIG cuboid rod \nwas modeled with dimensions of w × w × h mm3, where w = 4 mm and h = 10.8 mm. The \nsaturation magnetization 4 πMs, linewidth ΔH, and relative permittivity εr of the YIG rod were \nthe same as those in the experiments. A plane wave was assumed for the incident \nelectromagnetic field, with polarization conditions corresponding to an electric field along the \nx axis and a magnetic field along the y axis. The bias magnetic field was applied in the z \ndirection. Numerical predictions of the tr ansmission spectra were calculated using the \ncommercial time-domain package CST Microwave Studio TM. \nMicrowave measurements. The sample was placed between two horn waveguides connected \nto an HP 8720ES network analy zer, as shown in Fig. 3a. Th e propagation of the incident \nelectromagnetic wave was along the y axis, and the electric field and magnetic field were \nalong the z and x axes, respectively. The bias magnetic  field provided by the electromagnets \nwas applied in the z direction. \n \nReferences  \n1 Kim, K. T. & Kim, C. I. Structure and dielectrical prope rties of (Pb,Sr)TiO 3 thin films \nfor tunable microwave device. Thin Solid Films 420-421 , 544-547 (2002). \n2 Cole, M. W., Nothwang, W. D., Hubbard, C., Ngo, E. & Ervin, M. Low dielectric loss \nand enhanced tunability of Ba 0.6Sr0.4TiO 3 based thin films via material compositional \ndesign and optimized film processing methods. J. Appl. Phys. 93, 9218-9225, (2003). \n3 Colea, M. W., Joshia, P. C., Ervina, M.  H., Wooda, M. C. & Pfefferb, R. L. The \ninfluence of Mg doping on the materials properties of Ba 1-xSrxTiO 3 thin films for \ntunable device applications. Thin Solid Films 374, 34-41 (2000). \n4 Somiya, Y., Bhalla, A. S. & Cross, L. E. Study of (Sr,Pb)TiO 3 ceramics on dielectric \nand physical properties.  Int. J. Inorg. Mater.  3, 709-714 (2001). \n5 Stingaciu, M., Reuvekamp, P.  G., Tai, C. W., Kremer, R. K. & Johnsson, M. The \nmagnetodielectric effect in BaTiO 3–SrFe 12O19 nanocomposites. J Mater. Chem. C  2, \n325, (2014). \n6 Chen, Y., Zhang, X.-Y., Vittoria, C. & Harris, V. G. Giant magnetodielectric effect \nand magnetic field tunable dielectric resonance in spinel MnZn ferrite. Appl. Phys. \nLett. 94, 102906, (2009). \n7 Castel, V. & Brosseau, C. Magnetic field dependence of the eff ective permittivity in \nBaTiO 3/Ni nanocomposites observed via microwave spectroscopy. Appl. Phys. Lett. \n92, 233110, (2008). \n8 Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and Negative \nRefractive Index. Science 305, 788-792, (2004). \n 7  \n9 Bi, K., Dong, G., Fu, X. & Zhou, J. Ferri te based metamaterials with thermo-tunable \nnegative refractive index. Appl. Phys. Lett. 103, 131915, (2013). \n10 Schurig, D.  et al. Metamaterial Electromagnetic Cloak at Microwave Frequencies. \nScience 314, 977-980, (2006). \n11 Chen, P.-Y., Farhat, M. & Alù, A. Bi stable and Self-Tunable Negative-Index \nMetamaterial at Optical Frequencies. Phys. Rev. Lett. 106, 105503, (2011). \n12 Wu, Y., Lai, Y. & Zhang, Z.-Q. Elastic Metamaterials with Simultaneously Negative \nEffective Shear Modulus and Mass Density. Phys. Rev. Lett. 107, 105506, (2011). \n13 Zhao, Q., Zhou, J., Zhang, F. L. & Lippens, D. Mie resonance-based dielectric \nmetamaterials. Mater. Today 12, 60-69 (2009). \n14 Kang, L. & Lippens, D. Mie resonance base d left-handed metamaterial in the visible \nfrequency range. Phys. Rev. B  83, 195125, (2011). \n15 Kuznetsov, A. I., Miroshni chenko, A. E., Fu, Y. H., Zhang, J. & Luk'yanchuk, B. \nMagnetic light. Sci. rep. 2, 492, (2012). \n16 Zhang, F. L., Kang, L., Zhao, Q., Zhou,  J. & Lippens, D. Magnetic and electric \ncoupling effects of dielectric metamaterial. New J. Phys. 14, 033031, (2012). \n17 Zhao, Q.  et al. Experimental Demonstration of Is otropic Negative Permeability in a \nThree-Dimensional Dielectric Composite. Phys. Rev. Lett. 101, 027402, (2008). \n18 Zhao, Q.  et al. Isotropic negative permeability composite based on Mie resonance of \nthe BST-MgO dielectric medium. Chin. Sci. Bull. 53, 3272-3276, (2008). \n19 Peng, L.  et al. Experimental Observation of Left-Handed Behavior in an Array of \nStandard Dielectric Resonators. Phys. Rev. Lett. 98, (2007). \n20 Tsang, L., Kong, J. A. & Ding, K. H. Scattering of Electromagnetic Wave . Vol. 1 41 \n(Wiley, 2000). \n21 Zhao, H., Zhou, J., Kang, L. & Zhao, Q. Tunable two-dimensional left-handed \nmaterial consisting of ferrite rods and metallic wires. Opt. Express 17, 13373-13380 \n(2009). \n22 Smith, D. R., Schultz, S., Markoš, P. & Soukoulis, C. M. Determination of effective \npermittivity and permeability of metamaterials from reflection and transmission \ncoefficients.  Phys. Rev. B  65, 195104 (2002). \n23 Croënne, C., Fabre, B., Gaillot, D., Vanbésien, O. & Lippens, D. Bloch impedance in \nnegative index photonic crystals Phys. Rev. B  77, 125333 (2008). \n24 Chen, X., Grzegorczyk, T. M., Wu, B., P acheco, J. & Kong, J. A. Robust method to \nretrieve the constitutive effective parameters of metamaterials. Phys. Rev. E  70, \n016608 (2004). \n \nAcknowledgments \nThis work was supported by the National High Technology Research and Development \nProgram of China under Grant No. 2012AA030403;  the National Natural Science Foundation \nof China under Grant Nos. 51402163, 61376018, 51032003, 11274198, 51102148 and \n51221291; and the China Postdoctoral Resear ch Foundation under Grant Nos. 2013M530042 \nand 2014T70075.  \nAuthor contributions \n 8  \nJ.Z. conceived and designed the experiments.  K.B. and X.M.L. performed the experiments \nand the numerical calculations. K.B. and J.Z. wrote the paper. All au thors contributed to \nscientific discussions and the critical revision of the article.  \n \nAdditional information \nCompeting financial interests:  The authors declare no competing financial interests. \n \n 9  \nFigures \n \nFigure 1 | Schematic diagram of the ferrite-based me tamaterial illustrating the effect of \nthe ferromagnetic resonance on the electric Mie-type resonance.  The length of the ferrite \nrod is parallel to the z axis. The propagation of the incident electromagnetic wave is along the \ny axis, and the electric field and magnetic field are along the z and x  axes, respectively. The \nbias magnetic field is applied in the z direction.  \n 10  \n \nFigure 2 | Simulated transmission spectra.  (a) Simulated transmission spectra for the unit \ncell of the metamaterial under a se ries of applied magnetic fields H . (b) Real parts of the \neffective permittivities retrieved from the simu lated scattering parameters under a series of \napplied magnetic fields H. (c) Magnetic-field dependence of the effective permittivity of the \nunit cell of the metamaterial at 11.296 GHz. \n 11  \n \nFigure 3 | Electric and magnetic  field distributions.  Simulated ( a) electric field distribution \nin yz-plane and ( b) magnetic field distribution in xy-plane for the ferrite rod with applied \nmagnetic field H  = 0 at 11.24 GHz; Simulated ( c) electric field distribution in yz-plane and ( d) \nmagnetic field distribution in xy-plane for the ferrite rod with applied magnetic field H = 500 \nOe at 11.296 GHz. \n \n 12  \n 13 \n \nFigure 4 | Experiment demonstrating th e magnetodielectric effect.  (a) Diagram of the \nexperimental setup. The sample is placed be tween two horn waveguides. The propagation of \nthe incident electroma gnetic wave is along the y axis, and the electric field and magnetic field \nare along the z and x  axes, respectively. The bias ma gnetic field is generated by an \nelectromagnet in the z direction. The inset shows a photograph of the metamaterial. ( b) \nExperimental transmission spectra for the meta material under a series of applied magnetic \nfields H. (c) Real parts of the effective permittivities retrieved from the experimental \nscattering parameters under a seri es of applied magnetic fields H. (d) Magnetic-field \ndependence of the effective permittivity of the metamaterial at a series of frequency f. The \ninset provides a close-up of the plot of the effective permittivity vs. the magnetic field that \nillustrates the strong dependence of the permittivity on the magnetic field. \n \n  \n "    },    {        "title": "2212.14861v1.Preparation_of_CuxCe___0_3_X__Ni___0_7__Fe__2_O__4__ferrite_nanoparticles_as_a_nitrogen_dioxide_gas_sensor.pdf",        "content": "Preparation of Cu xCe0.3-XNi0.7Fe2O4 ferrite nanoparticles as a nitrogen dioxide \ngas sensor  \nShaymaa A . Kadhim 1 and Tagreed M. Al - Saadi2 \n1,2College of Education for Pure Science/Ibn Al - Haitham, University of Baghdad, Baghdad, Iraq  \n1Shaimaa.Ahmed1104a@ihcoedu.uobaghdad.edu.iq  \nAbstract: In this work, the ferrite nanocomposite Cu xCe0.3-XNi0.7Fe2O4 is prepared (where: x = 0, 0.05, 0.1, \n0.15, 0.2, 0.25) was prepared using th e auto combustion technique (sol -gel), and citric acid was utilized as \nthe fuel for Auto  combustion. The results of X -ray diffraction (XRD), emitting field scanning electron \nmicroscope (FE -SEM), and energy dispersive X -ray analyzer (EDX) tests revealed tha t the prepared \ncompound has a face -centered cubic structure (FCC) polycrystalline, and the lattice constant increases with \nan increase in the percentage of doping for the copper ion, and decreases for the cerium  ion and that the \ncompound is porous, and its  molecules are spherical, and there are no additional elements present other \nthan those used in the synthesis of the compound, indicating that it is of high purity, and the combination \nhas a high sensitivity to Nitrogen dioxide (NO 2) gas, as determined by the gas detecting equipment.  \nKey words: nano ferrite, structural properties, NO 2 gas, sensitivity.  \n1. Introduction:  \n       The need for sensors for hazardous gases including CO, CO 2, NO 2, H 2S, and others has seen growing \nattention as environmental pollutio n concerns and awareness of the need to monitor hazardous gases grow. \nA variety of solid -state device sensors for gases have been developed as a result of the demand for  their \ndetection and monitoring [1]. The popularity of semiconductor -based chemical sen sors is due to their \ncompact size, straightforward operation, high sensitivity, selectivity, and reasonably straightforward \nauxiliary electronics [2]. However, the lack of selectivity is a disadvantage when detecting a target gas in a \nmixture of gases. One  of the most prevalent methods of increasing sensor selectivity and sensitivity is \ndoping with different compounds [1, 3]. The use of various unique semiconductor oxides as sensing \ncomponents for gas sensing in bulk ceramics, thick films, and thin -film forms has been investigated [4]. \nSpinel ferrites have been employed as an alternative material in the gas sensor business. Several sensors \nwill be considered before focusing on ferrites as gas sensors, their crystal structure, and manufacturing \nprocess es. Gas sensors detect changes in the electrical, acoustic, visual, mass, or calorimetric characteristics \nof a substance. Because it is simple, quick, and inexpensive, detection based on variations in electrical \ncharacteristics is receiving the most attent ion. The need for sensors to be integrated into smart devices for \nremote sensing is increasing, and portability and operating system compatibility are hastening the \ndevelopment of ele ctrical detection -based sensors [5, 6]. It has been discovered that MFe2O 4 type spinel \nsemiconductor oxides are a sensitive formula. Substances react with bo th oxidizing and reducing gases [7]. \nResearchers are interested in nano -ferrites because of their readily adjustable properties and wide range of \npotential applications in sensors, microwave devices, magnetic recording, adsorbents, and data storage. \nHundreds of metal oxide materials are utilized as active layers in the spinel ferrite structure of gas sensors \nas thick or extremely thin films for the cation site. Spinel is mad e up of 32 oxygen atoms arranged in a \ncubic crystal form with 64 tetrahedral sites. 32 -site octahedral gas sensors can help with chemical \nmanagement, home security, and environmental monitoring. More new materials are being explored for \nhigh-performance so lid-state gas sensors [8]. The ferrite's structural, electrical, and magnetic properties are \nimpacted by the Fe -Fe reactions. [9]. Finally, the purpose  of this work is to investigate the effect of replacing \nCe ion with Cu on the structural and sensitivity to NO 2 gas features of (sol -gel) generated ferrite \nnanoparticles Cu xCe0.3-XNi0.7Fe2O4. 2. Experimental:  \n          Auto combustion (sol -gel) was employed to prepare the raw materials for utilization. CuxCe0.3-\nxNi0.7Fe2O4. The chemicals collected are listed in Table (1).  \nTable (1). Masses of raw materials used in the preparation of ferrite nanocomposite samples Cu xCe0.3-\nxNi0.7Fe2O4 and their molar ratios.  \niron nitrate  nickel nitrate  copper nitrate  cerium  nitrate  citric acid  \nm(g)  n m(g)  n m(g)  nx m(g)  n0.3-x m(g)  n \n32.32  2 8.14268  0.7 0 0 5.21075  0.3 23.0556  3 \n32.32  2 8.14268  0.7 0.4832  0.05 4.3423  0.25 23.0556  3 \n32.32  2 8.14268  0.7 0.9664  0.1 3.47384  0.2 23.0556  3 \n32.32  2 8.14268  0.7 1.4496  0.15 2.60538  0.15 23.0556  3 \n32.32  2 8.14268  0.7 1.9328  0.2 1.73692  0.1 23.0556  3 \n32.32  2 8.14268  0.7 2.416  0.25 0.86846  0.05 23.0556  3 \n \nIn a 1000 mL heat -resistant glass beaker, the metal nitrate was added to 40 ml of water. In a separate beaker, \nthe citric acid was added, then (40 ml) of deionized water, and finally the acid solution to the nitrate solution. \nThe two solutions are thorough ly blended without heating using a magnetic stirring device, and then a little \namount of ammonia in the form of drops was added to the mixture until the pH is equalized to (7). The \nmagnetic stirrer heater is then activated until the mixture reaches about ( 90℃). The mixing process was \ncontinued with heating until the mixture became a gel, at which point the stirrer motor is turned off, while \nthe heating continued until the gel ignites automatically and entirely. The resultant ferrite is then allowed \nto cool before being ground with a mortar. The nano ferrite powder is then placed in the oven for two hours \nfor each sample.  The structural characteristics of the resultant ferrite powder are then examined using XRD, \nFE-SEM, and EDX methods. Following the measurem ents, 1.5 g of powder from each sample was collected \nand physically pressed for one minute at 200 bar pressure, resulting in a disc with a diameter of 1 cm and a \nthickness of 3.5 mm for each sample. After two hours in the oven at 900℃, six samples of the s ynthesized \nferrite were generated. The gas sensitivity method was then used to make electrodes for each sample and \nassess their sensitivity to NO 2 gas. \n3. Results and Discussion :  \n3.1.  X-Ray Diffraction : \nFigure (1) represents the X -ray diffraction patterns of CuxCe0.3-xNi0.7Fe2O4  nano f errite samples that match \nthe NiFe 2O4 diffraction pattern of JCPDS Standard Card No. (10-0325 ). \nThe X -ray diffraction patterns of the prepared ferrites samples show more tha n seven clear peaks within the \nrange (20 °-80°) belonging to the surfaces: (111), (220), (311), (400), (422), (511), and (440), and the \napparent peaks indicate the nature of the crystal structure of the prepared compound's ferrite powder, which \nwas of the face-centered cubic spinel -type (FCC) [10].  \nThe lattice parameters were determined using the \"Fullprof suit software,\" and the crystallite size was \ncalculated using the \"Scherrer equation\" [11, 12].  \n𝐷𝑆ℎ = 𝐾 λ / β cosθ      ………………………………………………………… (1)  \nWher e: λ the wavelength of X -ray (1.54 Å), β the full width at half maximum, and θ the incident angle.    \n \n \n \n \n \n \n \n \n \nFigure (1). The X -ray diffraction patterns of Cu xCe0.3-XNi0.7Fe2O4 ferrite nanocomposite samples.  \nTable (2). Lattice constants (lattice constant, crystallite size and density) . \n \n           \n \n \n  \n \nBy comparing the data in Table (2) to the molar concentrations of copper ion (x = 0, 0.05, 0.1, 0.15, 0.2, \n0.25, 0.3) with the exception of one reading in Table (2), it can observe that the  lattice constant increases \nas the proportion of copper ion increases. The addition of dopants and their increasing ratio raises the value \nof the lattice constant due to the migration of iron cations Fe+3 from the tetrahedral spaces to the octahedral \nspace s to be replaced by impurity cations and the widening of the tetrahedral spaces as a consequence of \nthe additional impurities [13]. The surface reconstruction also has an effect on the lattice constant, affecting \nits value. Because nanocrystals have a high  surface area to volume ratio, this shift in the lattice constant \nvalue is very important [14]. This change in the lattice constant indicates that alternative ions entered the \ncrystal structure in a substitution or interstitial manner between the iron ions , resulting in lattice widening \nand a decrease in density, which may also be attributed to extra impurities [15].  \n3.2. SEM and EDX Analysis : \nSamples of the prepared ferrite ( CuxCe0.3-XNi0.7Fe2O4) were photographed using the Field emission scanning \nelectron  microscopy (FE -SEM) technique to clearly characterize the nature of the surface and shape of the \nparticles, as well as their rate of grain size. Figure (2) demonstrates that the material is truly in the nanoscale \nrange. The nanoparticles of the specified material are spherical or semi -spherical in form, with some \ngroupings or agglomerations. There are also spaces between the conglomerates or agglomerations in the \narea, and these holes indicate the porous quality of the substance's surface, which is require d for gas Cu Content \n(mole)  Lattice constant \n(Å) Crystalli te size \n(nm)  Density \n(g/cm3) \n0 \n0.05 \n0.1 \n0.15 \n0.2 \n0.25 \n 8.33375  \n8.34517  \n8.34678  \n8.35238  \n8.34467  \n8.35222  26.35101482  \n30.41050846  \n29.47659557  \n31.86366219  \n28.51289329  \n23.46597741  5.314  \n5.292  \n5.289  \n5.278  \n5.293  \n5.279  0100020003000400050006000700080009000\n0 10 20 30 40 50 60 70 80 90Intensity (a.u.)\n2Ɵ (degree)x=0x=0.05x=0.1x=0.15x=0.2x=0.25(111)(221)(311)\n(400)(422)(511)(440)adsorption [16]. The existence of holes is caused by the presence of impurities, which raises the value of \nthe crystal lattice constant, increasing the specific surface area with respect to the compound's volume. The \nabove results in the formatio n of a porous structure, which improves the sensor's reaction to the test gas \n[17].  \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure (2) . FE-SEM images of the Cu xCe0.3-xNi0.7Fe2O4 ferrite nanocomposite samples.  \nThe energy -dispersive X -ray spectroscopy (EDS) used in conjunction with the emitting field scanning \nelectron microscope (FE -SEM) to confirm the presence of the elements of the prepared compound ( CuxCe0.3-\nxNi0.7Fe2O4), as sho wn in Figure (3), shows that all of the elements of the two prepared compounds appear \nand that all samples are pure and free of impurities.  \n \n \n  \n \n \n \n  \n \nX=0 X=0.05  \nX=0.1  X=0.15  \nX=0.2  X=0.25    \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFigure (3). EDS images of the ferrite nanocomposite samples Cu xCe0.3-xNi0.7Fe2O4 \n3.3. Sensing properties:  \nEquation (2) [18] was used to calculate the sensitivity of CuxCe0.3-xNi0.7Fe2O4 samples to nitrogen dioxide  \ngas ( NO 2), and the results indicated that the sensitivity to NO 2 gas changes as the operating temperature \nchanges, as illustrated in Figure (4).   \nS = (|Ra - Rg|/Ra)*100%    …………………………………………………………… (2)  \nWhere: Where: Ra the sensor model's electrical resistance in air , Rg the gas -sensitive model's electrical \nresistance.  \n  \n \n \n  \n  \n \n  \n \n  \nX=0 X=0.05  \nX=0.1  X=0.15  \nX=0.2  X=0.25  \n 0510152025\n150 250 350Sensitivity (%)\nOperation temperature (oC) \n 010203040\n150 250 350Sensitivity (%)\nOperation temperature (oC) X=0 X=0.05   \n \n \n \n \n \n \n \n \n \n \n \n \nFigure (4) . The sensitivity relationship to the operating temperature of the Cu xCe0.3-xNi0.7Fe2O4 samples.  \n \nTable (3) shows the highest sensitivity values for the samples of the prepared compound, and it is noted \nthat the highest sensitivity value was at 300 ⁰C when Cu Content is 0.20 mole . \nTable (3). The highest sensitivity value s of the  NO 2 gas  for C uxCe0.3-xNi0.7Fe2O4 nanoparticles . \n \n \n \n \n \n \n \n \n \nThe sensitivity of CuxCe0.3-xNi0.7Fe2O4 samples to oxidizing nitrogen dioxide (NO 2) was investigated. The \nsamples demonstrated an acceptable response to the aforementioned gas, allowing it to be used in various \napplications. The voltage barrier between the surfaces of molecules is considerable in oxidizing gases, \nresulting in more resistance to the flow of negative charge carriers, which are el ectrons, than in reducing \ngases [19]. The results reveal that the activation process of the ferrite nanoparticles NiFe 2O4 raises  the value \nof the crystal lattice constant, resulting in a porous structure that raises the specific surface area of the \ncompound and, as a result, raises the senso r's sensitivity to the test gas [20].  \n Cu Content \n(mole) Operating temperature ( ℃)  Highest sensitivity value \n(%) \n0 \n0.05 \n0.1 \n0.15 \n0.2 \n0.25 200 \n200 \n200 \n200 \n300 \n200 33.2197615  \n22.02247191  \n31.89987163  \n24.0987984  \n34.28285857  \n28.50678733   010203040\n150 250 350Sensitivity (%)Operation temperature (oC)  010203040\n150 250 350Sensitivity (%)\nOperation temperature (oC) \n 0102030\n150 250 350Sensitivity (%)Operation temperature (oC)  0102030\n150 250 350Sensitivity (%)\nOperation temperature (oC) X=0.1  X=0.15  \nX=0.2  X=0.25    \n \n \n \n \n \n \n  \n \n \n \n \n  \n \n \n \n \n \n \nFigure ( 5). Relationship of response time and recovery time of NO 2 gas at operating temperature for \nferrite nanoparticles CuxCe0.3-xNi0.7Fe2O4. Where the red line represents the response time, while the blue \nline represents the recovery time  \nFigure (5) illustrates that due to the impurities' influence on the lattice constant value, the addition of \nimpurities to each new ion in specific proportions influences both the reac tion time and the recovery time \n[21]. The reaction time and recovery time are influenced by the speed of the interaction between oxygen \natoms in the environment and the gas atoms to be detected with atoms of the granular surface of the sensor \nmaterial, as well as the geomet ric form of the columns or electrodes. In turn, these two parameters are \naffected by the operating temperature as an external, readily controllable component, as w ell as the structure \nof the sample [22]. Because there are times when the same sample has a f aster reaction and recovery time, \nthe samples that best fit the required application are picked.  \nTable (4) ) shows that the minimum response time for NO 2 gas for samples of the prepared compound \nwas at an operating temperature of 200 °C, while the minimum recovery time was at an operating \ntemperature of 300  °C. \n  020406080100\n23242526272829\n150 250 350\nRecovery Time (S)Responce Time (S)\nOperation Temperature (oC)  020406080100120\n2526272829\n150 250 350\nRecovery Time (S)Responce Time (S)\nOperation Temperature (oC) \n 020406080100\n15202530\n150 250 350\nRecovery Time (S)Responce Time (S)\nOperation Temperature (oC)  050100150\n2021222324\n150 250 350\nRecovery Time (S)Responce Time (S)\nOperation Temperature (oC) \n 020406080100\n0102030\n150 250 350\nRecovery Time (S)Responce Time (S)\nOperation Temperature (oC)  020406080100\n051015202530\n150 250 350\nRecovery Time (S)Responce Time (S)\nOperation Temperature (oC) X=0.05  \n \nX=0.15  \n X=0 \n \nX=0.10  \n \nX=0. 20 \n X=0.25  \n  \nTable (4): Minimum response time and recovery time for ferrite nanoparticles Cu xCe0.3-xNi0.7Fe2O4 \nsamples to NO 2 gas.  \nContent        \n(mole) Minimum \nresponse time \n(sec) Operating \ntemperature (⁰C) Minimum \nrecovery time \n(sec) Operating \ntemperature (⁰C) \n0 \n.0.0 \n.00 \n.000 \n.00 \n.000 \n 24.3 \n26.1 \n21.6 \n20.7 \n21.6 \n23.4 \n 200,250  \n300 \n0.. \n200 \n200 \n300 \n 45.9 \n38.7 \n50.4 \n63 \n46.8 \n48.6 \n 300 \n0.. \n0.. \n0.. \n0.. \n0.. \n \n \n4. Conclusion:  \n            The auto-combustion sol -gel approach was utilized to effectively produce nickel, cerium, and \ncopper ferrite single -phase nanoparticles (Cu xCe0.3-xNi0.7Fe2O4). The XRD and FE -SEM examinations of \nthe manufactured chemical samples indicated that it is a ferrite nanoparticle of a kind of spinel with a multi -\ncrystalline face -centered cubic (FCC) structure and is monophasic. This increased the specific surface area \nof the compound, and doping the resulting compound with aluminum improved its crystal lattice constant . \nThe samples made for the compound demonstrated an acceptable sensitivity to NO 2 gas at various operating \ntemperatures, with the samples recording the highest sensitivity to it at an operating temperature of 300 °C, \nand the samples' minimum response time was at 200 °C, while the minimum recovery time was at 300 °C.  \n5. References:  \n1. Devi, G. S., Manorama, S., & Rao, V. J. (1995). High sensitivity and selectivity of an SnO2 sensor to \nH2S at around 100° C.  Sensors and Actuators B: Chemical , 28(1), 31 -37. \n2. Maekawa, T., Tamaki, J., Miura, N., & Yamazoe, N. (1991). Sensing behavior of CuO -loaded SnO2 \nelement for H2S detection.  Chemistry Letters , 20(4), 575 -578. \n3. Tamaki, J., Maekawa, T., Miura, N., & Yamazoe, N. (19 92). CuO -SnO2 element for highly sensitive and \nselective detection of H2S.  Sensors and Actuators B: Chemical , 9(3), 197 -203. \n4. Wang, C., Yin, L., Zhang, L., Xiang, D., & Gao, R. (2010). Metal oxide gas sensors: sensitivity and \ninfluencing factors.  sensors , 10(3), 2088 -2106.  \n5. Deng, Y. (2019). Sensing mechanism and evaluation criteria of semiconducting metal oxides gas sensors. \nIn Semiconducting Metal Oxides for Gas Sensing  (pp. 23 -51). Springer, Singapore.  \n6. Ayesh, A. I., Alyafei, A. A., Anjum, R. S., Mo hamed, R. M., Abuharb, M. B., Salah, B., & El -Muraikhi, \nM. (2019). Production of sensitive gas sensors using CuO/SnO2 nanoparticles.  Applied Physics A , 125(8), \n1-8. \n7. Jain, A., Baranwal, R. K., Bharti, A., Vakil, Z., & Prajapati, C. S. (2013). Study of Zn-Cu ferrite \nnanoparticles for LPG sensing.  The Scientific World Journal , 2013 . \n8. Laith Saheb1 , Tagreed M. Al -Saadi (2021). Synthesis, Characterization, and NH 3 Sensing Properties \nof (Zn 0.7 Mn 0.3-x Cex Fe2O4) Nano -Ferrite. Journal of Physics: Conferenc e Series 2114 , 012040.  9. Ahmed, O. A., Abed, A. H., & Al‐Saadi, T. M. (2022, February). Magnetic Properties and Structural \nAnalysis of Ce‐Doped Mg –Cr Nano‐Ferrites Synthesized Using Auto‐Combustion Technique. \nIn Macromolecular Symposia  (Vol. 401, No. 1, p . 2100311).  \n10. Tsvetkov, M., Milanova, M., Ivanova, I., Neov, D., Cherkezova -Zheleva, Z., Zaharieva, J., & Abrashev, \nM. (2019). Phase composition and crystal structure determination of cobalt ferrite, modified with Ce, Nd \nand Dy ions by X -ray and neutron diffraction.  Journal of Molecular Structure , 1179 , 233 -241. \n11. Musa, K. H.,  Al-Saadi, T. M.  (2022). Investigating the Structural and Magnetic Properties of Nickel \nOxide Nanoparticles Prepared by Precipitation Method.  Ibn Al -Haitham Journal For Pure and A pplied \nSciences , 35(4).  \n12. Mustafa, H. J., & Al -Saadi, T. M. (2021). Effects of Gum Arabic -Coated Magnetite Nanoparticles on \nthe Removal of Pb Ions from Aqueous Solutions.  Iraqi Journal of Science , 889 -896. \n13. Al-Saadi, T. M., Abed, A. H., & Salih, A. A. (2018). Synthesis and Characterization of Al yCu0.15Zn0. 85 -\nyFe2O4 Ferrite Prepared by the Sol -Gel Method.  Int. J. Electrochem. Sci , 13, 8295 -8302.  \n14. Al-Saadi, T. M., & Jihad, M. A. (2016). Preparation of graphene flakes and studying its structural \nproperties.  Iraqi Journal of Science , 57(1), 145 -153. \n15. Kumar, A., Arora, M., Yadav, M. S., & Panta, R. P. (2010). Induced size effect on Ni doped nickel \nzinc ferrite nanoparticles.  Physics Procedia , 9, 20-23. \n16. Jacob, B. P., Thankachan, S., Xavier, S., & Mohammed, E. M. (2012). Dielectric behavior and AC \nconductivity of Tb3+ doped Ni 0.4Zn0.6Fe2O4 nanoparticles.  Journal of Alloys and Compounds , 541, 29-35.  \n17. Hankare, P. P., Vader, V. T., Patil, N. M., Jadhav, S. D., Sankpal, U. B., Kadam, M. R., ... & Gajbhiye,  \nN. S. (2009). Synthesis, characterization and studies on magnetic and electrical properties of Mg ferrite  \nwith Cr substitution.  Materials Chemistry and Physics , 113(1), 233 -238. \n18. Suryawanshi, S. S., Deshpande, V. V., Deshmukh, U. B., Kabur, S.  M., Chaudhari, N. D., & Sawant, \nS. R. (1999). XRD analysis and bulk magnetic properties of Al3+ substituted Cu –Cd ferrites.  Materials \nchemistry and physics , 59(3), 199 -203. \n19. Vader, V. T., Pandav, R. S., & Delekar, S. D. (2013). Structural and electrica l studies on sol –gel \nsynthesized fine particles of Mg –Ni ferrichromite.  Journal of Materials Science: Materials in \nElectronics , 24(10), 4085 -4091.  \n20. Xuan, J., Zhao, G., Sun, M., Jia, F., Wang, X., Zhou, T., ... & Liu, B. (2020). Low -temperature operating  \nZnO-based NO 2 sensors: a review.  RSC advances , 10(65), 39786 -39807.  \n21.Yahya, K. (2010).  Characterization of Pure and Dopant TiO 2 Thin Films for Gas Sensors \nApplications,”  (Doctoral dissertation, Ph. D Thesis, University of Technology Department of Applied \nScience, 1 -147).  \n22. Yüce, A., & Saruhan, B. (2012). 1.1. 3 Al -doped TiO2 semiconductor gas sensor for NO2 -detection at \nelevated temperatures.  Tagungsband , 68-71. \n "    },    {        "title": "1506.00505v1.Evaluation_of__BH_max_and_magnetic_anisotropy_of_cobalt_ferrite_nanoparticles_synthesized_in_gelatin.pdf",        "content": "1 \n Accepted to be published in Ceramics International: 10.1016/j.ceramint.2015.05.14 8 \n \nEvaluation of  (BH)max and magnetic anisotropy of cobalt ferrite nano particles  \nsynthesized in gelatin  \n   \nA. C. Lima1, M. A. Morales1*, J. H. Araújo1, J. M. Soares2, D. M. A. Melo3, A. S. Carriço1. \n1Departamento de Física Teórica e Experi mental , UFRN, Natal, RN 59078 -970, Brazil  \n2Departamento de Física , UERN, Mossoró, RN 59610 -210, Brazil  \n3Programa de Pós -Graduação em Ci ência e Engenharia de Materiais , UFRN , Natal, RN 59078 -970, \nBrazil  \n*Corresponding author.  \nE-mail address: Marco.MoralesTorres @gmail.com ( M.A. Morales ) \nAbstract  \nCoFe 2O4 nanoparticles were synthesized using gelatin as a polymerizing  agent. Structural , \nmorpholog ical and magnetic properties  of samples  treated  at different  temperatures were  investigated  by \nX-ray diffraction , scanning electron microscopy, Mössbauer spectroscopy  and magnet ization \nmeasurements . Our results  revealed  that the sample s annealed at 623 K and temperatures above 973 K \nhave a cation distribution s given by  (Co 0.19Fe0.81)[Co 0.81Fe1.19]O4 and (Co 0.06Fe0.94)[Co 0.94Fe1.06]O4, \nrespectively . The particle  sizes varied from 73 to 296 nm  and the magnetocrystalline anisotropy, K 1, has \nvalues ranging from 2.60x106 to 2.71x106 J/m3, as det ermined from the law of approach to s aturation  \napplied to the M xH data at high field . At 5 K, the saturation magnetization , coercive field and (BH) max \nvaried from 76 to 9 5 Am2/kg, 479.9  to 278.5 kA/m  and 9.7 to 20.9 kJ/m3, respectively . The reported \nvalues are in good  agreement with near-stoichiometric cobalt ferrite  samples . \n \nKeywords:   Gelatin ; CoFe2O4 ;  Mössbauer spectroscopy;  Magnetic properties ; nanoparticles .  \n \n \n 2 \n 1. Introduction  \nRecently , there is a considerable interest  in research for n ew methods to synthesize no n  rare \nearth based hard magnetic materials. Accordingly, magnetic ferrites have drawn attention due their wide \ntechnological applications [1-2]. CoFe 2O4 is a well -known magnetic material with  high coercivity and \nremanence, moderate saturation magnetization, good  chemical stabilit y and mechanical hardness [ 3-4]. \nThese characteristics  make  it a candidate in applications such as magnetic recording, permanent magnets , \nmagneto -hyperthermia, magnetic drug delivery  and magnetic resonance imaging [ 5-6]. However , to \nobtain Co ferrites  for these  applications  is important to optimize  their chemical composition, structure and \nmagnetic  properties . These  properties  are sensitive to shape  and particle  size as well as  the occupancy of \ntetrahedral and octahedral  sites by the metal ions [ 7].  \nSeveral  methods to synthesize CoFe 2O4 nano particles have  been extensively studied , such as sol -\ngel process , thermal decomposition, co -precipitation, microemulsions, hydrothermal, and combustion  \nreaction  [8-10]. Among these , solution -phase chemical methods have att racted attention  because allow to \nprepare  nanocrystalline materials with high purity and controlled particle size  at relatively low \ntemperatures.  \nRecent works  have reported  a wet chemical method using gelatin as a polymerizing  agent  [11-\n13]. Gelatin is a protein produced by partial hydrolysis of collagen extracted from bon es, connective \ntissues, organs of animals such as cattle, pigs, and  horses. Because  its solubility in water and ability to \ninteract with metal ions in solution through the amino and carbo xylic groups present in its structure , \ngelatin  can be used as  a binder gel  to synthesize nanometer scale precursor particles . After the burning of \nthis gel, nanof errites phases can be obtained  at lower  temperature compared to  other methods [ 13].  \nCosta et al. [11] have synthesized CuFe 2O4 and CuFeCrO 4 nanoparticles using gelatin  for \napplication as ceramic pigments.  Their results showed that the onset of crystallization of samples \noccurred  at 625 K , but the spinel phase was obtained at temperatures  above 775 K. For the CuFe 2O4 and \nCuFeCrO 4 phases, t he crystallite  sizes ranged  from 50 to 70 nm and 47 to 60 nm, respectively . \nFurthermore, they observed that color of pigments varied as a function of composition and heat treatment . \nPeres et al. [12] prepared NiCo 2O4 nanoparticles  using Ni and Co nitrates and commercial gelatin [12]. \nThe results show ed the formation of NiCo 2O4 and Ni xCo1−xO phases  with sizes ranging from 2 0 to 100 \nnm, when the sample was annealed  from 633 to 1223  K. 3 \n Despite several studies found in the literature, we noted that there is no t any report on the \nsynthesis of  Co ferrites by chemical method using gelatin. Thus,  the aim of this work is to report  the \npreparation  of Co ferrite by this method  and study its chemical composition , structur e and magnetic  \nproperties .  \n  \n2. Experimental  \n Cobalt ferrite  nanoparticles  were synthesized by using Co(NO 3)2.6H 2O (VETEC), \nFe(NO 3)3.9H 2O (VETEC) and gelatin . The masses  of reagents  were 6.202  x 10-3 kg of Co(NO 3)2.6H 2O, \n17.221  x 10-3 kg of Fe(NO 3)3.9H 2O and 5  x 10-3 kg of gelatin . Initially, gelatin was dispersed  in distilled \nwater at 323 K. Then , Co(NO 3)2.6H 2O and Fe(NO 3)3.9H 2O were added to the above  solution  and kept \nunder stirring at 353 K until the formation of a viscous gel.  To obtain the precursor powder, the gel was \nheat treated  at 623 K for 3h , then, the precursor was finely crushed and again annealed  for 2  h at 973, \n1173  and 1273 K . The samples annealed  at 623, 9 73, 1173 and 1273 K were named S1 , S2, S3 and S3, \nrespectively.  \n Structural characterization of s amples  was carried out by  X-ray diffraction (XRD) using a Mini \nFlex II Rigaku  diffractometer and Cu Kα radiation.  XRD data were collected  in the 2θ range between  10° \nand 80° with a scan rate of 5° min-1 and 0.02° step. Crystalline phases were identified using the ICDD  \ndatabase. Relative concentration of phases , lattice  parameters and crystallite size were obtained by using \nthe Rietveld refinement method . The m orphology and particle size distribution  of samples were analyzed \non a TESCAN  MIRA3 field emission scanning electron  microscope  (SEM) . Mössbauer spectra were \nrecorded in transmission mode , at room temperature , using a spectrometer from Wiessel with a 57Co:Rh \nsource and activity of 25 mCi. Isomer shifts values are related to  -Fe. Magnetic measurements were \nperformed as a function of temperature ( 5 to 300 K ) and magnetic field (up to 10T) by using a \ncommercial VSM - Physical Properties Measurement System (PPMS) Dynacool from Quantum Design.   \n \n3. Results and discussion  \n The XRD patterns of CoFe 2O4 samples  treated  at different temperatures are shown in Fig. 1. \nSimilar di ffractograms  were observed for all samples and were  indexed to cubic spinel phase  (109044 -\nICSD ). Besides the spinel phase, a  small amount of CoO  (9865 -ICSD)  was identified as a secondary  4 \n phase for sample S1. We noted  that crystallite size increased with heat treat ment  temperature , this may \nhappen  as result of  coalescence of particles [14]. The l attice parameter s and crystallite  sizes varied  from \n8.373 to 8.387 Å , and 73 to 296 nm, respectively . The lattice parameter s are in good agreement  with those \nreported in  literature for cobalt ferrite [15]. Table 1 shows  the results obtained from the  Rietveld \nrefinement .  \n \nFig. 1. XRD patterns  of CoFe 2O4 samples  (a) S1, (b) S2, (c) S3 and (d) S4. Symbols are related to phases:  \n CoFe 2O4,  CoO  \n \n \n5 \n Table 1.  Refined parameters  of CoFe 2O4 samples  \nSamples  Phases  \n% Dm \nCoFe 2O4 \n(nm)  Lattice parameter  \nCoFe 2O4 \n(Å) \n CoFe 2O4 CoO  \nS1 94 6 73 8.373  \nS2 100 - 128 8.384  \nS3 100 - 189 8.387  \nS4 100 - 296 8.386  \n \nSEM images of samples  S1 and S4 are shown  in Fig. 2. The micrograph for sample S1 (Fig. 2a) \nrevealed  rounded particles with uniform size distribution.  Elongated particles  observed in figure 2b are \nmay be due to  coalescence  of small particles . The sample S4 show  agglomerated and pores , the porous \nstructure is formed by escaping gases during  heat treatment . In fact, ge latin provides a large amount of \norganic matter to the system, which may promotes the appearance of pores [11].  Inset in the top right  \nshow a histogram  indicating the particle size distribution . The distributions were  lognormal with average  \nparticle sizes of 53 and 308 nm. In both cases , the average  particle sizes were  of the same order as the \nones determined from  the XRD analysis . \n \nFigure. 2. SEM images  of CoFe 2O4 samples  (a) S1 and (b) S4. Insets  to the right  show histograms \nrevealing the l ognormal size distribution  \n \n(c) (d) 6 \n  Mössbauer spectra  (MS) recorded  at room temperature are shown in Fig. 3. The MS were fit ted \nto two sextets related to the Zeeman interaction between the hyperfine magnetic field and the nuclear \nmagnetic moment. These subspectra  are assigned to iron ions located in the tetrahedral (Fe-Tetr) and \noctahedral (Fe-Oct) coordination  symmetry . The isomer shift (IS), hyperfine magnetic field (Hhf) and \nquadrople splitting (QS) values are typical for cobalt ferrite samples [16] . In these sites, Fe3+ is \ncoordinated by four and six oxy gens. No doublet or singlet related to superparamagnetic particles or \nparamagnetic phases were  observed. When the annealing temperature  is increase d, we observe d a small \ndecrease in the Fe -Oct relative absorption area (RA ), accompanied by an equivalent increase in the RA  of \nFe-Tetr. The chemical formula  unit (f.u.)  of cobalt ferrites , (Co 1-xFex)[Co xFe2-x]O4 , can be obtained from \ndegree of inversion  parameter (x), which is defined as the  fraction  of tetrahedral sites occupied by Fe3+. In \nthe above formula, cations enclosed  in round and square brackets  are ions in tetrahedral  (A-sites)  and \noctahedral  (B-sites) sites , respectively.  Co ferrite is completely inversed when x=1. The degree of \ninversion  can be calculated from the ratio of sub spectra areas, RA(A)/ RA(B)=f A/fB(x/(2 -x)), where the \nratio of recoilless  fraction between octahedral and tetrahedral sites  at 300K  is f B/fA = 0.94  [16]. Table 2 \nshow the hyperfine parameters determined from the fits . The samples heat treated  at 623 K  and above 973 \nK, have RA(A)/RA(B) ratios of 0.73 and 0.97, respectively. The f.u. determined from these values w ere \nof Co0.19Fe0.81)[Co 0.81Fe1.19]O4 and (Co 0.06Fe0.94)[Co 0.94Fe1.06]O4, respectively . \nThe linewidth attributed to the Fe -Oct is larger  indicating different surroundings for Fe  ions \nlocated at this site.  In fact, the broadening of the B -site line was interpreted as being due to a distribution \nin Hhf caused by several configuration of Co and Fe nearest A -site neighbors [ 17]. Similar results have \nbeen observed in cobalt ferrite samples prepa red by using several cooling rates [17, 18]. 7 \n  \nFigure 3. Mössbauer spectra recorded at 300  K for CoFe 2O4 samples (a) S1, (b) S2 and (c) S4.  \n \nTable  2. Hyperfine  parameters of CoFe 2O4 samples  \nSamples  Fe Sites  Hhf  \n(T ) QS \n(mm/s)  IS  \n(mm/s)  RA \n(%) Linew idth \n(mm/s)  RA(A)/RA(B)  \nS1 Fe-Oct (B) \nFe-Tetr (A) 50.3 \n49.8 0.18 \n-0.07 0.48 \n0.18 58 \n42 0.60 \n0.40 0.73 \nS2 Fe-Oct (B) \nFe-Tetr (A) 49.3 \n48.6 0.16 \n-0.06 0.46 \n0.22 51 \n49 0.65 \n0.40 0.97 \nS4 Fe-Oct (B) \nFe-Tetr (A) 49.5 \n48.8 0.16 \n-0.06 0.45 \n0.22 51 \n49 0.67 \n0.41 0.97 \n \n \nZero f ield cool ed magnetization (ZFCM)  measurements versus temperature under a field of 1 0 T \nshowed a nearly constant magnetization value below 100  K, indicating that samp les have reached the  \nsaturated  regime . Figure 4c shows these measurements for samples S1, S2 and S4.  \nMagnetization versus magnetic field measurements were recorded at 5K and 300 K under a n \napplied  magnetic field of up to 10 T, figures 4a and 4b show  these measurements . Conversion magnetic \n8 \n units from CGS to IS are 1emu/g =1Am2/kg, and 1 Oe = 79.58 A/m.  For all the samples, the upper and \nlower branches of the hy steresis loops approach each other asymptotically at magnetic fields above 6 T. \nThe anisotropy constant was determined at 5 K by fitting the high field regions (H » coercive field ) to the \nLaw of Approach to Saturation (LAS), based on  the assumption that at sufficiently high field only \nrotational processes remain . According to the LAS , the magnetization as a function of magnetic field is \nusually writte n as [19]: \n        \n      \n     \n  \nwhere the numerical coefficient 8/105 h olds for random polycrystalline samples with cubic anisotropy \nand K 1 is the anisotropy constant.  The anisotropy con stant, K1, varied from 2.60 x106  to 2.71 x106 J/m3 in \nagreement with results obtained from magnetic torque measurements [ 20] and by fitting the LAS equation \nto MxH  magnetic measurements [21] in Co ferrite samples . The high K1 values are related to  the strong \nanisotropy of Co ferrite ions and to their presence in octahedral -B sites of the spinel structure  [20]. These \nfindings were confirmed  through the f.u. obtained from  the MS analysis,  which show  that the amount of \nCo2+ increases with annealing temperature . Table 3  shows t he saturation magnetization values obtained \nfrom the LAS fittings . The magnetic moment (M m) per f.u. can be determined from the Ms values . Thus, \nMm=WxMsx10-3 /(Nax9.274 x10-24), where W is the molecular weight of Co ferrite and Na is the \nAvogadro’s number . Therefore, the values 3.19 µB, 3.78  µB and 3.95 µB are the magnetic moments  per \nf.u. for samples S1, S2 and S4, respectively.  The higher magnetic moments for samples S2 and S4 reflects \nthe higher occupancy of Co ions in the octahedral sites.  These values are in agreement with the ones \nreported for Co ferrites  with different  stoichiometries and indicates  the spin and orbital magnetic \ncontribution of Co ions [17, 22]. 9 \n  \nFigure 4  – Magnetization of samples S1, S2 and S4  measured at (a) 5K and (b) 300K. (c) ZFCM  \nmeasurements under a magnetic field of 10 T . (d) Fit to the LAS of the high field of the MxH-2 data for \nsample S4. \n \nThe magnetic parameters obtained from hys teresis loops,  such as  saturation magnetization (M s), \nremanent magnetization (M r), coercivity (H c) and ratio M r/Ms, are shown in Table 3.  The values in \nparenthesis corr espon d to measurements performed at 300 K, while the other s correspond to \nmeasurements performed at 5 K. The crossover from the single domain to multi domain magnetic system  \nis related to the magnetocrystalline anisotropy. In CoFe 2O4, the particle size to form a multidomain \nsystem is about  70 nm [ 23], crystallites exceeding this size will have reduced Hc values. Although, r ecent \nstudies showed that CoFe 2O4 nanoparticles with a partial ly inverse structure ha d a maximum  value of Hc \nat size between 25 -30 nm, and small values above 45 nm [ 24]. Our sample s exhibited  decreasing Hc  \n10 \n values when part icle size increas ed, as expected for particles  with sizes above the critical diameter to \nform a multi domain regime.  \nTable 3 .  Magnetic parameters of Co  ferrite samples  \nSample  Ms  \n(Am2/kg) Mr  \n(Am2/kg) Hc  \n(kA/m ) Mr/Ms K1 \n(J/m3) (BH)max  \n(kJ/m3) \nS1 76 (72 ) 40 (40) 479.9  (167.1 ) 0.53 (0.56)  2.40x106 9.7 \nS2 90 (78)  58 (34)  369.3 (87.5 ) 0.64 (0.45)  2.65x106 18.8 \nS4 95 (82)  65 (33) 278.5 (65.3 ) 0.68 (0.40)  2.71x106 20.9 \nParameters in parenthesis are results from  measurements performed at 300 K. Other values are related to  \nmeasurements  recorded at 5 K. \n \n Figure 5a shows the B=  o (H + M) versus H curve for sample S4 measured at 5  K. An \nimportant  parameter for hard magnetic materials is the (BH)max value , which is the largest area of the \nrectangle that can fit in the demagnetizing B versus H curve at the second quadrant , see figure 5b. Figure \n5c shows the modulus  of the product B*H versus H , where  the maximum value determined from th is plot \nwas 2 0.9 kJ/m3. The (BH)max valu es show a strong increase from sample S1 to S2 and from sample S2 to \nS4 did not change to much . This result is in agreement with the large value  of remanence magnetization \nand high anisotropy constant for samples S2 and S4 . 11 \n  \nFigure 5  – Magnetization of sample S4. (a) B or J  versus magnetic field  H. (b) Second quadrant of the \ndemagnetizing curve. (c) Modulus (BH) versus magnetic field.  \n \n4. Conclusions  \n The synthesis using gelatin is an alternative route, simple and inexpensive to prepare oxide \nnanoparticles.  Cobalt ferrite nanocrystals with diameters ranging from 73 to 296 nm were prepared in \ngelatin. The samples  have diameter compatible wit h multi  domain magnetic particles. Mössbauer \nspectroscopy measurements showed that the annealing process of the cobalt ferrite nanocrystals affect ed \nthe average crystallite size but also the distribution of Fe ions within A - and B -sites in the spinel struc ture. \nWe found a degree of inversion close to 1.0 for samples heat treated  above 973 K . The anisotrop y values \nare in agreement with hard magnetic material s. The saturation magnetization showed magnetic moments \nper f.u. compatible with near-stoichiometric Co ferrite.  \n \n \n12 \n 5. Acknowledgments  \n A.C. Lima thanks to CNPq/PNPD (561256/2010 -1) by the financial support.  \n6- References  \n[1] M.A.G. Soler, E.C.D. Lima, S.W. daSilva, T.F.O. Melo, A.C.M. Pimenta, J.P. Sinnecker, R.B. \nAzevedo, V.K. Garg , A.C. Oliveira, M.A. Novak, P.C. Morais, Aging Investigation of Cobalt Ferrite \nNanoparticles in Low pH Magnetic Fluid, Langmuir 23 (2007) 9611.  \n[2] E. Manova, B. Kunev, D. Paneva, I. Mitov, L. Petrov, C. Estournés, C. D’Orléans, J. -L. Rehspringer,  \nM. Kurmoo,  Mechano -Synthesis, Characterization, and Magnetic Properties of Nanoparticles of Cobalt \nFerrite, CoFe 2O4, Chem.  Mater.  16 (2004)  5689.  \n[3] L.D. Tung, V. Kolesnichenko, D. Caruntu, N.H. Chou, C.J. O’Connor, L. Spinu, Magnetic properties \nof ultrafine  cobalt ferrite particles, J. Appl. Phys. 93 (2003) 7486.  \n[4] L. Ai, J. Jiang , Influence of annealing temperature on the formation, microstructure and magnetic \nproperties of spinel nanocrystalline cobalt ferrites,  Curr. Appl . Phys . 10 (2010 ) 284 . \n[5] D.-H. Kim, D.E. Nikles, D.T. Johnson, C.S. Brazel , Heat generation of aqueously dispersed CoFe 2O4 \nnanoparticles as heating agents for magnetically activated drug delivery and hyperthermia,  J. Magn . \nMagn . Mater . 320 ( 2008 ) 2390 . \n[6] Q. Song, Z.J. Zhang , Shape Control and Associated Magnetic Properties of Spinel Cobalt Ferrite \nNanocrystals,  J. Am. Chem . Soc. 126 ( 2004 ) 6164 . \n [7] S.R. Naik, A.V. Salker, S.M. Yusuf, S.S. Meena, Influence of Co2+ distribution and spin –orbit \ncoupling on the resultant magnetic properties of spinel cobalt ferrite nanocrystals, J. Alloys Compd 566 \n(2013) 54.  \n[8] M. Shi, R. Zuo, Y. Xu, Y. Jiang, G. Yu, H. Su, J. Zhong , Preparation  and  characterization  of \nCoFe 2O4 powders and films via the sol –gel method,  J. Alloys Compd . 512 ( 2012 ) 165 . \n[9] P. Kumar, S.K. Sharma, M. Knobel, M. Singh , Effect of La3+ doping on the electric, dielectric and \nmagnetic properties of cobalt ferrite processed by co -precipitation technique, J. Alloys Compd . 508 \n(2010 ) 115 .  \n [10] X. Zhang, W. Jiang, D. Song, H. Sun, Z. Sun, F. Li, Salt-assisted combustion synthesis of highly \ndispersed superparamagnetic CoFe 2O4 nanoparticles, J. Alloys Compd . 475 ( 2009 ) L34 . 13 \n  [11] A.F. Costa, P.M. Pimentel, F.M. Aquino, D.M.A. Melo , M.A.F. Melo, I.M.G. Santos , Gelatin \nsynthesis of CuFe 2O4 and CuFeCrO 4 ceramic pigments, Mater . Lett. 112 ( 2013 ) 58. \n[12] A.P.S. Peres, A.C. Lima, B.S Barros, D.M.A. Melo , Synthesis and characterization of NiCo2O4 \nspinel using gelatin as an organic precursor,  Mater . Lett. 89 (2012 ) 36. \n[13] M.A. Gabal, Y.M. Al Angari, A.Y. Obaid, A. Qusti , Structural analysis and magnetic properties of \nnanocrystalline NiCuZn ferrites synthesized via a novel gelatin method,  Adv. Powder Techn . 25 ( 2014 ) \n457. \n[14] M. Gharagozlou , Synthesis, characterization and influence of calcination temperature on magnetic \nproperties of nanocrystalline spinel Co -ferrite prepared by polymeric precursor method,  J Alloys Compd \n486 ( 2009 ) 660 .  \n[15] J.D. Baraliya, H.H. Joshi , Spectroscopy investigation of nanometric cobalt ferrite synthesized by  \ndifferent techniques, Vibrational Spectroscopy 74 ( 2014 ) 75. \n[16] G.A. Sawatzky , F. Van der Woude , A.H. Morrish, Recoilless -Fraction Ratios for Fe57 in Octahedral \nand Tetrahedra l Sites of a Spinel and a Garnet,  Phys. Rev. 183 ( 1969 ) 383.  \n[17] G. A. Sawatzky, F . Van der Woude, A. H. Morrish, Cation Distributions in Octahedral and \nTetrahedral Sites of the Ferrimagnetic Spinel CoFe 2O4, J. Appl . Phys.  39 (1968 ) 1204.  \n[18] M. R. De Guire, R.C. O’Handley, G. Kalonji, The cooling rate dependence of cation distributions in \nCoFe 2O4, J. Appl. Phys.  65 (1989) 3167.  \n[19] S. Chikazumi, Physics o f Ferromagnetism, Second ed ., Oxford University Press, Oxford, 1997 . \n[20] H. Shenker , Magnetic Anisotropy of Cobalt Ferrite (Co 1.01Fe2.00O3.62) and Nickel Cobalt Ferrite \n(Ni 0.72Fe0.20Co0.08Fe2O4), Phys. Rev.  107 (1957) 1246 . \n[21] A. Franco , F.L.A. Machado, V.S. Zapf, Magnetic properties of nanoparticles of cobalt ferrite at high \nmagnetic field, J Appl. Phys 110 (2011) 053913 . \n[22]- W. Gorter, Saturation magnetization and crystal chemistry of ferromagnetic oxides,  Philips  Res. \nRep. 9 (1954) 295 . \n[23] A.E. Berkowitz, W.J. Schuelle, Magnetic properties of some ferrite micropowde rs, J. Appl. Phys. 30 \n(1959) 134S . \n[24] K. Maaz, A. Mumtaz, S.K. Hasanain, A. Ceylan, Synthesis and magnetic properties of cobalt ferrite \n(CoFe 2O4) nanoparticles prepared by wet chemical route, J. Magn. Magn. Mater. 308 (2007) 289.  "    },    {        "title": "2011.12721v1.Nanoscale_ferroelectricity_in_pseudo_cubic_sol_gel_derived_barium_titanate____bismuth_ferrite__BaTiO__3__BiFeO__3___solid_solutions.pdf",        "content": "1 \n Nanoscale ferroelectricity in pseudo -cubic sol -gel \nderived barium titanate - bismuth ferrite  \n(BaTiO 3- BiFeO 3) solid solutions  \nA. Pakalniškis1 A. Lukowiak2, G. Niaura3, P. Głuchowski2,4, D. V. Karpinsky5,6, \nD. O. Alikin8,9, A.S. Abramov8, A. Zhaludkevich5, M. Silibin6,7, A.L. Kholkin8,9, R. \nSkaudžius1, W. Strek2, A. Kareiva1,* \n1Institute of Chemistry, Vilnius University, Naugarduko 24, LT -03225 Vilnius, Lithuania  \n2Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Okolna 2, \nPL-50422 Wroclaw, Poland  \n 3Institute of Chemical Physics, Faculty of Physics, Vilnius University, Sauletekio Ave. 9, LT -\n10222, Vilnius Lithuania  \n4Nanoceramics Spolka  Akcyjna,  Okolna 2, PL -50422 Wroclaw, Poland  \n5Scientific -Practical Materials Research Centre of NAS of Belarus, 220072 Minsk, Belarus  \n6National Research University of Electronic Technology \"MIET\", 124498 Moscow, Russia  \n7Institute for Bionic Technologies an d Engineering, I.M. Sechenov First Moscow State Medical \nUniversity, Moscow 119991, Russia  \n8School of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia  \n9Department of Physics & CICECO – Aveiro Institute of Materials, University  of Aveiro, Aveiro, \nPortugal;  \nAbstract  \nSingle phase barium titanate –bismuth ferrite ((1 -x)BaTiO 3-(x)BiFeO 3, BTO -BFO) solid solutions \nwere prepared using citric acid and ethylene glycol assisted sol -gel synthesis method. Depending \non the dopant content the samples are characterized by tetragonal, tetragonal -pseudocubic, \npseudocubic and rhombohedral structure as confirmed by Raman spectroscopy and XRD \nmeasurements.  An increase of the BFO content leads to a reduction in the cell parameters \naccompan ied by a decrease in polar distortion of the unit cell wherein an average particle size \nincreases from 60 up to 350 nm. Non zero piezoresponse was observed in the compounds with \npseudocubic structure while no polar distortion was detected in their crystal structure using X -ray \ndiffraction method. The origin of the observed non -negligible piezoresponse was discussed \nassuming a coexistence of nanoscale polar and non -polar phases attributed to the solid solutions \nwith high BFO content. A coexistence of the nan oscale regions having polar and non -polar 2 \n character is considered as a key factor to increase macroscopic piezoresponse in the related \ncompounds due to increased mobility of the domain walls and phase boundaries.  \nKeywords : BTO -BFO; solid solutions; sol -gel processing; phase diagram; PFM; SEM.  \n1. Introduction  \n     At room temperature bismuth ferrite is a multiferroic having  a rhombohedral perovskite \nstructure described by  R3c space group [1]. While having both its ferroelectric Curie temperature \nTc ~ 1100 K and antiferromagnetic Néel temperature T N ~ 640 K it has attracted a lot of attention \n[2,3] . As a multiferroic, it can be used in magnetic sensors [4], energy harvesting devices [5] or \nmem ory devices [6]. As a piezoelectric material, it is a potential substitute for currently most used \nPbZr xTi1-xO3 due to enormously high polarization being measured in the form of thin films [7]. \nWhile being a more ecological material since it contains no le ad, it is additionally good candidate \nfor high temperature piezoelectric applications due to its high Curie temperature [8,9] . \n     The most critical problem of BiFeO 3 is large leakage current significantly reduce applications \nand partially determined by poor phase stability [3]. Synthesis of single -phase  bismuth ferrite is a \ndifficult procedure because none -perovskite secondary phases of Bi 25FeO 40 and Bi 2Fe4O9 are \nform ed during the fabrication process [10,11] . To avoid the problem of secondary phase formation \nmany approaches were undertaken like using different synthesis methods such as hydrothermal \n[12], sol-gel [13], mechanochemical method [14] and more. It is also re ported that pure bismuth \nferrite can be obtained by using extremely pure oxides as precursors with purity over 99.999 % \n[15]. The third way of stabilization for BiFeO 3 structure was to make solid solutions with other \nperovskite material. While the latter m ethod of stabilization is useful it also affects properties of \nthe original bismuth ferrite phase [16]. On the other hand, BaTiO 3 is one of the most well-known  \nferroelectric  materials with  low leakage and is easy to be sintered by  a liquid chemistry route [17]. 3 \n These two materials seem to be very promising for form ation of  solid solution due to the \nenhancement of polarization, stabilization of the structure and improving overall piezoelectric \nperformance of the ceramics.  \n     In this work, we report on citric acid and ethylene glycol assisted sol -gel synthesis method for \nthe preparation of single phase (1 -x)BaTiO 3-(x)BiFeO 3 (BTO -BFO) solid solutions. X -ray \ndiffraction analysis and Raman spectroscopy were used for the deter mination of phase purity. The \ncell parameters were calculated using the results of Rietveld refinement based on the X -ray \ndiffraction data . The surface morphology of sol -gel derived BTO -BFO solid solutions and \npiezoelectric properties are also investigated  and discussed.  \n2. Experimental  \n     Analytical grade chemicals of Bi(NO 3)3·5H 2O, C 12H28O4Ti, Fe(NO 3)3·9H 2O, Ba(CH 3COO) 2, \nethylene glycol and citric acid were used as starting materials. For a typical synthesis of 1 g final \nproduct the following procedure has been carried out. Firstly, citric acid was dissolved in 20 ml of \ndistilled water at a molar ratio of 3:1 to the final cation amount at 80 °C. Secondly, titanium \nisopropoxide was added  to the above solution. Next, barium acetate, iron nitrate, bismuth nitrate \nwere dissolved in the same solution. Finally, when all materials have been dissolved, the 4 ml of \nethylene glycol was added to the present solution. Then the solution was stirred f or 1.5 h and \nevaporated at 200 °C. Obtained gel was then dried at 220 °C overnight. Then xerogel was ground \nin an agate mortar and heated in a furnace at 650 °C for 5 h with a heating rate of 1 °C/min.  \n    X-ray diffraction (XRD) analysis was performed usi ng Rigaku MiniFlex di ffractometer on a \nglass sample holder. Measurements were performed using Cu Kα λ = 1.541874 Å radiation \nmeasuring from 10° to 70° while moving 10°/min.  4 \n Raman spectra were recorded using inVia  Raman (Renishaw, United Kingdom) spectrometer \nequipped with thermoelectrically cooled ( −70 °C) CCD camera and microscope. Raman spectra \nwere excited with 532 nm beam. Parameters of the bands were determined by fitting the \nexperimental spectra with Gaussia n-Lorentzian shape components using GRAMS/A1 8.0 (Thermo \nScientific, USA) software.  \nScanning electron microscopy (SEM) images were taken for the morphology characterization \nwith Hitachi SU -70 SEM.  \nPiezoresponse force microscopy measurements was used to ch aracterize local piezoelectric \nproperties. Experiments have been carried out using MFP -3D commercial scanning probe \nmicroscope (Oxford Instruments, UK). The measurements were performed with 17 N/m spring \nconstant, 10 nm tip radius commercial HA_HR Scansens  tips with W 2C coating under ac voltage \nwith the amplitude Vac = 5 V and frequency f = 20 kHz. Calibration of the probe tip displacements \nand cantilever displacements in PFM measurements were made by the  following  method s \ndescribed in [18]. Amplitude of the out -of-plane PFM response obtained from quasi -static \ncalibrations was divided by shape factor and amplitude of AC voltage excitation in order to \nevaluate effective d 33 coefficient. Corresponding correction of R ·CosΘ piezoresponse signal was  \ndone before by phase shift maximizing in -phase R ·CosΘ signal and minimize out -of-phase R ·SinΘ \nsignal [19]. Other signals for all images can be found separately in supplementary materials.  \n3. Results and discussion  \n     The BaTiO 3 (BTO) and BiFeO 3 (BFO) solid solutions were prepared using different molar ratio \nof components (BTO:BFO = 1:9, 1:4, 3:7, 2:3, 1:1, 3:2, 7:3, 4:1 and 9:1). The XRD patterns of \nnine different solid solutions are given in Fig. 1.  as a contour map. The blue c olour indicates the \nlowest intensity (background) meanwhile the red colour represents the most intensive points (the 5 \n peaks). The black columns designate the reference XRD data of BaTiO 3 taken from the \ncrystallography open database. According to the PDF (CO D 96 -150-7757) data the desired \nproducts were obtained no matter the ratio of solid solution has been chosen. Nevertheless, a slight \nshift of the peaks towards lager 2θ values is observed upon increase of BFO content which \nindicates a decrease in unit cell  parameters.  \n     For the deeper analysis of structure development, the Rietveld refinement was employed. The \ncell parameters calculated by Rietveld analysis are presented in Fig. 2. In general, barium titanate \nexists in three different structures – cubic (C -phase), te tragonal (T -phase) and trigonal \n(rhombohedral axes, labelled as R -phase), meanwhile bismuth ferrite belongs to trigonal crystal \nsystem with hexagonal or rhombohedral axes. Calculated a and c parameters for primitive lattice \nallow to classify the solid solutions by the crystal structure. Note  that, during the structure \nrefinement of R -phase a and c parameters were recalculated in order to obtain the reduced values \nwhich are closer to each othe r and easy to compare.  \n \n      The following equations were used:  \n𝑎(𝑟𝑒𝑑𝑢𝑐𝑒𝑑 )=𝑎(𝑝𝑟𝑖𝑚𝑖𝑡𝑖𝑣𝑒 )\n√2 (1) \n𝑐(𝑟𝑒𝑑𝑢𝑐𝑒𝑑 )= 𝑐(𝑝𝑟𝑖𝑚𝑖𝑡𝑖𝑣𝑒 )\n2√3 (2) \nAccording to Rietveld analysis data three different blocks of different structures are ident ified. The \nphase transitions from tetragonal to cubic and finally to trigonal with rhombohedral axes are \nobserved with increasing amount of BFO.  \n     The phase transitions in the investigated system were also observed by Raman spectroscopy. \nThe results giv e additional information and confirming the results of X -ray diffraction \nmeasurements. Raman spectroscopy is able to provide detailed information on short range 6 \n structure or local symmetry. Fig. 3 compares Raman spectra of bulk BaTiO 3 and BiFeO 3. The \nsharp  band near 308 cm−1 associated with B1 and E symmetries of longitudinal optical (LO) and \ntransverse optical (TO) phonon modes [ B1, E(TO+LO)] and high frequency band near 715 cm−1 \n[A1, E(LO)] are characteristic for BaTiO 3 ferroelectric phase with tetragonal symmetry [20–22]. It \nshould be noted that observed bands corresponds to several phonons because frequencies of the \nmodes are very close [20]. The other dominant bands are relatively broad features located at 257 \ncm−1 [A1(TO)] and 518 cm−1 [A1, E(TO)]. All observed bands are characteristic for BaTiO 3 [20–\n25]. The intensity of Raman bands of BiFeO 3 decreases by a factor of 20 comparing with spectrum \nof BaTiO 3 (Fig. 3). Four sharp characteristic Raman bands of BiFeO 3 are vi sible at 77 cm−1 (E), \n141 cm−1 (A1), 174 cm−1 (A1), and 220 cm−1 (A1) [26]. Theoretical analysis has indicated that Bi \natom participates mainly in vibrational modes lower than 167 cm−1, while oxygen atoms are \ninvolved in vibrational modes higher than 262 cm−1 [27]. The broad band near 1256 cm−1 involves \noxygen atom stretching vibrations. Similar high frequency band is clearly visible in the spectra of \nlepidocrocite (γ -FeOOH) and maghemite (γ -Fe2O3) at 1300 and 1360 cm−1, respectively [28,29] . \nIt was su ggested that relative intensity of these bands depends on the excitation wavelength \n(resonance enhancement) [28,29] . The intense band near 1310 cm−1 was also observed in the \nspectrum of haematite (α -Fe2O3) [28,29] . \nFig. 4 demonstrates the dependence of Ram an spectra on the composition of  (1- x)BaTiO 3-\n(x)BiFeO 3 solid solution structures. Introduction of 10  % of BiFeO 3 results in considerable spectral \nchanges; first of all, the sharp peak near 308 cm−1 completely disappears, indicating phase \ntransformation has started.  \nAnyway, the tetragonal BaTiO 3 phase in this new structure is still the dominant phase according \nto the crystal lattice data obtained by Rietveld analysis. In addition, the peak at 518 cm−1 shifts to 7 \n 511 cm−1 and a new low -frequency band near 186 cm−1 appears. Such spectral changes are similar \nto previously observed Fe -doping induced formation of distorted  tetragonal/cubic phase BaTiO 3 \nstructure [25]. The 186 -cm−1 peak might be associated with the presence of small amount of TiO 2 \nanatase phase undetectable by XRD measurements and which is usually visible in the low \ncrystalline samples [25]. An increase in i ntensity and broadening of 724 -cm−1 band points on the \npresence of Ba2+ defects in the BaTiO 3 lattice [25]. Similar Raman bands with progressive decrease \nin intensity were observed with increasing x part up to 0.3 (Fig. 4). Addition of higher BiFeO 3 \namount  results in changes in the Raman spectrum indicating alterations in the local lattice \nstructure. No clear bands characteristic to BiFeO 3 is visible in the low -frequency spectral range; \nhowever,  the broad feature due to oxygen atom stretching vibrations app ears near 1355 cm−1 at \nx = 0.6. This band clearly shifts to lower wavenumbers with increasing content of BiFeO 3. Such \nfrequency shift indicates changes in the geometry of oxygen octahedra around the Fe cations. In \naddition, the new band appears near 681−683 cm−1 reaching the highest relative intensity at x  = 0.7 \nof BiFeO 3 content. The results again confirm the constructed phase diagram.  \n     SEM micrographs of all samples are given in Fig. 5. The size of the particles was measured \nusing open -source Fi ji software by accidentally choosing appropriate particles [30]. It is clearly \nseen that with increasing the amount of BFO the particle size also increases. The particle size \nvaries from 60 to 120 nm for the samples which SEM images are presented in Fig. 5 A, B, C and \nD. Additionally, the boundaries between the particles vanished. The particles start to gain a more \ndistinct shape with a larger size which in some cases exceeds over 350 nm for the sample with the \nequal ratio of BTO and BFO (1:1) (Fig. 5E) and for the samples with higher amount of BFO in the \nsolid solutions (Fig. 5F, G H and I). This could be related with the changes of the crystal structure. \nThe change from tetragonal to cubic and finally to trigonal structure causes the formation of 8 \n particles with bigger size. Note  that, independently on the ratio of BTO and BFO in the solid \nsolution the large size distribution of the particles was observed. The semispherically shaped \nparticles have formed when barium titanate is dominating in the solid solutio n and rectangular \nparticles are predominating in the samples with increasing amount of bismuth ferrite.  \nFinally, the sol -gel method leads to the formation of slightly agglomerated irregular spherical -\nrectangular shape particles with rather broad size dist ribution [31]. The particle size is dependent \non the molar ratio of constituents in the BTO -BFO solid solutions. The increase of the particle size \nis caused by  the different melting points of BFO and BTO. It has been previously reported that \nmixing the higher melting point component, in this case BaTiO 3, with another component having \na lower melting point, in this case BiFeO 3, leads to better crystallinity and improved particle \ngrowth  [32].  \n     Analysis of the piezoelectric properties of (0.4)BaTiO 3-(0.6)BiFeO 3, (0.3)BaTiO 3-(0.7)BiFeO 3 \nand (0.2)BaTiO 3-(0.8)BiFeO 3 composition at Bi -rich side was done locally  by piezoresponse force \nmicroscopy [18]. Piezoresponse was analyse d before and after local poling by ±35 V DC voltage. \nLocal switching o f the polarization has been done by scanning of rectangular areas with positively \nand negatively biased tip. Fig 6 demonstrates out -of-plane PFM images before and after local \npoling for three discussed compositions. In the PFM RCosΘ images, the contrast co rresponds to \nvalue and sign of the effective d 33 coefficient. Thereby, “bright” areas represent domains with \napproximately upward polarization orientation, meanwhile dark contrast areas represent  the \nopposite case (approximately downward polarization). It is clear ly seen from these series of images \nthat increase of the BaTiO 3 content in solid solution tends to degrade piezoelectric properties of \nthe material. Before poling both (0.2)BaTiO 3 –(0.8)BiFeO 3 and (0.3)BaTiO 3-(0.7)BiFeO 3 \ncompositions revealed clust ers of polar phase with high effective d 33 and clusters with 9 \n piezoresponse close to zero, while (0. 4)BaTiO 3 –(0.6)BiFeO 3 composition didn’t show any \ndistinguishable response. Surprisingly, after poling bi-polar contrast can be observed in all three \ncompositions. This is indicative of partial polarization switching across the rectangular area.  \nIt must be noted that small size  of the grains can significantly act onto results of PFM \nmeasurements due to limitation of PFM spatial resolution. Close to zero piezoresponse inspected \nbefore poling can be sourced by effect of averaging the piezoresponse from amount of nanosized \ndomains with different polarization orientation. After poling all disordered polarization states \nbecome aligned and thereby can be probed by PFM. However, due to meta -stable structural state \nof BFO -BTO solid solution we cannot exclude as well that electric field c an induce phase transition \nfrom non -polar state to polar as such transformation is likely in rare earth doped BFO [33]. \nFurther we analysed in -plane piezoresponse at the smaller scale. In -plane piezoresponse is \nindicative of piezoelectric activity and excl udes most of the known PFM parasitic contributions \n[34]. The behaviour of in -plane response was similar to out -of-plane (Fig. 7). Comparison of the \npiezoresponse with topography in (0.2)BaTiO 3–(0.8)BiFeO 3 composition with largest grain s \nrevealed that indiv idual grains before poling consisted of small scale domains, while after poling \nthe polarization become aligned (fig 7a, d). At the same time, we didn’t reveal any transformation \nof the phase without piezoelectric response to piezoelectrically active phase  in this composition. \nFollowing the decrease of the grain size with increase of the BaTiO 3 concentration domains as \nwell became smaller and finally indistinguishable by PFM in (0.4)BaTiO 3-(0.6)BiFeO 3 \ncomposition. After local poling all composition revealed  clear bi -polar domain pattern as well as \nan out-of-plane response.  \nFraction of polar phase can be roughly estimated from PFM histograms according approach from \n[35]. It was found to be around 95 % for (0.2)BaTiO 3-(0.8)BiFeO 3 composition and decreases 10 \n down to 18  % for (0.4)BaTiO 3-(0.6)BiFeO 3 composition. This trend of piezoelectrically active area \ndecrease is followed by median effective d 33 value reduce (fig 7g -i). This is qualitatively fit to \nmacroscopically observed trend of  rhombohedral -pseudocubic structural transformations revealed \nby XRD measurements. Thus, we postulate that phase macroscopically identified as pseudo -cubic \nis actually in coexistence of the local nanoscale phases  similar to known phase coexistence at \nmorph otropic phase boundary and polymorphic phase boundary in different piezoelectric materials \n[36]. Further insight into the details of this unusual phase coexistence can be obtained by using  \nmethods with enhanced spatial resolution and sensitivity.  The XRD method used to describe the \nphase transformation  is not well suitable to characterize nanoscale domains  observed by PFM \nmethod . While one can observe notable widening of the X -ray diffracti on reflections in the region \nascribed to the pseudo cubic phase (Fig. 2) which points at a decrease in the average size of the \ncrystallites  and support the results obtained by local scale measurements . To conclude, an \nincreasing amount of BaTiO 3 leads to degradation of piezoresponse, probably caused by decrease \nof piezoelectrically active phase amount and a gradual change into a more symmetric pseudo cubic \nstructure induced by BTO. Transformation of the cell to centrosymmetric state extracted fro m \nXRD must be followed by cell dipole moment reduction and, consequently, degradation of \nmacroscopic polarization and effective piezoelectric coefficient. We confirmed here this trend by \neffective d 33 measurements. Nevertheless, for all measured samples th e polarization was \nswitchable, meaning that each solid solution retains ferroelectric properties.  \n4. Conclusions  \nIn conclusion , a systematic study on the structure, morphology and piezoelectric properties of \nBTO -BFO solid solutions was performed. The Rietv eld analysis data has demonstrated that \nintroducing bismuth ferrite into the barium titanate  matrix  leads to the structur al evolution from 11 \n tetragonal  to (pseudo)cubic and finally to trigonal (with rhombohedral axes). All phase structure \nmodification s are concluded in the structure phase diagram. Moreover, increasing amount of BFO \nin the solid solutions causes not only the structure modifications but it also induces a formation of \nlarger size d, distinct ly shape particle  which exceed in som e cases over 350 nm. Domain structure \ncorresponds to grain size and domains become large towards to Bi rich boundary in the solid \nsolution. Surprisingly, compositions nominally being centrosymmetric exhibit ferroelectricity that \nwas shown to be sourced by nanosized structural states clear ly visible after local poling. The \nexplored piezoresponse force measurements have demonstrated that an increasing amount of \nBaTiO 3 leads to degradation of piezoresponse of the solid solution.  \nAcknowledgments  \nThe work has been done in frame of the project TransFerr. This project has received funding from \nthe European Union’s Horizon 2020 research and innovation programme under the Marie \nSklodowska -Curie grant agreement No. 778070. The scanning probe microscopy study was funded \nby RFBR (grant No. 19 -52-04015) and BRFFR (grant No. F19RM -008). The equipment of the \nUral Center for Shared Use “Modern nanotechnology” UrFU was used. Sample structural \ncharacterization was funded by RFBR (grant #18 -38-20020 mol_a_ved). M.S. also acknowledges \nRussian academic excellence project \"5 -100\" for Sechenov University. This work was developed \nwithin the scope of the project CICECO -Aveiro Institute of Materials, POCI -01-0145 -FEDER -\n007679 (FCT Ref. UID/CTM/50011/2013 ), financed by national funds through the FCT/MEC and \nwhen appropriate co -financed by FEDER under the PT2020 Partnership Agreement.  \n \n \nReferences  12 \n [1] J.M. Moreau, C. Michel, R. Gerson, W.J. James, Ferroelectric BiFeO3 X -ray and neutron \ndiffraction study, J. Phys. Chem. Solids. 32 (1971) 1315 –1320. \nhttps://doi.org/10.1016/S0022 -3697(71)80189 -0. \n[2] G. Catalan, J.F. Scott, Physics and Applications of Bismuth Ferrite, (2008). \nhttps://doi.org/10.1002/adma.200802849.  \n[3] T. Rojac, A. Bencan, B. Malic, G. Tutuncu, J.L. Jones, J.E. Daniels, D. Damjanovic, \nBiFeO 3 Ceramics: Processing, Electrical, and Electromechanical Properties, J. Am. \nCeram. Soc. 97 (2014) 1993 –2011. https://doi.org/10.1111/jace.12982.  \n[4] M.I. Bichurin, V.M. Petrov, R. V. Pet rov, Y. V. Kiliba, F.I. Bukashev, A.Y. Smirnov, \nD.N. Eliseev, Magnetoelectric sensor of magnetic field, in: Ferroelectrics,  Taylor & \nFrancis Group , 2002: pp. 199 –202. https://doi.org/10.1080/00150190214814.  \n[5] X. Bai, Y. Wen, J. Yang, P. Li, J. Qiu, Y. Zhu, A magnetoelectric energy harvester with \nthe magnetic coupling to enhance the output performance, in: J. Appl. Phys., American \nInstitute of Physics, 2012: p. 07A938. https://doi.org/10.1063/1.3677877.  \n[6] A.N. Kalinkin, E.M. Kozhbakhteev, A.E. Polyakov , V.M. Skorikov, Application of \nBiFeO3 and Bi4Ti3O12 in ferroelectric memory, phase shifters of a phased array, and \nmicrowave HEMTs, Inorg. Mater. 49 (2013) 1031 –1043. \nhttps://doi.org/10.1134/S0020168513100038.  \n[7] S. Fujino, M. Murakami, V. Anbusathaiah, S.H. Lim, V. Nagarajan, C.J. Fennie, M. \nWuttig, L. Salamanca -Riba, I. Takeuchi, Combinatorial discovery of a lead -free \nmorphotropic phase boundary in a thin -film piezoelectric perovskite, Appl. Phys. Lett. 92 \n(2008). https://doi.org/10.1063/1.2931706.  \n[8] C. Sun, X. Chen, J. Wang, G. Yuan, J. Yin, Z. Liu, Structure and piezoelectric properties \nof BiFeO 3 and Bi 0.92Dy 0.08FeO 3 multiferroics at high temperature, Solid State \nCommun. 152 (2012) 1194 –1198. https://doi.org/10.1016/j.ssc.2012.04.067.  \n[9] H. Yang , C. Zhou, X. Liu, Q. Zhou, G. Chen, H. Wang, W. Li, Structural, microstructural \nand electrical properties of BiFeO 3 -BaTiO 3 ceramics with high thermal stability, Mater. \nRes. Bull. 47 (2012) 4233 –4239. https://doi.org/10.1016/j.materresbull.2012.09.027.  \n[10] T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, M. Fiebig, Magnetic \nphase control by an electric field, Nature. 430 (2004) 541 –544. \nhttps://doi.org/10.1038/nature02728.  13 \n [11] W. Eerenstein, N.D. Mathur, J.F. Scott, Multiferroic and magnet oelectric materials, \nNature. 442 (2006) 759 –765. https://doi.org/10.1038/nature05023.  \n[12] S.H. Han, K.S. Kim, H.G. Kim, H.G. Lee, H.W. Kang, J.S. Kim, C. Il Cheon, Synthesis \nand characterization of multiferroic BiFeO3 powders fabricated by hydrothermal me thod, \nCeram. Int. 36 (2010) 1365 –1372. https://doi.org/10.1016/j.ceramint.2010.01.020.  \n[13] J.K. Kim, S.S. Kim, W.J. Kim, Sol -gel synthesis and properties of multiferroic BiFeO3, \nMater. Lett. 59 (2005) 4006 –4009. https://doi.org/10.1016/j.matlet.2005.07.05 0. \n[14] E. Markiewicz, B. Hilczer, M. Błaszyk, A. Pietraszko, E. Talik, Dielectric properties of \nBiFeO 3 ceramics obtained from mechanochemically synthesized nanopowders, J. \nElectroceramics. 27 (2011) 154 –161. https://doi.org/10.1007/s10832 -011-9660 -9. \n[15] *,† Matjaz  Valant,  and Anna -Karin  Axelsson, N. Alford, Peculiarities of a Solid -State \nSynthesis of Multiferroic Polycrystalline BiFeO3, (2007). \nhttps://doi.org/10.1021/CM071730+.  \n[16] N. Itoh, T. Shimura, W. Sakamoto, T. Yogo, Fabrication and characte rization of BiFeO3 -\nBaTiO3 ceramics by solid state reaction, in: Ferroelectrics, 2007: pp. 19 –23. \nhttps://doi.org/10.1080/00150190701508860.  \n[17] A. Kareiva, S. Tautkus, R. Rapalaviciute, J.E. Jørgensen, B. Lundtoft, Sol -gel synthesis \nand characterization o f barium titanate powders, J. Mater. Sci. 34 (1999) 4853 –4857. \nhttps://doi.org/10.1023/A:1004615912473.  \n[18] N. Balke, S. Jesse, P. Yu, B. Carmichael, S. V. Kalinin, A. Tselev, Quantification of \nsurface displacements and electromechanical phenomena via dynamic atomic force \nmicroscopy, Nanotechnology. 27 (2016) 425707. https://doi.org/10.1088/0957 -\n4484/27/42/425707.  \n[19] E. Soergel, Piezoresponse force microscopy (PFM), J. Phys. D. Appl. Phys. 44 (2011). \nhttps://doi.org/10.1088/0022 -3727/44/ 46/464003.  \n[20] U.D. Venkateswaran, V.M. Naik, High -pressure Raman studies of polycrystalline, Phys. \nRev. B - Condens. Matter Mater. Phys. 58 (1998) 14256 –14260. \nhttps://doi.org/10.1103/PhysRevB.58.14256.  \n[21] J. Pokorný, U.M. Pasha, L. Ben, O.P. Thakur, D.C. Sinclair, I.M. Reaney, Use of Raman \nspectroscopy to determine the site occupancy of dopants in BaTiO 3, J. Appl. Phys. 109 \n(2011) 114110. https://doi.org/10.1063/1.3592192.  14 \n [22] L. Huang, Z. Chen, J.D. Wils on, S. Banerjee, R.D. Robinson, I.P. Herman, R. Laibowitz, \nS. O’Brien, Barium titanate nanocrystals and nanocrystal thin films: Synthesis, \nferroelectricity, and dielectric properties, J. Appl. Phys. 100 (2006) 034316. \nhttps://doi.org/10.1063/1.2218765.  \n[23] S. Wei Lu, B.I. Lee, Z. Lin Wang, W.D. Samuels, Hydrothermal synthesis and structural \ncharacterization of BaTiO nanocrystals, 2000.  \n[24] I.J. Clark, T. Takeuchi, N. Ohtori, D.C. Sinclair, Hydrothermal synthesis and \ncharacterisation of BaTiO3 fine powders : precursors, polymorphism and properties, J. \nMater. Chem. 9 (1999) 83 –91. https://doi.org/10.1039/a805756g.  \n[25] K.C. Verma, V. Gupta, J. Kaur, R.K. Kotnala, Raman spectra, photoluminescence, \nmagnetism and magnetoelectric coupling in pure and Fe doped BaT iO3 nanostructures, J. \nAlloys Compd. 578 (2013) 5 –11. https://doi.org/10.1016/j.jallcom.2013.05.025.  \n[26] A. Ahlawat, S. Satapathy, V.G. Sathe, R.J. Choudhary, M.K. Singh, R. Kumar, T.K. \nSharma, P.K. Gupta, Modification in structure of La and Nd co -doped e pitaxial BiFeO 3 \nthin films probed by micro Raman spectroscopy, J. Raman Spectrosc. 46 (2015) 636 –643. \nhttps://doi.org/10.1002/jrs.4701.  \n[27] P. Hermet, M. Goffinet, J. Kreisel, P. Ghosez, Raman and infrared spectra of multiferroic \nbismuth ferrite from fir st principles, Phys. Rev. B - Condens. Matter Mater. Phys. 75 \n(2007). https://doi.org/10.1103/PhysRevB.75.220102.  \n[28] P. Colomban, S. Cherifi, G. Despert, Raman identification of corrosion products on \nautomotive galvanized steel sheets, J. Raman Spectrosc . 39 (2008) 881 –886. \nhttps://doi.org/10.1002/jrs.1927.  \n[29] F. Froment, A. Tournié, P. Colomban, Raman identification of natural red to yellow \npigments: ochre and iron -containing ores, J. Raman Spectrosc. 39 (2008) 560 –568. \nhttps://doi.org/10.1002/jrs.1858 . \n[30] J. Schindelin, I. Arganda -Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. \nPreibisch, C. Rueden, S. Saalfeld, B. Schmid, J.Y. Tinevez, D.J. White, V. Hartenstein, K. \nEliceiri, P. Tomancak, A. Cardona, Fiji: An open -source platform for biol ogical -image \nanalysis, Nat. Methods. 9 (2012) 676 –682. https://doi.org/10.1038/nmeth.2019.  \n[31] A. Gatelyte, D. Jasaitis, A. Beganskiene, A. Kareiva, Sol -gel synthesis and \ncharacterization of selected transition metal nano -ferrites, Medziagotyra. 17 (2011)  302–15 \n 307. https://doi.org/10.5755/j01.ms.17.3.598.  \n[32] S. Cho, C. Yun, Y.S. Kim, H. Wang, J. Jian, W. Zhang, J. Huang, X. Wang, H. Wang, J.L. \nMacManus -Driscoll, Strongly enhanced dielectric and energy storage properties in lead -\nfree perovskite titanate th in films by alloying, Nano Energy. 45 (2018) 398 –406. \nhttps://doi.org/10.1016/j.nanoen.2018.01.003.  \n[33] J. Walker, H. Simons, D.O. Alikin, A.P. Turygin, V.Y. Shur, A.L. Kholkin, H. Ursic, A. \nBencan, B. Malic, V. Nagarajan, T. Rojac, Dual strain mechanisms  in a lead -free \nmorphotropic phase boundary ferroelectric, Sci. Rep. 6 (2016) 1 –8. \nhttps://doi.org/10.1038/srep19630.  \n[34] R.K. Vasudevan, N. Balke, P. Maksymovych, S. Jesse, S. V. Kalinin, Ferroelectric or non -\nferroelectric: Why so many materials exhibit “ferroelectricity” on the nanoscale, Appl. \nPhys. Rev. 4 (2017) 021302. https://doi.org/10.1063/1.4979015.  \n[35] D.O. Alikin, A.P. Turygin, J. Walker, T. Rojac, V. V. Shvartsman, V.Y. Shur, A.L. \nKholkin, Quantitative phase separation in multiferroic Bi0.88Sm 0.12FeO3 ceramics via \npiezoresponse force microscopy, J. Appl. Phys. 118 (2015) 072004. \nhttps://doi.org/10.1063/1.4927812.  \n[36] T.R. Shrout, S.J. Zhang, Lead -free piezoelectric ceramics: Alternatives for PZT?, J. \nElectroceramics. 19 (2007) 111 –124. https:/ /doi.org/10.1007/s10832 -007-9047 -0. \n \n \n \n \n \n \n \n \n \n \n 16 \n Titles of figure s \n \nFig. 1.  XRD data of (10 -x)BaTiO 3 – (x)BiFeO 3 solid solutions, where 0 < x < 10.  \n17 \n  \nFig. 2.  Phase diagram of (1 -x)BaTiO 3 – (x)BiFeO 3 solid solutions.  \n18 \n  \nFig 3.  Raman spectra of bulk BaTiO 3 and BiFeO 3 compounds. The excitation wavelength is \n532 nm (0.3 mW).  \n19 \n  \nFig. 4.  Composition dependent Raman spectra of BTO -BFO solid solutions: (a) (0.9)BaTiO 3- \n(0.1)BiFeO 3; (b) (0.8)BaTiO 3-(0.2)BiFeO 3; (c) (0.7)BaTiO 3-(0.3)BiF eO3; (d) (0.4)BaTiO 3-\n(0.6)BiFeO 3; (e) (0.3)BaTiO 3-(0.7)BiFeO 3; (f) (0.2)BaTiO 3-(0.8)BiFeO 3. The excitation \nwavelength is 532 nm (0.3 mW).  \n20 \n  \nFig. 5 . SEM images of BTO -BFO solid solutions: A - (0.9)BaTiO 3–(0.1)BiFeO 3, B \n-  (0.8)BaTiO 3–(0.2)BiFeO 3, C - (0.7)B aTiO 3–(0.3)BiFeO 3, D - (0.6)BaTiO 3–(0.4)BiFeO 3, E - \n(0.5)BaTiO 3–(0.5)BiFeO 3, F - (0.4)BaTiO 3–(0.6)BiFeO 3, G - (0.3)BaTiO 3–(0.7)BiFeO 3, H - \n(0.2)BaTiO 3–(0.8)BiFeO 3 and J -  (0.1)BaTiO 3–(0.9)BiFeO 3.  \n21 \n  \nFig. 6. Quantified out -of-plane  PFM images. RCosθ piezoresponse signal with meaning of the \neffective d 33 coefficient: (a) -(c) before and (d) -(f) after local poling of bi -square area by ±35 V DC \nvoltage (left part is poled negatively, while right part - positively). (g) -(i) Corresponding \nhistograms of effective d 33 distribution across scan area and inside poled region.  (a), (d), (g) \n0.8BiFeO 3 - 0.2BaTiO 3; (b), (e), (h)  0.7BiFeO 3 - 0.3BaTiO 3; (c), (f), (i) (0.6)BiFeO 3-(0.4)BaTiO 3-\nsolid solutions. Calculated median effective d 33 is display ed at (g) -(i). \n22 \n  \nFig. 7. In-plane  PFM images. (a) -(c) Topography, RCosθ piezoresponse signal: (d) -(f) before and \n(g)-(h) after local poling of bi -square area by ±35 V DC voltage (left part is poled negatively, while \nright part - positively). (a), (d), (g) 0.8BiFeO 3 - 0.2BaTiO 3; (b), (e), (h) 0.7BiFeO 3 - 0.3BaTiO 3; \n(c), (f), (i) (0.6)BiFeO 3-(0.4)BaTiO 3-solid solutions. Displayed topography is measured \nsimultaneously with PFM before poling and thereby shifted slightly after poling due to thermal \ndrift.  \n \n"    },    {        "title": "1103.5024v1.Temperature_dependence_of_spin_resonance_in_cobalt_substituted_NiZnCu_ferrites.pdf",        "content": "PreprintfromAppl.Phys.Lett. 97,182502(2010)\nTemperature Dependence Of Spin Resonance In Cobalt Substituted  \nNiZnCu Ferrites\nA. Lucas 1,2, R. Lebourgeois 1, F. Mazaleyrat 2,E. Labouré2\n1. THALES R&T, Campus Polytechnique, 1 avenue Augustin Fresnel, 91767 Palaiseau, France\n2. SATIE, ENS de Cachan, 61 av. du Président Wilson, 94235 Cachan, France\nAbstract : Cobalt substitutions were investigated in Ni 0.4Zn0.4Cu0.2Fe2O4 ferrites, initial complex  \npermeability was then measured from 1 MHz to 1 GHz. It appears that cobalt substitution led to a  \ndecrease of the permeability and an increase of the µ s×fr factor. As well, it gave to the permeability  \nspectrum  a  sharp  resonance  character.  We  also  observed  a  spin  reorientation  occuring  at  a  \ntemperature depending on the cobalt content. Study of the complex permeability versus temperature  \nhighlighted that the most resonant character was obtained at this temperature. This shows that cobalt  \ncontribution to second order magneto-crystalline anisotropy plays a leading role at this temperature. \nKeywords : NiZnCu ferrites, cobalt substitutions, complex permeability, induced anisotropy\nNickel-zinc-copper ferrites are interesting materials because of their high permeability in MHz range. Moreover,  \ntheir low sintering temperatures make them suitable for the realization of integrated components in power  \nelectronic. As for nickel-zinc ferrites, cobalt substitution is an efficient technique to decrease permeability [1]  \nand magnetic losses of nickel-zinc-copper ferrites [2]. It has been proposed that the effect of cobalt is to produce  \npinning of the domain walls because of anisotropy enhancement due Co2+ ions ordering [3]. The aim of this  \npaper is to study the effect of cobalt substitution and particularly the role of the cobalt contribution to anisotropy.  \nFerrites of formula (Ni0.4Zn0.4Cu0.2)1-xCoxFe1.98O4 were studied for cobalt substitutions up to 0.035 mol.\nFerrites were synthesized using the conventional ceramic route. The raw materials (Fe 2O3, NiO, ZnO, CuO) were  \nball milled for 24h hours in water. Co 3O4 was then added before the calcination at 760°C in air for 2 hours. The  \ncalcined ferrite powder was then milled by attrition for 30 min. The resulting powder was compacted using axial  \npressing.  The sintering was performed at 935°C for 2 hours in air. Magnetic characterizations were done on ring  \nshaped samples with the following dimensions: external diameter = 6.8 mm; internal diameter = 3.15 mm; height  \n= 4 mm. Initial complex permeability (µ’ and µ’’) was measured versus frequency between 1 MHz and 1 GHz  \nusing an impedance-meter HP 4291. Static initial permeability (µ s) was defined as µ’ at 1 MHz because for these  \nferrites µ’(1 MHz) = µ’(100 Hz). For permeability versus temperature measurements, the rings were wound with  \na copper wire and placed in an oven going from –70°C to 200°C. µ s was deduced from the inductance measured  \nat 100 kHz by an impedance-meter Agilent 4194A.\nThe samples sintered at 935°C have all the pure spinel crystalline structure and a density higher than 96% of the  \ntheoretical density. Table I shows evolution of the permeability of the  (Ni0.4Zn0.4Cu0.2)1-xCoxFe1.98O4 ferrites. \nCobalt substitutions lead to a decrease of the initial complex permeability and an increase of the µ s×fr factor \nwhich is maximum for Co = 0.021 mol (f r is the frequency resonance defined as the maximum of µ’’). The raise  \nof this factor shows that f r increases faster than µ s decreases.\nFigure 1 shows the initial complex permeability versus frequency for (Ni 0.4Zn0.4Cu0.2)1-xCoxFe1.98O4 ferrites with \ndifferent cobalt content. One can see that the spectra become sharper when the cobalt rate increases. It is  \naccepted  that  the  permeability  has  two  contributions  :  at  low  frequency  wall  domain  displacements  are  \npreponderant and at higher frequency,  permeability is mainly due to the spin rotation [4].  In general, the  \nrelaxation behavior of domain walls essentially hides the spin resonance, but cobalt is known to inhibit the  \ndomain wall displacements [5], which produces two effect: (i) the initial permeability is decreasing with cobalt  \ncontent; (ii)  at higher frequency,  the  cobalt seems to promote  the  spin rotation by shifting the frequency  \nresonance (maximum of µ”) toward higher frequencies. Consequently, the magnetic losses due to domain wall  \ndisplacements are lowered, leading to a stronger dissymmetry in the shape of µ” peak. The magnetic losses rise  \nat higher frequency but with a steeper slope.\nThe cobalt has also an effect on the temperature variation of the permeability. In order to understand this  \nphenomenon, the permeability dependence on temperature has been studied (figure 2). \n\n1PreprintfromAppl.Phys.Lett. 97,182502(2010)\nThe cobalt free  ferrite  (curve A) shows a monotonous increase in this temperature range.  In contrast, the \nbehavior is different for the cobalt-substituted ferrites, for which a local maximum in the initial permeability  \nappears. This is the consequence of the magneto-crystalline anisotropy compensation due to the cobalt ions  \ncontribution. Indeed, the first order anisotropy constant of the Ni(ZnCu) ferrite host crystal is negative, whereas  \nCo ferrite has a positive one. As previously described by Van Den Burgt [6] for a certain amount of Co within  \nthe order of 0.1/u.f., it results that a spin reorientation transition occurs ( SRT, i.e. a change in easy axis)  at a  \ntemperature  T0, increasing with cobalt content. The permeability is described by the following relation :\neffs\nKMµ2\n'α [6]\nMs is the saturation magnetization and K eff the effective anisotropy. K eff consists of three components due to :  \nmagneto-crystalline anisotropy (K 1) of the host crystal, the cobalt ions contribution to anisotropy, higher order  \ncontributions and magneto-elastic energy [8]. This  spin reorientation  leads to an increase of the permeability  \ncharacterised by a local maximum around T 0. Below the SRT, K1>0 and K2>0 as the Co contribution dominates,  \nand  above  SRT  K1<0,  corresponding  to  a  change  from  [100]  to  [110]  easy  axis.  Figure  2,  shows  that  \n(Ni0.40Zn0.40Cu0.20)0.979Co0.035Fe1.98O4 ferrite has a SRT close to room temperature. The strong resonant character of  \nthe permeability at this point could be explained by the strong pinning of domain wall due to high second order  \nanisotropy contribution. \nIn order to go deeper insight the effect of cobalt on the magnetic behavior, the initial complex permeability  \nspectra were recorded near the SRT on two ferrites : \n-a (Ni0.4Zn0.4Cu0.2)0.965Co0.035Fe1.98O4 ferrite, which has a SRT around 10°C. \n-a Ni0.4Zn0.4Cu0.2Fe1.98O4 ferrite which doesn’t exhibits SRT. \nFigure 3 shows µ’(f) spectra between –50°C and 180°C of these two materials .  To quantify the resonant  \ncharacter of the µ’ spectrum versus frequency, we defined the following resonance factor F res :\n100')''(max×−=\nstaticstaticresµµµF\nwhich variation for the two compositions is shown on figure 4.\nThe cobalt free ferrite has a low F res (around 15%) slightly decreasing with temperature. This behavior can be  \nexplained by the decrease of the magnetization saturation. In contrast, t he permeability spectra of the cobalt-\nsubstituted ferrite strongly depend on the temperature. Figures 3 and 4 show that the sharpest resonant character  \nis obtained around 10°C, corresponding to the SRT. It can also be noted that, in this range of temperature, the  \nresonance factor of the cobalt-substituted ferrites is always higher than one of the cobalt free ferrite. As the  \nmagnetization is constantly decreasing in this temperature range, such a change in the permeability behaviour is  \nnecessarily due to a change in the effective anisotropy.\nIn the case of Co substituted ferrite, the resonance should be explained if one considers that domain wall are  \npinned (case of strong anisotropy) and the spins rotates freely (case of vanishing anisotropy), so there is an  \napparent  contradiction.  However,  near  the  SRT,  the  situation  is  much  different  compared  to  usual:  K 1 is \nvanishing but K2 is not necessarily dropping to zero accordingly. In the limit of  K1 = 0, there arte two main  \nconsequences. Firstly, the domain wall energy is not vanishing but γ = 2(AK2)1/2 [9], so the pinning energy may  \nbe still important. Secondly, development of anisotropy energy reduces to 2322212αααKEA=Δ. If one of the \ndirection cosines is null (case of {100} and equivalent planes) there is no anisotropy variation. So, a possible  \nexplanation of the strong resonance observed only in the cobalt-substituted sample would be nearly free spin  \nrotation in the  {100}, {010} and {001} planes [10]. If the magnetization turns in the {110} from 110 to \n111, the anisotropy change is at most K2/8. As the static permeability is relatively small, this would mean that  \nK2 is relatively strong in this material near the SRT, explaining also why the µ S(T) maximum is relatively smooth  \nIn  conclusion,  the  study  of  permeability  spectra  of  cobalt  substituted  NiZnCu  ferrites  as  a  function  of  \ntemperature shows that cobalt substitution can shift the spin reorientation transition close to room temperature  \ndue to cancellation of first order anisotropy constants of Co ion and the host crystal. As a consequence of the  \n2PreprintfromAppl.Phys.Lett. 97,182502(2010)\nnon-zero second order anisotropy constant, spin resonance damping is very small resulting in a strong resonance  \nrevealed by a very large overshoot (60%) of µ’ spectra and a sharp absorption peak in µ” spectra in the vicinity  \nof SRT.\nReferences\n[1] T. Y. Byun, S. C. Byeon, K. S. Hong, Factors affecting initial permeability of Co-substituted Ni-Zn-Cu  \nferrites, IEEE, vol 35, Issue 5, Part 2, pages : 3445-3447, sept 99\n[2] R. Lebourgeois, J. Ageron, H. Vincent and J-P. Ganne, low losses NiZnCu ferrites (ICF8), Kyoto and Tokyo,  \nJapan 2000\n[3] J. G. M. De Lau, A. Broese van Groenoul, Journal de  Physique 38, 1977, page Cl-17\nL. Néel, J. Phys. Radium 13, 249, 1952\n[4] T. Tsutaoka, M. Ueshima and T. Tokunaga, J. Appl. Phys. 78 (6), p 3983-3991, 1995\n[5] A.P. Greifer, V. Nakada, H. Lessoff, J. Appl. Phys., vol 32, 382-383, 1961\n[6] C. M. van der Burgt, Philips Research Report 12, 97-122, 1957\n[7] H. Pascard, SMM13, J. Phys. IV France, 8, 1998\n[8] A. Globus and P. Duplex, J. Appl. Phys., vol 39, no.2 (part I) 727-729, 1968\n[10] R. Skomski, J.M.D. Coey,Permanent Magnetism, Taylor & Francis, 1999, p. 156\n[11] S. Chikazumi, Physics of Ferromagnetism, 2nd ed., Oxford Science Pub., 1997, p. 252\nTable I : Static permeability and resonance frequency of (Ni 0.40Zn0.40Cu0.20)1-єCoєFe1.98O4 ferrites\nmol CobaltStatic µ’fr (MHz)µs×fr (GHz)\nCo = 027022.16\nCo = 0.00718536.36.7\nCo = 0.01416045.67.3\nCo = 0.02114550.77.35\nCo = 0.02813056.57.35\nCo = 0.03511563\nList of figu  res :   \nFigure 1 : Complex permeability versus frequency of (Ni 0.4Zn0.4Cu0.2)1-xCoxFe1.98O4 ferrites\n3\nPreprintfromAppl.Phys.Lett. 97,182502(2010)\nFigure 2 : Initial permeability versus temperature of  (Ni 0.4Zn0.4Cu0.2)1-xCoxFe1.98O4 ferrites.\nFigure 3 : (A) : Ni0.4Zn0.4Cu0.2Fe1.98O4  µ’(f) spectrum from 1 MHz to 110 MHz for temperature between –40°C to  \n130°C.\n4PreprintfromAppl.Phys.Lett. 97,182502(2010)\n        (B) : (Ni0.4Zn0.4Cu0.2)0.965Co0.035Fe1.98O4  µ’(f) spectrum from 1 MHz to 110 MHz for temperature  \nbetween –50°C to 180°C.\nFigure 4 : Fres versus temperature of Ni 0.4Zn0.4Cu0.2Fe1.98O4 and (Ni0.4Zn0.4Cu0.2)0.965Co0.035Fe1.98O4 ferrites.\n5\n"    },    {        "title": "1211.1366v1.Exact_asymptotic_behavior_of_magnetic_stripe_domain_arrays.pdf",        "content": "arXiv:1211.1366v1  [cond-mat.mtrl-sci]  5 Nov 2012Exact asymptotic behavior of magnetic stripe domain arrays\nTom H. Johansen,1,2,3Alexey V. Pan,3and Yuri M. Galperin1,2,4,5\n1Department of Physics, University of Oslo, 0316 Oslo, Norwa y\n2Centre for Advanced Study at the Norwegian Academy of Scienc e and Letters, 0271 Oslo, Norway\n3Institute for Superconducting and Electronic Materials,\nUniversity of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia.\n4Physico-Technical Institute RAS, 194021 St. Petersburg, R ussian Federation\n5Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 6 0439, U. S. A.\n(Dated: June 16, 2021)\nThe classical problem of magnetic stripe domain behavior in films and plates with uniaxial mag-\nnetic anisotropy is addressed. Exact analytical results ar e derived for the stripe domain widths as\nfunction of applied perpendicular field, H, in the regime where the domain period becomes large.\nThe stripe period diverges as ( Hc−H)−1/2, whereHcis the critical (infinite period) field, an exact\nresult confirming a previous conjecture. The magnetization approaches saturation as ( Hc−H)1/2,\na behavior which compares excellently with experimental da ta obtained for a 4 µm thick ferrite gar-\nnet film. The exact analytical solution provides a new basis f or precise characterization of uniaxial\nmagnetic films and plates, illustrated by a simple way to meas ure the domain wall energy. The\nmathematical approach is applicable for similar analysis o f a wide class of systems with competing\ninteractions where a stripe domain phase is formed.\nSystems with competing interactions, in particular\nthose with short-range attractive and long-range repul-\nsive interactions, commonly develop modulations in the\norder parameter and form domain structures often con-\nsisting of a stripe pattern [1]. Realizations are found in\nwidevarietyofsystems, suchasmagneticfilmsandplates\nwith uniaxial anisotropy [2], magnetic liquids [3], type-\nI superconductors in the intermediate state [4], doped\nMott insulators [5], quantum Hall structures [6], and\nmonomolecular amphiphilic (“Langmuir”) films [7].\nThe uniaxial magnetic films, where ferrite garnets is\na classical material studied extensively decades ago for\nuse in bubble memory devices, [8] may be regarded as a\nprototype system for stripe domain behavior. Recently,\nthe dynamical behavior of the domains in thick garnet\nfilms showed a vast potential for manipulation of micron-\nsized superparamagneticbeads dispersed in a water layer\ncovering the film. By applying magnetic fields with os-\ncillating in- and out-of-plane components, new principles\nfor micromachines like colloidal ratchets, size separators,\nmicro-tweezers and stirrers, etc. were demonstrated [9].\nMoreover,it has been shown that the magnetic stripe do-\nmain structure, when placed adjacent to type-II super-\nconductors, can stronglyinteract with the vortex matter,\nboth in a manipulative way [10], and as a method to en-\nhance flux pinning in the superconductor [11]. Thus, one\nsees today considerable renewed interest in the collective\nbehavior of magnetic stripe domains.\nOn the theoretical side, the treatment of magnetic do-\nmains in plates with perpendicular easy-axis anisotropy\nplaced in an external magnetic field is challenging. Even\nsolving the magnetostatic problem of one isolated linear\nstripe surrounded by reverse magnetization turned out\nrather complicated analytically, and for a regular array\nof alternating stripes results were so far obtained only by\nnumerical calculations [12]. In this work, based on thewall-energy model [2], i.e., assuming domains separated\nby infinitely thin walls oriented normal to the plate, we\nderive an exact analytical solution for the behavior of a\nperiodic array of interacting stripe domains in increasing\napplied field.\nConsider a uniaxial plate of arbitrary thickness, t,\nwhere magnetic domains form a periodic lattice of par-\nallel stripes with alternating magnetization ±Ms, see\nFig. 1. In an applied perpendicular field, H, the domains\nmagnetized parallel and antiparallel to the field are char-\nacterized by their respective widths a↑anda↓, and the\nmagnetization of the plate is M=Ms(a↑−a↓)/a, where\na=a↑+a↓is the period of the stripe lattice.Exact asymptotic behavior of magnetic stripe domain films \nTom H. Johansen, 1,2,3 Alexey Pan, and Yuri M. Galperin 1,3,4 \nDepartment of Physics, University of Oslo, 0316 Oslo, Norway \nInstitute for Superconducting and Electronic Materials, U niversity of Wollongong, Australia \nCentre for Advanced Study at the Norwegian Academy of Scienc e and Letters, 0271 Oslo, Norway \nArgonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 6 0439, U. S. A. \n(Dated: October 27, 2012) \nThe classical problem of magnetic stripe domain behavior in fil ms with uniaxial magnetic \nanisotropy is treated. Exact analytical results are derived for th e stripe domain widths (majority \nand minority domains) as function of applied perpendicular fiel d in the regime where the domain \nperiod becomes large and approaches infinity. The predicted asym ptotic behavior of the magneti- \nzation versus field is compared with experimental data obtained for a ferrite garnet film. The exact \nanalytical solution provides basis for a new simple way to meas ure the domain wall energy. \n... some more ... \nFIG. 1. Cross-section of a stripe domain pattern, and numer- \nical results for the domain widths as function of applied field \nfor the case Λ = 0 05. FIG. 1. Cross-section of a plate with magnetic stripe domain\npattern (top), and numerical results for the domain widths a s\nfunction of applied field for the case Λ = 0 .05 (bottom).2\nFollowing the analysis of Kooy and Enz [2], the energy\ndensity has three contributions; ( i) the cost of forming\ndomain walls, characterized by the energy σwper unit\nwall area, ( ii) the energy gain of aligning the magne-\ntization with the applied field, −µ0HM, and (iii) the\nself-energy of the domain structure (demagnetization en-\nergy). The total energy, U, per unit volume of the plate\ncan then be written as [8]\nU(m,a)\nµ0M2s= 2Λt\na−mh+1\n2m2\n+2a\nt∞/summationdisplay\nn=1sin2[nπ(1+m)/2]\n(nπ)3(1−e−n2πt/a).(1)\nHerem=M/Ms,h=H/Ms, and Λ = λ/twhere\nλ=σw/µ0M2\nsis a characteristic length. The equilib-\nrium magnetization and stripe period at a given applied\nfield is given by, ∂U/∂m=∂U/∂a= 0, and expressed by\nthe two equations,\n1−2x−2\nπF(2πx,2πy) =h, (2)\nG(2πx,2πy) = 2πΛ. (3)\nHerex≡a↓/a= (1−m)/2 andy≡t/a, and\nF(x,y)≡∞/summationdisplay\nn=1sinnx\nn21−e−ny\ny, (4)\nG(x,y)≡8∞/summationdisplay\nn=1sin2(nx/2)\nn31−(1+ny)e−ny\ny2.(5)\nTheparticularchoiceofnewvariablesismotivatedbythe\nnumerical solution of the problem shown graphically in\nthe lower panel of Fig. 1 only for reference. The striking\nfeature is that when the applied field approaches a criti-\ncal value, Hc=hcMswherehc<1, both the period, a,\nof the domain lattice, and the width, a↑, of the domains\nmagnetized parallel to the field will diverge, whereas the\nreverse domains contract only moderately and terminate\nat a finite width a↓c. At fields above Hc, the material re-\nmains single-domain. In the new variables the approach\ntowards the critical values corresponds to both x,y→0,\nwhile the ratio r≡x/y=a↓/tremains finite [13].\nFocus of the present analysis is to determine analyt-\nically the exact behavior as the field approaches the\ncritical value. We first derive the relation between hc\nanda↓c. For this, we introduce the auxiliary function\npk(z)≡/summationtext∞\nn=1n−(k+1)e−nz= polylog( k,−z),and write\nF(x,y) = Im[p1(−ix)−p1(y−ix)]/y. (6)\nFor small |z|one has\np1(z) = (π2/6)+z(lnz−1)−(z2/4)+(z3/72)+...,(7)\nwhich results in the following series expansion,\nF(x,y) = arctan(x\ny)+x\nyln/radicalbigg\n1+y2\nx2−x\n2\n+xy\n24+2yx3−xy3\n2880+.... (8)Inserted in Eq. (2) it takes the form\nh= 1−2\nπ/bracketleftBig\narctan(r)+rln/radicalbig\n1+r−2/bracketrightBig\n−π\n3rx2+π3\n90r(2−r−2)x4+... . (9)\nThe critical field is therefore given by\nhc=2\nπarctan(r−1\nc)−rc\nπln(1+r−2\nc),(10)\nwhererc=a↓c/tis the critical, i. e., the terminal width\nof the minority (anti-parallel to H) domains.\nTo find a relation between rcand the material param-\neter Λ, a similar treatment is given to Eq. (3), using that\nG(x,y) can be expressed as a combination of the real\nparts of both p1(z) andp2(z) with complex arguments\nlike those in Eq. (6). For small |z|, one has\np2(z) =ζ(3)−π2z\n6+(3−2lnz)z2\n4+z3\n12−z4\n288+...(11)\nwhereζ(n) is the Riemann zeta-function, and Eq. (3)\nbecomes\nln(1+r2)+r2ln(1+r−2)−π2\n3x2\n−π4\n270(3−9r−2+r−4)x4+...= 2πΛ.(12)\nThe terminal width of the minority domains is therefore\ngiven by\nln(1+r2\nc)+r2\ncln(1+r−2\nc) = 2πΛ,(13)\nand is shown graphically in Fig. 2. The figure also shows\nthe dependence hc(Λ), which follows from Eqs. (10) and\n(13). Both these curves, if replotted as functions of Λ−1,\nagree excellently with the numerical solutions presented\nFIG. 2. The critical field, hc=Hc/Ms, and terminal minority\ndomain width, rc, as functions of Λ = σw/(µ0M2\nst). The\ndashed line represents hc(Λ) = (√e/π)exp(−πΛ)3\nFIG. 3. Magnetic moment of a ferrite garnet film versus ap-\nplied perpendicular field. The straight line represents the con-\ntribution from the paramagnetic GGG substrate. The inset\nshows a schematic of the two contributions to the moment.\nin Fig. 7 of the Ref. 12. Note that for any material,\ni. e., given σwandMs, the critical field decreases with\nΛ, and for Λ >0.2 this dependence rapidly approaches\nhc= (√e/π)exp(−πΛ), shown as a dashed line in Fig. 2.\nConsider next the behavior in the vicinity of h=hc.\nExpanding the Eqs. (9) and (12) in Taylor series around\nthe critical point one finds to the lowestorder that πx2=\n2rc(hc−h). It then followsthatthe stripepatternperiod,\na/t=r/x, diverges according to\na\nt=/radicalbiggπrc\n2(hc−h)−1/2. (14)\nAt the same time, the reverse domain approaches its ter-\nminal width as\na↓\nt=rc+π(hc−h)\n3 ln(1+ r−2c), (15)\nand the magnetization, m= 1−2rt/a, approaches satu-\nration according to\nm= 1−/radicalbigg\n8rc\nπ(hc−h)1/2(16)\nTo compare the analytical results with the quantita-\ntive behavior of a typical sample with magnetic stripe\ndomains, we prepared a film of bismuth-substituted fer-\nrite garnet, (Y,Lu,Bi) 3(FeGa) 5O12, by liquid phase epi-\ntaxialgrowthona(111)orientedgadoliniumgalliumgar-\nnet (GGG) substrate. Oxide powders of the constituent\nrare earths, bismuth, iron and gallium, as well as PbO\nand B 2O3, were initially melted in a thick-walled plat-\ninum crucible. To ensure homogeneity of the solution a\nstirrer mixed the melt while being kept in the 3-zone re-\nsistive furnace at 1050◦C for 30 minutes. Prior to the\nFIG. 4. Reduced magnetization ( Ms−M)/Ms, experimen-\ntal data and fitted model behavior, Eq.(13), versus applied\nmagnetic field. Upper inset: The linear fit to the reduced\nmagnetization squared. Lower inset: Magneto-optical imag e\nshowing that the FGF sample displays a parallel stripe do-\nmain pattern.\nfilm growth the melt temperature wasreduced to 700◦C.\nThe GGG wafer was mounted horizontally in a 3-finger\nplatinum holder attached to a shaft rotating by 60 rpm,\nand brought slowly down towards the melt. Finally, the\nsubstrate was dipped into the melted for 8 minutes re-\nsulting in a macroscopically uniform ferrite garnet film\n(FGF) grown on one side of the substrate. A nearly\nsquare plate of area A= 21 mm2was selected for mea-\nsurements. The thickness of the FGF was determined by\nviewing the sample edge-on in a scanning electron micro-\nscope, where a sharp contrast between the film and the\nsubstrate becomes visible. The ferrite garnet thickness\nwast= (4.0±0.2)µm.\nShown in Fig. 3 is the result of dc-magnetization mea-\nsurements performed using a Quantum Design Magnetic\nProperty Measurement System (SQUID magnetometer)\nwiththeFGFmountedperpendiculartotheappliedfield.\nAbove the field of 17 kA/m, the data show linear in-\ncrease, which is due to the paramagnetic substrate, in\ncombination with the FGF being single domain having a\nconstant moment. The fitted straight line intersects the\nvertical axis at a point which determines the saturation\nmoment of the FGF sample, µs= 2.91 10−6Am2, which\ncorresponds to Ms= 34.6 kA/m.\nFigure 4 shows the reduced magnetic moment of the\nFGF obtained by subtracting the paramagnetic back-\nground from the raw data. Based on the model result,\nEq. (16), the reduced magnetization was fitted to the\npredicted asymptotic form ( Hc−H)1/2using data over\na field range below the point where the moment satu-\nrates. The best linear fit of the reduced moment squared\nis seen in the upper inset, from which we find a criti-4\ncal field of Hc= 13.9 kA/m, and thus hc= 0.40. It\nfollows then from Eq. (10) that rc= 0.605, and from\nEq. (13) one finds Λ = 0 .126, and λ= 0.126t= 0.504\nmicrons. The specific wall energy has therefore the value\nσw= 7.58·10−4J/m2.\nIn previous analyses of the stripe domain problem, see\ne.g., Ref. 12, it was suggested that as the applied field\napproaches hc, the stripe period diverges with a power\nβ≈0.5. In this work it has been shown that β= 1/2\nis an exact result. Consider next what is the field range\nover which the asymptotic behavior is expected to be ob-\nserved. Therearepreviousworks[12]whereexperimental\ndata were fitted by numerical M−Hcurves approaching\nsaturation seemingly with a finite slope. Furthermore,\nin the classical book Ref. 8, the Fig. 2.3 shows M−H\ncurvesapproachingsaturationwithafinite slopestrongly\ndepending on the sample thickness. To resolve this ap-\nparent inconsistency, we analyzed the Eqs. (9) and (12)\nup to the next order, i. e., expanding them to ( r−rc)2\nand keeping the terms ∝x4. The analysis shows that\nEqs. (14)–(16) provide a good description as long as\n(hc−h)/lessorsimilarmin{rc,1}. (17)\nThus, for thick plates, t≫λ, one has a very small 2 πΛ\nandrc≈[2πΛ/ln(1/2πΛ)]1/2, which is much less than\nunity. Thus, it follows that the asymptotic behavior (16)\nwill be observed only very close to hc. In practice, the\nfieldintervalmaybebeyondexperimentalresolution, and\nthe slope of the magnetization curve near h=hcappears\nfinite. For thinner plates and films, rcrapidly increases,\nsee Fig. 2, and the inequality (17) becomes much weaker,\nand the range where one should observe the critical be-\nhavior Eq. (16) will be sizable, as demonstrated in the\npresent experiments.\nFinally, note the presence of a small shoulder in the\nreduced magnetization data in Fig. 4 seen just above Hc.\nHere the behavior deviates significantly from the model\nprediction, and is caused by topological fluctuations in\nthe domain pattern. The role of material defects caus-\ning wall pinning becomes significant, and the stripes lose\ntheir alignment, a scenario which is readily seen visually\nby following the behavior using magneto-optical imag-\ning [14].\nIn summary, we have presented an analytical asymp-\ntotic solution to the problem of modeling the behavior of\nan infinite array of parallel alternating magnetic stripe\ndomains subjected to a transverse field. The mathemat-\nical approach used in this work can be applied to derive\nexact results also for other systems [3, 15] where stripe\ndomain phases are formed and described by a configu-\nrational energy term similar to the one treated in the\npresent case.\nThe work was financially supported by the Aus-\ntralian Research Council International Linkage Project\nLX0990073 and Discovery Project DP0879933, andthe Norwegian Research Council. YG is grateful to\nI. Lukyanchuk and A. Mel’nikov for discussions.\n[1] M. Seul and D. Adelman, Science 267, 476 (1995). C.\nSagui, E. Asciutto and C. Roland, Nano Lett. 5, 389\n(2005).\n[2] C. Kooy and U. Enz, Philips Res. Repts. 15, 7 (1960).\n[3] C. Flament, J.-C. Bacri, A. Cebers, F. Elias and R.\nPerzynski Europhys. Lett. 34, 225 (1996). M. F. Islam,\nK. H. Lin, D. Lacoste, T. C. Lubensky and A. G. Yodh\nPhys. Rev. E 67, 021402 (2003).\n[4] R. P. Huebener Magnetic Flux Structures of Supercon-\nductors(Springer-Verlag, New York, 2001). R. Prozorov,\nPhys. Rev. Lett. 98, 257001 (2007).\n[5] J. M. Tranquada, B. J. Sternlieb, J. D. Axe, Y. Naka-\nmura, and S. Uchida, Nature 375, 561 (1995).\n[6] M. M. Fogler, A. A.Koulakov, and B. I. Shklovskii, Phys.\nRev. B54, 1853 (1996). A. A. Koulakov, M .M. Fogler,\nand B. I. Shklovskii, Phys. Rev. Lett. 76, 499 (1996).\n[7] P. G. De Gennes and C. Taupin, J. Phys. Chem. 86, 2294\n(1982). W. M. Gelbart andA. Ben-Shaul, J. Phys. Chem.\n100, 13169 (1996).\n[8] A. H. Bobeck and E. Della Torre Magnetic Bubbles :\n(American Elsevier, New York, 1975).\n[9] L. E. Helseth, T. M. Fischer and T. H. Johansen, Phys.\nRev.Lett. 91, 208302 (2003).L.E.Helseth, L.E.Wen,R.\nW. Hansen, T. H. Johansen, P. Heinig and T. M. Fischer\nLangmuir 20, 7323 (2004). P. Tierno, T. H.Johansen and\nTh. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007). P.\nTierno, Th. M. Fischer, T. H. Johansen and F. Sagues,\nPhys. Rev. Lett. 100, 148304 (2008).\n[10] P. E. Goa, H. Hauglin, A. A. F. Olsen, D. V. Shantsev,\nT. H. Johansen, Appl. Phys. Lett. 82, 79 (2003). L. E.\nHelseth, P. E. Goa, H. Hauglin, D. V. Shantsev, T. H. Jo-\nhansen, Y. M. Galperin, Phys. Rev. B 65, 132514 (2002).\nJ. I. Vestg˚ arden, D. V. Shantsev, T. H. Johansen, Y. M.\nGalperin, P. E. Goa and V. V. Yurchenko, Phys. Rev.\nLett.98, 117002 (2007).\n[11] V. H. Dao, S. Burdin, and A. Buzdin, Phys. Rev. B. 84,\n134503 (2011). M. Iavarone, A. Scarfato, F. Bobba, M.\nLongobardi, G. Karapetrov, V. Novosad, V. Yefremenko,\nF. Giubileo, and A. M. Cucolo, Phys. Rev. B. 84, 024596\n(2011). V. Vlasko-Vlasov, A. Buzdin, A. Melnikov, U.\nWelp, D. Rosenman, L. Uspenskaya, V. Fratello, and W.\nKwok, Phys. Rev. B 85, 064505 (2012).\n[12] J. A. Cape and G. W. Lehman, J. Appl. Phys. 42, 5732\n(1971). K. L. Babcock and R. M. Westervelt, Phys. Rev.\nA40, 2022 (1989).\n[13] From the Eqs. (2) and (3) it is not evident that such a\ncritical point should exist. Our choice of variables was\nmade by postulating an hcwhereddiverges and a↓re-\nmains finite (as suggested by numerics), and realizing\nthat the leading terms in the analytical functions repre-\nsenting the Fourier sums depend only on x/yasx,y→0.\n[14] P. E. Goa, H. Hauglin, A. A. F. Olsen, M. Baziljevich\nand T. H. Johansen, Rev. Sci. Instrum. 74, 141 (2003).\n[15] R. Goldstein, D. P. Jackson and A. T. Dorsey, Phys. Rev.\nLett.76, 3818 (1996). A. T. Dorsey and R. Goldstein,\nPhys. Rev. B 57, 3058 (1998)."    },    {        "title": "1701.01410v1.Transforming_Single_Domain_Magnetic_CoFe2O4_Nanoparticles_from_Hydrophobic_to_Hydrophilic_By_Novel_Mechanochemical_Ligand_Exchange.pdf",        "content": "Page 1 of 26 \n Transform ing Single Domain Magnetic CoFe 2O4 Nanoparticles from Hydrophobic to \nHydrophilic By Novel Mechanochemical Ligand Exchange  \nSandeep Munjal and Neeraj Khare*  \nDepartment of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi -110016, \nIndia.  \nAbstract  \nSingle phase, uniform size (~9 nm) Cobalt Ferrite (CFO) nanoparticles have been \nsynthesized by hydrothermal synthesis using oleic acid as  a surfactant. The as synthesized oleic \nacid coated CFO (OA -CFO) nanoparticles were well dispersible in nonpolar solvents but not \ndispersible in water. The OA -CFO nanoparticles have been successfully  transformed to highly \nwater dispersible citric acid coated  CFO (CA -CFO) nanoparticles using a novel single step \nligand exchange process  by mechanochemical milling , in which  small chain citric acid \nmolecules replace  the original large chain oleic acid molecules available on CFO nanoparticles. \nThe OA -CFO nanopartic le’s hexane solution and CA -CFO nanoparticle’s water solution \nremain stable even after six months, and shows no agglomeration  and their dispersion  stability \nwas confirme d by zeta potential measurements.  The contact angle measurement shows  that \nOA-CFO nanoparticles are hydrophobic whereas CA -CFO nanoparticles are superhydrophilic \nin nature. The potentiality  of as synthesized OA-CFO and  mechanochemically  transformed  \nCA-CFO nanoparticles for the demulsification of highly stabilized water -in-oil and oil -in-water \nemulsions has been demonstrated.  \nKEYWORDS:  CoFe 2O4; Ligand Exchange; Hydrophobic; Magnetic Nanoparticles  \n*Authors to whom all correspondence should be addressed.  \nE-mail: nkhare@physics.iitd.ernet.in  \n Journal of Nanoparticle Research (Accepted Manuscript  02-Dec-2016)  Page 2 of 26 \n 1. Introduction  \nMagnetic nanoparticles have attracted a great attention of scientific community due to \ntheir potentiality in many advanced and novel applications such as for high -density data storage  \n(Reiss and Hütten 2005) , targeted drug delivery (Arruebo et al. 2007) , catalysis (Kharisov \n2014) , as contrast enhancement agents i n magnetic resonance imaging (Wang et al. 2011) , in \nmagnetic hyperthermia treatments as heat mediators (Brollo et al. 2016) , for resistive switching \napplications (Munjal, Kumari, et al. 2016)  ,and for oil−water multiphase separation  etc. The \nsurface of these magnetic nanoparticles is functio nalized by organic (Wang et al. 2011)  or \ninorganic  shell as per the requirement of the application, and by changing the surface chemistry \nthe properties like mutual interaction between the nanoparticles or wettability behaviour can \nbe influenced  (Bajwa et al. 2016) . In order to control the size/shape of these nanoparticles \nsurfactants are used during the growth process. These  surfactant molecules acts as a stab ilizing \nagent that prevent the agglomeration and slow down the growth rate of the nanoparticles \n(Kumar et al. 2015) . Such nanoparticles, synthesized in the presence of surfactant are \ndispersible in organic /nonpolar solvents like hexane, toluene etc. On the other hand , this \nhydrophobic nature of the magnetic nanoparticles limits their use in many applications \nincluding the application in biochemistry , biomedi cal (Huang and Juang 2011)  and thin film \nfabrication . For all these applications the nanoparticles must be dispersible in polar  solvents \nlike water or ethanol  and this requires a further modification of the nanoparticles suface in \norder to make them hydrophilic. This modification of surface can be done in two ways; (a)  \nbinding an amphiphilic molecule to the original surfactant layer through hydrophobic \ninteracti ons and forming a micellar structure that encapsulates the magnetic na noparticles   or \n(b) replacing the native hydrophobic /Oleophilic  surfactants  a by small chain hydrophilic \nmolecule  that have higher affinity for the metal ion present in the magnetic nanop articles  \n(Kumar et al. 2015) . The later one is called ligand exchange process. The ligand, replacing the \nJournal of Nanoparticle Research (Accepted Manuscript  02-Dec-2016)  Page 3 of 26 \n native hydrophobic surfactant must have an anchoring group (phosphonic acid, dopamine etc.) \nthat binds to the surface of magnetic nanoparticles and the other end of this ligand must be \nhydrophilic that is exposed to the surrounding H 2O molecules and gives a colloidal stability to \nthe magnetic nanoparticles in the aqueous medium.  However , the c onventional method s of \nligand  exchange  may take  many hours  and are generally multistep  (Hatakeyama et al. 2011) . \nThe development of simple methods to generate magnetic nanoparticles  stable in aqueous \nenvironments remains the subject of vigorous inquiry.  \nIron oxide magnetic nanoparticles such as Fe3O4 (Tamer et al. 2010)  and γ−Fe2O3  (Hergt \net al. 2004)   have been extensively explored for these applications. The anothe r alternate can \nbe spinel ferrite [ MFe 2O4, M=Co, Ni, Zn etc]  magnetic nanoparticles, and specially cobalt \nferrite (CoFe 2O4) due to its large C urie temperature, high effective anisotropy and moderate \nsaturation magnetizati on (Bricen  et al. 2012)  . CoFe 2O4 (CFO) has an inverse spinel structure \nwith general form ula AB 2O4 (A = Fe and B = Co, Fe) where half of the Fe3+ occup ies the \noctahedral sites and the other half Fe3+ occupies the tetrahedral sites whereas all the Co2+ \noccu pies the octahedral sites (Munjal, Khare, et al. 2016) . Several techniques such as \nmicroemulsion (Mathew and Juang 2007) , coprecipitation (Kim, Kim, and Lee 2003)  , ball \nmilling (Manova et al. 2004)  , sol−gel (Lavela and Tirado 2007)  , thermal decomposition \n(Kalpanadevi, Sinduja, and Manimekalai 2014)  and sonochemical (Saffari et al. 2014)  method \nhave been employed for the synthesis of magnetic nanoparti cles but all these synthesis methods \noften produce larger size nanoparticles with wide particle size distribution. But most of the \nabove stated applications require s a narrow particle size distribution, as the performance of the \nmagnetic nanoparticles stro ngly depends upon the particle size and  particle size distribution .  \nIn the present work, we report the synthesis of uniform size oleic acid coated CFO (OA -\nCFO) nanoparticles by hydrothermal synthesis method  (Chaudhary, Khare, and Vankar 2016) , \nwhich are not water soluble and the conversion of these OA -CFO nanoparticles through a rapid  Page 4 of 26 \n and novel mechanochemical ligand exchange process using cit ric acid as a hydrophilic ligand \nto replace oleic acid from the surface of OA -CFO nanoparticles  in a single step . Due to the \nshort carbon chain and the presence of multiple carboxylic groups the citric acid becomes a \nsuitable candidate for the ligand exchange process.  A direct evidence of wettability of these \nCoFe 2O4 magnetic nanoparticles has been given by contact angle measurements. The use of \nOA-CFO and CA -CFO nanoparticles for the demulsification of highly stabilized oil  in water \nemulsions  and wat er in oil emulsions is also demonstrated .  \nConventional ligand exchange methods like s tirring based method  (Munjal, Khare, et al. \n2016)  or Solid -state photochemical ligand exchange  (Loim, N.M., Khruscheva, N.S., Lukashov \n1999)  suffers from time consumption and may take from 24 h to 48 h.  Our presented \nmechanochemical ligand exchange process is rapid and takes only ~ 30 minutes. We have \nrepeated this method se veral times and each time the results are reproducible. Application of \nour process may have impacts on the modification of hydrophobic magnetic nanoparticles and \npreparation of hydrophilic magnetic nanoparticles.  \nThe synthesized CA -CFO has many practical a pplications in biomedical. These water \ndispersible magnetic nanoparticles can be used (a)  for targeted drug delivery  (b) as contrast \nenhancement agents in magnetic resonance imaging (MRI) and ( c) in hyperthermia treatments \nas heat mediators . Beside all these applications , these nanoparticles can also be used as Draw \nSolutes in Forward Osmosis for Water reuse (Ge et al. 2011) . \n2. Experimental Section  \n2.1 Synthesis of hydrophobic OA -CFO nanoparticles  \nOleic acid coated c obalt ferrite (OA-CFO) nanoparticles have been synthesized by \nhydrothermal method using cobalt nitrate hexahydrate (Co(NO 3)2·6H 2O) and ferric nitrate \nnonahydrate (Fe(NO 3)3.9H 2O) as starting precursors and oleic acid as a surfactant. A solution Page 5 of 26 \n of 1.5 mmol  Co(NO 3)2.6H 2O and 3 mmol Fe(NO 3)3.9H 2O in ethanol was mixed with a 15 \nmmol NaOH solution and 0.2 M oleic acid. The resultant reaction solution was thoroughly \nstirred and poure d into a Teflon lined stainless steel autoclave. The autoclave was placed into \nan oven for 15 hours, which was preheated at 220 OC. After cooling the liquid phase was \ndiscarded and synthesized nanoparticles were thoroughly washed with hexane and ethanol. \nEach time, the synthesized CFO nanoparticles were separated from the liquid using a \npermanent magnet.  \n2.2 Transforming OA -CFO nanoparticles into CA -CFO nanoparticles  by \nmechanochemical milling  \nFig. 1  (a) Schematic of steps in the synthesis of OA -CFO and CA-CFO nanoparticles, (b) OA -\nCFO and (c) CA -CFO nanoparticles in toluene and water.  \nIn order to exchange the ligand coated on the OA -CFO nanoparticles (i.e. Oleic acid) by \ncitric acid, the OA -CFO nanoparticles were mixed with citric acid (1:5 wt/wt). Liqui d assisted \nPage 6 of 26 \n grinding was conducted by adding toluene to this mixture, taking the ratio of liquid volume to \nmass of solid (OA -CFO) nanoparticles as 5 μL mg−1 and the mixture was grinded for 30 \nminutes at room temperature. The modified nanoparticles were wash ed with a solution of \nacetone and ethanol. The finally obtained nanoparticles were dispersible in water without any \nresidue.  These citric acid coated nanoparticles are named as CA -CFO in the subsequent \ndiscussion. This novel mechanochemical ligand exchange  is single step and rapid compared to \nthe conven tional ligand exchange methods (Wang et al. 2014) .The schematic of steps in the \nsynthesis of OA -CFO nanoparticles and conversion of these nanoparticles into CA -CFO \nnanoparticles by the novel mechanochemi cal ligand exchange process is shown in Fig. 1 (a ). \nThe as synthesized OA -CFO nanoparticles makes stable colloidal solution when dispersed in \norganic nonpolar solvent, but not in water or polar solvents. The modified CA -CFO \nnanoparticles are well dispersib le in water or in any other polar solvent but not in nonpolar \nsolvents. Fig. 1 (b) and 1 (c) shows the macroscopic observations of OA -CFO and CA -CFO \nnanoparticles before and after the phase transfer. Fig. 1(b) confirms  that the as synthesized OA -\nCFO nanoparticles are soluble in nonpolar organic solvents like toluene or oil only and are \nimmiscible in water. The presence of OA -CFO nanoparticles can be o bserved by the \nbrown/black colouring  of the toluene layer over water , which verifies the hydrophobic a nd \nOleophilic nature of the OA -CFO nanoparticles. After ligand exchange with citric acid the \nmodified CA -CFO nanoparticles are soluble in water , but not soluble in organic solvents (Fig. \n1(c)) which is an evidence of hydrophilic nature of the CA -CFO nanopa rticles. The OA -\nCFO/CA -CFO nanoparticles does not go to the water/organic phase even after shaking that \nconfirms the colloidal stability of these nanoparticles in nonpolar/polar solvents.  \n2.3 Preparation of Water in Oil and Oil in Water emulsions  \nSurfactan t-stabilized water in oil (W/O) and oil in water (O/W) emulsions were \nprepared by taking  toluene as oil phase. Toluene in water emulsion was prepared by mixing Page 7 of 26 \n water and toluene (99:1, v/v) with the addition of 0.1 mg of SDS per ml of emulsion. W ater in \ntoluene emulsion was prepared by mixing water and toluene (1:99, v/v) with addition of 1 mg \nof Span -80 per ml of emulsion. The mixtures were stirred rigorously for 3 h. This gives very \nstable toluene in water and water in toluene emulsions which are referred  as O/W and W/O \nemulsions in the subsequent discussion.  \n2.4  Characterization methods  \nThe crystallographic studies of OA -CFO and CA -CFO nanoparticles have been carried out \nby Rigaku Ultima IV X -ray diffractometer (XRD ) with  CuKα radiation (λ= 1.54  Å) operated \nat 40 kV and 20 mA. The samples were taken in powder form and the XRD patterns were \nrecorded in gonio scan mode for 2θ value ranging from 20º to 80º with a step size of 0.05 º and \nscanning speed 6 º /min.  The morphology of the nanoparticle sam ples were characterized by \nusing a JEOL JEM -2200 -FS Transmission electron microscope (TEM).  Magnetic \nmeasurements of the CFO nanoparticles were performed at room temperature using the \nAlternating Gradient Magnetometer (AGM), in the magnetic field range of  -1 to 1 Tesla. For \nthe magnetic measurements, the CA -CFO nanoparticles were added in DI water (20 mg/mL) \nand OA -CFO nanoparticles were added in toluene (20 mg/mL) and then drop casted (20 µL) \nonto glass substrates (0.4cm × 0.4 cm) and dried properly. This  step was repeated 5 times and \nfinally obtained samples were used for magnetic measurements . FTIR studies of OA -CFO and \nCA-CFO nanoparticles were carried out using Thermo Scientific™ Nicolet™ iS™ 50 FT -IR \nSpectrometer. High performance liquid chromatograph y deionized water droplets ( ∼3 μL) with \na typical resistivity value of 18.2 MΩ cm at 25 °C were deposited on the sample surfaces for \ncontact angle measurements. The image of the droplet on sample was captured using CMOS \ncamera equipped with a magnifying lens. The contact angle of the droplet was measured using \nthe ImageJ software (National Institute of Health, USA), with a plugin Drop Shape Analysis.  Page 8 of 26 \n 3. Results and discussion  \n3.1  XRD and TEM studies  \nXRD patterns of OA -CFO and CA -CFO nanoparticles are shown in Fig. 2. The peaks \nobserved at 2θ = 30.22º, 35.48º, 43.18º, 53.56º, 57.12º and 62.67º corresponds to (220), (311), \n(400), (422), (511) and (440) planes of spinel CoFe 2O4 respectively (JCPDS No. 22 -1086),  \nwhich confirms the formation of single phase cubic spinel structure of CoFe 2O4 nano particles. \nThe average crystallite size of CFO nanoparticles was determined by Scherrer’s formula \n(Munjal and Khare 2016) ; \nDXRD  = 0.9λ\nβ  cosθ      (1) \n  \nFig. 2  X-Ray diffraction patterns of OA -CFO and CA -CFO nanoparticles.  \nWhere β represents the full width at half maximum of the XRD peak,  λ is the \nwavelength of X -ray (1.542 Å), θ is the Bragg’s angle, and D XRD is the average crystallite size. \nPage 9 of 26 \n The average crystallite sizes for OA -CFO and CA -CFO nanoparticles are found as   ̴ 10.6 nm \nand ~10.1 nm respectively . \n. Fig. 3  shows the TEM images,  histogra m of particle size distribution and  High \nResolution TEM (HRTEM) images of OA -CFO and CA -CFO nanopartic les. Clear fringes can \nbe seen in the HRTEM images of OA -CFO and CA -CFO nanoparticles that corresponds to \n(400)  and (440) planes of inverse spinel cobalt ferrite structure and confirms good crystalline \ngrowth of nanoparticles.  \n \nFig. 3  TEM images of (a) O A-CFO and (d) CA -CFO nanoparticles. High resolution TEM \nimages of (b) OA -CFO and (e) CA -CFO nanoparticles. The inset in (b) and (e) shows \nthe fast fourier transform (FFT) of the selected section. Fig. 3 (c) and 3 (f) shows the \nlog normal distribution of pa rticle size of OA -CFO and CA -CFO nanoparticles.  \nIt is clear from the size distribution of OA -CFO and CA -CFO nanoparticles that the \nsize of maximum number of particles lies within a very narrow range i.e. from 7 nm to 12 nm.  \nPage 10 of 26 \n The particle size distribution of OA -CFO nanoparticles shows a log normal distribution peak \n(DTEM) at ~ 9.2 nm whereas for CA -CFO it is at ~ 8.9 nm.  \n3.2  Magnetic Measurements  \nThe magnetization vs. magnetic field (M -H) loops for OA -CFO and CA -CFO nanoparticles \nat room temperature are shown in Fig. 4. Both particles shows the ferromagnetic behaviour. \nThe value of the M s and H c for OA -CFO nanoparticles are found as ~ 53 emu/gm and ~ 0.052 \nTesla respectively, whereas for CA -CFO nanoparticles, these are ~ 49 emu/gm and ~ 0.048 \nTesla respectively . \n \n \n \n \n \n \n \n \n \nFig. 4  M-H loops for OA -CFO and CA -CFO nanoparticles.  \nA decrease in magnetization of CFO nanoparticles after the ligand exchange completion \nwas observed. This reduction in saturation magnetization from OA -CFO (53 emu/gm) to CA -\nCFO (49 emu/gm) is attributed to the mechanochemical ligand exchange of the OA -CFO \nnanoparticles. During ligand exchange process removal of some surface cations takes place \nPage 11 of 26 \n and formation of a new Ligand -metal bond may further contribute in the decrease of the Ms \nvalues  (Palma et al. 2015) . The ligand exchange process reduces the core size (~ 4 %) of the \nnanoparticle which was confirmed by the TEM image s. \n3.3  FTIR Studies  \n \n \n \n \n \n \n \n \n \n \n \n  \nFig. 5  FTIR spectr a of bare CFO nanoparticles, neat oleic acid, OA -CFO nanoparticles, neat \ncitric acid and CA -CFO nanoparticles.  \nFig. 5 shows the FTIR spectr a of bare CFO nanoparticle (synthesized by the same rout e \nwithout OA), neat oleic acid, OA -CFO nanoparticles, neat citric acid and CA -CFO \nnanoparticles in the wavenumber ranging from 4000 cm-1 to 500  cm-1.  \nPage 12 of 26 \n The FTIR spectra of neat oleic shows distinct peaks at  2850 cm-1 and 2920 cm-1 (due \nto stretching of  =CH - alkene group ) and broad feature from 3500 cm-1 to 2500 cm-1 is \ncharacteristic of the O –H stretching band of the acid and the broadness of this band is caused \nby in tramolecular hydrogen bonding . The characteristic carbonyl ban d appears at 1713 cm-1 . \nThe two absorption peaks that appear at 1418 cm-1 and 1285 cm-1 are due to O –H bending and \nC–O stretching  (Zhang, He, and Gu 2006) . For bare CFO nanoparticles, the only one peak is \npresent at 5 90 cm-1 and can be attributed to stretching  of metal ion -oxygen bond (Pilapong et \nal. 2015) . \nThe presence of oleic acid on as synthesized oleic acid coated samples OA -CFO \nnanoparticles was confirmed by two -CH 2 stretching near 2920 cm-1 and 2850 cm-1 present in \nFTIR  spectra of the OA -CFO sample  (Wu et al. 2004) . The carboxyl group has character istic \nbands of the asymmetric stretch ( υas[-COO-]) and the symmetric stre tch (υs[-COO-]). Two bands \nappears near 1538 and 1410 cm-1, corresponds to υas[-COO-] and υs[-COO-]. -COO- and -CH 3 \nstretching bands confirms the pre sence of OA on coated samples  (Patil et al. 2014) . The p eak \nnear 1710 cm-1 represents the C=O stretch band of the carboxyl group present in oleic acid, \nwhich was found absent in the spectrum of the o leic acid coated nanoparticles.  This indicates \nthat oleic acid was chemisorbed onto the surface of CFO nanoparticles via its carbox ylate group  \n(Zhang et al. 2006) . \nNow , during the mechanochemical milling, as the ligand exchange process occurs the \ncitric acid starts replacing the oleic acid from the surface of CFO nanoparticles. The citric acid \nis a tridentate ligand that has three - COO- groups on a relatively small carbon chain (Tang  al. \n2013) . After surface modification by citric acid three absorption peaks were observed near \n3727, 1576, and 1402 cm-1. The former is attributed to the stretching band of hydroxyl group \n(-OH) and the others were attributed to the υas[-COO-] and υs[-COO-] stretching band of t he carboxyl  \ngroup, respectively (Liao et al. 2015) . This indicates that the surface of the CA -CFO Page 13 of 26 \n nanoparticles was covered with carboxylate species of citric acid. An intense peak at ∼590 \ncm−1 is observed, that can be attributed to the stretching of the metal ion at the tetrahedral A -\nsite, M A↔O (Pilapong  et al. 2015) . \nFig. 6  Representation of different possibilities of attachment of ligands on the surface in the \ncase of (a) OA -CFO nanoparticles and (b) -(e) CA -CFO nanoparticles.  \nPage 14 of 26 \n It is also evident from the FTIR spectra that, after the surface modification, two -CH 3 \nstretching near 2920 cm-1 and 2850cm-1 becomes weaker  (Palma et al. 2015)  , which confirms \nthat ligand exchange takes place between the oleic acid capping and citric acid and after this \nexchange only citric acid layer covers the nanoparticles.  \nThere are many possible ways of attachment of citric acid on the surface of cobalt ferrite \nnanoparticles. The citric acid can get attached with the nanoparticle by one of the COO-  groups \npresent at the corner or middle of the chain as shown in Fig. 6 (c) and 6 (d), or by two -COO-  \ngroups present at th e cor ner of the carbon chain [F ig. 6 (b)]. However all these conditions or a \nmixed condition [Fig. 6(e)] are possible and in each case at least one -COO- group remains on \nthe outer surface of the CA -CFO nanoparticles.  \nThe hexane dispersion of OA -CFO nanoparticl es and water dispersion of CA -CFO \nnanoparticles remains stable even after 6 months. This stability was confirmed by zeta potential \n(ζ) measurements. The zeta potential (ζ) values of as synthesized OA -CFO sample in hexane \nwas − 38 mV and after 6 months its value was obtained as − 36 mV. It is clear that ζ values are \nvery large even after a long time that gives the stability to OA -CFO nanoparticles in organic \nsolvents like hexane . On the other hand, the ζ of CA -CFO nanoparticle changes from − 39 mV \nto − 27 mV  after 6 months but still remains sufficiently large. The large enough negative value \nof ζ even after a long time confirms the stability of the CA -CFO nanoparticles in water . \nHydrodynamic diameter (D H) and histograms for grain size distribution (as synthes ized \nand after six months) for CA -CFO nanoparticles suspended in hexane and CA -CFO \nnanoparticles suspended in water are shown in the Fig. 7 .  Page 15 of 26 \n Fig. 7 Histograms for Hydrodynamic diameter distribution for OA -CFO nanoparticles \nsuspended in hexane (a) as synthesized, (b) after 6 months and for CA -CFO nanoparticles \nsuspended in water (c) as synthesized, (d) after 6 months.  \nIt is to note that hydrodynamic diameter of OA -CFO in hexane is larger than that of \nCA-CFO nanoparticles in water.  \nThis can be explaine d by the nature of bonding between ligand present on the surface \nof nanoparticles and the solvent molecules. As hexane is an organic/nonpolar solvent and thus \nmixing of the OA -CFO nanoparticles in it that has free “ -CH 3” groups on their outer surface, \nit does not make any hydrogen bond with the surface of the nanoparticle. On the other hand , \nnegatively charged “ -COO-“ group present on the outer surface of the CA -CFO nanoparticle \nPage 16 of 26 \n makes hydrogen bonds with the water solvent that increases the D H values of CA -CFO \nnanoparticles in water medium compared to OA -CFO nanoparticles in hexane.   \nIt is also observed that hydrodynamic diameters of OA -CFO and CA -CFO \nnanoparticles are larger than the diameters of the nanoparticles obtained by the TEM images. \nAs the hydrodynamic diameters gives us information of the CFO core along with coating \nmaterial and the solvent layer attached to the particle. While estimating size by TEM, this \nhydration layer is not present , hence we get information only about the CFO core.  \n3.4  Contact angle measurements  \nContact angle ( θC) measuremen ts for OA -CFO and CA -CFO have been performed for \nstudying the hydrophobic or the hydrophilic behaviour of any surface.  For θC measurements, \nthe thin films of OA -CFO and CA -CFO nanoparticles were deposited by mixing th e \nnanoparticles in isopropanol. For this, 100 mg of OA -CFO or CA -CFO nanoparticles were  \nmixed in 20 ml isopropanol and then spray coated on a glass substrate kept at 100 ºC. A water \ndroplet of 3 µL was deposited on these films  for stu dying the h ydrophobic/hydrophilic \nbehaviour . Fig. 8 shows the photographs of water droplet s on the OA -CFO and CA -CFO \nsample surface for different duration of time after the water droplet was left on the surface. Fig. \n9 shows the measured contact angles ( θC) for the water droplet on the two surfaces for different \ndeposition time.  \nThe water contact angle on the OA -CFO sample ’s surface was very high (~145o) and \nwater droplet deposited on the surface was almost perfect sphere, that confirms the \nhydrophobic beha viour of the OA -CFO sample (Sharp et al. 2014) . This hydrophobic nature \nof these OA -CFO nanoparticles can be attributed to the presence of –CH 3 on the outer surface \nof these nanoparticles. One of the two ends of OA has -COO- group whereas the other end has \n-CH 3 group. The -COO- group behaves like a hydrophilic group whereas the –CH 3 group Page 17 of 26 \n behave like a hydrophobic group (Lei et al. 2015) . In the case of OA -CFO the – COO- groups  \nare the anchoring group, bonded to the surface of CFO nanoparticles and –CH 3 groups remain  \nfree on the outer surface of the OA -CFO nanoparticles. The presence of hydrophobic group s \nat the outer layer of the OA -CFO nanoparticles makes them hydrop hobic and Oleophilic.  \n \nFig. 8 The photographs of the 3 µL water droplet on the  film of OA -CFO nanoparticles at (a) \n0.3 sec. and (b) 2.0 sec. and on the film of CA -CFO nanoparticles at (c) 0.3 sec. (d) 1.0 \nsec. and (e) 2.0 sec., after water droplet left on the surface.  \nPage 18 of 26 \n For the CA -CFO nanoparticles surface the  water contact angle reduces to 8o in a few \nseconds , which confirms the hydrophilic behaviour of CA -CFO nanoparticles  (Sharp et al. \n2014) . This hydrophilic behaviour can be attributed to t he presence of – COO- groups.  After \nthe mechanochemical ligand exchange a significant change in the surface chemistry of the \nnanoparticles and hence in the water contact angle with the CA -CFO have been observed.  \n \n \nFig. 9 Variations in water contact angle with time for the thin film of spray coated nanoparticles \nof (a) OA -CFO and (b) CA -CFO.  \nAs clear by the FTIR studies discussed above at least one -COO- group per citric acid \nmolecule remains on the outer surface of the CA -CFO nanoparticles, that makes the outer \nsurface of the CA -CFO nanoparticle negatively charged an d the CA -CFO nanoparticles show  \nhydrophilic behaviour.  \n3.5 Demulsification Tests and Recycling  \nThe potentiality of OA -CFO and CA -CFO nanoparticles in demulsificati on of O/W and \nW/O emulsions was examined by placing these nanoparticles in emulsion.   In order to check \nthe stability of O/W (oil in water) and W/O (water in oil) emulsions we prepared fresh samples \nof the two emulsions by the method as described in experi mental section . Fig. 10 (a) shows the \nPage 19 of 26 \n fresh samples of O/W and W/O and Fig. 10 (b) shows the same emulsions after 10 h of the \npreparation. It is clear from the figures that the emulsions are stable with time without \ndemulsification even after 10 h.  Fig. 10 (c) (1) and 10 (d) (1) shows the photographs of oil  in \nwater and water in oil emulsions. For testing the demulsification potential of these coated CFO \n(OA-CFO and CA -CFO) nanoparticles, the nanoparticles were mixed in O/W and W/O \nemulsions (40 mg CFO na noparticles for per ml of emulsion) respectively an d ultrasonicated \nfor 60 minutes  (Fig. 10 (c) (2) and Fig. 10 (d) (2)). After adding the nanoparticles and \nultrasonication, the mixture gives a uniform colour , indicating that the nanoparticles  were well \ndispersed in the emulsion.  \n  \nFig. 10 Stability test of the O/W and W/O emulsions. (a) fresh samples and (b) samples after \n10 h.  Photographs of ( c) (1) O/W emulsion, (2) OA -CFO dispersed in O/W emulsion \nPage 20 of 26 \n and, (3) after demulsification of O/W emulsions. ( d) (1) W/O emulsion, (2) CA -CFO \ndispersed in W/O emulsion and, (3) after demulsification of W/O emulsions.   \nAs OA -CFO nanoparticles are Oleophilic in nature, they bind small oil droplets with \nthem in O/W emulsion. Similarly CA -CFO nanoparticle s bind water droplets with them in W/O \nemulsion due  to their hydrophilic nature. When a hand magnet was placed nea r the mixture \nsolution , the black OA -CFO and CA -CFO nanoparticles together with their tagged water/oil \nphase were attracted towards the magnet and the system became nearly transparent and \ncolourless  (Fig. 10 (c) (3) and ( d) (3). This demonstrates that  the toluene droplets in O/W and \nwater droplets in W/O emulsions were very effectively separated from the emulsion using OA -\nCFO and CA -CFO nanoparticles respectively. After the demulsification, the magnetic \nnanoparticles were collected using a small perman ent magnet and washed using chloroform \n(CHCl 3) and ethanol for 3 times. Before reusing the nanoparticles for the demulsification , FTIR \nstudies were carried out . No significant change in the surface properties of  the nanoparticles \nwas observed and the n anop articles have been  reused for the demulsification.  \n4. Conclusion  \nWe have successfully synthesized oleic acid capped, single phase, uniform size (~9 nm) \nCFO nanoparticles by hydrothermal method and demonstrated the conversion of these \nnanoparticles to a citric acid (CA) coated CFO nanoparticles in short time (~30 min.) using a \nrapid and novel mechanochemical ligand  exchange method. The FTIR spectra confirms the \npresence oleic acid on OA -CFO nanoparticles and exchange of oleic acid with citric acid. The \nattachment of anchoring groups on OA -CFO and CA -CFO nanoparticles is a lso explained. \nContact angle measurements confirm  the hydrophobic and hydrophilic behaviour of oleic acid \ncoated and citric acid coated CFO nanoparticles respectively. It is demonstrated that the \nhydrophobic and hydrophilic behaviour of these magnetic nano particles can be used for the Page 21 of 26 \n demulsification of oil in water and water in oil emulsions. These nanoparticles can be reused \nafter washing them and no significant change in their surface properties was observed after the \ndemulsification. FTIR studies reveal ed that for OA-CFO and CA -CFO nanoparticles , the –CH 3 \nand –COO- groups are exposed to the surrounding solvent that makes them hydrophobic \n(oleophilic ) and hydrophilic r espectively.  The novel mechanochemical milling method is  \nproposed as a rapid and efficient mthod for ligand exchange.  \n5. Acknowledgments  \n  The authors are thankful to the DeitY (project no. RP02395) and one of the authors \n(Sandeep Munjal) is thankful to Council of Scientific and Industrial Research (CSIR), New \nDelhi for Senior Research Fellowship (SRF) Grant  (09/086(1179)/2013 -EMR1 ). It is \ndeclared that authors have no other conflict of interest.  \n \n \n \n \n \n \n \n \n \n \n Page 22 of 26 \n Figure Captions  \nFig. 1  (a) Schematic of steps in the synthesis of OA -CFO and CA -CFO nanoparticles, (b) OA -\nCFO and (c) CA -CFO nanoparticles in toluene and water.  \nFig. 2  X-Ray diffraction patterns of OA -CFO and CA -CFO nanoparticles.  \nFig. 3  TEM images of (a) OA -CFO and (d) CA -CFO nanoparticles. High resolution TEM \nimages of (b) OA -CFO and (e) CA -CFO nanoparticle s. The inset in (b) and (e) shows \nthe fast fourier transform (FFT) of the selected section. Fig. 3 (c) and 3 (f) shows the \nlog normal distribution of particle size of OA -CFO and CA -CFO nanoparticles.  \nFig. 4 M-H loops for OA -CFO and CA -CFO nanoparticles.  \nFig. 5 . FTIR spectr a of bare CFO nanoparticles, neat oleic acid, OA -CFO nanoparticles, neat \ncitric acid and CA -CFO nanoparticles.  \nFig. 6 Representation  of different possibilities of attachment of ligands on the surface in the \ncase of (a) OA -CFO nanoparticl es and (b) -(e) CA -CFO nanoparticles.  \nFig. 7 Histograms for Hydrodynamic diameter distribution for OA -CFO nanoparticles \nsuspended in hexane (a) as synthesized, (b) after 6 months and for CA -CFO \nnanoparticles suspended in water (c) as synthesized, (d) after 6 months.  \nFig. 8. The photographs of the 3 µL water droplet on the  film of OA -CFO nanoparticles at (a) \n0.3 sec. and (b) 2.0 sec. and on the film of CA -CFO nanoparticles at (c) 0.3 sec. (d) 1.0 \nsec. and (e) 2.0 sec., after  water droplet left on the surface . \nFig. 9 Variation s in water contact angle with time for the thin film of spray coated nanoparticles \nof (a) OA -CFO and (b) CA -CFO.  Page 23 of 26 \n Fig. 10 Stability test of the O/W and W/O emulsions. (a) fresh samples and (b) samples after \n10 h.  Photographs of ( c) (1) O/W  emulsion, (2) OA -CFO dispersed in O/W emulsion \nand, (3) after demulsification of O/W emulsions. ( d) (1) W/O emulsion, (2) CA -CFO \ndispersed in W/O emulsion and, (3) after demulsification of W/O emulsions.   \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Page 24 of 26 \n REFERENCES  \nArruebo, Manuel, Rodrigo Fernández -pacheco, M. Ricardo Ibarra, and Jesús Santamaría. 2007. \n“Magnetic Nanoparticles Controlled Release of Drugs from Nanostructured Functional \nMaterials.” Nano Today  2(3):22 –32. \nBajwa, Rizwan Sarwar, Zulfiqar Khan, Vasilios Bakolas, and Wolfgang Braun. 2016. “Water -\nLubricated Ni -Based Composite ( Ni –Al2O3 , Ni –SiC and Ni –ZrO2 ) Thin Film Coatings \nfor Industrial Applications.” Acta Metallurgica Sinica (English Letters)  29(1):8 –16. \nRetrieved (\"http://dx.doi.org/10.1007/s40195 -015-0354 -1). \nBricen, Sarah et al. 2012. “Effects of Synthesis Variables on the Magnetic Properties of \nCoFe2O4 Nanoparticles.” Journal of Magnetism and Magnetic Materials  324:2926 –31. \nBrollo, M. E. F. et al. 2016. “Magnetic Hyperthermia in Brick -like Ag@Fe3O4 Core –shell \nNanoparticles.” Journal of Magnetism and Magnetic Materials  397:20 –27. Retrieved \n(http://linkinghub.elsevier.com/retrieve/pii/S0304885315305072).  \nChaudhary, Deepti, Neeraj Khare, and V. D. Vankar. 20 16. “Ag Nanoparticles Loaded \nTiO2/MWCNT Ternary Nanocomposite: A Visible - Light -Driven Photocatalyst with \nEnhanced Photocatalytic Performance and Stability.” Ceramics International  42:15861 –\n67. Retrieved (http://dx.doi.org/10.1016/j.ceramint.2016.07.056).  \nGe, Qingchun, Jincai Su, Tai -Shung Chung, and Gary Amy. 2011. “Hydrophilic \nSuperparamagnetic Nanoparticles: Synthesis , Characterization , and Performance in \nForward Osmosis Processes.” Industrial & Engineering Chemistry Research  50:382 –88. \nRetrieved (htt p://dx.doi.org/10.1021/ie101013w).  \nHatakeyama, Mamoru et al. 2011. “A Two -Step Ligand Exchange Reaction Generates Highly \nWater -Dispersed Magnetic Nanoparticles for Biomedical Applications.” Journal of \nMaterials Chemistry  21:5959 –66. \nHergt, R., R. Hiergeist , I. Hilger, W. A. Kaiser, and Y. Lapatnikov. 2004. “Maghemite \nNanoparticles with Very High AC -Losses for Application in RF -Magnetic \nHyperthermia.” Journal of Magnetism and Magnetic Materials  270:345 –57. \nHuang, Shih -hung, and Ruey -shin Juang. 2011. “Bioche mical and Biomedical Applications of \nMultifunctional Magnetic Nanoparticles: A Review.” Journal of Nanoparticle Research  \n13:4411 –30. \nKalpanadevi, K., C. R. Sinduja, and R. Manimekalai. 2014. “A Facile Thermal Decomposition \nRoute to Synthesise CoFe2O4 Nanostructures.” Materials Science -Poland  32(1):34 –38. \nRetrieved (http://link.springer.com/10.2478/s13536 -013-0153 -1). \nKharisov, Boris I. 2014. “Mini -Review: Ferrite Nanoparticles in the Catalysis.” Arabian \nJournal of Chemistry . \nKim, Yeong Il, Don Kim, and Choong Sub Lee. 2003. “Synthesis and Characterization of \nCoFe2O4 Magnetic Nanoparticles Prepared by Temperature -Controlled Coprecipitati on \nMethod.” Physica B: Condensed Matter  337(1 -4):42 –51. \nKumar, Amit, Subhashis Gangopadhyay, Chien -hsiang Chang, Surojit Pande, and Subit \nKumar. 2015. “Study on Metal Nanoparticles Synthesis and Orientation of Gemini \nSurfactant Molecules Used as Stabilizer .” Journal of colloid and interface science  \n445:76 –83. Retrieved (http://dx.doi.org/10.1016/j.jcis.2014.12.064).  \nLavela, P., and J. L. Tirado. 2007. “CoFe2O4 and NiFe2O4 Synthesized by Sol -Gel Procedures \nfor Their Use as Anode Materials for Li Ion Batterie s.” Journal of Power Sources  Page 25 of 26 \n 172(1):379 –87. \nLei, Chang et al. 2015. “Mesoporous Materials Modified by Aptamers and Hydrophobic \nGroups Assist Ultra -Sensitive Insulin Detection in Serum.” Chemical Communications  \n51:13642 –45. Retrieved (http://dx.doi.org/10.1 039/C5CC04458H).  \nLiao, Han et al. 2015. “One -Pot Synthesis of gadolinium(III) Doped Carbon Dots for \nFluorescence/magnetic Resonance Bimodal Imaging.” RSC Advances  5:66575 –81. \nRetrieved (http://dx.doi.org/10.1039/C5RA09948J).  \nLoim, N.M., Khruscheva, N.S., Lukashov, Y. S. et al. 1999. “Solid -State Photochemical \nLigand Exchange in the Cymantrene Series.” Russ Chem Bull  48:198.  \nManova, Elina et al. 2004. “Mechano -Synthesis, Characterization, and Magnetic Properties of \nNanoparticle s of Cobalt Ferrite , CoFe2O4.” Chemistry of Materials  (d):5689 –96. \nMathew, Daliya S., and Ruey -shin Juang. 2007. “An Overview of the Structure and Magnetism \nof Spinel Ferrite Nanoparticles and Their Synthesis in Microemulsions.” Chemical \nEngineering Journ al 129:51 –65. \nMunjal, Sandeep, and Neeraj Khare. 2016. “Cobalt Ferrite Nanoparticles with Improved \nAqueous Colloidal Stability and Electrophoretic Mobility.” P. 020092 in AIP Conference \nProceedings , vol. 1724.  \nMunjal  Sandeep, Neeraj Khare, Chetan Nehate, and Veena Koul. 2016. “Water Dispersible \nCoFe2O4 Nanoparticles with Improved Colloidal Stability for Biomedical Applications.” \nJournal of Magnetism and Magnetic Materials  404:166 –69. \nMunjal Sandeep, Pallavi Kumari, M ohd Zubair Ansari, and Neeraj Kh are (2016 ) Bipolar \nresisti ve switching in Bi25FeO40: PCBM nanocomposite thin fi lm. P. 020540 in AIP \nConference Proceedings, vol. 1728.    \nPalma, Susana I. C. J. et al. 2015. “Effects of Phase Transfer Ligands on Monodisperse Iron \nOxide Magnetic Nanoparticles.” Journal of Colloid and Interface Science  437:147 –55. \nRetrieved (http://dx.doi.org/10.1016/j.jcis.2014.09.019).  \nPatil, R. M. et al. 20 14. “Non -Aqueous to Aqueous Phase Transfer of Oleic Acid Coated Iron \nOxide Nanoparticles for Hyperthermia Application.” RSC Advances  4:4515 –22. \nPilapong, C. et al. 2015. “Magnetic -EpCAM Nanoprobe as a New Platform for Efficient \nTargeting, Isolating and Ima ging Hepatocellular Carcinoma.” RSC Advances  5:30687 –93. \nRetrieved (http://dx.doi.org/10.1039/C5RA01566A).  \nReiss, G., and Andreas Hütten. 2005. “Magnetic Nanoparticles: Applications beyond Data \nStorage.” Nature materials  4(October):725 –26. \nSaffari, Jilla, Davood Ghanbari, Noshin Mir, and Khatereh Khandan -Barani. 2014. \n“Sonochemical Synthesis of CoFe2O4 Nanoparticles and Their Application in Magnetic \nPolystyrene Nanocomposites.” Journal of Industrial and Engineering Chemistry  \n20(6):4119 –23. Retrieved \n(http:/ /www.sciencedirect.com/science/article/pii/S1226086X14000483).  \nSharp, Emma L., Hamza Al -shehri, Tommy S. Horozov, D. Stoyanov, and Vesselin N. Paunov. \n2014. “Adsorption of Shape -Anisotropic and Porous Particles at the Air –water and the \nDecane –water Interfa ce Studied by the Gel Trapping Technique.” RSC Advances  4:2205 –\n13. \nTamer, Ugur, Yusuf Gundogdu, Ismail Hakki Boyaci, and Kadir Pekmez. 2010. “Synthesis of \nMagnetic Core – Shell Fe3O4 –Au Nanoparticle for Biomolecule Immobilization and \nDetection.” Journal of  Nanoparticle Research  12:1187 –96. Page 26 of 26 \n Tang, Wenshu, Yu Su, Qi Li, Shian Gao, and Jian Ku Shang. 2013. “Well -Dispersed, \nUltrasmall, Superparamagnetic Magnesium Ferrite Nanocrystallites with Controlled \nHydrophilicity/hydrophobicity and High Saturation Magnetiza tion.” RSC Advances  \n3:13961 –67. \nWang, Lingyun, Hongxia Zhang, Chao Lu, and Lixia Zhao. 2014. “Journal of Colloid and \nInterface Science Ligand Exchange on the Surface of Cadmium Telluride Quantum Dots \nwith Fluorosurfactant -Capped Gold Nanoparticles: Synthe sis , Characterization and \nToxicity Evaluation.” Journal of Colloid And Interface Science  413:140 –46. Retrieved \n(http://dx.doi.org/10.1016/j.jcis.2013.09.034).  \nWang, Y. M. et al. 2011. “Synthesis of Fe3O4 Magnetic Fluid Used for Magnetic Resonance \nImaging and Hyperthermia.” Journal of Magnetism and Magnetic Materials  323:2953 –\n59. \nWu, Nianqiang et al. 2004. “Interaction of Fatty Acid Monolayers with Cobalt Nanoparticles.” \nNano Letters  4:383 –86. \nZhang, Ling, Rong He, and Hong -chen Gu. 2006. “Oleic Acid Coatin g on the Monodisperse \nMagnetite Nanoparticles.” Applied Surface Science  253:2611 –17. \n "    },    {        "title": "0805.0518v1.Magnetoelectric_oscillations_in_quasi_2D_ferrite_disk_particles.pdf",        "content": "Magnetoelectric oscillations in quasi-2D ferrite disk particles \n \nM. Sigalov, E.O. Kamenetskii, and R. Shavit \n \nMicrowave Magnetic Laboratory \nDepartment of Electrical and Computer Engineering \nBen Gurion University of the Negev, Israel \nEmail: kmntsk@ee.bgu.ac.il \n \narXiv  [cond-mat] May 5, 2008 \n \nAbstract \n \nIn this paper we show that magnetic-dipolar-m ode (MDM) oscillations of a quasi-2D ferrite \ndisk are characterized by unique  symmetry features with topological phases resulting in \nappearance of the magnetoelectric (ME) prope rties. The entire ferrite disk can be \ncharacterized as a pair of two, electric and ma gnetic, coupled eigen moments. However, there \nis no a \"glued pair\" of two dipoles. An external electromagnetic field in the near-field region \n\"views\" such a ME particle, as a system with a normally oriented eige n electric moment and \nan in-plane rotating eigen magnetic dipole moment.    \n \n1. Introduction \n \nAn idea of possible existence of  a local coupling between electric and magnetic dipoles in an \nelectromagnetic medium is not new. Tellegen considered an assembly of electric-magnetic \ndipole twins, all of them lined up in the same fashion (either parallel or anti-parallel) [1]. \nSince 1948, when Tellegen suggested such \"glued pa irs\" as structural el ements for composite \nmaterials, the electrodynamics of  these complex media was a subject of serious theoretical \nstudies (see, e.g. [2 – 4]). Till now, however, th e question of realization of a Tellegen medium \nis a subject of numerous discussions. In this pa per we show that a quasi-2D ferrite disk with \nthe MDM oscillation spectrum can be characteri zed as a pair of two, electric and magnetic, \ncoupled eigen moments. But there is no a \"glu ed pair\" of two dipole s. For an external \nelectromagnetic field such a ME particle is \"viewed\" as a system with a normally oriented eigen electric moment and an in-plane ro tating eigen magnetic dipole moment.   . \n \n2. The energy eigenstates, eigen electric fl uxes and anapole moments in MDM ferrite \ndisks    \nGenerally, in classical electromagnetic probl em solutions for time-varying fields, the \npotentials are introduced as formal quantities fo r a more convenient way to solve the problem \nand a set of equations for potentia ls are equivalent in  all respects to the Maxwell equations for \nfields [5]. The situation can become completely different if one supposes to solve the \nelectromagnetic boundary proble m for wave processes in sm all samples of a strongly \ntemporally dispersive medium. In small ferrite samples with strong tempor al dispersion of the \npermeability tensor: \n)( ωµµtt= , variation of the electric energy is negligibly small compared \nto variation of the magnetic en ergy and so one can neglect the el ectric displacement current in \nMaxwell equations [6]. These magnetic sample s exhibit the magnetostatic (MS) resonance \nbehaviours in microwaves, which are descri bed by the MS-potential wave functions ),(trrψ .  2Such a MS-potential-wave-functi on description stands out also  against a background of the \nmagnetization-fluctuation description. MS fe rromagnetism has a character essentially \ndifferent from exchange ferromagnetism [7] and the propagating MS fields are not the \nexchange-interaction magnetization waves.  \n    For MDMs in a quasi-2D ferrite disk described by MS-potential wave functions ),(trrψ  \none has evident quantum-like attributes and the spectrum is characterized by energy \neigenstate [8, 9]. It was shown, however, that  because of the boundary condition on a lateral \nsurface of a ferrite disk, membrane MS functi ons cannot be considered as single-valued \nfunctions. This leads to the topological effect s which result in appearance of the fluxes of \npseudo-electric fields and eigen electric moment s – the anapole moments [9]. An observation \nof such anapole moments was realized in recent microwave experiments [10]. \n    The complete-set MDM oscillating spect rum is obtained in neglect of the electric \ndisplacement currents and so there should be no influence of a diel ectric loading on the \nspectral peak positions in a ferrite disk. Ne vertheless, our experiments show such an \ninfluence. In experiments we used a ferrite sample of a diameter mm 3 2=ℜ made of the YIG \nfilm on the GGG substrate (the YIG film thickness mkm 50=d , saturation magnetization \nG 1880  40=Mπ , linewidth Oe 8.0=∆H ) and a short-wall rect angular waveguide. A \nnormally magnetized ferrite disk was placed in a maximal RF electric fiel d of the TE10 mode \nand is oriented normally to the E-field. We analyze the MDM spectra with respect to \nfrequency at constant DC magnetic  field. A bias magnetic field is =0H 4900 Oe. A ferrite disk \nis placed on a GGG substrate which has th e dielectric permittivity parameter of 15=rε . Now \nwe put dielectric samples above a ferrite disk. There are dielectric disks of a diameter 3 mm \nand thickness 2 mm. We used a set of disks of commercial microwave dielectric (non \nmagnetic) materials with the dielectric permittivity parameters of 15=rε  (K-15; TCI \nCeramics Inc), 30=rε  (K-30; TCI Ceramics Inc), and 100=rε  (K-100; TCI Ceramics Inc). \nWe observed strong variations of the spectral pictures when dielectr ic disks were placed \nabove a ferrite disk. These transformations of  the spectra become most evident when we \nmatch (by proper small shifts of the bias magnetic fields) positions of the first peaks in the spectra. From the absorption spectra shown in Fig. 1 one can see that as the dielectric \npermittivity parameter of a dielectric sample incr eases, the frequency shift of the mode peak \nposition increases as well.   3               \n  \n  \nFig. 1: The frequency shift of th e odd MDM peak positions for a ferrite disk with dielectric \nloading due to the eigen electric fluxes. The first peaks in the spectra are matched by proper \ncorrelations of bias magnetic fields.  \n3. In-plane rotating eigen magnetic dipole moments \n \nFrom the solved spectral problem for MS-poten tial wave functions, one can obtain the field \ndistributions inside a quasi-2D ferrite disk. It can be easily shown that for the eigen curl \nelectric field inside a disk one has the Poisson equation:  \n \n                                                                       \nej Err\n 42π=∇ ,                                                   (1) \n \nwhere m ije rrr\n×∇≡ω , mr is RF magnetization. For a norma lly magnetized quasi-2D disk, the \neigen curl electric fields can be experimentally  observed via appearance of effective magnetic \ndipoles.  The electric field has th e in-plane orientation with the contrarily directed vectors on \nthe upper and lower disk planes . Recently, it was shown that  eigenfunction patterns of a \nnumerically solved (based on the HFSS program ) non-integrable electr omagnetic problem of \na quasi-2D ferrite disks in a rectangular-wav eguide cavity are in a very good correspondence \nwith the analytically studied MDMs [11]. This allows making a detailed analysis of the field \npatterns inside a ferrite disk. Fi g. 2 gives a top view of the nu merically solved electric field \ndistributions for the first MDM on the upper plane of a ferrite di sk at different time phases.  \n  4                                   \n  \n \n  Fig. 2: A top view of electri c field distributions for the fi rst MDM on the upper plane of a \nferrite disk at different time phases. In-p lane linear magnetic currents are oriented \nperpendicular to the electric field vectors.      The in-plane electric fields on the upper a nd lower planes of a ferr ite disk are in opposite \ndirections at any time phase. Si nce the disk thickness is much, much less than the rectangular \nwaveguide height, the disk in a cavity can be clearly replaced  by a magnetic-current sheet. A \nsurface density of the effective ma gnetic current is expressed as \n \n                                                         \nm\nlower upper icE Enr rrr π4) ( −=−× ,                                         (2) \n \nwhere upperEr\n and lowerEr\n are, respectively, in-plane electric fields on the upper and lower \nplanes of a ferrite disk and nr is a normal to a disk plane directed along a bias magnetic field. \nEvidently, lower upper E Err\n−= . Following pictures in Fig. 2, one can conclude that there are \nrotating linear magnetic currents. Non-zero curren t-line divergence of such magnetic currents \ngives equivalent magnetic charges. As a result of  this equivalent representation, one has an \nevidence for an in-plane rotating magnetic dipoles for the entire ferrite disk with MDM oscillations. Due to such rotating magnetic dipol es one has excitation of MDMs in a quasi-2D \nferrite disk shown in well-known experiments [12]. \n \n4. Conclusion \n \nBased on experimental studies and numerical simulation results  we showed that a quasi-2D \nferrite disk with MDM oscillati ons can be characterized as a system of a normally oriented \neigen electric moment and an in-plane rotating eigen magnetic  dipole moment. The observed \ncharacteristics of ferrite-based microwave ME  particles arise from the fact that MDM °=0 tω °=90 tω\n°=180 tω°=270 tω 5oscillations in quasi-2D ferrite disks are macroscopic quantum c oherence states with discrete \nenergy levels and topologi cal vortex structures.  \n \nReferences \n \n[1] B. D. H. Tellegen, Philips. Res. Rep. 3, 81 (1948).  \n[2] E. J. Post, Formal Structure of Electromagnetics  (Amsterdam, North-Holland, 1962). \n[3] I. V. Lindell, A. H. Sihvola, S. A. Tretyakov and A J Viitanen,  Electromagnetic Waves in \nChiral and Bi-Isotropic Media  (Boston, MA, Artech House, 1994). \n[4] A. Lakhtakia,  Beltrami Fields in Chiral Media  (Singapore, World Scientific, 1994). \n[5] J.D. Jackson, Classical Electrodynamics , 2nd ed. (Wiley, New York, 1975). \n[6] L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media , 2nd ed. (Pergamon, \nOxford, 1984). \n[7] J. M. Luttinger and L. Tisza, Phys. Rev. 70, 954 (1946); H. Puszkarski, M. Krawczyk, and  \nJ.-C. S. Levy, Phys. Rev. B 71, 014421 (2005). \n[8] E. O. Kamenetskii, Phys. Rev. E 63, 066612 (2001). \n[9] E.O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007).  \n[10] E. O. Kamenetskii, A.K. Saha, and I. Awai, Phys. Lett. A 332, 303 (2004). \n[11] E. O. Kamenetskii, M. Siga lov, and R. Shavit, Phys. Rev. E 74, 036620 (2006); M. \nSigalov, E. O. Kamenetskii, and R. Shavit, J. Appl. Phys. 103, 013904 (2008); M. \nSigalov, E. O. Kamenetskii,  and R. Shavit (unpublished). \n[12] J. F. Dillon Jr., J. Appl. Phys.  31, 1605 (1960); T. Yukawa and K. Abe, J. Appl. Phys. 45, \n3146 (1974). \n "    },    {        "title": "0801.1626v1.Linear_and_Nonlinear_Optical_constants_of_BiFeO_3.pdf",        "content": "arXiv:0801.1626v1  [cond-mat.mtrl-sci]  10 Jan 2008Linear and Nonlinear Optical Constants of BiFeO 3\nAmit Kumar,1Ram C. Rai,2Nikolas J. Podraza,1Sava Denev,1Mariola Ramirez,1\nYing-Hao Chu,3Jon Ihlefeld,1T. Heeg,4J. Schubert,4Darrell G. Schlom,1J. Orenstein,5\nR. Ramesh,3Robert W. Collins,6Janice L. Musfeldt,2and Venkatraman Gopalan1\n1Department of Materials Science and Engineering, Pennsylv ania State University,\nMRL Bldg., University Park, Pennsylvania 16802, USA\n2Department of Chemistry, University of Tennessee, Knoxvil le, TN 37996,USA\n3Department of Materials Science and Engineering, Universi ty of California,\nBerkeley, Hearst Mining Building, Berkeley, California 94 720, USA\n4Institute of Bio- and Nano-Systems (IBN1-IT),\nResearch Centre J ¨ulich, D-52425 J ¨ulich, Germany\n5Department of Physics, University of California, Berkeley , California 94720, USA\n6Department of Physics and Astronomy, University of Toledo, Toledo, OH, 43606, USA\nUsing spectroscopic ellipsometry, the refractive index an d absorption versus wavelength of the\nferroelectric antiferromagnet Bismuth Ferrite, BiFeO 3is reported. The material has a direct band-\ngap at 442 nmwavelength (2.81 eV).Usingoptical second harm onic generation, the nonlinear optical\ncoefficientsweredeterminedtobe d15/d22= 0.20±0.01,d31/d22= 0.35±0.02,d33/d22=−11.4±0.20\nand|d22|= 298.4±6.1 pm/V at a fundamental wavelength of 800 nm.\nBiFeO 3(BFO) is an antiferromagnetic, ferroelectric\nwith Neel temperature T N= 643 K, and ferroelectric\nCurie temperature T C= 1103 K.[1, 2, 3] It is presently\none of the most studied multiferroic materials due to its\nlarge ferroelectric polarization of ∼100µC/cm2in thin\nfilms, and the possibility of coupling between magnetic\nand ferroelectric order parameters, thus enabling manip-\nulation of one through the other.[1] Linear and nonlinear\nopticalspectroscopytoolsareideallysuited tostudy such\ncoupling.[4] While the mean refractive index for bulk sin-\ngle crystal BiFeO 3has been previously investigated,[5]\nthe optical constants of thin films have not been pre-\nsented thus far. Also, an indirect gap at 673 nm (1.84\neV) was reported before[6], which is shown here to be\nan absorption onset potentially due to a joint density\nof states effect and not associated with phonon partic-\nipation. In our analysis, the material appears to have\na direct gap with a bandedge at 442 nm instead. No\nstudies of nonlinear optical coefficients of BiFeO 3, in any\nform, exist. In this letter, we measure large second order\noptical nonlinearities in BFO.\nEpitaxial and phase-pure BFO thin films were syn-\nthesized by pulsed-laser deposition (PLD) as well as\nmolecular-beam epitaxy (MBE) on (111) SrTiO 3(STO)\nsubstrates.[1, 7] The films studied here are epitaxial\nwith orientation relationship BFO(0001)//STO(111)and\n[2¯1¯10]BFO//[1 ¯10] STO. We note specifically that unlike\nmany epitaxial thin films, these films do not haveany ad-\nditionalstructuralvariants,includinganyrotationalvari-\nantswithinthefilmgrowthplane. Thus, these(0001)ori-\nented films have nearly single crystalline perfection, with\nthree well-defined crystallographic x-[2¯1¯10], and y-[1¯100]\naxes within the film plane, and the z-[0001] axis normal\nto the plane. The three y-zmirrorplanes in the 3 mpoint\ngroup symmetry for BFO are thus well defined and al-\nlow us to extract nonlinear coefficients precisely without\nambiguity. Typical film stoichiometry, as determined by\nRutherford backscattering spectrometry (RBS), was sto-/g1/g2/g3/g3 /g1/g2/g1/g4 /g1/g2/g4/g3 /g1/g2/g5/g4 /g6/g2/g3/g3 /g6/g2/g1/g4/g3/g2/g7/g3/g2/g1/g3/g2/g6/g3/g2/g8\n/g1α/g2/g3/g2/g4/g5/g2/g1/g6/g7/g8/g9/g2/g10/g11/g12/g13/g14/g4/g1α/g2/g3/g2/g4/g15/g16/g5/g2/g1/g6/g7/g8/g9/g2/g10/g11/g12/g13/g14/g4\n/g17/g18/g19/g13/g19/g11/g2/g3/g11/g20/g7/g21/g22/g2/g1/g20/g23/g4/g3/g2/g3/g3/g3/g3/g2/g3/g3/g1/g3/g2/g3/g3/g8/g3/g2/g3/g3/g9/g3/g2/g3/g3/g10\n/g1/g2/g3/g2/g4/g5/g6/g7/g2/g8/g9/g6/g3/g3 /g9/g3/g3 /g11/g3/g3 /g7/g1/g3/g3 /g7/g4/g3/g3/g3/g7/g1/g6/g8\n/g10/g11/g7/g12/g13/g12/g1/g12/g12/g14/g12/g1/g2/g8/g9/g12/g15/g12/g3/g2/g3/g7/g12/g16/g17\n/g12/g12/g12Γ/g12/g14/g12/g3/g2/g6/g9/g12/g15/g12/g3/g2/g3/g4/g12/g16/g17/g12/g18/g12/g13/g12/g14/g12/g7/g7/g2/g9/g3/g12/g15/g12/g1/g2/g8/g3/g12/g16/g17/g10/g11/g4/g2/g13/g12/g1/g12/g12/g14/g12/g6/g2/g3/g7/g12/g15/g12/g3/g2/g3/g7/g12/g16/g17\n/g12/g12/g12Γ/g12/g14/g12/g3/g2/g4/g5/g12/g15/g12/g3/g2/g3/g6/g12/g16/g17/g12/g18/g12/g13/g12/g14/g12/g6/g7/g2/g6/g9/g12/g15/g12/g1/g2/g1/g1/g12/g16/g17/g10/g11/g14/g12/g13/g12/g1/g12/g12/g14/g12/g8/g2/g7/g7/g12/g15/g12/g3/g2/g3/g1/g12/g16/g17\n/g12/g12/g12Γ/g12/g14/g12/g7/g2/g5/g7/g12/g15/g12/g3/g2/g3/g9/g12/g16/g17/g12/g18/g12/g13/g12/g14/g12/g9/g7/g2/g5/g8/g12/g15/g12/g4/g2/g3/g3/g12/g16/g17\n/g15/g16/g12/g12\n/g19/g18/g20\n/g24/g6/g25/g20/g26/g20/g11/g21/g13/g18/g2/g1/g11/g27/g4\n/g12/g21/g22/g23\n/g21/g24/g23\nFIG. 1: (a)Index of refraction (n) and extinction coefficient\n(k) for BiFeO 3deposited on (111) SrTiO 3over a spectral\nrange from 190 to 1670 nm. Also shown are the dielectric\nfunction parameters for the three Tauc-Lorentz oscillator s\n(TL 1, TL 2, TL 3) within the spectral range. The param-\neterization also includes an additional oscillator outsid e the\nspectral range with E 0= 7.29±0.06 eV, Γ = 4.28 ±0.34 eV\nand A = 51.19 ±2.78 eV. (b) Plot of ( αE)1/2and (αE)2vs.\nphoton energy E where a linear extrapolation of ( αE)2to 0\nsuggests a direct bandgap at 2.81 eV.\nichiometric within 3 % error of the measurement (Bi:Fe\n= 0.98-0.99:1). There were no amorphous or secondary\nphases as confirmed by transmissionelectron microscopy.2\n/g1/g1/g2ω/g3φ/g4\n/g1/g5/g2ω/g3φ/g4/g6/g7/g8/g9/g6/g7/g8/g9 /g6/g7/g8/g9/g6/g7/g8/g9\n/g1\n/g2\n/g1/g2/g3/g4/g5/g6/g7/g8/g4 θ/g4/g4/g9/g4/g4/g10/g11/g10/g10\n/g10/g6/g7/g11/g12\n/g6/g7/g11/g12/g6/g7/g11/g12/g6/g7/g11/g12\n/g1/g12/g3/g4/g5/g6/g7/g8/g4 θ/g4/g4/g9/g4/g13/g4/g14/g15/g11/g10/g10\n/g10/g10/g3\n/g13/g9 /g4/g5ω\n/g2ω/g9\n/g14\n/g15φ θ\nFIG. 2: Variation of pandspolarized SHG intensity with\nincident polarization angle for a BFO//STO(111) film with\nx-axis perpendicular to the plane of incidence in (a) Normal\nincidence θ= 0◦and (b)θ= 45◦tilt.\nEllipsometric spectra in (∆ ,Ψ) were collected ex situ\nfor a BiFeO 3film prepared by MBE on (111) SrTiO 3at\nθi= 55◦and 70◦angles of incidence using a variable-\nangle rotating-compensator multichannel spectroscopic\nellipsometer[8] with a spectral range from 190 to 1670\nnm. The optical properties (n, k) shown in Fig. 1(a) and\nthe corresponding dielectric function spectra ( ε1,ε2) are\nextracted by using a least squaresregressionanalysis and\na weighted root mean square error[9], to fit the ellipso-\nmetric spectra to a four-medium optical model consist-\ning of a semi-infinite STO substrate / bulk film / surface\nroughness / air ambient structure. The free parameters\ncorrespond to the bulk and surface roughness thicknesses\nof the film and a parameterization of the BiFeO 3dielec-\ntric function. The dielectric function parameterization\nof BiFeO 3consists of four Tauc-Lorentz oscillators [10]\nsharing a common band gap and a constant additive\nterm to ε1denoted by ε∞(equal to 1 for this model).\nThe parameters corresponding to each oscillator include\nan oscillator amplitude A, broadening parameter Γ, res-\nonance energy E0, and a Tauc gap Egcommon to all os-\ncillators. The optical properties of the surface roughness\nlayer are represented by a Bruggeman effective medium\napproximation consisting of a 0.50 bulk film / 0.50 void\nmixture.[11] This model yields the common Tauc gap E g\n= 2.15±0.06 eV, bulk thickness d b= 468.93 ±0.78˚A, and\nsurface roughness thickness d s= 75.39±0.4˚A.\nWe note that though the Tauc gap at 2.15 eV (577\nnm) represents the onset of absorption, it is notthe in-\ndirect gap, as claimed in literature.[6] A plot of α2E2\nvs. photon energy E ( α= 4πk/λ) and the linear ex-\ntrapolation to α2E2= 0 indicates a direct gap at 2.81\neV (442 nm) as shown in Fig. 1(b). This value is in\ngood agreement with that obtained from more recent\noptical measurements.[12] Band gap measurements on\ndifferent MBE-grown BiFeO 3films grown on (001) and\n(111) SrTiO 3substrates revealed a direct band gap inall cases with E g= 2.77±0.04 eV. The presence of two\ndistinct slopes in ( αE)1/2vs. E characteristic of an indi-\nrect band gap [13] is not observed. We obtain the linear\ncomplex indices from this model to be ˜Nω\nf=2.836+0 iand\n˜N2ω\nf=3.444+0.981 ifor corresponding wavelengths of 800\nand 400 nm, respectively. It should be noted that al-\nthough BiFeO 3is uniaxially anisotropic, only the optical\nproperties of the ordinary index of refraction have been\nobtained for this film.[14]\nThe crystal symmetry of epitaxial BFO(111) films has\nbeen shown to be point group 3 musing optical SHG\nand diffraction techniques.[7] Optical SHG[15] involves\nthe conversion of light (electric field Eω) at a frequency\nωinto an optical signal at a frequency 2 ωby a nonlin-\near medium, through the creation of a nonlinear polar-\nizationP2ω\ni∝dijkEω\njEω\nk, wheredijkrepresent the non-\nlinear optical coefficients. BFO film with thickness of\nabout 50 nm grown on STO(111) substrates was used for\nthis study. STO is centrosymmetric (cubic) and does not\ncontribute SHG signals of its own for the incident powers\nused. The SHG experiment was performed with a funda-\nmental wave generated from a tunable Ti-sapphire laser\nwith 65 fs pulses of wavelength 800 nm incident from\nthe substrate side at variable tilt angles θto the sample\nsurface normal.\nAs shown in Fig. 2, the crystallographic y-zplane in\nthe BFO film was aligned with the incidence plane. The\npolarization direction of incident light is at an angle φ\nfrom the xaxis, which was rotated continuously using a\nhalf-wave plate . The intensity I2ω\njof the output SHG\nsignal at 400 nm wavelength from the film was detected\nalong either j=p,spolarization directions as a function\nof polarization angle φof incident light. The resulting\npolar plots of SHG intensity for pands-polarized output\natθ= 0◦andθ= 45◦are shown in Fig. 2(a) and (b)\nrespectively. If the incident beam has intensity I0then\nthe nonlinearpolarizationsforBFO(111)film with x-axis\nperpendiculartotheplaneofincidenceisgivenby[16, 17],\nPNL\nx=I0fxsin2φ(d15fzsinθ−d22fycosθ)\nPNL\ny=I0(−d22cos2φf2\nx+d22f2\nycos2θsin2φ\n+d15fyfzsin2θsin2φ)\nPNL\nz=I0(−d31cos2φf2\nx+d31f2\nycos2θsin2φ\n+d33f2\nzsin2θsin2φ) (1)\nwheredijare nonlinear coefficients and fiare effective\nlinear Fresnel coefficients. The measured intensity of the\npandspolarized SHG in transmission geometry (ne-\nglecting birefringence) is proportional to nonlinear po-\nlarization. The expected SHG intensity expressions for p\nandsoutput polarizationsin the predicted 3 msymmetry\nsystem of BFO are:\nI2ω\np=A(cos2φ+Bsin2φ)2\nI2ω\ns=Csin22φ (2)\nwhere B and C are given by3\nB=K15fyfzsin2θcosθB+K31f2\nycos2θsinθB+K33f2\nzsin2θ+f2\nycos2θcosθB\nK31f2xsinθB−f2xcosθB\nC=D(K15fzfxsinθ−fxfycosθ) (3)\n/g1 /g2/g1 /g3/g1 /g4/g1 /g5/g1 /g6/g1 /g7/g1/g5/g1/g7/g1/g8/g1/g2/g1/g1\n/g1/g2\n/g1/g2/g2/g3/g4/g5/g4/g6/g7/g8/g7/g5/g9/g2/g2/g3/g4/g5/g4/g6/g7/g8/g7/g5\n/g10/g11/g12/g13/g7/g2/g14/g15/g2/g8/g16/g13/g8/g2 θ/g2/g2/g17/g18/g7/g12/g19/g10/g2/g11/g6/g10/g2/g11/g5/g10/g2/g11/g4/g10/g2/g11/g3/g10/g2/g11/g2/g10/g2/g11/g1\nFIG. 3: Variation of extracted B parameter from ppolar-\nized SHG signal ( Bexpt=−[I2ω\np(φ=90◦)\nI2ωp(φ=0◦)]1\n2) and C Parameter\n(Cexpt=I2ω\ns(φ= 45◦)) as a function of tilt angle, θ. The\nsolid lines show theoretical fits to the data.\nHereK15=d15/d22,K31=d31/d22andK33=\nd33/d22arethe ratiosofthe nonlinearopticalcoefficients,\nA and D are scaling parameters, and θBis the angle that\nthe generated second harmonic wave makes with the sur-\nface normal insidethe film. Theoretical fits to the ex-\nperimental polar plots based on Eq. 2 are excellent both\nin normal incidence and tilted configuration as shown in\nFig. 2(a) and (b), respectively, for both pandspolar-\nized SHG output. In normal incidence ( θ= 0◦), only the\nd22coefficient is involved in the generated I2ω\np(φ= 0◦).\nUsing the d22=1.672 pm/V coefficient of a single crystal\nz-cut LiTaO 3used as a reference, the d 22coefficient of\nthe BFO film is calculated by employing the following\nequation[18],\nd2\neff\nd2r=P2ω\nfAfn2ω\nf\nP2ωrArn2ωr/parenleftBigPω\nrTω\nrnω\nf\nPω\nfTω\nfnωr/parenrightBig2lc,f\nlc,rlc,r/integraltext\n0x2e−α2ω\nr(lc,r−x)dx\nlc,f/integraltext\n0x2e−α2ω\nf(lc,f−x)dx,\n(4)\nwhere the subscripts randfrefer to the reference andthe film, respectively, P2ω(Pω) are the second-harmonic\n(fundamental) signal powers measured, T is the trans-\nmission coefficient of the fundamental, A is the area of\nthe probed beam, nare the indices of refraction, lcthe\ncoherence lengths and α= 4πk/λis the absorption coef-\nficient at 2 ω. For this experiment, Af=Ar=π(60µm)2\nand the coherence length of the film lc(film) is equal to\nthe film thickness.\nThe B and C parameters, which contain the ratios of\nnonlinearcoefficients,areexperimentallyobtainedbycol-\nlecting the p-in-p-outI2ω\np(φ= 90◦),s-in-p-outI2ω\np(φ=\n0◦) and 45-in- s-outI2ω\ns(φ= 45◦) SHG signals for dif-\nferent angles of tilt θabout the xaxis. The experimen-\ntal data for B and C parameters (Fig. 3) is then fit-\nted to Eq. 3 to extract the ratios K15= 0.20±0.01,\nK31= 0.35±0.02 andK33=−11.4±0.20. Taking ab-\nsorption into account, the estimated effective coefficients\nare\n|d22|= 298.4±6.1 pm/V,|d31|= 59.7±4.2 pm/V\n|d15|= 104.4±8.1 pm/V,|d33|= 3401±129 pm/V .\nNote that only the signs of the ratios K15,K31andK33\nwere determined unambiguously. The absolute signs of\nthedijcoefficients were not determined, except to state\nthat the d33coefficient has the opposite sign to the other\ncoefficients. The large values of dijcoefficients most\nlikely arise due to electronic resonances at the 400 nm\nSHG wavelength.\nTo conclude, we report the complex index of refraction\nversus wavelength and optical second harmonic genera-\ntion coefficients in BiFeO 3thin films. These studies will\nbe important in performing further linear and nonlinear\noptical spectroscopy of the magnetism and ferroelectric-\nity in this material.\nWe would like to acknowledge support from NSF un-\nder grant Nos. DMR-0507146, DMR-0512165, DMR-\n0602986 and DMR-0213623. At Univ. of Tennessee, the\nresearch was supported by the Materials Science Divi-\nsion, BES, U.S. DoE (DE-FG02-01ER45885).\n[1] J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B.\nOgale, B. Liu, D. Viehland, V. Vaithyanathan, D. G.\nSchlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe,\nM. Wuttig, and R. Ramesh, Science 299, 1719 (2003).\n[2] C. Ederer and N. A. Spaldin, Phys. Rev. B 71, 060401(2005).\n[3] N. A. Spaldin and M. Fiebig, Science 309, 391 (2005).\n[4] M. Fiebig, Th. Lottermoser, D. Frhlich, A. V. Goltsev,\nand R. V. Pisarev, Nature 419, 818 (2002)\n[5] J. -P. Rivera and H. Schmid, Ferroelectrics 204, 234\n(1997).\n[6] V. Fruth, E. Tenea, M. Gartner, M. Anastasescu, D.\nBerger, R. Ramer, and M. Zaharescu, Jour. Euro. Cer.\nSoc. 27, 937 (2007).\n[7] J.F. Ihlefeld, A. Kumar, V. Gopalan, Y.B. Shen, X.Q.\nPan, T. Heeg, J. Schubert, X. Ke, P. Schiffer, J. Oren-\nstein, L.W. Martin, Y.H. Chu, R. Ramesh, and D.G.\nSchlom, Appl. Phys. Lett. 91, 071922 (2007).\n[8] J. Lee, P.I. Rovira, I. An, and R.W. Collins, Rev. Sci.\nInstrum. 69, 1800 (1998).\n[9] G.E. Jellison, Thin Solid Films 313, 33 (1998).\n[10] G.E. Jellison, Jr. and F.A. Modine, Appl. Phys. Lett. 69 ,\n371, 2137 (1996).\n[11] H. Fujiwara, J. Koh, P.I. Rovira, and R.W. Collins, Phys .\nRev. B. 61, 10832 (2000).[12] R.C. Rai, S.R. Basu, L.W. Martin, Y.H. Chu, M. Gajek,\nR. Ramesh, andJ.C. Musfeldt (SubmittedtoAppl.Phys.\nLett.).\n[13] J.I. Pankov, Optical Processes in Semiconductors, Dov er\nPublications Inc., New York, p. 37 (1975).\n[14] D.E. Aspnes, J. Opt. Soc. Am. 70, 1275 (1980).\n[15] A. Kirilyuk, J. Phys. D , R189 (2002).\n[16] W. Y. Hsu, C. S. Willand, V. Gopalan, and M. C. Gupta,\nAppl. Phys. Lett. 61, 19 (1992).\n[17] B. Dick, A. Gierulski, G. Marowsky, and G. A. Reider,\nAppl. Phys. B. 38, 107 (1985).\n[18] A. Sharan, I. An, C. Chen, R. W. Collins, J. Lettieri, Y.\nJia, D. G. Schlom and V. Gopalan, Appl. Phys. Lett. 83,\n25 (2003)."    },    {        "title": "1908.02780v1.Fast_response_of_pulsed_laser_deposited_Zinc_ferrite_thin_film_as_a_chemo_resistive_gas_sensor.pdf",        "content": "This \narticle\n \nha\ns\n \nbeen submitted in a\n \npeer reviewed \nreputable\n \nJ\nournal for\n \npossible\n \npublication.\n \n \n \nFast response of pulsed laser deposited \nZinc ferrite\n \nthin film as a chemo\n-\nresistive gas sensor\n \nSaptarshi De \n \nDepartment\n \nof \nMetallurgical Engineering and Materials Science\n \nIndian Institute of Technology Bombay, Mumbai, India.\n \nEmail:  \nsapjaki@gmail.com\n \n \n \nAbstract\n—\n \nThin films of ZnFe\n2\nO\n4\n \ndeposite\nd by pulsed laser \ntechnique are \nhere demonstrated as one of the \ninteresting \nmaterials for sensing of ethanol. The response transients were \nfitted well to one\n-\nsite Langmuir adsorption model. Activation \nenergies for (I) adsorption and reaction of ethanol and (II) \ndesorption (i.e. recovery process) of ethanol from zinc fe\nrrite thin \nfilm surface were obtained on the basis of this model. In this \npaper, we showed the effect of operating temperature and gas\n-\nconcentration on the response time\n \nof thin film sensor materials. \nAt the operating temperature 340\no\nC, the ZnFe\n2\nO\n4\n \nthin fi\nlm \nshowed high (84%) as well as immediate response to 500 ppm of \nethanol, with its resistance being saturated within ~12 seconds, \nwhich stands far superior to the response time of nano crystalline \npowders.\n \nThose films were also observed to have a good \nrepe\natability of their sensor response, thus representing a major \nstep towards low\n-\ncost large\n-\nscale production of this class of \ndevices.\n \nKeywords\n—\nEthanol sensing\n, Zinc Ferrite, thin film gas\n \nsensor, \nheterogeneous catalyst c\nomponent\n \nI.\n \n \nIntroduction \n \nEarlier, gas \nsensors were made of simple oxides including \nZnO, SnO\n2 \nand TiO\n2\n \n[\n1\n,\n2\n,\n3\n]. They were used as sensing \nmaterials in pellets, thick films, thin film and nanowires forms \n[\n4\n]. But the problems with these simple oxide gas sensors are \ntheir poor selectivity and hig\nh operating temperature (400 \n–\n \n550 °C). Use of mixed valence oxides and composite oxides \nmay improve the selectivity of gas sensors in comparison to \nsimple oxides, as the activation energies for adsorption \n–\n \ndesorption of gas species on metal oxide surface\n \nmay differ \nfor cations. \nAn alternative for these metal oxides are complex \noxides e.g. ferrites, as complex oxides have periodic electronic \nstructure and there has been increased interest on the use of \nferrites as gas sensors. Ferrites have high resistivit\ny which \nchanges when the surrounding gaseous atmosphere changes \n[\n5\n]\n.\n \n \nAlmost all ferrites, MFe\n2\nO\n4\n \n(with M = Zn, Mg, Ni, Cd, Bi, \nCo and Cu) has been observed to have interesting gas sensing \nproperties [\n6\n,\n7\n,\n8\n,\n9\n,\n10\n,\n11\n]. Spinel ferrite in different forms e.g. \nnanoparticles, thick films and thin films have been utilized for \ngas sensing. There are reports on gas sensors made of \nnanocrystalline particles, which have been synthesized by \nvarious techniques including sol gel, combustion synthesis, \nchemical co\n-\nprecipi\ntation method and hydrothermal method \n[\n6\n-\n8\n]. These powders were either directly made pellets or \nmade as thick film by using a suitable binder and casting in \nsubstrates like glass and used for gas sensing [\n6\n-\n10\n]. \nAmong \nall ferrites, only zinc ferrite was used in “resistive thin film \ngas sensing device” and the sensing layers \nwere fabricated \nusing spray pyrolysis [\n12\n,\n13\n]\n \nor spin coat technique [\n14\n]\n \ndue \nto its low resistivity comparing\n \nto\n \nthe \nother ferrites\n.\n \nGas \nsensing properties should be studied with dense ferrite thin \nfilms deposited by any physical vapour deposition system (e.\ng. \nradio freequency\n \nsputtering or pulsed laser ablation), where \nonly top surface is available for sensing. Moreover, due to its \nhigh intrinsic surface\n-\nto\n-\nvolume ratio, thin film technology \nexhibits high capabilities for miniaturization and very short \nrespo\nnse. \nHere, in this report the gas sensing properties of \nZinc ferrite thin films deposited by pulsed laser deposition \n(PLD) technique are studied.\n \n \nIt is seen that like other semiconducting metal oxide gas \nsensors, \nmaximum\n \neffort was given to achieve promis\ning gas \nsensing characteristics by the synthesis of pure phase, porous, \nnano\n-\ncrystalline ferrite particles.\n \nThe sensing mechanism was \nexplained on the basis of reactivity with adsorbed oxygen, but \nthe quantification of activation energy for this reaction w\nas not \ndone\n \nfor ethanol vapor mixture on zinc ferrite surface\n. \nIn this \nreport an \napproach\n \n(using\n \none\n-\nsite Langmuir adsorption \nmodel\n)\n \nwas made to find out the values of those activation \nenergies.\n \nII.\n \nExperimental\n \nZinc ferrite (ZFO) thin films were deposited on \namorphous \nfused silica\n \nsubstrate by pulsed laser deposition apparatus \nusing a home\n-\nmade sintered ceramic target of pure ZnFe\n2\nO\n4\n \nwith a relative density of 92%. Eximer laser (KrF) of 242 nm \nwith 10 ns pulsed width was \nused to ablate the ZFO target. \nLaser \nfluence and repetition rate of the laser shots were fixed \nat 4 J/cm\n2\n \nand 10\n \nHz respectively. \nThe pressure inside the \ndeposition chamber was 5×10\n−6\n \nmbar or lower b\nefore \ndeposition was commenced.\n \nDuring the deposition of films, \nthe oxygen pressure in\nside\n \nthe\n \nchamber and the target\n-\nto\n-\nsubstrate distance were kept at 1.3\n×10\n-\n1\n \nmbar\n \nand 4.5 cm \nrespectively.\n \nAt room temperature\n \n(RT)\n \n(substrate temperature \nT\ns\n= \n20\no\nC\n), 4×10\n4 \nlaser shots were used to get approximately \n500 nm thick ZFO films. Thickness calibrations wer\ne \nperformed with DEKTAK profilometer \nand cross section view \nthrough FEI \nQuanta 200\n \nFEG\n-\nSEM. \nThe phase and structural \nproperties were determined by X\n-\nray Diffraction using \nPananlytical diffractometer with the CuK\n\n \nradiation This \narticle\n \nha\ns\n \nbeen submitted in a\n \npeer reviewed \nreputable\n \nJ\nournal for\n \npossible\n \npublication.\n \n \n \n(\n\n=1.5418 Å).  Microscopic studie\ns were carried out also with \nQuanta 200\n \nSEM. Our simplified chemo\n-\nresistive gas sensor \nconsists of a electrically insulated \nsilica\n \nsubstrate, the sensitive \nZFO layer and two interdigitated silver electrodes on top of \nthe \nZFO layer. After thermal annealing \nof ZFO thin films, 1 \nmicron thick silve\nr electrodes were deposited on\n \nthe surface of \nthe ZFO layer by DC sputtering technique. The electrical \nresponse of the sensing layer was investigated by Keithley \n2635 source meter as a function of temperature, time, a\nnd test \ngas concentration. The test devices were placed on a PID \ncontrolled heater operating inside a chamber with controlled \natmosphere. Resistance measurement \nof the sensor films \nwas \ncarried out\n \nwith\n \ntwo\n \ntypes of gas \natmospheres: dry air and a \nmixture of \n“\nair+test gas\n”\n.  Calibrated ethanol of 500 ppm \n(balanced with dry air) \nwas\n \nused as test gases.  \nT\notal flow \nof \ngases \ninside the chamber was fixed at 100 cm\n3\n/min. \nFurther, \ntest gas concentration was varied by mixing of d\nry air and the \ncalibrated gases from \ntwo \nseparate\n \ncylinders with the help of \nmass flow controller \n(MKS 647B)\n.\n \nThe concentration of \nmixed gas in the reaction chamber could be calc\nulated using \nfollowing relation\n \nC\nmixed test gas \n= [C\ntest gas \n(dV\ntest gas \n/dt)]\n/\n \n[dV\ntest gas \n/dt + dV\ndry air \n/dt]\n  \n(1)\n \nIII.\n \nResult and discussion\n \nFig\n.\n \n1 shows XRD patterns of the sintered ZFO target used \nfor thin film deposition, as\n-\ndeposited ZFO thin film and the \nfilm\ns annealed in air for 2 hours. \nXRD pattern of the sintered \npellet \nmatched well with single phase cubic zinc fe\nrrite \n(JCPDS no. 01\n-\n089\n-\n4926). \nCrystalline growth was observed \nfor the films annealed above 250\no\nC. \nAverage \ncrystallite\n \nsize \nwas calculated using Scherrer formula and tabulated in table 1.  \n \n \nFig. 1\n \nXRD pattern of \nZFO\n \nthin films deposited at room temperature, \nannealed at different temperature and target material\n \n \nTable I: \nCrystallite size of \nZFO\n \nthin films calculated using Scherrer formula\n \nAnnealing temperature \n \nCrystallite size \n \nRT (as\n-\ndeposited)\n \n-\n \n250\no\nC\n \n-\n \n350\no\nC\n \n~19nm\n \n450\no\nC\n \n~25nm\n \n550\no\nC\n \n~31nm\n \n650\no\nC\n \n~36nm\n \n \nIt is known that the gas sensing performance is better in the \nsemiconducting ceramic oxides with finer crystallite size; \ntherefore, in the present gas sensing study we choose the \nsample which \nwas annealed at 350\no\nC. Fig\n.\n \n2 show\ns\n \nthe surface \nand cross sectional view of ZFO thin film annealed at 350\no\nC. \nIt shows dense column\nar grain growth of zinc ferrite \nupon \nthermal treatment of as deposited samples, whereas significant \nchange in particle size al\nong surface can’t be observed from \ntop view SEM.\n \n \nFig. 2 \nSEM micrograph of Zn\n-\nferrite thin film deposited on \nfused silica\n \nsubstrate at room temperature and annealed at 350\nO\nC, top view (left\n) and cross \nsectional view (\nright\n)\n \n \nFig\n. \n3\n \nshows\n \nresponse and \nrecovery transient of the ZFO \nthin film sensor towards 500 ppm of ethanol at operating \ntemperature of 340\no\nC.  Base line (resistance of the sensor in \nair) drift (~9%) was observed over long time (more than 3hr) \nexposure of sensing element to air and also wh\nen the ambient \natmosphere of the sensor was switched back and forth between \nair and test gas.  Whereas sensitivity (S=ΔR/R\nair\n \nx 100%) of \nthis sensor at 340\no\nC varies in between 84\n-\n86% towards 500 \nppm of ethanol.\n \n3\n6\n8\n1 1\n1 4\n0\n5\n1 0\n1 5\nO p e r a t i n g  t e m p e r a t u r e   3 4 0\no\nC\nE t h a n o l\no f f  &  a ir  o n\nE t h a n o l\no n\nT im e ( in  h r )\nResistance (in MOhm)\nFig. \n3\n \nRepeatabilit\ny\n \nof the sensor: resistance transient of Zn\n-\nferrite thin film \ngas sensor to 500 ppm of ethanol at 340\no\nC operating temperature\n \n \nAs reported in several research journals, the reaction \nmechanism for the sensing of reducing gases by \nan\n \nn type Zinc \nferrite semiconductor could be summarized as follow\ns\n \n[\n1\n-\n14\n]\n. \nIn a first step,\n \nat \nthe \noperating temperature, oxygen is \nphysiadsorbed in the sensor surface followed by the electron \ntransfer from the semiconducting ferrite to adsorbed oxygen to \nform chemical bond between the adsorbed oxygen and the \nsemiconducting oxide\ns.  These reactions are described in Eqs.\n \n2\n \nand \n3 respectively\n \nO\n2\n \n+ sensor\nsurface \n↔ O\nad\n-\nsurface \n    \n(physiadsorption)\n \n(2)\n \nO\nad\n-\nsurface \n+ e \n↔ O\nad\n−\n                \n(chemiadsorption)\n \n(3)\n \nThe exact nature of chemiadsorbed oxygen is subject to debate \nand dependin\ng on the temperature of adsorption oxygen may \nbe atomic or molecular origin. When the sensor is exposed to \nreducing gas (R) atmosphere, the reducing gas is \nphysiadsorbed on the sensor surface and reacts with the \nadsorbed ox\nygen according to the reaction \n4\n \nand \n5\n \nand the by\n-\nproducts go out (Eq.6)\n.\n \n20\n40\n60\n650\nO\nC\n550\nO\nC\n450\nO\nC\n350\nO\nC\n250\nO\nC\nas-deposited\n(440)\n(333)\n(422)\n(400)\n(222)\n(311)\n(220)\n(111)\n Intensity (a.u.)\n2\n\n (degree)\n \n \nTarget (bulk)\nThis \narticle\n \nha\ns\n \nbeen submitted in a\n \npeer reviewed \nreputable\n \nJ\nournal for\n \npossible\n \npublication.\n \n \n \nR + [sensor] \n↔ R\nad\n \n(physiadsorption)\n \n \n(4)\n \nR\nad\n+ O\nad\n−\n↔R\n-\nO\nad\n \n+ e\n \n \n \n \n(5)\n \nR\n-\nO\nad\n↔By\n-\nproducts\ngas\n↑+ sensor\nsurface\n \n \n \n(6)\n \nFollowing the above reaction sequence, the ethanol sensing \nbehavior of n type zinc ferrite can be \nenvisaged as follows: as \nthe sensing material was sintered at lower temperature \n(350°C), grain to grain contact has been established.  Due to \nthe chemiadsorption of oxygen (molecular or atomic anionic \nspecies) an electron depleted layer is formed at the gr\nain \nsurface which eventually leads to the formation of potential \nbarrier for grain to grain electron\n-\npercolation.  At temperature \nT, the conductance\n \n(G)\n \nof the sensor is determined by the \nbarrier height through the well \nknown Schottky relation\n \n[\n15\n,\n16\n]\n \nG = G\no\n \nexp(\n-\neV\ns\n/\n \nk\nB\nT) \n \n \n \n \n(7)\n \nWhere eV\ns\n \nis the Schottky barrier and k\nB\n \nis the Boltzmann \nconstant.  When the sensor is exposed to ethanol, it reacts with \nchemiadsorbed ox\nygen species (see Eq.5), resulting the \nlowering of potential barrier which leads to the increase in \nconductance (or decrease in resistance). At constant T, \nassuming Langmuir isotherm adsorption kinetics for a single \nadsorption site, the conductance transie\nnt for response \n[G(t\nresponse\n)] was given\n \nby the following equation \n8.\n \nG(t\nresponse\n)= G\no\n \n+ G\n1\n[(1 \n− exp(− t/ \nτ\nresponse\n)]\n \n \n(8)\n \nWhere, G\no\n \nis base \nconductance\n \n(saturated \nconductance\n \nwith \ntest gas\n) of the sensing material and τ\nresponse \nis response time.  \nSimilarly, for the recovery process the transient conductance \ncould be expressed as \n \nG(t\nrecovery\n)= G\no\n’\n \n+ G\n1\n’\nexp(\n− t/ \nτ\nrecovery\n).\n \n \n(9)\n \nWhere, G\no\n’\n \nis saturated \nconductance\n \nin air \nand τ\nrecovery \nis the \nrecovery time.\n \n0\n1 0 0 0\n2 0 0 0\n3 0 0 0\n4 0 0 0\n0 . 0\n2 . 0 x 1 0\n- 7\n4 . 0 x 1 0\n- 7\n6 . 0 x 1 0\n- 7\n8 . 0 x 1 0\n- 7\nConductance (in mho)\nT i m e  ( i n  s e c )\nT i m e  ( i n  s e c )\nE t h a n o l\no f f\n8 3 0\n8 4 0\n8 5 0\n8 6 0\n8 7 0\n8 8 0\n2 .0 x 1 0\n-7\n4 .0 x 1 0\n-7\n6 .0 x 1 0\n-7\n8 .0 x 1 0\n-7\n \n \n \n \nE t h a n o l\no n\n \nFig. 4 Fitting of conduction transient for response and recovery of ZFO \nthin film sensor\n \nfor 500 ppm ethanol measured at 340 \n℃ using Langmuir \nadsorption model. Inset figure shows fast response time 10 sec, towards 500 \nppm of ethanol measured at 340 \n℃.\n \n \nFigure \n4\n \nshows conduction transient for response and recovery \nof \nZFO\n \nfilm sensor, fitted with one site Langmuir adsorption \nmodel. The response and recovery curves were fitted well with \nR\n2\n \nvalue ~0.98.  Inset figure (enlarged response curve) shows \nfast satu\nration of conductance within ~12 seconds for 500 ppm \nethanol measured at 340\no\nC.  Small oscillation in conduction \ntransient was due to periodic heating by PID controller.  \nEquation 8 & 9 used to find out response and recovery time of \nZFO thin film sensor op\nerated at various temperature range \n(260\n-\n340\no\nC) and ethanol concentration (5\n-\n500ppm) for further \ncalculations.  \n \n1.60\n1.65\n1.70\n1.75\n1.80\n1.85\n1.90\n3\n4\n5\n6\n7\n3\n4\n5\n6\n7\nln \n\n\nrec\n)\n \n \n(I) Response \n(\n\nres\n)\n; A.E=\n140 KJ/mol K\n ,\n experimental data\n fitted curve\n(II) Recovery \n(\n\nrec\n)\n; A.E=\n72 KJ/mol K\nln \n\n\nres\n)\n1000/T (K)\n-1\n \nFig\n. \n5\n \nVariation of response or recovery time (\n\n) with the operating \ntemperature at fixed ethanol concentration (500\n \nppm) of Zn\n-\nferrite thin film \ngas sensor\n.\n \n \nThe response and recovery time obtained from response \ntransient using eq. 8 and 9 measured at various temperature (at \nfixed concentration, 500 ppm ethanol) plotted in figure \n5\n. \nIt is \nobserved that response and rec\novery time was inversely \nproportional to the operating temperature. \nWhen the kinetics \nof sensor response is controlled by adsorption/desorption \nprocess the response time (τ) constant usually follow the \nfollowing temperature depe\nndence equations\n \n[\n16\n]\n.\n \n \nτ = τ\no \nexp(E\nA\n/2kT)  or  τ = τ\no \nexp(E\nD\n/2kT)    \n \n \n \n(10)\n \nWhere E\nA\n \nis the activation energy (A.E) for the chemi\n-\nadsorption followed by surface reaction (with oxygen) of \nethanol and E\nD\n \nis the activation energy during the recovery \nprocess.\n \nAs predicted by the above equation, a linear fit was \nobtained when ln τ was plotted with inverse of temperature.  \nFrom the slope of the linear fit, the activation energy for \nadsorption of ethanol was found to be 1.46 eV (140 kJ/mol K), \nand for recovery it \nwas 0.75 eV (72 kJ/mol K). \nThis type of \nfittings to obtain the values of \nactivation energies towards \nethanol \nis also not available for metal oxide systems. Whereas \nthe reported values of \nE\nA\n \nand \nE\nD \nare \n0.27 eV and 0.42 eV \nrespectively \nfor hydrogen\n, from the\n \ncombination of two site \nmodel used in \nnano\n-\ncrystalline magnesium\n-\nzinc ferrite \npowders [\n17\n]; \nand for the same system these (E\nA\n \nand \nE\nD\n) \nvalues are 1.03 and 0.19 eV for CO gas. Similarly for nano\n-\ncrystalline zinc ferrite powder\n,\n \nE\nA\n \nand \nE\nD \nare reported as 0.56\n \nand 0.75 eV respectively for H\n2 \n[\n16\n]. For pure magnesium \nferrite nano powders; E\nA\n \nand \nE\nD \nare reported as 1.45 and 0.51 \neV respectively for\n \nH\n2\n, and 0.61 and 0.47 eV \nrespectively for \nCO\n \n[\n18\n]\n. From the figure 4.20, it is clear that the ‘response \ntime’ or ‘recovery time’ will be shorter means the adsorption \nor desorption process will be faster with rising of operating \ntemperature in the case of high A.E.\n \n \n‘Response time’ \n(τ\nres\n) obtained by the fitting of response \ncurve (eq. \n8\n) which was recorded at different ethanol and \nhydrogen\n \n(in addition)\n \ngas concentration is plotted in figure \n6\n. \nFor higher than 50 ppm of gas concentration, the ‘response \ntime’ seems to be less dependen\nt on the gas\n-\nconcentration. A\nn\n \nexplanation could be given as, saturation of response time \n(\n\nres\n \n) at higher test\n-\ngas concentration may be due to reduction of \navailable reactive sites (pre adsorbed oxygen at active sites on This \narticle\n \nha\ns\n \nbeen submitted in a\n \npeer reviewed \nreputable\n \nJ\nournal for\n \npossible\n \npublication.\n \n \n \nthis sensor\n-\nsurface). So, below 5\n0 ppm of gas concentration, \nthe variation in τ\nres\n \nis fitted by power law of time constant [τ = \nτ\no\nC\ngas\n-\n\n′\n\n\n\n\nnot shown in the figure\n\nand \n\n′\n\nwas found\n\n0.74 \ntowards ethanol for zinc ferrite thin film sensor.\n \n \nFig\n. \n6\n \nVariation of response time (\n\nres\n) of \nZFO\n \nthin film gas sensor with \nvarious ethanol and H\n2\n \nconcentration, measured at \n340 \n℃.\n \n \nSimilarly for the H\n2\n \ngas, value of \n\n′\n\nwas obtained as 0.32. This \ntype of fittings (assuming single site) with ethanol and \nhydrogen is not available for ferrite systems. Mu\nkherjee et al. \nused two sites model for nano\n-\ncrystalline zinc ferrite powder \ntowards H\n2\n \ngas and the value of \n\n′\n\n \nfor each site was ~0.43 \n[\n16\n15\n]. They also observed a tending to saturation in ‘site 2’ at \nhigher gas concentration (> 500 ppm). Similarly, they have \nreported the value of \n\n′\n\nfor magnesium ferrite nano powder as \n0.48 \nand 0.60 for H\n2\n \nand CO respectively\n \n[\n18\n]. The derivation \nof this power law [“response time vs gas\n-\nconcentration”] is \nnot available in the literature. Mukherjee et a\nl.\n \n[\n16\n15\n,\n18\n] used \nthis empirical equation to ch\naracterize the sensor material.\n \n \nIn conclusion, \na\n \nsingle\n-\nsite gas adsorption model is \nenough to fit the response transients of the zinc ferrite thin \nfilms whereas double\n-\nsite model is required for the ‘sensor\n-\npellet’ made from nano crystalline zinc ferrite powder\n \n[\n16\n]\n. \nT\nhe thin film deposited by PLD technique has the shortest \nresponse time\n \n(\n~1\n2 s)\n \ntowards reducing gas (ethanol) in \ncomparison to the zinc ferrite thin film deposited by other \ntechniques i.e. spray pyrolysis and spin coat [\n13\n-\n14\n].\n \nAn \nindirect method was used \nthrough the kinetic analyses of the \nconductance transients during response and recovery, we have \nestimated the activation energies for relevant gas adso\nrption \n(E\nA\n) and desorption (E\nD\n) during ethanol sensing\n.\n \nAcknowledgment\n \nThe above research work was partially supported by the \nresearch grant from DST\n-\nANR research project (Project \nCode.14IFCPAR001). We would like to thank IRCC, IIT \nBombay for BDS Facility \nand SAIF, IIT Bombay for SEM of \nthe samples.\n \nReferences\n \n[1]\n \nH. C. Chiu, C. S. Yeh, “Hydrothermal Synthesis of SnO\n2\n \nNanoparticles \nand Their Gas\n-\nSensing of Alcohol”, The\nJournal of Physical Chemistry \nC, 2007 \n111(20),\npp. 7256\n-\n7259.\n \n[2]\n \nQ. Wan, Q.H. Li, Y.J. Chen, T.H.\n \nWang, X.L. He, J.P. Li, C.L. Lin, \n“Fabrication and\n \nethanol sensing characteristics of ZnO nanowire gas \nsensors”, \nApplied Physics Lett\ners, 2004, 84(18),\npp. 3654\n-\n3656\n.\n \n[3]\n \nS. Akbar, P. Dutta, C. Lee, “High\n-\nTemperature Ceramic Gas Sensors: A \nReview”, \nInternation\nal Journal of Applied Ceramic Technology, 2006, \n3(4), pp. \n302 \n-\n311.\n \n[4]\n \nG. Korotcenkov, V. Golovanov, V. Brinzari, A. Cornet, J. Morante, M. \nIvanov,\n \n“Distinguishing feature of metal oxide films’ structural \nengineering for gas sensor\n \napplications”, \nJournal of P\nhysics: Conference \nSeries, 2005, \n15, pp. \n256\n–\n261.\n \n[5]\n \nN. Rezlescu, E. Rezlescu, P.D. Popa, F. Tudorache, “A model of \nhumidity sensor with a\n \nMg\n-\nbased ferrite\n”, \nJournal of Optoelectronics \nand Advanced Materials\n, 2005, \n7(2), pp.\n \n907\n-\n910.\n \n[6]\n \nN.N. Gedam , P.R. Padole,\n \nS.K. Rithe , G.N. Chaudhari, “Ammonia gas \nsensor based on a spinel semiconductor, Co\n0.8\nNi\n0.2\nFe\n2\nO\n4\n \nnanomaterial”, \nJournal of Sol\n-\nGel Science and Technology, 2009, 50(3), pp. 296\n–\n300.\n \n[7]\n \nA.S. Poghossian, H.V. Abovian, P.B. Avakian, S.H. Mkrtchian, V.M. \nHaroutu\nnian,\n \n“Bismuth ferrites: New materials for semiconductor gas \nsensors”, \nSensors and Actuators B: Chemical, 1991, \n4\n(3\n-\n4), pp. 545\n-\n549.\n \n[8]\n \nZ. Tianshu, P. Hing, Z.Jiancheng, K. Lingbing , “Ethanol\n-\nsensing \ncharacteristics of cadmium ferrite prepared by chemical \nco\nprecipitation”, \nMaterials Chemistry and Physics\n, 1999, \n61\n(3), pp. 192\n-\n198.\n \n[9]\n \nP.P. Hankare, S.D. Jadhav, U.B. Sankpal, R.P. Patil, R. Sasikala, I.S. \nMulla , “Gas sensing properties of magnesium ferrite prepared by co\n-\nprecipitation Method”, \nJournal of  Alloys \nand Compounds\n, 2009, \n488\n(1), \npp. 270\n-\n272.\n \n[10]\n \nR.B. Kamble, V.L. Mathe, “Nanocrystalline nickel ferrite thick film as \nan efficient gas\n \nsensor at room temperature”, \nSensors and Actuators B: \nChemical, 2008, \n131\n(1), pp. 205\n–\n209.\n \n[11]\n \nA. Chapelle, F. Oudrhiri\n-\nHassani, L\n. Presmanes, A. Barnabé, Ph. \nTailhades, “CO2 sensing properties of semiconducting copper oxide and \nspinel ferrite nanocomposite thin film”, \nApplied Surface Science\n, 2010, \n256\n(14), pp. 4715\n-\n4719.\n \n[12]\n \nJiao, Z., Wu, M., Gu, J., & Qin, Z. (2003). Preparation and g\nas\n-\nsensing \ncharacteristics of nanocrystalline spinel zinc ferrite thin films. \nIEEE \nSensors Journal\n, \n3\n(4), 435\n–\n438\n.\n \n[13]\n \nA. Sutka, J. Zavickis, G. Mezinskis, D. Jakovlevs, J. Barloti, “Ethanol \nmonitoring by ZnFe2O4 thin film obtained by spray pyrolysis”, \nSensor.\n \nActuat. B\n, \n176\n \n(2013)330 \n–\n \n334.\n \n[14]\n \nA. Singh, A. Singh, S. Singh, P. Tandon, B. C. Yadav, R. R. Yadav, \n“Synthesis, characterization and performance of zinc ferrite nanorods for \nroom temperature sensing applications”, \nJ.Alloy. Compd\n., \n618 \n(2015) \n475\n–\n483.\n \n[15]\n \nC. \nWang, X.Q. Fu, X.Y. Xue, Y.G. Wang, and T.H. Wang; Surface \naccumulation conduction controlled sensing characteristic of p\n-\ntype \nCuOnano rods induced by oxygen adsorption; Nanotechnology; 2007; \n18, pp 145506\n–\n145511\n.\n \n[16]\n \nK. Mukherjee, S. B. Majumder, “Analyses of\n \nresponse and recovery \nkinetics of zinc ferrite as hydrogen gas sensor”, \nJournal of Applied \nPhysics, 2009,\n106\n, 064912.\n \n[17]\n \nK. Mukherjee, S.B. Majumder, “Reducing gas sensing behavior of nano\n-\ncrystalline magnesium\n–\nzinc ferrite Powders”, \nTalanta\n, 2010, \n81\n(4\n-\n5), \npp. 1826\n-\n1832.\n \n[18]\n \nMukherjee, K., Bharti, D. C., & Majumder, S. B. (2010). Sensors and \nActuators B\n: Chemical Solution synthesis and kinetic analyses of the \ngas sensing characteristics of magnesium ferrite particles. \nSensors & \nActuators: B. Chemical\n, \n146\n(1), \n91\n–\n97.\n \n \n \n \n \n \n \n \n \n"    },    {        "title": "1302.4602v1.On_the_evolution_of_the_non_exchange_spring_behaviour_to_the_exchange_spring_behaviour__A_First_Order_Reversal_Curve_Analysis.pdf",        "content": "On the evolution of the non exchange spring behaviour to the \nexchange spring behaviour: A First Order Reversal Curve \nAnalysis \nDebangsu Roy*, Sreenivasulu K V and P S Anil Kumar \nDepartment of Physics, Indian Inst itute of Science, Bangalore 560012, India \n \nThe magnetization behaviour of the soft Cobalt Ferr ite-hard Strontium Ferrite  nanocomposite is tuned \nfrom the non exchange spring nature to the exchange spring nature, by controlling the particle size of \nthe soft Cobalt Ferrite in the Cobalt Ferrite: St rontium Ferrite (1:8) nanocomposite. The relative \nstrength of the interaction governin g the magnetization process in the nanocomposites is investigated \nusing Henkel plot and First Order Reversal Curve (FORC) method. The FORC method has been \nutilized to understand the magnetization reversal beha viour as well as the extent of the irreversible \nmagnetization present in both the nanocomposites having sm aller and larger particle size of the Cobalt \nFerrite. The magnetization process is primarily controlled by the domain wall movement in the nanocomposites. Using the FORC distribution in the (H\na, H b) co-ordinate, the onset of the nucleation \nfield, invasion of the domain wall from the soft to the hard phase, domain wall annihilation and the \npresence of the reversible magnetization with the applied reversal field for both the nanocomposites \nhas been investigated. It has been  found that for the composite having lower particle size of the soft \nphase shows a single switching behaviour corresponding to  the coherent reversal of the both soft and \nhard phases. However, the composite having highe r Cobalt Ferrite particle size shows two peak \nbehaviour in the FORC distribution resembling indi vidual switching of the soft and hard phases. The \nFORC distribution in (H u, H c) co-ordinate and the Henkel measurement confirms the dominant \nexchange interaction in the nanocomposites exhi biting exchange spring behaviour where as the \noccurrence of both the dipolar and exchange interact ion is substantiated for the non exchange coupled \nnanocomposite. The asymmetric nature of the FORC distribution at H c= 0 Oe for both the \nnanocomposites validates the intercoupled nature of th e reversible and irrevers ible magnetizations in \nboth the nanocomposites. It is also concluded that the contribution of the reversible magnetization is \nmore in the nanocomposite havi ng lower particle size of the Cobalt Ferrite compared to the \nnanocomposite having higher partic le size of the Cobalt Ferrite. \n \n  \n*debangsu@physics.iisc.ernet.in I. Introduction: \nIn the recent years, increasing attention has been paid in th e field of nanocomposite magnet 1, \n2 as it provides an integrated system comprising of components whose properties are \ncomplementary to each other. One such active field of research is the exchange spring \nmagnet3-7, where high saturation magnetization of th e soft and the high magnetic anisotropy \nof the hard magnetic phases are exchange coupled in the nanometric scale. Both the experimental studies and th e Micromagnetic calculations\n8-11 reveal that significant \nimprovements in terms of magnetic energy product (BH) max can be achieved using the \nexchange spring magnet. It has also been sugge sted that the exchange  coupling between the \nhard and soft phase should be rigid8 which will lead to the good squareness and higher \n(BH) max. Coherent rotation of the sp ins at the hard-soft interface is the key for the rigid \nexchange coupling9. Thus the better understanding of th e interactions pr esent between the \nsoft and hard phases will lead to the improvement of the nanocomposite magnet with improved magnetic properties compared to the individual soft and hard magnetic phases. The \nhysteresis and reversible processes are central  to the investigation of the microscopic \ninteractions\n12.  In general, the competition between the reversible and the irreversible \nswitching processes determines the magnetic interaction present in the system. In the case of exchange spring the switching field correspondi ng to the soft and hard phases manifests the \ninter-phase coupling strength. We have previous ly showed the effect of the soft phase \n(Ni\n0.8Zn0.2Fe2O4) on the coercivity mechanism13 of the nanocomposite \nNi0.8Zn0.2Fe2O4/BaFe 12O19. We have also demonstrated the occurrence of the exchange spring \nin the case of oxide ferrites 14 and enhancement of (BH) max in all oxide exchange spring \nsystem15. However, we have not investigated the evolution of the exchange spring \nmechanism in these systems.  \nIn this article, we compare the magnetization reversal processes in the hard-soft Strontium \nFerrite-Cobalt Ferrite na nocomposites that exhibit exchange spring and non exchange spring \nnature. In order to realize the reversal mech anism, one needs to vary the strength of the \nmagnetic interaction in the nanocomposites. In  addition, one needs to have a suitable \ntechnique to quantify the effect of the interact ion. The particle size of the soft phases has \nbeen varied to understand the evolution from  the non exchange spring behaviour to the \nexchange spring behaviour in the Strontium Ferrite-Cobalt Ferrite na nocomposite. We have \nused the first-order reversal curve (FORC)16-19 and Henkel Plot20, 21 technique to understand \nthe reversal mechanism present in these tw o systems. The FORC method is based on the procedure described by Mayergoyz22. It is a versatile yet a si mple technique which provides \nplethora of quantitative information apart from  the evaluations of the interaction in the \nhysteretic system regardless of whether it is bulk23, thin film24-29, nanowire30-32, magnetic \ntunnel junction33, 34, ferroelectric switching19, 35, patterned system36, 37 and permanent \nmagnets38. In the present work, the irreversible switching processes during the magnetization \nreversal have been investig ated for two systems namely viz. non exchange spring and \nexchange spring. We have also investigated th e switching field distribu tion (interaction field \nor bias field distribut ion) and coercive field distribution for both the systems. Using these \nprofile distribution for both the systems, the existence of the pinni ng, homogeneity of the \nsample has been determined. The occurren ce of the nucleation, domain wall annihilation \nprocesses involving the magneti zation switching for both the exchange and non exchange \ncoupled composite has been analysed with the variation of the applie d reversal field. The \namount of magnetization irreversibility has also  been measured and it is found that the \nirreversibility is more when the nanocomposite is  in the exchange spring regime compared to \nthe non exchange spring regime.  Furtherm ore the coupling betw een reversible and \nirreversible magnetization ha s also been investigated. \nII. Experiments: \nThe hard ferrite, Strontium Ferrite (SrFe 12O19) has been prepared by the citrate gel method. In \nthis method precursors of Strontium Nitrate and Ferric Nitrate molar solutions were mixed in \nthe appropriate ratio and subse quently mixed with the citrate gel and then subjected to the \nheat treatment at 3000 C. The soft ferrite with the re presentative composition of CoFe 2O4 has \nbeen prepared by the citrate gel method using C obalt Nitrate and Ferric Nitrate. Firstly, the \n3000 C heated Cobalt Ferrite was separated into tw o batches. One batch was heat treated at \n1000 0C for 3 hours where as the other batc h was kept as such. Then the 3000C heated Cobalt \nFerrite was mixed with the 3000 C heated Strontium Ferrite in the weight ratio of 1:8. The \nobtained mixture was furthe r heat treated at 10000 C for 3 hours. This sample is named as Set \nA. For the second sample, the 10000C heated Cobalt Ferrite wa s taken and mixed in the \nweight ratio of 1:8 with the 3000 C heated Strontium Ferrite. Th e resultant mixture was then \nsubjected to the heat  treatment at 10000C for 3 hours. This sample is termed as Set B. Powder \nX-ray diffraction (XRD) with a Bruker D8 Advance System having Cu K α source was used \nfor identifying the phase and the crystal struct ure of the nanocomposite. Henkel measurement \nwas performed in a Quantum Design SQUID to evaluate the quantity δM(H) in the following \nmanner, which can be expressed as  δM(H)= [J d(H)-J r(∞)+2J r(H)] / J r(∞). Here, the isothermal remanent magnetization (J r) curve can be measured experimentally by starting \nwith a fresh sample and consequent applicat ion and removal of the applied field in one \ndirection (IRM). Similarly, the dc  demagnetization (DCD) remanence (J d) can be measured \nby saturating the sample in one direction follo wed by subsequent applic ation and removal of \nthe applied field in the reve rse direction. The Quantum Desi gn PPMS was utilized for the \nmeasurements of FORC in addition to the standa rd major loops at the room temperature. A \nlarge number of (>102) partial hysteresis curve called First Order Reversal Curve (FORC) has \nbeen obtained using the below me ntioned procedure. Initially, the sample was subjected to \nthe positive saturation after which the field wa s reduced to a reversal field value of H a. From \nthis reversal field until the pos itive saturation, the magnetization has been measured which \ntraces out a single First Order Reversal Curve.  A suite of FORC has been measured using the \nmentioned procedure for a series of decreasing re versal field. It has to be noted that, equal \nfield spacing has been maintained throughout the measurement thus filling the interior of the \nmajor loop which act as an outer boundary for the measured FORCs. The magnetization on a \nFORC curve at an applied field H b  for a reversal field of H a is denoted by M(H a, H b) where \nHb ≥ H a. The FORC distribution obtained from  consecutive measurements point on \nsuccessive reversal curve can be define d as the mixed second order derivative17, 39, 40 given \nby, \n    ()( )2, 1,2ab\nab\nabMHHHHHHρ∂=−∂∂   ( 1 )  \nwhere baHH> . The FORC distribution and related diagram has been calculated using \nFORCinel which use locally-weighted regression smoothing algorithm (LOESS)41 for the \ncalculation. Usually it is convenient to  define a new set of co-ordinates ( ),ucHH instead \nof( ),abHH  [( ( )2 , ( )2 , )ua b cb aHH H HH H=+ =− ] for the representation of the FORC \ndiagram thus rotating the FORC diagram by 45 ° from ( ),abHH  plane to ( ),ucHH  plane40. \nWe have used both the coordinate system fo r the discussion of the results. In this \nmeasurement both the composites were initially subjected to the maximum field of 50000 Oe \nwhich is assumed to be the ground state for both th e samples, thus neglecting the effect of the \nmetastable domain walls. Afterwards we have varied the reversal fi eld from 2300 Oe to -\n7800 Oe with the field spacing of 100 Oe in th e previously mentioned manner. Thus the \nFORC distribution can be visualized in a top do wn fashion and from left to right for a given \nreversal field.  In order to quantify the differe nce in the interaction and reversal mechanism in the samples of Set A and Set B, a statistical an alysis has been carried out for the coercivity \nand interaction distribution prof ile. The details of the findings are discussed later in this \narticle.  \nIII. Results and Discussion: \nFigure 1 shows the X ray diffraction pattern for the Set A and Set B. It is clearly evident from \nthe XRD pattern that the characteristic peaks of  hard Strontium Ferrite (*) and soft Cobalt \nFerrite (+) is present in both the Set A and B. No extra peak within the resolution of the XRD \ntechnique is detected in both the XRD patterns although  the samples have undergone \ndifferent processing prior to  the heat treatment at 10000C.  \n25 30 35 40 45 50 55 60 65Set A\n*\n******\n**\n*++\n+++++\n*\n* peaks corresponding to SrFe12O19 \n+ peaks corresponding to CoFe2O4Set BIntensity in arb. unit*** *** *****++\n++\n++\n2θ+\n\nFigure 1:  X-ray diffraction pattern for Set A and Set B. The symbol (+) and (*) represents \nthe soft Cobalt Ferrite as well as the hard Strontium Ferrite. \nFrom the XRD pattern of the composites, it is observed that there is no change in the peak \nposition for the composite Set A and Set B. The br oadening and the change in the intensity of \nthe peaks between the two samples is the result of the difference in the particle size for the \ncomposites Set A and Set B. Using the Scherrer formulae42, the average particle size \ncorresponding to the Strontium Ferrite and Coba lt Ferrite present in Set A and Set B, has \nbeen calculated. It has been found that in bot h Set A and Set B, the average particle size \ncorresponding to the hard Strontiu m Ferrite is >50 nm. The simila rity in the average particle \nsize for Strontium Ferrite corresponds to the fact that in both the Sets, the Strontium Ferrite particles has undergone similar processing conditi on. But the average particle size for the \nCobalt Ferrite in both the Set A and Set B has been calculated as < 50 nm and > 70 nm \nrespectively. This is in accordance with the fact  that in Set A, as prepared Cobalt Ferrite were \nmixed with the as prepared Stront ium Ferrite where as in Set B 10000C sintered Cobalt \nFerrite were mixed with the as prepared Stron tium Ferrite and subseque ntly heat treated at \n10000C for both the mixtures. This result is  corroborated with the Scanning Electron \nMicroscopy images. This confirms the existenc e of the two independent major phases in the \ncomposite, without any chemical reaction. \nFigure 2 shows the magnetic hysteresis loop fo r both the Set A and Set B. The inset shows \nthe enlarged view of the magnetic hysteresis loop at low field.  \n-60000 -40000 -20000 0 20000 40000 60000-80-60-40-20020406080\n-6000 -4000 -2000 0 2000 4000 6000-80-60-40-20020406080M (emu/gm)\nH (Oe)Set A\nSet BM (emu/gm)\nH (Oe) Set A\n Set B\n\nFigure 2 : Magnetization vs. Applied Magnetic Field for the nanocomposites Set A and Set B. \nInset shows the zoomed view of th e magnetization loop for both the sets. \nFrom the inset of the figure 2, it is seen that the coercivity and remanence for both Set A and \nSet B are 1850 Oe, 50% and 1150 Oe and 39% respect ively. It is observed that in the case of \nthe nanocomposite Set A, though crystallographi cally it showed two phase behaviour but \nmagnetically it gives a good single phase behaviour. This suggests that the magnetic hard and \nsoft phases are well exchange coupled to each other which will be demonstrated later in this \narticle. But for Set B, the magnetic loop show s a two step hysteresis loop. This corresponds \nto the fact  that magnetic reversal consist of  two stage processes i.e.  individual switching of \nthe soft and hard phases , suggesting the absenc e of the exchange coupling between the hard and soft phase. In fact, the magnetic property of the two phase nanocomposite magnet \ndepends on the size of the grains, their distribution and their shape9. In addition to this, the \nexchange as well as the dipolar  interaction plays a major role  for the determination of the \nmagnetic property.  \nAs the composite is a mixture of  the soft and hard phases, three types of magnetic interaction \nbetween the soft and hard grains can be considered. The major one is the exchange \ninteraction between the soft and hard phase wher e as the others two are between the soft and \nsoft phases and between th e hard and hard phases wh ich are dipolar in nature9. It has to be \nnoted that, the magnetocrystalline energy and the respective anisotropy direction of the hard \nand soft phases determine the extent of the exchange interact ion in the isotropic \nnanocomposite. When an external magnetic field is applied, then it tries to align all the domains in its own direction to make it more energetically favourable. Thus there will be a \ncompetition between the magnetocrystalline en ergy, the exchange interaction and the \ninteraction between the applied field and the magnetic moments of the nanocomposite. Since \nthe soft phase is having less magnetocrystallin e anisotropy energy compared to that of the \nhard phase, it can be easily aligned in the direction of the applied field. But in the nanocomposite, if both the phases are sufficien tly exchange coupled , then the magnetic \nmoment of the hard grains will try to preven t it. So the relative strength of the exchange \ninteraction between the soft and hard phases acts as a tuning factor for determining the \nmagnetic property of the nanocompo site. If one considers dipolar  interaction as well, then \nalong with the hard and soft exchange interaction, the co mpeting dipolar interaction also \ndecides the magnetization in the soft grains. So , the relative importance of the exchange and \ndipolar interaction in the composite becomes necessary for better understanding of the system \nand thus the same can be understood if one obtains the Henkel plot. Figure 3 shows the \nHenkel plot for the Set A and Set B. The positive value of the δM(H), for Set A in the figure \n3 corresponds to the fact that the exchange in teraction between the so ft and hard phases is \ndominant\n20 in the nanocomposite. Whereas there is a crossover from the negative to positive \nvalue of the δM(H) for Set B which suggests that unt il a field range ~1200 Oe, the dipolar \ninteraction is more pronounced. This also suppor ts the fact that the remanence in Set A is \nhigher than the remanence in Set B. Generally in the Henkel plot, the value of the applied reversal field at which the δM(H) shows the maximum value is cl ose to the coercive field  of \nthe system\n43. From the figure 3, the value of the reversal field for which δM(H) value \nbecomes maximum, has been found as ~ 2500 Oe and 3000 Oe for Set A and Set B respectively. The deviation of the reversal field values from  the respective coercive field \nvalues for Set A and Set B could be the mani festation of the magnetically mixed phase.  \n0 10000 20000 30000 40000 50000-0.3-0.2-0.10.00.10.20.30.40.5\nApplied field in Oeδm Set A\n Set B\n\nFigure 3 : Variation of the δm vs. Applied Field for the nanocomposite Set A and Set B. \nIn addition there arise some limitation of Henkel plot analysis which is based on the \nassumption that 1. All the switching is a resu lt of coherent rotation and 2. Domain wall does \nnot exist in the thermally demagnetized state44. This assumption may not be completely valid \nfor the systems we are investigating as the hard phase could be multi-domain in nature in both the Set A and Set B. It has also been sugg ested in the literature that the Henkel plot \ncannot differentiate between the mean interactio n field and local field variance. According to \nBertotti and Brasso et al \n45, the variance in  the local in teraction field with the mean \ninteraction field can lead to positive as well as the negative  δM(H) curve depending on the \nrelative weight of the variance and mean interaction field. T hus a positive mean interaction \nfield does not always ensure the positive δM(H) curve if one considers the local variance as \nwell. Thus the Henkel plot measurement is a qua litative tool for the investigation of the \nexchange interaction present in our system. To overcome this difficulty as well as to study the \ndifferent magnetization processes occurring during the magnetization reversal, we have \nobtained the FORC diagram for the nanocomposite Set A and Set B.  \nFigure 4(a) and (c) shows the experimentally obta ined first order reversal curve for the Set A \nand Set B where the major hysteresis loop delin eates the outer boundary for the FORC curve. It is evident from the equa tion (1), that FORC distribu tion becomes non zero when the \nmagnetization reversal invol ves irreversible switching39. Similarly the reversible processes \noccurring during magnetization reversal wi ll correspond to the zero FORC distribution46. In \ncase of reversible magnetic switching, ther e will be no change in the magnetization value \nM(H a, H b) while going from one reversal point to another consid ering reversible \nmagnetization switching. Thus, the magnetization will solely depend on the applied field H b, \nmaking the FORC distribution zero.  The inset of  the figure 4(a) and (c ) shows five different \npoint of the reversal in the major hystere sis loop which will be discussed in the FORC \ncontext. We will be discussing the respective stages of the reversal for the nanocomposite Set A and Set B separately. For Set A, the reversal  is initiated by the formation of the domain \nwall and the successive movements of them in the soft phase\n4. This is reflected in the point 1 \n(line 1, around +1000 Oe ) of the major loop (inset 4(a) ). Here, we are assuming that soft and \nhard phases are exchange coupled thr ough their phase boundaries. The corresponding \nhorizontal line scan at that H a along H b, representing FORC distribution ρ has been shown in \nthe figure 4(b). The zero value of ρ corresponds to the fact that magnetization change is \nreversible in nature. This has also been observed by the closeness and overlap of the \nsuccessive reversal curves. After the start of the domain wall movement with decreasing \nreversal field, the FORC di stribution becoming non zero near  to the zero reverse field \nindicating the onset of the irre versible processes. The irre versible process peaks around a \nreversal field value of -370 Oe (point 2 in the in set of the figure 4(a) and line 2 at figure 4(b)) \nand the same can be observed in the major loop with a decrease in the magnetization. This irreversible process can also be visualized from the uneven separation of the successive \nFORCs\n27. This is happening as the do mains present in the soft pha se have suddenly started to \ninvade the hard phases leading to  the irreversible switching of both the hard and soft phases. \nThis corresponds to the fact th at both the soft and hard phas es are exchange coupled with \neach other. This field corresponds to the nucleati on field of the composite. This is similar to \nthe switching behaviour of FeN i/FePt exchange spring bilayer as described by Davies et al26. \nThe FORC distribution is appa rently without any new feat ure apart from existing non zero \ndistribution between line s 2 and 3 (-370 Oe > H a >-1800 Oe ) as evident in the figure 4(b). It \nhas been found that between line 3 and line 4( point around -3700 Oe) in the figure 4(b), the \nFORC distribution shows number of negative peaks in a positive background. In this reversal \nfield range, the slope of th e reversal curve initially stay constant but around H b>0 Oe shows \nan abrupt increase thus resulting in the pos itive background-negative  peak in the FORC \ndistribution27, 47.  -50000 -25000 0 25000 50000-80-60-40-20020406080\n-8000 -4000 0 4000 8000-60-40-200204060\n5432M (emu/gm)\nH (Oe)Set A1M (emu/gm)\nH (Oe)Set A\n\nFigure 4(a):  Magnetization loop for the nanocompos ite Set A delineating FORC curves. \nInset shows the zoomed view of the magneti zation loop for the Set A showing 5 different \nreversal points. \n \nFigure 4(b):  FORC distributions for the nanocomposite Set A in the H a-Hb co-ordinate. \nThe occurrence of the negative-pos itive pairing is a result of the decrease and increase of the \nreversal field susceptibility as the domain stat e responds differently with the applied field. \nThis is the onset of the domain annihilation  as the nanocomposite approaches negative \nsaturation. Until the point -6200 Oe, the FORC distribution shows the presence of the \nirreversible magnetization. If one considers that the nanocomposite has reached its negative \nsaturation then the irreversible switching will be over and the FORC di stribution will be zero and nearly overlap the region Ha > -370 Oe. Since the applicati on of the reversal field is \nconstrained by the experimental limitation (lack of higher field to saturate the magnetization) \nwe could only achieve the state where the revers al field corresponds to the approach to the \nnegative saturation of the composite Set A. So  for the field range Ha< -6200 Oe, we could \nobserve a reversible magnetizati on change as well as discrete positive negative pair of the \nFORC distribution. \n-50000 -25000 0 25000 50000-100-80-60-40-20020406080100\n-8000 -4000 0 4000 8000-60-40-200204060\n54321M (emu/gm)\nH (Oe)Set BM (emu/gm)\nH (Oe)Set B\n\nFigure 4(c): Magnetization loop for the nanocomposite Set B delineating FORC curves. Inset \nshows the zoomed view of the magnetization lo op for the Set A showing 5 different reversal \npoints. \n \nFigure 4(d):  FORC distributions for the nanocomposite Set B in the H a-Hb co-ordinate. Figure 4(d) shows the FORC di stribution of Set B in (H a, H b) co-ordinate. In Set B, prior to \nthe Line 1 (point +1000 Oe in the inset of the figure 4(c) ) in the figure 4(d), a very low value \nof FORC distribution corresponds  to the reversible switching of the moment is seen. The \nonset of irreversible switching is  demonstrated around the line 1. (H a < +1000 Oe). This \ncorresponds to the individual switching of th e soft phase present in the system. This \nirreversible switching shoots up between the line 1 and line 2 (point 2, -1050 Oe), in the \nFORC distribution as evident from the figure 4(d). The first peak corresponding to the \nirreversible switching in the nanocomposite Set B is a result of the individual switching of the soft phase (around ~-300 Oe) and correspondi ngly the second peak is because of the \nswitching of hard phase (point 2). This irreversibi lity is also evident from  the fact that the gap \nof FORC curve widens up during this reverse field range. The line scan around -300 Oe and -\n1050 Oe reveals that, the strength of irreversibilit y is more in case of -1050 Oe reversal field \ncompared to -300 Oe. This corresponds to the f act that both the soft and hard phase are not \nsufficiently exchange coupled in the nanocom posite Set B and does individual switching as \ncompared to Set A which gives rise to a single  peak of irreversibil ity revealing coherent \nrotation of the soft and hard pha ses.  Generally domain wall movement require less energy \ncompared to the coherent rotation of the magne tization. So as the field is reversed after \nsaturation without changing the sign of the applie d field, the domain wall starts moving from \none energy minima to the other. In this process if the system reaches nucleation and \nconsequently the applied field is ramped b ack, the system will not  achieve the initial \ncondition thus giving rise to an irreversible magn etization.  Thus, it can be concluded that the  \ndomain nucleation is happening at the field ra nge of < +1000 Oe. Thus with the decreasing \nreversal field, the composite mostly composed  of “down” domains compared to the “up” \ndomains thus resulting an abrupt change in  magnetization around 0 Oe . This irreversible \nprocess of converting “up” domains into “dow n” domain configuration continues until a \nreversal field value of the ~ -1800 Oe as evid ent from the FORC distribution shown in figure \n4(d). (between line 2 and 3). This also results in the two stage hystere sis loop. Between line 3 \nand line 4 (point -5050 Oe), the FORC distributi on shows a negligible i rreversible processes \nbut a non zero tails of the FORC distribution aris es when the reversible field corresponds to \nH\na > -5050 Oe. The reappearance of the significan t irreversible processes is because of the \nonset of the annihilation of the domains which continues until negative saturation. This \nfeature is evident unt il the line 5 (point 5 in the Major loop, H a < -6200 Oe.). Afterwards the \nnanocomposite shows a reversible behaviour for th e rest of the reversal  field value until -\n7800 Oe.  So, it has been found that in case of Set B, tw o peaks corresponding to the irreversible change in magnetizat ion occurs compared to the singl e peak of the irreversibility \nobserved in Set A.  In order to discuss the distribution of the magne tic characteristics like interaction mechanism, \ncoercivity distribution in the nanocomposite of Set A and Set B,  we have obtained the FORC \ndistribution as a contour plot in (H\nu, H c) coordinate. Figure 5(a) and 6(a) shows the FORC \ndistribution for Set A and Set B in (H u, H c) space with the correspondin g colour scale kept at \nthe side by side as a measur e of the FORC distribution.  \n \nFigure 5(a):  FORC distributions for the nanocomposite Set A in the H u- H c coordinate. \n0 500 1000 1500 2000 2500 3000 35000.00000.00050.00100.00150.00200.00250.00300.0035Arb Weight\nHc (Oe)Set A\n\nFigure 5(b):  Coercivity profile for Set A. In both the cases, the maximum weight of the ρ is indicated by the red colour where as the \nminimum is shown in the blue co lour. Generally, the projection of ρ onto the H c axes, can be \ncharacterized as coercivity distribution prof ile. This in turn de pends on the respective \nanisotropy distribution, size variation, defect as well as the homogeneity in the \nnanocomposite23.  \n \nFigure 6(a):  FORC distributions for the nanocomposite Set B in the H u- H c coordinate. \n0 500 1000 1500 2000 2500 3000 35000.00000.00050.00100.00150.00200.0025Arb Weight\nHc (Oe) Coercivity distribution at negative Hu\n Coercivity distribution at positive Hu\nSet B\n\nFigure 6(b):  Coercivity profile for Set B. \nFigure 5(b) and 6(b) correspond to the coercive field distribution profile for Set A and Set B \nwhich was obtained at the field values indicated by the black li nes through the maxima of the FORC distribution.  Sim ilarly the projection of ρ on to H u axis at a particular coercive field \nvalue can be visualized as the distribution of the interaction field strength. In the context of \nthe investigated nanocomposite of Set A and Set B, this interaction field profile is a characteristic of the strength of  the exchange coupling between soft and hard phases as well \nas the dipolar interaction present be tween soft-soft and hard- hard phases\n23. The figure 7 \nshows the respective variation of the interaction field profile for Set A and Set B. \n-3000 -2000 -1000 0 1000 2000 30000.0000.0010.0020.003\n<Hu2> :-500 Oe\nFWHM of <Hu2>: 569 Oe Set A\n Set Bρ (Arb. Weight )\nHu(Oe)Set A , <Hu1> :-110 Oe\nFWHM of <Hu1>: 468 Oe\nSet B, <Hu1> :+270 Oe\nFWHM of <Hu1>: 900 Oe\n\nFigure 7:  Interaction field profile for Set A and Set B. The blue lin e corresponds to the \nGaussian fitting in both the cases. The fitting parameters are describes inside the graph. \n It has been found from the FORC distribution for Set A and Set B in figure 5(a) and 6(a), \nthat the contour diverges from the H c= 0 axis and are much more pronounced at the lower \nfield value of H c. This kind of contour patterning suggests that the investigated \nnanocomposite is multi-domain in nature40. According to Robert et al40, the origin for the \ndiverging contour pattern can  be related to the domain wall pinning and domain wall \nnucleation and annihilation. For the nanoc omposite Set A, the maximum value of ρ is 3.1 X \n10-3where as for Set B it is 2.2 X 10-3\n. Generally the small concentration of the ferromagnetic \nphases present in the system will lead to the smaller value of ρ46. Thus the higher value of the \nρ in Set A compared to Set B indicates the presence of lesser amount of ferromagnetic \ninteraction in Set B compared to Set A thus  giving rises to lesse r irreversibility. To \nunderstand the variance of coer cive and interaction field dist ribution in Set A and Set B, a \nstatistical analysis has been performed48. The bias or interaction field distribution which was obtained at the field values indicated by the blue lines th rough the maxima of the FORC \ndistribution in figure 5(a)  and 6(a) for Set A and Set B has been fitted considering Gaussian \ndistribution. The fitting has been shown in the figur e 7. It has to be noted that for Set B since \nthe distribution of ρ shows two peaks, we have consid ered double peak Gaussian for fitting \nthe Set B distribution. It has b een found from the figure 5(b) a nd 6(b) respectively, that the \naverage coercivity for Set B is ~527 Oe while th e Set A shows average coercive field as ~378 \nOe. From the figure 5(a) , It has also been found that the maximum FO RC distribution in case \nof Set A is centred around H u= -110 Oe and is tilted towards negative H u where as for Set B \nthe variation of ρ shows two maxima as evident in th e figure 6(a). The first maxima lies \naround H u = 270 Oe while the second maxi ma is concentrated at H u = -500 Oe. The pattern \nfor Set A is in well agreement with the FORC distribution as previously showed for \npolycrystalline single phas e LSCO with doping x=0.3023 indicating the presence of the long \nrange ferromagnetic interaction , reduction in  pinning and multi-domain type reversal. \nAccording to C R Pike et al17, theoretically when an mean interacting field was introduced in \nthe assembly of model non interacting singl e domain particles, the peak of the FORC \ndistribution generally displaces off the H u=0 axis depending on the nature of the mean field \ninteraction. If the interaction is dipolar in nature, then the distri bution goes upward off the \nHu= 0 axis thus giving a maxima centred at positive H u. But the exchange interaction causes a \nnegative shift of the FORC distribution which causes the FORC distribution peaks at negative \nHu. So we can conclude that in Set A the mean in teracting field is excha nge in nature but in \nSet B both dipolar as well as the exchange type of interaction is present. This is in well agreement with the Henkel plot  showed in figure 4. Howe ver we have also found that, \nnegative shift of the FORC distribution is more pronounced in Set B compared to Set A. This \nwill be explained in conjunction with the revers ible magnetization present in the system. It \nhas also been found from the figure 7, that the spread in the interactio n field distribution for \nSet A is less compared to the spread in both th e peaks for Set B. Generally the extent of the \nspread can be used as a measure of the exte nt of the domain wall pinning, nucleation and \nannihilation present\n40 in the system. Thus for Set A,  the domain wall pinning is less \npronounced compared to Set B. This corroborates  well with the higher average coercive field \nvalue for Set B compared to Set A. The origin  of these pinning centr es could be the grain \nboundary13 present between soft and hard phases.  The extent of the FORC distribution ρ can \nbe related to the ferromagnetic component (strength of the interaction) present in the system.  Thus one can consider a lesser magnitude of the ρ for a system which contains weak \nferromagnetic component. Generally by integrating ρ(H\nu, H c) over the (H u, H c) coordinate, one can visualize the part of the system which has taken part in the irreversible switching. \nThus irreversible magnetization M irr can be formulated \nas ,,irr u c u c u c u cM H H dH dH H H H H = ρ () ≈ ρ () Δ Δ ∑ ∫. Here ucH H Δ, Δ corresponds to the \nrelative field spacing of the H u, H c coordinate. We have obtained the fraction of the \nirreversible magnetization (M irr/Ms) after proper scaling of the re versal curve data for Set A \nand Set B for significant comparison. The fraction of the irreversible magnetization for Set A and Set B has been obtained as 69% and 55% resp ectively.  The greater value of the quantity \n(M\nirr/Ms) for Set A compared to the Set B can be correlated to the dominant exchange \ncoupling between the soft and hard phase in Se t A in comparison to the nanocomposite Set B. \nThis information corroborate well with the Henk el plot depicted in th e figure 4 where for Set \nA the magnitude of the δM(H) lies above Set B. This quantit ative finding is also in agreement \nwith the previous depiction of FORC distribution in (H a, Hb) space. It has to be noted that the \ncalculated M irr cannot be accounted for the entire saturation magnetization of the \nnanocomposite Set A and Set B. This deviation is because of the fact that we did not consider \nthe contribution from the reversible  magnetization during our calculation39, 47.   \nIn order to understand the re versible magnetization contribu tion during the magnetization \nreversal process, we have obtained the FO RC distribution for both Set A and Set B at H c= 0 \nOe which have contribution from the pure reve rsal process present in the system. This \ndistribution is termed as “reversible ridge”39 and is shown in the figure 8.  \n-8000 -6000 -4000 -2000 0 2000 40000.00.20.40.60.81.0 Set A\n Set Bρ (emu/gm*Oe2)\nHu (Oe)Hc =  0 Oe\n\nFigure 8:  Reversible ridge for the nanocomposites Set A and Set B. It has been found that for both the Set A and Se t B, the reversible ridge as a function of H u is \nnot symmetric about H u. According to C R Pike39, if the reversible magnetization is not \ncoupled to the irreversible pa rt, then the reversible ridge should be symmetric about H u. Thus \nthe asymmetry of the reversible ridge for Set A and Set B corresponds to the fact that both the \nirreversible and reversible magnetization is coup led with each other. This can be explained by \nconsidering the curvi linear hysteron models39 as described in literature. According to this \ntheoretical prediction, the upper and lower branch  susceptibility of the curvilinear hysteron is \ndifferent from each other thus resulting in an asymmetry of reversible ridge about H u axis. \nFigure 8 shows that the peak of the “reversibl e ridge” for Set A and Set B lay at -1700 Oe and \n-900 Oe respectively. This feat ure is indeed interesting as the interaction field for the \nreversible magnetization is greater in case for Set A than in Set B. Thus if we consider the coercivity in a system as a combination of both the interaction field resulting from reversible \nas well as irreversible magne tization processes without the presence of the domain wall \npinning, in-homogeneity,  then the calculated coercivity for Set A and Set B lies in the range \n1810 Oe(1700+110) and 1400 Oe (500+900). It has b een found that the cal culated coercivity \n1810 Oe for Set A agrees well with coercivity  value of 1850 Oe obtained from the major \nhysteresis loop. But for Set B, the calculated coercivity 1400 Oe is more compared to the obtained coercive field of 1150 Oe. This indicates the presence of domain wall pinning due to \nthe grain boundary and inhomogeneity  in Set B compared to Set A. This is in well agreement \nwith the interaction and coercive  field profile distribution obta ined from reversal curves. A \ncareful examination of the reversible ridge in figure 8 reveals that  the ridge shows two \nmaxima for Set B thus correlating two stage reversals observed in Set B form the major \nhysteresis loop measurement. So the contribution of the reversible magnetization towards the \nmagnetization switching process in Set A is more pronounced th an in Set B thus indicating \noccurrence of the exchange spring behaviour in Set A relative to the non exchange spring \nbehaviour in Set B. \nIV. Conclusion: \n In conclusion, we have successfully tailor ed the magnetization behaviour of the Cobalt \nFerrite-Strontium Ferrite nanocomposite from non exchange spring behaviour to exchange \nspring, by tuning the size of the soft Coba lt Ferrite. We have achieved single magnetic \nhysteresis loop behaviour for Se t A thus confirming the excha nge spring behaviour whereas \nthe double step hysteresis behaviour for Set B corresponds to the non exchange spring \nbehaviour. The relative strength of the interaction governing th e magnetization process in the composite Set A and Set B has been studied us ing Henkel plot and First Order Reversal \nCurve method. The FORC method has been utili zed to understand the magnetization reversal \nbehaviour as well as the extent of the irrevers ible magnetization present in both Set A and Set \nB. It has been concluded that the magnetizatio n process is primarily controlled by the domain \nwall movement in the composites. Us ing the FORC distribution in the (H a, H b) co-ordinate, \nwe could trace out the onset of the nucleation fi eld, invasion of the domain wall from the soft \nto the hard phase, domain wall annihilation and the presence of the reversible magnetization \nwith the applied reversal field for both the composite Set A and Set B. We have obtained \nsingle FORC distribution maxima fo r Set A at a negative interaction field axis where as Set B \ngives rise to two consecutive maxima, one at positive and another at negative interaction field. This result is consistent with the fi ndings from the obtained Henkel measurement for \nSet A and Set B. The projection of ρ on H\nu and H c axis clearly shows the presence of higher \ndomain wall pinning because of the grain bounda ry in Set B compared to the Set A.  By \nprojecting the FORC distribution over H u and H c axis we quantitatively calculated the \nirreversible magnetization taking part in the magnetization reversal. The pronounced \nirreversible magnetization in Set A compared  to Set B indicates that the ferromagnetic \ninteraction is more prominent in Set A relative  to Set B. By analysing the FORC distribution \nat H c=0 Oe which is asymmetric about H u for both Set A and Set B, we could confirm that \nreversible and irreversible magnetizations are coupled with each other in both the composites. \nBy taking into account of the interacti on field corresponding  to the maxima of ρ distribution \nin reversible as well as irreversible process fo r  Set A and Set B, we could calculate back the \ncoercivity obtained from major hysteresis loop. This indicates that reversible magnetization should also be taken into account while discussi ng the magnetization reversal process. It was \nconcluded that the extent of the reversible magnetization is more in Set A compared to Set B. Furthermore this result confirms that FORC met hod is an effective tool for the investigation \nof the interaction and magneti zation reversal processes in the exchange spring magnet. \n \nReferences: \n1G. Asti, M. Solzi, M. Ghidini, and F. M. Neri, Phys. Rev. B 69, 174401 (2004). \n2S. Erokhin, D. Berkov, N. Gorn, and A. Michels, Phys. Rev. B 85, 024410 (2012). \n3V. M. Uzdin, A. Vega, A. Khrenov, W. Keune, V. E. Kuncser, J. S. Jiang, and S. D. Bader, \nPhys. Rev. B 85, 024409 (2012). \n4E. F. Kneller and R. Hawig, Magnetics, IEEE Trans. Magn. 27, 3588 (1991). 5J. E. Shield, J. Zhou, S. Aich, V. K. Ravindran, R. Skomski, and D. J. Sellmyer,  \nJ. Appl. Phys. 99, 08B508 (2006). \n6J. Zhou, R. Skomski, Y. Liu, Y. C. Sui, W. Liu, and D. J. Sellmyer, J. Appl. Phys. 97, \n10K304 (2005). \n7D. Suess, T. Schrefl, S. Fahler, M. Kirschner,  G. Hrkac, F. Dorfbauer, and J. Fidler, Appl. \nPhys. Lett. 87, 012504 (2005). \n8R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993). \n9T. Schrefl, J. Fidler, and H. Kronmüller, Phys. Rev. B 49, 6100 (1994). \n10W. Rodewald, B. Wall, M. Katter, and K. Uestuener, Magnetics,  IEEE Trans. Magn. 38, \n2955 (2002). \n11J. P. Liu, Y. Liu, R. Skomski, and D. J. Sellmyer, Magnetics, IEEE Trans. Magn. 35, 3241 \n(1999). \n12E. E. Fullerton, J. S. Jiang, and S. D. Bader, J. Magn. Magn. Mater. 200, 392 (1999). \n13D. Roy, C. Shivakumara, and P. S. A. Kumar, J. Appl. Phys. 109, 07A761 (2011). \n14D. Roy, C. Shivakumara, and P. S. Anil Kumar, J. Magn. Magn. Mater. 321, L11 (2009). \n15D. Roy and P. S. A. Kumar, J. Appl. Phys. 106, 073902 (2009). \n16H. G. Katzgraber, F. Pázmándi, C.  R. Pike, K. Liu, R. T. Scale ttar, K. L. Verosub, and G. T. \nZimányi, Phys. Rev. Lett. 89, 257202 (2002). \n17C. R. Pike, A. P. Roberts, and K. L. Verosub, J. Appl. Phys. 85, 6660 (1999). \n18A. Stancu, C. Pike, L. Stoleriu, P. Post olache, and D. Cimpoesu, J. Appl. Phys. 93,  \n6620 (2003). \n19A. Stancu, D. Ricinschi, L. Mitoseriu, P. Postolache, and M. Okuya ma, Appl. Phys. Lett. \n83, 3767 (2003). \n20O.Henkel, Phys. Status Solidi 7, 319 (1964). \n21D. Roy and P. S. A. Kumar, J. Appl. Phys. 111, 07A315 (2012). \n22I. Mayergoyz, Magnetics, IEEE Trans. Magn. 22, 603 (1986). \n23J. E. Davies, J. Wu, C. Leight on, and K. Liu, Phys. Rev. B 72, 134419 (2005). \n24J. E. Davies, O. Hellwig, E. E. Fullerton, and K. Liu, Phys. Rev. B 77, 014421 (2008). \n25V. Bonanni, Y. Fang, R. K. Dumas, C. Zha, S. Bonetti, J. Nogues, and J. Akerman, Appl. \nPhys. Lett. 97, 202501 (2010). \n26J. E. Davies, O. Hellwig, E. E. Fullerton, J. S. Jiang, S. D. Bader, G. T. Zimanyi, and K. \nLiu, Appl. Phys. Lett. 86, 262503 (2005). \n27J. E. Davies, O. Hellwig, E. E. Fullerton, G. Denbeaux, J. B. Kortright, and K. Liu, Phys. \nRev. B 70, 224434 (2004). 28J. Olamit, K. Liu, Z.-P. Li, and I. K. Schuller, Appl. Phys. Lett. 90, 032510 (2007). \n29J. E. Davies, O. Hellwig, E. E. Fullerton, M.  Winklhofer, R. D. Shull, and K. Liu, Appl. \nPhys. Lett. 95, 022505 (2009). \n30A. Rotaru, J.-H. Lim, D. Lenormand, A. Diaconu,  J. B. Wiley, P. Postolache, A. Stancu, \nand L. Spinu, Phys. Rev. B 84, 134431 (2011). \n31L. G. Vivas, M. Vazquez, J. Escrig, S. Allende, D. Altbir, D. C. Leitao, and J. P. Araujo, \nPhys. Rev. B 85, 035439 (2012). \n32J. Wong, P. Greene, R. K. Dumas, and K. Liu, Appl. Phys. Lett. 94, 032504 (2009). \n33J. M. Pomeroy and J. C. Read, Appl. Phys. Lett. 99, 092505 (2011). \n34J. M. Pomeroy, T. C. White, H. Grube, J. C.  Read, and J. E. Davi es, Appl. Phys. Lett. 95, \n022514 (2009). \n35L. Stoleriu, A. Stancu, L. Mitoseriu, D. Piazza, and C. Galassi, Phys. Rev. B 74, 174107 \n(2006). \n36R. K. Dumas, C.-P. Li, I. V. Roshchin, I. K. Schuller, and K. Liu, Phys. Rev. B 75, 134405 \n(2007). \n37R. K. Dumas, T. Gredig, C.-P. Li, I. K. Schuller, and K. Liu, Phys. Rev. B 80, 014416 \n(2009). \n38T. Schrefl, T. Shoji, M. Winklhofer, H. Oeze lt, M. Yano, and G. Zimanyi, J. Appl. Phys. \n111, 07A728 (2012). \n39C. R. Pike, Phys. Rev. B 68, 104424 (2003). \n40A. P. Roberts, C. R. Pike, and K. L. Verosub, J. Geophys. Res. 105, 28461 (2000). \n41R. J. Harrison and J. M. Feinberg, Geochem. Geophys. Geosyst. 9, Q05016 (2008). \n42B. D. Cullity, Elements of x-ray diffraction  (Addison-Wesley Pub. Co, 1956). \n43R. W. Gao, D. H. Zhang, W. Li, X. M. Li , and J. C. Zhang, J. Magn. Magn. Mater. 208, 239 \n(2000). \n44F. Vajda, E. Della Torre, and R.  D. McMichael, J. Appl. Phys. 75, 5689 (1994). \n45G. Bertotti and V. Basso, J. Appl. Phys. 73, 5827 (1993). \n46I. Mayergoyz, Mathematical Models of Hyst eresis and their Applications  (Elsevier Science \nInc., New York, 2003). \n47C. R. Pike, C. A. Ross, R. T. Scal ettar, and G. Zimanyi, Phys. Rev. B 71, 134407 (2005). \n48R. Tanasa, C. Enachescu, A. Stancu, J. Linares, E. Codjovi, F. Varret, and J. Haasnoot, \nPhys. Rev. B 71, 014431 (2005). \n List of Figures: \nFigure 1:  X-ray diffraction pattern for Set A and Set B. The symbol (+) and (*) represents \nthe soft Cobalt Ferrite as well as the hard Strontium Ferrite. \nFigure 2 : Magnetization vs. Applied Magnetic Field for the nanocomposites Set A and Set B. \nInset shows the zoomed view of th e magnetization loop for both the sets. \nFigure 3 : Variation of the δm vs. Applied Field for the nanocomposite Set A and Set B. \nFigure 4(a):  Magnetization loop for the nanocompos ite Set A delineating FORC curves. \nInset shows the zoomed view of the magneti zation loop for the Set A showing 5 different \nreversal points. \nFigure 4(b):  FORC distributions for the nanocomposite Set A in the H a-Hb co-ordinate. \nFigure 4(c): Magnetization loop for the nanocomposite Set B delineating FORC curves. Inset \nshows the zoomed view of the magnetization lo op for the Set A showing 5 different reversal \npoints. \nFigure 4(d):  FORC distributions for the nanocomposite Set B in the H a-Hb co-ordinate. \nFigure 5(a):  FORC distributions for the nanocomposite Set A in the H u- H c coordinate. \nFigure 5(b):  Coercivity profile for Set A. \nFigure 6(a):  FORC distributions for the nanocomposite Set B in the H u- H c coordinate. \nFigure 6(b):  Coercivity profile for Set B. \nFigure 7:  Interaction field profile for Set A and Set B. The blue lin e corresponds to the \nGaussian fitting in both the cases. The fitting parameters are describes inside the graph. \nFigure 8:  Reversible ridge for the nanocomposites Set A and Set B. \n  "    },    {        "title": "2303.08800v1.Electromagnetic_Waves_Propagation_along_Tangentially_Magnetised_Bihyrotropic_Layer__with_Example_of_Spin_Waves_in_Ferrite_Plate_.pdf",        "content": " \nElectromagnetic Waves Propagati on along Tangentially \nMagnetised Bihyrotropic Layer (with Example of Spin \nWaves in Ferrite Plate)  \n \nEdwin H. Lock  and Sergey V. Gerus  \n \n(Kotel’nikov Instutute of Radio Engineering and Electronics (Fryazino branch), \nRussian Acad emy of Sciences, Fryazino, Moscow region, Russia ) \n \nAnalytically, without magnetostatic approximation, the problem of electromagnetic wave \npropagation along arbitrary direction in a tangentially magnetized bihyrotropic layer has been \nsolved. It is found tha t one can bring the Maxwell equations for this problem to the fourth order \ndifferential equation  and the obtained  biquadratic characteristic equation determines two different \nwave numbers kx21 and kx22 describing the wave distribution over the layer’s thick ness. The \ndispersion equation describing wave propagation in the bihyrotropic layer was obtained  for the \ncase of real kx21 and kx22 values.  It is shown that in a ferrite plate, which is a special case of a \nbihyrotropic layer, three types of wave distributio n over the plate ’s thickness  can take place : \nsurface -surface ( when kx21 and kx22 are real numbers), volume -surface ( kx21 is imaginary and kx22 \nis real) and volume -volume distribution  (kx21 and kx22 are imaginary numbers). Characteristics  of \nthe surface spin w ave in ferrite plate are investigated. It is found that dependences of the wave \nnumbers kx21 and kx22 on the wave vector orientation are significantly different from the similar \nmagnetostatic dependence for a large part of the wave spectrum.   \n \n1. Introducti on  \nAs a result of dynamical development of magnonics in the last decade, there \nare a lot of new data about spin waves characteristics and physical effects that can \nbe realized by means of these waves  in structures based on ferrites and \nantiferromagnetics [1 - 10]. It is well known that spin waves (SW) with wave \nnumbers ~ 0 < k < 104 cm-1 are still usually described in magnetostatic \napproximation with assumption that spin wave number k >> k0  /c (here  is  \ncyclic frequency  of SW and c – light velocity ) and, therefore one can use the \nmagnetostatic equations to describe these waves, that is, to neglect terms containing \nmultipliers /c in Maxwell equations.  Such a way of SW description  has been \nproposed in [11], which is still the most cited theoretical work devoted to SW. Due \nto mathematical simplicity, the results obtained in [11] have been used for more than \nsixty years in calculations of SW characteristics and in the design of various spin \nelectronics devices [12 - 14]. SW are often named as magnetostatic waves (MSW) \nbecause of the use of magnetostatic approximation in their description [11].   \nAt the same time, approximately in 80's of the twentieth century, researchers \nof SW had questions, the answers to which could not be found within description of \nSW in magnetostatic approximation.  As a result, articles with studies of SW \npropertie s without magnetostatic approximation began to appear  [13, 15 - 28]. The \nchange of SW characteristics for small wave numbers k was studied  in some of these \npapers [15 - 23], including studies [18, 19, 22], where it was studied the mechanism \nof radiation arising from nonuniformly magnetized ferrite -dielectric structure during \npropagation of surface MSW  at k → k0. The influence of dielectric permittivity of \nthe medium surrounding ferrite layer on the SW dispersion dependence was \ninvestigated  in [20] . It was also shown [25], that calculation of SW’s  Poynting vector \nin magnetostatic approximation by the formula \nRe( * ) / 8i  PB  are not \ncorrect, therefore one should calculat e the Poynting vector and the power flux of \nSW from the known formula \n Re / 8cP EH *1, finding the electric microwave \nfield E from the first Maxwell equation2. Calculations of vector lines distribution \nfor microwave field of surface SW [26 - 28] allowed us to understand mechanism \nof the wave propagation.  In particular, it was found that vector lines of microwave \nmagnetic induction form two rows of vortices localized near opposite surfaces of \nferrite plate, and the vector lines of adjacent vortic es always direct oppositely. The \n                                                           \n1 In the mentioned formulas E and H are microwave electric and magnetic field vectors, B is \nmagnetic induction vector and Ψ –magnet ostat ic potential  of SW .  \n2 See the first equation in (4) below.   \nboundary between these rows of vortices is a plane (lying inside ferrite plate) on \nwhich the amplitude of microwave electric field of SW  is zero. Thus, surface SW \nmay be considered as magnetic induction vortices propagating  in time and space  \nalong ferrite plate in various ferrite structure s.  \nIt should be noted that in all of mentioned studies, performed without \nmagnetostatic approximation, the SW characteristics were investigated only for the \ncase whe re the vectors of group  and phase velocities of SW are collinear3 (i.e., when \nthe wave propagates perpendicular to the external magnetic field direction or along \nit). It is obvious that for further development of magnonics, it would be important \nto find an analytical solution of  the problem of spin wave propagation in an arbitrary \ndirection based on Maxwell's equations (without magnetostatic approximation ). The \nsolution of this problem would lead the description of SW to a qualitatively new \nlevel and would finally allow one not o nly to make accurate calculations of \ncharacteristics  for SW with a non -collinear orientation of the wave vector and group \nvelocity vector but also to calculate, for the first time, the Poynting vector, direction \nand density of energy flux and the structure  of magnetic and electric microwave \nfield vector lines for such waves. Moreover, the following consideration will show \nthat solution of this problem will result in the description of fundamentally new \nproperties of SW.  \n2. Problem statement.  \nIt will be sh own below that mathematics makes it possible to solve \nanalytically the system of Maxwell equations (without magnetostatic \napproximation) and find the dispersion equation for electromagnetic waves \npropagating in an arbitrary direction in tangentially magnet ized bihyrotropic layer \nof thickness s, (Fig. 1), which is characteri zed by dielectric and magnetic \npermeabilities described by second rank Hermite tensors  \n2\n and \n2\n \n                                                           \n3 The only exception are papers [16, 23], which describe SW propagation in an arbitrary direction; \nhowever, as will be shown below, the results pres ented in these papers are not correct.    \n20\n0\n00zzi\ni\n   \n\n,        (1) \n20\n0\n00zzig\nig\n   \n\n.        (2) \nNote that the mathematical description of this problem is rather cumbersome, so we \nwill be forced to skip the intermediate calculations below, and for a compact writing \nof obtained results we will introduce some notation s for the different intermediate \nquantities.   \n \nFig. 1 . Geometry of the problem: 1 and 3 - vacuum half -spaces, 2 - bihyrotropic  \nlayer (in particular case – ferrite plate) of thickness s.  \nSince the results obtained below may be useful for researchers of \nelectromagnetic waves in different media – gyrotropic layers of ferrite, \nantiferromagnetic or plasma (which are special cases of bihyrotropic media  and have \neither tensor \n2\n  or tensor \n2\n  corresponding to expres sions (1) and (2) ), all \nmathematical deductions  and formulas will be presented for the general case of wave \npropagation in bihyrotropic layer. At the same time, to avoid looking rather  abstract, \nthe obtained formulas will be used to calculate (as an exampl e) the characteristics \nof electromagnetic waves propagating in a ferrite plate, for which the diagonal and \nnon-diagonal components of the tensor are described by expressions [13].  \n \n \n221MH\nH   , \n22M\nH        (3) \nwhere ωH = γH0, ωM = 4πγ M0, γ is gyromagnetic constant, 4πM0 – ferrite saturation \nmagnetization, f = ω/2π  – electromagnetic wave frequency. The frequency \ndependences of the diagonal and non -diagonal components of the tensor \n2\n  will not \nbe detailed in this paper because the consideration below is valid for any form of \nthese dependences , including the case where dielectric permittivity of layer 2 in Fig. \n1 is a scalar quantity.   \n3. Equations describing electromagnetic wave propagation in a t angentially \nmagnetised bihyrotropic layer.   \nConsider an infinite plane  bihyrotropic layer 2 of thickness s, surrounded by \nvacuum half -spaces 1 and 3 (Fig. 1).  To characterize the electromagnetic fields in \nmedia 1 – 3, let us associate with them the corresp onding indices j = 1, 2 or 3. Layer \n2 is magnetized to saturation by a tangential uniform  magnetic field H0 and is \ncharacterized by dielectric and magnetic permeability tensors \n2\n  and \n2\n according \nto expressi ons (1) and (2). The half -spaces 1 and 3 have scalar relative dielectric and \nmagnetic permittivities ε1, μ1 и ε3, μ3.  \nAn electromagnetic field with frequency ω, propagating in the plane of a \nbihyrotropic layer and changing in time according to the harmonic law ~ exp( iωt), \nmust satisfy to the system of Maxwell equations4 for complex amplitudes in each \nmedium  \nrot / 0\ndiv 0\nrot / 0\ndiv 0ic\nic  \n  \njj\nj\njj\njEB\nB\nHD\nD\n        (4) \n                                                           \n4 Exchange interaction will not be taken into account in this study.   \nwhere Ej, Hj and Dj, Bj are the complex amplitudes of the vectors of microwave \nelectric and magnetic field strengths and of electric and magnetic induction, which \nare related by the formulas   \njjjDE\n,  \njjjBH\n         (5) \nNote here that in the previous papers in which attempts have been made to \nsolve this problem (see, for example, [16, 23]), to describe wave propagation in a \nferrite medium it was immediately proposed to find a solution of system (4) in the \nform of a plane wave of type ~ \nxp –(– ) e–x y zik x ik y ik z . We think that from a \nmathematical point of view, this approach is wrong and will not allow one to find a \ngeneral solution of Maxwell equations (4). In a mathematically  correct approach, \nthe dependence of the wave on the coordinate x (normal to the bihyrotropic layer) \nshould be found as a result of solving differential equations obtained by simplifying \nsystem (4) in accordance with the geometry of the problem. Therefore,  we should \nlook for solutions of system (4) in the form of homogeneous plane wave propagating \nin the layer plane yz and characterized by an arbitrary wave vector k. That is, in \ncontrast to [16, 23], we leave arbitrary dependence of the field components Ej and \nHj on x-coordinate and consider that these components change in the layer plane, as \nwell as in time, according to the harmonic law in accordance with expressions   \n( )exp( )xijjE e kr\n  or  \n, , , , ( )exp( )xj yj zj xj yj zj y zE e x ik y ik z   ,   (6) \n( )exp( )xijjH h kr\n or  \n, , , , ( )exp( )xj yj zj xj yj zj y zH h x ik y ik z   .  (7) \nBesides the Cartesian coordinate system ΣD = {x; y; z}, we also introduce here the \ncorresponding polar (cylindrical) coordinate system ΣP = {x; r; φ}, in which the \nangles φ are counted from the y axis, and the count erclockwise direction is taken as \nthe positive direction of the angles. The coordinates of the systems ΣP and ΣD are \nrelated by the formulas  y = r cosφ , z = r sinφ. Obviously, the wave vector modulus \nk and its components ky and kz are also related by expre ssions ky = k cosφ, kz = k sinφ \nand \n2 2 2\nyz k k k .   \nSubstituting expressions (6) and (7) into (5), and (5) into (4), and solving \nsystem (4) for the bihyrotropic medium 2 by analogy with [29, 30], we obtain a \nsystem of two equations containing only x-dependent amplitudes ez2 and hz2 of \nelectromagnetic field components Ez2 and Hz2: \n2\n2\n22 22\n0\n2\n2\n22 22\n010\n10z\nz zz g z\nz\ng z zz g zeF e i F hkx\nhF h i F ekx\n      \n,      (8) \nwhere the dimensionless functions Fν, Fg and Fνg have the next form in the \ncoordinate systems ΣD and ΣP  \n2 22\n2 2 2 2\n2 2 2\n0 0 0( ) cos siny zz z zz zz\nzzk kkFk k k                \n, (9) \n2 22\n2 2 2 2\n2 2 2\n0 0 0( ) cos siny zz z zz zz\ng zzk kkFgk k k                \n, (10) \n00sinz\ngk g k gFkk                \n,      (11) \nand the following notations are also used  \n22( ) /    \n,         (12) \n22( ) / g    \n.          (13) \nNote here that both non -diagonal components ν and g of the tensors \n2\n  и \n2\n enter \nonly into Fνg function, whereas the ν component enters only into Fν function and the \ng component - only into Fg function (th at explains the use of introduced notations).  \nFinding t he value hz2 from the first equation of system (8) and substituting it \ninto the second equation, we obtain the following differential equation for the \namplitude ez2  \n42\n22\n2 4220zz\nzeeexx   \n,       (14) \nwhere   \n2\n0 /2g k F F \n        (15)  \n4 4 2\n00 g zz zz g k F F k F  \n.        (16) \nThe following characteristic equation, corresponding to equation (14), determines \nthe values of wave number kx2 inside the bihyrotropic layer   \n42\n2220xxkk  \n.        (17) \nUsing expressions (15) and (16), it is  easy to show that discriminant of equation (1 7) \ncan take only positive values:  \n 22 4 4 2\n00 /4g g zz zz g k F F k F F F         \n \n242\n0 / 4 0g zz zz g k F F F    \n.      (18) \nThe characteristic equation (17) has four roots defined by the expression  \n222 2 2 0\n2 42x g g zz zz gkk F F F F F            \n  (19) \nand all roots are simple (not multiples):  \n222\n21 01422g\nx g zz zz gFFk k F F F\n         \n, (20) \n222\n22 01422g\nx g zz zz gFFk k F F F\n         \n, (21) \n23 21xxkk\n,          (22) \n24 22xxkk\n.          (23) \n4. Solutions describing electromagnetic waves in a bihyrotropic l ayer . \nTo determine solutions of the differential equation (14), we need to find out \nwhat values the roots kx21 – kx24 can take. First, note that the roots kx21 – kx24 cannot \nbe complex numbers (since according to (18) always η2 - α > 0), but can take only \nreal or imaginary values, depending on the sign of radicand s in (20) and (21). As \ncan be seen from these expressions, if α < 0, then |η| is always smaller than value \n2 \n, the sign before which determines the radicand sign; in this case kx21 is \nalways imaginary, while kx22 is always real ( for any sign of η ). If α > 0, conversely,  \nit is always \n2    , and both kx21 and kx22 have imaginary values when η > 0, \nand real values when η < 0.   \nThus, following the conditions formulated above and using expressions (15), \n(16) and (9)  – (11), one can plot the boundary surfaces for certain parameters of \nbihyrotropic layer in coordinate space s {ky, kz, f} or { k, φ, f}. The equations f or these \nsurfaces according to (15) and (16) can  be written in the next form   \nη = 0 or \n0g FF         (24) \nα = 0 or \n20g zz zz gF F F   ,       (25) \nThe boundary surfaces have a simple physical meaning: intersecting certain \ndispersion surface  f(ky,kz) of electromagnetic waves5, the boundary surfaces will \nseparate on it areas with real and imaginary values of the roots kx21 – kx24.  \nNote first of all that e xpression (25) is identical to the dispersion equation for \nelectromagnetic waves in an unbounded bihyrotropic medium (see relations (20) – \n(23) in [30]), if this equation would be  simplified to the  two-dimensional case, by \nequating to zero the wave number for one of coordinates normal to vector H0 (for \nexample, choosing  kx = 0 in relations (20) – (23) in [30]).  \nTo imagine clearl y the surfaces α = 0 and η = 0, let us make calculations for \nthe case where layer 2 in Fig. 1 is a ferrite plate (which is a special case of a \nbihyrotropic layer) having saturation magnetization 4πM0 = 1750 Gc and dielectric \npermittivity ε 2 = 15. The value  of homogeneous magnetic field H0 magneti zing the \nplate to saturation was equal to 300 Oe in calculations.   \nNote at once that for the case with ferrite plate the value α changes sign when \nthe frequency changes from value \nff  to value  \nff  (since according to (3) \nand (12) we have μ = 0 and \n   at \nff ).  \nNow, to find out in which regions of space {ky, kz, f} the roots kx21 и kx22 take \nreal values, and in which regions t hey take imaginary values, we calculate and graph \nin this space the surfaces α = 0, η = 0 and the plane \nff . The spatial regions \n                                                           \n5 For example, a dispersion surface for some  type of spin wave s propagating in a ferrite plate.   \nbounded by these surfaces and cross sections of these surfaces with planes ky = 0, kz \n= 0 and f = 7000 M Hz are shown in Fig. 2.   \nThe meaning of 3 -D chart in Fig.2 is that we know  what distribution over the \nthickness of tangentially magnetized ferrite layer (with an arbitrary thickness!) the \nwave will have if its dispersion surface will be in a certain region  of space {ky, kz, f}. \nThat is, we know about th ese space regions now, based only on the properties of \ndifferential equation (14), although we have not yet got the dispersion equation of \nthe wave!   \n \nFig. 2. Spatial regions SS, VS and VV defining the chara cter of wave \ndistribution in a ferrite plate cross section. The boundaries of the SS, VS and VV \nregions are defined by the united  surface α = 0 (which itself includes several surfaces) \nand the plane \nff . Curves 1 - 3, 4 - 6 and 7 - 8 correspond to  sections of the \nsurface α = 0 by planes ky = 0, kz = 0 and f = 7000 MHz respectively . Lines 9 and 10 \nare sections of plane \nff  by planes ky = 0 and kz = 0 respectively . Dashed curves \n11 - 12, 13 - 14 and 15 are section s of the surface η = 0 by planes ky = 0, kz = 0 and f \n= 7000 MHz respectively.   \n \nAnalysing  Fig. 2, we note that the most voluminous in Fig. 2 are the SS-\nregions highlighted by yellow, where α > 0 and η < 0. The part s of the wave \ndispersion surface  located i n the SS-region s will describe solutions with real values \nof roots kx21 и kx22, to which corresponds the general solution of differential equation \n(14) in the form  \n2 21 21 22 22 exp( ) exp( ) exp( ) exp( )z x x x xe A k x B k x C k x D k x     \n. (26) \nThat is, the wave distribution over the ferrite plate thic kness for th ese parts of the \ndispersion surface, will be described only by exponential functions and such a wave \ncan be conventionally called a surface -surface or SS-wave.  \nThe smallest space in Figure 2 is occupied by VV-regions , highlighted by \norange, wh ere α > 0 and η > 0. The part s of the wave dispersion surface located in \nVV-regions  will describe solutions with imaginary values of roots kx21 and kx22, to \nwhich corresponds a general solution of the differential equation (22) in the form of  \n2 21 21 22 22 cos( ) sin( ) cos( ) sin( )z x x x xe A k x B k x C k x D k x     \n.  (27) \nThus, the wave distribution over the ferrite plate thickness for this part of the \ndispersion surface, will be described only by trigonometric functions and such a \nwave can be conventionally called a volume -volume or VV -wave.   \nThe relat ion α < 0 is valid for the VS -regions highlighted by blue in Fig. 2, \nand the surfaces η = 0 (their cross sections 11 – 15 are shown by dashed curves) \nalways lie within VS -regions. As mentioned above, the value kx21 is imaginary and \nthe value kx22 is real in these regions regardless of the sign of η . That is, the part s of \nthe wave dispersion surface located in the VS -region s will describe waves \ncorresponding to the general solution of the differential equation (22) of the form  \n2 21 21 22 22 cos( ) sin( ) exp( ) exp( )z x x x xe A k x B k x C k x D k x     \n.  (28) \nIn other words, the distribution over the ferrite plate thickness for th ese parts of the \ndispersion surface,  will be described by both trigonometric and exponential \nfunctions and the wave can be conventionally called a bulk -surface or VS -wave.   \nIt shoul d be noted that the last case, when a general solution of the differential \nequation (22) has the form,   \n2 21 21 22 22 exp( ) exp( ) cos( ) sin( )z x x x xe A k x B k x C k x D k x     \n,  (29) \ncorresponding to real values of kx21 and imaginary values of kx22, is never realized in \nthe ferrite plate.  \nThus, the wave distribution inside the ferrite plate can vary depending on the \nwave parameters and on the part of dispersion or isofrequency dependence6 this \ndistribution can correspond, for example, to SS -wave (described by expression (26)) \nand on another part to V S-wave (described by expression (28)). This is an essential \ndifference between the exact SW description and SW description in magnetostatic \napproximation [11], where e very SW dispersion surface was characterized by the \ncertain type of SW distribution (surf ace or volume).  \nIt is also evident that there is a single -valued correspondence between the \nregions of space { ky, kz, f} and the type of wave distribution in the ferrite layer \nregardless of the boundary problem we will be considering further – it can be a  \nsimple ferrite plate surrounded by vacuum half -spaces, a one -sided metallized ferrite \nplate, a metal -dielectric -ferrite - dielectric -metal structure, etc.   \nBelow we obtain the dispersion equation and expressions for the microwave \nelectromagnetic field comp onents inside the bihyrotropic layer for SS-waves \ndescribed by expression (26). Obviously, similar relations for other types of waves \ncan be obtained by the same way.   \n5. Expressions for electromagnetic field components inside bihyrotropic layer  \nTo obtain  expressions for all microwave components of electromagnetic wave \ninside bihyrotropic layer, it is necessary first to find expressions for their amplitudes  \nex2, ey2, hx2, hy2 и hz2.  \nSubstituting expression (26) into the first equation of system (8), we find the \nexpression for the amplitude  hz2  \n                                                           \n6 It is well known that the dispersion and isofrequ ency dependences are cross sections of the \ndispersion surface, so all that has been said above about intersections of this surface with boundary \nsurfaces is applicable to these dependences too.    \n  2 1 21 21 2 22 22 exp( ) exp( ) exp( ) exp( )z x x x xh i A k x B k x i C k x D k x       \n, (30) \nwhere   \n2\n21\n1 2\n01x\nzz gkFFk\n   \n,       (31) \n2\n22\n2 2\n01x\nzz gkFFk\n   \n.       (32) \nSubstituting exp ressions (6) and (7) into (5) and then (5) into system (4), we obtain   \n2 2 0 2 0 2 0y z z y x yk e k e k h ik h     \n      (33) \n2\n2 0 2 0 2 0z\nz x x yeik e k h ik hx      \n      (34) \n2\n2 0 2 0y\ny x zz zeik e ik hx   \n       (35) \n2 2\n2 2 2 0y x\ny y y x zz z zh hik h i ik h i k hxx          \n    (36) \n2 2 0 2 0 2 0y z z y x yk h k h k e ik ge    \n      (37) \n2\n2 0 2 0 2 0z\nz x x yhik h k ge ik ex    \n      (38) \n2\n2 0 2 0y\ny x zz zhik h ik ex   \n       (39) \n2 2\n2 2 2 0y x\ny y y x z zz ze eik e ig ik e ik exx         \n    (40) \nFrom equations (33) and (37), we can respectively obtain the expressions   \n2 2 2 2\n00y z\nx z y yk kh e e i hkk    \n,       (41) \n2 2 2 2\n00y z\nx z y yk kge h h i ekk    \n.       (42) \nSubstituting expressions (41) and (42) into equations (34) and (38), we obtain the \nfollowing relations    \n2\n2 2 2 2 2 2\n0 0 010y z y z\nz y g y zk k k ei h iF h F e ek k k x       \n,    (43) \n2\n2 2 2 2 2 2\n0 0 010y z y z\nz g y g y zk k gk hi e iF e F h hk k k x       \n,    (44) \nwhere the dimensionless functions Fν2 and Fg2 have the form   \n2\n2 2\n0zkFk \n,          (45) \n2\n2 2\n0z\ngkFk \n,         (46) \nLet us multiply expression (43) and iFνg. Then let's multiply expression (44) and Fν2. \nSumming the resulting expression s, we find the value ey2  \n2 2 2\n2 0 2 2 2\n2001 g zz\ny z zFe F he a e ia h iF k x k x      \n.     (47) \nNow  let us multiply  expression  (43) and iFg2. Then let's multiply expression (44) \nand Fνg. Summing the obtained relations, we find the value hy2  \n2 22\n2 0 2 2 2\n2001 gg zz\ny z zFFheh ib e b h iF k x k x      \n.     (48) \nIn expressions (47) and (48) we have introduced the following notations   \n2\n2 2 2 gg F F F F\n,         (49) \n02 2\n00y z y\ngk k ka F Fkk\n,        (50) \n22 2\n00y z y\ngk k gka F Fkk\n,        (51) \n02 2\n00y z y\nggk k kb F Fkk\n,        (52) \n22 2\n00y z y\nggk k gkb F Fkk \n.        (53) \nAs can be seen from (47) and (48), the amplitudes ey2 and hy2 are expressed \nonly through the amplitudes ez2, hz2 and their x-coordinate derivatives. Substituting  \nexpressions (47) and (48) into (41) and (42), we obtain similar expressions for the \namplitudes ex2 and hx2. To concisely record the x-coordinate dependenc ies of all \namplitudes, we introduce such dimensionless functions Σ0, Σ1, Σ2 and Σ3, that the \nfollowing relations are satisfied   \n20 ()zex\n, \n2\n01()zekxx , \n()z2 2h i x , \n2\n03()zhik xx .  (54) \nSubstituti ng formulae (26) and (30)  into relations (54) , we obtain the next \nexpressions for the functions Σ0, Σ1, Σ2 and Σ3  \n0 21 21 22 22( ) exp( ) exp( ) exp( ) exp( )x x x x x A k x B k x C k x D k x      \n (55) \n 21\n1 21 21\n0( ) exp( ) exp( )x\nxxkx A k x B k xk    \n  \n 22\n22 22\n0exp( ) exp( )x\nxxkC k x D k xk  \n      (56) \n 1 21 21 ( ) exp( ) exp( )2 x xx A k x B k x    \n \n 2 22 22exp( ) exp( )xx C k x D k x  \n,      (57) \n 21\n3 1 21 21\n0( ) exp( ) exp( )x\nxxkx A k x B k xk     \n \n 22\n2 22 22\n0exp( ) exp( )x\nxxkC k x D k xk   \n    (58) \nTo explain the introduced notations, note that numerical indexes of the values Σ0 – \nΣ3 correspond to the maximum power of the wave numbers kx21 and kx22 in \nmultipliers near the exponents entering in expressions (55 ) – (58) (the power of kx21 \nand kx22 in relations (31) and (32) for values β 1 and β 2 is taken into account  too).  \nSubstituting relations (54) - (58) into expressions (26), (30), (41), (42), (47) \nand (48) for amplitu des ex2, ey2, hx2, hy2 and hz2 and then substituting obtained \nexpressions into formulae (6) and (7), we find all components of the microwave \nelectromagnetic field inside the bihyrotropic  layer   \n  2 0 0 2 1 2 2 3 2 2\n2 0 0y z\nx g gk ikE b F b F FF k k          \n  \n  0 0 1 2 2 2 3 exp( )g y z g a F a F ik y ik z          \n,   (59) \n  2 2 0 0 0 1 2 2 2 3\n2 0 01 y z\nxgk kH F a F a FF k k          \n \n  0 0 2 1 2 2 3 exp( )g g y z b F b F ik y ik z          \n,   (60) \n2 0 0 1 2 2 2 3\n21exp( )y g y zE a F a F ik y ik zF         \n,   (61) \n2 0 0 2 1 2 2 3\n2exp( )y g g y ziH b F b F ik y ik zF          \n,   (62) \n0( )exp( )z2 y zE x ik y ik z  \n,       (63) \n2( )exp( )z2 y zH i x ik y ik z   \n,       (64) \n6. Expressions for electromagnetic field compo nents outside bihyrotropic \nlayer   \nLet us now consider microwave fields arising outside the bihyrotropic layer \nin media 1 and 3 characterized by scalar dielectric and magnetic permittivities ε1, μ1 \nand ε3, μ3. Substituting solutions of the form (6) and (7) into Maxwell equations (4), \nwe obtain instead of system (8) two independent differential equations with respect \nto amplitudes ez1,3 and hz1,3:  \n 2\n1,3 2 2 2\n0 1,3 1,3 1,3 20z\nz y zek k k ex     \n,      (65) \n 2\n1,3 2 2 2\n0 1,3 1,3 1,3 20z\nz y zhk k k hx     \n,      (66) \nThe following characteristic equatio n determines the solutions of equations \n(65) and (66)  \n2 2 2 2\n1,3 0 1,3 1,3x z yk k k k    \n.        (67) \nSince the microwave fields should exponentially decay far away from the layer, the \nsolutions of equations (65) and (66) in medium 1 will be looked for in the for m  \n11 exp( )zxe N k x\n,        (68)  \n11 exp( )zxh iG k x\n,        (69) \nand in medium 3 – in the form  \n33 exp( )zxe K k x\n,         (70) \n33 exp( )zxh iL k x\n,         (71) \nwhere N, G, L and K are independent coefficients .  \nTransform ing the system of Maxwell equations (4), we express the values \nex1,3, hy1,3 and hx1,3 through the values ez1,3 and hz1,3, described by expressions (68) – \n(71), and then we substitute all obtained relations in (6), (7) and find expressions for \nmicrowave fie ld components in half -spaces 1 and 3:  \n  1 0 1 1 1 2\n1exp( )x y z x x y ziE Gk k Nk k k x ik y ik zq     \n.   (72) \n  1 1 0 1 1 2\n11exp( )x z x y x y zH Gk k Nk k k x ik y ik zq     \n,   (73) \n  1 1 0 1 1 2\n11exp( )y y z x x y zE Nk k Gk k k x ik y ik zq     \n,    (74) \n  1 1 0 1 1 2\n1exp( )y y z x x y ziH Gk k Nk k k x ik y ik zq     \n,    (75) \n11 exp( )z x y zE N k x ik y ik z   \n,      (76) \n11 exp( )z x y zH iG k x ik y ik z   \n,      (77) \n  3 0 3 3 3 2\n3exp( )x y z x x y ziE Lk k Kk k k x ik y ik zq    \n.   (78) \n  3 3 0 3 3 2\n31exp( )x z x y x y zH Lk k Kk k k x ik y ik zq    \n,   (79) \n  3 3 0 3 3 2\n31exp( )y y z x x y zE Kk k Lk k k x ik y ik zq    \n,    (80) \n  3 3 0 3 3 2\n3exp( )y y z x x y ziH Lk k Kk k k x ik y ik zq    \n,    (81) \n33 exp( )z x y zE K k x ik y ik z  \n,       (82)  \n33 exp( )z x y zH iL k x ik y ik z  \n,      (83) \nwhere the values q1 and q3 are desc ribed by the following expression  \n2 2 2\n1,3 0 1,3 1,3 z q k k   \n.        (84) \n7. Dispersion equation for electromagnetic waves in bihyrotropic layer  \nLet us now proceed to the derivation of the dispersion equation describing the \npropagation of electromagnetic w aves in a bihyrotropic layer. Satisfying the \nboundary conditions of continuity of tangential components Ey, Ez, Hy and Hz at x = \n0 and x = s, one can obtain the following system of eight equations for constant \ncoefficients A, B, C, D, G, N, K, L:  \n10\n1 1 0\n2 0 0 1 2 2 2 3 2\n11\n12\n1 1 0\n2 0 0 2 1 2 2 3 2\n11\n0\n3 3 0\n2 0 0 1 2\n3exp( ) ( )\n( ) ( ) ( ) ( )exp( )\nexp( ) ( )\n( ) ( ) ( ) ( )exp( )\n(0)\n(0) (0x\ny z x\ng\nx\nx\ny z x\ngg\nx\ny z x\ngN k s s\nNk k G k kF a s F s a s F sq k s\nG k s s\nGk k N k kF b s F s b s F sq k s\nK\nKk k L k kF a Fq\n\n \n       \n \n       \n\n   2 2 2 3\n2\n3 3 0\n2 0 0 2 1 2 2 3 2\n3) (0) (0)\n(0)\n(0) (0) (0) (0)y z x\nggaF\nL\nLk k K k kF b F b Fq\n   \n\n       \n  (85) \nSubstituting the values N, G, K and L from the first, third, fifth and seventh \nequations into the second, fourth, sixth and eighth equations of system (85), we \nobtain a system of four equations for the coefficients A, B, C and D (entering into \nthe values Σ 0 – Σ3):   \n1 1 0\n0 2 0 1 2 2 2 2 3 22\n11\n1 1 0\n0 2 0 2 1 2 2 2 3 22\n11\n3 3 0\n0 2 0 1 2 2 2 22\n33( ) ( ) ( ) ( ) 0\n( ) ( ) ( ) ( ) 0\n(0) (0) (0)yz x\ng\nyz x\ngg\nyz x\ngkk kka F s F s a F s F sqq\nkk kkb F s F s b F s F sqq\nkk kka F F a Fqq\n\n                   \n               \n   \n              \n   23\n3 3 0\n0 2 0 2 1 2 2 2 3 22\n33(0) 0\n(0) (0) (0) (0) 0yz x\nggF\nkk kkb F F b F Fqq\n\n               \n   \n. (86) \nSubstituting expressions (55) - (58) describing the values Σ0 – Σ3 into the \nsystem (86), and collect ing similar summands with the same coefficients A, B, C \nand D, we obtain a system of equations  \n11 12 13 14\n21 22 23 24\n31 32 33 34\n41 42 43 440\n0\n0\n0d A d B d C d D\nd A d B d C d D\nd A d B d C d D\nd A d B d C d D   \n      \n   \n ,      (87) \nwhere the matrix elements have the form  \n21 1 1 0 21\n11 0 2 1 2 2 2 21 22\n1 0 1 0exp( )yz x x x\ngxkk k k k kd a F F a F F k sq k q k       \n \n (88) \n21 1 1 0 21\n12 0 2 1 2 2 2 21 22\n1 0 1 0exp( )yz x x x\ngxkk k k k kd a F F a F F k sq k q k        \n \n (89) \n22 1 1 0 22\n13 0 2 2 2 2 2 22 22\n1 0 1 0exp( )yz x x x\ngxkk k k k kd a F F a F F k sq k q k       \n \n (90) \n22 1 1 0 22\n14 0 2 2 2 2 2 22 22\n1 0 1 0exp( )yz x x x\ngxkk k k k kd a F F a F F k sq k q k        \n \n (91) \n1 1 0 21 21\n21 0 2 2 1 2 2 21 22\n1 0 1 0exp( )yz x x x\ng g xkk k k k kd b F F b F F k sq k q k        \n \n (92) \n1 1 0 21 21\n22 0 2 2 1 2 2 21 22\n1 0 1 0exp( )yz x x x\ng g xkk k k k kd b F F b F F k sq k q k         \n \n (93)  \n1 1 0 22 22\n23 0 2 2 2 2 2 22 22\n1 0 1 0exp( )yz x x x\ng g xkk k k k kd b F F b F F k sq k q k        \n \n (94) \n1 1 0 22 22\n24 0 2 2 2 2 2 22 22\n1 0 1 0exp( )yz x x x\ng g xkk k k k kd b F F b F F k sq k q k         \n \n (95) \n21 3 3 0 21\n31 0 2 1 2 2 2 22\n3 0 3 0yz x x x\ngkk k k k kd a F F a F Fq k q k      \n\n   (96) \n21 3 3 0 21\n32 0 2 1 2 2 2 22\n3 0 3 0yz x x x\ngkk k k k kd a F F a F Fq k q k      \n\n   (97) \n22 3 3 0 22\n33 0 2 2 2 2 2 22\n3 0 3 0yz x x x\ngkk k k k kd a F F a F Fq k q k      \n\n   (98) \n22 3 3 0 22\n34 0 2 2 2 2 2 22\n3 0 3 0yz x x x\ngkk k k k kd a F F a F Fq k q k      \n\n   (99) \n3 3 0 21 21\n41 0 2 2 1 2 2 22\n3 0 3 0yz x x x\nggkk k k k kd b F F b F Fq k q k       \n\n   (100) \n3 3 0 21 21\n42 0 2 2 1 2 2 22\n3 0 3 0yz x x x\nggkk k k k kd b F F b F Fq k q k       \n\n    (101) \n3 3 0 22 22\n43 0 2 2 2 2 2 22\n3 0 3 0yz x x x\nggkk k k k kd b F F b F Fq k q k       \n\n   (102) \n3 3 0 22 22\n44 0 2 2 2 2 2 22\n3 0 3 0yz x x x\nggkk k k k kd b F F b F Fq k q k       \n\n    (103) \nThus, the dispersion equation for electromagnetic waves propagating in a \nbihyrotropic layer is a fourth -order determinant for a system of homogeneous \nequations  (87) with coefficients defined by expressions (88) – (103).  \n8. Calculations of surface spin waves characteristics in ferrite plate   \nAs an example , demonstrating the functionality and usability of the dispersion \nequation (87), let us consider  some charact eristics of SW in a ferrite plate.    \nIt is already clear that for SW the main difference between the obtained \ndescription and former descriptions in magnetostatic approximation [11] and \nwithout it [16, 23], is that the wave distribution inside ferrite plate  along the x-\ncoordinate is described by two wave numbers7 – kx21 и kx22!  \nLet us demonstrate how this difference influences on the characteristics of the \nsurface SW. Isofrequency dependences for surface SW with different frequencies \nare presented in Fig. 3, where red curves 1 – 4 are calculated according with \npresented theory , and black curves 1' – 4' are calculated in magnetostatic \napproximation. The calculations were carried out at the following parameters: H0 = \n300 Oe, 4πM0 = 1750 Gs, s = 40 µm.   \nFig. 3 shows that the isofrequency curves 1 – 4 and the corresponding curves \n1' - 4' differ from each other only at frequencies close to the value \n2\nHM / 2 / 2 f       \n= 2197.7 MHz. However, if we look how the wave \nnumbers kx21 and kx22 characteriz ing the microwave field distribution over the ferrite \nplate thickness vary along the iso -frequency curves and compares this variation with \na similar variation of the wave number kx2ms calculated in magnetostatic \napproximation [11], we can see significant differences (see Fig.4).   \nAs can be seen from F ig. 4, at angles φ close to the cut -off angles of wave \nvector, the magnetostatic dependences kx2ms(φ) pass near the curves  kx22(φ), while at \nφ = 0 these dependences pass near the curves  kx21(φ), and the difference in the values \nkx22(φ = 0) and kx21(φ = 0) depends significantly on frequency, changing from 255 \ncm-1 at f = 2198 MHz to 2 cm-1 at f = 2500 MHz .  \n \n                                                           \n7 This is agree with earlier results for backward SW propagat ing along the direction of vector H0 \nin a tangentially magnetized ferrite plate [24].   \n \nFig. 3. Isofrequency dependences of the surface SW in the tangentially  \nmagnetized ferrite plate for frequencies 2198 ( 1 and 1'), 2216.3 ( 2 and 2'), 2250 ( 3 \nand 3') and 2300 MHz ( 4 and 4') (only half-plane for  ky > 0 is shown). Curves 1' – 4' \n(black) are calculated in magnetostatic approximation and curves 1 – 4 (red) – \nwitho ut this approximation. Here are also shown curves 1'' and 4'', which are the \nintersection of surface α = 0 and planes f = 2198 MHz and f = 2300 MHz, respectively \n(curve 1'' separates on curve 1 the region  with a SS-waves  and the region with VS-\nwave s for f = 2198 MHz , while curve 4'' does not intersect curve 4).  \n \n \nFig. 4. Dependences of the wave numbers kx21 (green curves 1 – 4), kx22 (red \ncurves 1' – 4') and kx2ms (black curves 1'' – 4'') for frequencies 2198, 2 216.3, 2300 \nand 2500 MHz respectively on the angle φ indicating the wave vector orientation. \nCurve 1' is not shown in the figure because  it is located above of ~ 250 cm-1. In the \npart of curve 1 shown in purple, kx21 takes on imaginary values corresponding  to the \nVS-wave (the value | kx21| is shown in the ordinate axis).  \n9. Comparison of surface spin wave propagation along y-axis with results \nobtained earlier  \nIt is well known that description (without magnetostatic approximation) of \nthe surface SW propagati ng in a tangentially magnetized ferrite plate perpendicular \nto magnetic field vector H0 was obtained many years ago (see, for example, [17, \n18]). For this case the Maxwell equations are known to be solved quite easily and \nthe resulting distribution of surf ace SW over the ferrite plate thickness is \n \ncharacterized by one single wave number but not two. Thus, at first sight one can \nsee a clear contradiction between the above description of surface SV and the \ndescription obtained earlier. In fact, as will be sho wn below, this contradiction is \nonly seeming.   \nObviously, the case of SW propagation perpendicularly to the vector H0 is \nobtained from the general case of wave propagation in arbitrary direction if we put \nkz = 0 (or φ = 0) in the above consideration. In this case (when kz = 0), the system of \nMaxwell equations (4) splits into two independent subsystems, one of which \nincludes only field components Ez2, Hx2 and Hy2, and the other one – Hz2, Ex2 and Ey2. \nSince, when kz = 0 from (11) we obtain Fνg = 0, the resulting equations system (8) \nfor amplitudes ez2 and hz2 turns into two independent homogeneous Helmholtz \nequations, one for the amplitude ez2 and the other for the amplitude hz2. The first \nequation describes the known s urface SW ( H-wave with components Ez2, Hx2 and \nHy2) for which \n22\n22 0 0xyk k F k k     (this value of kx22 is the result of \nsubstituting of equality Fνg = 0 into expression (21)), and the second equation \ndescribes the surface electromagnetic wave ( E-wave  with components Hz2, Ex2 and \nEy2, typical for a layer of usual dielectric)  for which \n22\n21 0 0x g y zzk k F k k     \n(this value of kx21 is the result of  substituting of equality Fνg = 0 into expression (20) ). \nAs can be seen, the mentioned  values kx22 and kx21 correspond to results previously \nobtained (see, for example, [13, 17, 29]).   \nHowever, the reader who has carefully studied Figure 4 may see a discrepancy \nwith the above arguments and say: but how so  – it is clear that, according to the \ncalculations in Fig . 4 the surface SW is characterized not by a single wave number \nat φ = 0 and kz = 0 (as it was established earlier), but by two wave numbers kx21 and \nkx22?!  \nTo answer this observation, the change of coefficients A, B and C, normalized \nto coefficient D, as a function of the  wave number kz, is calculated below (Fig. 5). \nRemind here  that coefficients A, B, C, and D define amplitudes of exponential  \nfunctions in expression (26). And as we can see from Fig. 5, the coefficients A and \nB near the exponents \n21 exp( )xkx  and \n21 exp( )xkx  become zero at kz = 0 (or φ = 0), \nwhile the coefficients C and D near the exponents \n22 exp( )xkx and \n22 exp( )xkx  do \nnot become zero!  Thus, it is clear  that at kz = 0 (or φ = 0) the surface SW distribution \nover the ferrite plate thickness is described by a single wave number  kx22.  \n \nFig. 5. Dependencies of coefficients ratio A/D (light-blue curves 1 – 5), B/D \n(blue curves 1' – 5') and C/D (red curves 1'' – 5''') on the wave number kz for \nfrequencies 2217, 2300, 2500, 2800 and 3200 MHz respectively.  \nBasin g on the data of Fig. 4, we note that when φ ~ 0 and kz ~ 0, the \ndependence kx21 (φ) does not really describe the SW distribution over the ferrite plate \nthickness, since, as can be seen from Fig. 5, the coefficients A and B for all \nfrequencies are practica lly equal to zero at kz ~ 0. Thus, in accordance with formulas \n(55) – (64), the main contribution to the microwave field amplitude distribution at \nφ ~ 0 and kz ~ 0 is provided by the coefficients C and D and their corresponding \n \nwave number kx22. Therefore,  it should be taken into account that description of the \nsurface SW distribution over the ferrite  thickness in magnetostatic approximation is \nrather imprecise for the initial part of the SW spectrum (in the range ~ 200 MHz \nabove the frequency \nf ) at φ ~ 0 and kz ~ 0, where kx2ms(φ) dependences almost \ncoincide with kx21(φ) dependences, but lie quite far from kx22(φ) dependences.   \n10. Conclusion   \nAnalytically, without magnetostatic approximation, there is solved the \ngeneral problem of electromagnet ic wave propagation along  arbitrary direction in \ntangentially magnetized plane -parallel bigyrotropic layer described by the dielectric \nand magnetic permittivities in the form of Hermit ian tensors  of second rank . It is \nshown that by presenting a solution of  the Maxwell equations in the layer ’s plane as \nthe wave of form ~\nexp( )yzik y ik z  and by leaving an arbitrary the wave \ndependence on x-coordinate (that is normal to the layer ’s plane ), one can bring the \nMaxwell equations to a system of two differ ential equations containing only x-\ndependent amplitudes of the microwave electric and magnetic fields, parallel to the \nvector of constant homogeneous magnetic field H0. In its turn, this system is reduced \nto a fourth order linear differential equation, to which corresponds the biquadratic \ncharacteristic equation determin ing the wave numbers of electromagnetic wave \ndistribution over the layer ’s thickness. It is shown that this characteristic equation \nhas four simple (non -multiple) roots kx21, kx22, kx23 = -kx21 and kx24 = -kx22, which \ncannot be complex numbers and can take only real or imaginary values.  \nA boundary problem for propagation of electromagnetic waves with real \nvalues of kx21 and kx22 in a bihyrotropic layer surrounded by dielectric half -spaces is \nsolved and the dispersion equation  presenting the fourth -order determinant for a \nsystem of homogeneous linear equations is derived for these waves.  It is shown that \nthe electromagnetic wave propagating in the layer’s plane in an arbitrary direction \nhas al l six components of the microwave electromagnetic field – three magnetic and \nthree electrical – both in the ferrite layer and in the adjacent half -spaces. Physically,  \nthis means that satisfying of the boundary conditions on the layer’s surfaces results \nin appearance of both E-wave and H-wave in the adjacent half -spaces, and these two \nwaves are interconnected to each other by means of the bihyrotropic layer.  \nBased on this theory, the characteristics of spin waves in a ferrite plate, which \nis a special case of a bihyrotropic layer, have been studied. It is shown that in the \nferrite plate and in the simplest structures based on it, the wave distribution inside \nferrite plate can be described by both exponential and trigonometric functions \ncorresponding to the s urface and volume wave distributions. Thus, on the waves \ndispersion surfaces f(ky, kz) corresponding to these structures, there can be areas \ndescribing three types of propagating waves with different distributions over the \nferrite thickness: surface -surfac e waves ( kx21 and kx22 are real numbers), volume -\nsurface waves ( kx21 is imaginary and kx22 is real) and volume -volume waves ( kx21 and \nkx22 are imaginary numbers). The fourth case of the surface -volume wave (where \nkx21 is real number and kx22 is imaginary n umber) is not realised in the ferrite plate \nand in structures based on it. In the {ky, kz, f} coordinate space we graph the \nboundary surfaces that, by crossing a certain dispersion surface of spin waves, would \nseparate on it areas with different wave distr ibutions. It is shown that the boundary \nsurfaces are described by equation identical to the dispersion equation for \nelectromagnetic waves in unbounded ferrite (bihyrotropic) medium if the latter \nwould be  simplified to the two -dimensional case.  \nThe characte ristics of surface SW calculated in magnetostatic approximation \nhave been compared with similar characteristics calculated without it. It is found \nthat the isofrequency dependences calculated by both methods differ appreciably \nonly in the region of small w ave numbers k < ~ 3 cm-1 for a frequency interval ~ 20 \nMHz lying above the frequency \nf . It is shown that coefficients A and B near the \nexponents \n21 exp( )xkx  and \n21 exp( )xkx  in SW distribution over the ferrite thickness \nbecome equal to zero at kz = 0 (or φ = 0), so the wave distribution in this case is \ndescribe d by the single wave number kx22. It is found  that dependences of the wave \nnumbers kx21 and kx22 on the orientation φ of the wave vector for the surface SW are  \nsignificantly different from the an alogous magnetostatic dependence kx2ms(φ) in the \nwide frequency band ~ 200 MHz lying above the frequency \nf . In particular, at \nangles φ close to the wave vector cut -off angles, the kx2ms(φ) dependences pass near \nthe kx22(φ) curves a nd at φ ~ 0 near the kx21(φ) curves, and the difference in the \nkx22(φ = 0) and kx21(φ = 0) values changes significantly with frequency from ~ \n255 cm-1 at \n~ff  to ~ 2 cm-1 at \n~ 300ff  MHz. Therefore, the magnetostatic  \ndescription of surface SW distribution over the ferrite thickness is rather imprecise \nfor the initial part of surface SW spectrum at φ ~ 0 and kz ~ 0, where the kx2ms(φ) \ndependences lie far from the kx22(φ) dependences and almost coincide with the \nkx21(φ) dependences, really not describing the wave  (since A(φ = 0) = B(φ = 0) = 0 ).  \nThe obtained solution of the problem on propagation of electromagnetic \nwaves in a tangentially magnetized bihyrotropic layer opens wide possibilities for \ncalculation of exact wa ve’s characteristics in layers of such media as ferrite, \nantiferromagnetic and plasma. In particular, not only the Poynting vector, direction \nand density of energy flux and vector lines for the studied waves can be calculated \nby means of the presented theo ry but also more complicated problems can be solved \non the basis of available electrodynamic methods.   \nFunding  \nThis work was performed as part of State Task of Kotel’nikov Instutute of \nRadio Engineering and Electronics of Russian Academy of Sciences.  \nReferences  \n1. S. A. Nikitov, D. V. Kalyabin, I. V. Lisenkov  et al, Physics -Uspekhi 58 (2015) \n1002.  \n2. A. V. Chumak, V. I. Vasyuchka, A. A. Serga, B. Hillebrands, Nature Physics 11 \n(2015) 453.  \n3. X. S. Wang, H. W. Zhang, X. R. Wang, Phys. Rev. Appl. 9 (2018) 024029    \n4. A. Yu. Annenkov, S. V. Gerus, E. H. Lock, EPL ( Euro Phys. Lett. ) 123 (2018 ) \n44003.   \n5. S. A.  Nikitov , A. R.  Safin , D. V . Kalyabin et al, Physics -Uspekhi  63 (2020)  945.  \n6. P. Pirro, V. I. Vasyuchka, A. A. Serga, B. H illebrands, Nat Rev Mater 6 (2021)  \n1114 .  \n7. A. Barman, G. Gubbiotti, S. Ladak et al, Journa l of Physics: Condensed Matter \n33 (2021) 413001   \n8. A. Chumak, P. Kabos, M. Wu et al, IEEE Transactions on Magnetics 58 (2022) \n1  \n9. S. A. Odintsov, S. E. Sheshukova, S. A. Nikitov, E. H. Lock, E. N. Beginin, A. \nV. Sadovnikov, Journal of Magnetism and Magnetic Materials, 546 (2022) \n168736  \n10. S. V. Gerus, A. Yu. Annenkov, E. H. Lock , Journal  of Magnetism  and Magnetic  \nMaterials , 563 (2022) 169747  \n11. R. W. Damon, J. R. Eshbach, J. Phys. Chem. Solids 19 (1961) 308 .  \n12. A. V.  Vashkovskii , V. S.  Stalmakhov , Y. P.  Sharaevskii , Magnetostatic Waves \nin Microwave Electronics (Saratov Gos. Univ., in Russian) 1993.   \n13. A. G. Gurevich and G. A.  Melkov , Magnetization Oscillations and Waves (CRC, \nBoca Raton, Fl.) 1996.   \n14. D. D. Stancil , A. Prabhakar, Spin Waves. Theory and applications  (New -York: \nSpringer Science + Business Media ) 2009 .  \n15. O. G. Vendik , B. A. Kalinikos , S. I. Miteva , Izvestiya vuzov USSR. \nRadioelectronics. XXIV  (1981 ) 52  \n16. R. Ruppin , Journal of Applied Physics 62 (1987 ) 11.  \n17. V. V.  Danilov , I. V. Zavislyak , and M. G  Balinskii , Spin Wave Electrodynamics \n(Libid ’, Kiev) 1991.  \n18. A. V. Vashkovskii , E. G. Lokk , J. Commun. Technol. Electron. , 46 (2001 ) 674.  \n19. A. V. Vashkovskii , E. G. Lokk , J. Commun. Technol. Electron. , 46 (2001 ) 1163 .  \n20. A. V. Vashkovskii , E. G. Lokk , J. Commun. Technol. Electron. , 47 (2002) 87.   \n21. E. G. Lokk , J. Commun. Technol. Electron. , 48 (2003 ) 1369 .  \n22. A. V. Vashkovskii , E. G. Lokk , J. Commun. Technol. Electron. , 54 (2009) 456.  \n23. S. A. Vyatkina , R. K. Babichev , V. N. Ivanov , Electromagnetic  Waves  and \nElectronic  Systems , 16 (2011 ) 64.  \n24. A. V. Vashkovskii , E. G. Lokk , J. Commun. Technol. Electron. , 57 (2012) 490 .  \n25. A. V. Vashkovsky , E. H. Lock , Physics -Uspekhi 54 (2011) 281.  \n26. E. H. Lock, Solid State Phenomena , 233-234 (2015) 476.  \n27. E. G. Lokk , J. Commun. Technol. Electron. , 61 (2016)  33  \n28. E. G. Lokk , A. V. Vashkovskii , J. Commun. Technol. Electron. , 61 (2016)  877.  \n29. A. G. Gurevich , Ferrites at microwave frequencies (Moscow, State. Publishing \nHouse of Physical literature ) 1960.   \n30. E. H. Lock, A. V. Lugovskoi, S. V. Gerus, J. Commun. Technol. Electron. 66, \n(2021)  834.  \n "    },    {        "title": "1602.06684v1.Flexible_heat_flow_sensing_sheets_based_on_the_longitudinal_spin_Seebeck_effect_using_one_dimensional_spin_current_conducting_films.pdf",        "content": "1 \n Flexible heat-flow sensing sheets base d on the longitudinal spin Seebeck \neffect using one-dimensional spin-current conducting films \n \nAkihiro Kirihara1,2*, Koichi Kondo3, Masahiko Ishida1,2, Kazuki Ihara1,2, Yuma Iwasaki1, Hiroko \nSomeya1,2, Asuka Matsuba1, Ken-ichi Uchida4,5, Eiji Saitoh2,4,6,7, Naoharu Yamamoto3, Shigeru \nKohmoto1 and Tomoo Murakami1 \n \n1Smart Energy Research Laboratories, NEC Corporation, Tsukuba, 305-8501, Japan \n2Spin Quantum Rectification Project, ERATO, Japan Science and Technology Agency, Sendai, 980-8577, Japan \n3NEC TOKIN Corporation, Sendai, 982-8510, Japan \n4Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan \n5PRESTO, Japan Science and Technology Agency, Saitama, 332-0012, Japan \n6WPI, Advanced Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan \n7Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, 319-1195, Japan \n* e-mail: a-kirihara@cw.jp.nec.com \n \nHeat-flow sensing is expected to be an important technological component of smart thermal management in the \nfuture. Conventionally, the thermoelectric (TE) conversion technique, which is based on the Seebeck effect, has \nbeen used to measure a heat flow by converting the flow into electric voltage. However, for ubiquitous heat-flow \nvisualization, thin and flexible sensors with extremel y low thermal resistance are highly desired. Recently, \nanother type of TE effect, the longitudinal spin Seebeck effect (LSSE), has aroused great interest because the \nLSSE potentially offers favourable features for TE applications such as simple thin-film device structures. Here \nwe demonstrate an LSSE-based flexible TE sheet that is especially suitable for a heat-flow sensing application. \nThis TE sheet contained a Ni 0.2Zn0.3Fe2.5O4 film which was formed on a flexible plastic sheet using a spray-\ncoating method known as “ferrite plating”. The experimental results suggest that the ferrite-plated film, which \nhas a columnar crystal structure aligned perpendicular to the film plane, functions as a unique one-dimensional \nspin-current conductor suitable for bendable LSSE-based sensors. This newly developed thin TE sheet may be \nattached to differently shaped heat sources without obstructing an innate heat flux, paving the way to versatile \nheat-flow measurements and management.    2 \n        As efficient energy utilization is becoming a crucially important issue for sustainable future, a heat management \ntechnique to optimally control the flow of omnipresent thermal energy is currently of great interest. To realize smart thermal \nmanagement with real-time controllability, there has been a growing demand for visualizing the flow of heat in various \nplaces such as industrial facilities and large-scale data centres. The thermoelectric (TE) conversion technique [1-3], which \ndirectly converts a thermal gradient into an electric current, is one of the most powerful methods utilized to sense a heat flo w \nas a voltage signal. In fact, heat-flow sensors based on the Seebeck effect [4], which have thermopile structures consisting of  \nπ-structured thermocouples, are commercially available and used for various purposes such as the evaluation of materials.  \nTo further extend heat-flow-sensing capabilities to other widespread applications, however, such conventional devices \nface certain challenges. First, because Seebeck-based TE devices exhibit a relatively high heat resistance, the introduction of  \nthese devices into a heat-flow environment inevitably obstructs the heat flux and alters the distribution of the heat flow. \nTherefore, it is difficult to correctly evaluate the innate heat flux which we actually want to determine. Second, most of the \ncommercially available heat-flow sensors are rigid and not easily applied to curved or uneven surfaces, making it difficult to \nmonitor the heat flux around irregularly shaped heat sources. Because conventional TE devices, in which thermocouples are \nconnected electrically in series, are intrinsically vulnerable to bending stresses, materials and structures for flexible TE \ndevices have been extensively studied [5-7].  \n For such sensing applications, an emerging research field, spin caloritronics [8,9], will provide new device-design \nopportunities. For example, TE devices based on the anomalous Nernst effect (ANE), which exhibit transverse TE voltage in \nferromagnetic metals (FM), can be suitably utilized for sensing purposes [9-13]. In this work, we present another promising \napproach to realizing flexible heat flow sensors using the longitudinal spin Seebeck effect (LSSE) [14-18]. First reported in \n2010, the LSSE offers an unconventional method to design TE devices by making use of a physical quantity called a spin \ncurrent. The LSSE devices, typically composed of a ferromagnetic insulator (FI) and a normal metallic film (NM), have \ngained attention because of the simple device structure and novel scaling capability, leading to novel TE devices [16]. The \nLSSE also has potential to realize practical sensing applications. It is recently reported that (FI/NM) n multilayer structure \nunexpectedly exhibit significantly enhanced LSSE signal [19], which may lead to high-sensitive heat-flow sensors. \nFurthermore, combination of the LSSE and ANE is also a quite hopeful approach. In hybrid TE devices consisting of FI and \nFM layers, both the LSSE and ANE can constructively contribute to the output voltage, leading to largely enhanced TE \nsignals [20,21]. To pave the way for practical sensing applications using the LSSE, here we have demonstrated LSSE-based \nheat-flow sensing sheets.  3 \n  The concept of the LSSE-based flexible TE sheet is schematically depicted in Fig. 1. The sheet consists of a magnetic \n(ferro- or ferrimagnetic) film with in-plane magnetization M and a metallic film formed on a flexible substrate. When a heat \nflux q flows through the TE sheet perpendicularly to the film plane, a spin current density js is induced by q via the LSSE. \nThe value of js is proportional to q (|js| ∝ q). Then, js is converted into an electric field in the transverse direction via the \ninverse spin Hall effect (ISHE) [22,23]:  \n \nMMj Es ISHE × = ) ( ρ θSH (1). \nIn the above equation, θSH and ρ represent the spin-Hall angle and resistivity of the metallic film, respectively. Therefore, the \nvoltage signal V between the two ends of the TE sheet can be employed to evaluate the heat flux q penetrating through the \nsheet, because V is proportional to q (V = EISHE l ∝ q). Here, it should also be emphasized that a longer sheet length l \nstraightforwardly leads to larger output voltage V. This scaling law is in stark contrast to that of conventional TE devices, in \nwhich TE voltage scales with the number of thermocouples connected within the devices. These features enable us to design \nsimple bilayer-structured devices suitable for heat-flow sensors.  \n But there is a problem when we use the above setup for broad heat-flow sensing purposes. When q flows obliquely to the \nTE sheet, the in-plain component of q gives rise to another TE effect called the transverse spin Seebeck effect (TSSE) [24-28], \nwhich can also contribute to the output voltage. Since the mixed output signals from the LSSE and TSSE cannot be \ndistinguished from each other, the TSSE becomes an encumbrance to the correct evaluation of q penetrating the TE sheet in \nthis case. To exclude the TSSE contribution, here we used unique  one-dimensional (1D) spin-current conductor, which \nenables us to detect only the LSSE contribution and to correctly evaluate q flowing across the TE sheet.  \n  \nResults  \nFabrication of the LSSE-based TE sheet  To demonstrate such an LSSE-based flexible TE sheet, we used a spray-coating \ntechnique known as “ferrite plating” to grow ferrimagnetic films. Ferrites refer to oxide ceramics containing iron, which \ntypically exhibit ferromagnetic properties and have been successfully used as magnetic materials for LSSE devices [29,30]. \nHowever, conventional ferrite-film preparation techniques, such as liquid phase epitaxy and pulsed-laser deposition, require a \nhigh temperature process (400 – 800 °C) for crystallizing the ferrites, hindering the formation of films on soft-surfaced \nmaterials, such as plastics. By contrast, ferrite plating is based on a chemical reaction process in which the Fe ion is oxidiz ed 4 \n (Fe2+→Fe3+); therefore, no high-temperature processes, such as annealing, are required [31,32]. This feature enables us to \ncoat ferrite films on a variety of substrates, including plastic films.  \n In this work, we prepared a ferrite Ni 0.2Zn0.3Fe2.5O4 film using this method. As schematically illustrated in Fig. 2(a), we \ngrew the film by simultaneously spraying an aqueous reaction solution (FeCl 2+NiCl 2+ZnCl 2) and an oxidizer \n(NaNO 2+CH 3COONH 4) onto a substrate. In this process, the oxidizer oxidizes the chlorides in the reaction solution, forming \na Ni 0.2Zn0.3Fe2.5O4 film on the substrate. All the processes were performed below 100 °C.  \nA noticeable feature of the ferrite film, grown via such a layer-by-layer chemical process, was its columnar-crystal grain \nstructure. Figure 2(b) depicts the cross-sectional scanning electron microscope (SEM) image of a Ni 0.2Zn0.3Fe2.5O4 film that \nwas grown on a SiO 2/Si substrate for the purpose of the SEM observation. The diameter of the columnar grain was typically \napproximately 100 nm. We also verified via transmission electron microscopy and electron diffraction measurements that the \ncrystal orientation of the Ni 0.2Zn0.3Fe2.5O4 was coherently aligned within a single columnar grain. Such a columnar structure \ncan function as a 1D spin-current conductor favorable for LSSE-based (and TSSE-free) heat-flow sensors because of the \nfollowing two reasons. First, in the LSSE configuration shown in Fig. 1, a magnon spin current is driven along the columnar \ngrain and is thus less subject to grain scattering, effectively leading to the LSSE signal. Second, since the columnar-grain \nboundaries impede the transverse propagation of both magnons and phonons, in-plane components of a heat flow cannot \neffectively produce the TSSE in the light of previous studies (e.g., see ref. [33,34]). Thus we can exclude the possible TSSE \ncontribution, enabling us to correctly measure a heat flow penetrating the TE sheet via the LSSE.  \n Using the ferrite plating technique, we successfully fabricated a flexible TE sheet based on the LSSE. Fig. 2(c) \nrepresents a photograph of the prepared TE sheet. First, a 500-nm-thick Ni 0.2Zn0.3Fe2.5O4 film was grown on a 25- μm-thick \npolyimide substrate. Then, a Pt film with a thickness of 5 nm was formed on the Ni 0.2Zn0.3Fe2.5O4 film by means of \nmagnetron sputter deposition. As shown in Fig. 2(c), our TE sheet was highly flexible and easily bent without breaking the \nPt/Ni 0.2Zn0.3Fe2.5O4 film. The sheet was then cut into small pieces with a size of 8 × 4 mm2 for TE measurements.  \n \nDemonstration of the LSSE-based TE sheet for heat-flow sensing   To evaluate how well the LSSE-based TE sheet \nfunctioned as a heat-flow sensor, we investigated its TE property in the following fashion. A heat flux q was driven across \nthe 4 ×4-mm2 central area of the TE-sheet sample by sandwiching the sheet between two Peltier modules. While driving the \nheat flow in such a manner, we simultaneously monitored the exact value of q penetrating the TE-sheet sample with a \ncommercially available thin-plate-shaped heat-flow sensor, which was set immediately above the sample. Because the 5 \n commercial heat-flow sensor was placed in direct contact with the central area of the TE-sheet sample, we could assume that \nthe heat flux value monitored by the sensor was the same as the q actually penetrating across the sample. An external \nmagnetic field H, which controls the direction of the magnetization M of the Ni 0.2Zn0.3Fe2.5O4 films, was also applied to the \nentire system. The TE voltage V between the two ends of the Pt film was measured with two contact probes. The resistance of \nthe Pt film was determined to be RPt = 238 Ω.   \nFigure 2(d) represents V as a function of H, measured when heat fluxes of q = -13.7, -6.5, 0.0, 5.6, and 11.6 kW/m2 were \ndriven across the TE-sheet sample. The TE voltage was observed along the direction perpendicular to the direction of both q \nand H, as derived from equation 1 (see the inset of Fig. 2(d)). The result shows that the sign of V is flipped when q or H is \nreversed, which is a typical behaviour of LSSE-based devices. The heat-flux dependence of the TE voltage in Fig. 2(e) \nclearly demonstrates that V is proportional to q. The heat-flow sensitivity derived from the fitted line is V/q = 0.98 nV/(W/m2). \nThe demonstration of this linear relationship between V and q suggests that our LSSE-based TE sheet functioned as a heat-\nflow sensor.  \nIn an additional experiment, we have confirmed that the TE sheet exhibits no output signal when a temperature gradient \nwas applied in the in-plane direction (see Supplementary Information). It suggests that the TSSE is negligibly small in our \nferrite-plated film because of its 1D spin-current conducting property.  \n \nFerrite-thickness dependence of the LSSE-based TE sheet  We performed additional experiments to ascertain the origin \nof the observed TE signal. Given that a ferrite composed of Ni 0.2Zn0.3Fe2.5O4 is typically a semiconducting ferrimagnet with a \nsmall but non-zero electrical conductivity, it can exhibit the ANE, which also produces a transverse voltage in the same \nexperimental configuration as the LSSE. In our ferrite plated film, however, the in-plane electrical resistance of the \nNi0.2Zn0.3Fe2.5O4 film was too high to be measured, which may be partly attributed to the vertically oriented grain boundaries \nof the columnar-structured film. Due to this transverse electric insulation, we could not observe any signals originating from \nthe bulk ANE in the Ni 0.2Zn0.3Fe2.5O4. However, there still remains a possibility that the TE signal includes ANE contribution \ncaused by magnetic proximity effects at the Pt/Ni 0.2Zn0.3Fe2.5O4 interface [35].  \n To shed light on such TE conversion mechanism, we investigated the TE properties of samples with varied ferrite-film \nthicknesses tF.  Figure 3 presents the ferrite-thickness dependence of the heat-flow sensitivity ( V/q)Norm normalized to the \nsensitivity at tF = 500 nm. The ( V/q)Norm values monotonically increase for tF < 100 nm, whereas the tF dependence of V \nbecomes saturated for tF > 100 nm. The plots are well fitted to an exponential curve ( V/q)Norm = 1 - exp(- tF/λ) with λ = 71 nm. 6 \n Similar to recent LSSE studies using yttrium iron garnet (YIG) films [36], this ferrite-thickness dependence is consistently \nexplained according to the magnon-driven LSSE scenario [27,28,37,38], in which a certain ferrite thickness region \n(corresponding to the magnon-propagation length) below the Pt/ferrite interface effectively contributes to the voltage \ngeneration. On the other hand, the proximity-ANE scenario, which can occur at the Pt/Ni 0.2Zn0.3Fe2.5O4 interface, is not able \nto explain this dependence. Thus, our finding suggests that the obtained signal originated mainly from the bulk magnon spin \ncurrent driven by the LSSE. The result also suggests that our columnar-crystalline film possesses good spin-current-\nconduction properties suitable for LSSE-based sensors. Though it is beyond the scope of this work, such 1D spin-current \nconductors might have unconventional magnon-propagation properties which is different from that of 3D conductors, \nbecause magnon-scattering events can be altered in such confined structure. Control of magnon propagation in low-\ndimensional conductors will be an exciting research topic for future work from both academic and practical viewpoints.  \n  \nBending-curvature dependence of the LSSE-based TE sheet Finally, we investigated heat-flow-sensing capability of \nthe flexible LSSE-based TE sheet when the sheet was bent. Figure 4(a) and 4(b) depicts the H-dependence of the TE voltage \nV for the same Pt/Ni 0.2Zn0.3Fe2.5O4/polyimide sample when a heat flux q was applied across the samples over a 20 ×20-mm2 \narea under condition where the sample was flat or bent (with a radius of curvature of r = 17 mm), respectively. The \ndependence of the heat-flow sensitivity, V/q, on the curvature r-1 is presented in Fig. 4(c). The result clearly demonstrates that \nV/q is nearly constant independent of r-1, suggesting that the bending stresses applied to the Pt/Ni 0.2Zn0.3Fe2.5O4 films do not \nsignificantly affect the TE conversion process consisting of the LSSE and the ISHE. This TE property, i.e., the TE conversion \nis  independent of bending condition, is quite desirable for heat-flow sensing applications on various curved surfaces, because  \nwe are able to avoid additional calibration steps that depend on individual measuring objects with various surface curvature.  \n \nDiscussion \nWe successfully demonstrated that an LSSE-based flexible TE sheet with 1D spin-current conducting film functions as a \nheat-flow sensor. The ferrite-thickness dependence of the TE voltage suggests that the TE signal was caused predominantly \nby the LSSE, which is consistent with other reports using Pt/NiFe 2O4 [39]. The magnon-propagation length in our \nNi0.2Zn0.3Fe2.5O4 film perpendicular to the film plane is approximately 71 nm. The TE sheet exhibit nearly identical heat-flow \nsensitivity regardless of bending curvature, suggesting that our columnar-crystalline film retains good 1D spin-current-\nconduction properties even when bent. 7 \n Though the heat-flow sensitivity V/q of our TE sheet is not high in this stage, the outstanding features of it in contrast to \ncurrently available sensors are high flexibility in shape and remarkably low thermal resistance, which is a highly desirable \nfeature for versatile heat-flow sensing. Although we formed ferrite films on plastic substrates in this work, it is also possib le \nto directly plate various heat sources with ferrite films, thereby offering a thermal-sensing function while minimally \nobstructing the innate heat flux. Such features will offer a variety of opportunities for less destructive heat-flow \nmeasurements.  \nTo use the TE sheets for a wide range of practical applications, the heat-flow sensitivity V/q must be further improved. A \nstraightforward method to enhance the V/q is to enlarge the size of the TE sheet, as the output voltage scales linearly with the \nfilm length l. We can also increase the effective length  l inside a certain area by adopting meandering-patterned metallic film \nstructures [20,40]. Another strategy is to replace Pt. We investigated TE-sheet samples with different metallic materials \ninstead of Pt, and found that heat-flow sensitivity V/q of W/Ni 0.2Zn0.3Fe2.5O4 was 3.5-fold larger than that of \nPt/Ni 0.2Zn0.3Fe2.5O4 (see Supplementary Information). Moreover, we can enhance the sensitivity further by adopting recently \nreported (FI/NM) n multilayer structures [19], or FI/FM structure which can utilize both the SSE and ANE [20,21]. Although \nwe applied an external magnetic field H to the TE sheet for our experimental demonstration, this step is not necessary if the \nspontaneous magnetization M of the ferrite is sufficiently stable. The improvement of such magnetic stability is realized, for \nexample, by doping cobalt into ferrite-plated films, which is known to enhance a coercive field of the ferrites [41]. The \nLSSE-based heat-flow-sensing technique, in which a heat flux induces an electrical signal indirectly via an LSSE-driven spin \ncurrent, offers unconventional device-design opportunities, leading to novel heat-managing applications.  \n  8 \n Reference \n[1] Rowe, D.M. CRC Handbook of Thermoelectrics: Macro to Nano  (CRC Press, 2005). \n[2] Goldsmid, H. J. Introduction to Thermoelectricity  (Springer, 2010). \n[3] Bell, L. E. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science  321, \n1457-1461 (2008). \n[4] Van Herwaarden, A. W. & Sarro, P. M. Thermal sensors based on the Seebeck effect. Sensors and Actuators  10, 321-346 \n(1986). \n[5] Nonoguchi, Y. et al. Systematic conversion of single walled carbon nanotubes into n-type thermoelectric materials by \nmolecular dopants. Sci. Rep.  3, 3344 (2013). \n[6] Suemori, K., Hoshino, S. & Kamata, T. Flexible and lightweight thermoelectric generators composed of carbon nanotube-\npolystyrene composites printed on film substrate. Appl. Phys. Lett.  103, 153902 (2013).  \n[7] Fukumaru, T., Fujigaya, T. & Nakashima, N. Development of n-type cobaltocene-encapsulated carbon nanotubes with \nremarkable thermoelectric property. Sci. Rep. 5, 7951 (2015). \n[8] Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics. Nature Mater.  11, 391-399 (2012). \n[9] Boona, S. R., Myer, R. C. & He remans, J. P. Spin caloritronics. Energy Environ. Sci.  7, 885-910 (2014). \n[10] Lee, W.-L., Watauchi, S., Miller, V. L., Cava, R. J. & On g, N. P. Anomalous Hall heat current and Nernst effect in the \nCuCr 2Se4-xBrx ferromagnet. Phys. Rev. Lett.  93, 226601 (2004). \n[11] Miyasato, T. et al. Crossover behavior of the anomalous Hall effect and anomalous Nernst effect in itinerant \nferromagnets. Phys. Rev. Lett. 99, 086602 (2007). \n[12] Mizuguchi, M., Ohata, S., Uchida, K., Saitoh, E. & Takanashi, K. Anomalous Nernst effect in L1 0-ordered epitaxial FePt \nthin film. Appl. Phys. Express  5, 093002 (2012). \n[13] Sakuraba, Y. et al. Anomalous Nernst effect in L1 0-FePt/MnGa thermopiles for new thermoelectric applications. Appl. \nPhys. Express  6, 033003 (2013).   \n[14] Uchida K. et al. Observation of longitudinal spin-Seebeck effect in magnetic insulator. Appl. Phys. Lett. 97, 172505 \n(2010).  \n[15] Uchida, K. et al. Longitudinal spin Seebeck effect: from fundamentals to applilcations. J. Phys.: Condens. Matter  26, \n343202 (2014). \n[16] Kirihara, A. et al. Spin-current-driven thermoelectric coating. Nat. Mater.  11, 686-689 (2012). 9 \n [17] Siegel, G., Prestgard, M. C., Teng, S. & Tiwari, A. Robust longitudinal spin-Seebeck effect in Bi-YIG thin films. Sci. \nRep. 4, 4429 (2014). \n[18] Saiga, Y. et al. Platinum thickness dependence and annealing effect of the spin-Seebeck voltage in platinum yttrium iron \ngarnet structures. Appl. Phys. Express  7, 093001 (2014). \n[19] Ramos, R. et al. Unconventional scaling and significant enhancement of the spin Seebeck effect in multilayers. Phys. \nRev. B  92, 220407(R) (2015). \n[20] Miao, B. F., Huang, S. Y., Qu, D. & Chien, C. L. Inverse spin Hall effect in a ferromagnetic metal.  Phys. Rev. Lett.  111, \n066602 (2013). \n[21] Kikkawa, T. et al. Separation of longitudinal spin Seebeck effect from anomalous Nernst effect: Determination of origin \nof transverse thermoelectric voltage in metal/insulator junctions. Phys. Rev. B  88, 214403 (2013). \n[22] Saitoh, E., Ueda, M., Miyajima, H. & Tatara G. Conversion of spin current into charge current at room temperature: \nInverse spin-Hall effect. Appl. Phys. Lett.  88, 182509 (2006). \n[23] Valenzuela, S. O. & Tinkham, M. Direct electronic measurement of the spin hall effect. Nature  442, 176-179 (2006). \n[24] Uchida, K. et al. Observation of the spin Seebeck effect. Nature  455, 778-781 (2008). \n[25] Uchida, K. et al. Spin Seebeck insulator. Nat. Mater. 9, 894-897 (2010). \n[26] Jaworski, C. et al. Observation of the spin-Seebeck effect in a ferromagnetic semiconductor. Nat. Mater.  9, 898-903 \n(2010). \n[27] Xiao, J., Bauer, G. E. W., Uchida, K., Saitoh, E. & Maekawa, S. Theory of magnon-driven spin Seebeck effect. Phys. \nRev. B  81, 214418 (2010). \n[28] Adachi, H., Ohe, J., Takahashi, S. & Maekawa, S. Linear-response theory of spin seebeck effect in ferromagnetic \ninsulator. Phys. Rev. B  83, 094410 (2011). \n[29] Uchida, K., Nonaka, T., Ota, T. & Saitoh, E. Longitudinal spin-Seebeck effect in sintered polycrystalline (Mn,Zn)Fe 2O4. \nAppl. Phys. Lett.  97, 262504 (2010). \n[30] Uchida, K., Nonaka, T., Kikkawa, T., Kajiwara. Y. & Saitoh, E. Longitudinal spin Seebeck effect in various garnet \nferrites. Phys. Rev. B 87, 104412 (2013). \n[31] Abe, M., Itoh, T. & Tamaura, Y. Magnetic and biomagnetic films obtained by ferrite plating in aqueous solution. Thin \nSolid Films 216, 155-161 (1992). \n[32] Kondo, K., Yoshida, S., Ono, H. & Abe, M. Spin sprayed Ni(-Zn)-Co ferrite films with natural resonance frequency \nexceeding 3 GHz. J. Appl. Phys.  101, 09M502 (2007). 10 \n [33] Uchida, K. et al. Thermal spin pumping and magnon-phonon-mediated spin-Seebeck effect. J. Appl. Phys.  111,  103903 \n(2012). \n[34] Adachi, H., Uchida, K., Saitoh, E. & Maekawa, S. Theory of the spin Seebeck effect. Rep. Prog. Phys. 76, 036501 \n(2013). \n[35] Huang, S. Y. et al. Transport magnetic proximity effects in Platinum. Phys. Lev. Lett.  109, 107204 (2012). \n[36] Kehlberger, A. et al. Length scale of the spin Seebeck effect. Phys. Lev. Lett.  115, 096602 (2015). \n[37] Hoffman, S., Sato, K., & Tserkovnyak, Landau-Lifshitz theory of the longitudinal spin Seebeck effect. Phys. Rev. B  88, \n064408 (2013). \n[38] Rezende, S. M. et al. Magnon spin-current theory for the longitudinal spin-Seebeck effect. Phys. Rev. B 89, 014416 \n(2014). \n[39] Meier, D. et al. Thermally driven spin and charge currents in thin NiFe 2O4/Pt films.  Phys. Rev. B 87, 054421 (2013). \n[40] Uchida, K. et al. Enhancement of spin-Seebeck voltage by spin-hall thermopile. Appl. Phys. Express  5, 093001 (2012). \n[41] Matsushita N., Nakamura T. & Abe, M. Ni-Zn-Co ferrite films prepared at 90 °C having  μ”=30 at 3 GHz. IEEE Trans. \nMagn.  38, 3111-3113 (2002).   F\nf\ns\nc\nb\nFigure 1 | Co\nfilm and a ma\nsheet, a spin c\nconverted int o\nbilayer struct u\nncept of TE s\nagnetic (ferro- \ncurrent js is in d\no an electric v o\nure of the TE s\nsheet for hea t\nor ferrimagn e\nduced and inj e\noltage V as a r\nsheet allows u\nt-flow sensin g\netic) film for m\nected from th e\nresult of the i n\nus to design n o\n11 g based on th e\nmed on a flexi b\ne ferrite film i n\nnverse spin H a\novel hea t-flow \ne LSSE . The L\nble substrate. W\nnto the metall i\nall effect (ISH E\nsensors with l\nLSSE- based T\nWhen a heat f l\nic film by the L\nE) in the met a\nlow thermal r e\nTE shee t consi\nlux q flows th r\nLSSE. Then t h\nallic film. The \nesistance and a\n \nsts of a metal l\nrough the TE \nhe js is finally \nthin and sim p\na flexible sha p\nlic \nple \npe.   F\nA\nm\nm\n(\np\na\nf\n \nFigure 2 | De m\nAn aqueous r e\nmounted on a \nmethod. The f\n(c) Photograp h\npolyimide su b\nacross the TE \nfunction of q. \nmonstration o\neaction soluti o\nrotating stag e\nfilm exhibits a\nh of an LSSE -\nbstrate.  (d) T E\nsheet. The si g\nFrom the fitti\nof heat-flow- s\non (FeCl 2+NiC\ne. (b) SEM im a\na columna r-cry\n-based flexibl e\nE voltage V as \ngn of V is rev e\nng with the s o\nsensin g TE s h\nCl2+ZnCl 2) and\nage of a Ni 0.2Z\nystal structure\ne TE sheet, in \na function of \nersed, when t h\nolid line, the h\n12 heet based o n\nd an oxidizer (\nZn0.3Fe2.5O4 fil\n. The typical d\nwhich a Pt/N i\nan external m\nhe sign of H or\nheat-flow sens i\nn the LSSE.   (\n(NaNO 2+CH 3\nlm grown on a\ndiameter of th e\ni0.2Zn0.3Fe2.5O4\nmagnetic field H\nr q changes. ( e\nitivity of this T\na) Schematic \nCOONH 4) are\na SiO 2/Si sub s\ne columnar g r\n4 film was for\nH, measured w\ne) TE voltage f\nTE sheet was \n \nof the ferrite- p\ne sprayed ont o\nstrate using th e\nrains is appro x\nmed on a 25- μ\nwhen a heat fl u\nfrom the TE s h\nV/q = 0.98 n V\nplating metho d\no a substrate \ne ferrite-plati n\nximately 100 n\nμm-thick \nux q was appl i\nheet as a \nV/(W/m2).  d. \nng \nnm. \nied  F\ne\n \nF\nf\na\nFigure 3 | Fe r\nV/q, where th e\nexponential c u\nFigure 4 | He\nfunction of a n\narea. (b) H dep\nrrite-film-thi c\ne longitudinal \nurve (V/q)Norm \nat-flow sensi n\nn external ma g\npendence of t h\nckness depen\naxis is norm a\n= 1-exp(- tF/λ\nng with a be n\ngnetic field H m\nhe TE voltag e\ndence of LS S\nalized by the s e\nλ) with λ = 71 \nnt TE sheet.  (a\nmeasured wh e\ne V from a Pt/ N\n13 SE-based TE s\nensitivity a t tF\nnm, consiste n\na) TE voltage \nen the heat flu x\nNi0.2Zn0.3Fe2.5O\n \nsheets.  The tF\n= 500 nm. T h\nnt with the ma g\nV from a flat P\nx q was appli e\nO4/polyimide s\nF dependence o\nhe dependenc e\ngnon-driven L\nPt/Ni 0.2Zn0.3Fe\ned across the s\nsample that w\nof the hea t-flo\ne is well fitted \nLSSE scenario\ne2.5O4/polyim i\nsample over a \nwas bent with a\now sensitivity \nby an \n.  \nide sample as \n20×20-mm2 \na radius of \n \na \n14 \n curvature  r = 17 mm, when the heat flux q was applied across the sample over a 20 ×20-mm2 area. (c) Heat-flow sensitivity \nV/q as a function of curvature r-1, indicating that V/q is almost independent of r-1.   \n \n  15 \n Methods \nSample preparation. To prepare the Ni 0.2Zn0.3Fe2.5O4 film for the TE sheet via a ferrite plating method, we first mounted a \n25-μm-thick polyimide substrate on a rotating stage and then sprayed an aqueous reaction solution (FeCl 2+NiCl 2+ZnCl 2) and \nan oxidizer (NaNO 2+CH 3COONH 4) from two nozzles placed above the stage, as shown in Fig. 2a. This setup enabled us to \ngrow the ferrite film by alternating adsorption and oxidation of the ingredient materials (including Fe, Ni, and Zn). During \nthe process, the temperature of the stage was maintained at approximately 90 °C. The thickness of the Ni 0.2Zn0.3Fe2.5O4 film \nwas controlled via the time period of this formation process. The composition of the ferrite film was analysed by inductively \ncoupled plasma spectroscopy (ICPS).A Pt film was deposited on the top of the Ni 0.2Zn0.3Fe2.5O4 film with a magnetron \nsputtering system. Immediately before the sputtering process, the sample was exposed to argon plasma for 10 s to clean the \nsurface of the Ni 0.2Zn0.3Fe2.5O4.    \n \nTE conversion measurements. To evaluate the TE conversion of a heat flow to electric voltage, the sample was cut into \nsmall 8 × 4-mm2 pieces using a cutter. To investigate the heat-flow-sensing properties of the LSSE-based TE sheet, we drove \na heat flow across the sheet using two commercial 4 × 4-mm2 Peltier modules. The two Peltier modules were attached to the \ntop and bottom of the TE sheet, enabling us to heat one side and cool the other side of the TE sheet. The temperature \ndifference, applied in such a manner, led to a heat flux penetrating through the TE sheet. Because the in-plane thermal \nconductance in our thin TE sheet was quite small, we can assume that the direction of the heat flux was nearly perpendicular \nto the TE sheet. While driving the heat flow, we simultaneously monitored the exact value of q penetrating the TE sheet \nusing a commercial thin-plate-shaped heat-flow sensor. The sensor was placed between the upper Peltier module and the TE \nsheet, in direct contact with the Pt film of the TE sheet. With this setup, we can assume that the same amount of heat flux q \nflowed across both the TE sheet and the sensor. The generated TE voltage was measured with a digital multimeter.  \n \nTE measurements of the bent samples.  To evaluate bent LSSE-based TE sheets as shown in Fig. 4, we used pairs of oxide-\ncoated aluminium blocks with curved (concave and convex) surfaces. In the experiments, the TE sheet was sandwiched by \nthe concave and convex blocks with a certain bending curvature. To investigate the bending-curvature dependence, we \nprepared several pairs of such blocks with different surface curvatures, in which the lateral size of the blocks was fixed to \n20×20 mm2. The heat-flow-sensing properties of the bent TE sheets were evaluated in the same manner as described above. \nThe heat flux was driven across the TE sheet by two Peltier modules attached to the top and bottom of the block pair that 16 \n sandwiched the sheet. Commercially available 20 ×20-mm2 heat-flux sensors were also used to monitor the level of the heat \nflux penetrating across the TE sheet.  \n \nAcknowledgements  \nThis work was partially supported by PRESTO “Phase Interfaces for Highly Efficient Energy Utilization” from JST, Japan, \nGrant-in-Aid for Scientific Research on Innovative Area, “Nano Spin Conversion Science” (No. 26103005), Grant-in-Aid for \nChallenging Exploratory Research (No. 26600067), and Grant-in-Aid for Scientific Research (A) (No. 15H02012) from \nMEXT, Japan.  \n \nAuthor contributions  \nA. K., M. I., K. U., E. S., S. K. and T. M. designed the experi mental plan. A. K., K. K., H. S. and N. Y. mainly worked on \nsample preparation. A. K., M. I., K. I., Y. I. and A. M. performed the TE-conversion experiments. All the authors contributed \nto the analysis and discussion of the research.  \n \nAdditional information  \nThe authors declare no competing financial interests.  \n  17 \n Supplementary Information:  \nFlexible heat-flow sensing sheets base d on the longitudinal spin Seebeck \neffect using one-dimensional spin-current conducting films \n \nAkihiro Kirihara1,2*, Koichi Kondo3, Masahiko Ishida1,2, Kazuki Ihara1,2, Yuma Iwasaki1, Hiroko \nSomeya1,2, Asuka Matsuba1, Ken-ichi Uchida4,5, Eiji Saitoh2,4,6,7, Naoharu Yamamoto3, Shigeru \nKohmoto1 and Tomoo Murakami1 \n \n1Smart Energy Research Laboratories, NEC Corporation, Tsukuba, 305-8501, Japan \n2Spin Quantum Rectification Project, ERATO, Japan Science and Technology Agency, Sendai, 980-8577, Japan \n3NEC TOKIN Corporation, Sendai, 982-8510, Japan \n4Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan \n5PRESTO, Japan Science and Technology Agency, Saitama, 332-0012, Japan \n6WPI, Advanced Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan \n7Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, 319-1195, Japan \n  \nTE experiment in TSSE setup  We have performed additional experiments to check whether transverse spin Seebeck \neffect (TSSE) [1-3] contributes to the TE signal in our devices. The schematics of the experimental setup is shown in Fig \nS1(a). For the TSSE experiment, we prepared a TE-sheet sample in a similar fashion as described in the main article. In the \nsample, a 20 × 5-mm2 Pt strip with a thickness of 5 nm was formed on an edge of 20 × 20-mm2 ferrite-plated film, as shown \nin Fig. S1(a). To investigate the TSSE, output voltage V along the y-direction between two ends of the Pt strip was measured, \nwhen a temperature difference ΔT was applied in the x-direction. To magnetize the ferrite-plated film, an external magnetic \nfield H was also applied in the x-direction. If the TE-sheet sample exhibits the TSSE, output voltage is expected to occur in \nthe y-direction. Figure S1(b) shows the measured V as a function of H when ΔT = 1.1K was applied to the sample, where no \noutput signal was clearly observed. The result suggests that our TE sheet with a ferrite-plated film having one-dimensional \nspin-current conducting properties does not exhibit any TE voltage originating from the TSSE, since a transverse spin current \nis effectively blocked by its columnar crystalline structure.  \n \nLSSE-based TE sheets with different metallic films  To gain further insights into the TE mechanism, we also prepared \nand evaluated TE sheets using different metal-film materials instead of Pt. TE measurements were performed in the same \nexperimental configuration as mentioned above. Figure S2(a) represents the TE voltage from a sample composed of a 10-nm-\nthick Cu film and a 500-nm- thick Ni 0.2Zn0.3Fe2.5O4 film on a polyimide substrate, showing that the output voltage from the 18 \n Cu film is negligibly small. This result is consistent with the negligible ISHE in Cu, which has a weak spin-orbit interaction.  \nFigure S2(b) shows the experimental result of a TE sheet in which a W film with a thickness of 5 nm was deposited on the \nsame Ni 0.2Zn0.3Fe2.5O4/polyimide substrate. In this case, the clear TE voltage V was observed and its sign was found to be \nopposite to that of the Pt/ Ni 0.2Zn0.3Fe2.5O4 sample (compare Fig. S2(b) with Fig. 2(d) in the main article), which is consistent \nwith the fact that the spin-Hall angle of W has a sign opposite to that of Pt [4,5]. Notably, the heat-flow sensitivity of the \nW/Ni 0.2Zn0.3Fe2.5O4 sensor is V/q = 3.55 nV/(W/m2), a value 3.5-fold greater than that of the Pt/Ni 0.2Zn0.3Fe2.5O4, although the \nW-film resistance between the ends of the sample ( RW = 2.04 k Ω) was an order of magnitude greater than that of the Pt film. \nThis large value suggests that W appears to be a promising material for heat-flow sensing applications.  \n \nReference \n[1] Uchida, K. et al. Observation of the spin Seebeck effect. Nature  455, 778-781 (2008). \n[2] Uchida, K. et al. Spin Seebeck insulator. Nat. Mater. 9, 894-897 (2010). \n[3] Jaworski, C. et al. Observation of the spin-Seebeck effect in a ferromagnetic semiconductor. Nat. Mater.  9, 898-903 \n(2010). \n[4] Tanaka, T. et al. Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals. Phys. Rev. B  77, 165117 \n(2008). \n[5] Ishida, M. et al. Observation of longitudinal spin Seebeck effect with various transition metal films. arXiv:1307.3320. \n    \nF\nv\ni\nv\n \nF\ns\nv\no\nFigure S1 | T\nvoltage V alon\nin the x-direc t\nvoltage V as a\nFigure S2 | S S\nsample as a f u\nvoltage was n\nobtained with \nE experimen t\nng the y-direc t\ntion. To magn e\na function of e x\nSE-based TE\nunction of an e\negligibly sma l\nthe same me a\nt in transver s\ntion between t\netize the ferri t\nxternal magn e\n sheets with d\nexternal magn\nll, due to the s\nasurement set u\nse-SSE setup .\ntwo ends of th e\nte, an external \netic fiel d H wh\ndifferent met a\netic field H, m\nsmall ISHE in \nup. The volta g\n19 . (a) Experim e\ne Pt strip was \nmagnetic fiel\nhen ΔT = 1.1 K\nallic films.  (a)\nmeasured whe n\nCu. (b) TE v o\nge signal has a \nental set up fo r\nmeasured wh e\nd H was also a\nK was applied t\n) TE voltage V\nn the heat flu x\noltage V from \nsign opposit e\nr checking the\nen temperatu r\napplied in the \nto the sample .\nV from a Cu/ N\nx q was applie d\na W/Ni 0.2Zn0.3\ne to that of the \n transverse S S\nre difference Δ\nx-direction. ( b\n. \nNi0.2Zn0.3Fe2.5O\nd across the s a\n3Fe2.5O4/polyi\nPt/Ni0.2Zn0.3F\n \nSE. Output \nΔT was applie d\nb) Measured \nO4/polyimide \nample. The \nmide sample \nFe2.5O4 sampl e\nd \n \ne \n20 \n because the spin-Hall angle of W has the opposite sign to that of Pt. (c) TE voltage from the TE sheet W/Ni 0.2Zn0.3Fe2.5O4 \ncompared with that from Pt/Ni 0.2Zn0.3Fe2.5O4 as a function of q. According to the fitting with the solid line, the heat-flow \nsensitivity of W/Ni 0.2Zn0.3Fe2.5O4 was evaluated to be V/q = 3.55 nV/(W/m2), which is more than 3 times larger than that of \nPt/Ni 0.2Zn0.3Fe2.5O4. \n "    },    {        "title": "2302.03100v1.Observation_of_Coherently_Coupled_Cation_Spin_Dynamics_in_an_Insulating_Ferrimagnetic_Oxide.pdf",        "content": "Observation of Coherently Coupled Cation Spin Dynamics in an Insulating\nFerrimagnetic Oxide\nC. Klewe,1,a)P. Shafer,1J. E. Shoup,2C. Kons,2Y. Pogoryelov,3R. Knut,3B. A. Gray,4H.-M. Jeon,5\nB. M. Howe,4O. Karis,3Y. Suzuki,6, 7E. Arenholz,1D. A. Arena,2,b)and S. Emori6, 8,c)\n1)Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA,\nUSA\n2)Department of Physics, University of South Florida, Tampa, FL, USA\n3)Department of Physics and Astronomy, Molecular and Condensed Matter Physics, Uppsala University, Uppsala,\nSweden\n4)Materials and Manufacturing Directorate, Air Force Research Lab, Wright Patterson Air Force Base, OH,\nUSA\n5)KBR, Beavercreek, OH, USA\n6)Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA,\nUSA\n7)Department of Applied Physics, Stanford University, Stanford, CA, USA\n8)Department of Physics, Virginia Tech, Blacksburg, VA, USA\n(Dated: 9 January 2023)\nMany technologically useful magnetic oxides are ferrimagnetic insulators, which consist of chemically distinct\ncations. Here, we examine the spin dynamics of di\u000berent magnetic cations in ferrimagnetic NiZnAl-ferrite\n(Ni0:65Zn0:35Al0:8Fe1:2O4) under continuous microwave excitation. Speci\fcally, we employ time-resolved x-ray\nferromagnetic resonance to separately probe Fe2+=3+and Ni2+cations on di\u000berent sublattice sites. Our results\nshow that the precessing cation moments retain a rigid, collinear con\fguration to within \u00192\u000e. Moreover, the\ne\u000bective spin relaxation is identical to within <10% for all magnetic cations in the ferrite. We thus validate\nthe oft-assumed \\ferromagnetic-like\" dynamics in resonantly driven ferrimagnetic oxides, where the magnetic\nmoments from di\u000berent cations precess as a coherent, collective magnetization.\nMagnetic insulators are essential materials for\ncomputing and communications devices that rely\non spin transport without net charge transport1,2.\nMost room-temperature magnetic insulators possess\nantiferromagnetically coupled sublattices3{7. Many\nare true antiferromagnets with prospects for ultrafast\nspintronic devices3{5. Yet, challenges remain in\ncontrolling and probing the magnetic states of\nantiferromagnets8{10. For practical applications,\nperhaps more promising insulators are ferrimagnetic\noxides6,7,11{ such as iron garnets and spinel ferrites {\nthat possess unequal sublattices incorporating di\u000berent\ncations. The magnetization state in such ferrimagnets\ncan be straightforwardly controlled and probed by well-\nestablished methods, i.e., via applied magnetic \felds and\nspin currents7. Further, the properties of ferrimagnetic\noxides (e.g., damping, anisotropy) can be engineered\nby deliberately selecting the cations occupying each\nsublattice6,11,12.\nMost studies to date have e\u000bectively treated\nferrimagnetic oxides as ferro magnets: the cation\nmagnetic moments are presumed to remain collinear\nand coherent while they are excited, such that they\nbehave as one \\net\" magnetization (i.e., the vector sum\nof the cation moments). However, it is reasonable\na)Electronic mail: cklewe@lbl.gov\nb)Electronic mail: darena@usf.edu\nc)Electronic mail: semori@vt.eduto question how much these cation moments can\ndeviate from the ferromagnetic-like dynamics. Such\ndeviations may be plausible, considering that the\ncoupling among the cations may not be perfectly rigid\nor that di\u000berent magnetic cations in the sublattices\nmay exhibit di\u000berent rates of spin relaxation (e\u000bective\ndamping)11,12. Indeed, a recent experimental study on\nbiaxial yttrium iron garnet demonstrates peculiar spin-\ntorque switching results13, suggesting that ferrimagnetic\noxides { even with a large net magnetization { could\ndeviate from the expected ferromagnetic-like dynamics.\nGiven the application potential and fundamental interest,\nit is timely to explore the dynamics of speci\fc sublattices\nand cations in ferrimagnetic oxides.\nIn this Letter, we present unprecedented experimental\ninsight into resonant spin dynamics in a multi-\ncation ferrimagnetic oxide. Speci\fcally, we investigate\nsublattice- and cation-speci\fc dynamics in NiZnAl-\nferrite (Ni 0:65Zn0:35Al0:8Fe1:2O4), a spinel ferrimagnetic\noxide with two magnetic sublattices [Fig. 1]: (i) the\ntetrahedrally coordinated sublattice, Td, predominantly\nconsisting of Fe3+\nTdcations and (ii) the octahedrally\ncoordinated sublattice, Oh, predominantly consisting\nof Fe3+\nOh, Fe2+\nOh, and Ni2+\nOhcations. We utilize x-ray\nferromagnetic resonance (XFMR)14{26, which leverages\nx-ray magnetic circular dichroism (XMCD) that is\nsensitive to chemical elements, site coordination, and\nvalence states. With this XFMR technique, we detect\nthe precessional phase and amplitude for each magnetic\ncation species.\nOur cation-speci\fc XFMR measurements are furtherarXiv:2302.03100v1  [cond-mat.mtrl-sci]  6 Feb 20232\naugmented by the following attributes of NiZnAl-ferrite.\nFirst, the NiZnAl-ferrite \flm exhibits about two orders\nof magnitude lower magnetic damping than the ferrite\nin an earlier XFMR study19, yielding a far greater\nsignal-to-noise ratio in XFMR measurements. This\npermits comprehensive measurements at multiple applied\nmagnetic \felds, which allow precise quanti\fcation of the\nprecessional phase lags among the cation species. Second,\nNiZnAl-ferrite is an intriguing test-bed for exploring\nwhether the excited magnetic cations retain collinear\ncoupling. The nonmagnetic Zn2+and Al3+cations dilute\nthe magnetic exchange coupling in NiZnAl-ferrite27, as\nevidenced by a modest Curie temperature of \u0019450 K28,\nsuch that the magnetic Fe2+=3+and Ni2+cations may\nnot remain rigidly aligned. Lastly, with diverse magnetic\ncations in NiZnAl-ferrite, we address whether cations\nwith di\u000berent spin-orbit coupling can exhibit distinct\nspin relaxation12by quantifying the FMR linewidths and\nprecessional cone angles for the di\u000berent cations. Taken\ntogether, we are able to probe { with high precision { the\npossible deviation from the oft-assumed ferromagnetic-\nlike dynamics in the ferrimagnetic oxide.\nOur study focuses on a 23-nm thick epitaxial NiZnAl-\nferrite \flm grown on (001) oriented, isostructural\nMgAl 2O4substrates by pulsed laser deposition28.\nThe NiZnAl-ferrite \flm, magnetized along the [100]\ndirection, was probed at room temperature with a\ncircularly polarized x-ray beam at Beamline 4.0.2 at\nthe Advanced Light Source (ALS), Lawrence Berkeley\nNational Laboratory. The XFMR measurements follow\na pump-probe method: the RF excitation (4-GHz pump)\nis synchronized to a higher harmonic of the x-ray\npulse frequency (500-MHz probe), and the transverse\ncomponent of the precessing magnetization is probed\nstroboscopically. A variable delay between the RF\npump signal and the timing of the x-ray pulses enables\nmapping of the complete magnetization precession cycle.\nA photodiode mounted behind the sample collects\nthe luminescence yield from the subjacent MgAl 2O4\nsubstrate. The luminescence yield detection enables the\nFIG. 1. Schematic of a portion of the spinel structure,\nshowing two cations (e.g., Fe3+\nOh, Ni2+\nOh) occupying the\noctahedrally-coordinated sublattice (green and purple) and\na cation (e.g., Fe3+\nTd) occupying the tetrahedrally-coordinated\nsublattice (blue). The gray spheres represent oxygen anions.\n858 856 854 852\nenergy (eV)-0.15-0.10-0.050.000.050.10XMCD (arb. units)\n712 710 708 706\nenergy (eV)Fe2+\nOhFe3+\nOh\nFe3+\nTdNi2+\nOhFIG. 2. Static XMCD spectra taken at the L3edge of\nFe and Ni. The characteristic peaks are attributed to\nthe corresponding cation valence states and sublattice site\noccupation.\ninvestigation of high-quality epitaxial \flms on single-\ncrystal substrates20,22,23,26. This is in contrast to\ntransmission detection that is limited to polycrystalline\n\flms on thin membrane substrates17,19. A more detailed\ndescription of the XFMR setup is provided in Refs. 25\nand 26.\nBy tuning the photon energy to the element- and\ncoordination-speci\fc features in the static XMCD\nspectra, we are able to probe the magnetism of\ndi\u000berent elements, valence states, and sublattice sites\nindividually . Static XMCD spectra at the L3edge of\nFe and Ni are shown in Fig. 2. The spectra show\npronounced peaks from di\u000berent cations on the Ohand\nTdsublattices. While an XMCD spectrum is generally\na complicated superposition of di\u000berent coordinations\nand valence states, the three distinct peaks in the Fe\nL3spectrum at 708 :0 eV, 709:2 eV, and 710 :0 eV are\nattributed to Fe2+\nOh, Fe3+\nTd, and Fe3+\nOh, respectively, to a\ngood approximation29,30. The opposite polarities of the\nFe3+\nTdand Fe2+=3+\nOhpeaks re\rect the antiferromagnetic\ncoupling between the TdandOhsublattices at static\nequilibrium. Ni2+cations predominantly occupy the Oh\nsublattice28,29, such that the XMCD peak at 853 :5 eV is\nassigned to Ni2+\nOh.\nXFMR measurements were carried out at the photon\nenergies speci\fc to the cations found above. For\neach cation, we performed phase delay scans to map\nout the precession at di\u000berent \feld values across the\nresonance \feld \u00160Hres. Figure 3(a) displays a set of\nphase delay scans taken at a photon energy of 710 :0 eV,\ncorresponding to Fe3+\nOh. Each scan was taken at a \fxed\nbias \feld between 17 :0 mT and 21 :6 mT. The phase delay\nscans exhibit pronounced oscillations with a periodicity\nof 250 ps in accordance with the 4-GHz excitation.\nFigure 3(b) depicts delay scans for Fe3+\nTd(709:2 eV) and\nFe3+\nOh(710:0 eV) taken at \u00160H= 19.3 mT (center of\nthe resonance curve). The opposite sign of the two\noscillations indicates a phase shift of about 180\u000ebetween\nthe two sublattices. The result in Fig. 3(b) thus suggests\nthat the moments of Fe3+\nTd(709:2 eV) and Fe3+\nOhin NiZnAl-3\nXFMR (arb. units)17.0 mT\n17.9 mT\n18.3 mT\n18.5 mT\n18.7 mT\n18.9 mT\n19.1 mT\n19.3 mT\n19.5 mT\n19.7 mT\n19.9 mT\n20.1 mT\n20.3 mT\n20.7 mT\n21.6 mTexp. data Sine fit Fe3+\nOh\n500 400 300 200 100\nphase delay (ps)(a) XFMR (arb. units)\n500 400 300 200 100\nphase delay (ps)(b)Fe3+\nOhSine fit Fe3+\nTdSine fit\n(19.3    0.1) mT +\nFIG. 3. (a) Bias \feld resolved phase delay scans at the\nresonant core level excitation energy of Fe3+\nOh(710:0 eV). The\ndashed curve highlights the characteristic shift across the\nresonance. (b) Comparison between delay scans of Fe3+\nTd\n(709:2 eV) and Fe3+\nOh(710:0 eV) cations taken at 19 :3 mT.\nferrite maintain an antiferromagnetic alignment during\nresonant precession.\nIn the remainder of this Letter, we quantify the\nprecessional phase and relaxation of each cation\nby analyzing our \feld-dependent XFMR results,\nsummarized in Fig. 4. Figure 4(a) shows that all cations\nin NiZnAl-ferrite exhibit a characteristic 180\u000ephase\nreversal across the resonance of a damped harmonic\noscillator. Quick visual inspection reveals that all Oh\ncations are approximately in phase. Further, the Oh\nandTdcations are approximately 180\u000eout of phase,\nas expected for the precession of antiferromagnetically\ncoupled moments.\nTo quantify the phase lag among the cations precisely,\nthe \feld dependence of the precessional phase \u001efor each\ncation is modeled with\n\u001e=\u001e0+ arctan\u0012\u0001Hhwhm\nH\u0000Hres\u0013\n; (1)where\u001e0is the baseline of the precessional phase (set\nto 0 for Fe3+\nOh) and \u0001Hhwhm is the half-width-at-half-\nmaximum FMR linewidth. Equation 1 is equivalent\nto the expressions in Refs. 17 and 21 and valid when\nthe e\u000bective magnetization (including the out-of-plane\nmagnetic anisotropy) \u00160Me\u000b\u00191 T28is much larger than\nthe applied bias \feld \u00160H\u001920 mT. We quantify Hres\nandHhwhm by simultaneously \ftting the \feld dependence\nof the precessional phase \u001e[Eq. 1] and of the precessional\namplitudeA,\nA/s\n\u0001Hhwhm2\n\u0001Hhwhm2+ (H\u0000Hres)2: (2)\nTo account for reduced sensitivity far from the resonance,\nthe \fts in Fig. 4(a,c) are weighted using the error\nbars from the sinusoidal \fts of the phase delay scans\n(e.g., Fig. 3(b)). The results of the \ftting are shown\nin Fig. 4(a,c) and Table I.\nIf the magnetic moments of the four cations were\nperfectly collinear, the phase lag should be \u001e0= 0 for\ntheOhcation species whereas \u001e0= 180\u000efor theTd\ncation species. Taking Fe3+\nOhas the reference, the results\nin Table I show that \u001e0deviates by\u00191.5\u000efrom the\nperfect collinear scenario. However, we caution that the\nuncertainty of \u001e0in Table I is likely underestimated.\nIndeed, by examining the residuals of the \fts displayed\nin Fig. 4(b), we observe a scatter in the measured\nprecessional phase of at least \u00192\u000e. It is sensible\nto conclude that the Ohcations maintain a relative\nprecessional phase lag of (0 \u00062)\u000e, whereas the Ohand\nTdcations maintain a phase lag of (180 \u00062)\u000e. Even with\nthe diluted exchange coupling from nonmagnetic Zn2+\nand Al3+cations, the magnetic Fe2+=3+and Ni2+cations\nretain a coherent, collinear alignment.\nReducing the experimental uncertainty to well below\n2\u000ewould be extremely challenging. For each cation, a\nsmall drift in the beamline photon energy with respect\nto its XMCD peak (Fig. 2) might shift its apparent\nprecession phase, due to an overlap in the cation speci\fc\nXMCD features. For instance, considering that the\ndi\u000berence between the Fe3+\nTdand Fe3+\nOhpeaks is only\u00190.8\neV, an energy drift of \u00190.01 eV could cause a phase shift\nof\u00192\u000e. The nominal resolution of the electromagnet at\n\u00190.1 mT may also contribute to the scatter in the \feld\ndependence of XFMR phase. Moreover, the timing jitter\nof the master oscillator of up to \u00193 ps limits the time\nresolution of the phase delay scans. Taking all the above\nfactors into account, the resolution of \u00192\u000ein our present\nstudy is in fact at the practical limit.\nWe now provide insight into the spin relaxation of each\nmagnetic cation species by quantifying the cation-speci\fc\nFMR linewidth \u0001 Hhwhm . In particular, we examine\nwhether di\u000berent spin relaxation emerges for magnetic\ncations with di\u000berent strengths of spin-orbit coupling {\ne.g., Fe3+with nominally zero orbital angular momentum\nvs Fe2+with likely nonzero orbital angular momentum12.\nHowever, Fig. 4(c) and Table I show that all magnetic4\n17 18 19 20 21 22-270-180-90090\n      \n \n      phase (deg.)\nfield m0H (mT)Fe𝑂ℎ3+\nFe𝑂ℎ2+\nNi𝑂ℎ2+\nFe𝑇𝑑3+\n18.0 18.5 19.0 19.5 20.0-4-2024residual phase (deg.)\nfield m0H (mT)\n18.0 18.5 19.0 19.5 20.0\nfield m0H (mT)\n18.0 18.5 19.0 19.5 20.0\nfield m0H (mT)\nFe𝑇𝑑3++180O\n17 18 19 20 21 220.00.20.40.6      \n \n \n amplitude (mV)\nfield m0H (mT)Fe𝑂ℎ3+\nFe𝑂ℎ2+\nNi𝑂ℎ2+\nFe𝑇𝑑3+\nFe𝑂ℎ3+Fe𝑂ℎ2+Ni𝑂ℎ2+(a) (c)\n(b)\n18.0 18.5 19.0 19.5 20.0\nfield m0H (mT)\nFIG. 4. (a) Field dependence of the precessional phase for each magnetic cation species. The solid curve indicates the \ft\nresult with Eq. 1. (b) Residuals of the precessional phase (i.e., di\u000berence between the experimentally measured data and the\narctan(\u0001H=(H\u0000Hres)) part of the \ft curve) in the vicinity of the resonance \feld. The dashed horizontal line indicates the\nphase lag\u001e0relative to the precessional phase of Fe3+\nOh. The shaded area indicates the standard deviation of the data points\nshown in each panel. (c) Field dependence of the precessional amplitude. The solid curve indicates the \ft result with Eq. 2.\ncations in NiZnAl-ferrite exhibit essentially the same\nlinewidth, \u00160\u0001Hhwhm = (0:43\u00060:03) mT, consistent\nwith the value obtained from conventional FMR for\nNiZnAl-ferrite28. Our \fnding thus indicates that the\nexchange interaction in NiZnAl-ferrite leads to uniform\nspin relaxation across all magnetic cations.\nTo further characterize cation-speci\fc spin relaxation,\nwe quantify the precessional cone angle \u0012cone of each\nmagnetic cation species. Speci\fcally, \u0012coneis obtained\nfrom the amplitudes of the XFMR signal IXFMR and\nXMCD peak IXMCD via\n\u0012cone= 2 arcsin\u0012IXFMR\nIXMCD\u0013\n: (3)\nWe \fnd that all cation moments precess with a cone\nangle of\u0012\u00191:0\u00001:1\u000e. Our results con\frm the\nexchange interaction in NiZnAl-ferrite is strong enough\nto lock all magnetic cations at the same relaxation rate,\nas evidenced by the invariance of the linewidth and\nprecessional cone angle to within .10%.\nOur \fnding is distinct from recent work on a\nferrimagnetic DyCo alloy, showing di\u000berent damping\nparameters for two magnetic sublattices afterfemtosecond-laser-induced demagnetization31. In\nRef. 31, the laser pulse produces a highly nonequilibrium\ndistribution of spins, which in turn quenches the\nexchange interactions, and the two ferrimagnetic\nsublattices are free to relax quasi-independently of\neach other. In this case, the rare-earth Dy sublattice\nwith stronger spin-orbit coupling exhibits a higher\ndamping parameter than the transition-metal Co\nsublattice. By contrast, the magnetic moments in\nour experiment are forced to oscillate by continuous\nmicrowave excitation, yet remain at near-equilibrium\nacross the entire resonance curve. The near-equilibrium\nforced oscillations { in concert with the exchange\ninteractions { favor the rigid, coherent coupling among\nthe magnetic cations and sublattices.\nIn summary, we have investigated time-resolved,\ncation-speci\fc resonant magnetic prcession at room\ntemperature in an epitaxial thin \flm of NiZnAl-ferrite,\na spinel-structure insulating ferrimagnetic oxide. The\nlow damping of this ferrite \flm yields a large XFMR\nsignal-to-noise ratio, allowing us to resolve precessional\ndynamics with high precision. In particular, we have\nobtained two key \fndings. First, the magnetic cations\nretain a coherent, collinear con\fguration, to within an5\nTABLE I. Resonance \feld Hres, linewidth \u0001 Hhwhm , relative\nprecessional phase lag \u001e0, and precessional cone angle \u0012conefor\neach magnetic cation species, as derived from \ftting the \feld\ndependence of the precessional phase [Eq. 1] and amplitude\n[Eq. 2].\nCation \u00160Hres\u00160\u0001Hhwhm \u001e0\u0012cone\n(mT) (mT) (degree) (degree)\nFe3+\nOh19:21\u00060:03 0:43\u00060:03 0 1 :0\u00060:1\nFe2+\nOh19:22\u00060:03 0:44\u00060:03 1:7\u00061:2 1:0\u00060:1\nNi2+\nOh19:23\u00060:02 0:43\u00060:02 1:5\u00061:2 1:1\u00060:1\nFe3+\nTd19:22\u00060:03 0:43\u00060:03\u0000178:5\u00061:4 1:1\u00060:1\nuncertainty in the precessional phase of \u00192\u000e. Second, the\nstrongly coupled magnetic cations experience the same\nmagnitude of spin relaxation, to within an uncertainty\nof.10%. Thus, the oft-assumed \\ferromagnet-like\"\ndynamics remain robust in the ferrimagnetic oxide,\neven with high contents of nonmagnetic Zn2+and\nAl3+cations that reduce the exchange sti\u000bness. We\nemphasize that our conclusion is speci\fc to the resonant\ndynamics under a continuous-wave excitation. Future\ntime-resolved XMCD measurements may resolve cation-\nspeci\fc dynamics in ferrimagnetic oxides driven by\nsub-nanosecond pulses , e.g., of electric-current-induced\ntorques, with potential implications for ultrafast device\ntechnologies.\nACKNOWLEDGEMENTS\nC.K. acknowledges \fnancial support by the Alexander\nvon Humboldt foundation. S.E. and Y.S. were funded by\nthe Vannevar Bush Faculty Fellowship of the Department\nof Defense under Contract No. N00014-15-1-0045. Work\nby S.E. was also supported in part by the Air Force\nO\u000ece of Scienti\fc Research under Grant No. FA9550-\n21-1-0365. Y.S. was also funded by the Air Force O\u000ece\nof Scienti\fc Research under Grant No. FA9550-20-1-\n0293. D.A.A. acknowledges the support of the National\nScience Foundation under Grant No. ECCS-1952957\nand also the USF Nexus Initiative and the Swedish\nFulbright Commission. The Advanced Light Source is\nsupported by the Director, O\u000ece of Science, O\u000ece of\nBasic Energy Sciences, of the U.S. Department of Energy\nunder Contract No. DE-AC02-05CH11231.\nDATA AVAILABILITY\nThe data that support the \fndings of this study are\navailable from the corresponding author upon reasonable\nrequest.1A. Brataas, B. van Wees, O. Klein, G. de Loubens, and M. Viret,\nPhys. Rep. 885, 1 (2020).\n2A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands,\nNat. Phys. 11, 453 (2015).\n3T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Nat.\nNanotechnol. 11, 231 (2016).\n4O. Gomonay, T. Jungwirth, and J. Sinova, Phys. status solidi\n^ a€\\ Rapid Res. Lett. 11, 1700022 (2017).\n5V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and\nY. Tserkovnyak, Rev. Mod. Phys. 90, 015005 (2018).\n6S. Emori and P. Li, Ferrimagnetic insulators for spintronics:\nBeyond garnets, 2021.\n7S. K. Kim, G. S. Beach, K. J. Lee, T. Ono, T. Rasing, and\nH. Yang, Nat. Mater. 2021 211 21, 24 (2021).\n8I. Gray, T. Moriyama, N. Sivadas, G. M. Stiehl, J. T. Heron,\nR. Need, B. J. Kirby, D. H. Low, K. C. Nowack, D. G. Schlom,\nD. C. Ralph, T. Ono, and G. D. Fuchs, Phys. Rev. X 9, 041016\n(2019).\n9H. Meer, F. Schreiber, C. Schmitt, R. Ramos, E. Saitoh,\nO. Gomonay, J. Sinova, L. Baldrati, and M. Kl aui, Nano Lett.\n21, 114 (2021).\n10E. Cogulu, N. N. Statuto, Y. Cheng, F. Yang, R. V. Chopdekar,\nH. Ohldag, and A. D. Kent, Phys. Rev. B 103, L100405 (2021).\n11V. G. Harris, IEEE Trans. Magn. 48, 1075 (2012).\n12G. F. Dionne, IEEE Trans. Magn. 47, 272 (2011).\n13Y. Zhou, C. Guo, C. Wan, X. Chen, X. Zhou, R. Zhang, Y. Gu,\nR. Chen, H. Wu, X. Han, F. Pan, and C. Song, Phys. Rev. Appl.\n13, 064051 (2020).\n14G. Boero, S. Rusponi, P. Bencok, R. S. Popovic, H. Brune, and\nP. Gambardella, Appl. Phys. Lett. 87, 152503 (2005).\n15D. A. Arena, E. Vescovo, C.-C. Kao, Y. Guan, and W. E. Bailey,\nPhys. Rev. B 74, 064409 (2006).\n16D. A. Arena, E. Vescovo, C.-C. Kao, Y. Guan, and W. E. Bailey,\nJournal of Applied Physics 101, 09C109 (2007).\n17Y. Guan, W. Bailey, E. Vescovo, C.-C. Kao, and D. Arena, J.\nMagn. Magn. Mater. 312, 374 (2007).\n18D. A. Arena, Y. Ding, E. Vescovo, S. Zohar, Y. Guan, and W. E.\nBailey, Review of Scienti\fc Instruments 80, 083903 (2009).\n19P. Warnicke, E. Stavitski, J.-S. Lee, A. Yang, Z. Chen, X. Zuo,\nS. Zohar, W. E. Bailey, V. G. Harris, and D. A. Arena, Phys.\nRev. B 92, 104402 (2015).\n20A. A. Baker, A. I. Figueroa, C. J. Love, S. A. Cavill, T. Hesjedal,\nand G. van der Laan, Phys. Rev. Lett. 116, 047201 (2016).\n21J. Li, L. R. Shelford, P. Shafer, A. Tan, J. X. Deng, P. S. Keatley,\nC. Hwang, E. Arenholz, G. van der Laan, R. J. Hicken, and Z. Q.\nQiu, Phys. Rev. Lett. 117, 076602 (2016).\n22Q. Li, M. Yang, C. Klewe, P. Shafer, A. T. N'Diaye, D. Hou,\nT. Y. Wang, N. Gao, E. Saitoh, C. Hwang, R. J. Hicken, J. Li,\nE. Arenholz, and Z. Q. Qiu, Nat. Commun. 10, 5265 (2019).\n23M. D\u0018 abrowski, T. Nakano, D. M. Burn, A. Frisk, D. G. Newman,\nC. Klewe, Q. Li, M. Yang, P. Shafer, E. Arenholz, T. Hesjedal,\nG. van der Laan, Z. Q. Qiu, and R. J. Hicken, Phys. Rev. Lett.\n124, 217201 (2020).\n24S. Emori, C. Klewe, J. M. Schmalhorst, J. Krieft, P. Shafer,\nY. Lim, D. A. Smith, A. Sapkota, A. Srivastava, C. Mewes,\nZ. Jiang, B. Khodadadi, H. Elmkharram, J. J. Heremans,\nE. Arenholz, G. Reiss, and T. Mewes, Nano Lett. 20, 7828 (2020).\n25C. Klewe, Q. Li, M. Yang, A. T. N'Diaye, D. M. Burn,\nT. Hesjedal, A. I. Figueroa, C. Hwang, J. Li, R. J. Hicken,\nP. Shafer, E. Arenholz, G. van der Laan, and Z. Qiu, Synchrotron\nRadiat. News 33, 12 (2020).\n26C. Klewe, S. Emori, Q. Li, M. Yang, B. A. Gray, H. M. Jeon,\nB. M. Howe, Y. Suzuki, Z. Q. Qiu, P. Shafer, and E. Arenholz,\nNew J. Phys. 24, 013030 (2022).\n27W. D. Wilber, P. Kabos, and C. E. Patton, IEEE Trans. Magn.\n19, 1862 (1983).\n28S. Emori, B. Gray, H.-M. Jeon, J. Peoples, M. Schmitt,\nK. Mahalingam, M. Hill, M. Mcconney, M. Gray, U. Alaan,\nA. Bornstein, P. Shafer, A. N'Diaye, E. Arenholz, G. Haugstad,\nK.-Y. Meng, F. Yang, D. Li, S. Mahat, D. Cahill, P. Dhagat,6\nA. Jander, N. Sun, Y. Suzuki, and B. Howe, Adv. Mater. 29,\n1701130 (2017).\n29R. A. D. Pattrick, G. van der Laan, C. M. B. Henderson,\nP. Kupier, E. Dudzik, and D. J. Vaughan, Eur. J. Mineral. 14,\n1095 (2002).\n30M. Hoppe, S. D oring, M. Gorgoi, S. Cramm, and M. M uller,\nPhys. Rev. B - Condens. Matter Mater. Phys. 91, 054418 (2015).31R. Abrudan, M. Hennecke, F. Radu, T. Kachel, K. Holldack,\nR. Mitzner, A. Donges, S. Khmelevskyi, A. De\u0013 ak, L. Szunyogh,\nU. Nowak, S. Eisebitt, and I. Radu, Phys. status solidi ^ a €\\\nRapid Res. Lett. 15, 2100047 (2021)."    },    {        "title": "1712.05632v1.Tunable_polymorphism_of_epitaxial_iron_oxides_in_the_four_in_one_ferroic_on_GaN_system_with_magnetically_ordered_α___γ___ε_Fe2O3_and_Fe3O4_layers.pdf",        "content": "T\nunable polymorphism of epitaxial iron oxides \nin the \nfour\n-\nin\n-\none\n \nferroic\n-\non\n-\nGaN \nsystem with \nmagnetically ordered \nα\n-\n, γ\n-\n, ε\n-\nFe\n2\nO\n3\n \nand Fe\n3\nO\n4\n \nlayers\n \nS. M. Suturin\n1\n, A. M. Korovin\n1\n, \nS.V. \nGastev\n1\n, \nM\n. P. Volkov\n1\n, M. Tabuchi\n2\n, \nN. S.\n \nSokolov\n1\n \n1\n \nIoffe Institute, \n26 Polytechnicheskaya str., St. Petersburg, 194021 Russia\n \n2\n \nSynchrotron Radiation Research Center, \nNagoya University, Furo\n-\ncho, Chikusa, Nagoya 464\n-\n8603, Japan\n \n* Correspondence e\n-\nmail: \nsuturin@mail.ioffe.ru\n \nHybridization of semiconducting and magnetic \nmaterials\n \ninto a single heterostructure \nis \nbelieved to \nbe potentially applicable to the \ndesign \nof \nnovel functional spintronic devices. In \nthe present work \nwe report \nepitaxial stabilization \nof four \nmagnetically ordered \niron oxide \nphases (Fe\n3\nO\n4\n, \nγ\n-\nFe\n2\nO\n3\n, \nα\n-\nFe\n2\nO\n3\n \nand \nmost \nexotic metastable \nε\n-\nFe\n2\nO\n3\n) in the form of \nnanometer sized \nsingle crystalline \nfilms\n \non GaN(0001) surface\n. \nT\nhe \nepitaxial growth \nof \nas \nmany \nas \nfour \ndistinctly different \niron oxide phases \nis demonstrated \nwithin \nthe same \nsingle\n-\ntarget \nLaser MBE \ntechnological process\n \non a\n \nGaN \nsemiconductor substrate\n \nwidely used for \nelectronic device fabrication\n.\n \nThe \ndiscussed \niron oxides belong to a family of \nsimple formula \nmagnetic material\ns exhibiting a rich variety of outstanding physical properties \nincluding \npeculiar \nVerwey and Morin \nphase transitions in Fe\n3\nO\n4\n \nand α\n-\nFe\n2\nO\n3\n \nand \nmultiferroic behavior \nin \nmetastable \nmagnetically hard \nε\n-\nFe\n2\nO\n3\n \nferrite\n. \nThe \nphysical \nreasons standing behind the \nnucleation of a particular \nphase in an \nepitaxial \ngrowth \nprocess deserve interest from the \nfundamental point of view\n.\n \nT\nhe practical side of the presented study is to exploit the \ntunable polymorphism of iron oxides for creation of \nferroic\n-\non\n-\nsemiconductor \nhe\nterostructures usable in \nnovel \nspintronic \ndevices. By application of a wide range of \nexperimental \ntechniques \nthe surface morphology, crystalline structure, electronic and \nmagnetic properties of the single phase iron oxide epitaxial films on GaN\n \nhave been studied. \nA c\nomprehensive comparison has been made to the properties of the \nsame ferrite\n \nmaterials\n \nin the \nbulk and nanostructured \nform \nreported by other research groups\n.\n \nI. INTRODUCTION\n \nH\nybrid heterostructures\n \ncombining closely spaced semiconducting and magnetic layers \nare \nbelieved to be \npromising candidates to be used \nin \nfunctional spintronic devices. Unlike \ndiluted magnetic semiconductors, the hybrid heterostructures\n \nallow separate control over the \nmagnetic and electrical properties. The magnetic layers in such heterostructures must \npreferably \nbe \ndielectric or have controllable conductivity \nas the \nhigh concentration of free \ncharge carriers at \nthe \ninterface would provi\nde an additional non\n-\nradiative recombination \nchannel leading to significant deterioration of the semiconducting properties. Transparency of \nthe magnetic layer in the visible range would be another demand as long as \nthe \noptoelectronic \nfeatures of the semico\nnduct\ning\n \ndevice are to be exploited. Making choice \nof the \nmagnetic layer \nmaterial \nfor \nthe \nhybrid heterostructure one could consider iron oxides\n \nas suitable candidates\n. \nIncluding \nFeO, Fe\n3\nO\n4\n \nand a \nnumber \nof Fe\n2\nO\n3\n \npolymorphs \nthe iron oxides \nmake up a big fami\nly of \nmagnetic materials exhibiting a rich variety of outstanding physical properties\n, \npresent\ning\n \ninterest both for technological applications and fundamental studies. \nBelow \na \nshort description \nof the four iron oxides discussed in this paper\n \nwill be given\n \nwith stress put on the very different \nstructural, magnetic and electric properties of these materials\n.\n \nMagnetite\n \n(\nFe\n3\nO\n4\n) \nis crystallized in the \ncubic \ninverse \nspinel \nlattice (\nFd\n-\n3m space group, \na=\n8.398 Å\n)\n. The easy magnetization axis lies along the [111] d\nirection. \nHaving \nthe largest \nmagnetic moment among \nthe \niron oxides (2.66 μ\nB\n \n/ formula unit (f.u.), \nM\ns\n=\n4\n8\n0 emu/cm\n3\n, \n4πM\ns\n \n= 6000 G) and \nNéel \ntemperature of 850 K \nFe\n3\nO\n4\n \nhas been \nlong \nused \nin \nmagnetic recording\n \napplications\n. \nMagnetite is \na half\n-\nmetal with full\n \nspin polarization at the Fermi level\n \n1\n. Below the \nVerwey \ntransition temperature of 120 K \nthe conductivity \nand \nmagnetizatio\nn \nin high purity \nmagnetite \ndrops by \nseveral orders of magnitude\n \ndue to the \ncharge ordering in the \nFe tetrahedral sites.\n \nThe ferromagnetic order in magnetite \ncomes from the \niron \nmagnetic \nmoments: parallel to \nthe magnetic \nfield in \noctahedral sites \nand antipa\nrallel in \ntetrahedral sites.\n \nMaghemite\n \n(\nγ\n-\nFe\n2\nO\n3\n) \ncan be considered as fully oxidized magnetite \nand \ncrystalliz\nes\n \nin \nthe \nsame \ninverse \nspinel lattice (a=8.330 Å)\n.\n \nThe \nFe\nIII\n \nvacancy distribution in octahedral positions \ngive\ns\n \nrise to several \npossible \ncrystal symmetries: \nthe \nrandom distribution (space group Fd\n-\n3m\n \nas \nin Fe\n3\nO\n4\n), partially ordered distribution (space group P4\n1\n32\n \nas in LiFe\n5\nO\n8\n) and ordered \ndistribution (space group P4\n3\n2\n1\n2). Maghemite exhibits ferrimagnetic order with a high Néel\n \ntemperature \nof \n950 K.\n \nBeing insulating and having a magnetic moment of 2.5 μ\nB\n \n/ \nf.u. (M\ns\n=3\n8\n0 \nemu/cm\n3\n, 4πM\ns\n \n= 4800 G)\n \nit is supposed a good candidate to act as a tunnel barrier for \nthe \nspin \nfiltering \ndevices \n2\n. \nMaghemite \nis \nalso \nwidely used in \nmagnetic storage\n,\n \ngas sens\ning\n \nand \nbio\nmedical applications \n3\n–\n5\n.\n \nHematite \n(α\n-\nFe\n2\nO\n3\n) is the most \nthermodynamically stable\n \niron oxide\n \ncrystallizing in the \nR\n-\n3c:H space group\n \n(a=5.0355 Å, c=\n13.7471 Å).\n \nBetween Morin transition temperature of 250 K \nand Neel temperature of 950 K \nthe low symmetry Fe\nIII\n \nsites allow\n \nspin\n–\norbit coupling to cause \ncanting of the moments lying in \nbasal \nplane perpendicular to the c axis. \nThe corresponding \nmagnetic moment is very s\nmall (\n<0.02 μ\nB\n \n/ f.u., \nM\ns\n<2 emu/cm\n3\n, \n4πM\ns\n \n< 30 G)\n.\n \nBelow \nthe \nMorin \ntransition the anisotropy \nmakes the \nmoments align antiferromagnetically along the c axis. Th\nis\n \ntransition \nis sometimes \nsuppressed in the nanoscale objects as well as in the bulk crystals due \nto \nthe presence of \nimpurities and defects.\n \nM\netastable \nepsilon ferrite \n(\nε\n-\nFe\n2\nO\n3\n) iron oxide\n \nreceiv\ning\n \nmuch attention \nnowadays \ndue \nto its exotic properties \nhas an orthorhombic \nnoncentrosymmetric \nlattice \n(Pna2\n1\n \nspace group, \na=5.089 Å, b=8.780 Å, c=9.471 Å) \n6\n \nisostructural to GaFeO\n3\n \n7\n, \nAlFeO\n3\n \n8\n, kGa\n2\nO\n3\n \n9\n \nand kAl\n2\nO\n3\n \n10\n. \nIron atoms \nin εFe\n2\nO\n3\n \noccupy\n \nfour nonequivalent crystallographic sites, including one tetrahedral \n(T\nd\n) \nsite and three octahedral \n(O\nh\n) \nsites. \nThe uncompensated magnetic moments of distorted\n \nT\nd\n \nand undistorted O\nh\n \nsublattices \naccount for \nferrimagnetic \nbehavior of \nε\nFe\n2\nO\n3\n \nbelow T\nN\n=490\n-\n500 \nK with resultant magnetization of \n0.\n6\n \nμ\nB\n \n/ f.u. at RT \n(\nM\ns\n=100 emu/cm\n3\n, 4πM\ns\n \n= 1300 G\n)\n \n11\n.\n \nThe \ndistortions of the two O\nh\n \nand one T\nd\n \nsites explain the large orbital moment leading to significant \nspin\n-\norbit coupling \n11\n, \nhigh magnetocrystalline anisotropy \n(\nK=\n4·\n10\n6\n \nerg / cm\n3\n) and \nvery high \ncoercivity \n(above \n2\n \nT\n)\n \n12\n. \nThe \nepsilon ferrite exhibits \nroom temperature \nmultiferroic properties \n13\n,\n \nmagn\netoelectric coupling \n14\n \nand \nmillimeter wave 190 GHz absorption at room temperature \n15,16\n. \nBecause \nof \nεFe\n2\nO\n3\n \nmetastab\nility\n \nmost works deal with randomly oriented nanoparticles\n \n17\n–\n19\n. \nOnly f\new works \nreport epitaxial growth of \nε\n-\nFe\n2\nO\n3\n \nlayers \non STO, Al\n2\nO\n3\n \nand YSZ using GaFeO\n3\n \nor AlFeO\n3\n \ntransition layers\n \n13,20\n–\n22\n.\n \nDue to numerous applications and intrinsic magnetic properties the \nfabrication of \nvarious \niron oxides in nanoscale form\n \nha\ns\n \nbeen widely studied \nduring the past decades\n. \nGrowth \nof \niron ferrite \nnanoparticles \nhas been performed by \na variety of methods including laser \npyrolysis, co\n-\nprecipitation, sol\n–\ngel, microemulsion \nand \nball\n-\nmilling \n3\n. Epitaxial layers \nhave been \ngrown \non different substrates (\nInAs, GaAs, MgAl\n2\nO\n4\n, Si, etc.\n) using \nreactive oxygen or ozone \nassisted molecular beam epitaxy, reactive magnetron sputtering and pulsed laser deposition\n.  \nSurprisingly \nt\nhere are \nvery few \nworks describing \niron oxide hybridization with \nGaN\n \nsemiconductor \nwidely utilized \nin \nmodern \nhigh\n-\npower electronics\n. \nGrowth of various \nother \noxides (SiO\n2\n, Al\n2\nO\n3\n, HfO\n2\n, Ga\n2\nO\n3\n) on GaN has been \nthe object of study \ni\nn search \nof \nappropriate \ngate i\nnsulato\nrs \nfor \nmetal\n-\noxide\n-\nsemiconductor \ndevices \n23\n–\n26\n.\n \nThe advantage of iron oxides is that \nthey feature \ncontrollable spontaneous magnetization/p\nolarization \nthat \nmay add \nnew \nfunctionality\n \nto the GaN\n-\nbased semiconductor devices\n, e.g. can be used for \nimpedance \nmatching \nspin injection into GaN \n(from half metallic \nFe\n3\nO\n4\n \nor \nvia \ntunneling \nthrough insulating γ\n-\nFe\n2\nO\n3\n)\n \nor for ferroelectric gate insulators\n. \nThe \nGaN\n-\nbased spin relaxation measurements \nhave \nshown \nspin lifetimes of 20 ns at 5 K\n \n27\n \nwhile theoretical calculations predict that spin lifetime in pure GaN is about three orders of magnitude larger than in GaAs \n28\n. \nThe examples of using iron \noxides for spin filterin\ng (though not \nin combination with \nGaN) are \ndiscussed \nin \n2\n \nwhere epitaxial \nγ\n-\nFe\n2\nO\n3\n \nfilms were fabricated \non \nNb:SrTiO\n3\n. O\nf various iron oxides only Fe\n3\nO\n4\n \nhas been \never \ngrown on \nGaN\n \n29,30\n \nby \ncombining room temperature \ndeposition \nof iron \nin UHV with \nshort \npost \ngrowth annealing in \noxygen\n.\n \nThe growth of \nFe\n3\nO\n4\n \nonto GaN by MOCVD using Ga\n2\nO\n3\n \nbuffer layer \nhas been also reported \n31\n.\n \nFollowing our earlier brief \ncommunication\n32\n, \nthe present work report\ns\n \nthe recent \nprogress in epitaxial stabilization of \nthe \nfour structurally and magnetically different iron oxide \nphases (Fe\n3\nO\n4\n, \nα\n-\nFe\n2\nO\n3\n, \nγ\n-\nFe\n2\nO\n3\n \nand \nthe \nmost exotic \nε\n-\nFe\n2\nO\n3\n)\n \nin the form of nanometer sized \nsingle crystalline films on GaN(0001) surface. \nA\nfter describing the experimental details in \nsection II\n, the\n \ngrowth \nand identification \nof \nthe \nfour iron oxide phase\ns\n \nwill be \ndiscussed \nin detail \nin section III\n. \nUpon \nintroducing \nthe \nepitaxial \ntechnolog\ny\n \nand speaking about the surface \nmorphology of the grown films\n,\n \nthe \ncommon \nbuilding principles of the iron oxide direct and \nreciprocal lattices\n \nwill be \naddressed\n. \nH\naving \nsettled \na \nconvenient coordinate system \nto work in, \nwe \nwill \ndiscuss the ways \nto \nidentif\ny\n \nthe \ncrystal structure and epitaxial relations \nin the studied \nsystem \nby \nusing high energy electron diffraction \n3D reciprocal space mapping\n. \nSection IV is \ndedicated to \nthe complementary \nX\n-\nray \ndiffraction stud\nies\n. \nS\npecular \ncrystal\n \ntruncation rod\ns \nare \nanaly\nzed to give accurate evaluation of the out\n-\nof\n-\nplane \ninterlayer spacing\n \nin the stabilized iron \noxide phases and the interface transition layer.\n \nX\n-\nray absorption and X\n-\nray magnetic circular \ndichroism \nare applied \nin section V \nto \ninve\nstigate \noxidation state\n \nand\n \ncoordination \nof \niron atoms \nin \nthe \nferri\nmagnetic\nally ordered\n \nsublattices\n \nof the studied oxides. A comparison to the \nproperties of the corresponding bulk materials is carried out. Finally t\nhe in\n-\nplane magnetization \nreve\nrsal \nin Fe\nx\nO\ny\n \n/ GaN layers \nis described in section VI\n \nand the summary is given \nin section VII\n.\n \n \n \nII. EXPERIMENTAL\n \nThe \nfew micrometer \nthick \nGa terminated GaN \nlayers acting as the host surface for the \niron oxide deposition \nwere \ngrown \nin Ioffe Institute \nby means of MO\nVPE\n \n33\n \non the Al\n2\nO\n3\n(0001) \nsubstrates. \nThe \ni\nron oxide films having thickness of 10\n-\n60 nm were grown on\nto\n \nthe GaN (0001)\n \nsurface \nby means of \nlaser molecular beam epitaxy\n.\n \nThe \nα\n-\nFe\n2\nO\n3\n \ntarget \nwas ablated by pulses of \nKrF excimer laser \n(\n\n \n= \n248 nm\n)\n \nat a fluence of \n2\n-\n6\n \nJ/cm\n2\n, the exact value having no \nimmediate \neffect on the physical properties of the grown films\n. \nT\nhe \niron oxide \ngrowth was performed in \noxygen, nitrogen \nand\n \nargon atmosphere \nat \npressure\ns\n \nranging from \n0.02\n \nto \n0.5\n \nmbar. \nThe \nsubstrate temperature \nduring iron oxide \ndeposition \nwas \nvar\nied\n \nfrom room temperature \n(RT) \nto \n850\n°C \nas \nmeasured inside the stainless steel sample holder to which the sample was cl\namped\n. \nAs the GaN / Al\n2\nO\n3\n \nsubstrates are transparent to the infra\n-\nred irradiation and the only heat \ntransfer is through \nthe \ndirect contact \nto the \nsample holder, \nthe real substrate temperature may \nbe lower than \nmeasured\n.\n \nFor \nthe \nreal time \ncontrol \nover \nthe oxide layer lattice structure and orientation, an \nadvanced 3D reciprocal space mapping \nby high\n-\nenergy electron diffraction (RHEED)\n \nwas used.\n \nTh\ne general idea of this \napproach was described in detail in our recent publication \n34\n \nwhere \nthe \nincidence angle was varied during \nimage acquisition\n. \nIn the present work \nthe \nmuch more \ninformative \nvariable\n-\nazimuth \nmapping \nhas been applied\n \nwith \nRHEED \npatterns \ncollected \nduring \nsample rotation around the surface normal\n \n35\n.\n \nFollowing this\n \napproach\n, \nthe \nraw patterns \n(\nthat \nare essentially \nspherical \nreciprocal space \ncuts) \nare used to build \n3D intensity map\ns\n. The \nplanar \ncuts and \northogonal \nprojections \nof th\ne\n \nresulting \nmap\ns\n \nwill be \npresented \nin this paper \nto \ndescribe the reciproca\nl space structure of the studied sample\ns\n. \nT\nhe “side\n-\nview\ns\n”\n \n(cuts performed perpendicular to the sample surface)\n \nare flattened improvements over \nthe \ntraditionally published raw patterns\n;\n \nt\nhe \nless conventional \n“plan\n-\nview\ns\n”\n \n(\nprojections \nalong the \nlines parallel to the surface \nnormal\n)\n \ncannot be visualized \ntaking \na single raw \nRHEED \npattern \nand \nare \nvery informative in understanding the in\n-\nplane reciprocal space structure\n \nespecially \nwhen \nused to \nvisualiz\ne\n \nthe \ndiffuse scattering features\n.\n \nThe dedicated \nOpenGL \nsoftware \nutilizing the \nextremely fast image processing capabilities of \nhundreds core \nmodern graphic processing unit\ns\n \nhas been developed by the authors \nto process \nthe \nraw diffraction patterns\n.\n \nThe developed \nsoftware is capable of on\n-\nthe\n-\nfly calculation of \nreciprocal space coordinates for \nclouds \nconsisting of \nhalf billion \npixel\ns\n \nand building \n3D intensity map\ns\n \nsuitable\n \nfor \nvisualization and \ncomparison to the model reciprocal lattices\n. \nTo accommoda\nte the wide range of RHEED map \nintensities within \nthe \n8 bit gray scale images\n,\n \na \nb\nackground subtraction \nroutine \nhas been \napplied\n \nto the \nmaps \npresented in this paper\n.\n \nIt is worth noting that \nthe main aim of the applied \n3D mapping \ntechnique \nis to measure and model reflection positions \nand shapes \nrather than \ntheir \nabsolute \nintensities as the latter are known to be subject to rather strong dynamical \neffects.\n \nThe modelled reciprocal lattices shown on top of the maps take into account the \nsystema\ntic absences of the corresponding space groups. Though the\n \nextinction rules\n \ncan be \nsometimes violated in electron diffraction due to multiple scattering effects\n \n(e.g. for bright \nmany\n-\nspot patterns taken in symmetric azimuths), these effects can be easily r\nuled out by \ndetuning from high symmetry azimuths as it is done in precession electron direction used in \ntransmission electron microscopy.\n \nThe \nX\n-\nray diffraction (XRD) measurements \nwere \ncarried out ex\n-\nsitu at BL3A beamline of \nPhoton Facto\nry synchrotron (Tsuk\nuba, Japan). \nThe s\nurface morphology was \nstudied \nusing \nambie\nnt air NT\n-\nMDT atomic force microscope\n. \nThe m\nagnetic properties were measured \nat \nroom temperature \n(RT) \nusing a \nlongitudinal MOKE \nsetup described in \n35\n \nas well as using \nthe \nQuant\num Design PPMS VSM magnetometer\n \nat \nRT \nand at 100 K\n. \nThe \nX\n-\nray absorption (XAS) and \nX\n-\nray circular magnetic dichroism (XMCD) studies have been carried out at \nRT at \nBL16 beamline \nof Photon Factory synchrotron (Tsukuba, Japan).\n \nTo be sensitive to the in\n-\nplane magnetization \nthe light incident angle was set to 30 deg while the magnetic field (up to 5 T) was applied \nparallel to the light propagation direction.\n \n \n \nIII. GROWTH OF \nIRON OXIDES ON GALLIUM NITRIDE \nCONTROLLED BY RHEED RECIPRO\nCAL \nSPACE \n3D MAPPING\n \nA\n. Outline of the growth technology\n \nIn the present \nwork the \ngrowth of four distinctly different \nα\n-\nFe\n2\nO\n3\n, \nγ\n-\nFe\n2\nO\n3\n, \nε\n-\nFe\n2\nO\n3\n \nand \nFe\n3\nO\n4\n \niron oxides on GaN(0001) surface has been achieved through \ncontrolled variation of \nsubstrate \ntemperature, \ndeposition \nrate, background gas composition and pressure. The outline \nof the developed technology \nis sketched \nin Fig. \n1\n.\n \nThree essentially distinct technological stages \nwere used to grow iron oxides: growth in oxygen, annealing in oxygen and g\nrowth in nitrogen. \nGrowth in oxygen \nresults \nin formation \nof either \nα\n-\nFe\n2\nO\n3\n \nphase at lower substrate temperature \nand pressure (T=400\n-\n600°C; p<0.02 mbar) or \nε\n-\nFe\n2\nO\n3\n \nphase \nat \nelevated temperature and \npressure (\nT=\n800°C\n; p=\n0.2\n-\n0.4 mbar). \nG\nrowth in nitrogen (\nT=\n600\n-\n800°C @ 0.02\n-\n0.2 mbar) result\ns\n \nin \nFe\n3\nO\n4\n \nphase stabilization\n. Finally \nthe \nγ\n-\nFe\n2\nO\n3\n \ncan be produced by exposing \nFe\n3\nO\n4\n \nlayers to \noxygen at 600°C\n-\n800°C.\n \nAs confirmed by the AFM measurements the iron oxides form uniform layers on the GaN\n \nstep\n-\nand\n-\nterrace surface (Fig. 1 bottom). On the nanometer scale the film surface consists of mounds 15\n-\n20 nm in width and 1\n-\n3 nm in height. The flattest surface is achieved for the films \ngrown at 600°C. Even in 40\n-\n60 nm films the step\n-\nand\n-\nterrace pattern\n \ninherited from the GaN \nsurface can still be recognized indicating that surface roughness does not drastically increase \nwith film thickness. The films grown at 800°C show a more pronounce height variation. The \nreasons for which the mounds are formed at the\n \nsurface will be discussed later in this paper.\n \n \nF\nIG\n. \n1\n. The outline of the Laser MBE technology developed to grow epitaxial layers of various \niron oxides on the GaN (0001) surface.\n \nThe growth is performed by ablating a hematite target in \nO\n2\n \nor N\n2\n \nbackground atmosphere while the substrate is kept at 400\n-\n800°C. \nP\nost\n-\ngrowth \nannealing in oxygen is carried out to convert Fe\n3\nO\n4\n \nfilms to γ\n-\nFe\n2\nO\n3\n.\n \nAFM images show the step\n-\nand\n-\nterrace GaN\n \nsurface as well as the typical columnar surface morphology of the iron oxide \nfilms grown at 600\n-\n800°C.\n \n \nB\n. \nLattice\n \nstructure \nof iron oxides \nand\n \nGaN \n-\n \ndirect space\n \nAt first glance the trigonal \nα\n-\nFe\n2\nO\n3\n \n(\na\n=5.036 Å\n, \nc=13.747 \nÅ\n), \ncubic Fe\n3\nO\n4\n \n/\n \nγ\n-\nFe\n3\nO\n4\n \n/ FeO \n(a=8.399\n \nÅ /\n \n8.33\n \nÅ\n \n/ 4.332 Å\n) \nand ortho\nrhombic\n \nε\n-\nFe\n2\nO\n3\n \n(a=5.089 Å, b=8.780 Å, c=9.471 Å) \nhave \nvery \ndifferent \nlattice \nsymmetries and \ndrastically \nnon\n-\ncoincident lattice parameters. \nHowever at closer look \nthe \nbuilding principles of the \nfour lattices \nappear \nto be rather similar \n-\n \nas shown in Fig. 2\n \n(\na) they consist\n \nof alternating oxygen and iron layers\n. \nThe \noxygen \nplanes \nare \narranged in slightly distorted \n(see Fig. 2b) \nclose packed sequences with AB\n-\nAB stacking in \nα\n-\nFe\n2\nO\n3\n, ABC\n-\nABC stacking in \nγ\n-\nFe\n2\nO\n3\n \n/\n \nFe\n3\nO\n4\n \n/ \nFeO and ABCB\n-\nABCB\n \nstacking in εFe\n2\nO\n3\n. \nThe \noxygen planes \nthough differently indexed exhibit \nvery similar \ninterplane distance\ns\n: \n2\n.\n424\n \nÅ\n,\n \n2\n.\n405\n \nÅ\n \nand\n \n2.50 Å\n \nbetween \nthe (111) planes in Fe\n3\nO\n4\n, γ\n-\nFe\n2\nO\n3\n \nand FeO\n;\n \n2.368 Å \nbetween \nthe \nε\n-\nFe\n2\nO\n3\n \n(001) planes \nand \n2.291 Å \nbetween \nthe \nα\n-\nFe\n2\nO\n3\n \n(0001) planes\n. \nThe \nfour oxides \nalso \ndiffer\n \nin \nthe \nway the \niron\n \natoms \npopulat\ne the slightly distorted \ntetrahedral and octahedral sites between \nthe \noxygen planes\n \n(see Fig. 2(a))\n. \nAs will be shown below the \niron oxide \ngrowth \ndirection is \nperpendicular to the oxygen planes\n,\n \nthus the phase \nchoice is controlled \nsimply by \nthe way \nhow the \noxygen \nand iron atoms \nare stacked\n \nupon deposition\n.\n \n \nF\nIG\n. \n2\n.\n \nEpitaxial relations \nin the iron\n-\noxide\n-\non\n-\nGaN\n \nsystem. Side view \nlattice \nprojections (a) show\n \nthe s\ntacking sequence of \nGa\n-\nN plane\ns in gallium nitride and Fe\n-\nO planes in iron oxides. \nP\nlan view \nlattice \nprojection\ns\n \n(b) \nhighlight \nthe \nslightly distorted hexagonal arrangement of F\ne\n-\nO atoms in \nthe iron oxides\n.\n \nPlan view lattice cut\ns\n \n(c) \nshow\n \nsingle \nanion \nplanes together with the \ncorresponding \nbulk unit cell vectors\n.\n \nHere and below projections \nrepresent the \nbulk \nlattice \nviewed along a certain direction\n, while cuts are \nlattice \ncross\n-\nsections\n \ncontaining just one plane \nof atoms or recipro\ncal lattice nodes\n.\n \nThe nitrogen \n(0001) planes in GaN are arranged similar to the oxygen planes in iron \noxides (Fig. 2). As will be shown later \nthese planes \nget aligned \n(O\n-\nO and N\n-\nN triangle sides \nparallel to each other) \nin the Fe\nx\nO\ny\n \n/ GaN system \nresulting in \nlateral substrate\n-\nfilm mismatch \nof \napproximately 7.5 %.\n \nFor better understanding the \no\nrientation of the oxygen and nitrogen \ntriangles \n(\nwithin \na \nsingle anion plane\n)\n \nrelative \nto the crystallographic axes is shown in Fig. 2\n \n(\nc\n)\n. \nThe averaged orie\nntations and lengths of the in\n-\nplane O\n-\nO and N\n-\nN vectors are \nas follows\n: \n|1\n \n0\n \n0|=3.19 Å in GaN, |1/3 \n-\n1/3 0|=2.91 Å in \nα\n-\nFe\n2\nO\n3\n, |1/4 \n-\n1/4 0|=2.97 Å in \nFe\n3\nO\n4\n, |1/4 \n-\n1/4 \n0|=2.95 Å in \nγ\n-\nFe\n2\nO\n3\n \nand \n|0 1/3 0|=2.93 Å in \nε\n-\nFe\n2\nO\n3\n.\n \n \nC\n. \nL\nattice structure \nof iron oxides \nand GaN \n-\n \nreciprocal space\n Assuming the \noxygen and nitrogen planes are aligned \nas described in the previous \nsection, \nthe \niron oxide phase\ns\n \ncan be readily \nidentified at the growth stage by \ncarrying out \nRHEED \nreciprocal\n \nspace mapping and \nanalyzing \nthe \nthree \northogonal \nreciprocal lattice \nviews\n \nas \nshown in Fig. 3\n. \n \n \nFIG. 3. In\n-\nplane epitaxial relations and reciprocal lattice matching between Al\n2\nO\n3\n, GaN \nand iron oxides.\n \nThe reciprocal space plan view projection (a) shows a pronounced similarity \nbetween the in\n-\nplane periodicities of the heterostructure components explaining the expected \nstreak patterns to be observed in the two high symmetry reciprocal space zones named c\nuts A \nand B. The streak patterns provide a reliable way to distinguish between the cubic (2\n×\n2), \ntrigonal (3\n×\n1) and orthorhombic (6\n×\n1) iron oxide phases (b)\n.\n \nT\nhe \n\"\nplan view\n\"\n \nrepresents the reciprocal space \nprojection \nonto \nthe substrate surface\n. \nT\nhe two \northogonal \n\"\nside\n-\nview\n\" reciprocal space cuts \n(zones) \nare \ncarried out perpendicular to \nt\nhe substrate surface and pass\n \nthrough the origin\n.\n \nD\neal\ning\n \nwith \nthe \nfour different \ncrystal \nstructures it is convenient to address the cuts \nas \n\"\ncut\n \nA\"\n \n-\n \nparallel \nand \"cut \nB\" perpendicular \nto \nthe \nO\n-\nO (N\n-\nN) \ntriangle sides \n(Fig. 2\n \n(\nc\n)\n)\n. \nFig. 3\n \nshows the sketch of the three orthogonal \nreciprocal space \nviews with \n\"cut\n \nA\n\"\n \nand \n\"cut \nB\n\"\n \ndirections marked \non the plan view. \nTaking into \naccount \nthe \nlow out\n-\nof\n-\nplane resolution of RHEED \noperating \na\nt \na \ngrazing incidence to \nthe \nflat \nsurface\n, \nthe sketch of the side\n-\nview cuts in \nFig. 3\n \n(\nb\n)\n \nshow\ns\n \nstreaks \nin place of Bragg \nreflections. \nThe experimentally observed Bragg reflections as will be shown later do really get elongated \nperpendicular to \nthe surface.\n \nThe 1×1 in\n-\nplane periodicity of the GaN(0001) surface is defined by the atom \narrangement in a single nitrogen plane. The iron oxide lattices are approximately \ncommensurate to GaN but have few times larger in\n-\nplane periodicities (except for FeO\n) due to \noxygen sublattice distortion and particular iron distribution. This gives rise to N×M streak \npatterns: 3×1 for \nα\n-\nFe\n2\nO\n3\n, 2×2 for \nFe\n3\nO\n4\n \n/ \nγ\n-\nFe\n2\nO\n3\n \nand 6×1 for \nε\n-\nFe\n2\nO\n3\n \n(Fig. 3 (a))\n. Taking into \naccount the higher symmetry of the GaN (0001) surface com\npared to that of the iron oxides, \nmultiple symmetry related domains are expected \n–\n \nthree domains at 120 deg to each other for \nε\n-\nFe\n2\nO\n3\n \nand two domains at 180 deg to each other for α\n-\nFe\n2\nO\n3\n, γ\n-\nFe\n2\nO\n3\n \nand Fe\n3\nO\n4\n. In the \nfollowing sections the experimentally \nobtained RHEED maps will be shown to fully comply with \nthe sketch in Fig. 3.\n \n \n \n \nD\n.\n \nRHEED 3D mapping of c\nlean GaN surface and iron oxide transition layer\n \n \nThe three orthogonal reciprocal space maps of the initial GaN(0001) surface are shown \nin Fig. 4 with the\n \nsuperimposed modeled reflection positions. Here and below the modeled \nreflections are shown only on half of the map to provide a non\n-\nobscured view of the \nexperimental data. The GaN reflections with the low out\n-\nof\n-\nplane momentum transfer are \nconsiderably e\nlongated perpendicular to the surface. This is indicative of total external \nreflection experienced by electrons at a grazing incidence to a flat step\n-\nand\n-\nterrace substrate \nsurface (see AFM morphology images below). The horizontal lines present in the cuts \nA and B \nare traces of Kikuchi lines that appear very bright for the clean GaN surface.\n \n \nF\nIG\n. \n4\n.\n \nRHEED reciprocal space map \nof \nthe\n \nclean \nGaN (0001) substrate\n \nprior to the iron oxide \ndeposition\n. \nT\nhree orthogonal views including the plan view projection and \nthe two side view \nreciprocal space cuts A and B\n \nare shown in the same scale\n.\n \nThe circles represent the \nmodeled \nGaN reflections. The triangles mark lateral positions of the GaN streaks providing a convenient \ncoordinate system for further examination of the \niron oxide reciprocal lattice structure.\n \nDistance \nbetween GaN [\n20L] and [00L] is 0.724\n \nÅ\n \n-\n1\n.\n \n \n \n \n \n  \n \nUpon deposition of about 1 nm of iron oxide the GaN 1×1 map is gradually replaced by a \nslightly different 1×1 map with extra faint half order streaks visible in re\nciprocal space cut A \n(Fig. 5). As indicated by arrows the distance between integer streaks gets slightly larger than in \nGaN corresponding well to the in\n-\nplane periodicity being reduced from 3.19 Å of GaN to ~2.9 Å \ntypical for the iron oxides.\n \n \nF\nIG\n. \n5\n. \nRHEED reciprocal space map\n \nof \nthe iron oxide t\nransition layer\n.\n \nThree orthogonal views \nincluding the plan view projection and the two side view reciprocal space cuts A and B are \nshown in the same scale. \nPositions of the overgrown \nGaN \nstreaks are \nmarked\n \nto e\nmphasize the \nslight \ndifference of \nGaN and iron oxide \nin\n-\nplane \nperiodicities\n.\n \nDistance between GaN [20L] and \n[00L] streaks shown for scale with blue triangles is 0.724 Å\n \n-\n1\n.\n As derived from the previous section\n,\n \nneither 1×1 nor 1×2 in\n-\nplane periodicities are \ncharacteristic of the Fe\n2\nO\n3\n \n/ Fe\n3\nO\n4\n \niron oxides. \nPresumably \nat this stage a transition layer is \nformed with no resemblance to any particular iron oxide phase due to a large number of \nstacking faults and antip\nhase boundaries inevitably occurring when a film has \na \nlower surface \nsymmetry and \na \nlarger surface cell \ncompared to \nthe substrate. Interestingly the plan view \nprojection shows that the half\n-\norder streaks labeled as 1/2 and 3/2 in the cut\n-\nA maps are not \ntru\ne 1D streaks but rather the 2D diffuse scattering \"walls\" connecting the true streaks. Such \n\"walls\" are present because the 1×1 streaks experience anisotropic in\n-\nplane widening due to \nthe lack of order in the direction perpendicular to the O\n-\nO (N\n-\nN) in\n-\npla\nne vectors.\n \n \nAccording to \nthe \nRHEED \nmaps \nthe only well pronounced in\n-\nplane periodicity present in \nthe transition layer is that of the hexagonal arrangement of atoms within oxygen planes (like in \nFeO\n). The out\n-\nof\n-\nplane periodicity\n \nis \ndifficult to extract fr\nom the low modulated streaks, \nbut it \nstill \ncan \nbe derived \nfrom \nRHEED \nspecular beam \nintensity oscillations observed during transition \nlayer nucleation\n \n(Fig. \n6\n)\n.\n \n \nF\nIG\n. \n6\n. RHEED \nspecular beam \nintensity oscillations observed \nat the beginning of \nα\n-\nFe\n2\nO\n3\n \n(a), \nFe\n3\nO\n4\n \n(b) and ε\n-\nFe\n2\nO\n3\n \n(c)\n \ndeposition\n.\n \nThe most pronounced oscillations corresponding to the \nlayer by layer growth are observed at 600°C and below.\n \nThe oscillation period after stabilization \nis approximately 2.4 Å corresponding to a single O\n-\nFe bilaye\nr.\n \nThe first few oscillations show a not easily interpreted shape as it often happens in \nheteroepitaxy. The reason for this is that during first monolayer nucleation too many \nparameters are changed at the same time (structure factor of the top layer, refra\nction of the e\n-\nbeam, terrace width and surface roughness).\n \nIt may be however claimed that i\nndependent on \nthe growth conditions t\nhe \n~2.4 Å \noscillation \nperiod \nroughly corresponds to \nthe \nO\n-\nFe\n \nsingle \nbilayer \n(like in α\n-\nFe\n2\nO\n3\n \nand FeO) \nrather than\n \nto \nthe \nO\n-\nFe\n-\nO\n-\nFe double \nbilayer \n(like in \nFe\n3\nO\n4\n \nand \nε\n-\nFe\n2\nO\n3\n)\n. \nThe most pronounce\nd\n \noscillations are observed d\nuring nucleation and growth of α\n-\nFe\n2\nO\n3\n \nin 0.02 mbar of oxygen\n \n(Fig. \n6\n \n(\na\n)\n) at 400°C (lowest damping) and 600°C (slightly higher \ndamping)\n. \nSuch behavior \ncorresponds to the layer by layer growth with slow surface \nroughening. \nA\nt growth conditions favorable for \nnucleation of Fe\n3\nO\n4\n \n(0.02\n-\n02\n \nmbar of nitrogen \nat 600\n-\n800\n°\nC) and \nε\n-\nFe\n2\nO\n3\n \n(0.2 mbar of oxygen at 800\n°\nC) only few \npronounced\n \noscillations \nare \nobserved\n \nat \nthe beginning\n \nof deposition\n. The much weaker oscillations \nare \noften\n \npresent \nafterwards \nbeing \nmore pronounced at \nl\nower substrate temperature and \nlower growth rate\n. \nTh\ne \nobserved behavior\n \ncorresponds \nto the Stranski\n–\nKrastanov \nscenario in which \nthe \nfirst \nfe\nw \nmono\nlayer\ns\n \nare grown in a layer by layer mode after which the \ngrowth switches to island \nnucleation\n \nregime\n. It is usually at th\nat\n \nmoment \nthat the \nintensity stops oscillating \nand \nthe \nadditional features \nof \nparticular iron oxide \ngradually \nappear\n.\n \nTo \ncomplete\nly\n \nstabilize the \nparticular iron oxide phase \nwith \na well recognizable diffraction pattern one needs to \ngrow film \nhaving thickness over \n5\n-\n8 nm. \nIn the next section the 3D reciprocal space maps of \neven thicker 20\n-\n40 nm \nα\n-\nFe\n2\nO\n3\n, Fe\n3\nO\n4\n \n, γ\n-\nFe\n3\nO\n4\n \nand ε\n-\nFe\n2\nO\n3\n \nfilms \non GaN\n \nwill be discussed in more details. \nC\nompar\nison\n \nto the modeled reciprocal lattices \nallow\ns\n \nphase \nidentification, spotting all the \nsymmetry related domains and \nconfirming the expected \nepitaxial relations\n.\n \nE\n. \nRHEED 3D mapping of \nα\n-\nFe\n2\nO\n3\n \nlayer\n \n(hematite)\n \nDepositing \nFe\n2\nO\n3\n \nonto GaN(0001) \nat 400\n-\n600\n°C\n \nin 0.02 mbar of oxygen \nthe \nstreak \narrangement\n \nis \ngradually \ntransformed \nfrom the 1×1 \npattern of \nthe transition layer \nto the \n\n3×\n\n3 \nR30 \npattern of \nthe α\n-\nFe\n2\nO\n3\n \nphase\n \n(Fig. 7)\n. \nDepending on the growth \nrate and temperature t\nhe \nα\n-\nFe\n2\nO\n3\n \npattern\n \nstarts to appear \nafter 5\n-\n8 nm of deposition.\n \n \nF\nIG\n. \n7\n. 3D RHEED reciprocal space map\ns\n \nof \nα\n-\nFe\n2\nO\n3\n \nlayer. \nThree orthogonal views including the \nplan view projection and the two side view reciprocal space cuts A and B \nare shown in the same \nscale. The circles represent the modeled α\n-\nFe\n2\nO\n3\n \nreflections. Distance between GaN [20L] and \n[00L] streaks shown for scale with blue triangles is 0.724 Å\n \n-\n1\n.\n \nThe observed epitaxial relations are in agreement with those described above\n \n(assuming \nmutual alignment of the O\n-\nO and N\n-\nN triangles): out\n-\nof\n-\nplane: GaN[001] || α\n-\nFe\n2\nO\n3\n \n[001]; in\n-\nplane: GaN[1\n-\n10] || α\n-\nFe\n2\nO\n3\n \n[1\n10] or [\n-\n1\n-\n10]. The two\n-\nfold ambiguity of the in\n-\nplane epitaxial \nrelations appears due to the symmetry reasons as the two \nequally probable orientations may \noccur when trigonal α\n-\nFe\n2\nO\n3\n \nlattice is placed over the hexagonal GaN lattice. The appearance of the \n\n3×\n\n3 R30 set of streaks is readily visible upon comparing the plan\n-\nview in Fig. 7 to the plan \nview of the initial GaN sur\nface in Fig. 5. \nUsing the side views t\nhe αFe\n2\nO\n3\n \nphase can be \nunmistakably identified by \nthe presence of \nN/3 streaks\n \nin the reciprocal space \"cut A\" and no \nadditional features in the reciprocal space \"cut B\". Being first weaker that the integer ones the \nN/3\n \nstreaks\n \nfully develop after about 10\n \nnm of deposition at which moment they also get \nmodulated in full correspondence with the modeled \nα\n-\nFe\n2\nO\n3\n \nreciprocal lattice structure (see \ncircles in Fig. 7). The resulting hematite films are insulating, non\n-\nmagnetic a\nnd have red\n-\norange \ntint.\n \nF\n. \nRHEED 3D mapping of \nFe\n3\nO\n4\n \nand γ\n-\nFe\n3\nO\n4\n \nlayers (magnetite\n \nand maghemite\n)\n \nDepositing Fe\n2\nO\n3\n \nat 600\n-\n800°C in 0.02 \n–\n \n0.2 mbar of nitrogen was found to \nstabilize the \nFe\n3\nO\n4\n \nphase\n. \nAlready after 2\n-\n3 nm of deposition the 1×1 streak \npattern of the transition layer \nstarts transforming to the 2×2 streak pattern. The latter is characteristic for the cubic lattice of \nFe\n3\nO\n4\n \n(or γ\n-\nFe\n2\nO\n3\n) with t\nhe following epitaxial relations\n: o\nut\n-\nof\n-\nplane: GaN[001] || Fe\n3\nO\n4\n \n[111]; \nin\n-\nplane: GaN[1\n-\n10] || Fe\n3\nO\n4\n \n[11\n-\n2] or [\n-\n1\n-\n12]. The two\n-\nfold ambiguity of the in\n-\nplane epitaxial \nrelations emerges due to symmetry reasons \nas the \ncubic \niron oxide \nis placed over \nhexagonal \nGaN. \nThe half streaks develop in both \"cut A\" and \"cut B\" maps gradually getting modulated in\n \nfull resemblance of the expected Bragg reflection positions \nof Fe\n3\nO\n4\n \nor γ\n-\nFe\n2\nO\n3\n \n(Fig. \n8\n).\n \nFrom electron diffraction maps it is almost impossible to distinguish Fe\n3\nO\n4\n \nfrom γ\n-\nFe\n2\nO\n3\n \nas both oxides obtain the same lattice structure and almost the same lattice constant. The films \ngrown in nitrogen are identified as magnetite (or at least as magnetite\n-\nrich) because they have \ndistinct gray metallic tint and are conducting at room tempera\nture. As will be shown below \nboth these properties are not observed in the γ\n-\nFe\n2\nO\n3\n \nfilms. It is important to note that \nsubstitution of Fe\nIII\n \nions with Fe\nII\n \nmust be the direct consequence of an increased Fe:O ratio in \nthe plume. The latter can hardly be due\n \nto the increased amount of iron but more likely due to \nthe reduced amount of oxygen. Interestingly growing in oxygen deficient (reducing) UHV \nconditions does not lead to Fe\n3\nO\n4\n \nstabilization. One needs to use nitrogen background \natmosphere (argon would not\n \nwork) at a pressure no less than 0.02 mbar to stabilize \nmagnetite, otherwise α\n-\nFe\n2\nO\n3\n \nwould eventually grow. \nIncreasing nitrogen pressure to 0.2 mbar \nleads to faster magnetite nucleation and subsequently brighter diffraction patterns. \nThe \nprobable explanat\nion could be that nitrogen acts as a sort of oxygen absorber forming NOx \ncompounds. Interestingly the same approach of using nitrogen background atmosphere (to be \nsoon reported elsewhere by the authors) has proved efficient to make Fe\n3\nO\n4\n \ngrow on MgO(001) \nw\nhereas in oxygen one usually gets γ\n-\nFe\n2\nO\n3\n \nas the main growing phase. The observed Fe\n3\nO\n4\n \n/ \nGaN epitaxial relations are in agreement with those discussed in Ref. \n29\n \nwhere Fe\n3\nO\n4\n \nfilms on \nGaN were obtained by oxidation of Fe\n \n/\n \nGaN\n \nlayers. Apparently iron oxidation technology leads \nto formation of a partially disordered magnetite film as in the diffraction patterns presented in \nRef. \n29\n \nthe half order streaks are considerably weaker than the integer ones. In contrast t\no this \nour magnetite films \nare\n \nfully ordered as confirmed by \nuniform \nstreak brightness.\n \n  \nF\nIG\n. \n8\n. 3D RHEED reciprocal space map\ns\n \nof \nFe\n3\nO\n4\n \nlayer. \nThree orthogonal views including the \nplan view projection and the two side view reciprocal space cuts A and B \nare shown in the same \nscale. The circles represent the modeled Fe\n3\nO\n4\n \nreflections. Distance between GaN [20L] and \n[00L] streaks shown for scale with blue triangles is 0.724 Å\n \n-\n1\n.\n \nThe \nFe\n3\nO\n4\n \n–\n \nγ\n-\nFe\n2\nO\n3\n \ntransformation \nin films grown on GaN \naffects\n \nthe full volume when \nthe film thickness is below 20 nm. \nTherefore t\no grow thicker maghemite layers\n,\n \nthe growth / \noxidation procedure \nhas to be \nrepeated multiple times.\n \nIt is noteworthy that the magnetite \n–\n \nmaghemite transformation is expected to proceed through creation of iron octahedral \nvacancies, that is, iron must travel out of the film volume to meet oxygen at the surface. This \nprocess would involve not only volume\n \ntransformation but also crystallization of extra material \nat the surface. Though the lattice structure and epitaxial relations do not change upon \noxidation a certain amount of surface roughening upon Fe\n3\nO\n4\n \noxidation is observed by AFM.\n \nG\n. \nRHEED 3D mapping\n \nof \nε\n-\nFe\n2\nO\n3\n \nlayers\n \nThe most interesting result of the present investigation is the epitaxial stabilization of \nmetastable εFe\n2\nO\n3\n \nphase on \na \nGaN\n \nsurface\n. The ε\n-\nFe\n2\nO\n3\n \npolymorph was shown to grow on GaN \nin 0.2 mbar \nof oxygen at \n800°C. The diffraction pattern \ncharacteristic for εFe\n2\nO\n3\n \nappears after \nabout 5 nm of deposition and stays stable up to the maximum tested thickness of 40 nm. The unmistakable characteristic of εFe\n2\nO\n3\n \nphase is the appearance of reflections on the \nN\n/6 streaks \nin \nthe cut\n-\nA reciprocal space\n \nmaps (Fig. \n9\n).\n \nThe following epitaxial relations are observed. Out\n-\nof\n-\nplane: GaN[001] || ε\n-\nFe\n2\nO\n3\n \n[001]; in\n-\nplane: GaN[1\n-\n10] || ε\n-\nFe\n2\nO\n3\n \n[100] or [\n-\n1\n-\n1\n0] or [\n-\n11\n0]. \nThe three\n-\nfold ambiguity of the in\n-\nplane epitaxial relations appears due to symmetry reasons\n \nwhen placing orthorhombic ε\n-\nFe\n2\nO\n3\n \nlattice over hexagonal GaN lattice. Noteworthy the \n\"\nb\n\"\n \nlattice parameter of ε\n-\nFe\n2\nO\n3\n \nis \n\n3 times larger than \nthe \"\na\n\"\n \nlattice parameter. This accounts for \nthe \ncoincidence of a great deal of reflections \nupon \n120 deg rotation\n \naround the surface normal. \nThe ε\n-\nFe\n2\nO\n3\n \nfilms are \nochre \nand insulating.\n \n \nF\nIG\n. \n9\n. 3D RHEED reciprocal space map measured for \nε\n-\nFe\n2\nO\n3\n \nlayer. \nThree orthogonal views \nincluding the plan view projection and the two side view reciprocal space cuts A and B are \nshown in the same scale. The circles represent the modeled \nε\n-\nFe\n2\nO\n3\n \nreflections. Distance \nbetween GaN [20L] and [00L] streaks shown for scale w\nith blue triangles is 0.724 Å\n \n-\n1\n.\n \nIV. X\n-\nRAY DIFFRACTION STUDIES\n \nWhile \nRHEED \nhas an excellent surface sensitivity it is in general less precise than XRD in \nsolving \nlattice \nstructures due to dynamic effects and often lower mechanical accuracy of the \nin\n-\nvacuum goniometer\ns\n. \nMoreover since RHEED probes only a thin near surface region it has a \nlimited out\n-\nof\n-\nplane resolution and cannot rule out recrystallization effects possibly occurring deep \ninside the film \nduring or after growth. \nTo accurately evaluate\n \nthe out\n-\nof\n-\nplane interlayer \nspacings present in the studied system we have carried out \npost growth X\n-\nray diffraction \nanaly\nsis\n \nof the \nintensity distribution along the specular crystal truncation rods\n.\n \nFig. \n1\n0\n \nshows \nsuch \nintensity profiles \nmeasured in \n40 nm\n \nfilms of the four different iron oxide\ns\n \ngrown on GaN. \nThe \nintensity is given as a function of momentum transfer perpendicular to the surface \n(Q\nz\n) \nthat \nhas been corrected for possible \nmisalignment\n \nusing the Al\n2\nO\n3\n \nand GaN reflections as a \nreference. \nThe obs\nerved \niron oxide \nreflections are in good agreement with the \nepitaxial \nrelations \nobserved earlier by \nRHEED\n.\n \n \nF\nIG\n. \n1\n0\n. XRD specular intensity profiles measured in \nFe\n3\nO\n4\n, γ\n-\nFe\n2\nO\n3\n, ε\n-\nFe\n2\nO\n3\n \nand α\n-\nFe\n2\nO\n3\n \nepitaxial layers on GaN(0001).\n \nApart from the brightest peaks belonging to GaN and Al\n2\nO\n3\n \ndistinct Bragg reflections of the corresponding iron oxide phases are present. In \nε\n-\nFe\n2\nO\n3\n \nand α\n-\nFe\n2\nO\n3\n \nsamples additional two peaks corresponding to the transition layer are clearly visible \n(labeled\n \nwith question mark).\n \nA\nn accurate evaluation of \nthe out\n-\nof\n-\nplane lattice periodicity \nhas been done\n \nfrom the \nXRD profiles\n. As was discussed earlier this periodicity is mainly defined by the distance between \nthe oxygen planes in the iron oxide lattice struct\nure and is phase dependent due to different \narrangement of the O\nh\n \nand T\nd\n \niron sites as well as the different stacking order of the oxygen \nplanes. Moreover in γ\n-\nFe\n2\nO\n3\n, Fe\n3\nO\n4\n \nand ε\n-\nFe\n2\nO\n3\n \nthe monolayer contains two oxygen planes \nleading to twice higher reflection frequency than in α\n-\nFe\n2\nO\n3\n \nin which the monolayer contains \nonly one oxygen plane.\n \nIt follows from the shown profiles that t\nhe \nFe\n3\nO\n4\n \nand\n \nγ\n-\nFe\n2\nO\n3\n \n(111) \nlayers a\nre \nslightly expanded p\nerpendicular to the surface while the \nα\n-\nFe\n2\nO\n3\n \n(0001) and ε\n-\nFe\n2\nO\n3\n \n(001) layers are slightly compressed. Below are listed the \nmeasured distances between the \noxygen planes and the corresponding \nlattice parameters\n \ntogether with \ngiven in parentheses \nbulk values. \nThe lattice parameters for Fe\n3\nO\n4\n \nand γ\n-\nFe\n2\nO\n3\n \nare calculated assuming that the\nir\n \nlattice remains cubic.\n \nFe\n3\nO\n4\n:\n \n \nd=2.428 Å \n(\n2.424 Å\n \n+ 0.1 %\n)\n \na=2\n\n3d=8.41 Å (8.398 Å)\n \n \n \nγ\n-\nFe\n2\nO\n3\n: \n \nd=2.41\n1\n \nÅ \n \n(2.405 Å\n \n+ 0.3 %\n)\n \na=\n2\n\n3d=\n8.354 Å (8.33 Å)\n \n \n \nt\nr\nan\ns\n. \nlayer:\n \n \nd=2.395 \nÅ\n \nε\n-\nFe\n2\nO\n3\n:\n \nd=2.36\n0 Å\n \n(2.368 Å\n \n-\n \n0.3 %\n)\n \nc=4d=9.438 Å (9.471 Å)\n \n \n \nα\n-\nFe\n2\nO\n3\n:\n \nd=2.285 Å\n \n(2.291 Å\n \n-\n \n0.3 %\n)\n \nc=6d=13.708 Å (13.747 Å)\n \n Interestingly \nthe \ntwo \nextra \nnon\n-\nhematite \npeaks \n(\nlabeled with question marks\n \nin Fig. 1\n0\n)\n \nare \npresent \non the \nα\n-\nFe\n2\nO\n3\n \nspecular profile\n. \nThese peaks are \nmuch \nwide\nr\n \nand weaker than the main \nα\n-\nFe\n2\nO\n3\n \nreflections. \nTheir contribution \nwas shown to decrease\n \nwith film thickness indicating \nthat the\ny originate from a thin \nlayer located at the \nGaN \ninterface\n.\n \nM\nost likely \nthis is the \nfingerprint of the \ntransition layer discussed \nearlier in \nthis paper\n.\n \nThe interlayer distance \ncorresponds \nto 2.395 \nÅ\n \nwhich is approximately the distance between oxygen planes in \nundistorted \nγ\n-\nFe\n2\nO\n3\n. \nT\nh\ne transition layer peaks are \nvery \nwell distinguished \nin \nthe α\n-\nFe\n2\nO\n3\n \nlayer\n.\n \nThe peak width corresponds to a 5 nm film \nin good agreement with RHEED \nobservations \nshow\ning\n \nthe onset of the α\n-\nFe\n2\nO\n3\n \nphase nucleation after 5.5 nm of deposition. \nIn ε\n-\nFe\n2\nO\n3\n \nlayers \na\n \nsmall \nhump \non the low\n-\nq side of the (008) reflection \nis \napproximately at the same place \nand \nof the same width \nas the transition layer reflection in α\n-\nFe\n2\nO\n3\n. \nIn \nFe\n3\nO\n4\n \nand γ\n-\nFe\n2\nO\n3\n \nthe \ntransition layer peak \ncannot be distinguished likely because this layer is few times thinner\n \nthan \nin \nα\n-\nFe\n2\nO\n3\n. \nIn agreement with the period of RHEED oscillations the periodicity of the transition \nlayer corresponds to single rather than double O monolayer. Interestingly the \ntransition layer \nBragg peaks show destructive interference with the high\n-\nQ\nz\n \nslopes of \nthe GaN\n \n(0002) and GaN \n(0004) reflections\n \nmaking them \nhighly asymmetrical. Th\ne observed coherence between \ncrystal \ntruncation rods of the substrate and the layer indicat\ne\n \nthat there is a \nsharp interface between \nthem\n. \nThis kind of interference often results in noti\nceable shift of the film peak maximum and \ncan be used to estimate\n \nthe \nlayer spacing at the \ninterface.\n \nFurther study of the nature of the \ntransition layer \nassumed responsible for the nucleation of \nthe \nexotic ε\n-\nFe\n2\nO\n3\n \nphase goes \nbeyond the \nscope of this work \nand will be highlighted in a separate publication.\n \nTo conclude, it \nbec\nomes\n \nclear from the XRD studies that \nthe iron oxide films are single phase\n \nwith out\n-\nof\n-\nplane \ninterlayer spacing\n \nslightly modified with respect to the corresponding bulk \nvalues\n.\n \nN\no post \ng\nrowth phase conversion \nhas been observed so far. Finally the\n \napproximately \n5 nm \nthick \ntransition layer \npresent in α\n-\n \nand \nε\n-\nFe\n2\nO\n3\n \nfilms has sharp interfaces and the \ninterlayer \nspacing \nnoticeably different from the \nknown \niron oxides\n.\n \nV. X\n-\nRAY ABSORPTION \nSPECTROSCOPY AND MAGNETIC CIRCULAR DICHROISM\n \nX\n-\nray absorption and X\n-\nray magnetic circular dichroism have been applied in this work to \nprobe oxidation states and coordination of \nthe Fe \natoms in ferrimagnetically ordered \nsublattices of the studied \niron \noxide\ns. While the diffraction techniques are sensitive to the \ncrystal structure\n, \nthe soft X\n-\nray spectroscopy provides the way to prove that the iron atoms are \nin \nthe \nexpected chemical environment. \nMost important is that the method is sensible to the \nnon\n-\ncrystal\nline fractions (e.g. segregated metallic iron) that cannot be observed with diffraction \ntechniques. \nTh\ne analysis of electronic and magnetic structure \nis done \nin this section \nthrough \ncomparison \nto the known absorption spectra \nof the corresponding bulk mater\nials.\n \nThe L\n23\n \nspectra of transition metals \ncorrespond to \nthe dipole\n-\nallowed 2p\n \n-\n \n3d transitions\n \nand \nconsist of L\n3\n \nand L\n2\n \nmain peaks resulting from \nthe \nspin\n-\norbit coupling. \nIn iron oxides the \nligand field of the oxygen atoms \nsplits \nthe Fe 3d into \ne\ng\n \nand \nt\n2g\n \norbitals\n \nprovid\ning\n \na highly \nsensitive tool to probe the coordination environment and the magnetization\n \nof individual \nsublattices\n. \nThe Fe L\n23\n \nXAS spectra measured in the iron oxide films grown on GaN are shown in \nFig. \n1\n1\n \ntogether with \nthe \nreference spectra\n \nadopted from\n \n11,36,37\n. In all the studied samples the \nL\n3\n \npeak exhibits two majo\nr components: a larger peak at 709.5 eV and a smaller satellite at 708 \neV. This spectral shape is characteristic of \nthe oxidized \niron as opposed to the metallic \none \n38\n.\n \n \nIn thick 40 nm α\n-\nFe\n2\nO\n3\n \nfilm the splitting is most pronounced originating from the pure \noctahedral coordination of Fe\nIII\n \nions in hematite \n36,38,39\n. In 40 nm γ\n-\nFe\n2\nO\n3\n \nand ε\n-\nFe\n2\nO\n3\n \nfilms the \nL\n3\n \nsplitting is less pronounced in agreement with the earlier studies of these materials: γ\n-\nFe\n2\nO\n3\n \n36,39,40\n \nand ε\n-\nFe\n2\nO\n3\n \n11\n. While the separation between the 708 eV and 709.5 eV components is \nthe same as in α\n-\nFe\n2\nO\n3\n, the intensity drop between the peaks becomes less pronounce\nd due to the presence of a Fe\nIII\n \nT\nd\n \npeak right in the middle between the two O\nh\n \npeaks. Interestingly the \nsame shape of L\n3\n \nedge as in γ\n-\nFe\n2\nO\n3\n \nand ε\n-\nFe\n2\nO\n3\n \nis observed in the 5 nm transition layer \n(preceding α\n-\nFe\n2\nO\n3\n \nformation) indicating the presence of T\nd\n \nsi\ntes near the interface. The non\n-\nhematite nature of the transition layer is in agreement with our diffraction data presented \nearlier in this paper.\n \n \n \n       \n \n \nF\nIG\n. \n1\n1\n.\n \nX\n-\nray absorption spectra \nobtained from the iron oxide epitaxial films on GaN\n \nshowing \nthe full L\n23\n \nspectral range (a) and the detailed L\n3\n \nand L\n2\n \nspectra (c, d)\n. Reference data adopted \nfrom \n11,36,37\n \nis shown for comparison\n \n(b).\n \nThe features \nin the spectra \nbelonging to Fe II and Fe III \nas well as to \nthe octahedral (Oh) and tetrahedral (Td) iron sites are marked.\n \nXMCD spectra \nobtained from the iron oxide epitaxia\nl films on GaN (e). Reference data adopted from \n11,36,37\n \nis \nshown for comparison\n \n(f).\n It is noteworthy that in the only existing paper \n11\n \ndescribing \nX\n-\nray absorption in \nε\n-\nFe\n2\nO\n3\n, \nthe \nspectrum is more like in α\n-\nFe\n2\nO\n3\n \nwith high contrast L\n3\n \nsplitting \n(\nFig. 11\n \n(\nb\n)\n) \nw\nhile our data show \nresemblance to γ\n-\nFe\n2\nO\n3\n. The latter seems more natural as unlike in α\n-\nFe\n2\nO\n3\n \nin ε\n-\nFe\n2\nO\n3\n \nthe T\nd\n \niron sublattice is known to exist in addition to the three distorted O\nh\n \nsublattices. In contrast to \nthe pure trivalent oxides, \nour \nFe\n3\nO\n4\n \nfilms exhibit an extra shoulder at 706.5 eV and a \nconsiderably higher satellite at 709.5 eV. These features are known to be characteristic of O\nh\n \nFe\nII\n \nsites in magnetite \n38\n–\n43\n. The shape of the L\n2\n \npeaks in the studied iron oxide films bears some \nsimilarity to the L\n3\n \npeak exhibiting the Fe\nII\n \nlow energy shoulder in Fe\n3\nO\n4\n \nand a better resolved \nsatellite in α\n-\nFe\n2\nO\n3\n.\n \nThe \nXMCD measurements \nat Fe L\n23\n \nedge \nhave been carried \nout \nto investigate magnetic \nnature of Fe sublattices \nmaking comparison \nto the corresponding bulk materials. \nWithin the \nexperiment accuracy no \ndichroic signal has been detected in the \nexpected to be weak \nferrimagnetic \nα\n-\nFe\n2\nO\n3\n \nfilms. \nThe\n \nXM\nCD spectra \nof the other three iron oxides \ncompared to the \nreference spectra \nare shown in Fig\ns\n. \n1\n1 (e, f)\n.\n \nThe general trend is that the L\n3\n \nXMCD spectra are \ndominated by two negative peaks corresponding to the Fe magnetic moments in O\nh\n \nsites \naligned parallel to the field and a positive peak in between the O\nh\n \npeaks corresponding to the \nFe magnetic moments in T\nd\n \nsite aligned antiparallel to the field. In the pure Fe\nIII\n \noxides \n(γ\n-\nFe\n2\nO\n3\n,\n \nε\n-\nFe\n2\nO\n3\n) \nthe higher energy O\nh\n \npeak is dominant (see r\neference spectra in Fig. \n1\n1\n \n(\nf\n)\n \nadopted \nfrom \n11,36\n). In the mixed II\n \n/\n \nIII \nFe\n3\nO\n4\n \nthe low energy peak is higher and wider due to the \npresence of \nthe \nO\nh\n \nFe\nII\n \nions\n \n29,44\n. \nThe net magnetization in ferr\ni\nmagnetic iron oxides results \nfrom \nthe \nantiparallel alignment of \nmagnetic moments at \nthe octahedral and \ntetrahedral Fe sites. In \ncontrast to the XMCD spectra of metallic iron for which the L\n3\n \npeaks measured at opposite light \nhelicities show different heights, in iron oxides the\nse peaks are shifted in energy.\n \nTo summarize, the \nsoft X\n-\nray absorption spectrosco\npy has confirmed that \nin the grown \nfilms \niron \natoms reside\n \nin the expected oxidation state a\nnd crystallographic environment and \nthat the films may be considered chemically pure. For all the cases the distinction \ncan be \nmade \nbetween the tetrahedrally and oc\ntahedrally coordinated iron atoms both in XAS and XMCD \nspectra. \nThis makes possible a more detailed XMCD study of individual magnetic sublattices in \nthe ferrimagnetic iron oxides. \nInterestingly t\nhe transition layer \nwas found to be different from \nαFe\n2\nO\n3\n \nin that it \ncontains\n \ntetrahedrally coordinated iron.\n \n \nVI\n. IN\n-\nPLANE MAGNETIZATION REVERSAL IN THE IRON OXIDE LAYERS ON GAN\n \nIn plane magnetization reversal curves of the iron oxide layers have been investigated \nb\ny MOKE and VSM\n \nto compare the magnetic proper\nties of the \ngrown \nfilms \nto those of the same \nmaterials in bulk or nanoscale form\n. Fig. 12\n \n(\na\n)\n \nemphasizes the big difference of the typical \nM(H) curves \nmeasured \nin Fe\n3\nO\n4\n, \nα\n-\nFe\n2\nO\n3\n, \nγ\n-\nFe\n2\nO\n3\n \nand ε\n-\nFe\n2\nO\n3\n \nlayers\n.\n \nA. \nEpsilon ferrite\n \nIn \nε\n-\nFe\n2\nO\n3\n \n(001) layers the easy magnetization [100] axis \nshould lie in the film \nplane \naccounting for\n \nthe\n \nhard magnetic nature of the in\n-\nplane magnetization curves. Such curves \nhave been measured by VSM showing saturation of 1\n1\n0 emu/cc, coercivity of 8 kOe and \nsatur\nation field of 20 kOe (Fig. 12\n \n(\nc\n)\n). These values are typical for \nεFe\n2\nO\n3\n \nnanoparticles and \nfilm\ns reported by different authors\n \n13,17\n–\n22\n.\n \nSimilar to \nthe \nother reports we observe loops of \nwasp\n-\nwaist shape exhibiting abrupt magnetization jumps \nat zero \nmagnetic field. Th\ne wasp waist \nloop \nis explained by \nthe presence of magnetically hard and soft components in \nε\n-\nFe\n2\nO\n3\n \nfilm. An \nexample of \nloop \nd\necomposition is shown in Fig. 12\n \n(\nc\n)\n. The hard magnetic component loop \nshape is in agreement with the idea of \nε\n-\nFe\n2\nO\n3\n \nfilm consisting of domains with\n \nthree possible orientations of the easy magnetization \nε\n-\nFe\n2\nO\n3\n \n[100] \naxis at 120 deg to each other. \nIn this \nconfiguration the magnetic field is always at an angle with the easy axis of at least two domains \nwhich makes the magnetization \nloops \nno\nn\n-\nrectangular\n. The origin of the soft component loop is \narguable \n–\n \ndifferent works \nrelate it to the presence of magnetite or maghemite\n \nimpurities\n, \nto \nthe antiphase boundaries or to \nthe \nmagnetically soft behavior of \nthe undistorted O\nh\n \nsublattices. \nAccording t\no our diffraction measurements the only \nparasitic phase \nthat can be present \nto \nsome extent at the near surface region of the not optimally grown \nε\n-\nFe\n2\nO\n3\n \nfilms is hematite\n. \nHowever due to the \nnegligible \nmagneti\nc moment\n, hematite cannot account for magnetically \nsoft component that in some \nε\n-\nFe\n2\nO\n3\n \ngets as strong as 40 emu/cc in saturation\n. \nIt is likely that \nt\nhe soft loop \nis related to \nthe transition layer \nthat is rich in \nsmall superparamagnetic \nε\n-\nFe\n2\nO\n3\n \ngrains \nforming at \nthe nucleation stage.\n \nAccording to our experiments increasing the transition \nlayer thickness (e.g. by decreasing the growth temperature by 50°C \n–\n \n100°C) makes the soft \nloop more pronounced.\n \n \nF\nIG\n. 12\n. \n(A) \nA comparison chart of typical \nin\n-\nplane magnetization reversal curves \nmeasured by \nlongitudinal Kerr effect at \nλ=\n405 nm and VSM \nfor α\n-\nFe\n2\nO\n3\n, \nFe\n3\nO\n4\n, \nγ\n-\nFe\n2\nO\n3\n \nand \nε\n-\nFe\n2\nO\n3\n \nfilms on \nGaN\n.\n \nThe drastic variation of iron oxide magnetic properties is visible. \n(B) \nIn\n-\nplane MOKE \nmagnetization curves\n \nin Fe\n3\nO\n4\n \nfilms of different thickness and in \nγ\n-\nFe\n2\nO\n3\n \nshowing gradual \ntransition from small might be superparamagnetic to large ferromagnetic grains\n. \n(C) \nIn\n-\nplane \nVSM magnetization curve in \nε\n-\nFe\n2\nO\n3\n \nfilm decomposed into magnetically hard and magnetically \nsoft components.\n \nB. \nHematite\n \nWe have also looked for the presence of \nthe \nweak ferro\nmagnetism in α\n-\nFe\n2\nO\n3\n \nfilms\n \ngrown on GaN\n. At above the Morin transition temperature of 250 K t\nhe \ncanted \nantiferromagneti\ncally coupled\n \nmagnetic moments \nin α\n-\nFe\n2\nO\n3\n \nare known to result in \nspontaneous magnetization lying in the (0001) \nbasal \nplane \n45,46\n. \nAs \nthe canting angle \nis just \na \nfraction of a \ndegree\n,\n \nthe resulting magnetic moment is \nvery small \n-\n \nof the order of \nfew emu/cc. \nSuch small \nmagnetization \ncould not be detected \nin our \nXMCD\n \nexperiments\n. \nNeither was \nVSM \ncapable to accurately measure \na \nmagnetization \nloop\n \nin \na \n40 nm \nα\n-\nFe\n2\nO\n3\n \nfilm\n.\n \nA\n \nvery \nnoisy \nVSM \nloop \nin Fig. 15a \nis shown \nto \nemphasize \nthe \ntiny \n<\n5 emu/cc \nsaturation magnetization \nin \nα\n-\nFe\n2\nO\n3\n \ncompared \nto \nthe \nmuch larger \n11\n0 emu/cc \nvalue\n \nmeasured \nfor ε\n-\nFe\n2\nO\n3\n. \nInterestingly\n,\n \ndespite the \nsmall magnetic moment \na very pronounced Kerr polarization rotation \nwas observed in \nthe\n \nstudied \nα\n-\nFe\n2\nO\n3\n \nfilms \n(Fig. 12\n \n(\na\n)\n)\n. \nThe anomalously strong magnetooptical effects in weak \nferromagnets are known to occur\n \ndue to dependence \non the antiferromagnetic vector \nrather \nthan \njust on \nthe total \nmagnetization\n \n47\n. \nIn the \nvery \nearl\ny\n \nworks \nlinear magnetic birefringence \n48\n \nand \nKerr effect \n49\n \nin hematite have been rep\norted\n. The Kerr rotation \nin hematite is \nclaimed\n \nto \nbe as strong as in the rare earth iron garnets \n50\n \nand \ncan \nbe used to visualize magnetic domains \nwith polariz\nation\n \nmicroscopy\n \n51\n.\n \nSurprisingly there are no \nrecent \nworks on magnetooptics in \nhematite\n \nfilms though it \nappears that the ratio of \nMOKE \nto \nVSM \nsignal at saturation \nprovide\ns\n \na very \nsensitive tool \nto distinguish \nαFe\n2\nO\n3\n \nfrom other iron oxide phases\n.\n \nThe observed \nMOKE \nloop \nshape in \nour \nα\n-\nFe\n2\nO\n3\n \n/ GaN \nfilms \nis in general agreement with the \nVSM \n \nmagnetization curves \nreported by different authors for \nbulk samples containing \nhematite single domain nanoparticles\n \nexhibiting \ncoercivity of few kOe and saturat\nion field \nabove 20 k\nOe \n52\n–\n54\n.\n \nSuch \nmagnetization \nbehavior is in contrast with the properties of \nthe \nlarge natural hematite crystals that have very \nmuch lower coercive forces \nof \n3\n-\n30 \nOe \n55\n. The main source of the high coercivity in \nnanoparticles is \nbe\nlieved to be \nthe magnetoelastic anisotropy \nthat can be \nassociated \nwith \nsubparticle structure, \nstrain \nor \ntwinning \n56,57\n.\n \nC. \nMagnetite and maghemite\n \nThe MOKE magnetization loops of \n20 nm \nFe\n3\nO\n4\n \nlayers grown in \na \nrange of growth \ncond\nitions (600\n-\n800°C in \n0.02 to 0.\n5 mbar of nitrogen) \nexhibit \ncoercivity of 300\n-\n400 Oe and \nremanence of about 70%\n \nof the saturation value (Fig 12\n \n(\nb\n)\n). \nVery similar magnetization loops \nhave been observed in Fe\n3\nO\n4\n \nfilms grown \nby PLD \non Si(001)\n \n58\n. \nA similar loop shape with \nsomewhat lower coercivity of 120\n-\n150 Oe was observed \nin \nFe\n3\nO\n4\n \n/ GaN(0001) films grown by \noxidiz\ning a few nm thick iron layer\n \n29\n. \nThe Kerr rotation of the γFe\n2\nO\n3\n \nlayers is typically 1.5 times \nweaker compared to that of Fe\n3\nO\n4\n. \nWith decreasing magnetite layer thickness \nfrom 20 nm to 6 \nnm and \nfurther to \n2 nm \nthe \nsaturation field gets \nlower \nwhile the remanent magnetization \ndisappears resembling \napproach to \nsuperparama\ngnetic\n \nbehavior\n.\n \n \nD. \nSingle vs multiple domains\n \nThe aforementioned thickness dependence for the magnetite films indicates that at \nnucleation stage the film is not uniform but consists of magnetically non interacting small \ngrains. The high coercive field \nobserved in α\n-\nFe\n2\nO\n3\n \nand \nε\n-\nFe\n2\nO\n3\n \nfilms \nis\n \nalso indicative of the \nsingle domain particles rather than a multiple domain film.\n \nIt is well known that the maximum \ncoercivity for a given material occurs within its single domain range whe\nre\n \nthe \nmagnetization \nreversal is through \nsynchronous magnetic moment rotation of the \nwhole \ngrain\n. \nTo o\nvercom\ne\n \nthe magnetocrystalline anisotropy\n \nin this case requires more energy than \nto move the d\nomain \nwall\n \nin \na multiple domain film\n. \nThe critical size for single domain behavior depends on several \nfactors including, the saturation magnetization. \nIt is \nestimate\nd\n \nto be \nabout \n80\n \nnm\n \nfor \nmagnetite\n \n59\n \nand 20\n-\n100 micrometers f\nor hematite (\n20\n-\n100\n \nmicrometers)\n \n60\n. \nThe diameter of \nthe mounds\n \nobserved in our films by AFM is in the single domain region. \nOne has to take into \naccount also that for very small single domain (superparamagnetic) particles \nthe ran\ndomizing \neffect\n \nof thermal energy\n \nbecomes important making the material magnetically soft\n.\n \nThe idea of \nthe film consisting of single crystal columns separated by antiphase boundaries is supported by \ndiffraction data (showing the presence of multiple symmetry related crystallographic \norientations) and by \nthe \nsurface\n \nmorphology studies \nshowing m\nounds \nat column \ntops.\n \nThe \ncolumnar structure \nis the result of \nhigher symmetry and lower unit cell of the GaN substrate \ncompared to that of the iron oxides. The islands nucleate in phase with GaN but with a phase \nshift with respect to each other. Upon coale\nscence \nan antiphase boundary is formed and \nthe \nislands keep growing vertically\n \nforming columns\n.\n \n \nTo summarize, the conducted magnetization reversal measurements have proved that \nthe \nin\n-\nplane magnetic behavior in thick \niron oxide films \ngrown on GaN \nis characterized by semi\n-\nrectangular magnetization loops with reasonably high values of remanence. The lowest \ncoercivity has been observed in magnetite and maghemite films, while the largest coercivity \ntakes place as expected in the \nε\n-\nFe\n2\nO\n3\n \nlayers. Unexpec\ntedly high magneto\n-\noptic response has \nbeen observed in hematite films. \nA two\n-\ncomponent loop in agreement with the other studies is \nobserved in \nεFe\n2\nO\n3\n \nfilms. \nIndications are obtained of that the building blocks of the iron oxide films are single domain magn\netic particles. \nIn general \nthe grow\nth of\n \niron oxide films \non GaN is \nproved applicable for creation of magnetic\n-\non\n-\nsemiconductor heterostructures.\n \nVII\n. SUMMARY\n \nIn the present work \nwe have investigated the tunable polymorphism of epitaxial iron \noxides on GaN\n(0001) surface. Four crystallographically and magnetically different iron oxide \nphases \n-\n \nFe\n3\nO\n4\n, γ\n-\nFe\n2\nO\n3\n, ε\n-\nFe\n2\nO\n3\n \nand α\n-\nFe\n2\nO\n3\n \n-\n \nhave been stabilized by means of \nthe single \ntarget \nLaser MBE techn\nology\n. \nFabrication of single phase layers b\ny controllable var\niation of \nsubstrate temperature\n, \nbuffer gas\n \ncomposition and pressure\n \nhas been demonstrated\n.\n \nAmong \nthe stabilized iron oxide films the most \nintriguing \nis the metastable epsilon ferrite \nε\n-\nFe\n2\nO\n3\n \nthe \ngrowth of which in the form of epitaxial layer\ns\n \nhas been reported in very few works\n \nup to now\n.\n \nThe epitaxial \ncontrol over the \niron oxide \npolymorphism \non GaN is \nclaimed \nfeasible because of \nthe particular \niron oxide lattice \nstructure \nconsist\ning\n \nof a \nclose packed stack of oxygen planes \nand \niron atoms sand\nwiched in between\n \nthese planes\n. \nThough the oxygen planes are indexed \ndifferently \n-\n \nFe\n3\nO\n4\n \n(111), γ\n-\nFe\n2\nO\n3\n \n(111), ε\n-\nFe\n2\nO\n3\n \n(001) and α\n-\nFe\n2\nO\n3\n \n(0001) \n-\n \ntheir internal slightly \ndistorted hexagonal structure is quite similar. \nOur RHEED and XRD studies have shown that the \niron oxide layers \ncrystallize \nwith the oxygen planes parallel to the GaN (0001) surface\n \nand the \nin\n-\nplane epitaxial relations defined by \nthe \ncoincidence of \nthe \nO\n-\nO and N\n-\nN vectors within the \ncorresponding planes\n.\n \nWith these epitaxial relations the \niron oxide \nphase may be \neasily \nswitched \nduring \nthe \ngrowth in the way similar to the ABC\n-\nABC / AB\n-\nAB\n-\nAB stacking \nswitching \nobserved \nin FCC / HCP lattices \n61\n \nwith the difference that in the case of iron oxides there exist \nmore than two stacking orders. The lower symmetry of the iron oxide planes compared to GaN \naccounts for \nmultiple possible in\n-\nplane orientations \n–\n \ntwo for Fe\n3\nO\n4\n, γ\n-\nFe\n2\nO\n3\n, α\n-\nFe\n2\nO\n3\n \nand three \nfor \nε\n-\nFe\n2\nO\n3\n. This \nambiguity \ntogether with the \nfew times \nlarger in\n-\nplane lattice periodicity \nof the \niron oxide \nis supposed to \nbe responsible for the appearance \nof phase shifted regions \nduring \nthe \nfilm nucleation \nstage. The thick film \nare shown \nto \nbe uniform \nwith low surface roughness (as \nconfirmed by AFM) \nand are supposed \nconsist\ning\n \nof \nsingle crystalline \ncolumns\n \nseparated by \nantiphase boundaries\n.\n \nAn important component of the \nFe\nx\nO\ny \n/ \nGaN technology is the transition layer \nthat forms \nat the initial \ngrowth \nstag\ne. This layer has the out\n-\nof\n-\nplane periodicity coincid\nent\n \nwith \nthe \nsingle \noxygen interplane distance and the in\n-\nplane periodicity \ndefined by that of \nthe \nwould\n-\nbe\n-\nideal \nhexagonal \noxygen plane. The longer \nin\n-\nplane \nperiodicities characteristic of the \nbulk \niron oxides \nare not present \nat this stage as shown by \ndiffraction indicating that \nthe transition layer \nconsists \nof small regions being in phase with GaN but out of phase with each other. The defect rich \ntransition layer is the thickest in αFe\n2\nO\n3\n \nand \nεFe\n2\nO\n3\n \nfilms and much thinner in Fe\n3\nO\n4\n, \nand \nγ\n-\nFe\n2\nO\n3\n \nlayers.\n \nInterestingly the transition layer was shown to contain tetrahedrally coordinated \niron.\n \nThe observed surface morphology might be the result of the island nucleation and \ncoalescence mechanism. This kind \nof growth was reported earlier for εFe\n2\nO\n3\n \nlayers on STO and \nYSZ \n13,21,22\n.\n \nThe columnar structure explains well the magnetic behavior of the \niron oxide \nfilms \non GaN \nsuggesting that columns are single magnetic domains. In \na \nsingle domain system\n \nthe \ncoercivity is known to be the highest as the magnetocrystalline anisotropy has to be overcome \nupon \nsimultaneous magnetization rotation of the whole domain. \nThis is well demonstrated for \nthe case of \nε\n-\nFe\n2\nO\n3\n \nfilms in which coercivity of 10 kOe\n \nand saturation field of 20 kOe have been \nobserved. The reason for \nthe \nhard magnetic behavior is the extremely high magnetocrystalline \nanisotropy in \nε\n-\nFe\n2\nO\n3\n. Much softer \nin\n-\nplane magnetization \nbehavior has been observed in \nFe\n3\nO\n4\n \nand γ\n-\nFe\n2\nO\n3\n \nfilms \nwith typi\ncal \ncoercivity \nvalues of \n300\n-\n400 Oe \nin agreement with \nother works\n. \nDecreasing film thickness was shown to result in appearance of superparamagnetic loop shape \nmost likely due to the small size of the single domain particles \npresent \nat the nucleation stage. Interestingly the \nrather hard magnetic behavior was \nalso \nobserved in α\n-\nFe\n2\nO\n3\n \nfilms in \nagreement with various studies of hematite nanoparticles. The very low total magnetization in \nthin α\n-\nFe\n2\nO\n3\n \nfilms makes it difficult to apply VSM.\n \nHowever the rather \nhigh magneto\n-\noptical \neffects in hematite \nma\nde\n \nit possible to monitor magnetization reversal in \nα\n-\nFe\n2\nO\n3\n \nfilms by \nmeans of MOKE.\n \nThe X\n-\nray absorption \nspectra measured \nat \nthe \nL edge of iron \nwere shown to be \nin \ngood \nagreement with the reference spectra obtained in a number of works \ndescribing different \niron \noxides \nin bulk and nano\ncrystalline form\ns\n. \nThis is an important proof of the chemical pureness of \nthe grown films. \nA careful analysis of the spectral shap\ne allows d\nistinguishing between the \noctahedral and tetrahedral coordination of iron as well as the iron oxidation state being \ndifferent for different oxides. The latter observation makes possible further studies of the \nindividual magnetic sublattices in the ferromag\nnetic iron oxides by means of XMCD. This is \nespecially challenging to be carried out for the scarcely studied epsilon ferrite obtaining four \nferrimagnetically ordered iron sublattices.\n \nIn general t\nhe obtained results \nrelated to \niron oxide stabilization on \nGaN(0001) are \nbelieved to be \nhelp\nful\n \nin clarifying the influence of technological parameters on the laser MBE \nprocess and in getting hold of the mechanisms guiding the particular phase choice during film \nnucleation and growth. \nThe shown \nflexibility in \nphas\ne stabilization \nby \nappropriately \ntuning the \nLaser MBE technological \nparameters makes it possible to predict that a similar approach may \nbe used to grow iron oxides on the AlGaN (0001) surface\n.\n \nM\nore complex compounds like \nFe\nx\nGa\ny\nAl\n1\n-\nx\n-\ny\nO\n3\n \ncan be\n \nalso\n \ntried \nfor the role of the ferromagnetic layer.\n \nCombining epitaxial \nlayers of magnetically ordered materials \nwith a highly suitable for device applications \nGaN \nsemiconductor surface \nis \nsupposed to present potential interest for designing novel (opto\n-\n) \nelectronic \nand spintronic devices for room temperature operation.\n \nACKNOWLEDGMENTS\n \nThe authors wish to acknowledge \nW\n. V. Lundin for providing GaN / Al\n2\nO\n3\n \nwafers, the \nbeamline staff at PF for kind assistance in conducting experiments. Beamtime\n \nat PF was granted \nfor projects 2014G726\n, \n2014G725\n \nand 2016G684\n. Support for \nconducting synchrotron \nmeasurements \nhas been received from Nagoya University.\n \nThis work has been supported by \nRSF (project no. 17\n-\n12\n-\n01508) in part related to development of \nthe \nferrite\n-\non\n-\nGaN\n \ngrowth \ntechnology and by \nGovernment of the Russian Federation (Program P220, project \nNo.14.B25.31.0025)\n \nin part related to \nsample \ncharacterization.\n \n \n1\n \nY.S. Dedkov, U. Rüdiger, and G. Güntherodt, P\nhys. Rev. B \n65\n, 64417 (2002).\n \n2\n \nP. Li, C. Xia, Z. Zhu, Y. Wen, Q. Zhang, H.N. Alshareef, and X.\n-\nX. Zhang, Adv. Funct. Mater. \n26\n, \n5679 (2016).\n \n3\n \nE. Parsianpour, M. Gholami, N. Shahbazi, and F. Samavat, Surf. Interface Anal. \n47\n, 612 (2015).\n \n4\n \nH. Nagano, Y. Machida, M. Iwata, T. Imada, Y. Noguchi, A. Matsumoto, and T. Nagai, Int. J. \nPharm. \n147\n, 119 (1997).\n \n5\n \nJ. Wang, M. Tong, X. Wang, Y. Ma, D. Liu, J. Wu, D. Gao, and G. Du, Sensors Actuators, B Chem. \n84\n, 95 (2002).\n \n6\n \nE. Tronc, C. Chaneác, and \nJ.P. Jolivet, J. Solid State Chem. \n139\n, 93 (1998).\n \n7\n \nS.C. Abrahams, J.M. Reddy, and J.L. Bernstein, J. Chem. Phys. \n42\n, 3957 (1965).\n \n8\n \nF. Bouree, J.L. Baudour, E. Elbadraoui, J. Musso, C. Laurent, and A. Rousset, Acta Crystallogr. Sect. B Struct. Sci. \n52\n, 2\n17 (1996).\n \n9\n \nH.Y. Playford, A.C. Hannon, E.R. Barney, and R.I. Walton, Chem. \n-\n \nA Eur. J. \n19\n, 2803 (2013).\n \n10\n \nB. Ollivier, R. Retoux, P. Lacorre, D. Massiot, and G. Férey, J. Mater. Chem. \n7\n, 1049 (1997).\n \n11\n \nY.\n-\nC. Tseng, N.M. Souza\n-\nNeto, D. Haskel, M. Gich, \nC. Frontera, A. Roig, M. van Veenendaal, \nand J. Nogués, Phys. Rev. B \n79\n, 94404 (2009).\n \n12\n \nJ. Jin, S. Ohkoshi, and K. Hashimoto, Adv. Mater. \n16\n, 48 (2004).\n \n13\n \nM. Gich, I. Fina, A. Morelli, F. Sánchez, M. Alexe, J. Gàzquez, J. Fontcuberta, and A. Roig, Adv. \nMater. \n26\n, 4645 (2014).\n \n14\n \nM. Gich, C. Frontera, A. Roig, J. Fontcuberta, E. Molins, N. Bellido, C. Simon, and C. Fleta, \nNanotechnology \n17\n, 687 (2006).\n \n15\n \nS. Ohkoshi, S. Kuroki, S. Sakurai, K. Matsumoto, K. Sato, and S. Sasaki, Angew. Chemie Int. Ed. \n46\n, \n8392 (2007).\n \n16\n \nA. Namai, S. Sakurai, M. Nakajima, T. Suemoto, K. Matsumoto, M. Goto, S. Sasaki, and S. \nOhkoshi, J. Am. Chem. Soc. \n131\n, 1170 (2009).\n \n17\n \nJ. López\n-\nSánchez, A. Serrano, A. Del Campo, M. Abuín, O. Rodríguez de la Fuente, and N. \nCarmona, Chem. M\nater. \n28\n, 511 (2016).\n \n18\n \nS.\n-\nI. Ohkoshi, A. Namai, K. Imoto, M. Yoshikiyo, W. Tarora, K. Nakagawa, M. Komine, Y. \nMiyamoto, T. Nasu, S. Oka, and H. Tokoro, Sci. Rep. \n5\n, 14414 (2015).\n \n19\n \nA. Namai, M. Yoshikiyo, K. Yamada, S. Sakurai, T. Goto, T. Yoshida, T. M\niyazaki, M. Nakajima, \nT. Suemoto, H. Tokoro, and S. Ohkoshi, Nat. Commun. \n3\n, 1035 (2012).\n \n20\n \nM. Gich, J. Gazquez, A. Roig, A. Crespi, J. Fontcuberta, J.C. Idrobo, S.J. Pennycook, M. Varela, \nV. Skumryev, and M. Varela, Appl. Phys. Lett. \n96\n, 112508 (2010).\n \n21\n \nT.M.N. Thai, D.T. Nguyen, N.\n-\nS. Lee, J.\n-\nS. Rhyee, J. Song, and H.\n-\nJ. Kim, J. Appl. Phys. \n120\n, \n185304 (2016).\n \n22\n \nL. Corbellini, C. Lacroix, C. Harnagea, A. Korinek, G.A. Botton, D. Ménard, and A. Pignolet, Sci. \nRep. \n7\n, 3712 (2017).\n \n23\n \nZ. Yatabe, Y. Hori,\n \nS. Kim, and T. Hashizume, Appl. Phys. Express \n6\n, 16502 (2013).\n \n24\n \nX. Qin, H. Dong, J. Kim, and R.M. Wallace, Appl. Phys. Lett. \n105\n, 141604 (2014).\n \n25\n \nR. Asahara, M. Nozaki, T. Yamada, J. Ito, S. Nakazawa, M. Ishida, T. Ueda, A. Yoshigoe, T. \nHosoi, T. Shim\nura, and H. Watanabe, Appl. Phys. Express \n9\n, 101002 (2016).\n \n26\n \nT. Yamada, J. Ito, R. Asahara, K. Watanabe, M. Nozaki, S. Nakazawa, Y. Anda, M. Ishida, T. \nUeda, A. Yoshigoe, T. Hosoi, T. Shimura, and H. Watanabe, J. Appl. Phys. \n121\n, 35303 (2017).\n \n27\n \nB. Besc\nhoten, E. Johnston\n-\nHalperin, D.K. Young, M. Poggio, J.E. Grimaldi, S. Keller, S.P. \nDenBaars, U.K. Mishra, E.L. Hu, and D.D. Awschalom, Phys. Rev. B \n63\n, 121202 (2001).\n \n28\n \nS. Krishnamurthy, M. van Schilfgaarde, and N. Newman, Appl. Phys. Lett. \n83\n, 1761 \n(2003).\n \n29\n \nP.K.J. Wong, W. Zhang, X.G. Cui, Y.B. Xu, J. Wu, Z.K. Tao, X. Li, Z.L. Xie, R. Zhang, and G. van \nder Laan, Phys. Rev. B \n81\n, 35419 (2010).\n \n30\n \nX. Zou, J. Wu, P.K.J. Wong, Y.B. Xu, R. Zhang, Y. Zhai, C. Bunce, and R.W. Chantrell, J. Appl. \nPhys. \n109\n, 07D341 (2011).\n \n31\n \nZ. Xu, S. Huang, K. Tang, S. Gu, S. Zhu, J. Ye, M. Xu, W. Wang, and Y. Zheng, Appl. Surf. Sci. 388\n, 141 (2016).\n \n32\n \nS.M. Suturin, A.M. Korovin, V. V Fedorov, S. V Gastev, V.P. Volkov, Y.Y. Petrova, M. Tabuchi, \nand N.S. Sokolov, in \n24th I\nnt. Symp. “Nanostructures Phys. Technol. Saint Petersburg, June 27\n–\nJuly 1, 2016\n \n(2016), pp. 37\n–\n38.\n \n33\n \nW. V Lundin, A. V Sakharov, A.F. Tsatsulnikov, and V.M. Ustinov, Semicond. Sci. Technol. \n26\n, \n14039 (2011).\n \n34\n \nS.M. Suturin, A.M. Korovin, V. V. Fedorov, G\n.A. Valkovsky, M. Tabuchi, and N.S. Sokolov, J. \nAppl. Crystallogr. \n49\n, 1532 (2016).\n \n35\n \nB.B. Krichevtsov, S. V Gastev, S.M. Suturin, V. V Fedorov, A.M. Korovin, V.E. Bursian, A.G. \nBanshchikov, M.P. Volkov, M. Tabuchi, and N.S. Sokolov, Sci. Technol. Adv. Ma\nter. \n18\n, 351 \n(2017).\n \n36\n \nD.H. Kim, H.J. Lee, G. Kim, Y.S. Koo, J.H. Jung, H.J. Shin, J.\n-\nY. Kim, and J.\n-\nS. Kang, Phys. Rev. B \n79\n, 33402 (2009).\n \n37\n \nK. Kuepper, I. Balasz, H. Hesse, A. Winiarski, K.C. Prince, M. Matteucci, D. Wett, R. Szargan, E. \nBurzo, and M.\n \nNeumann, Phys. Status Solidi \n201\n, 3252 (2004).\n \n38\n \nT.J. Regan, H. Ohldag, C. Stamm, F. Nolting, J. Lüning, J. Stöhr, and R.L. White, Phys. Rev. B \n64\n, \n214422 (2001).\n \n39\n \nD. Peak and T. Regier, Environ. Sci. Technol. \n46\n, 3163 (2012).\n \n40\n \nL. Signorini, L. Pasquini, F. Boscherini, E. Bonetti, I. Letard, S. Brice\n-\nProfeta, and P. Sainctavit, \nPhys. Rev. B \n74\n, 14426 (2006).\n \n41\n \nJ. Chen, D.J. Huang, A. Tanaka, C.F. Chang, S.C. Chung, W.B. Wu, and C.T. Chen, Phys. Rev. B \n69\n, 85107 (2004).\n \n42\n \nW.Q. \nLiu, Y.B. Xu, P.K.J. Wong, N.J. Maltby, S.P. Li, X.F. Wang, J. Du, B. You, J. Wu, P. Bencok, \nand R. Zhang, Appl. Phys. Lett. \n104\n, 142407 (2014).\n \n43\n \nD.J. Huang, C.F. Chang, H.\n-\nT. Jeng, G.Y. Guo, H.\n-\nJ. Lin, W.B. Wu, H.C. Ku, A. Fujimori, Y. \nTakahashi, and C.\nT. Chen, Phys. Rev. Lett. \n93\n, 77204 (2004).\n \n44\n \nW.Q. Liu, M.Y. Song, N.J. Maltby, S.P. Li, J.G. Lin, M.G. Samant, S.S.P. Parkin, P. Bencok, P. \nSteadman, A. Dobrynin, Y.B. Xu, and R. Zhang, J. Appl. Phys. \n117\n, 2 (2015).\n \n45\n \nI. Dzyaloshinsky, J. Phys. Chem. So\nlids \n4\n, 241 (1958).\n \n46\n \nT. Moriya, Phys. Rev. \n117\n, 635 (1960).\n \n47\n \nA.H. Morrish, in \nCanted Antiferromagnetism: Hematite\n, ISBN: 978\n-\n \n(WORLD SCIENTIFIC, \n1995), pp. 81\n–\n85.\n \n48\n \nH. Le Gall, C. Leycuras, D. Minella, E.G. Rudashewsky, and V.S. Merkoulov, Phys. B+C \n86\n–\n88\n, \n1223 (1977).\n \n49\n \nG.S. Krinchik and V.E. Zubov, JETP Lett. \n20\n, 137 (1974).\n \n50\n \nG.S. Krinchik, A.P. Khrebtov, A.A. Askochenskii, and V.E. Zubov, JETP Lett. \n17\n, 335 (1973).\n \n51\n \nA.T. Karaev and B.Y. Sokolov, Tech. Phys. \n48\n, 651 (2003).\n \n52\n \nÖ. Özdemir and D.J. Dunlop, J. Geophys. Res. Solid Earth \n119\n, 2582 (2014).\n \n53\n \nY. Yang, J.B. Yi, X.L. Huang, J.M. Xue, and J. Ding, IEEE Trans. Magn. \n47\n, 3340 (2011).\n \n54\n \nB. Vallina, J.D. Rodriguez\n-\nBlanco,  a. P. Brown, L.G. Benning, and J. a. Blanco, J. Na\nnoparticle Res. \n16\n, 2322 (2014).\n \n55\n \nÖ. Özdemir and D.J. Dunlop, J. Geophys. Res. Solid Earth \n110\n, 1 (2005).\n \n56\n \nI. Sunagawa and P.J. Flanders, Philos. Mag. \n11\n, 747 (1965).\n \n57\n \nH. Porath and C.B. Raleigh, J. Appl. Phys. \n38\n, 2401 (1967).\n \n58\n \nM.L. Paramês, J. Ma\nriano, Z. Viskadourakis, N. Popovici, M.S. Rogalski, J. Giapintzakis, and O. \nConde, Appl. Surf. Sci. \n252\n, 4610 (2006).\n \n59\n \nR.F. Butler and S.K. Banerjee, J. Geophys. Res. \n80\n, 4049 (1975).\n \n60\n \nS. Banerjee, Nat. Phys. Sci. \n232\n, 15 (1971).\n \n61\n \nS.M. Suturin, V. V Fedorov, A.M. Korovin, G.A. Valkovskiy, S.G. Konnikov, M. Tabuchi, and N.S. \nSokolov, J. Appl. \nCrystallogr. \n46\n, 874 (2013).\n \n "    },    {        "title": "1506.07684v1.Topological_magnetoelectric_effects_in_microwave_far_field_radiation.pdf",        "content": "Topological magnetoelectric effect s in microwave far-field radiation  \n \nM. Berezin, E.O. Kamenetskii, and R. Shavit   \n \nMicrowave Magnetic Laboratory,  \nDepartment of Electrical and Computer Engineering, \nBen Gurion University of the Negev, Beer Sheva, Israel \n \nJune 25, 2015 \n \nAbstract \nSimilar to electromagnetism, described by the Maxwell equations, the physics of magnetoelectric (ME) phenomena deals with the fundamental problem of the relationship \nbetween electric and magnetic fields. Despite a formal resemblance between the two notions, \nthey concern effects of different natures. In ge neral, ME-coupling effect s manifest in numerous \nmacroscopic phenomena in solids with space and time symmetry breakings. Recently it was \nshown that the near fields in the proximity of  a small ferrite particle  with magnetic-dipolar-\nmode (MDM) oscillations have the space and time symmetry breakings and topological \nproperties of these fields are different fro m topological properties of the free-space \nelectromagnetic (EM) fields. Such MDM-origin ated fields – called magnetoelectric (ME) \nfields – carry both spin and orbital angular momentums. They are characterized by power-flow \nvortices and non-zero helicity. In this paper, we  report on observation of the topological ME \neffects in far-field microwave radiation base d on a small microwave antenna with a MDM \nferrite resonator. We show that the microwav e far-field radiation can be manifested with a \ntorsion structure where an angle between the electric and magnetic field vectors varies. We discuss the question on observation of the re gions of localized ME energy in far-field \nmicrowave radiation.  \n  \nPACS number(s): 41.20.Jb; 42.50.Tx; 76.50.+g \n \nI. INTRODUCTION \n In a large variety of light-matter-interaction phen omena, novel engineered fields are considered \nas very attractive instruments for study different enantiomeric structures. Recently, significant \ninterest has been aroused by a rediscovered measure of helicity in optical radiation – \ncommonly termed optical chirality density – based on the Lipkin's \"zilch\" for the fields [1]. \nThe optical chirality density is defined as [1 – 4]: \n \n                                                     \n0\n01\n22EE BB   \n.                                           (1) \n \nThis is a time-even, parity-odd pseudoscalar para meter. Lipkin showed [1], that the chirality \ndensity is zero for a linearly polarized plane wave. However, for a circularly polarized wave, \nEq. (1) gives a nonvanishing quantity. Moreover, fo r right- and left-circularly polarized waves \none has opposite signs of parameter . The optical chirality density is related to the \ncorresponding chirality flow via the differential conservation law: \n \n                                                                  0ft \n,                                                         (2)  2 \nwhere \n \n                                                    2\n0\n2cf EB BE          \n.                                   (3) \n \nFor time-harmonic fields (with the field time dependence ite), the time-averaged optical \nchirality density is calculated as [1 – 4] \n \n                                                                  * 0Im2EB \n,                                               (4) \n \nwhere vectors E\n and B\n are complex amplitudes of the electric and magnetic fields. \n    The effect of optical chirality was applied recently for experimental detection and \ncharacterization of biomolecules [5]. The chiral fields were generated by the optical excitation of plasmonic planar chiral structures. Excitation of molecules is considered as a product of the \nparameter of optical chirality with the inherent  enantiometric properties of the material. In \nexperiments [5], the evanescent near-field mode s of plasmonic oscillations are involved. In \ncontinuation of these studies, a detailed and sy stematic numerical analysis of the near-field \nchirality in different plasmonic nanostractures was made in Ref [6]. Importantly, the near-field \nchiroptical properties shown in Refs. [5, 6], are beyond the scope of the Lipkin's analysis, \nwhich was made based only on the plane wave consideration. So, an important question arises: \nWhether, in general, the expressions (1), (4) obtained for propagating waves are applicable for \ndescription of the chiroptic al near-field response?  \n    In a case of Eq. (4), the electric field is parallel to the magnetic field with a time-phase delay \nof \n90. In Ref. [7], it was supposed that in an electromagnetic standing-wave structure, \ndesigned by interference of two counter-propagating circular polarized plane waves with the \nsame amplitudes, there are certain planes where the electric and magnetic fields are collinear with each other and are not time-phase shifted. The authors state that such a field structure \nresults in appearance of the energy density expressed as \n \n                                                                 \n() * 1Re2meWE B \n,                                             (5) \n \nwhich is called as the magnetoelectric (ME) energy [7]. In the vicinity of the electric nodes \n(1 2 ) kz n , 0,1, 2,...n , one has pronounced resonances which can be interpreted as \nlocalized regions of the ME energy. Based on this  analysis, authors of Ref. [7] propose a method \nof ultrasensitive local probing of the ME effect which can be observed in natural and artificial \nstructures. Intuitively, it was also assumed in Ref. [7] that this ME energy density of plane \nmonochromatic waves can be related to the reac tive power flow density (or imaginary Poynting \nvector) [8]: \n \n                                                                  () * 1Im2meSE B  \n.                                           (6) \n \n    For plane waves, Eq. (1) describes the local (in the sense of subwavelength scales of electromagnetic radiation) relationships betwee n the fields and space derivatives of these \nfields. But the question arises for the regions of interaction with small electric and/or magnetic  3dipoles. In these regions, the near-field reactive energy should be taken into account and the \ncoupling between the fields and space derivative s of the fields (in other words, the coupling \nbetween the electric and magnetic fields) appears as an effect of the first-order quantity ka, \nwhere k is the EM wavenumber and a is a particle size. Certainly, this problem of nonlocality \nis not overcome when we use superposition of mu ltiple plane waves [2]. The same question of \nlocality arises when we are talking about relations (5), (6) introduced in Ref. [7].  \n    Recently, in Refs. [9 – 13], it was shown that the ME properties can be observed in the \nvacuum-region fields in the proximity of a ferrite-disk particle with MDM oscillations. \nContrary to Refs. [2, 7], there are not the stat es of propagating-wave fields. In a case of the \nMDM oscillations in a small ferrite disk, we ha ve the electric-magnetic coupling effects – the \nME effects – on scales of MDMka , where MDMk  is the MDM wavenumber and a is a \ncharacteristic size of a ferrite particle. At the microwave frequencies, MDMkk . Free-space \nmicrowave fields, originating from magnetization dynamics in a quasi-2D ferrite disk, carry \nboth spin and orbital angular momentums and ar e characterized by power-flow vortices and \nnon-zero helicity (chirality). Topological properties of these fields – called ME fields – are \ndifferent from topological properties of free-sp ace EM fields. There are localized quantized \nstates of the near fields [9 – 16]. A time average helicity (chirality) parameter for the near fields of the ferrite disk with MDM oscillations is defined as [9 – 13] \n \n                                       \n 0\n00** 1\n4Im Re4FE E E H        \n                              (7) \n \nOne can also introduce a normalized helicity parameter, which shows a time-averaged space \nangle between rotating vectors E\n and H\n in vacuum:                                                                 \n \n                                                 *\n* Im Re\ncosEE EH\nEE E H  \n\n \n   .                                  (8) \n \nIn the near-field regions where the helicity parameter is not equal to zero, a space angle \nbetween the vectors E\n  and H\n is different from π/2. Such a near-field structure breaks the \nfield structure of Maxwell electrodynamics. The helicity states of the ME fields are \ntopologically protected quantum-like states. It was shown [17] that at the MDM resonances, the helicity densities of the near fields are re lated to an imaginary part of the complex power-\nflow density defined as \n \n                                                            \n* 1Im2rSE H \n.                                                       (9) \n \nThe regions where the helicity density is non-zer o are the regions of non-zero ME energy [17]. \n    In studies of the ME fields, a fundamental question arises: Whether the ME-field topology \nobserved in a subwavelength (near-field) region or iginated from a MDM ferrite disk can form \nspecific far fields with unique topological characteristics? There is a very important question in \na view of some topical problems of the microw ave far-field radiation. As it was preliminary \ndiscussed in Ref. [7], the propagating fields with ME energy can be effectively used for \nsensitive probing of molecular chirality. Recently, it was shown that via microwave-radiation \nspectroscopy one can successfully determine the rota tional energy levels of chiral molecules in \nthe gas phase. For this study, a special experimental setup for microwave three-wave mixing  4was used [18]. A chiral particle is modele d as three mutually orthogonal electric-dipole \nmoments and the handedness is identified by a sign of a triple product of these dipole moments \n[18]. Rotational spectroscopy is a branch of fundamental science to study the rotational spectra \nof molecules. Based on the rotational prope rties of the fields originated from MDM \nresonances, we can propose that novel engineered  fields with ME energy can be used for \nremote microwave detecting and identifying the handedness of biological objects and metamaterial structures.  \n    The near-field topologica l singularities originated from a MDM ferrite particle can be \ntransmitted to the far-field region. In this pape r, we report on observation of topological ME \neffects in the far-field microwave radiation. Fo r study of the far-field topology we use a small \nmicrowave antenna with a MDM ferrite-disk resonator as a basic building block. At the frequency far from the MDM resona nce, a ferrite disk appears as a small obstacle in a \nwaveguide and our microwave structure behaves as usual waveguide-hall antenna. The \nsituation is cardinally changed when we are at the MDM resonance frequency. In such a case, \nwe observe the helicity density in the far-field stru cture. The helicity densities of the far fields \nare related to an imaginary part of the complex power-flow density. The observed effects of far-field microwave transportation of ME ener gy allow better understanding of interaction \nbetween MDM magnons and microwave radiation. \n \nII. LOCALIZED REGIONS OF THE ME ENERGY: THE ME FIELDS NEAR A \nFERRITE DISK WITH MDM SPECTRA \n \nFollowing an analysis in Ref. [7] on the localized regions of the ME fields, let us suppose that \nthe fields (1) (1),EH\n and (2) (2),EH\n are two counterpropagating plane waves with the same \namplitudes and circular polarizat ions of the same direction: \n \n                                   (1)\n0ˆˆ()ikzEE x i y e ,  (1)\n0ˆˆ()ikzHH y i x e  ,                                     \n \n                                   (2)\n0ˆˆ()ikzEE x i y e   , (2)\n0ˆˆ()ikzHH y i x e   ,                                    (11) \n \nwhere 1  determines the circular-polarization di rection. For a standing wave formed by \nthese two fields we have \n \n                                    (1) (2)\n0ˆˆ ˆˆ() ()ikz ikzE E E E xi y e xi y e           , \n                                         \n                                     (1) (2)\n0ˆˆ ˆˆ() ()ikz ikzHH H H y i x e y i x e           .                           (12) \n \nFrom such a field configuration, we obtain \n \n                                                      *\n001Re 2 sin(2 )2EH E H k z   \n.                                      (13) \n \nIn the vicinity of the electric nodes (1 2 ) kz n , 0,1, 2,...n , one has pronounced resonances \nwhich can be interpreted as localized regions of the ME energy. Based on this analysis, authors \nof Ref. [7] propose a method of ultrasensitive local probing of the ME effect which can be \nobserved in natural and artificial structures.    5    The above statement that based on only two EM plane waves in vacuum counterpropagating \nwith the same circular polarizations one can obtain localized regions of the ME energy raises, \nhowever, the questions of a fundamental char acter. This assertion appears more as a \nmathematical, but not a physically realizable co ncept. In observation of the ME phenomena by \npure EM means, the problem of nonlocality plays the underlying role. In other words, for pure \nEM interactions, “magnetoelictricity” appears only due to field nonlocality. Optically active media, chiral biological materials, and bianis otropic metamaterials are spatially dispersive \nstructures. The ME properties are exhibited as the effect of the first-order quantity \nka, where k is \nthe EM wavenumber and a is a characteristic size (the particle size or the distance between \nparticles) [19 – 21]. Evidently, this problem of  nonlocality cannot be overcome when one uses \nsuperposition of multiple plane waves [7]. \n    The ME energy, defined by Eq. (13), transf orms as a pseudo-scalar under space reflection  \nand it is odd under time reversal .  When such a quadratic form exists, the Maxwell \nelectrodynamics should be extended to so -called axion-electrodynamics [22]. Axion \nelectrodynamics, i.e., the standard electrodynam ics modified by an additional axion field, \nprovides a theoretical framework for a possible vi olation of parity and Lorentz invariance. An \naxion-electrodynamics term, added to the ordinary Maxwell Lagrangian [22]:  \n                                                                \nEB\n ,                                                              (14)                     \n \nwhere  is a coupling constant, results in modified electrodynamics equations with the electric \ncharge and current densities replaced by [22, 23]  \n                                                               \n() ()eeB    \n,                                                 (15) \n \n                                                        () ()eej jB Et     \n.                                       (16)         \n  \nThe form of these terms reflects the discrete symmetries of :  is  and  odd. A dynamical \npseudoscalar field , called an axion field, which couples to EB\n. The  term is topological in \nthe sense that it does not depend on the space-time  metric. Whenever a ps eudo-scalar axion-like \nfield  is introduced in the theory, the dual symmetry between the electric and magnetic fields is \nspontaneously and explicitly broken. The form of the effective action implies that an electric \nfield can induce a magnetic polarization, wher eas a magnetic field can induce an electric \npolarization. This effect is known as the topological ME effect and  is related to the ME \npolarization. Axion-like fields and their interact ion with the electromagnetic fields have been \nintensively studied and they have recently received  attention due to their possible role played in \nbuilding topological insulators [24 – 28]. A topologi cal isolator is characterized by additional \nparameter  that couples the pseudo-scal ar product of the electric and magnetic fields in the \neffective topological action. For , the axion-electrodynamics Lagrangian describes the \nunusual ME properties of the topological isolator. In some materials, the axion field couples \nlinearly to light, resulting in the axionic polariton. Contrary to optically active media, chiral \nbiological materials, and bianisotropic metamateri als, the topological ME is basically a surface \neffect rather than a bulk one. Spin 12 particles exhibit the counterintuitive property that their \nwave function acquires the  phase upon 2 rotation. If spin and orbital degrees of freedom are \nmixed in a particular way, the momenta can feel important effects of this  Berry’s phase,  6which can lead to a new phase of waves whose de scription requires a fundamental redress of the \ntheory of electromagnetic radiation. \n    In contrast to a formal representation of the “ME energy density” in Ref. [7], expressed by \nEqs. (5), (13), the helicity parameter F for the near fields of a ferrite particle with MDM \noscillations [described by Eq. (7)] is justified physically as a quantity related to an axion-\nelectrodynamics term [9, 10, 13 – 15]. A ferrite materi al, by itself is not a ME material.  In a case \nof a MDM ferrite disk, the ME coupling is the topological effect which arises through the chiral \nedge states. For MDMs, the magnetic field is a potential field: H\n, where  is the \nmagnetostatic-potential (MS-potential) wave fu nction. In an assumption of separation of \nvariables, a magnetostatic-potential (MS-potential) wave function in a ferrite disk is represented \nin cylindrical coordinates , , zr as   ,, ( ) ,rzC z r   , where  is a dimensionless \nmembrane MS-potential wave function, ( ) z  is a dimensionless amplitude factor,  and C is a \ndimensional coefficient. On a lateral surface of a quasi-2D ferrite disk of radius , a MS-\npotential membrane wave function is expressed as: rr     , ~ is a singlevalued \nmembrane function and  is a double-valued edge wave function on contour 2 . \nFunction  changes its sign when the regular-coordinate angle  is rotated by 2. As a result, \none has the eigenstate spectrum of MDM oscillat ions with topological phases accumulated by \nthe edge wave function . On a lateral surface of a quasi-2D  ferrite disk, one can distinguish \ntwo different functions , which are the counterclockwise and clockwise rotating-wave edge \nfunctions with respect to a membrane function ~. A line integral around a singular contour : \n2\n**\n01()  ()\nrid i d\n \n\n         \n  is an observable quantity. Because of the \nexisting the geometrical phase factor on a lateral boundary of a ferrite disk, MDMs are \ncharacterized by a pseudo-electr ic field (the gauge field) €\n. The pseudo-electric field €\n can be \nfound as ()m\n€ € \n. The field €\n is the Berry curvature. The corresponding flux of the \ngauge field €\n through a circle of radius  is obtained as: \n  () ( )2me\n€\nSK €d S K d K q        \n , where ()e\n  are quantized fluxes of \npseudo-electric fields. Each MDM is quantized to  a quantum of an emergent electric flux. There \nare the positive and negative eigenfluxes. These different-sign fluxes should be nonequivalent to \navoid the cancellation. It is evident that while integration of the Berry curvature over the regular-coordinate angle \n is quantized in units of 2, integration over the spin-coordinate angle  \n1\n2 is quantized in units of . The physical meaning of coefficient K concerns the \nproperty of a flux of a pseudo-electric field. The Berry mechanism provides a microscopic basis \nfor the surface magnetic current at the interface between gyrotropic and nongyrotropic media. Following the spectrum analysis of MDMs in a quasi-2D ferrite disk one obtains pseudo-scalar \naxion-like fields and edge chiral magnetic currents. Topological properties of ME fields (non-\nzero helicity factor) arise from the presence of geometric phases on a border circle of a MDM \nferrite disk.  \n    In the near-field vacuum area of a quasi-2 D ferrite disk with MDM resonances, one has in-\nplane rotating electric- and magnetic-field vectors loca lized at a center of a disk [21]. This field \nstructure, shown schematically in Fig. 1, is characterized by the helicity factor, which is related  7to the product EB\n. In a numerical analysis we use the yttrium iron garnet (YIG) disk of \ndiameter of 3 mm.  The disk thickness is 0.05 mm. The disk is normally magnetized by a bias \nmagnetic field 04760 H Oe; the saturation magnetization of a ferrite is  1880  4sM G. For \nbetter understanding the field structures, in a numerical analysis we use a ferrite disk with a very \nsmall linewidth of 0.1 OeH . The numerically calculated helicity density for the main MDM \nis shown in Fig.1 for two opposite direct ions of a bias magnetic field.  \n     While, for MDMs, the magnetic field in a vacuum region near a ferrite disk is a potential \nfield, H\n, the electric field has two parts: the curl-field component cE\n and the potential-\nfield component pE\n. The curl electric field cE\n in vacuum we define from the Maxwell equation \n0 cHEt \n. The potential electric field pE\n in vacuum is calculated by integration over \nthe ferrite-disk region, where the sources (magnetic currents ()m mjt\n) are given. Here m is \ndynamical magnetization in a ferrite disk. Eq. (7) for the helicity density of the ME field is non-\nzero when one has non-zero scalar product  pcEE \n [9, 10, 13 – 15]. With representation of \nthe potential electric field as pE\n, we can write for ME fields in vacuum: \n \n                             ** 00 0Re Re44MDM MDMEB F           \n.                             (17) \n \nIn Ref. [17], it was shown that the vacuum regions above and below a quasi-2D ferrite disk, where the helicity density parameter \nF is nonzero, are also the regions where the imaginary part \nof a vector *EH\n exist as well. For the near-field vacuum  areas, localized at an axis of a quasi-\n2D ferrite disk, this connection is represented by the following relation:  \n \n                                                      ** 11Re Im22 zEH E H      \n.                                        (18)                       \n \nThe right-hand side of this equation describes a projection of the reactive power flow on the axis \nof a ferrite disk. Fig. 2 shows ME-field power flows near a ferrite disk for the main MDM \noscillation.     When a MDM ferrite disk is placed inside a microwave structure, a time-averaged space angle \nbetween rotating vectors \nE\n and H\n in vacuum [described by Eq. (8)] varies because of a role of \nthe curl fields of a microwave structure. This vari ation of an angle between spinning electric and \nmagnetic fields along the disk z-axis for the main MDM is shown in Fig. 3. This angle gives \nevidence for a torsion structure of the ME fiel d above and below a ferrite disk. The ME-energy \ndensity appears due to the torsion degree of freedom of the field.  \n \nIII. FAR-FIELD TOPOLOGICAL ME EFFECTS  \n Axion-like fields can interact with the EM fields, but cannot be eliminated by the EM fields. It \nmeans that the torsion degree of freedom observed due to an axion-electrodynamics term in the \nnear-field region of a MDM ferrite resonator, ca nnot be removed “electromagnetically” in the \nfar-field region of microwave radiation. To find the transfer of the to pological ME effects in \nthe far-field region, a microwave antenna shoul d not have other resonant elements except the  8MDM resonant structure. For this purpose, we use a rectangular waveguide with a hole in a \nwide wall and the diameter of this hole is much  less than a half wavelength of microwave \nradiation. At the MDM resonance, the topological singularities in the radiation field appear due \nto topological singularities in the electric curre nt distributions on the external surface of a \nwaveguide wall. These current singularities are well distinguished in a microwave antenna with \nsymmetrical geometry. For this reason, the hole in a waveguide wide wall is situated symmetrically.  \n     A microwave antenna used in our studies is shown in Fig. 4. This is a waveguide radiation \nstructure with a hole in a wide wall and a thin-film ferrite disk as a basic building block. A ferrite \ndisk is placed inside a \n10TE -mode rectangular X-band waveguide symmetrically to its walls so \nthat a disk axis is perpendicular to a wide wall of a waveguide. For numerical studies, the disk \nhas the same parameters as discussed in Sectio n II. The waveguide walls are made of a perfect \nelectric conductor (PEC). A hole in a wide wall has a diameter of 8 mm, which is much less than \na half wavelength of microwave radiation at the frequency regions from 8.0 GHz till 8.5 GHz, used in our studies. \n    Fig. 5 shows the numerical reflection characteristics for the \n10TE waveguide mode in our \nmicrowave antenna. The spectrum is quite emasculated compared to a multiresonant spectrum of \nMDM oscillations observed in non-radiating microwave structures [9 – 12]. Because of the \npresence of a radiation hole, high-order MDMs ar e not excited quite effectively. Numerically, we \nprimarily observe excitation of the first (main)  MDM oscillation. The forms of the resonance \npeaks in Fig. 5 give evidence for the Fano-type interaction. The underlying physics of the Fano \nresonances finds its origin in wave interference which occurs in the systems characterized by discrete energy states that interact with the continuum spectrum (an entire continuum composed \nby the internal waveguide and external free-space regions). The forward and backward \npropagating modes within the waveguide are coupled via the defects. This coupling becomes \nhighly sensitive to the resonant properties of the defect states. For such a case, the coupling can \nbe associated with the Fano resonances. In the corresponding transmission dependencies, the interference effect leads to either perfect tran smission or perfect reflection, producing a sharp \nasymmetric response. We have a “bright” a nd a “dark” resonances, which produce the Fano-\nresonance form in the reflection spectra. In our study we will use the first “bright” peak – the \npeak \n1 – where the most intensive radiation is observed. At the resonance peak 1 frequency the \nfield structure near a ferrite disk is typical for the main MDM excited in a closed waveguide system [9 – 12, 17]: there are rotating electric an d magnetic field, the active power flow vortex, \nthe reactive power flow and the reactive power flow. Far-field topological properties of ME \nfields arise from the presence of geometric phases in the radiation near-field region. These \ngeometric phases should have opposite signs for th e frequencies situated to the left and to the \nright from the resonance frequency of peak \n1. The resonance frequency of the peak 1 in Fig. 5 \nis f = 8.139GHz. To show a role of geometric pha ses in the far-field radiation, in the further \nanalysis we will use the frequencies f = 8.138GHz and f = 8.140GHz. There are, respectively, the \nfrequencies on the left and right slopes of the re sonance peak, very close to the top of this \nresonance peak.    \n    To observe the far-field topological ME effects originated from a MDM ferrite particle, we should create the regions with localized intensities  of the electric and magnetic fields in vacuum. \nFor this purpose, we place a dielectric ( 10\nr) plate above the antenna. The plate with sizes \n40 40 1 mm is disposed parallel to the waveguide surface at distance about 03.5, where 0 is \nthe electromagnetic wavelength in vacuum. Fig. 6 shows a normalized helicity parameter in a \nvacuum far-field region calculated base d on Eq. (8). At the frequency f = 8.138GHz one observes \nstriations of the positive and negative quantities of  the normalized helicity parameter. Periodicity \nof the striations is associated with the standi ng-wave behavior of regular EM waves in vacuum.  9Since a sign of a dynamical pseudoscalar field  in Eq. (14) is correlated with a direction of a \nbias magnetic field applied to a ferrite disk, the helicity-parameter striations change their signs, \nwhen a bias magnetic field is in an opposite direction.   \n    Fig. 7 represents a detailed analysis of the helicity parameter distribution in a vacuum far-field \nregion between an antenna and a dielectric plate. Figs. 7 ( a), (b), show the regions of localization \nof the helicity parameter in different vacuum hor izontal planes. From Figs. 7 (c) (d), we can see \nhow the helicity parameter is correlated with the regions of localized reactive power flows. As it was shown in Ref. [17] at the MDM resonances, the regions of localization of ME energy are \ncorrelated with the regions of the localized field intensities and the regions of localized reactive \npower flows near a ferrite disk. The similar situation we have in a far-field region. Along \nz-axis, \nthe maximums of the helicity-parameter modulus are at the same positions as the regions of \nmaximal gradient modulus of the reactive-power flow. Also, we can see that the maximums of \nthe helicity-parameter modulus are at the regions of maximal gradient modulus of the field (both electric and magnetic) intensities. The positions of striations with the positive and negative \nhelicity parameters are correlated with the EM standing-wave structure. For a given radiation \nfrequency (\nf = 8.138GHz), these positions remain the sa me when one uses a dielectric plate with \nanother permittivity parameters, but the same sizes. When the intensity of the electric and magnetic fields in the EM standing-wave struct ure increases the intensity of the striations \nincreases as well. Fig. 8 shows the pictures of the helicity parameter distributions for two \ndifferent permittivity paramete rs of the dielectric plates. \n     Striations of the positive and negative quantities of the normalized helicity parameter are \nregions of the positive and negative ME energy. In these regions, the electric and magnetic fields have components that are mutually parallel (antiparallel) and are not time-phase shifted. At the \nsame time, small chiral particles being excited by an electromagnetic field have the electric field \nparallel to the magnetic field but with a time-phase delay of \n90[2]. Since the ME field \noriginated from a MDM ferrite disk and the field originated from a chiral particle are \nfundamentally different, no strong perturbation of the ME-field structure by chiral particles \nshould be observed. Fig. 9 illustrates this situation. In this figure, an array of small metallic \nhelices, oriented along z axis, is placed in space between an antenna and a dielectric plate \n(1 0r). The helix diameter is 1.5mm and the height is 2.0mm. The helices are made of a PEC \nwire with diameter of 0.1mm. The number of helix turns is five. One can see that the helices do \nnot change positions of the helicity-parameter st riations. However, the regions inside every helix \nbecome green colored. It means that the electric and magnetic fields inside helices become time-\nphase shifted with 90. So, inside helices we ha ve restoration of a regular EM-field behavior.     \n     As we discussed above, topological prope rties of ME fields arise from the presence of \ngeometric phases in MDM oscillations. If it is  so, the change of a sign of a dynamical \npseudoscalar field in Eq. (14) will simultane ously change a sign of a scalar product EB\n. All the \nabove results were obta ined for the frequency f = 8.138GHz, which on the left slope of the \nresonance peak. When we go to the frequency  f = 8.140GHz, situated on right slope of the \nresonance peak, we will have an opposite sign of a geometric phase leading to change a sign of a \nhelicity factor –  a sign of a scalar product EB\n. Fig. 10 shows far-field helicity-factor \ndistributions for the frequency f = 8.138GHz (the left slope of the resonance peak) and the \nfrequency  f = 8.140GHz (the right slope of the resonance peak). The selected regions show the \nhelicity-factor distributions near a ferrite disk a nd near an antenna aperture. Near a ferrite disk, \nthe ME field is very strong compared to the EM field in a waveguide. In this region, no ME-EM \nfield interaction takes place and a sign of a helicity  factor is determined only by a direction of a \nbias magnetic field. However, near an antenna aperture one observes the ME-EM field \ninteraction. In this near-field region, the helicity-factor dist ributions are different for the \nfrequencies f = 8.138GHz and f = 8.140GHz. Different helicity-factor distributions in the  10radiation near-field region are origins of different  helicity-factor distributions in the far-field \nregion.      \n     For the optical chilrality , expressed by Eqs. (1), it is evident that for monochromatic \nelectromagnetic waves we have  \n \n                             *** 00 0 0Im Im Re 044 2EE HH E H               \n.         (19) \n \nLet us denote, formally, the terms in this equation as follows \n \n                                *() 0Im4EFE E  \n   and   *() 0Im4HFH H     \n.              (20) \n \nFor monochromatic EM waves, we have, evidently  \n \n                                                         ()0EF and ()0HF.                                                     (21) \n \nAt the same time, for the ME near fields, we have [9] \n \n         () 0\n00** 104Im Re4EFF E E E H        \n    and     ()0HF.           (22) \n \nIf we suppose that for the ME far fields both()0EF and ()0HF, we will have  \n \n                                           *() * 00 0Im Re44EFE E E H        \n,                             (23)                \n \n                  *() * * 00 0 0 0Im Re Re44 4HFH H H E E H                \n.           (24) \n   \nSo, \n                                                               () ( )E HF F .                                                           (25) \n \nThis gives  \n                                                                      \n() ( )0EHF F.                                                 (26) \n \n    The above formal consideration can be verifi ed by the following analysis of transfer of the \ntopological ME effects in the far-field region. As we can see from Eq. (17), in the near-field \nregion both the electric and magnetic fields ar e potential fields. There are the topological-\nnature fields. If we assume that such potentia l (topological) fields also exist in the far-field \nradiation, we should consider the total fields as the composite fields containing both the curl \nand potential (topological) field components: \n \n                                                   tcpEEE\n  and  tcpHHH\n.                                          (27) \n \nFor these fields components we have the equations:  11 \n                                           0t\ncHEt \n,              0pE\n, \n \n                                             0t\ncEHt \n,               0pH\n.                                           (28) \n \nThe curl fields, cE\n and cH\n are the Maxwellian fields  and the potential fields, pE\n and pH\n are \ntopological fields originated from a MDM partic le. For time harmonic fields in the far-field \nregion we can write: \n \n                          () 00 0\n22E\ncp c cp c p FE E E i E E H H             \n,                       (29)          \n \n                         () 00 0\n22H\ncp c cp c p FH H H i H H E E            \n.                       (30)                      \n \nTaking into account that 0ccEH\n, we obtain \n \n                                   *() * * 00 0Im Re44E\np cp c p p FE E E H E H            \n,                 (31)              \n \n \n                                   \n*() * * 00 0\n** 00Re44\n       Re .4H\np cp c p p\ncp ppFH H H E H E\nEH EH  \n        \n      \n                  (32)    \n \nAssuming Eq. (26), we have \n \n                                                    **Re Rep cc p EH EH   \n.                                                (33) \n \n    This analysis of the topological ME effect  shows that in the far-fi eld region we have two \nkinds of the torsion fields. There the “electric- torsion” fields characterizing by the helicity \nparameter ()EF and the “magnetic-torsion” fields characterizing by the helicity parameter \n()HF . For a given sign of a dynamical pseudoscalar field , an axion-electrodynamics term, \nexpressed by Eq. (14), has different signs for the “electric” and “magnetic” helicities. Fig. 11 \nshows normalized helicity parameters in a vacuum far-field region at the frequency f = \n8.138GHz, calculated based on the equations: \n     \n                          *Im\ncosEE\nEE \n\n\n       and      *Im\ncosHH\nHH \n\n\n .                  (34) \n  12In spite of the fact that both the “electric” and “magnetic” helicities exist, they annihilate one \nanother. Fig. 12 illustrates this situation. In the far-field region, the turn of a total electric field \ntcpEEE\n with respect to a curl magnetic field cH\n is compensated by the turn of a total \nmagnetic field tcpHHH\n with respect to a curl electric field cE\n. This results in mutual \nperpendicularity between tE\n and tH\n. In a local point in the fa r-field region, the “red” and \n“blue” helicity factors being superposed one to an other, give the “green” (zero) helicity factor. \nIn other words, the negative ME energy is compensated by the positive ME energy. These local \nproperties of the “helicity neutrality” mean that in the far-field region the field structure, being \ncomposed with the “electric-torsion” and “electric-torsion” components becomes non-\ndistinguishable from the regular EM-field structure. \n     The standard means do not give possibility to observe the ME-field structure in the far-field \nregion. The only possibility is to use another MDM ferrite disk as an indicator. This ferrite disk will, definitely, distinguish the “electric” helicity from the “magnetic” helicity.  \n \nIV. CONCLUSION \n \nIn this paper we analyzed interaction between MDM magnons and far-field microwave \nradiation. We showed that the near-field topological singularities originated from a MDM \nferrite particle can be transmitted to the far-fiel d region. For study of the far-field topology we \nused a small microwave antenna with a MDM ferri te-disk resonator as a basic building block. \nAt the frequency far from the MDM resonance, a ferrite disk appears as a small obstacle in a \nwaveguide and our microwave structure behaves as usual waveguide-hall antenna. The situation is cardinally changed when we are at the MDM resonance frequency.  \n     The microwave far-field radiation can be manifested with a torsion structure where an angle \nbetween the electric and magnetic field v ectors varies. We discussed the question on \nobservation of the regions of localized ME en ergy in far-field microwave radiation. The \nstandard means do not give possibility to observe the ME-field structure in the far-field region. This our statement contradicts to the assertion in Ref. [7], that one can observe the ME-field \nregions for propagating EM plain waves. We conclude that the only way to observe the ME-\nfield structure in the far-field regi on is to use another MDM ferrite disk as an indicator. In Ref. \n[11] we showed that interactions between two MDM disks are manifested at distances much \nlarger than the EM wavelength. The frequency region of these interactions is within the scales of the MDM resonance peak width. Our future studies are aimed to use a MDM ferrite antenna \ntogether with a MDM indicator to show experi mentally the ME-field structure in the far-field \nregion of microwave radiation. \n \nReferences \n[1] D. M. Lipkin, J. Math. Phys. 5, 696 (1964).  \n[2] Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010). \n[3] K. Bliokh and F. Nori, Phys. Rev. A 83, 021803(R) (2011). \n[4] J. S. Choi and M. Cho, Phys. Rev. A 86, 063834 (2012). \n[5]  E. Hendry et al, Nat. Nanotechnol. 5, 783 (2010). \n[6] M. Schäferling, D. Dregely, M. Hentschel, and H. Giessen, Phys. Rev. X 2, 031010 (2012). \n[7] K. Y. Bliokh, Y. S. Kivshar and F. Nori, Phys. Rev. Lett. 113, 033601 (2014). \n[8] J. D. Jackson, Classical Electrodynamics , 2nd ed. (Wiley, New York, 1975). \n[9] E.O. Kamenetskii, R. Joffe, R. Shavit, Phys. Rev. E 87, 023201 (2013).  \n[10] R. Joffe, E.O. Kamenetskii and R. Shavit, J. Appl. Phys. 113, 063912 (2013).  \n[11] M. Berezin, E. O. Kamenetskii, and R. Shavit, J. Opt. 14, 125602 (2012). \n[12] M. Berezin, E. O. Kamenetskii, and R. Shavit, Phys. Rev. E 89, 023207 (2014).  13[13] E. O. Kamenetskii, E. Hollander, R. Joffe, R. Shavit, J. Opt. 17, 025601 (2015). \n[14] E. O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007). \n[15] E. O. Kamenetskii, J. Phys.: Condens. Matter 22, 486005 (2010). \n[16] E. O. Kamenetskii, R. Joffe, and R. Shavit, Phys. Rev. A 84, 023836 (2011). \n[17] E. O. Kamenetskii, M. Berezin, R. Shavit, arXiv:1502.00220. \n[18] D. Patterson, M. Schnell, and J. M. Doyle, Nature 497, 475 (2013). \n[19] L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media , 2nd ed. (Pergamon,  \n       Oxford, 1984). \n[20] V.M. Agranovich and V.L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons , \n2nd ed. (Springer-Verlag, New York, 1984). \n[21] E.O. Kamenetskii, M. Sigalov, and R. Shavit, J. Appl. Phys. 105, 013537 (2009). \n[22] F. Wilczek, Phys. Rev. Lett. 58, 1799 (1987). \n[23] L. Visinelli, arXiv:1111.2268 (2011). \n[24]  X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Phys. Rev. B 78, 195424 (2008). \n[25] A. M. Essin, J. E. Moore, and D. Vanderbilt, Phys. Rev. Lett. 102, 146805 (2009). \n[26] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010). \n[27] R. Li, J. Wang, X.-L. Qi, and S.-C. Zhang, Nature Phys. 6, 284 (2010). \n[28] H. Ooguri and M. Oshikawa,  Phys. Rev. Lett. 108, 161803 (2012).  \n \n \n    \n  \n                                         ( a)                                             ( b)                              ( c) \n Fig. 1. The topological eigen characteristics of a ferrite disk for the main MDM oscillation. ( a) \nSpinning electric- and magnetic-field vectors in vacuum regions above and below a MDM-\nresonance ferrite disk. ( b) and ( c) the helicity factor. Evidently, we have a topological “helicity \ndipole”, which is aligned with the bias magnetic field. It means that ME properties are non-\ndegenerate with respect to the direction of the magnetic field. So, the MDM ferrite disk, being placed in a normal DC magnetic field, has a ME energy. Also, a topological “helicity dipole” is \nspatially anti-symmetric with respect to the disk middle plane. The MDM ferrite disk behaves as \na \n-symmetrical structure.     \n \n        \n           \n                                         ( a)                                                               ( b)                               \n \nFig. 2. ME-field reactive power flow near a ferrite disk for the main MDM oscillation. ( a) A \nview on a vacuum plane parallel to the ferrite-disk plane above a disk, ( b) a view on a cross-\nsection plane perpendicular to the ferrite-disk plane.  14 \n \n              \n     \n  \n                                         ( a)                                                                    ( b) \n   \nFig. 3. Variation of the angle between spinning electric and magnetic fields along the disk z-axis \nfor the main MDM. This angle gives evidence fo r a torsion structure of the ME field above and \nbelow a ferrite disk. The ME-energy density appears due to the torsion degree of freedom of the \nfield. ( a) Angle  for an upward directed bias magnetic field; ( b) angle  for a downward \ndirected bias magnetic field.  \n \n \n \nFig. 4. MDM microwave antenna: a waveguide radiation structure with a hole in a wide wall and \na thin-film ferrite disk as a basic building block. A ferrite disk is placed inside a 10TE -mode \nrectangular X-band waveguide symmetrically to its walls so that a disk axis is perpendicular to a \nwide wall of a waveguide. A hole diameter is much  less than a half wavelength of microwave \nradiation at the frequency regions used in the studies. \n     15\n \n \nFig. 5. Numerical reflection characteristic. Because of the presence of a radiation hole, high-order MDMs are not excited quite effectively. The forms of the resonance peaks give evidence \nfor the Fano-type interaction. \n \n \n                                  ( a)                                           ( b)                                          ( c) \n \nFig. 6. A normalized helicity parameter in a va cuum far-field region calculated based on Eq. (8). \n(a), (b) At the frequency  f = 8.138GHz and opposite directions of a bias magnetic field; ( c) at \nthe frequency far from the MDM resonance,  f = 8.120GHz. Periodicity of the helicity-parameter \nstriations is associated with the standing-wave behavior of regular EM waves in vacuum. Since a \nsign of a dynamical pseudoscalar field  in Eq. (14) is correlated with a direction of a bias \nmagnetic field applied to a ferrite disk, the striations change their signs, when a bias magnetic \nfield is in an opposite direction. ( c) At the frequency far from the MDM resonance, f = \n8.120GHz, one does not observe any field helicity ( cos 0).   \n    16\n \n(a) \n \n                                                                     ( b) \n \n                                                                               ( c)  17 \n \n                                                                                  ( d) \n \nFig. 7. A detailed analysis of the helicity pa rameter distribution in a vacuum far-field region at \nthe frequency f = 8.138GHz and a bias magnetic field directed along z axis. ( a), (b), The regions \nof localization of the helicity parameter on va cuum horizontal planes A-A and B-B for opposite \ndirections of a bias magnetic field. ( c) Along z-axis, the helicity parameter is correlated with the \nregions of localized reactive power flows. The maximums of the helicity-parameter modulus are \nat the same positions as the the regions of maxi mal gradient modulus of the reactive-power flow. \n(d), The maximums of the helicity-parameter modulus are at the regions of maximal gradient \nmodulus of the field (both electr ic and magnetic) intensities. 0 is the electromagnetic \nwavelength in vacuum.  \n \n \n                 Diel. plate 10r                                 Diel. plate 20r  \n                                                     ( a)                                                      ( b)   \nFig. 8. The pictures of the helicity parameter dist ributions for two dielectri c plates with different \npermittivity parameters and the same sizes. ( a) 10r; (b) 20r . \n \n  18\n \n                                                       ( a)                                          ( b) \n      \n                                                       \n                                                         ( c)                                      ( d) \n \nFig. 9. An array of small metallic helices is placed in a space between an antenna and a dielectric \nplate ( 10r). The helices do not change positions of the helicity-parameter striations. \nHowever, the regions inside every helix become green colored. It means that inside helices we \nhave restoration of a regular EM-field behavior. ( a), (b) side views; ( c), (d) views on a vacuum \nhorizontal plane;  ( a), (c) left-handed helices; ( b), (d)  right-handed helices.    \n \n \n \n  19                                                ( a)                                                         ( b)   \n \nFig. 10. Far-field helicity-factor distributions for the frequency f = 8.138GHz (the left slope of \nthe resonance peak) and the frequency  f = 8.140GHz (the right slope of the resonance peak). The \nselected regions show the helicity-factor distributions near a ferrite disk and near an antenna \naperture. Near an antenna aperture the helicity-factor distributions are different for the frequencies f = 8.138GHz and f = 8.140GHz. Different helicity-factor distributions in the \nradiation near-field region are orig ins of different helicity-facto r distributions in the far-field \nregion. ( a) Frequency f = 8.138GHz;   ( b) frequency f = 8.140GHz.        \n \n  \n \n \n \n                                                     ( a)                                                              ( b)   \n \nFig. 11. Normalized “electric” ( a) and “magnetic” ( b) helicity parameters in a vacuum far-field \nregion at the frequency f = 8.138GHz, calculated based on the equations (34). \n  20\n \n \nFig. 12. In the far-field region, the turn of a total electric field tcpEEE\n with respect to a \ncurl magnetic field cH\n is compensated by the turn of a total magnetic field tcpHHH\n with \nrespect to a curl electric field cE\n. This results in mutual perpendicularity between tE\n and tH\n. \nIn a local point in the far-field region, the “red” and “blue” heli city factors being superposed \none to another, give the “green” (zero) helicity factor. In other words, the negative ME energy is compensated by the positive ME energy.  "    },    {        "title": "1103.4390v1.Magnetic_Interactions_in_Ball_Milled_Spinel_Ferrites.pdf",        "content": " \n \nMagnetic Interactions in Ball-Milled Spinel Ferrites \n \nG. F. Goya  \nInstituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, SP Brazil \n \nSpinel Fe 3O4 nanoparticles have been produced through ball milling in methyl-alcohol \n(CH 3OH), aiming to obtain samples with similar average particle sizes <d> and different \ninterparticle interactions. Three samples having Fe 3O4/CH 3(OH) mass ratios R of 3 %, 10 % and 50 \n% wt. were milled for several hours until particle size reached a steady value (<d> ~ 7-10 nm). A \ndetailed study of static and dynamic magnetic properties has been undertaken by measuring magnetization, ac susceptibility and Mössbauer data. As expected for small particles, the Verwey \ntransition was not observed, but instead supe rparamagnetic (SPM) behavior was found with \ntransition to a blocked state at T\nB ~ 10-20 K. Spin disorder of the resulting particles, independent of \nits concentration, was inferred from the decrease of saturation magnetization M S at low \ntemperatures. For samples having 3% wt. of magnetic particles, dynamic ac susceptibility \nmeasurements show a thermally activated Arrheni us dependence of the blocking temperature with \napplied frequency. This behaviour is found to change as interparticle interactions begin to rule the \ndynamics of the system, yielding a spin-glass-like  state at low temperatures for R = 50 wt.% \nsample.  \n  \n 2    \n \nIntroduction \nThe ball mill (BM) of solid/liquid mixtures has become a very common tool for making \nhomogeneous dispersion at indust rial scales, such as paint and coating production techniques. [1,2] \nAmong the advantages of obtaining nanoparticles from BM in liquid phases are the speed of \nreaching a finished dispersion and the narrower di stribution of particle size. However, using a \ncarrier liquid for high-energy ball milling usually re sults in cemical reaction with solid particles \nyielding non-desired surface phases or even dissolu tion of the solid phase onto the liquid carrier.  \nRegarding the magnetic properties of such na noparticles, the study  of the mechanisms \nlinking particle shape, size distribution and surface structure to the resulting magnetic properties is \nhindered by the concurrency of several mechanisms  on the observed properties. These relationships \nare important to tailor magnetic and transport properties of nanostructu red spinel ferrites AB 2O4 for \napplications in magnetic and magnetoresistive de vices. For example, the high Curie temperature ( TC \n~ 850 K) and nearly full spin polarization at room temperature of magnetite Fe 3O4 make this \nmaterial appealing for spin-devices. The botto m line is the limit imposed by superparamagnetic \n(SPM) relaxation in nanometric devices that curta ils potential applications  at room temperature. \nRelaxation effects are in turn strongly depende nt on the magnetic dipolar  interactions between \nparticles, and thus there is an apparent need of disentangling th e influence of the dipole-dipole \ninteractions from other e ffects, such as surface di sorder, shape anisotropy, cluster aggregation, etc. \nIn this work, we present a study on the effects of interparticle interactions in magnetite \nnanoparticles dispersed in an organi c liquid carrier in different concen trations, in order to study the \ninfluence of such interactions on th e transition to the frozen state.  \n   3  \n \n \nExperimental Procedure \nThree samples consisting of a dispersion of magnetite (Fe 3O4) particles in a liquid carrier, \nwith different concentrations, have been prepared by ball-milling in a planetary mill (Fristch \nPulverisette 4). A mixture of magnetite powder (99.99 %, mean particle size ~0.5 μm) and methyl \nalcohol (between 20 and 40 ml) were  introduced in a hardened stee l vial and sealed in an Ar \natmosphere. The samples with 50, 10 and 3 % wt. of  magnetic material will be labeled F50, F10 and \nF3, respectively. All samples were ground for se veral times, extracting partial amounts after \nselected intervals to follow the evolution of th e mean particle size <d> of the magnetite phase, \nstopping the experiment after reaching a plateau of  <d> ~ 6-10 nm. The milling parameters and the \nresulting properties are summarized in Table I.  \nX-ray diffraction (XRD) measurements were pe rformed using a commercial diffractometer \nwith Cu-K α radiation in the 2 θ range from 10 to 80 degrees, and the morphology of the milled \nsamples was analyzed by Transmission Electron Microscopy (TEM). Mössbauer spectroscopy (MS) \nmeasurements were performed between 20 and 294 K in dried samples. A conventional constant-\nacceleration spectrometer was used in  transmission geometry with a 57Co/Rh source. The recorded \nspectra were fitted by single-site and distribution programs, using α-Fe at 294 K to calibrate isomer \nshifts and velocity scale. For magnetic measur ements, all samples were conditioned in closed \ncontainers before quenching the magnetite/methyl -alcohol mixture below its freezing point ( ~265 \nK) from room temperature. A commercial SQUI D magnetometer was employed to perform static \nand dynamic measurements as a function field, temperature and driving frequency. Zero-field- \ncooled (ZFC) and field-cooled (FC) curves were taken between 5K and 250 K, to avoid the melting \nof the solvent in the most diluted samples. Data were obtained by first cooling the sample from \nroom temperature in zero applied field (ZFC proce ss) to the basal temperature, then a field was \napplied and the variation of magne tization was measured with increasing temperature up to T = 250 4    \n \nK. After the last point was measured, the sample was cooled again to the basal temperature keeping \nthe same field (FC pr ocess); then the M vs. T data was measured fo r increasing temperatures. \n \nResults and Discussion \nTEM images showed that all samples consisted of agglomerates of particles with average \ngrain size <d> ~ 6-10 nm (Fig. 1). The clusters of particles observed in TEM images were difficult \nto break with ultrasonic treatment, and thus it is not clear whether these clusters might also exist in \nthe as milled  dispersion. The x-ray diffractograms of the three samples along the milling series \nshowed the same features: starting from well-defined peaks (for the initial ~0.5 μm particles), the \nlinewidth increased steadily with increasing milli ng time. All patterns could be indexed with the \nFe3O4 single phase (see figure 1), without any eviden ce of new phases formed during milling. It is \nworth to notice that previous  results on the same particle s showed the oxidation to Fe 2O3 after some \nminutes of milling when milled in open vials. The Scherrer formula was used to estimate the <d> \nvalues from each diffractogram (see  Table I), without considering pos sible contributions of crystal \nstress to the observed linewidth. Estimations of <d> from TEM data indicated good agreement with XRD data, although XRD data slightly underestimat es the average diameter, probably due to the \ncontribution of structural stress to the linewidth in milled samples. \nThe Mössbauer spectra at room temperature for all samples showed a superparamagnetic \ndoublet with the same hyperfine parameters with in experimental error (see Table I). As the \ntemperature is decreased, a magnetic  sextet develops and coexists with the SPM  doublet. For T = 20 \nK, the spectra showed only the sextet with broa dened lines (Fig. 2), which could be fitted using a \nhyperfine field distribution with mean values <B\nhyp> = 51.9 T, 51.3 T, and 52.2 T for samples F3, \nF10 and F50 respectively. The effect of thermal fluc tuations for sample F3 can be still observed at T \n= 20 K, as a broadening on the inner side of the spectral lines, which is absent in sample F50. This difference is related to the proximity of the u nblocking temperature in this sample, since the   5  \n \n \nstronger dipolar interact ions in F50 shift T B to higher values, as observe d from magnetization data \n(see below).  \nMagnetite has a cubic spinel structur e (space group Fd3m) that contains Fe3+ ions at \ntetrahedral sites ( A) and Fe3+/Fe2+ at octahedral sites ( B), yielding ferrimagnetic order below T C. [3] \nAt low temperature (the Verwey temperature, T V ~120 K) the systems undergoes a structural \ntransition, and concurrently the ma gnetic and transport properties show a sudden change at this \ntemperature. The ZFC/FC curves (figure 3) of the three samples show cl early that the Verwey \ntransition is absent, and SPM behaviour is observed above the blocking temperature T B which in \nturn depends on the concentration.  \nFigure 4 displays the ac susceptibility χ(T,ω) data of sample F3. Both real χ'(T) and \nimaginary χ''(T) components display a maximum at a temperature T m that depends on the driving \nfrequency.[4] To identify the dynamic mechanisms of the freezing process, we used the empirical \nparameter \n) ( log TT\n10 mm\nf ΔΔ= Φ , where Δ Tm is the shift of T m within the Δlog 10(f) frequency interval. \nThis parameter provides a model- independent classification of the blocking/freezing transition. It \ncan be seen in Table I that this value decreases  strongly from for higher concentrations. The value \nof F3 sample is close to the Φ = 0.13 expected for SPM systems. On  the other side, it is known that \nsmaller values of Φ usually result from strong interparticle interactions,[5]  in agreement with the \nincreasing concentration of samples F10 and F50 shown in Table I.  \nThe dynamic response of an ensemble of fine particles is determined by the measuring time \nτm (or frequency) of each experi mental technique. As the reversion of the magnetic moment in a \nsingle-domain particle over th e anisotropy en ergy barrier E a is assisted by thermal phonons, the \nrelaxation time τ exhibits an exponential dependence on temperature characterized by a Néel-\nArrhenius law  6    \n \n⎟⎟\n⎠⎞\n⎜⎜\n⎝⎛=T kE\nBaexp0τ τ  \nwhere τ0 is in the 10-9 - 10-11 s range for SPM systems. In the absence of an external magnetic field, \nthe energy barrier is given by , where K eff is an effective anisot ropy constant and V is \nthe particle volume. It can be observed from  Fig. 4 (inset) that the dependence of ln( f ) vs. T B-1 is \nlinear with a good approximation for sample F3, and accordingly the data was fitted using the Néel-\nBrown law yielding E a = 5.2x10-21 J. If the average particle size from Table I is us ed, the resulting \neffective anisotropy turn out to be K eff = 46.2 kJ/m3. This value is larger than the magnetocrystalline \nanisotropy constant of bulk magnetite K 1bulk\n = 11-13 kJ/m3, and this is likely to originate in an extra \ncontribution from interparticle interactions (of di polar nature) which can also modify the effective \nenergy barrier. Previous works on Fe 3O4 particles have shown that  dipolar interactions are \nnoticeable for concentrations of ~2 % vol. of magne tic particles [6] and thus the present value of \nKeff is likely to include the effects of particle-p article interactions even for the F3 sample. V Keff=aE\nFor sample F50, the temperature dependence of the cusp in χac(T) curves is frequency-\ndependent  (fig. 5), yielding the smaller Φ value shown in Table I. Since this low value could be \noriginated in dipolar interactions, we have s earched for spin-glass behavior, through the dynamic \nscaling of a.c. susceptibility by conventional crit ical slowing down for relaxation of the magnetic \nmoments. When approaching the freezing temperat ure of a spin-glass tr ansition from above, the \ncharacteristic relaxation time τ of individual magnetic moments w ill show critical slowing down, \ncharacterized by a power law τ ~ ξz, where ξ  is the correlation length and z is called the dynamical \nscaling exponent. Since ξ  itself has a power-law depende nce on the reduced temperature t = (T – \nTC)/TC, where T C is the freezing temperature, in terms of f = τ-1 we can write \nνzt f~ ,        ( Ι )    7  \n \n \nwhere ν is the correlation-leng th critical exponent. When plotte d in a semi-logarithmic graph, the \nexperimental data show the expected linear incr ease within the available experimental frequency \nrange (five decades), indicating a glassy beha vior. From the fit using Eq.(I) we obtained zν = 21 ±2 \nand T C = 18(2) K, see inset of Fig. 5. We mention here  that complete determination of the critical \nexponents at the SG transition, perf ormed by a full dynamic scaling of χ ”(f,T), gave similar values. \nThe obtained critical parameter product z ν is much larger than those reported for conventional 3D \nspin-glasses, making dubious the existe nce of a true transition with T g > 0. Large critical exponents \nhave been previously f ound in polycrystalline (Cu 0.75Al0.25)1-xMn x samples [7] and also in ball-\nmilled Fe 61Re30Cr9 alloys [8]. Also, clear evidence of  a SG phase transition through dynamic \nscaling analysis has been also found in concentr ated Fe-C nanoparticles [9 ], and it was proposed \nthat the conditions for this transition to exist ar e a) strong interparticle in teractions and b) narrow \nparticle-size distribution. Regarding the dynamics of spin glasses, it is  known that for a broad \ntemperature range spanning the transition temperat ure, each atomic moment is dynamically active, \nwhereas for single-domain magnetic particles a variable fraction may be blocked in the \nexperimental time window. Unless a very large interp article distances (high dilution) is achieved in \nthese samples, the blocked fraction of particles will act as a random field on th at fraction that is \nunblocking (for a given temperature and time window). Our observation that for the present \nconcentrated sample, a scaling analysis is possibl e to achieve is intrigui ng, since these ball-milled \nsamples have a broad particle size distribution. This, in turn, should make impossible to reach the \nexperimental situation in which the characteristic time scale associated with collective dynamics exceeds the single-particle relaxation times in the experimental time window. More work is needed \nto clarify this point. \nIn summary, we have studied the structural and magnetic properties of ball-milled magnetite \nparticles dispersed in organic solvent, with diffe rent concentrations, show ing the gradual evolution 8    \n \nfrom SPM to spin-glass-like behavi or. Although spin disorder is likel y to occur in these samples, no \ndefinite evidence was found of enhancement of the magnetic anisotropy at the surface, nor of \nexchange coupling between particle surface and co re. We have found that the static and dynamic \nproperties can be understood by cons idering changes in the single- particle anisotropy energy E a \nthrough the effect of interpar ticle interactions in thes e concentrated systems.  \n \nAcknowledgements \nThe author wishes to express his gratitude to  the Brazilian agencies FAPESP and CNPq for \nproviding partial financial support. \n \n   9  \n \n \nReferences \n \n \n[1] P.K. Panigrahy, G. Goswami, J.D. Panda  and R.K. Panda, Cement Concrete Res. 33  (2003) 945. \n[2] I.A. Susorov, Russ. J. Appl. Chem., 71 (1998) 1825.  \n[3] R. M. Cornell and U. Schwertmann, in The Iron Oxides , VCH Publishers, New York (1996), \nCh. 2.  \n[4] J.L. Dormann, D. Fi orani and E. Tronc, in Advances in Chemical Physics , Ed. By I. Prigogine \nand S.A. Rice. Vol. XCVIII 326 (1997). [5] J.A. Mydosh, in “Spin Glasses: An Experimental Introduction” , edited by Taylor & Francis \n(1993). For Φ values of interacting ma gnetite nanoparticles, see G.F. Goya, T.S. Berquó, F.C. \nFonseca and M.P. Morales,  J. Appl. Phys. 94, 3520 (2003). \n[6] W. Luo, S.R. Nagel, T.F. Rosenbaum  and R.E. Rosensweig, Phys. Rev. Lett. 67, 2721 (1991). \n[7] E. Obradó, A. Planes, and B. Martínez, Phys. Rev. B 59, 11 450 (1999). \n[8] J. A. De Toro, M. A. López de la Torre, M. A. Arranz, J. M. Riveiro, J. L. Marínez, P. Palade, \nand G. Filoti, Phys. Rev. B 64, 094438 (2001). [9] T. Jonsson, P. Svedlindh, and M. F. Hansen, Phys. Rev. Lett. 81, 3976 (1998). \n \n \n \n \n \nFIGURE CAPTIONS \nFigure 1.  X-ray diffraction patte rn for sample F50. Insets s how the corresponding TEM image. \nFigure 2. Mössbauer spectra of sample F3 (a) a nd sample F50 (b) at T = 20 K. The solid lines \nare the best fit to experime ntal data (open circles).  \nFigure 3. Zero-Field Cooled (ZFC) and Field-C ooled (FC) curves for samples of different \nconcentrations, taken with H FC = 100 Oe.  \nFigure 4. Main panel: Temperature dependence of the real component χ’(ω,Τ) ac \nsusceptibility for F3 sample, at different  driven frequencies fro m 10 mHz to 1.5 kHz. \nArrows indicate increasing frequencies. Left lower panel: Imaginary component \nχ’’(T).  Upper panel: Arrhenius plot of the relaxation time τ vs. inverse blocking \ntemperature T B-1. Solid line is the best fit using Eq. (3) with τ0 = 1.3x10-14 s and \nEa/kB = 378 K. \n 10    \n \nFigure 5.  Main panel: Temperature dependence of the real component χ’(ω,Τ) ac susceptibility \nfor F50 sample, at different driven freque ncies from 10 mHz to 1.5 kHz. The arrow \nindicates the direction of increasing frequencies. Inse t: log-log plot for the reduced \ntemperature (T – T C)/TC versus external frequency. Solid  line is the best fit using eq. \n(I), with T C = 18(2) K and z ν = 21(1).  \n \n  \nTable Captions  \n \nTable I: Some properties of samples F3, F 10 and F50: weight ratio R = 100{Fe 3O4/CH 3(OH)}, \nball-milling time, average particle diameters <d > (from X-ray data), blocking temperature T B (dc \nmagnetization), relative shift of the ac susceptibility maxima Φ (see text), and hyperfine parameters \nat 20 and 294 K: hyperfine field (B hyp), quadrupolar splitting (Q S), Isomer shift (IS). \n    11  \n \n \n \n \n \n \n \n10 20 30 40 50 60 70 800100200300400500Intensity\n2θ (degrees)\n30 nm   \n                      \n  12    \n \n \n \n-12 -8 -4 0 4 8 12F50\n velocity (mm/s)F3\n  Transmission (a.u.)\n \n       13  \n \n \n 0 50 100 150 200 2500.00.30.6H = 100 Oe\n  \nT (K)51015F50\nF10\nF3\n \n M (emu/g)203040\n  14    \n \n \n \n0 1 02 03 04 00.91.2\n  χ' (x10 -4 emu/mol)\nT (K)10 20 30 40 χ'' (x10 -6 emu/mol)\n  \nT (K)10 12 14-8-404F3\n  ln(τ)\nTB-1 (x10 -2 K -1)\n \n \n    \n    15  \n \n \n \n   \n 0 30 60 90 120 1500.51.01.5\nF50 947 Hz\n 400 Hz\n 150 Hz\n 80 Hz\n 11 Hz\n 2 Hz\n 0.07 Hz\n 0.02 Hz\n  χ' (x10-2 emu/g)\nT (K)-1.1 -1.0 -0.9-202zν = 21(1)\nTC = 18(2) K\n log [ f (Hz)]\nlog [(T - TC ) / TC]"    },    {        "title": "1103.4935v2.Electronic_Structures__Born_Effective_Charges_and_Spontaneous_Polarization_in_Magnetoelectric_Gallium_Ferrite.pdf",        "content": " 1Electronic Structures, Born E ffective Charges and Spontaneous 1 \nPolarization in Magnet oelectric Gallium Ferrite 2 \n 3 \nAmritendu Roy1, Somdutta Mukherjee2, Rajeev Gupta2,3, Sushil Auluck4, Rajendra 4 \nPrasad2 and Ashish Garg1*  5 \n1 Department of Materials Science & Engi neering, Indian Institute of Technology, 6 \nKanpur - 208016, India 7 \n2 Department of Physics, Indian In stitute of Technology, Kanpur - 208016, India 8 \n3 Materials Science Programme, Indian Institute of Technol ogy, Kanpur - 208016, India 9 \n4 National Physical Laboratory, Dr. K. S. Krishnan Marg, New Delhi-110012, India 10 \n 11 \nABSTRACT 12 \n 13 \nWe present a theoretical study of the struct ure-property correlation in gallium ferrite, 14 \nbased on the first principles calculations followed by a subs equent comparison with the 15 \nexperiments. Local spin density approxima tion (LSDA+U) of the density functional 16 \ntheory has been used to cal culate the ground state structur e, electronic ba nd structure, 17 \ndensity of states and Born effective charges.  Calculations reveal that the ground state 18 \nstructure is orthorhombic Pc2 1n having A-type antiferromagnetic  spin confi guration, with 19 \nlattice parameters matching well with those obtained experimentally. Plots of partial 20 \ndensity of states of constituent ions exhibit noticeable hybridization of Fe 3d, Ga 4s, Ga 21 \n4p and O 2p states. However, the calculated char ge density and electron localization 22 \nfunction show largely ionic character of the Ga/Fe-O bonds which is also supported by 23 \nlack of any significant anomaly in the calcula ted Born effective charges with respect to 24 \nthe corresponding nominal ionic charges. The calculations show a spontaneous 25 \npolarization of ~ 59 C/cm2 along b-axis which is largely due to asymmetrically placed 26 \nGa1, Fe1, O1, O2 and O6 ions.  27 \n 28 \nKey Words:  First-principles calculations, Density functional theory, Gallium ferrite, 29 \nLSDA+U   30 \n 31 \nPACS No.:  71.15.Mb, 77.84.-s, 75.50.Pp, 72.80.Ng  32 \n 33 \n34 \n                                                 \n* Corresponding author, Tel: +91-512-2597904; FAX - +91-512-2597505, E-mail: ashishg@iitk.ac.in    2I. INTRODUCTION 1 \n 2 \nGallium ferrite (GaFeO 3 or GFO) is a piezoelectric a nd a ferrimagnet with its magnetic 3 \ntransition temperature close to the room  temperature (RT).[1, 2] The transition 4 \ntemperature is affected largely by the Fe:Ga ratio within the single phase region (0.67 ≤ 5 \nFe/Ga ≤ 1.86) [3] and can be tuned to the valu es above RT. [[1, 3-5] As a result, 6 \naccompanied by a good piezoelectric response,[ 6] compositionally modulated GFO is an 7 \nexciting room temperature magnetoelectric mate rial. Initial structural studies on this 8 \ncompound predicted the structure to be orthorhombic with Pc2 1n symmetry [4, 7, 8], 9 \nconfirmed subsequently by recent studies usi ng neutron [1, 2, 9, 10] and x-ray diffraction 10 \n[1, 3, 10, 11] investigations made on both powder and single crystals over a wide 11 \ntemperature range (4K-700K). The orthorhombi c unit-cell comprises of eight formula 12 \nunits and the RT lattice parameters are: a = 8.7512 Å, b = 9.3993 Å, c = 5.0806 Å.[8] The 13 \nunit-cell contains two nonequivalent Ga and Fe sites and there are six nonequivalent O 14 \nsites. While Ga2, Fe1 and Fe2 are octahedrally coordinated by oxygen, Ga1 has 15 \ntetrahedral coordination.[1] However, experi mental observations reveal considerable 16 \ncation site disorder indicating partial occupa ncy of Ga and Fe sites by Fe and Ga ions, 17 \nrespectively. [1, 8] The cation si te disorder is also believed to be responsible for observed 18 \nferrimagnetism in GFO.[1]. Although not mu ch has been reported on the structural 19 \ndistortion in GFO, asymmetric nature of Ga1-O tetrahedron is  believed to contribute to 20 \nthe piezoelectricity in GFO with its piezoel ectric coefficient being almost double to that 21 \nof quartz. [12]  22 \nDespite a series of experimental studi es, theoretical work, especially first- 23 \nprinciples based calculations on GFO, have not really progressed, presumably because of 24 \nthe complex crystal structure and partial site  occupancies of the cations. The only report 25 \nby Han et al. [13] emphasizes on the magnetic struct ure and spin-orbit coupling behavior 26 \nusing a linear combination of localized pse udoatomic orbitals (LCPAO). However, there 27 \nare no reports on the theoretical understand ing of the structure, bonding and Born 28 \neffective charges of GFO which is crucial to elucidate the structural distortion, nature of 29 \nbonds and resulting polarization in GFO. Here, we present a first-principles density 30 \nfunctional theory based calculation of the ground state structur e of GFO along with 31 \nexperimental determination of structural para meters of a polycrystal line sample at room 32 \ntemperature. The calculations confirm that the ground state st ructure of GFO is A-type 33 \nantiferromagnetic. We find that the Ga/Fe-O bo nds have largely ioni c character with no 34 \nanomaly in the magnitude of Born effectiv e charges. The calculations indicate the 35 \npresence of a large spontaneous polarization (P s) in GFO with a magnitude of ~ 59 36 \nC/cm2 along its b-axis.  37 \n 38 \nII. CALCULATION AND EXPERIMENTAL DETAILS 39 \n 40 \nOur entire calculation is based on the first-principles density  functional theory. [14]  41 \nVienna ab-initio simulation package (VASP) [15, 16] was used with the projector 42 \naugmented wave method (PAW) [17]. The Ko hn-Sham equation [18] was solved using 43 \nthe local spin density approximation (LSDA+U)  [19] with the Hubbard parameter, U = 5 44 \neV, and the exchange interaction, J = 1 eV. LS DA+U has been found to be quite efficient 45 \nin describing strongly correlated multiferro ic systems [20, 21] in comparison to the 46  3conventional local density approximation (LDA)  and generalized gradient approximation 1 \n(GGA). We employed the simplified, rotatio nally invariant approach introduced by 2 \nDudarev.[22] The value of U was optimized su ch that the moments of the magnetic ions 3 \nare satisfactorily described with respect to th e experiment. [1] We also checked that small 4 \nvariation of U from the optimized value does not alter the stru ctural stability.  5 \n 6 \nThe calculations are based on the stoi chiometric GFO assuming no partial 7 \noccupancies of the constituent ions. We  included 3 valence electrons of Ga ( 4s24p1), 8 for 8 \nFe (3d74s1) and 6 for O ( 2s22p4) ions. A plane wave energy cut-off of 550 eV was used. 9 \nThe conjugate gradient algorithm [23] was used  for the optimization of the structure. All 10 \nthe calculations were performed at 0 K.  Structural optimi zation and calculation of the 11 \nelectronic band structure and density of stat es were carried out using a Monkhorst-Pack 12 \n[24] 7×7×12 mesh. Born effective charges, and spontaneous polarization for the ground 13 \nstate structure were calculated using Berry  phase method [25] with a 3×3×3 mesh. A 14 \ncomparison of some of the results of th e 3×3×3 mesh agree quite well with those 15 \nobtained using a denser k-mes h. We also repeated some of  our calculations using the 16 \ngeneralized gradient approxi mation (GGA+U) with the optim ized version of Perdew- 17 \nBurke-Ernzerhof functional for solids (PBEsol) [26] to check the consistency of 18 \nLSDA+U calculations. The effect of Ga 3d semicore state was studied with LSDA+U 19 \nand GGA+U methods using a diffe rent pseudopotential of Ga  that includes 13 valence 20 \nelectrons ( 3d104s24p1), while keeping all other pse udopotentials same. The calculations 21 \nwere performed using a Monkhorst-Pack 3×3×3 mesh. We started our calculations with 22 \nthe experimental structural parameters obtained from the neutron diffraction spectra of 23 \ncrushed single crystals of GaFeO 3 obtained at 4 K.[1 ] In order to obtain the ground state 24 \nstructure, ionic positions, lattice parameters  and unit-cell shape were sequentially relaxed 25 \nin such a way that the pressure on the op timized structure is almost zero and the 26 \nHellmann-Feynman forces are less than 0.001 eV/Å.  27 \n 28 \nBorn effective charge (BEC) tensor of an atom k, is defined as: 29 \n                                    2\n, *\n,\n,, =                     (1)k\nk\nkkP F EZV \n\n \n     30 \n 31 \nwhere, Prepresents polarization induced by the periodic displacement ,k or by the 32 \nforce ,kF induced by an electric field . E is the total energy of the unit cell. In the 33 \npresent calculation we displa ced each ion by a small but fi nite distance along the three 34 \nright handed Cartesian axes (unit-cell paramete rs are along the Cartes ian axes), one at a 35 \ntime and calculated the polarization. Change in polarization with respect to undistorted 36 \nstructure divided by the displacement gives the elements of Born char ges in a particular 37 \ndirection for an ion.  38 \n 39 \nTo corroborate the calculations with th e experimental data, we synthesized a 40 \npolycrystalline GaFeO 3 (Fe:Ga – 1:1) sample using the conventional solid-state-reaction 41 \nroute by mixing - Ga 2O3 and -Fe 2O3 powders. Powder diffraction data of the sintered 42 \npellet was collected on a Philips X’Pert Pro MRD diffractometer using Cu K radiation. 43  4Further, Rietveld refinement of the data was done using the FULLPROF 2000 [27] 1 \npackage using orthorhombic Pc2 1n symmetry of GFO.  2 \n 3 \nIII. RESULTS AND DISCUSSION 4 \n 5 \nA. Structural Optimizati on: Ground state structure 6 \n 7 \nTo determine the ground state structure as well as to elucidate the magnetic structure of 8 \nGFO, we considered four possible antiferromagne tic spin configurations as shown in Fig. 9 \n1(a)-(d) i.e. AFM-1 (A-type), AFM-2 (C-type), AF M-3 (G-type) and AFM-4. It should 10 \nbe noted that AFM-4 represents a possible spin  configuration which is different from the 11 \nconventional A, C and G-type. In addition to the above, we also considered other possible 12 \nspin configurations which would ensure an tiferromagnetism in GFO,  but were found to 13 \nbe equivalent to one of the above shown in Fi g. 1(a)-(d).  While previous reports confirm 14 \nthe ground state structure of GFO to be antif erromagnetic [13], there is no discussion on 15 \nthe possible antiferromagnetic configurations. Th e results of total energy calculations of 16 \nthe four structures show that while ener gies of AFM-3 and AF M-4 structures are 17 \nmaximum (947.202 meV/unit-cell and 839.823 meV/ unit-cell, respectively higher than 18 \nAFM-1 structure); AFM-2 falls in the intermediate range with AFM-1 having the lowest 19 \nenergy. Hence, the stability of different spin  configurations can, be ordered as: AFM-1 > 20 \nAFM-2 > AFM-4 > AFM-3. On this basis,  we can conclude that AFM-1 spin 21 \nconfiguration is the most favored configuration in Pc2 1n symmetry of GFO in the ground 22 \nstate. Hence, all further calculations were performed on AFM-1 structure.  23 \n 24 \nGround state crystal structure was determin ed by further relaxing the size, shape 25 \nand ionic positions while maintaining AFM-1 spin configuration. The calculations show 26 \nthat the ground state structure retains the original Pc2 1n symmetry observed 27 \nexperimentally at 298 K [8] and at 4 K [1] and also corroborated by our XRD data 28 \n(shown in Fig. 2). A schematic representati on of the ground state crystal structure is 29 \nshown in the inset of Fig. 2. The calcu lated ground state lattice parameters, using 30 \nLSDA+U, are: a = 8.6717 Å, b = 9.3027 Å and c = 5.0403 Å which correspond well with 31 \nour experimental data:  a = 8.7345 Å, b = 9.3816 Å and c = 5.0766 Å. Our calculation 32 \nusing GGA+U method yielded the ground st ate lattice parameters as follows: a =  33 \n8.77119 Å, b =  9.40936Å and c = 5.09811Å. The calculate d and experimentally 34 \ndetermined lattice parameters are also in close agreement with the previously reported 35 \ndata: a = 8.71932 Å, b = 9.36838 Å and c =5.06723 Å at 4 K [1], a = 8.72569 Å, b = 36 \n9.37209 Å and c =5.07082 Å at 230 K [1], a = 8.7512 Å, b = 9.3993 Å and c =5.0806 Å 37 \nat 298 K [8]. Thus, the lattice parameters  calculated using GGA+ U and LSDA+U at 0 K 38 \nare in good agreement with the experimental da ta obtained at 4 K [1],  within a difference 39 \nof ~ ±7 %. This difference can  be attributed to the approximation schemes of LSDA and 40 \nGGA. Moreover, it should be noted that the ca lculated ground state st ructure is perfectly 41 \nordered while the experimental structures may consist of partial cati on site occupancies. 42 \nMany first-principles calculations on Ga containing oxides include Ga 3d as semicore 43 \nstates.[28] To investigate the effect of Ga 3d semicore state, we al so performed structural 44 \noptimization of GFO using LSDA+U and GGA+U with a different pseudopotential of Ga 45 \nthat includes 13 valence electrons ( 3d104s24p1), while keeping all other pseudopotentials 46  5same. Structural optimization showed that  the optimized lattice parameters are: a = 1 \n8.642695 Å, b = 9.271509 Å and c = 5.023425 Å for LSDA+U and ( a = 8.836875 Å, b = 2 \n9.479817 Å and c = 5.136288 Å) for GGA+U. A comparison of these values with the 3 \nexperimental data as shown above, shows these to be even farther from the experimental 4 \ndata. While a comparison with the values calculated without considering Ga 3 d semicore 5 \nstate shows that inclusion of Ga 3d semicore state slightly underestimates the lattice 6 \nparameters in LSDA+U but overestimates in GGA+U. We, therefore,  performed further 7 \ncalculations using the pseudopot ential of Ga that incl udes 3 valence electrons ( 4s24p1) 8 \nsince it provides a be tter accuracy of the st ructural parameters. 9 \n 10 \nThe present experimentally determined ionic positions of stoichiometric GFO, 11 \nalong with the calculated ground state ionic posi tions are listed in Table 1 which shows 12 \nthat Fe1 and Fe2 ions lie on alternate planes parallel to the ac-plane. Since Fe1 and Fe2 13 \nhave antiparallel spin configurations and ar e situated on alternat e parallel planes, we 14 \nconclude (see Fig 1) that the ground state magnetic stru cture of GFO is A-type 15 \nantiferromagnetic. Fig. 2 (inset) also show s the coordination of the cations by oxygen: 16 \nGa1 is tetrahedrally coordinated while Ga2, Fe1 and Fe 2 are octahe drally coordinated by 17 \nthe surrounding oxygen ions.  18 \n 19 \nFrom the positions of the ions in the cal culated ground state structures and in the 20 \nexperimentally determined stoichiometric GFO at 298 K, we calculated the bond lengths 21 \nof cations with neighboring oxygen ions. Tabl e 2 consisting of cal culated cation-oxygen 22 \nand cation-cation bond lengths, shows a good agr eement with the present and previous 23 \nXRD [8] and neutron data [1]. Mi nor differences can be attributed to a number of factors, 24 \nsuch as, temperature, site disorder a nd the limitation of the exchange correlation 25 \nfunctionals used in our study.  Using the bond length data  from Table 2, we also 26 \ncalculated the structural dist ortions of the oxygen polyhedra. [29] The distortion can be 27 \nquantified by determining the distorti on index [30] which is defined as: 28 \n 1() 1n\nia v\ni avllDInl\n     ( 2 )  29 \nwhere li is the bond length of ith coordinating ion and lav is the average bond length.  30 \n 31 \nThe calculations show DI values of Ga 1-O tetrahedron is ~ 0.006 (at ground state 32 \nfor both LSDA+U and GGA+U) and 0.008 at 298 K and as a result, the effective anion 33 \nco-ordination (~3.99 (LSDA+U and GGA+U), ~ 3. 98 (expt.)) is almost identical to that 34 \nof a regular tetrahedron  i.e. 4. Here, the effective coordi nation number (ECoN) [31] is 35 \ndefined as: 36 \n 37 \n 6\nexp 1i\ni avlECoNl\n\n     ( 3 )  38 \nIn contrast, Ga2-O octahedron shows apprec iable distortion (DI ~ 0.012 (LSDA+U), ~ 39 \n0.013 (GGA+U) and ~ 0.026 (expt.)) compared to a regular octahedron which is also 40 \nreflected in a smaller co-ordination number  of 5.93 (LSDA+U), 5.92 (GGA+U) and 5.75 41 \n(expt.) than the perfect octahedral co-ordination i.e. 6. This distortion is more significant 42  6in case of Fe1-O and Fe2-O octahedra w ith DI values of 0.056 (LSDA+U.), 0.057 1 \n(GGA+U) and 0.057 (expt.) and 0.063 (LSDA+ U.), 0.062 (GGA+U) and, 0.059 (expt.), 2 \nrespectively while the corres ponding average co-ordination numbers are 5.05 (LSDA+U.), 3 \n5.04 (GGA+U) and 4.74 (expt.) and 4.81 (L SDA+U.), 4.83 (GGA+U) and 4.92 (expt.), 4 \nrespectively. Thus, it is obse rved that for almost all the oxygen polyhedra, the cations are 5 \ndisplaced from the center of th e polyhedra. The significance of these distortions lies in 6 \nimparting the non-centrosymmetry to the structure which resu lts in the development of 7 \nspontaneous polarization in GFO, as  shown later in section III(C). 8 \n 9 \nB. Electronic Band Structure, De nsity of States and Bonding 10 \n 11 \nFig. 3 shows the LSDA+U calculated el ectronic band structure along high symmetry 12 \ndirections and total density of  states of GFO. The Fermi energy is fixed at 0 eV. The 13 \nfigure shows the plots of the band structure and total density of states  demonstrating that 14 \nthe bands are spread over three major en ergy windows. The uppe rmost part of the 15 \nvalence band spreads over -7.73 eV to 0 eV . Above the Fermi level, the conduction band 16 \ncan again be divided into two part s: first part in the energy ra nge from 1.77 eV to 2.45 eV 17 \nwhile another part in the energy range from 3.0 eV to 16.83 eV (s hown partially). The 18 \nangular momentum character of the bands sp read over different energy regions can be 19 \ndetermined from the partial density of stat es (PDOS) of the const ituent ions. PDOS of 20 \nFe1, Ga1 and O1 ions are shown in Fig. 4. As  the nature of PDOS of the other ions is 21 \nsimilar, these plots are not shown here. Thes e figures show that the valence band (-7.73 22 \neV to 0 eV) mainly consists of Fe 3d and O 2p states with signi ficant amount of Ga 4s 23 \nand Ga 4p characters also present in the lower energy side of this energy range. Beyond 24 \nthe Fermi level, a narrow energy band (1. 77 eV to 2.45 eV) contains mainly Fe 3d 25 \ncharacter. The highest energy window (3.0 eV  to 16.83 eV) has contributions from Fe 3d, 26 \nGa 4s, Ga 4p and O 2p states. More importantly, PDOS demonstrate significant 27 \nhybridization of Fe 3d, Ga 4p and O 2p states throughout the uppermost part of the 28 \nvalence band. Such hybridi zation of transition metal d state and O 2p state has been 29 \nfound to impart ferroelectricity in a number of perovskite ox ides [32, 33] and can be of 30 \ninterest in GFO too. 31 \n 32 \nAs shown in Fig. 3, our LSDA+U calcu lations yielded a direct band gap ( Eg) of 33 \n~2.0 eV ( Γ- Γ) while GGA+U calculations showed a direct band gap of ~ 2.25 eV. 34 \nCalculation of band structure using LSDA+ U method with pseudopot ential treating Ga 35 \n3d as semicore state, did not reveal any no ticeable change from that of our earlier 36 \ncalculation and a direct band gap ( Eg) of ~ 1.98 eV ( Γ- Γ) was obtained. However, 37 \nexperimental studies based on optical abso rption spectra of GFO report a band gap of 38 \n2.7-3.0 eV.[34] The difference between calculated band gap and the experimental data is 39 \nexpected (due to underestimation of ba nd gap by the LSDA and GGA methods) and is 40 \ncommon in electronic stru cture calculation of oxides. [35, 36]   41 \n 42 \nMoreover, PDOS data in Fig. 4 can al so shed light on the bonding behavior in 43 \nGFO, especially partial covalency of cation- anion bonds, which can be further correlated 44 \nwith the functional properties of GF O. From Fig. 4, we find that Fe  3d and O 2p states 45 \nare significantly hybridized in the uppermost part of the va lence band in GFO.  For a 46  7detailed analysis, we have plotted the charge density distribution calculated using 1 \nLSDA+U, on three principal planes of the unit cell as shown in Fig. 5(a). The figure 2 \nshows that although most of the charges are sy mmetrically distributed along the radius of 3 \nthe circles, indicating largel y ionic nature of bonding, sm all amount of covalency is 4 \nshown by minor asymmetry of the charges arou nd O ions connected to Fe1, Fe2, Ga1 and 5 \nGa2 ions.  6 \n 7 \nHowever, nature of binding interaction as  determined from the charge density 8 \ndistribution alone is not conclu sive. We, therefore, utilized electron localization function 9 \n(ELF) which provides a measure of the local  influence of the Pauli repulsion on the 10 \nbehavior of the electrons and allows  the mapping of core, bonding and nonbonding 11 \nregions of the crystal in real space. Thus ELF can be used as  a tool to differentiate the 12 \nnature of different types of bonds. [37] A la rge value of ELF function indicates a region 13 \nof small Pauli repulsion, in ot her words, space with anti-parallel spin configuration while 14 \nthe position with maximum ELF va lue has signature of electrons pair. [37]  Fig. 5(b) and 15 \n(c) show the ELF distribution in three principa l planes and in the entire unit cell of GFO, 16 \nrespectively, calculated by LSDA+U method. Fi g. 5(b) also depicts the maximum ELF 17 \nvalue at O sites and small values at Fe and Ga  sites indicating charge transfer interaction 18 \nfrom Fe/Ga to O sites. Comparing Fig. 5(a) a nd (b), we find that almost complete charge 19 \ntransfer takes place between Fe 2 and O3 ions. Similar charge  transfer, albeit to a lesser 20 \nextent, is also observed between  Fe1 and O1, O2 ions. Thus we  can conclude that the Fe- 21 \nO bonds in GFO are mostly ionic. In contrast , polarization of ELF from O sites toward 22 \nother O sites and finite value of ELF between O and Ga1 (Fig. 5(b)) indicate some degree 23 \nof covalent characteristics. Similar feature is expected for Ga2-O bonds as shown in Fig. 24 \n5(c). Therefore, from the charge density a nd electron localization f unction plots, we can 25 \nassert that Ga/Fe- O bonds in GFO are largely of ionic charac ter. The ionicity is greater 26 \nfor Fe-O bonds, while some degree of hybridiz ation is observed in Ga-O bonds indicating 27 \ncovalency.  28 \n 29 \n 30 \nC. Born Effective Charge and Spontaneous Polarization 31 \n 32 \nThe nature of bonding can further be correlate d with the Born effective charges (Z*), 33 \ndefined in section II. These charges are impor tant quantities in el ucidating the physical 34 \nunderstanding of piezoelectric and ferroelec tric properties since they describe the 35 \ncoupling between lattice displacements and th e electric field. Born charges are also 36 \nindicators of long range Coulomb interactio ns whose competition with the short range 37 \nforces leads to the ferroelectric transiti on. Previous studies on many perovskite 38 \nferroelectric show anomalously large Born charges for some of the ions [32, 33] which 39 \nare often explained as manifestation of st rong covalent character of bonds between the 40 \nspecific ions. In GFO, from the charge dens ity and ELF plots, we have observed that 41 \ncharge sharing between the Ga/Fe and O ions  in cation-oxygen bonds is not significant in 42 \ncomparison to conventional perovskite ferroel ectrics. [32, 33] On the other hand, from 43 \nthe structural data we find that the catio n-oxygen polyhedra are hi ghly distorted. Since 44 \nferroelectric and piezoelectric responses ar e combined manifestations of structural 45 \ndistortions and effective charges of the constituent ions [38], it is imperative to calculate 46  8the Born effective charges of the constituent io ns in GFO. Such a calculation would help 1 \nto elucidate the nature of cation-oxygen bond s and the origin of polarization in the 2 \nmaterial. 3 \n 4 \nIn the present work, we have calculated the Born effective charge tensors of 5 \nnonequivalent ions in Pc2 1n structure of GFO by slightly displacing each ion, one at a 6 \ntime, along three axes of the Cartesian co-ordinates and th en calculating the resulting 7 \ndifference in polarization, using Berry phase  method. [25] We used LSDA+U technique 8 \nfor this calculation. Table 3 lists the three diag onal elements of the Born effective charge 9 \ntensors of each ion along with  their nominal charges. Here, we observe that that Ga1 ion 10 \nhas elements of effective charge tensors clos e its nominal ionic char ge and hence, it is 11 \nconcluded that all the bonds between Ga1 and surrounding O i ons are primarily ionic in 12 \nnature. On the other hand, Ga2 develops a maximum effective charge of 3.53 , ~ 18 % 13 \nhigher with respect to its static charge of +3. In contrast, both Fe1 and Fe2 ions show 14 \nmuch higher increase in the effective char ges, 36 % and 27 % respectively, while oxygen 15 \nions show a maximum reduction of 39.5 % wi th respect to the nominal ionic charge. 16 \nInterestingly, all these elements that have maximum change with respect to the respective 17 \nstatic charges are along z-axis (except for Ga1). Howe ver, the direction of P s is along y- 18 \naxis i.e. crystallographic b-direction. [1] Hence, unlike in most perovskite ferroelectrics 19 \n[32, 33], the polarization in GFO is not due to large effective ionic charges. Instead, it is 20 \nmost likely to be caused by the structural  distortion and noncen trosymmetry of the 21 \nstructure.  22 \n 23 \nTo compare our results on Born effective charges with the effective charges 24 \ncalculated by other methods, we calculated th ese charges on each ionic site using bond 25 \nvalence method in which bond valen ce charge (V) is defined as:  26 \n0exp( )i\ni\niiR RVvb                             (4) 27 \nwhere, R0 is the ideal bond length for a bond with valence 1, Ri is measured bond length 28 \nand b is an empirical constant. We have also estimated effective charge distribution [29] 29 \nat different ionic sites based on the nomina l ionic charges and polyhedra parameters. The 30 \nresults obtained from both methods are show n in Table 3. Though these calculations are 31 \nin no way comparable to the ab-initio  calculations, they are useful in getting a trend of 32 \nthe effective charges. The comparison shows that although the calculated Born effective 33 \ncharges using ab-initio  method are larger than the effec tive charges calculated using bond 34 \nvalence method and charge distribution method,  all the calculations of effective charges 35 \npoint toward the fact that the cation- oxygen bonds in GFO are largely ionic and 36 \nsubstantiate the discussion in  the preceding paragraph. 37 \n 38 \nThe Born effective charges can also be used to quantify the spontaneous 39 \npolarization in GFO. Although previous studi es [1, 12] indicate the direction of P s along 40 \n[010]-direction, there is no conclusive experimental report on the value of P s. Although 41 \nArima et al [1] predicted a P s ~ 2.5 C/cm2 based on the displacement of Fe ions from 42 \nthe center of FeO 6 octahedra, such point  charge calculation does not provide a correct 43 \nestimate since various other contributions to P s were neglected. As we see later, these 44 \nother contributions are from the sources such  as Ga1-O tetrahedra and Ga2-O octahedra, 45  9and more importantly, effective ionic charges. To compare, we have calculated P s of 1 \nGFO in its ground state using both nominal ionic charges a nd calculated Born effective 2 \ncharges.  3 \n 4 \nFrom the crystallography perspective, GFO having Pc2 1n space group, allows 5 \nfollowing symmetry operations to be performed: (i) c-operation, a glide translation along 6 \nhalf the lattice vector of c-axis leading to (½–x, y, ½+z), (ii) 21 operation, 2-fold screw 7 \nrotation around b-axis leading to (-x, ½+y, -z) and (iii) n-operation, a glide translation 8 \nalong half of the face-diagonal leading to (½ +x, ½+y, ½-z). Here, we observe that the 9 \napplication of first and third operations ( c and n respectively) on the atom positions does 10 \nnot put any constraint on the displacement and in turn polarization vector remains 11 \nunrestricted. However, when 2 1 symmetry operator is applied i.e. when the cell is screw 12 \nrotated by 180° about [010]-axis i.e. b-axis, it changes the crystal polarization from (Px, 13 \nPy, Pz) to (-Px, Py, -Pz) as (x,y,z) becomes (-x,y,-z). This shows that the crystal 14 \npolarization along a- and c-axis is equal to zero and is non-zero along b-axis. Further, 15 \nusing the Born effective charges from Table 3, we calculated the spontaneous 16 \npolarization (P s) as ~ 58.63 C/cm2 which is an order of magnitude larger than that 17 \npredicted by Arima et al.  [1]. Similar calculation using the nominal ionic charges yielded 18 \nPs of ~ 30.53 C/cm2, almost half the value obtained us ing the Born effective charges. 19 \nWe, therefore, conclude that though the values  of Born charges of the constituent ions are 20 \nnot anomalously large unlike some perovskite  ferroelectrics [32, 33], they do seem to 21 \naffect the spontaneous polarization re sponse in GFO rather significantly.   22 \n 23 \nWe also calculated partial polarizat ion in order to estimate the relative 24 \ncontribution of individual ions. A schematic of  the partial polarizati on contributions from 25 \nindividual ions toward the total spontaneous pol arization has been shown in Fig. 6. It was 26 \nfound that while the cont ribution from Ga1 is the largest, it is counter-balanced by the 27 \nopposite contributions from Fe1, O1, O2 and O6 . Interestingly, the st ructure data (Table 28 \n1 and Fig. 2) also shows that these ions are the most asymmetrically placed around the 29 \ninversion center of symmetry while Ga2 and Fe2 cations maintain almost 30 \ncentrosymmetric configuration and contribute l east to the total polarization. Therefore, 31 \nwe conclude that the spontan eous polarization in GFO is primarily contributed by the 32 \nasymmetrically placed Ga1, Fe1, O1, O2 and O6 ions. However, at elevated temperatures, 33 \nthe site disordering between Fe1 and Ga1 site s is expected [1] which may substantially 34 \nlower the spontaneous pol arization. This should be of interest for further theoretical 35 \ninvestigations incorporating the e ffect of disorder on calculations.  36 \n 37 \nCONCLUSIONS 38 \n 39 \nWe have presented a theoretica l study of the structure-prop erty relationship in gallium 40 \nferrite (GFO), supported by the experimental data. First-principles density functional 41 \ntheory based calculations were performed to calculate the ground state structure of GFO. 42 \nThe calculations support an or thorhombic structure with Pc2 1n symmetry and A-type 43 \nantiferromagnetic spin configuration in the ground stat e with calculated ground state 44 \nlattice parameters, bond strength and bond angl es agreeing well with the experimental 45 \nresults. While, the electronic density of states show hybridization among Fe 3d, Ga 4s, 46  10Ga 4p and O 2p states, calculations of electronic charge density demonstrate almost 1 \nsymmetrical charge distribution on most of the major planes i ndicating an ionic nature of 2 \nbonds. Calculation of the elect ron localization function furt her supported a largely ionic 3 \ncharacter of Fe-O bonds and a finite degree of hybridization among O, Ga1 and Ga2 ions. 4 \nMoreover, lack of any significan t anomaly in the Born effec tive charges with respect to 5 \nthe corresponding nominal ionic charges again emphasized towards ionic character of the 6 \nbonds. Calculations also showed a spontaneous polarization of ~ 59 C/cm2 along b- 7 \ndirection i.e. [010]-axis, attributed primarily to the structural distortion.  8 \n 9 \nAcknowledgements 10 \n 11 \nAuthors thank Prof. M.K. Harbola (Physics, IIT Kanpur) for valuable discussions on the 12 \nwork and his suggestions. AR and SM thank Ministry of Human Resources, Government 13 \nof India for the financial support. 14 \n 15 \nReferences: 16 \n[1] Arima, T, Higashiyama, D, Kaneko, Y, He , J P, Goto, T, Miyasaka, S, Kimura, T,  17 \nOikawa, K, Kamiyama, T, Kumai, R and Tokura, Y 2004 Phys. Rev. B  70  064426. 18 \n[2] Kaneko, Y, Arima, T, He, J P, Kumai, R and Tokura, Y 2004 J. Magn. Magn. 19 \nMater.  272-276  555-556. 20 \n[3]      Mukherjee, S, Gupta, R., Garg, A., Unpublished . 21 \n[4] Remeika, J P 1960 J. Appl. Phys.  31 S263-S264. 22 \n[5] Nowlin, C H and Jones, R V 1963 J. Appl. Phys.  34 (4) 1262-1263. 23 \n[6] White, D. L 1960 Bull. Am. Phys. Soc.  5 189. 24 \n[7] Wood, E 1960 Acta Crystallogr.  13 (8) 682. 25 \n[8] Abrahams, S C, Reddy, J M and Bernstein, J L 1965  J. Chem. Phys.  42 (11) 26 \n3957-3968. 27 \n[9] Kang, K Uk, Kim, S B, An S Y, Cheong, S W and Kim, C S 2006 J. Magn. Magn. 28 \nMater.  304 (2) e769-e771. 29 \n[10] Mohamed, M B, Senyshyn, A, Ehrenberg, H and Fuess, H 2010 J. Alloys  Compd. 30 \n492 (1-2)  L20-L27. 31 \n[11] Kim, W, We, J H, Kim, S J and Kim, C S 2007 J. Appl. Phys.  101  09M515-3. 32 \n[12] Abrahams, S C and Reddy, J M. 1964 Phys. Rev. Lett. , 13 688. 33 \n[13] Han, M J, Ozaki, T and Yu, J 2007 Phys. Rev. B  75 060404. 34 \n[14] Jones, R O and Gunnarsson, O 1989 Rev. Mod. Phys.  61 689. 35 \n[15] Kresse, G and Furthmüller, J 1996 Phys. Rev. B  54 11169. 36 \n[16] Kresse, G and Joubert, D 1999 Phys. Rev. B  59 1758. 37 \n[17] Blöchl, P E 1994 Phys. Rev B  50 17953. 38 \n[18] Kohn, W and Sham, L J 1965 Phys. Rev.  140 A1133. 39 \n[19] Anisimov, V I, Aryasetiawan, F and Lichtenstein, A I 1997 J. Phys.: Condens. 40 \nMatter  9 767. 41 \n[20] Neaton, J B, Ederer, C, Waghmare , U V, Spaldin, N A and Rabe, K M 2005 Phys. 42 \nRev. B  71 014113. 43 \n[21] Cai, M.Q, Liu, J C, Yang, G W, Cao, Y L, Tan, X, Chen, X Y, Wang, Y G, Wang, 44 \nL L and Hu, W Y 2007 J. Chem. Phys.  126 154708-6. 45  11[22] Dudarev, S L, Botton, G A, Savrasov,  S Y, Humphreys, C J and Sutton, A P 1998 1 \nPhys. Rev. B  57 1505. 2 \n[23] Press, W H, Flannery, B P, Teukolsky, S A and Vetterling, W T em Numerical 3 \nRecipes . Cambridge University Press: New York, 1986. 4 \n[24] Monkhorst, H  J, Pack, J D 1976 Phys. Rev. B  13 5188. 5 \n[25] King-Smith, R D and Vanderbilt, D 1993 Phys. Rev. B  47 1651. 6 \n[26] Perdew, J P, Ruzsinszky, A, Csonka, G, Vydrov, O A, Scuseria, G. E, Constantin, 7 \nL A, Zhou, X and Burke, K 2008 Phys. Rev. Lett.  100 136406. 8 \n[27]     Rodríguez-Carvajal , J 1993 Physica B: Condens Matter 192(1-2) 55-69. 9 \n[28]     Yoshioka, S, hayashi, H, Kuwaba ra, A, Oba, F, Matsunaga, K and Tanaka, I 2007 10 \nJ. Phys.: Condens. Matter  19 346211.   11 \n[29] Momma, K and Izumi, F 2008 J. Appl. Crystallogr.  41 653-658. 12 \n[30] Baur, W H 1974 Acta Crystallogr. Sect. B: Struct. Sci.  30 1195. 13 \n[31] Hoppe, R, Voigt, S, Glaum, H, Kissel, J, Muller, H P and Bernet, K 1989 J. Less- 14 \nCommon Met.  156 105. 15 \n[32] Ghosez, P, Gonze, X, Lambin, P and Michenaud, J P, 1995 Phys. Rev. B  51 6765. 16 \n[33] Roy, A, Prasad, R, Auluck, S and Garg, A 2010 J. Phys.: Condens.Matter 22 17 \n165902. 18 \n[34] Sun, Z H, Dai, S, Zhou, Y L, Cao, L Z and Chen, Z H  2008 Thin Solid Films  516  19 \n7433-7436. 20 \n[35] Medeiros, S K, Albuquerque, E L, Maia, J F F, Caetano, E W S, Farias, G. A, 21 \nFreire, V N, Cavada, B S, Pe ssati, M L and Pessati, T L P 2005 Microelectronics Journal  22 \n36  1058-1061. 23 \n[36] Robertson, J, Xiong, K and Clark, S J 2006 Thin Solid Films  496, 1-7. 24 \n[37] Savin, A, Nesper, R, Wengert, S and Fässler, T F 1997 Angewandte Chemie 25 \nInternational Edition in English  36 1808-1832. 26 \n[38] Cohen, R. E 2008 Springer Series in Materials Science 114 471 27 \n 28 \n 29  12Tables  \nTable 1 – Calculated ground state ionic positions of orthorhombic ( Pc2 1n) GFO using LSDA+U and GGA+U along with Rietveld refined \nexperimental data.  \n \nIon LSDA+U GGA+U Experiment at 298 K \nX y z x Y z x y z \nGa1 (4 a) 0.15101 0.99844 0.17665 0.15125 0.99844 0.175969 0.15291 0.00000 0.17900 \nGa2 (4 a) 0.16068 0.30818 0.81637 0.16087 0.30817 0.81653 0.15902 0.30413 0.81446 \nFe1 (4 a) 0.15512 0.58224 0.18817 0.15477 0.58248 0.18690 0.15299 0.58079 0.20291 \nFe2 (4 a) 0.03075 0.79453 0.67380 0.03078 0.79453 0.67314 0.03197 0.79907 0.67050 \nO1  (4 a) 0.32292 0.42757 0.98443 0.32260 0.42709 0.98386 0.32120 0.42638 0.98250 \nO2  (4 a) 0.48576 0.43140 0.51922 0.48600 0.43128 0.51976 0.98915 0.43217 0.51623 \nO3  (4 a) 0.99672 0.20019 0.65659 0.99694 0.20084 0.65734 0.99730 0.19794 0.66331 \nO4  (4 a) 0.16218 0.19907 0.15803 0.16176 0.19902 0.15796 0.16015 0.19924 0.14523 \nO5  (4 a) 0.16719 0.67266 0.84410 0.16752 0.67224 0.84306 0.15901 0.66492 0.84351 \nO6  (4 a) 0.16636 0.93781 0.52144 0.16635 0.93800 0.52079 0.16260 0.94593 0.52414 \n  13Table 2 - Calculated bond lengths from the ground state ionic positions of orthorhombic ( Pc2 1n) GFO  along with experimental data from the \npresent work and previously reported data (*: Present work, $: Ref. [1], #: Ref. [7] ) \n \nBond length \n(Å) Theory  Experimental Da ta %Difference (LSDA+U- \nExperiment at 4 K) LSDA+U GGA+U  298 K*  4 K$ 298 K# \nGa1-O2 1.849 1.869  1.853 1.844 1.851 0.27 \nGa1-O6 1.832 1.852  1.826 1.822 1.813 0.55 \nGa1-O6' 1.854 1.873  1.863 1.836 1.867 0.98 \nGa1-O4 1.871 1.892  1.878 1.857 1.852 0.75 \nGa2-O3 1.918 1.935  1.891 1.892 1.927 1.37 \nGa2-O1 1.983 1.998  2.012 1.985 2.011 -0.10 \nGa2-O2 1.993 2.019  2.041 2.006 2.054 -0.65 \nGa2-O4 2.007 2.032  2.050 2.059 2.077 -2.53 \nGa2-O4' 1.999 2.021  1.946 1.996 2.037 0.15 \nGa2-O1' 2.013 2.037  2.046 2.053 2.051 -1.95 \nFe1-O1 2.082 2.114  2.041 2.064 2.058 0.87 \nFe1-O1' 2.291 2.319  2.347 2.354 2.361 -2.68 \nFe1-O2 2.046 2.068  2.094 2.074 2.06 -1.35 \nFe1-O3 1.884 1.908  1.842 1.905 1.866 -1.10 Fe1-O5 1.923 1.943  1.957 1.918 1.936 0.26 \nFe1-O5' 1.930 1.949  1.989 1.934 1.934 -0.21 \nFe2-O1 2.326 2.352  2.328 2.324 2.354 0.09 \nFe2-O2 2.042 2.064  2.056 2.025 2.064 0.84 \nFe2-O4 2.075 2.098  2.137 2.131 2.093 -2.63 \nFe2-O3 1.897 1.917  1.959 1.943 1.946 -2.37 \nFe2-O5 1.850 1.874  1.894 1.875 1.872 -1.33 Fe2-O6 1.936 1.959  1.937 1.958 1.971 -1.12 \nFe1-Fe2 3.201 3.240  3.164 3.201 3.234 0 \nGa1-Ga2 3.231 3.271  3.286 3.246 - -0.46 \nFe2-Ga2 3.062 3.100  3.102 3.089 3.007 -0.87 \nFe1-Ga1 3.320 3.354  3.387 3.328 - -0.24 \nFe1-Ga2 3.165 3.198  3.123 3.216 3.121 -1.59 \n   14 \nTable 3- Diagonal elements of the Born effec tive charge tensors computed using Berry phase \ntechnique within LSDA+U. The bond valen ce charges (V) were calculated using bond \nlength data based on the ground state structural  parameters.  Nominal ionic charges are \nalso provided for comparison.  \n  \nIon Nominal ionic \ncharge (e) Z* (e) Charge \ndistribution (e) Bond valence \ncharge (e) Zxx Z yy Z zz \nGa1 3 3.01 3.11 2.99 2.83 2.88 \nGa2 3 3.57 3.16 3.53 3.23 3.02 \nFe1 3 3.66 3.78 4.08 3.04 3.10 \nFe2 3 3.68 3.38 3.82 2.90 3.20 \nO1 -2 -2.29 -2.58 -2.79 -1.56 - \nO2 -2 -2.45 -2.29 -2.41 -2.12 - \nO3 -2 -2.54 -2.30 -2.75 -2.04 - \nO4 -2 -2.27 -2.85 -2.17 -2.02 - \nO5 -2 -2.50 -2.16 -2.79 -2.10 - \nO6 -2 -2.32 -2.08 -2.40 -2.16 - \n \n                           15List of Figures \n \nFig. 1 Schematics of different antiferromagnetic sp in configurations considered in the present \ncalculations. The configurations are assigned as (a) AFM-1 (A-type), (b) AFM-2 (C-type), \n(c) AFM-3 (G-type) and (d) AFM- 4 (Different variant).   \n Fig. 2  Rietveld refinement of room temperatur e XRD data of stoichiometric GFO. Inset shows \nschematic of the crystal structure of GaFeO\n3 having orthorhombic Pc2 1n symmetry. \n Fig. 3 Electronic structures of orthorhombic (\nPc2 1n) GaFeO 3 calculated using the LSDA+U \nmethod. Left panel shows plot of total density of states as a function of energy while right \npanel shows electronic band st ructure along high symmetry directions. The zero in the \nenergy axis is set at the highest occupied level. \n Fig. 4  PDOS plots of Ga1 4s and 4p states, Fe1 \n3d state and O1 2s and 2p states calculated using \nthe LSDA+U method. The vertical blue line indicates the Fermi level.  \n Fig. 5  Plots of (a) charge density  along three principal planes of GaFeO\n3 unit cell, (b) electron \nlocalization function calculat ed using the LSDA+U method al ong three principal planes \nof GaFeO 3 unit cell keeping the area of the planes in accordance with the respective \nlattice parameters and (c) 3-D image of elect ron localization functi on distribution in the \nGaFeO 3 unit cell.  \n Fig. 6  Schematic diagram showing partial pola rization of individual io ns along crystallographic \nb-direction. The strength and direction of polarization is depicted by the size and \ndirection of the arrows.  \n \n  \n  16\n \n \nFig. 1. Roy et al,  \n         17\n \n \nFig. 2. Roy et al,  \n                       18\n \n \nFig. 3. Roy et al,  \n     19\n \n \nFig. 4. Roy et al,  \n      20    \n  \n \nFig.5. Roy et al,  \n      21\n \n \nFig.6. Roy et al, \n      "    },    {        "title": "2305.14753v1.Time_reversal_Invariance_Violation_and_Quantum_Chaos_Induced_by_Magnetization_in_Ferrite_Loaded_Resonators.pdf",        "content": "Time-reversal Invariance Violation and Quantum Chaos Induced by Magnetization in\nFerrite-Loaded Resonators\nWeihua Zhang,1, 2Xiaodong Zhang,1and Barbara Dietz1, 2,∗\n1Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics,\nLanzhou University, Lanzhou, Gansu 730000, China\n2Center for Theoretical Physics of Complex Systems,\nInstitute for Basic Science (IBS), Daejeon 34126, Korea\n(Dated: May 25, 2023)\nWe investigate the fluctuation properties in the eigenfrequency spectra of flat cylindrical mi-\ncrowave cavities that are homogeneously filled with magnetized ferrite. These studies are motivated\nby experiments in which only small pieces of ferrite were embedded in the cavity and magnetized\nwith an external static magnetic field to induce partial time-reversal ( T) invariance violation. We\nuse two different shapes of the cavity, one exhibiting an integrable wave dynamics, the other one a\nchaotic one. We demonstrate that in the frequency region where only transverse-magnetic modes\nexist, the magnetization of the ferrites has no effect on the wave dynamics and does not induce\nT-invariance violation whereas it is fully violated above the cutoff frequency of the first transverse-\nelectric mode. Above all, independently of the shape of the resonator, it induces a chaotic wave\ndynamics in that frequency range in the sense that for both resonator geometries the spectral prop-\nerties coincide with those of quantum systems with a chaotic classical dynamics and same invariance\nproperties under application of the generalized Toperator associated with the resonator geometry.\nI. INTRODUCTION\nFlat, cylindrical microwave resonators are used since three decades to investigate in the context of Quantum\nChaos [1–9] the properties of the eigenfrequencies and wave functions of quantum systems with a chaotic dynamics\nin the classical limit [10–15]. Here, the analogy to quantum billiards of corresponding shape is used, which holds\nbelow the frequency of the first transverse-magnetic mode. Namely, in the frequency range, where the electric field\nstrength is parallel to the cylinder axis, the associated Helmholtz equation is identical to the Schr¨ odinger equation\nof the quantum billiard of corresponding shape. The classical counterpart of a quantum billiard consists of a two-\ndimensional bounded domain, in which a point-like particle moves freely and is reflected specularly on impact with\nthe boundary [16–19]. The dynamics of the billiard depends only on its shape. Therefore, such systems provide a\nsuitable model to investigate signatures of the classical dynamics in properties of the associated quantum system.\nExperiments have also been performed with three-dimensional microwave resonators [13, 20–24], where the analogy\nto the quantum billiard of corresponding shape is lost, because of the vectorial nature of the Helmholtz equations.\nTheir objective was the study of wave-dynamical chaos.\nIn the above mentioned experiments properties of quantum systems with a chaotic classical counterpart and pre-\nserved time-reversal ( T) invariance were investigated. In order to induce T-invariance violation in a quantum system\na magnetic field is introduced. Quantum billiards with partially violated Tinvariance were modeled experimentally\nwith flat, cylindrical microwave resonators containing one or more pieces of ferrite that were magnetized with an\nexternal magnetic field [25–32]. Time-reversal invariance is violated through the coupling of the spins in the ferrite,\nwhich precess with the Larmor frequency about the external magnetic field, to the magnetic-field component of the\nresonator modes, which depends on the rotational direction of polarization of the latter. The effect, that leads to\nT-invariance violation is especially pronounced in the vicinity of the ferromagnetic resonance and its harmonics or\nat the resonance frequencies of the ferrite piece that lead to trapped modes inside in it [30]. The motivation of the\npresent study is the understanding of the electrodynamical processes that take place inside a magnetized cylindrical\nferrite, especially of its wave-dynamical properties and dependence on its shape.\nIn this work we compute with COMSOL multiphysics the eigenfrequencies and electric field distributions of flat,\ncylindrical metallic resonators, that are homogeneously filled with fully magnetized ferrite material and investigate\nthe fluctuation properties in the eigenfrequency spectra in the realm of Quantum Chaos. We choose two different\nshapes, one which has the shape of a billiard with integrable dynamics, the other one with chaotic dynamics. The\nspectral properties are studied in the frequency range where only transverse-electric modes exist and the Helmholtz\n∗bdietzp@gmail.comarXiv:2305.14753v1  [nlin.CD]  24 May 20232\nequation is scalar, and in the region where it is vectorial. In Sec. II we review properties of ferrite and the associated\nwave equations. They reduce to that of the quantum billiard of corresponding shape with no magnetic field in the\ntwo-dimensional case. In Sec. III we present the models that are investigated and in Sec. IV the results for the\nspectral properties. Interestingly, in the region where also transverse-magnetic modes exist, even for the resonator\nwith the shape corresponding to a dielectric-loaded cavity with integrable wave dynamics, they coincide with those\nof a quantum system with chaotic classical dynamics. Our findings are discussed in Sec. V.\nII. REVIEW OF THE WAVE EQUATIONS FOR A METALLIC RESONATOR HOMOGENEOUSLY\nFILLED WITH MAGNETIZED FERRITE\nA ferrite is a non-conductive ceramic with a ferrimagnetic crystal structure. Similar to antiferromagnets, it consists\nof different sublattices whose magnetic moments are opposed and differ in magnitudes. When applying a static\nexternal magnetic field, these magnetic moments become aligned. This process can be effectively described as a\nmacroscopic magnetic moment. We consider a flat cylindrical resonator made of ferrite [33, 34] which is magnetized\nby a static magnetic field perpendicular to the resonator plane, and enclosed by a perfect electric conductor (PEC).\nThe macroscopic Maxwell equations for an electromagnetic field with harmonic time variation [35],\n⃗E(⃗ x, t) =⃗E(⃗ x)e−iωt,⃗B(⃗ x, t) =⃗B(⃗ x)e−iωt(1)\npropagating through the resonator read\n⃗∇ × ⃗E =iω⃗B (2)\n⃗∇ ×(ˆµ−1⃗B) =−iϵr(⃗ x)\nc2ω⃗E (3)\n⃗∇ ·⃗B = 0 (4)\n⃗∇ ·⃗E = 0, (5)\nwhere c=1√ϵ0µ0is the speed of light in vacuum, ϵ0andµ0are the permittivity and permeability in vacuum and\nϵris the relative permittivity, which due to the assumed homogeneity of the material does not depend on ⃗ xin\nthe bulk of the resonator. Furthermore, ˆ µrdenotes the permeability tensor, which may be expressed in terms\nof the susceptibility tensor ˆ χas ˆµr= 1+ ˆχ, and results from the magnetization ⃗M(⃗ x) = ˆχ⃗H(⃗ x) of the ferrite,\n⃗B(⃗ x) =µ0ˆµr⃗H(⃗ x) =µ0\u0010\n⃗H(⃗ x) +⃗M(⃗ x)\u0011\n.\nCombination of the first two equations yields wave equations for ⃗E(⃗ x) and ⃗B(⃗ x) [14, 25],\n⃗∇ ×h\nˆµ−1\nr∇ × ⃗E(⃗ x)i\n−ϵr(⃗ x)k2\n0⃗E(⃗ x) = 0 , (6)\n⃗∇ ×n\n⃗∇ ×h\nˆµ−1\nr⃗B(⃗ x)io\n−ϵr(⃗ x)k2\n0⃗B(⃗ x) = 0 , (7)\nwith k0=ω\ncdenoting the wavenumber in vacuum. The magnetization follows the equation of motion\nd⃗M\ndt=|γ|⃗M×⃗H, (8)\nresulting from the torque exerted by the magnetic field ⃗H(⃗ x) on ⃗M(⃗ x). Here, γ=−2.21·105mA−1s−1denotes the\ngyromagnetic ratio of the electron. The magnetic field ⃗H(⃗ x) is composed of the static magnetic field ⃗H0=H0⃗ ezapplied\nin the direction of the cylinder axis of the resonator, which is chosen parallel to the zaxis, and the magnetic-field\ncomponent of the electromagnetic field,\n⃗H(⃗ x) =H0⃗ ez+⃗h(⃗ x)eiωt. (9)\nWe assume that the strength H0is sufficiently large to ensure that the magnetization attains its saturation value\nMs=χ0H0, with χ0denoting the static susceptibility. Similarly, ⃗M(⃗ x) is given by a superposition of the static\nmagnetization Ms⃗ ezand the magnetization resulting from the electromagnetic field,\n⃗M=Ms⃗ ez+⃗ meiωt. (10)3\nThe magnetization ˆMis obtained by inserting Eqs. (9) and (10) into Eq. (8). We may assume that the contributions\noriginating from the electromagnetic field in Eqs. (9) and (10) are sufficiently small compared to that of the static\nparts, so that only terms linear in ⃗hand⃗ mneed to be taken into account, yielding ⃗M(⃗ x) = ˆχ⃗H(⃗ x) with\nˆχ=\nχ−iκ0\niκ χ 0\n0 0 χ0\n, (11)\nandχ(ω) =ωLωM\nω2\nL−ω2, κ(ω) =ωωM\nω2\nL−ω2. Here, ωM=|γ|MandωL=|γ|H0denote the precession frequency about the\nsaturation magnetization ⃗Msand the Larmor frequency, with which the magnetization ⃗Mpresesses about ⃗H0, respec-\ntively. The quantities χ(ω) and κ(ω) exhibit a pronounced resonance behavior around the ferromagnetic resonance\nω=ωL. With these notations the inverse of ˆ µris given by\nˆµ−1\nr= (1 + ˆχ)−1=\n1+χ\nδiκ\nδ0\n−iκ\nδ1+χ\nδ0\n0 01\n1+χ0\n, δ= (1 + χ)2−κ2. (12)\nThe resonators under consideration have a cylindrical shape with a non-circular cross section and the external magnetic\nfield is constant and perpendicular to the resonator plane. Furthermore, the ferrite material is homogeneous, that\nis, in the bulk the entries of ˆ µrandϵrare spatially constant and only depend on the angular frequency ωof the\nelectromagnetic field. This is distinct from the experiments presented in Refs. [25–32], where Tinvariance violation\nwas induced by inserting cylindrical ferrites with circular cross section into an evacuated metallic resonator. There,\nthe origin of the Tinvariance violation is the coupling of the spins of the ferrite to the magnetic field components of\nthe electromagnetic field excited in the resonator, which depends on their rotational direction. It is strongest in the\nvicinity of the ferromagnetic resonances and at resonance frequencies of the ferrite, were modes are trapped in it [30].\nIn these microwave resonators, ˆ µrandϵrare spatially dependent, since they experience a jump at the surface of the\nferrite.\nFor a ferrite enclosed by a PEC the boundary conditions are given by\n⃗ n(⃗ xS)×⃗E=⃗0, ⃗ n(⃗ xS)·⃗B= 0, (13)\nwith ⃗ n(⃗ xS) denoting the normal to the ferrite surface at ⃗ xSpointing away from the resonator. Here, the surface\ncharge density and surface current density may be neglected due to the high resistivity of the ferrite. Defining\n⃗E=Ex⃗ ex+Ey⃗ ey+Ez⃗ ez, this yields at the bottom and top planes of a flat, cylindrical resonator of height h, where\n−⃗ n(x, y, z = 0) = ⃗ n(x, y, z =h) =⃗ ez, the boundary conditions\nEx(x, y, z = 0) = Ex(x, y, z =h) =Ey(x, y, z = 0) = Ey(x, y, z =h) = 0 . (14)\nAlong the side wall they read\nnxEy=nyEx, Ez= 0, ⃗ nt= (nx(s), ny(s),0) (15)\nwith sparametrizing the contour of the resonator in a plane parallel to the ( x, y) plane. This condition leads to a\ncoupling of ExandEy.\nAccordingly, we may separate the electromagnetic field into modes propagating in the resonator plane, denoted by\nan index tand modes perpendicular to it, i.e., in zdirection.\n⃗E=⃗Et+Ez⃗ ez,⃗B=⃗Bt+Bz⃗ ez,⃗∇=⃗∇t+⃗ ez∂\n∂z(16)\nand\nˆµ−1\nr⃗∇= ˆm⃗∇t+m0⃗ ez∂\n∂z,ˆµ−1\nr⃗B= ˆm⃗Bt+m0Bz⃗ ez (17)\nwith\nˆm=\u00121+χ\nδiκ\nδ\n−iκ\nδ1+χ\nδ\u0013\n, m0=1\n1 +χ0. (18)\nFurthermore, due to the cylindrical shape we may assume that\n⃗E(x, y, z ) =⃗E(x, y)e−ikzz,⃗B(x, y, z ) =⃗B(x, y)e−ikzz. (19)4\nThe electromagnetic waves are reflected at the PECs terminating the resonator at the top and bottom, implying that\nkz=qπ\nh, q= 0,1, . . . , (20)\nthat is, k2=k2\nt+k2\nz=k2\nt+q2\u0000π\nh\u00012fork≥qπ\nh.\nThe Maxwell equations become\niω⃗Bt=h\nikz⃗Et+⃗∇tEzi\n×⃗ ez, iωB z=h\n⃗∇t×⃗Eti\n·⃗ ez (21)\n−iϵr(⃗ x)\nc2ω⃗Et=h\nm0⃗∇tBz+ikzˆm⃗Bti\n×⃗ ez, −iϵr(⃗ x)\nc2ωEz=h\n⃗∇t×\u0010\nˆm⃗Bt\u0011i\n·⃗ ez (22)\n⃗∇t·⃗Et=ikzEz, ⃗∇t·⃗Bt=ikzBz. (23)\nThe in-plane modes can be expressed in terms of the modes perpendicular to the plane. For this we insert the first\nequation of Eq. (21) into the first one of Eq. (22) and vice versa yielding\n−i\u0002\nϵrk2\n01−k2\nzˆm\u0003⃗Et=ωm0⃗∇tBz×⃗ ez−kzˆm⃗∇tEz (24)\ni\u0002\nϵrk2\n01−k2\nzˆm\u0003⃗Bt=kzm0⃗∇tBz+ϵr(⃗ x)\nc2ω⃗∇tEz×⃗ ez. (25)\nThe wave equation Eq. (6) can also be separated into in-plane modes and modes perpendicular to the resonator plane.\nNamely,\n⃗∇ ×h\nˆµ−1\nr⃗∇ × ⃗E(⃗ x)i\n= ˆµ−1\nr⃗∇\u0010\n⃗∇ ·⃗E\u0011\n+\u0010\nˆµ−1\nr⃗∇\u0011← −∇ ·⃗E−⃗∇ ·\u0010\nˆµ−1\nr⃗∇\u0011\n⃗E (26)\nwhere the gradient← −∇is applied to the term to its left. According to Eq. (5) the first term on the right hand side\nvanishes. Inserting this equation into Eq. (6) and separating into modes in the resonator plane and perpendicular to\nit yields\nh\n⃗∇t·\u0010\n1+χ\nδ⃗∇t\u0011\n−ikz∂\n∂zn\n1\n1+χ0o\n+i⃗∇t·\u0010\n⃗ ez×κ\nδ⃗∇t\u0011i\n⃗E (27)\n−\n\u0010\n⃗∇\b1+χ\nδ\t∂\n∂x−⃗∇\biκ\nδ\t∂\n∂y\u0011\n·⃗E\u0010\n⃗∇\b1+χ\nδ\t∂\n∂y+⃗∇\biκ\nδ\t∂\n∂x\u0011\n·⃗E\n−ikz⃗∇n\n1\n1+χ0o\n·⃗E\n=\u0010\n1\n1+χ0k2\nz−ϵrk2\n0\u0011\n⃗E, (28)\nwhere curly brackets mean that ⃗∇is only applied to the terms framed by them. For q= 0 in Eq. (20), i.e., kz= 0\nthe electric field is perpendicular to the resonator plane, ⃗E(r) =E(x, y)⃗ ezand Eq. (27) becomes\n\u0014\n⃗∇t·\u00121 +χ\nδ⃗∇t\u0013\n+i⃗∇t·\u0010\n⃗ ez×κ\nδ⃗∇t\u0011\u0015\nE(x, y) =−ϵrk2\n0E(x, y), E(x, y)\f\f\n∂Ω= 0 (29)\nwith Dirichlet boundary conditions along the boundary ∂Ω. For the case considered here, i.e., for spatially constant\nˆµr, the wave equation reduces to the scalar Helmholtz equation\n∆tE(x, y) =−ϵrδ\n1 +χk2\n0E(x, y) =−k2E(x, y), E(x, y)\f\f\n∂Ω= 0 (30)\nyielding the dispersion relation\nk=s\nϵrδ\n1 +χk0=s\nϵr(ωL+ωM)2−ω2\nωL(ωL+ωM)−ω2k0. (31)\nEquations (29)- (31) hold up to\nkcrit=π\nh(32)5\nor, equivalently, with ¯ ω2=(ωL+ωM)2+\u0010\ncπ\nh√ϵr\u00112\n2\nωcrit=vuut¯ω2±s\n¯ω4−ωL(ωM+ωL)\u0012cπ\nh√ϵr\u00132\n, (33)\nwhere for vanishing external field, i.e., for ωL=ωM= 0 the plus sign has to be taken in the radicand, yielding\nωcrit\nr=cπ\nh√ϵr. (34)\nFor nonzero ωLandωMthe minus sign applies. Thus, below the cutoff circular frequency of the first transverse-\nelectric mode, referred to as critical in the following, ωcritthe wave equation coincides with that of a quantum\nbilliard [16, 17, 19] in a dispersive medium [36–39]. This correspondence between quantum billiards and the scalar\nHelmholtz equation of flat, cylindrical microwave cavities has been used in numerous experiments to determine their\neigenvalues and eigenfunctions [10–12, 14, 15]. The corresponding classical billiard consists of a point particle which\nmoves freely inside a bounded two-dimensional domain and is reflected specularly at the wall.\nIII. NUMERICAL ANALYSIS\nWe investigated the spectral properties of ferrite-loaded metallic resonators with the shapes shown in Fig. 1, using\nCOMSOL multiphysics. We set the properties of the ferrite material to those of 18G 3ferrite from the Y-Ga-In\nseries, which has a low loss, of which the relative permittivity and saturation magnetization are εr= 14 .5 and\nMs= 1.47·105A/m, respectively. The other parameters are given in Tab. I.\nShape h AreaA ωL ωM ωcrit\nr ωcrit\nSector 20 mm 0.3355 m287.96 GHz 32.49 GHz 24.71 GHz 10.56 GHz\nAfrica 10 mm 0.0377 m243.98 GHz 32.49 GHz 12.35 GHz 18.34 GHz\nTABLE I. Parameters for the two resonator realizations.\nThe sector has a radius of 800 mm. The wave dynamics of microwave resonators with this shape is integrable [13, 20–\n23]. The boundary of the Africa shape [ x(r, φ), y(r, φ)] is defined in the complex plane w(r, φ) =x(r, φ) +iy(r, φ)\nby\nw(r, φ) =r0\u0010\nz+ 0.2z2+ 0.2z3eiπ/3\u0011\n, (35)\nwith z=reiφandr0= 100 mm. Below ωcritthe wave equation Eq. (27) reduces to the Schr¨ odinger equation for\nFIG. 1. Sketch of the ferrite-loaded cavities, which have the shape of a circle-sector billiard (left) with inner angle 60◦and of a\nAfrica billiard (right). The cavity is made of a PEC (brown lines), and the filling consists of magnetized ferrite (gray domain).\nthe quantum billiard of corresponding shape; see Eq. (30). For the sector quantum billiard the solutions of Eq. (30),6\nnamely, the eigenvalues kp,νand eigenfunctions Ψ p,ν(r, φ) are known,\nΨp,ν(r, φ) = sin\u00123\n2pφ\u0013\nJ3\n2p(kp,νr), J 3\n2p(kp,νr0) = 0 , (36)\nwhereas for the Africa billiard the dynamics is fully chaotic [40] so that they need to be computed numerically, e.g.,\nwith the boundary integral method [41]. We computed the eigenstates with COMSOL multiphysics which employes\na finite element method using the parameters listed in Tab. I. Note, that beyond the critical frequency ω≳ωcrit,\nwhere the Helmholtz equation becomes three-dimensional, the analogy to the three-dimensional quantum billiard of\ncorresponding shape is lost.\nIV. RESULTS\nA. Electric-Field Distributions\nBelow the critical frequency fcrit=ωcrit\n2πcorresponding to kz= 0, the electric field is perpendicular to the resonator\nplane ⃗E(x, y)eikzz=E(x, y)⃗ ez. Figures 2 and 3 present examples for the electric-field distributions E(x, y) of the\nsector and Africa resonators for four eigenfrequencies f=ω\n2π. As expected, the electric-field components in the\nFIG. 2. Electric field distributions for the sector-shaped resonator for ω < ωcritin the z= 10 mm plane for, from top left to\nbottom right, f=0.6598 GHz, 0.6625 GHz, 0.6649 GHz, 0.6668 GHz.\nresonator plane, Ex(r) and Ey(r), are identical to zero, and Ez(r) is constant in z-direction. This is no longer the\ncase for frequencies beyond the critical frequency, ω≳ωcritwhere for all components the zdependence is given\naccording to Eq. (20) by e−iqπ\nhzwith q≥1 and ⃗E(x, y) is governed by the wave equation Eq. (27) together with\nthe boundary conditions Eq. (14) and Eq. (15). In Fig. 4 and Fig. 5 we show examples for the case q= 1 for the\nsector- and Africa-shaped resonators, respectively. In the top and bottom plane the electric field has opposite signs\nfor given values ( x, y) as illustrated in the first row of both figures. Furthermore, in the\u0000\nz=h\n2\u0001\n-plane it vanishes,\nthus confirming that the zdependence is given by sin qπ\nhz. The second row of both figures shows ⃗E(x, y),Ex(x, y)\nandEy(x, y) for z=h\n2. We also confirmed that they fulfill the boundary condition Eq. (14), that is, vanish in the\ntop and bottom plane.7\nFIG. 3. Electric field distributions for the Africa-shaped resonator for ω < ωcritin the z= 5 mm plane for, from top left to\nbottom right, f= 0.9303 GHz, 0.9395 GHz, 0.9540 GHz, 0.9854 GHz.\nFIG. 4. Electric field distribution for the sector-shaped resonator in the ( x, y) plane at the eigenfrequency f= 2.0142 GHz,\nfor which q= 1. The top left and right figures show Ez(x, y) in the bottom ( z= 0) and top ( z=h) planes, respectively. The\nbottom left and right figures show Ex(x, y) and Ey(x, y) in the z=h\n2plane.\nB. Spectral Properties\nA central prediction within the field of Quantum Chaos is the Bohigas-Gianonni-Schmit (BGS) conjecture [42–\n44], which states that for typical quantum systems, whose corresponding classical dynamics is chaotic, the universal\nfluctuation properties in the eigenvalue spectra coincide with those of random matrices from the Gaussian orthogonal\nensemble (GOE) if Tinvariance is preserved, and from the Gaussian unitary ensemble (GUE) if it is violated [9, 14,\n19, 45]. On the other hand, if the classical dynamics is integrable they are well described by uncorrelated random8\nFIG. 5. Electric field distribution for the Africa-shaped resonator in the ( x, y) plane at the eigenfrequency f= 2.9652 GHz,\nfor which q= 1. The top left and right figures show Ez(x, y) in the bottom ( z= 0) and top ( z=h) planes, respectively. The\nbottom left and right figures show Ex(x, y) and Ey(x, y) in the z=h\n2plane.\nnumbers drawn from a Poisson process according to the Berry-Tabor (BT) conjecture [46]. To obtain information on\nuniversal fluctuation properties in the eigenfrequency spectra of the ferrite resonators, system-specific properties need\nto be extracted, that is, the eigenfrequencies have to be unfolded to a uniform average spectral density, respectively,\nto average spacing unity. Below ωcritthe integrated spectral density is well described by Weyl’s formula [47], as\nlong as the frequency interval is chosen such that the frequency dependence of the dispersion factor in Eq. (31) can\nbe neglected. Then, according to Weyl’s formula, the smooth part of the integrated spectral density is given by\nNWeyl(k) =A\n4πk2+L\n4πk+C0withAandLdenoting the area and perimeter of the resonator shape. Unfolding is\nachieved by replacing the eigenwavenumbers kpof Eq. (30) by the Weyl term ϵp=NWeyl(kp) [9].\nAbove the critical frequency, the Helmholtz equation becomes vectorial. For a three-dimensional metallic cavity\nwith a non-dispersive medium the smooth part of the integrated spectral density is given by a polynomial of third\norder in k[48], where the quadratic term vanishes. For a dispersive medium, like the cavities filled with magnetized\nferrite, it still provides a good description of the smooth part of the integrated spectral density, if the frequency\nrange is chosen such that the variation of the dispersion term with frequency is small. In Fig. 6 we show as red\nsolid lines the fluctuating part of the integrated spectral density, Nfluc(k) =N(k)−NWeyl(k) for the sector- and\nAfrica-shaped resonators. The wave dynamics of a three-dimensional sector-shaped PEC cavity is integrable, whereas\nthe Africa-shaped one comprises non-chaotic bouncing-ball orbits corresponding to microwaves that bounce back and\nforth between the top and bottom plate [22, 24, 49]. These occur in both resonators for ω≳ωcrit, that is, kz≥π\nh.\nThey are non-universal, since they depend on the height of the cavity and lead to deviations from BGS predictions\nfor cavities with otherwise chaotic dynamics, which are similar to those induced by the bouncing-ball orbits in the\ntwo- and three-dimensional stadium billiard [24, 49–51]. The slow oscillations Nosc(kp) in the fluctuating part of the\nintegrated spectral density, depicted as dashed black curves in Fig. 6, originate from these bouncing-ball orbits. We\nremoved them by unfolding the eigenvalues with ϵp=NWeyl(kp) +Nosc(kp) [24, 49] which, in addition to the smooth\nvariation, takes into account these oscillations. The resulting ˜Nfluc(kp) =Nfluc(kp)−Nosc(kp) is shown as thin\ndashed turquoise line.\nIn Fig. 7 we show length spectra, that is, the modulus of the Fourier transform of the fluctuating part of the spectral\ndensity from wavenumber to length. They are named length spectra because they exhibit peaks at the lengths of\nperiodic orbits of the corresponding classical system, as may be deduced from the semiclassical approximation for the\nfluctuating part of the spectral density [52, 53]. Shown are the length spectra for the sector-shaped (left) and Africa-\nshaped (right) resonators (turquoise solid lines) below the critical frequency compared to those computed from the\neigenvalues of the quantum billiard of corresponding geometry taking into account a similar number of eigenvalues\n(red solid lines). To match the lengths of the periodic orbits we employed the dispersion relation Eq. (31) which9\nFIG. 6. Fluctuating part of the integrated spectral density (red curves) and the slow oscillations (dashed black curve) resulting\nfrom bouncing-ball orbits for ω≳ωcritfor the sector-shaped (left) and Africa-shaped (right) resonators. The cyan curves show\nthe fluctuations after removal of the contributions from bouncing-ball orbits.\nprovides the relation between the eigenwave numbers of the empty metallic cavity, i.e., the quantum billiard, and\nferrite-loaded one. The black diamonds mark the lengths of classical periodic orbits. The agreement between the\nlength spectra is very good, as may be deduced from the fact that below the critical frequency the underlying wave\nequations are mathematically equivalent. Above the critical frequency this analogy is lost, because of the different\nstructures of the wave equation for an empty metallic cavity [35] and Eq. (27) for a cavity filled with magnetized\nferrite and the implicated dispersion relation, which also becomes vectorial.\nFIG. 7. Comparison of the length spectra of the sector-shaped and Africa-shaped resonators below the critical frequency\n(turquoise curves) with those obtained from the lowest 300 eigenvalues of the quantum billiard of corresponding shape (red\nlines). The black diamonds mark the lengths of classical periodic orbits.\nTo study the spectral properties of the ferrite-loaded resonators we analyzed the nearest-neighbor spacing distribu-\ntionP(s), the integrated nearest-neighbor spacing distribution I(s), the number variance Σ2(L) and the Dyson-Mehta\nstatistic ∆ 3(L), which is a measure for the rigidity of a spectrum [45, 54]. Furthermore, we computed distributions of\nthe ratios [55, 56] of consecutive spacings between nearest neighbors, rj=ϵj+1−ϵj\nϵj−ϵj−1. These are dimensionless implying\nthat unfolding is not required [55–57]. For the sector-shaped resonator, the spectral properties below (red histograms\nand dashed lines) and above (cyan histograms, circles and dots) the critical frequency fcrit= 1.68 GHz are shown\nin Fig. 8. They agree well with those of Poissonian random numbers, and thus with those of the corresponding\nquantum billiard below fcritand exhibit GOE statistics in the other case. Here, we used 500 eigenfrequencies in the\nfrequency range f∈[0.0854,1.5010] GHz and 321 eigenfrequencies in the range f∈[1.7104,1.9314] GHz, respectively.\nFor the Africa-shaped resonator, the spectral properties below (red histograms and dashed lines) and above (cyan10\nFIG. 8. Spectral properties of the eigenfrequencies of the sector-shaped resonator below (red histogram and dashed lines) and\nabove (cyan histograms, circles and dots) the critical frequency. They are compared to the spectral properties of Poissonian\nrandom numbers (dashed-dotted black lines), GOE (black solid lines), and the GUE (dashed black lines).\nhistograms, circles and dots) fcrit= 2.92 GHz are shown in Fig. 9, and agree with those of the corresponding quantum\nbilliard, that is with GOE below fcrit. Above fcritthey are well described by the GUE. We used 229 eigenfrequencies\nin the frequency range f∈[0.2115,2.6333] GHz and 309 eigenfrequencies in the range f∈[3.1655,3.9094] GHz.\nV. DISCUSSION AND CONCLUSIONS\nFor both realizations of a PEC resonator loaded with magnetized ferrite, the spectral properties agree with those of\nthe corresponding quantum billiard for f≲fcrit. Above the critical frequency, the spectral properties of the sector-\nshaped resonator coincide with those of random matrices from the GOE, implying that there the wave dynamics is\nchaotic, even though the shape corresponds to that of a three-dimensional billiard with integrable classical dynamics.\nAbove all, the spectral properties of a sector-shaped PEC resonator filled with a homogeneous dielectric exhibit\nPoissonian statistics [36, 58], that is, their wave dynamics is integrable. Thus we may conclude that the GOE\nbehavior of the sector-shaped resonator and the GUE behavior of the Africa-shaped one have their origin in the\nmagnetization of the ferrite, as may also be concluded from the structure of the wave equation Eq. (27). It comprises\npurely complex parts containing derivatives of the entries of ˆ µr, which are spatially independent in the bulk of the11\nFIG. 9. Same as Fig. 8 for the eigenfrequencies of the Africa-shaped resonator.\nferrite but experience jumps at the ferrite surface where it is terminated with a PEC. Thereby, the electric-field\ncomponents of ⃗E(x, y) are coupled for non-vanishing static external magnetic field H0, thus leading to the complexity\nof the dynamics. For H0= 0, that is for a dielectric medium, ˆ µrequals the identity matrix, so that such a coupling is\nabsent. The spectral properties of the sector-shaped resonator do not exhibit GUE behavior, but are well described\nby GOE statistics. This is attributed to the mirror symmetry, which implies a generalized Tinvariance [9]. In the\nexperiments presented in Refs. [25–30] cylindrical ferrites were introduced in a flat, metallic microwave resonator and\nmagnetized with an external magnetic field to induce T-invariance violation. Based on our findings we expect that,\nwhen choosing a circular shape of the resonator and inserting the ferrite at the circle center, it acts like a potential\nwhich induces wave-dynamical chaos above its critical frequency. XDZ is currently performing such experiments, and\npreliminary results confirm this assumption.\nDECLARATIONS\n•Funding: This work was supported by the NSF of China under Grant Nos. 11775100, 12047501, and\n11961131009. WZ acknowledges financial support from the China Scholarship Council (No. CSC-202106180044).\nBD and WZ acknowledge financial support from the Institute for Basic Science in Korea through the project12\nIBS-R024-D1. XDZ thanks the PCS IBS for hospitality and financial support during his visit of the group of\nSergej Flach.\n•Conflict of Interest: The authors declare no conflict of interest.\n•Data Avalaibility Statement: All data were generated with COMSOL multiphysics under license number\n9409425. The parameters to reproduce the data are provided in Tab. I and Sec. III. All data needed to\nsupport our findings are included in the figures of this article.\n•Authors’ Contributions: WZ and XZ contributed equally.\n[1] T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Random-matrix physics: spectrum and\nstrength fluctuations, Rev. Mod. Phys. 53, 385 (1981).\n[2] T. Zimmermann, H. K¨ oppel, L. S. Cederbaum, G. Persch, and W. Demtr¨ oder, Confirmation of random-matrix fluctuations\nin molecular spectra, Phys. Rev. Lett. 61, 3 (1988).\n[3] T. Guhr and H. A. Weidenm¨ uller, Coexistence of collectivity and chaos in nuclei, Ann. Phys. 193, 472 (1989).\n[4] T. Guhr, A. M¨ uller-Groeling, and H. A. Weidenm¨ uller, Random-matrix theories in quantum physics: common concepts,\nPhys. Rep. 299, 189 (1998).\n[5] H. Weidenm¨ uller and G. Mitchell, Random matrices and chaos in nuclear physics: Nuclear structure, Rev. Mod. Phys. 81,\n539 (2009).\n[6] J. G´ omez, K. Kar, V. Kota, R. Molina, A. Rela˜ no, and J. Retamosa, Many-body quantum chaos: Recent developments\nand applications to nuclei, Phys. Rep. 499, 103 (2011).\n[7] A. Frisch, M. Mark, K. Aikawa, F. Ferlaino, J. L. Bohn, C. Makrides, A. Petrov, and S. Kotochigova, Quantum chaos in\nultracold collisions of gas-phase erbium atoms, Nature 507, 474 (2014).\n[8] J. Mur-Petit and R. A. Molina, Spectral statistics of molecular resonances in Erbium isotopes: How chaotic are they?,\nPhys. Rev. E 92, 042906 (2015).\n[9] F. Haake, S. Gnutzmann, and M. Ku´ s, Quantum Signatures of Chaos (Springer-Verlag, Heidelberg, 2018).\n[10] S. Sridhar, Experimental observation of scarred eigenfunctions of chaotic microwave cavities, Phys. Rev. Lett. 67, 785\n(1991).\n[11] J. Stein and H.-J. St¨ ockmann, Experimental determination of billiard wave functions, Phys. Rev. Lett. 68, 2867 (1992).\n[12] H.-D. Gr¨ af, H. L. Harney, H. Lengeler, C. H. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt, and H. A. Weidenm¨ uller,\nDistribution of eigenmodes in a superconducting stadium billiard with chaotic dynamics, Phys. Rev. Lett. 69, 1296 (1992).\n[13] S. Deus, P. M. Koch, and L. Sirko, Statistical properties of the eigenfrequency distribution of three-dimensional microwave\ncavities, Phys. Rev. E 52, 1146 (1995).\n[14] H.-J. St¨ ockmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, 2000).\n[15] B. Dietz, T. Klaus, M. Miski-Oglu, and A. Richter, Spectral properties of superconducting microwave photonic crystals\nmodeling dirac billiards, Phys. Rev. B 91, 035411 (2015).\n[16] Y. G. Sinai, Dynamical systems with elastic reflections, Russ. Math. Surv. 25, 137 (1970).\n[17] L. A. Bunimovich, On the ergodic properties of nowhere dispersing billiards, Commun. Math. Phys. 65, 295 (1979).\n[18] M. V. Berry, Regularity and chaos in classical mechanics, illustrated by three deformations of a circular ’billiard’, Eur. J.\nPhys. 2, 91 (1981).\n[19] M. Giannoni, A. Voros, and J. Zinn-Justin, eds., Chaos and Quantum Physics (Elsevier, Amsterdam, 1989).\n[20] R. L. Weaver, Spectral statistics in elastodynamics, J. Acoust. Soc. Am. 85, 1005 (1989).\n[21] C. Ellegaard, T. Guhr, K. Lindemann, H. Lorensen, J. Nyg˚ ard, and M. Oxborrow, Spectral statistics of acoustic resonances\nin aluminum blocks, Phys. Rev. Lett. 75, 1546 (1995).\n[22] H. Alt, H.-D. Gr¨ af, R. Hofferbert, C. Rangacharyulu, H. Rehfeld, A. Richter, P. Schardt, and A. Wirzba, Chaotic dynamics\nin a three-dimensional superconducting microwave billiard, Phys. Rev. E 54, 2303 (1996).\n[23] H. Alt, C. Dembowski, H.-D. Gr¨ af, R. Hofferbert, H. Rehfeld, A. Richter, R. Schuhmann, and T. Weiland, Wave dynamical\nchaos in a superconducting three-dimensional sinai billiard, Phys. Rev. Lett. 79, 1026 (1997).\n[24] C. Dembowski, B. Dietz, H.-D. Gr¨ af, A. Heine, T. Papenbrock, A. Richter, and C. Richter, Experimental test of a trace\nformula for a chaotic three-dimensional microwave cavity, Phys. Rev. Lett. 89, 064101 (2002).\n[25] P. So, S. M. Anlage, E. Ott, and R. Oerter, Wave chaos experiments with and without time reversal symmetry: Gue and\ngoe statistics, Phys. Rev. Lett. 74, 2662 (1995).\n[26] D. H. Wu, J. S. A. Bridgewater, A. Gokirmak, and S. M. Anlage, Probability amplitude fluctuations in experimental wave\nchaotic eigenmodes with and without time-reversal symmetry, Phys. Rev. Lett. 81, 2890 (1998).\n[27] H. Schanze, E. R. P. Alves, C. H. Lewenkopf, and H.-J. St¨ ockmann, Transmission fluctuations in chaotic microwave billiards\nwith and without time-reversal symmetry, Phys. Rev. E 64, 065201 (2001).\n[28] B. Dietz, T. Friedrich, H. L. Harney, M. Miski-Oglu, A. Richter, F. Sch¨ afer, J. Verbaarschot, and H. A. Weidenm¨ uller,\nInduced violation of time-reversal invariance in the regime of weakly overlapping resonances, Phys. Rev. Lett. 103, 064101\n(2009).13\n[29] B. Dietz, T. Friedrich, H. L. Harney, M. Miski-Oglu, A. Richter, F. Sch¨ afer, and H. A. Weidenm¨ uller, Quantum chaotic\nscattering in microwave resonators, Phys. Rev. E 81, 036205 (2010).\n[30] B. Dietz, T. Klaus, M. Miski-Oglu, A. Richter, and M. Wunderle, Partial time-reversal invariance violation in a flat,\nsuperconducting microwave cavity with the shape of a chaotic africa billiard, Phys. Rev. Lett. 123, 174101 (2019).\n[31] M. Bia lous, B. Dietz, and L. Sirko, How time-reversal-invariance violation leads to enhanced backscattering with increasing\nopenness of a wave-chaotic system, Phys. Rev. E 102, 042206 (2020).\n[32] W. Zhang, X. Zhang, J. Che, J. Lu, M. Miski-Oglu, and B. Dietz, Experimental study of closed and open microwave\nwaveguide graphs with preserved and partially violated time-reversal invariance, Phys. Rev. E 106, 044209 (2022).\n[33] B. Lax and K. J. Button, Microwave ferrites and ferrimagnetics (McGraw-Hill, New York, 1962).\n[34] R. F. Soohoo, Theory and application of ferrites (Englewood Cliffs, Prentice-Hall, 1960).\n[35] J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1999).\n[36] M. Lebental, N. Djellali, C. Arnaud, J.-S. Lauret, J. Zyss, R. Dubertrand, C. Schmit, and E. Bogomolny, Inferring periodic\norbits from spectra of simply shaped microlasers, Phys. Rev. A 76, 023830 (2007).\n[37] E. Bogomolny, R. Dubertrand, and C. Schmit, Trace formula for dielectric cavities: General properties, Phys. Rev. E 78,\n056202 (2008).\n[38] S. Bittner, B. Dietz, R. Dubertrand, J. Isensee, M. Miski-Oglu, and A. Richter, Trace formula for chaotic dielectric\nresonators tested with microwave experiments, Phys. Rev. E 85, 056203 (2012).\n[39] S. Bittner, E. Bogomolny, B. Dietz, M. Miski-Oglu, and A. Richter, Application of a trace formula to the spectra of flat\nthree-dimensional dielectric resonators, Phys. Rev. E 85, 026203 (2012).\n[40] M. V. Berry and M. Robnik, Statistics of energy levels without time-reversal symmetry: Aharonov-Bohm chaotic billiards,\nJ. Phys. A 19, 649 (1986).\n[41] A. B¨ acker, Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems, in The\nMathematical Aspects of Quantum Maps , edited by M. D. Esposti and S. Graffi (Springer Berlin Heidelberg, Berlin,\nHeidelberg, 2003) pp. 91–144.\n[42] M. Berry, Structural stability in physics (Pergamon Press, Berlin, 1979).\n[43] G. Casati, F. Valz-Gris, and I. Guarnieri, On the connection between quantization of nonintegrable systems and statistical\ntheory of spectra, Lett. Nuovo Cimento 28, 279 (1980).\n[44] O. Bohigas, M. J. Giannoni, and C. Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation\nlaws, Phys. Rev. Lett. 52, 1 (1984).\n[45] M. L. Mehta, Random Matrices (Elsevier, Amsterdam, 2004).\n[46] M. V. Berry and M. Tabor, Level clustering in the regular spectrum, Proc. R. Soc. London A 356, 375 (1977).\n[47] H. Weyl, ¨Uber die Abh¨ angigkeit der Eigenschwingungen einer Membran und deren Begrenzung, J. Reine Angew. Math.\n141, 1 (1912).\n[48] R. Balian and C. Bloch, Distribution of eigenfrequencies for the wave equation in a finite domain: I. Three-dimensional\nproblem with smooth boundary surface, Annals of Physics 60, 401 (1970).\n[49] B. Dietz, T. Friedrich, H. L. Harney, M. Miski-Oglu, A. Richter, F. Sch¨ afer, and H. A. Weidenm¨ uller, Chaotic scattering\nin the regime of weakly overlapping resonances, Phys. Rev. E 78, 055204 (2008).\n[50] M. V. Berry, Semiclassical theory of spectral rigidity, Proc. R. Soc. London A 400, 229 (1985).\n[51] M. Sieber, U. Smilansky, S. C. Creagh, and R. G. Littlejohn, Non-generic spectral statistics in the quantized stadium\nbilliard, J. Phys. A 26, 6217 (1993).\n[52] M. V. Berry and M. Tabor, Closed orbits and the regular bound spectrum, Proc. R. Soc. London A 349, 101 (1976).\n[53] M. C. Gutzwiller, Periodic orbits and classical quantization conditions, J. Math. Phys. 12, 343 (1971).\n[54] O. Bohigas and M. J. Giannoni, Level density fluctuations and random matrix theory, Ann. Phys. 89, 393 (1974).\n[55] V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).\n[56] Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, Distribution of the ratio of consecutive level spacings in random\nmatrix ensembles, Phys. Rev. Lett. 110, 084101 (2013).\n[57] Y. Atas, E. Bogomolny, O. Giraud, P. Vivo, and E. Vivo, Joint probability densities of level spacing ratios in random\nmatrices, J. Phys. A 46, 355204 (2013).\n[58] H. G. L. Schwefel, A. D. Stone, and H. E. Tureci, Polarization properties and dispersion relations for spiral resonances of\na dielectric rod, J. Opt. Soc. B 22, 2295 (2005)."    },    {        "title": "0908.3488v1.Spinel_ferrite_nanocrystals_embedded_inside_ZnO__magnetic__electronic_and_magneto_transport_properties.pdf",        "content": "Spinel ferrite nanocrystals embedded inside ZnO: magnetic, electronic and\nmagneto-transport properties\nShengqiang Zhou,1,\u0003K. Potzger,1Qingyu Xu,2K. Kuepper,1G. Talut,1D. Mark\u0013 o,1\nA. M ucklich,1M. Helm,1J. Fassbender,1E. Arenholz,3and H. Schmidt1\n1Institute of Ion Beam Physics and Materials Research, Forschungszentrum\nDresden-Rossendorf, P.O. Box 510119, 01314 Dresden, Germany\n2Department of Physics, Southeast University, Nanjing 211189, China\n3Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA\n(Dated: January 23, 2018)\nIn this paper we show that spinel ferrite nanocrystals (NiFe 2O4, and CoFe 2O4) can be texturally\nembedded inside a ZnO matrix by ion implantation and post-annealing. The two kinds of ferrites\nshow di\u000berent magnetic properties, e.g.coercivity and magnetization. Anomalous Hall e\u000bect and\npositive magnetoresistance have been observed. Our study suggests a ferrimagnet/semiconductor\nhybrid system for potential applications in magneto-electronics. This hybrid system can be tuned by\nselecting di\u000berent transition metal ions (from Mn to Zn) to obtain various magnetic and electronic\nproperties.\nI. INTRODUCTION\nSpinel ferrites are materials with rich magnetic and\nelectronic properties1. As bulk materials, they can be\nhalf-metallic (such as Fe 3O4) or insulating (most spinel\nferrites), ferrimagnetic (most spinel ferrites) or anti-\nferromagnetic (ZnFe 2O4). Insulating ferrites (such as\nNiFe 2O4and ZnNiFe 2O4) are usually referred to as mag-\nnetic insulators. These kinds of materials are technolog-\nically important with various applications as permanent\nmagnets, microwave devices, and magnetic recording me-\ndia. Physically the magnetic and electronic properties\nof spinel ferrites are determined by the cation distribu-\ntion among the tetrahedral (A) and octahedral (B) sites.\nThe growth of low-dimensional spinel ferrites of both thin\n\flms and nanoparticles has shown the possibility to tune\nthe cation distribution, therefore resulting in magnetic\nand electrical properties drastically di\u000berent from bulk\nmaterials. L uders et al. have shown that the conductiv-\nity of NiFe 2O4thin \flms can be tuned over \fve orders of\nmagnitude by varying the growth atmosphere2. The sites\nof Fe3+can be changed from A to B sites in ZnFe 2O4\nnanoparticles, resulting in ferrimagnetism3. Geiler et\nal.proposed a method to design and control the cation\ndistribution in hexagonal BaFe 12\u0000xMnxO19ferrites at an\natomic scale, which results in the increase of magnetic\nmoment and N\u0013 eel temperature4. Moreover, most of tran-\nsition metals (TM) can form solid solutions with Fe 3O4,\nresulting in TM xFe3\u0000xO4spinel alloys with x ranging\nfrom 0 to 1, which provides an additional degree of free-\ndom to tune their magnetic and electronic properties5,6.\nIn previous research, anomalous Hall e\u000bect and magne-\ntoresistance have been found in spinel ferrite thin \flms\nor granules at room temperature, demonstrating spin-\npolarization of free carriers. Moreover, ferrite thin \flms\nNiFe 2O4and CoFe 2O4with di\u000berent conductivities have\nbeen demonstrated to be useful as electrodes or spin-\n\flter in magnetic tunnel junctions2,7,8,9,10. However, to\nour knowledge, very limited e\u000bort has been spent to in-tegrate ferrite oxides with semiconductors. The growth\nof ferrite oxides requires high temperatures and oxygen\nenvironment, which is detrimental to conventional semi-\nconductors like Si and GaAs11. This explains why oxide\ninsulators such as MgO, Al 2O3, and SrTiO 3are mostly\nused as the substrates to grow ferrite oxides12. In this\npaper, we show that TMFe 2O4nanocrystals (TM=Ni,\nCo) can be embedded inside ZnO, and we present a sys-\ntematic study on their magnetic, electronic, and trans-\nport properties. The various ferrites with di\u000berent mag-\nnetic properties synthesized inside a semiconducting ma-\ntrix open a new avenue for fabricating hybrid systems.\nII. EXPERIMENTS\nWe utilize di\u000berent methods to characterize the fer-\nrite/ZnO hybrid systems. The aim is to show the simi-\nlarity in structure, but variability in magnetic, electronic\nand magneto-transport properties.\nCommercial ZnO(0001) single crystals with the thick-\nness of 0.5 mm from Crystec were co-implanted with57Fe\nand Ni or Co ions at 623 K with a \ruence of 4 \u00021016\nand 2\u00021016cm\u00002, respectively. The implantation en-\nergy was 80 keV for all three kinds of elements. This\nenergy resulted in the projected range of RP= 38;37;37\nnm, and the longitudinal straggling of \u0001 RP= 17;17;17\nnm, respectively, for Fe, Co, and Ni. Therefore, the im-\nplanted Fe ions are in the same range as the Co and Ni\nions. The maximum atomic concentration is about 10%\nand 5% for Fe and Ni(Co), respectively (TRIM code13).\nThe maximum implanted depth is around 80 nm (around\n5% of the maximum concentration) from the surface.\nAnnealing was performed in a high vacuum (base pres-\nsure\u001410\u00006mbar) furnace at 1073 K for 60 minutes. In\nour previous study we have performed detailed anneal-\ning investigation for transition metal implanted ZnO sin-\ngle crystals3,14,15. Brie\ry, more metallic clusters formed\nwhen annealing at mild temperatures (823 K or 923 K),arXiv:0908.3488v1  [cond-mat.mtrl-sci]  24 Aug 20092\nwhile the oxidation starts at around 1073 K. Keeping this\nhigh temperature, a longer annealing time results in the\nformation of ferrites in Fe implanted ZnO.\nMagnetic properties were measured with supercon-\nducting quantum interference device (SQUID, Quantum\nDesign MPMS) magnetometery. The samples were mea-\nsured with the \feld along the sample surface. The tem-\nperature dependent magnetization measurement was car-\nried out in the following way. The sample was cooled in\nzero \feld from above room temperature to 5 K. Then a\n50 Oe \feld was applied, and the zero-\feld cooled (ZFC)\nmagnetization curve was measured with increasing tem-\nperature from 5 to 350 K, after which the \feld-cooled\n(FC) magnetization curve was measured in the same \feld\nfrom 350 to 5 K with decreasing temperature.\nStructural analysis was performed by synchrotron radi-\nation x-ray di\u000braction (SR-XRD) and transmission elec-\ntron microscopy (TEM, FEI Titan). SR-XRD was per-\nformed at the Rossendorf beamline (BM20) at the ESRF\nwith an x-ray wavelength of 0.154 nm. The cross-section\nspecimen for TEM investigation was prepared by the con-\nventional method including cutting, glueing, mechanical\npolishing, and dimpling procedures followed by Ar+ion-\nbeam milling until perforation. The ion-milling was per-\nformed using a \"Gatan PIPS\". The milling parameters\nwere: 4 keV, 10 \u0016A ion current at milling angle of 4\u000ewith\nrespect to the specimen surface. The area around the\nhole is electron-transparent (thickness <100 nm).\nElement-speci\fc electronic properties were investi-\ngated by X-ray absorption spectroscopy (XAS) and X-\nray magnetic circular dichroism (XMCD) at the Fe, Co\nand Ni L 2;3absorption edges. These experiments were\nperformed at beamlines 8.0.1 (XAS) and 6.3.1 (XMCD)\nof the Advanced Light Source (ALS) in Berkeley, respec-\ntively. Both total electron yield (TEY) and total \ruo-\nrescence yield (TFY) were recorded during the measure-\nment. While TFY is bulk sensitive, TEY probes the\nnear-surface region. For XMCD, the measurement was\ndone at the minimum achievable measurement tempera-\nture of 23 K in TEY mode. A magnetic \feld of \u00062000\nOe was applied parallel to the beam. The grazing angle\nof the incident light was \fxed at 30\u000ewith respect to the\nsample surface.\nConversion electron M ossbauer spectroscopy (CEMS)\nin constant-acceleration mode at room temperature (RT)\nwas used to investigate the Fe lattice sites, electronic con-\n\fguration and corresponding magnetic hyper\fne \felds.\nThe spectra were evaluated with Lorentzian lines using\na least squares \ft16. All isomer shifts are given with\nrespect to\u000b-Fe at RT.\nMagnetotransport properties were measured using Van\nder Pauw geometry with a magnetic \feld applied per-\npendicular to the \flm plane. Fields up to 60 kOe were\napplied over a wide temperature range from 5 K to 290\nK and the carrier concentration and the majority carrier\nmobility were extracted.\nFIG. 1: SR-XRD 2 \u0012-\u0012scan revealing the formation of\nNiFe 2O4and CoFe 2O4in (Ni, Fe) or (Co, Fe) co-implanted\nZnO. In both pattern, the di\u000braction peaks of (111), (222),\n(333) and (444) from ferrites are clearly visible. The di\u000brac-\ntion peaks (0002) and (0004) from ZnO are also indicated.\nThe small and sharp peaks at the left side of CoFe 2O4(111)\nand the right side of NiFe 2O4(111) cannot be identi\fed at this\nstage. The peak at the left side of CoFe 2O4(111) could be the\nforbidden peak of ZnO(0001), which appears due to the lat-\ntice damage. However, another forbidden peak of ZnO(0003)\ndoes not show up. Note that the two peaks in the two spectra\nare not at the same angular position, and both correspond to\nvery large lattice distances. Some noise-like peaks are also\nshown in other paper17and could not be identi\fed.\nIII. RESULTS AND DISCUSSION\nA. Structural properties\n1. X-ray di\u000braction\nFigure 1 shows the SR-XRD patterns for the annealed\nsamples. Besides the strong peaks from ZnO(0002) and\n(0004), four small peaks arise for each sample. They are\nassigned to (111), (222), (333) and (444) di\u000bractions for\nNiFe 2O4and CoFe 2O4, respectively. This implies that\nthese nanocrystals are (111) textured inside the ZnO ma-\ntrix. However, some nanocrystals with (400) orientation\nhave been also observed by TEM as shown below. The\ncrystallite size is estimated using the Scherrer formula18.\nd= 0:9\u0015=(\f\u0001cos\u0012); (1)\nwhere\u0015is the wavelength of the X-ray, \u0012the Bragg an-\ngle, and\fthe FWHM of 2 \u0012in radians. The average\ncrystallite size is deduced to be around 12 nm and 15 nm\nfor NiFe 2O4and CoFe 2O4nanocrystals, respectively.\n2. TEM\nIn order to con\frm the formation of ferrite nanocrys-\ntals, high resolution cross-section TEM was performed3\nFIG. 2: Cross-section TEM image of Fe and Ni co-implanted\nZnO after annealing (a) bright \feld and (b) dark \feld.\non selected samples. Fig. 2(a) displays the bright-\feld\nTEM images. In an overview, there are three features.\nThe grains of secondary phases are located in the surface\nregion, which are identi\fed as NiFe 2O4. Some planar ex-\ntended defects are indicated by arrows, and are parallel to\nthe basal plane of the ZnO wurtzite structure in a depth\nof around 60 nm. These extended defects are caused by\nion implantation in ZnO19and are usually populated at\nthe end of the ion range. The third feature is the dark-\nspot, which is also located in the depth of unimplanted\nZnO. The formation of NiFe 2O4at the near-surface depth\nis also con\frmed by the dark-\feld TEM image as shown\nin Fig. 2(b) of the same area of Fig. 2(a). The out-\ndi\u000busion of Fe upon annealing at high temperatures has\nbeen observed in ZnO20as well as in TiO 221.\nUsing high resolution TEM we identi\fed the secondary\nphase to con\frm the XRD results. As shown in Fig. 3(a),\nthe sample was tilted in order to have a better view on the\nnanocrystals. Note that the lattice planes are more clear\nin the nanocrystals than that in the ZnO substrate. The\ninset of Fig. 3(a) is the Fast Fourier Transform (FFT)\nof the image indicated by a square. The FFT clearly\nshows the cubic-symmetry of the nanocrystal. The two\nsets of lattice spacings amount to 0.291 nm and 0.207\nnm, and correspond to NiFe 2O4(220) and (004), respec-\ntively. Concerning the orientation between NiFe 2O4and\nthe ZnO matrix, XRD in general provides the integral\ninformation over a large area of the sample, while TEM\nis a rather localized method. By high resolution TEM,\nwe found some grains with [111] orientation as shown in\nFig. 3(b). By FFT two sets of lattice planes are identi\fed\nto NiFe 2O4f111g. One is parallel with the sample sur-\nface, while the other is around 71\u000eaway from the surface\n[ZnO(0001)]. This is in agreement with a fcc structure of\nFIG. 3: High resolution TEM image for representative\nNiFe 2O4nanocrystals. (a) the specimens is tilted by 11\u000e.\nNiFe 2O4nanocrystal is identi\fed. The black lines guide the\neyes to show the cubic symmetry of the secondary phase.\n(b) Another NiFe 2O4nanocrystals with the orientation of\n(111)kZnO(0001) as con\frmed by FFT patterns. The clearly\nvisible planes are NiFe 2O4(111) with an angle of \u001871\u000efrom\nthe surface. In FFT patterns the dashed lines indicate the\nsets of lattice planes.\nNiFe 2O4. However there are also some grains with [001]\norientation, e.g.the one in Fig. 3(a). One also can see\nsome moire fringes in the ZnO part due to the overlap of\nNiFe 2O4and ZnO.\nNote that the NiFe 2O4grains (see Fig. 2) are as large\nas 20-40 nm, and larger than the values determined from\nXRD. However, one grain does not have to correspond\nto one NiFe 2O4nanocrystal. On the other hand, in the\ndark-\feld image all the grains show similar sizes as that\nin the bright \feld. This is due to the fact that these\nnanocrystals are well oriented. By high resolution TEM\nwe examined more than 10 nanocrystals in di\u000berent areas\nof the specimens. Their diameters are in the range of 10-\n20 nm, which is in a qualitative agreement with the XRD\nmeasurement.\nB. Magnetic properties\nBy structural analysis, we have shown the formation\nof NiFe 2O4and CoFe 2O4nanocrystals inside the ZnO\nmatrix. In this section, we will compare their magnetic\nproperties. Fig. 4 shows the hysteresis loops measured at\n5 K. The di\u000berences between NiFe 2O4and CoFe 2O4are\nsigni\fcant. At 5 K, the coercivity of CoFe 2O4is 1900 Oe,\nand much larger than the coercivity of NiFe 2O4amount-\ning to 280 Oe, i.e.one is a hard magnet, and the other\nis a soft one. For comparison the saturation magne-\ntization of bulk crystals is also indicated in Fig. 4.\nNiFe 2O4nanocrystals have a slightly larger value than\nbulk NiFe 2O4, and a smaller value for CoFe 2O4nanocrys-4\nFIG. 4: Hysteresis loops measured at 5 K for NiFe 2O4and\nCoFe 2O4nanocrystals. They show drastic di\u000berence in coer-\ncivity \feld.\ntals. This could be due to the cation site exchange be-\ntween Ni2+(Co2+) and Fe3+and will be discussed in\nsection III C. However, another possibility is that there\nis a mixture of Ni2+and Fe2+at tetrahedral sites result-\ning in (Ni,Fe)Fe 2O4(Ni1\u0000xFe2+xO4). The magnetization\nfor bulk Fe 3O4is 4.1\u0016Bper formula unit. To verify this,\none needs to perform a precise local Fe, Ni(Co) concen-\ntration measurement. We performed an electron energy-\nloss spectroscopy (EELS) analysis to pro\fle the compo-\nsition of the ferrite nanocrystals during the TEM mea-\nsurements. We could not probe an elementally resolvable\nEELS signal possibly due to the similar atomic number\nof the embedding ZnO matrix and the ferrite, given the\ncomplex element types (Fe, Co/Ni and Zn) within the\nprobe area. Macroscopically, the appearance of Fe, Co,\nNi is clearly revealed by x-ray absorption as shown later\nin Sec. III C. In literature the application of EELS in\nsimilar cases (embedded nanocrystals) is mainly for qual-\nitative investigation22,23,24. On the other hand, exposing\nthe nanocrystals to the electron beam for a longer time\nresults in a heavy beam damage and contamination of\nthe specimens, as well as the structural modi\fcation of\nthe nanocrystals25.\nFig. 5 shows the temperature dependent saturation\nmagnetization and coercivity. One sees clearly that the\ncoercivity decreases exponentially with increasing tem-\nperature. This is expected for a magnetic nanoparticle\nsystem. According to the Stoner-Wohlfarth theory26, the\nmagnetic anisotropy energy E Aof a single domain parti-\ncle can be expressed as:\nEA=KVsin2\u0012; (2)\nwhere K is the magnetocrystalline anisotropy constant,\nV the volume of the nanoparticle, and \u0012is the angle be-\ntween the magnetization direction and the easy axis of\nthe nanoparticle. This anisotropy serves as the energy\nbarrier to prevent the change of magnetization direction.\nWhen the size of magnetic nanoparticles is reduced to a\ncritical value, E Ais comparable with thermal activation\nenergy,kBT, the magnetization direction of the nanopar-\nticle can be easily moved away from the easy axis by ther-\nmal activation and/or an external magnetic \feld. Thecoercivity of the nanoparticles is closely related to the\nmagnetic anisotropy. At a temperature below blocking\ntemperature T B, the coercivity corresponds to a mag-\nnetic \feld which provides the required energy in addition\nto the thermal activation energy to overcome the mag-\nnetic anisotropy. As temperature increases, the required\nmagnetic \feld (H C) for overcoming the anisotropy de-\ncreases. At the temperature of 0 K, where all the mag-\nnetic moments are blocked, the coercivity is equal to the\nvalue for single domains. At a high enough tempera-\nture, when all moments \ructuate with a relaxation time\nshorter than the measuring time, coercivity equals zero.\nIn the temperatures between the two extremes the coer-\ncivity H Ccan be evaluated by the following formula27:\nHC=HC0[1\u0000(T\nTB)1=2]; (3)\nwhereHC0is the coercivity at 0 K, and T Bthe block-\ning temperature. Fig. 5(b) shows a plot of H Cas a\nfunction of T1=2. For the NiFe 2O4systemHCroughly\nobeys a linear dependence on T1=2in the whole measured\ntemperature range. The deduced blocking temperature\nlies around 360 K, which is rather close to the value\nfound by the ZFC/FC magnetization as shown below.\nThe poor \ftting for the CoFe 2O4system may be due to\nthe fact that the magnetocrystalline anisotropy energy of\nCoFe 2O4is much larger (two orders of magnitude) than\nNiFe 2O4. For a similar grain size the blocking temper-\nature of CoFe 2O4can be much higher for NiFe 2O4. In\nsuch a case, the measured temperature range is not large\nenough compared to the high blocking temperature. This\nresults in a large error in the \ftting.\nFig. 6 shows the ZFC/FC magnetization curves mea-\nsured at 50 Oe. An irreversible behavior is observed in\nZFC/FC curves. Such an irreversibility originates from\nthe anisotropy barrier blocking of the magnetization ori-\nentation in the nanoparticles cooled under zero \feld. The\nmagnetization direction of the nanoparticles is frozen as\nthe initial status at high temperature, i.e., randomly ori-\nented. At low temperature (5 K in our case), a small\nmagnetic \feld of 50 Oe is applied. Some small nanopar-\nticles with small magnetic anisotropy energy \rip along\nthe \feld direction, while the large ones do not. With\nincreasing temperature, the thermal activation energy\ntogether with the \feld \rips the larger particles. This\nprocess results in the increase of the magnetization in\nthe ZFC curve with temperature. The size distribution\nof nanoparticles, i.e.the magnetic anisotropy is usually\nnot uniform in the randomly arranged nanoparticle sys-\ntems. The larger the particles, the higher the E A, and\na largerkBTis required to become superparamagnetic.\nThe gradual increase and the small upturn at around 20\nK in the ZFC curves is due to the size distribution of\nnanocrystals. In the ZFC curve for NiFe 2O4[Fig. 6(a)]\na broad maximum is observed at around 330 K, while\nfor CoFe 2O4[Fig. 6(a)] no maximum can be seen up to\n350 K. The mean blocking temperature for CoFe 2O4is\nwell above room temperature, which is evidenced also5\nFIG. 5: (a) Temperature dependent saturation magnetiza-\ntion and coercivity for NiFe 2O4(red solid symbols) and\nCoFe 2O4(black open symbols). The solid lines are guides\nfor eyes. (b) The plot of coercivity as a function of T1=2.\nfrom the rather large coercivity \feld of 80 Oe at 300 K\n(see Fig. 5). Note that the ZFC/FC magnetization of\nNiFe 2O4is much smaller than that of CoFe 2O4. This\nis due to the much larger coercivity \feld (magnetocrys-\ntalline constant K) of CoFe 2O4, which is well above the\nsmall applied \feld of 50 Oe.\nSince the blocking temperature is closely related to the\nmagnetic anisotropy energy E A, one can evaluate the size\nof nanomagnets by the measured T B. For a dc magneti-\nzation measurement in a small magnetic \feld by SQUID\nmagnetometry, T Bis given by\nTB;Squid\u0019KV\n30kB; (4)\nwhereKis the anisotropy energy density, Vthe particle\nvolume,kBthe Boltzmann constant28.Kis 6.3\u0002103and\n4.0\u0002105Jm\u00003for bulk NiFe 2O4and CoFe 2O4, respec-\ntively, at room temperature29,30. Due to its large mag-\nnetocrystalline anisotropy the maximum in ZFC curve of\nCoFe 2O4nanocrystals cannot be seen within the mea-\nsured temperature range. That means the blocking tem-\nperature is much larger than 350 K, which corresponds\nto an average diameter of CoFe 2O4larger than 9 nm\nif assuming the value of Kfor a bulk CoFe 2O4. For\nNiFe 2O4nanocrystals, Kis much smaller. Therefore, we\ncan see a maximum at around 320 K in the ZFC mag-\nnetization curve. Using the Kvalue for bulk NiFe 2O4,\nthe average diameter of NiFe 2O4can be calculated and\nFIG. 6: ZFC/FC magnetization curves measured with a \feld\nof 50 Oe. (a) NiFe 2O4and (b) CoFe 2O4. Up to 350 K, no\nZFC maximum was observed for CoFe 2O4.\namounts to 34 nm. This value, however, is larger than\nthat deduced from XRD and TEM measurements. The\nlarge discrepancy is resulting from the underestimation\nofKby assuming the value of a bulk crystal. Kcan\nbe largely enhanced due to strain, and surface e\u000bect in\nNiFe 2O4nanomagnets, but relatively less enhanced in\nCoFe 2O431. The later has been con\frmed in strained\nepitaxial CoFe 2O4thin \flms32.\nC. Electronic con\fguration\n1. X-ray absorption spectra\nThe magnetic properties of 3 dtransition metal ele-\nments, such as Fe, Co and Ni are determined by the 3d\nvalence electrons, which can be investigated by L-edge\nXAS measurements (transition from the 2 pshell to the\n3dshell). Fig. 7 shows the L 2;3XAS of Fe, Co and Ni\nin the two samples, measured in TEY mode. The spec-\ntra of pure metals and some oxides are also shown for\ncomparison. The metal spectra mainly show two broad\npeaks, re\recting the width of the empty d-bands, while\nthe oxide spectra exhibit a considerable \fne structure of\nthed-bands, the so-called multiplet structure. By com-\nparison with corresponding XAS of pure metals, one can\nqualitatively conclude that metallic Fe, Co and Ni are\nnot present in the samples. In Fig. 7(a) one can see\nthe multiplet structure of Fe L 2;3XAS. The most no-\nticeable feature is the rather pronounced peak at the low\nenergy part of the L 3edge. This is a common feature for\nferrite materials33. Multiplet calculations for FeO and\n\u000b-Fe2O3reveal that the shoulders at 705.5 eV and 718.5\neV [indicated by the vertical arrows in the Fig. 7(a)]\nare associated with Fe2+ions34. Note that these features\ndisappear in the spectrum of Fe 2O3. Following these ar-\nguments, the Fe ions in our samples are mainly Fe3+ions.\nThe Co-L 3edge [Fig. 7(b)] is composed of a \fne struc-\nture with four features, a small peak at 775.5 eV, the\ntotal maximum in absorption at 777 eV, followed by a\nshoulder at 778 eV and a further satellite at 780 eV.\nSince in this sample the Co is in pure Co2+con\fgura-\ntion, we can compare the spectrum with reference com-\npounds namely CoO (spectrum taken from Ref. 35) and6\nZn0:75Co0:25O (spectrum taken from Ref. 36). Co2+ions\nare at octahedral sites and at tetrahedral sites in CoO\nand Zn 0:75Co0:25O, respectively. From the comparison\nof the overall shape and satellite structure our spectrum\nis more similar to that of CoO, and also similar to the\nXAS of CoFe 2O4presented in Ref. 37. We can conclude\nthat the major part of Co2+ions are at octahedral sites.\nIn order to con\frm this conclusion, we performed simu-\nlations of the local electronic structure around the Co2+\nions by means of full multiplet calculations using the TT-\nMULTIPLETS program38,39. The energy levels of the\ninitial (2p63d7) and \fnal absorption state (2 p53d8) are\ncalculated by means of the corresponding Slater integrals\nwhich are subsequently reduced to 80% (corresponds to\ntheir atomic values). Then a tetrahedral or octahedral\ncrystal \feld was considered using a crystal \feld parame-\nter of 10 D q= -1 eV and 10 D q= +1 eV, respectively.\nFinally the calculated spectra were broadened with the\nexperimental resolution for comparison. As displayed in\nFigure 8, one can see that the measured spectrum reason-\nably reproduces the features in the simulated octahedral\ncoordination.\nFig. 7(c) shows the comparison of Ni L 2;3with that\nin NiFe 2O440. In the paper of Van der Laan et al.40,\nthe spectrum can be well simulated by considering Ni in\nan octahedral crystal-\feld coordination, i.e.Ni ions are\nfully at octahedral sites. However, the di\u000berence between\nthe two spectra is quite clear, especially at the L 2-edge.\nIt could be due to the fact that Ni ions are partially\nlocated at tetrahedral sites.\nThe XAS spectra (Fig. 9) were also recorded at the\nO K-edge and Zn L-edge to prove the formation of fer-\nrites and to check if Zn ions are signi\fcantly incorporated\ninto ferrites. All shown spectra were measured in TEY\nmode, which is more sensitive to the near surface-region\nwhere the ferrite nanocrystals were formed. For the O K-\nedge, the di\u000berence between the NiFe 2O4, CoFe 2O4and\nZnO is very clearly observed, which con\frms the coor-\ndination change of O ions. Actually the spectra in Fig.\n9(a) are very similar to those of Fe 2O3and Fe 3O442. Fig.\n9(b) shows the comparison of the Zn L-edge spectra be-\ntween ZnO embedded with NiFe 2O4, CoFe 2O4nanocrys-\ntals, and pure ZnO. The only di\u000berence is that the \fne\nstructure in the spectrum of ZnO is better resolved. This\ncould be due to the lattice damage in ZnO by ion im-\nplantation. No signi\fcant amount of Zn has been incor-\nporated into ferrites.\n2. XMCD\nCorrespondingly, XAS recorded at 23 K in TEY (total\nelectron yield) mode at the Fe, Co and Ni absorption edge\nrevealed a pronounced dichroic behavior under magneti-\nzation reversal. XMCD is a di\u000berence spectrum of two\nXA spectra, one taken with left circularly polarized light,\nand the other with right circularly polarized light.\nThe XMCD signal at the Fe L 3-edge XMCD for the\nFIG. 7: XAS of NiFe 2O4and CoFe 2O4along with reference\nspectra from pure metal and oxides at the (a) Fe L 2;3-edge,\n(b) Co L 2;3-edge and (c) Ni L 2;3-edge. The reference spectra\nare taken from published papers: Fe 2O341, Fe 3O441, CoO35,\nZnCoO36, NiFe 2O440and CoFe 2O437.\ntwo samples is shown in Fig. 10(a) and (b). From the\nliterature43, peak A is attributed to Fe2+at octahedral\nsites, while peaks B and C are due to Fe3+at tetrahe-\ndral and octahedral sites, respectively. By comparing the\nrelative height of peak A, B and C, we can draw some\nqualitative conclusions on the cation site distribution in\nNiFe 2O4and CoFe 2O4nanocrystals. Firstly, there are\nstill some Fe2+ions remaining, even if the ratio of im-\nplanted Ni(or Co) to Fe is exactly 1:2. This could be\ndue to the fact that Ni(or Co) and Fe ions are not fully\nchemically reacted at the given annealing condition. Rel-\natively, there are more Fe2+ions at octahedral sites in\nCoFe 2O4than in NiFe 2O4. Secondly, part of Fe3+ions\nare at tetrahedral sites in NiFe 2O4, while in CoFe 2O4the\nFe3+ions are mainly located at octahedral sites. Bulk\nNiFe 2O4and CoFe 2O4are inverse spinels. The Ni2+and\nCo2+ions are at octahedral sites, while half of the Fe3+\nions are at octahedral sites, and the other half are at\ntetrahedral sites. With this ordering, the moments of\nFe ions at octahedral and tetrahedral sites cancel out,\nwhich results in a saturation magnetization of 2 \u0016Bper\nNiFe 2O4formula unit44, and 3\u0016Bper CoFe 2O4formula\nunit45. However, in low dimensional spinels the cation\ndistribution is often di\u000berent from bulk materials44,46.7\nFIG. 8: The Co L 2;3-edge XAS spectrum of CoFe 2O4along\nwith theoretical calculations for a tetrahedral (10 D q= -1 eV)\nand an octahedral (10 D q= +1 eV) coordination of Co ions..\nFIG. 9: The XA spectra of total electron yield (TEY) at the\n(a) O K-edge, and (b) Zn L-edge.\nFor the case of NiFe 2O4, if all Ni2+replace the Fe3+at\ntetrahedral sites, resulting in a normal spinel structure,\nthe total magnetic moment can increase up to 4 \u0016Bper\nNiFe 2O4formula. Therefore, the larger magnetic mo-\nment in our NiFe 2O4nanocrystals as shown in Fig. 4\nis probably due to a small amount of Ni2+replacing the\nFe3+at tetrahedral sites. This cation distribution picture\nis in agreement with XAS analysis. However, as discussed\nin section III B, one needs a precise local concentration\nmeasurement to verify the ratio Fe:Ni= 2 : 1. Figs.\n10(c) and (d) show the XMCD signal at the L 2;3edge\nfor Ni and Co, respectively. They are comparable with\ncorresponding ferrites reported in literature33,40. Note\nthe fact that the relative strength of the XMCD signal\nof CoFe 2O4is much weaker than that of NiFe 2O4. This\nis due to their di\u000berent coercivity \felds. Due to the fa-\ncility capability, a maximum \feld of 2000 Oe was ap-\nplied during XAS measurements. The saturation \feld of\nCoFe 2O4is much larger than that of NiFe 2O4(see Fig.\n4).\nFIG. 10: XMCD at Fe, Ni and Co L 2;3absorption edge.\nNiFe 2O4: (a) and (c). CoFe 2O4: (b) and (d). Peak labels\nat Fe L 3-edge: A for Fe2+at octahedral sites, B for Fe3+at\ntetrahedral sites and C for Fe3+at octahedral sites43.\n3. CEMS\nCEMS allows one to identify di\u000berent site occupations,\ncharge and magnetic states of57Fe. Fig. 11 shows the\nCEM spectra taken at room temperature for two sam-\nples, containing NiFe 2O4and CoFe 2O4nanocrystals, re-\nspectively. The two samples exhibit similar spectra. Us-\ning a least-squares computer program, the spectra can\nbe \ftted well by three components. Two sets of sex-\ntet hyper\fne pattern and one doublet are resolved, all\nof which are related to Fe3+. The hyper\fne parame-\nters calculated according to the evaluations of the spectra\nare given in Table I. The outer sextet (S1) with a larger\nmagnetic hyper\fne \feld corresponds to octahedral sites,\nwhile the inner one (S2) with a smaller magnetic hyper-\n\fne \feld to Fe3+at tetrahedral sites47,48,49,50,51. This\nfeature of two sextets is a \fngerprint that identi\fes fer-\nrites. The relative line intensities of the sextets di\u000ber\nfrom those of a polycrystalline powder material indicat-\ning the presence of a texture. Note that the magnetic\nhyper\fne \feld is considerably smaller than the values of\naround 50 T for typical NiFe 2O4or CoFe 2O447,51, which\nresults from the size e\u000bect50. The doublet (D) is a more\nquestionable component. Most probably it corresponds\nto smaller ferrite nanocrystals, which are superparam-\nagnetic at room temperature. However, its isomer shift\nand electric quadrupole splitting values are considerably\nlarger than the values reported in Ref. 51.\nThe cation distribution between the two sublattices\ngenerally determines the magnetic properties of the\nspinel system and can be calculated as a ratio between\nthe relative areas of the respective hyper\fne \feld distri-\nbutions. As shown in Table I, there are more Fe3+ions\nat octahedral sites for both samples. That means that\nthe NiFe 2O4and CoFe 2O4nanocrystals are not purely8\nFIG. 11: Room temperature CEMS of NiFe 2O4/ZnO and\nCoFe 2O4/ZnO composites. The notations for the \ftting lines\nare given as D (doublet) and S1, S2 (sextet).\ninverted ferrites and Ni or Co ions partially occupy tetra-\nhedral sites, which is in good agreement with the results\nof XAS.\nD. Magneto-transport properties\nNote that both bulk NiFe 2O4and CoFe 2O4are in-\nsulators with resistivity of 102- 103\ncm at room\ntemperature2,9. The resistivity of NiFe 2O4single crystals\nmonotonically increases with decreasing temperature52.\nHowever, the corresponding thin \flm materials can be\nrather conductive2. In ref. 2, the authors show that\nthe NiFe 2O4\flms grown in pure Ar atmosphere have a\nroom temperature resistivity three orders-of-magnitude\nsmaller (\u001aaround 100 m\ncm). The temperature de-\npendence\u001a(T) is similar to that of magnetite. On the\nother hand, ZnO single crystals grown by the hydrother-\nmal method show a high bulk and surface resistivity,\nwith the bulk conduction dominated by a deep donor53.\nTypically, the free charge carrier concentration amounts\nto 1\u00021014cm\u00003and the mobility to 200 cm2V\u00001s\u00001\n(Ref. 54). We measured the temperature dependence of\nthe sheet resistance of the composites of NiFe 2O4and\nCoFe 2O4nanocrystals and ZnO from 20 or 40 to 290 K.\nFig. 12(a) shows the Arrhenius plot, the sheet resistance\nRson a logarithmic scale as a function of reciprocal tem-perature. Note that the resistivity of both samples is be-\nlow 0.1 \ncm at room temperature assuming a thickness\nof 80 nm, which is three orders of magnitude smaller than\nthat of bulk ferrites or ZnO54. The resistance/resistivity\nof composites of CoFe 2O4and ZnO is one order smaller\nthan that of NiFe 2O4and ZnO. The amount of n-type\ndefects in ZnO created by means of implantation and an-\nnealing is expected to be similar. Therefore, the larger\nconductivity in the composite of CoFe 2O4and ZnO is\ndue to the mixing of Fe2+and Fe3+ions at octahedral\nsites2. The temperature dependence of the resistance is\nmore or less the same for both samples. Two di\u000berent\nregimes are found. One is the high temperature part\n(above 150 K), where the resistance slightly decreases\nwith decreasing temperature. This is a hint of metallic\ncharacter. However, the electron concentration (around\n6\u00021018cm\u00003assuming a thickness of 80 nm) as shown\nin Fig. 12(b) is far below the critical value (4 \u00021019\ncm\u00003) of the metal-insulator transition in n-ZnO55. In\nRefs. 2,44, a metallic electrical conductivity has been ob-\ntained in ultrathin NiFe 2O4\flms, which is attributed to\nan anomalous distribution of the Fe and Ni cations among\ntetrahedral and octahedral sites. Therefore, we attribute\nthe metallic character in our samples to the presence of\nNiFe 2O4(or CoFe 2O4) nanocrystals. The second regime\nis in the temperature range below 150 K. In this regime,\nthe samples show a semiconducting conductivity. The\nthermal activation energy Eaof free carriers can be de-\ntermined according to the following equation:\n\u001a=eEa\nkBT+Rs0; (5)\nwherekBis the Boltzmann constant and Rs0a temper-\nature independent contribution to the resistivity. In Fig.\n12(a) the solid lines show the \ftting, resulting in a ther-\nmal activation energy of \u001828 meV for both samples. A\nsimilar thermal activation energy of 21 meV has been\nfound in hydrothermally grown ZnO single crystals af-\nter high-temperature annealing53. At low temperatures\nthe impurities freeze out. In Ref. 52, the authors show\nthat in their measured temperature range from around\n77 K to room temperature the NiFe 2O4single crystals\nexhibit semiconducting conductivity, and the activation\nenergy is around 60 meV. Fig. 12(b) displays the temper-\nature dependent carrier concentration and Hall mobility.\nThe sheet electron concentration increases with temper-\nature and reaches to 4.8 \u00021013cm\u00002. Its temperature\ndependence can be well \ftted by the function e\u0000Ea=kBT.\nFig. 12(b) also shows the temperature-dependent mobil-\nity. The electron mobility \u0016reaches a maximum of above\n900cm2=Vsat 65 K. Actually such large electron mobil-\nity and concentration were also observed in ion implanted\nZnO56and in virgin ZnO annealed in N 257.\nWe also measured the magnetic \feld dependent resis-\ntance (MR) for the composites of NiFe 2O4(CoFe 2O4)\nnanocrystal and ZnO as shown in Fig. 13. MR is de\fned\nas\nMR = (R[H]\u0000R[0])=R[0]: (6)9\nTABLE I: Hyper\fne parameters measured using CEMS for the two samples. The percentage of occupancies of tetrahedral-\nand octahedral-sites by Fe3+ions. B hf: hyper\fne \feld, A: relative area of each component, \u000e: isomer shift, \u0001: quadrupole\nspliting.\nS1 (octahedral) S2 (tetrahedral) D\nBhf A\u000e \u0001 Bhf A\u000e \u0001 A\u000e \u0001\nSample (T) (%) ( mm=s ) (mm=s ) (T) (%) ( mm=s ) (mm=s ) (%) (mm=s ) (mm=s )\nNiFe 2O4 43 47.7 0.26 0.03 36.5 39 0.28 0.09 13.3 0.34 0.63\nCoFe 2O4 41.4 47.1 0.28 0.06 34.9 40.8 0.31 0.05 12.1 0.38 0.62\nFIG. 12: (a) The temperature dependent sheet resistance (the\nsolid lines show the linear \ftting in the temperature range of\n60-100 K), and (b) free carrier concentration and mobility\nof the composites of NiFe 2O4or CoFe 2O4nanocrystals and\nZnO. The solid line is a \ftting of carrier concentration by the\nfunctione\u0000Ea=kBT.\nThe two samples exhibit a similar MR behavior. Only\npositive MR has been observed, and MR decreases\nquickly from around 16%(6 T) at 20 or 40 K to 0.2%\n(6 T) at 290 K. The overall shape of the \feld depen-\ndent MR is quadratic, and shows no sign of saturation.\nWe attribute it to ordinary MR e\u000bect resulting from the\ncurving of the electron trajectory due to Lorenz force in a\nmagnetic \feld. The characteristic quantity is the Landau\norbit,LH= (eH=\u0016hc)\u00001=2, which is temperature indepen-\ndent. Another parameter is the dephasing length LTh\nof electrons, the di\u000busing distance between two elastic\nscattering events, which decreases with increasing tem-\nperature. When the dephasing length is much smaller\nthan the Landau orbit, LTh2=LH2\u001c1, the magnetoresis-\ntance is quadratic and non saturating. Actually the \feld\ndependent MR can be \ftted well as a H2dependence\nFIG. 13: The \feld dependent MR of (a) the composites of\nNiFe 2O4nanocrystals and ZnO and (b) the composites of\nCoFe 2O4nanocrystals and ZnO. The solid lines are guides to\nthe eye.\n(not shown). That means the dephasing length is very\nsmall in this sample due to the presence of NiFe 2O4or\nCoFe 2O4nanocrystals. In the literature a large posi-\ntive MR up to several hundreds or thousands percent\nhas been observed in regularly ordered nanowires58or\nnanocolumns59. A non-saturating positive MR e\u000bect is\nexpected to be useful for wide-range \feld sensing. A pos-\nitive MR has also been observed in Co-doped ZnO \flms,\nand modelled by considering s\u0000dexchange55,60. Note\nthat the MR at 20 K in Fig. 13 exhibits a small contri-\nbution indicated by the arrows, which saturates at low\n\felds. This contribution could be due to s\u0000dexchange\nconsidering that a small amount of Co2+or Ni2+ions\nremains in a diluted state. On the other hand, no neg-\native MR has been observed, which often was found in\nthe hybrid system of MnAs and GaAs61,62.\nThe Hall resistivity\n\u001axy=RHB+RM\u00160M (7)10\nFIG. 14: Anomalous Hall voltage vs magnetic \feld for (a)\nthe composites of NiFe 2O4nanocrystals and ZnO and (b) the\ncomposites of CoFe 2O4nanocrystals and ZnO.\nis known to be a sum of the ordinary and anomalous\nHall terms, where Bis magnetic induction, \u00160magnetic\npermeability, Mmagnetization, RHthe ordinary Hall\ncoe\u000ecient, and RMthe anomalous Hall coe\u000ecient. The\nordinary and anomalous Hall term is linear in B and M,\nrespectively. After subtracting the linear part, the or-\ndinary Hall e\u000bect, a clear AHE also has been observed\nin the two samples, as shown in Fig. 14. AHE van-\nishes at temperatures above 100 K. Obviously the AHE\ncurve does not coincide with the magnetization curve as\nshown in Fig. 4 and Fig. 5. It is di\u000ecult to correlate\nthe observed AHE to NiFe 2O4or CoFe 2O4nanocrystals.\nUsually, AHE is not expected or very weak for a semi-\nconductor with embedded magnetic nanoparticles63,64. If\none considers that the shape of the AHE curves mimics\nthe M-H curves, the AHE is likely due to some param-\nagnetic contributions or magnetism induced by intrinsic\ndefects65.\nIV. CONCLUSIONS\n(I) Nano-scaled ferrite materials attract considerable\nresearch attention due to their cation distribution andapplications as dielectric materials46,66,67,68. Usually, fer-\nrite nanoparticles are formed by mechanical or chemi-\ncal methods. We have demonstrated the formation of\nNiFe 2O4and CoFe 2O4nanocrystals inside a ZnO ma-\ntrix. Ion beam synthesis has its own obvious advantage\nof allowing lateral patterning69.\n(II) NiFe 2O4and CoFe 2O4nanoparticles are crystal-\nlographically oriented with respect to the ZnO matrix.\nThey show similar structural properties, but di\u000berent\nmagnetic, and transport properties. Considering the rich\nphases of spinel ferrites (TMFe 2O4, TM=Ni, Co, Fe, Mn,\nCu, Zn), our results demonstrate the possibility to have a\nnew magnet/semiconductor hybrid system. This system\ncan be tuned over a large variety of magnetic and trans-\nport properties. However, the observed MR and AHE\nare likely not related to the presence of NiFe 2O4and\nCoFe 2O4nanocrystals. This could be due to the im-\nperfect interface between nanocrystals and ZnO matrix.\nThis problem could be solved by epitaxial growth meth-\nods, e.g., pulsed laser deposition. A multilayered struc-\nture of ferrites/ZnO could be grown, and opens a path\ntowards semiconducting spintronic devices.\n(III) Our results suggest the possible integration of fer-\nrites with semiconducting ZnO, which would allow the in-\ntegration of microwave with semiconductor devices. The\ncombination of ferrites and conventional semiconductors,\ne.g., Si and GaAs, proves to be challenging due to the re-\nquirements of oxygen atmosphere and high temperature\nfor ferrites11.\nV. ACKNOWLEDGEMENT\nThe authors (S.Z., Q.X. and H.S.) thank \fnancial\nfunding from the Bundesministerium f ur Bildung und\nForschung (FKZ03N8708). Q. X. is supported by the Na-\ntional Natural Science Foundation of China (50802041).\nThe Advanced Light Source is supported by the Direc-\ntor, O\u000ece of Science, O\u000ece of Basic Energy Sciences,\nof the U.S. Department of Energy under Contract No.\nDE-AC02-05CH11231.\nDuring the press of this manuscript, we observed that\nan all-oxide ferromagnet/semiconductor (Fe 3O4/ZnO)\nheterostructure has been realized by other groups using\npulsed laser deposition70.\n\u0003Electronic address: S.Zhou@fzd.de\n1S. Chikazumi, Physics of Ferromagnetism (Oxford Univer-\nsity Press, Oxford, 1997).2U. L uders, A. Barth\u0013 el\u0013 emy, M. Bibes, K. Bouzehouane,\nS. Fusil, E. Jacquet, J. P. Contour, J. F. Bobo, J. Fontcu-\nberta, and A. Fert, Adv. Mat. 18, 1733 (2006).11\n3S. Zhou, K. Potzger, H. Reuther, G. Talut, F. Eichhorn,\nJ. von Borany, W. Skorupa, M. Helm, and J. Fassbender,\nJ. Phys. D-Appl. Phys. 40, 964 (2007).\n4A. L. Geiler, A. Yang, X. Zuo, S. D. Yoon, Y. Chen, V. G.\nHarris, and C. Vittoria, Phys. Rev. Lett. 101, 067201\n(2008).\n5M. Ishikawa, H. Tanaka, and T. Kawai, Appl. Phys. Lett.\n86, 222504 (2005).\n6J. Takaobushi, H. Tanaka, T. Kawai, S. Ueda, J.-J.\nKim, M. Kobata, E. Ikenaga, M. Yabashi, K. Kobayashi,\nY. Nishino, D. Miwa, K. Tamasaku, T. Ishikawa, Appl.\nPhys. Lett. 89, 242507 (2006).\n7U. L uders, M. Bibes, K. Bouzehouane, E. Jacquet,\nJ.-P. Contour, S. Fusil, J.-F. Bobo, J. Fontcuberta,\nA. Barth\u0013 el\u0013 emy, and A. Fert, Appl. Phys. Lett. 88, 082505\n(2006).\n8A. V. Ramos, M.-J. Guittet, J.-B. Moussy, R. Mattana,\nC. Deranlot, F. Petro\u000b, and C. Gatel, Appl. Phys. Lett.\n91, 122107 (2007).\n9E. Snoeck, C. Gatel, R. Serra, G. BenAssayag, J.-B.\nMoussy, A. M. Bataille, M. Pannetier, and M. Gautier-\nSoyer, Phys. Rev. B 73, 104434 (2006).\n10A. V. Ramos, T. S. Santos, G. X. Miao, M.-J. Guittet, J.-\nB. Moussy, and J. S. Moodera, Phys. Rev. B 78, 180402\n(2008).\n11Z. Chen, A. Yang, A. Gieler, V. G. Harris, C. Vittoria,\nP. R. Ohodnicki, K. Y. Goh, M. E. McHenry, Z. Cai,\nT. L. Goodrich, K. S. Ziemer, Appl. Phys. Lett. 91, 182505\n(2007).\n12Y. Suzuki, Annu. Rev. Mater. Res. 31, 265 (2001).\n13J. Ziegler, J. Biersack, and U. Littmark, The stopping and\nrange of ions in matter (Pergamon, New York, 1985).\n14S. Zhou, K. Potzger, J. von Borany, R. Gr otzschel, W. Sko-\nrupa, M. Helm, and J. Fassbender, Phys. Rev. B 77,\n035209 (2008).\n15S. Zhou, K. Potzger, G. Talut, H. Reuther, J. von Bo-\nrany, R. Gr otzschel, W. Skorupa, M. Helm, J. Fassbender,\nN. Volbers, M. Lorenz, T. Herrmannsd orfer, J. Appl. Phys.\n103, 023902 (2008).\n16R. Brand, Nucl. Instrum. Methods Phys. Res. B 28 , 398\n(1987).\n17A. Bonanni, A. Navarro-Quezada, T. Li, M. Wegscheider,\nZ. Mat\u0014 ej, V. Hol\u0013 y, R. T. Lechner, G. Bauer, M. Rovezzi,\nF. D'Acapito, M. Kiecana, M. Sawichi, T. Dietl, Phys.\nRev. Lett. 101, 135502 (2008).\n18B. D. Cullity, Elements of X-ray Di\u000bractions (Reading,\nAddison-Wesley, 1978).\n19S. O. Kucheyev, J. S. Williams, C. Jagadish, J. Zou,\nC. Evans, A. J. Nelson, and A. V. Hamza, Phys. Rev.\nB67, 094115 (2003).\n20S. Zhou, K. Potzger, D. Buerger, K. Kuepper, M. Helm,\nJ. Fassbender, and H. Schmidt, Nucl. Instr. and Meth. B\n267, 1620 (2009).\n21S. Zhou, G. Talut, K. Potzger, A. Shalimov, J. Grenzer,\nW. Skorupa, M. Helm, J. Fassbender, E. \u0014Ci\u0014 zm\u0013 ar, S. A.\nZvyagin, J. Wosnitza, J. Appl. Phys. 103, 083907 (2008).\n22Y. J. Li, B. Zhang, W. Lu, Y. Wang, and J. Zou, Appl.\nPhys. Lett. 93, 131919 (2008).\n23Y. Wang, J. Zou, Y. Li, B. Zhang, and W. Lu, Acta Mater.\n57, 2291 (2009).\n24M. Opel, K.-W. Nielsen, S. Bauer, S. T. Goennenwein,\nJ. C. Cezar, D. Schmeisser, J. Simon, W. Mader, and\nR. Gross, Eur. Phys. J. B 63, 437 (2008).\n25B. Rellinghaus, S. Stappert, E. Wassermann, H. Sauer, andB. Splietho\u000b, Eur. Phys. J. D 16, 249 (2001).\n26E. C. Stoner and E. P. Wohlfarth, IEEE Trans. Magn. 27,\n3475 (1991).\n27G. A. Candela and R. A. Haines, Appl. Phys. Lett. 34, 868\n(1979).\n28M. Respaud, J. M. Broto, H. Rakoto, A. R. Fert,\nL. Thomas, B. Barbara, M. Verelst, E. Snoeck, P. Lecante,\nA. Mosset, J. Osuna, T. Ely, C. Amiens, B. Chaudret,\nPhys. Rev. B 57, 2925 (1998).\n29W. A. Yager, J. K. Galt, F. R. Merritt, and E. A. Wood,\nPhys. Rev. 80, 744 (1950).\n30R. M. Bozorth, E. F. Tilden, and A. J. Williams, Phys.\nRev.99, 1788 (1955).\n31H. T. Jeng and G. Y. Guo, J. Magn. Magn. Mater. 240,\n436 (2002).\n32Y. Suzuki, R. B. van Dover, E. M. Gyorgy, J. M. Phillips,\nV. Korenivski, D. J. Werder, C. H. Chen, R. J. Cava, J. J.\nKrajewski, W. F. Peck, K. B. Do, Appl. Phys. Lett. 68,\n714 (1996).\n33J. F. Hochepied, P. Sainctavit, and M. Pileni, J. Magn.\nMagn. Mater. 231, 315 (2001).\n34J. P. Crocombette, M. Pollak, F. Jollet, N. Thromat, and\nM. Gautier-Soyer, Phys. Rev. B 52, 3143 (1995).\n35F. M. F. de Groot, M. Abbate, J. van Elp, G. A. Sawatzky,\nY. J. Ma, C. T. Chen, and F. Sette, J. Phys.-Conden.\nMatter 5, 2277 (1993).\n36A. Barla, G. Schmerber, E. Beaurepaire, A. Dinia,\nH. Bieber, S. Colis, F. Scheurer, J.-P. Kappler, P. Imperia,\nF. Nolting, F. Wilhelm, A. Rogalev, D. M uller, J. J. Grob,\nPhys. Rev. B 76, 125201 (2007).\n37G. van der Laan, E. Arenholz, R. V. Chopdekar, and\nY. Suzuki, Phys. Rev. B 77, 064407 (2008).\n38F. M. F. de Groot, J. Electron Spectrosc. Relat. Phenom.\n67, 529 (1994).\n39F. M. F. de Groot, Coord. Chem. Rev. 249, 31 (2005).\n40G. van der Laan, C. M. B. Henderson, R. A. D. Pattrick,\nS. S. Dhesi, P. F. Scho\feld, E. Dudzik, and D. J. Vaughan,\nPhys. Rev. B 59, 4314 (1999).\n41K. Kuepper, I. Balasz, H. Hesse, A. Winiarski, K. C.\nPrince, M. Matteucci, D. Wett, R. Szargan, E. Burzo, and\nM. Neumann, Phys. Status Solidi A 201, 3252 (2004).\n42A. Gloter, A. Douiri, M. Tence, and C. Colliex, Ultrami-\ncroscopy 96, 385 (2003).\n43J. Takaobushi, M. Ishikawa, S. Ueda, E. Ikenaga, J.-\nJ. Kim, M. Kobata, Y. Takeda, Y. Saitoh, M. Yabashi,\nY. Nishino, D. Miwa, K. Tamasaku, T. Ishikawa, I. Satoh,\nH. Tanaka, K. Kobayashi, Phys. Rev. B 76, 205108 (2007).\n44U. L uders, M. Bibes, J.-F. Bobo, M. Cantoni, R. Bertacco,\nand J. Fontcuberta, Phys. Rev. B 71, 134419 (2005).\n45V. N. Antonov, B. N. Harmon, and A. N. Yaresko, Phys.\nRev. B 67, 024417 (2003).\n46C. N. Chinnasamy, A. Narayanasamy, N. Ponpandian,\nK. Chattopadhyay, H. Guerault, and J. M. Greneche, J.\nPhys.-Condens. Matter 12, 7795 (2000).\n47S. J. Kim, S. W. Lee, and C. S. Kim, Jpn. J. Appl. Phys.\n40, 4897 (2001).\n48N. Ponpandian, A. Narayanasamy, C. N. Chinnasamy,\nN. Sivakumar, J.-M. Greneche, K. Chattopadhyay,\nK. Shinoda, B. Jeyadevan, and K. Tohji, Appl. Phys. Lett.\n86, 192510 (2005).\n49J. P. Chen, C. M. Sorensen, K. J. Klabunde, G. C. Had-\njipanayis, E. Devlin, and A. Kostikas, Phys. Rev. B 54,\n9288 (1996).\n50S. Chakraverty, S. Mitra, K. Mandal, P. M. G. Nambissan,12\nand S. Chattopadhyay, Phys. Rev. B 71, 024115 (2005).\n51S. Mitra, K. Mandal, S. Sinha, P. M. G. Nambissan, and\nS. Kumar, J. Phys. D-Appl. Phys. 39, 4228 (2006).\n52A. V. Zalesskii, M. K. Gubkin, T. M. Perekalina, and T. A.\nKhimich, Crystallogr. Rep. 45, 678 (2000).\n53G. H. Kassier, M. Hayes, F. D. Auret, M. Mamor, and\nK. Bouziane, J. Appl. Phys. 102, 014903 (2007).\n54K. Maeda, M. Sato, I. Niikura, and T. Fukuda, Semicond.\nSci. Technol. 20, S49 (2005).\n55Q. Xu, L. Hartmann, H. Schmidt, H. Hochmuth,\nM. Lorenz, R. Schmidt-Grund, C. Sturm, D. Spemann,\nand M. Grundmann, Phys. Rev. B 73, 205342 (2006).\n56K. Potzger, K. Kuepper, Q. Xu, S. Zhou, H. Schmidt,\nM. Helm, and J. Fassbender, J. Appl. Phys. 104, 023510\n(2008).\n57D. C. Look, B. Cla\rin, and H. E. Smith, Appl. Phys. Lett.\n92, 122108 (2008).\n58K. Liu, C. L. Chien, P. C. Searson, and K. Yu-Zhang, Appl.\nPhys. Lett. 73, 1436 (1998).\n59M. Jamet, A. Barski, T. Devillers, V. Poydenot, R. Du-\njardin, P. Bayle-Guillemaud, J. Rothman, E. Bellet-\nAmalric, A. Marty, J. Cibert, R. Mattana, S. Tatarenko,\nNat. Mater. 5, 653 (2006).\n60Q. Xu, L. Hartmann, H. Schmidt, H. Hochmuth,\nM. Lorenz, D. Spemann, and M. Grundmann, Phys. Rev.\nB76, 134417 (2007).\n61P. J. Wellmann, J. M. Garcia, J. L. Feng, and P. M. Petro\u000b,\nAppl. Phys. Lett. 73, 3291 (1998).62H. Akinaga, J. De Boeck, G. Borghs, S. Miyanishi,\nA. Asamitsu, W. Van Roy, Y. Tomioka, and L. H. Kuo,\nAppl. Phys. Lett. 72, 3368 (1998).\n63S. R. Shinde, S. B. Ogale, J. S. Higgins, H. Zheng, A. J.\nMillis, V. N. Kulkarni, R. Ramesh, R. L. Greene, and\nT. Venkatesan, Phys. Rev. Lett. 92, 166601 (2004).\n64S. X. Zhang, W. Yu, S. B. Ogale, S. R. Shinde, D. C.\nKundaliya, W.-K. Tse, S. Y. Young, J. S. Higgins, L. G.\nSalamanca-Riba, M. Herrera, L. F. Fu, N. D. Browning,\nR. L. Greene, T. Venkatesan, Phys. Rev. B 76, 085323\n(2007).\n65Q. Xu, H. Schmidt, S. Zhou, K. Potzger, M. Helm,\nH. Hochmuth, M. Lorenz, A. Setzer, P. Esquinazi, C. Mei-\nnecke, M. Grundmann, Appl. Phys. Lett. 92, 082508\n(2008).\n66S. A. Oliver, H. H. Hamdeh, and J. C. Ho, Phys. Rev. B\n60, 3400 (1999).\n67M. Bohra, S. Prasad, N. Kumar, D. S. Misra, S. C. Sahoo,\nN. Venkataramani, and R. Krishnan, Appl. Phys. Lett. 88,\n262506 (2006).\n68S. Thakur, S. C. Katyal, and M. Singh, Appl. Phys. Lett.\n91, 262501 (2007).\n69J. Fassbender and J. McCord, J. Magn. Magn. Mater. 320,\n579 (2008).\n70A. Nielsen, A. Brandlmaier, M. Althammer, W. Kaiser,\nM. Opel, J. Simon, W. Mader, S. T. B. Goennenwein, and\nR. Gross, Appl. Phys. Lett. 93, 162510 (2008)."    },    {        "title": "2311.01879v1.Effects_of_Cr_content_on_ion_irradiation_hardening_of_FeCrAl_ODS_ferritic_steels_with_9_wt___Al.pdf",        "content": "Effects of Cr content on ion-irradiation hardening of FeCrAl ODS ferritic\nsteels with 9 wt% Al\nZhexian Zhanga,b,∗, Siwei Chena,b, Kiyohiro Yabuuchia\naInstitute of Advanced Energy, Kyoto University, Gokasho, Uji, 611-0011, Kyoto, Japan\nbDepartment of Nuclear Engineering, University of Tennessee, Knoxville, 37996, TN, USA\nAbstract\nFeCrAl ODS steels for accident tolerant fuel claddings are designed to bear high-Cr and Al for enhancing\noxidation resistance. In this study, we investigated the effects of Cr content on ion-irradiation hardening of\nthree ODS ferritic steels with different Cr contents added with 9 wt% Al, Fe12Cr9Al (SP12), Fe15Cr9Al\n(SP13), and Fe18Cr9Al (SP14). The specimens were irradiated with 6.4MeV Fe3+at 300 °C to nominal 3\ndpa. The irradiation hardening was measured by nanoindentation method, and the Nix-Gao plots were used\nto evaluate the bulk-equivalent hardness. The results showed that the irradiation hardening decreased with\nincreasing Cr content. The reason is due to the growth of dislocation loops hindered by solute Cr atoms.\nTEM observations showed both ⟨100⟩and 1/2⟨111⟩dislocation loops existed in the irradiated area. The\nirradiation hardening was estimated by dispersed barrier hardening (DBH) model with dislocation loops.\nKeywords:\nFeCrAl ODS steel, ion-irradiation, nanoindentation, dislocation loops, Cr content\n1. Introduction\nAccident tolerant fuel (ATF) cladding has been\nproposed to enhance the safety of light water reac-\ntors (LWR) under design-basis and beyond-design-\nbasis accident scenarios, aiming to delay the on-\nset of detrimental oxidation and chemical interac-\ntion processes with hot water[1, 2]. FeCrAl ODS\nferritic steels have been considered as a promis-\ning candidate because of its excellent mechanical\nproperties and good oxidation resistance at high\ntemperatures[3–5]. During operation, the FeCrAl\ncladdings experience neutron irradiation at oper-\nating temperature around 280 to 300 °C, which\ninduces generation of defects such as dislocation\nloops, voids, precipitates and so on. These defects\nmay lead to irradiation embrittlement, for exam-\nple, shift the ductile brittle transition temperature\n(DBTT) greatly over room temperature[6]. This\ndegradation could be reflected by the irradiation\nhardening accompanied by lowering ductility[7].\n∗corresponding author\nEmail address: zzhan124@utk.edu (Zhexian Zhang)The FeCrAl ODS steels are designed with differ-\nent Cr (<20wt%) and Al ( <10wt%) contents.\nThe upper-limit content of Cr can be due to the α-\nα′phase separation during service at elevated tem-\nperatures through spinodal and nucleation-growth\nmechanism according to the miscibility gap[8, 9].\nOn the other hand, the Al content is limited to\nbelow 10wt%, which is solubility limit of Al in Fe\nat around 300 °C[10]. High Al will also induce\nthe formation of Al-Ti enriched β′precipitates,\nwhich causes embrittlement during early aging at\n475 °C[11, 12].\nSo far, irradiation effects on FeCrAl ODS steels\nare mainly studied for the steels with Al around 3 6\nwt%[13–18]. However, high Al could shift the mis-\ncibility boundary of α−α′phase separation to a\nhigher Cr content[8,19][8, 19], consequently hinders\ntheα′precipitation hardening. Moreover, corro-\nsion tests showed that the addition of Al (2 4wt%)\nefficiently reduced the weight gains in supercritical\npressurized water (SCPW)[5]. With these merits of\nAl, it is benefit to investigate ion-irradiation hard-\nening of FeCrAl ODS steels with rather higher Al\ncontent. Zhou et al[20] studied the Al effect on\nformation of the dislocation loops in non-ODS Fe-\nPreprint submitted to arXiv November 6, 2023arXiv:2311.01879v1  [cond-mat.mtrl-sci]  3 Nov 2023CrAl steels. The results showed Al can effectively\nsuppress the growth of the dislocation loops due to\nenhanced pinning effect of Al atoms.\nAnother issue of FeCrAl alloys is the effect of\nCr content on irradiation hardening. As is well\nknown, Cr improves the corrosion resistance by\nforming protective Cr2O3layers. However, the\nirradiation embrittlement could be accelerated by\nincreasing Cr content which causes α−α′sepa-\nration by radiation enhanced diffusion[21]. The\nα′precipitation in FeCrAl steels has been stud-\nied and proved susceptible to alloy composite[22],\ntemperature[23] and grain morphology[24, 25], and\nthe precipitation kinetics under irradiation follows\ntypical Lifshitz-Slyozov-Wagner (LSW) theory[26].\nBoth the ion-irradiation and neutron irradiation\nshowed Cr-dependence of irradiation hardening in\nFeCrAl steels[27, 28].\nTo fill the gap of research in high-Al FeCrAl\nODS steels, we investigated the FeCrAl ODS ferritic\nsteels with 9wt% Al which is close to its up-limit.\nParticularly to understand the Cr-dependent irradi-\nation hardening, steels with different concentration\nof Cr (12, 15, 18wt%) were studied. These steels\nwere subjected to self-ion irradiation to nominal 3\ndpa at 300 °C. The hardness of steels was measured\nby nanoindentation, and microstructures were ob-\nserved by TEM. The Cr dependent hardening in\nFeCrAl ODS steels with high Al concentrations was\ndiscussed.\n2. Experimental\nThree FeCrAl ODS ferritic steels, of which the\nchemical compositions are shown in Table ??.\nThese steels were produced by mechanical alloying\nin Ar atmosphere. The mixed powder was encapsu-\nlated into a steel capsule, hot-extruded at 1150 °C\nand followed by the final step of the heat treatment\nat 1150 °C for 1hr followed by air cooling. The de-\ntail of production procedure is available in a recent\nreview[29]. Specimens for irradiation were cut so\nthat the irradiation surface is parallel to the extru-\nsion direction. The specimens were grinded with\nSiC paper and polished with 3 µm, 1µm, 0.25µm\ndiamond powders subsequently. Final surface treat-\nment included electrical polishing in 5% HClO 4\nand 95%CH3COOH for 60 sec, and low-energy\nAr ion milling for 10 min.\nIon irradiation was performed with Dual-beam\nFacility for Energy Science and Technology (DuET)\nin Kyoto University. DuET is composed of a 1.7\nFigure 1: Irradiation dose and implanted Fe ions distribu-\ntion calculated by SRIM. 3 dpa at 600 nm was selected as a\nnominal value.\nMV tandem accelerator for heavy ion irradiation\nand a 1.0MV single accelerator for helium implan-\ntation. Details of the construction can be found\nin Ref[30]. The ion source of Fe2O3was ionized\nby an 860 ionizer in Cesium reservoir. The ionized\ncharged particle, FeO−, was focused by Einzel lens\nand deflected by an injector magnet to accelerator.\nIn the tandem accelerator, the FeO−beam was first\naccelerated to 1.7 MeV halfway, then stripped into\n1.32 MeVFe3+and 0.38 MeV oxygen ions. The\nFe3+was accelerated again in the other half of the\naccelerator with the total energy of Fe3+becoming\n6.4MeV. A magnet accelerator was used thereafter\nto screen out ions other than 6.4 MeV Fe3+. Beam\nposition was finally adjusted by a steerer, and beam\ncurrent was measured by array of 21 Faraday cups.\nThe vacuum of the target chamber was 5 ×10−5\nPa. The beam irradiated on specimen was raster-\nscanned horizontally 1000 Hz and vertically 300 Hz.\nThe temperature of irradiated sample surface was\nmonitored by infrared thermography during irradi-\nation. The emissivity of materials was calculated\nby pre-calibration with a K-type thermocouple at-\ntached to the specimen surface at various tempera-\ntures before irradiation.\nThe irradiation damage and implanted ion dis-\ntribution (Fig.1) were estimated by SRIM[31] us-\ning the “Ion distribution and quick calculation of\ndamage” method. The displacement threshold en-\nergy(TDE) was selected by 40 eV[32] for iron-based\nsteels. The value at the depth of 600 nm was cho-\nsen as the nominal irradiation dose because there\n2Table 1: Chemical compositions of FeCrAl ODS ferritic steels (wt%, Bal. Fe)\nID Cr Al Ti Y C O N Ar\nFe12Cr9Al SP12 11.93 8.65 0.53 0.38 0.029 0.22 0.003 0.006\nFe15Cr9Al SP13 14.25 8.4 0.51 0.38 0.03 0.22 0.003 0.006\nFe18Cr9Al SP14 16.63 8.09 0.49 0.37 0.032 0.22 0.003 0.006\nTable 2: The dislocation loops and DBH hardening after irradiation.\nDislocation loops Hardening (GPa)\nDiameter (nm) Density ( ×1022/m3) Measured Calculated\nFe12Cr9Al (SP12) 11 .6±2.0 2 .26±0.34 1.45±0.27 1.28\nFe15Cr9Al (SP13) 12 .0±1.0 1 .84±0.85 1.35±0.33 1.18\nis barely interference of the implanted irons at\nthis range. The samples were irradiated to nom-\ninal 3 dpa at 300 ±10řCwith the beam flux of\n1.1±1012ions/cm2/s, which is corresponding to\n3.3±10−4dpa/s . The peak dose is located around\n1.6µm. The maximum damage distribution is\nabout 2.3µm.\nNano-hardness was measured by G200 nanoin-\ndentation with a Berkovich tip using continuous\nstiffness measurement (CSM) method. The oscil-\nlation amplitude was 2 nm, and the frequency was\n45 Hz. The strain rate is constant 0.05 s−1, which\nwas achieved by loading rate control[33]. The area\nfunction was calibrated on fused silica (E=72.0GPa,\nν= 0.17). Over 20 tests were performed on each\nsample. The tests were indented to maximum 2 µm\ndepth and held for 10 sec at the maximum loading.\nTensile tests were performed on the tensile ma-\nchine (INTESCO Co., Ltd) with a load cell of\n0.5 kN. The geometries of a dog-born sheet type\nof miniature tensile specimens measured gauge-\nlength=5 mm, width=1.2 mm and thickness=0.25\nmm with the gripping area on both sides of 4 ×\n4mm2. The displacement speed was 0.2 mm/min\nresulting in an initial strain rate of 6 .67×10−4/s.\nThe yield stress was defined as 0.2% off-set flow\nstress. Three tests for each material were done\nat room temperature. Micro-Vickers hardness\nwas measured at room temperature by a hardness\ntester, HMV-2T (Shimadzu Corp.), with 2 kg load\nand holding time for 10 sec.\nMicrostructures of specimens were observed by\nJeol 2010 TEM with a side-mount CCD camera.\nThe cross-section of irradiated specimens was fabri-\ncated by focused ion beam machining (FIB, Hitachi\nFB2200). TEM specimens were flashing-polished\nin 5% HClO4 and 95% CH3OH at -30 °C and 30V as final thinning. The images were taken un-\nder two-beam bright field condition, with (110) αFe\ndiffraction plane excited. The thickness of TEM\nspecimens was measured by extinction fringes along\nspecimen margins or inclined non-twinned large an-\ngle grain boundaries under g3g weak beam central\ndark field condition.\n3. Results\n3.1. The oxide morphology and mechanical proper-\nties before irradiation\nThe oxides in Al-added FeCrAl ODS steels are\nmainly Y-Al-O types. The lattice image analy-\nsis by Oono et al showed that most of the oxides\nwereY4Al2O9(YAP) and YAlO 3(YAM)[34]. The\nmorphology of dispersoids before irradiation were\nshown in Fig.2. Both dislocation lines and oxides\nexist in the materials. The dislocations are straight\nlines suggesting that the tensions to the disloca-\ntions are fully relieved during the heat treatment\nafter mechanical alloying. Some interactions be-\ntween dislocation lines and oxides can be observed\nbut there is still no curved dislocation line around\noxide particles.\nFig.3 shows the size distribution of oxide parti-\ncle diameters in the three as-received FeCrAl ODS\nsteels. The diameters are mainly located in a rather\nsmall range between 4 8 nm, which means the size\nof oxides are generally homogeneous. The average\ndiameter of the oxides tends to increase with de-\ncreasing Cr content. The Fe18Cr9Al has the highest\nnumber densities of oxides in the three steels. The\nestimated volume fractions are 0.51%, 0.62% and\n0.64% for Fe12Cr9Al, Fe15Cr9Al, and Fe18Cr9Al,\nrespectively.\n3Table 3: The bulk-equivalent nano-hardness (GPa) evaluated by different range of Nix-Gao plots.\nRange of Nix-Gao plots Fe12Cr9Al (SP12) irradiated Fe15Cr9Al (SP13) irradiated Fe18Cr9Al (SP14) irradiated\n100nm-250nm 6 .23±0.27 6 .22±0.35 5 .72±0.31\n100nm-300nm 6 .21±0.23 6 .19±0.31 5 .80±0.26\n100nm-350nm 6 .16±0.21 6 .16±0.27 5 .83±0.23\n150nm-250nm 6 .22±0.29 6 .14±0.38 5 .95±0.32\n200nm-300nm 6 .12±0.28 6 .08±0.27 6 .02±0.38\n200nm-350nm 5 .97±0.29 6 .04±0.30 5 .95±0.43\nFigure 2: The oxides morphology in a) Fe12Cr9Al, b) Fe15Cr9Al, c) Fe18Cr9Al ODS steels before irradiation.\nFigure 3: The size distribution of oxides in unirradi-\nated Fe12Cr9Al (SP12), Fe15Cr9Al (SP13), and Fe18Cr9Al\n(SP14) ODS steels. The red lines are fitted results by Weibull\ndistribution. The volume fractions were obtained by an av-\nerage of observed three areas.\nFigure 4: The relationship between nano-hardness (NH),\nVickers hardness (HV) and σ0.2yielding stress (YS) in the\nthree ODS ferritic steels before irradiation. The nano hard-\nness was obtained by Nix-Gao methods. The intercept was\npreset as zero for linear fitting.\n4Figure 5: The relationship between nano-hardness (NH), Vickers hardness (HV) and σ0.2yielding stress (YS) in the three ODS\nferritic steels before irradiation. The nano hardness was obtained by Nix-Gao methods. The intercept was preset as zero for\nlinear fitting.\nFigure 6: Microstructures of irradiated Fe15Cr9Al ODS steel (SP13), a) g=200, b) g=110. Dislocation loops projections were\nshown in each zone axis. The Moir ´efringes of oxides indicate crystal structure was kept under irradiation. The diffraction\npattern of the irradiated area along c) [011] direction and d) [133] direction.\n5Figure 7: The nano-indentation hardness profile of a) unirradiated and b) irradiated Fe12Cr9Al (SP12), c) unirradiated and\nd) irradiated Fe15Cr9Al (SP13), e) unirradiated and f) irradiated Fe18Cr9Al (SP14).\n6The bulk equivalent hardness from nanoindenta-\ntion tests were estimated by Nix-Gao method[35] in\nequation 1, where His the measured hardness, H0\nis the bulk equivalent hardness, h∗is a length scale\nindicator,his the indentation depth.\nH2=H2\n0/parenleftbigg\n1 +h∗\nh/parenrightbigg\n(1)\nBulk-equivalent nano-hardness of unirradiated\nmaterials were estimated by data between 100\nto 2000nm. Relationships among nano-hardness\n(NH), Vickers hardness (HV) and yielding\nstress (YS, σ0.2) were shown in Fig.4. The\nNH=0.01352HV is similar to the previous obtained\nresults[36]. However, the YS=2.764HV is some-\nwhat different from the common acknowledged 3\ntimes rules[37].\n3.2. The microstructure evolution after irradiation\nFig.5 shows the cross-section of irradiation dam-\naged Fe12Cr9Al (SP12). The overall damaged re-\ngion was compared to the SRIM calculated dose\nprofile (Fig.5a). The dislocation loops distributed\nto the maximum depth of 1.8 µm, which exceeded\nthe damage peak, but was shallower than the max-\nimum irradiation range calculated by SRIM. Fig.5b\nshows the microstructures in the region between\n150 770 nm, which was selected as the area for TEM\nanalysis. In this region, dislocation loops coexisted\nwith oxide particles and dislocation lines. Fig.5c\nshows the transition area of the irradiated region.\nIn this region, dislocation loops disappeared and\nonly dislocation lines and oxides existed in the unir-\nradiated area.\nFig.6 shows two different areas around 600 nm\ndepth of the irradiated Fe15Cr9Al (SP13) under\nzone axis [011] and [133], with g vectors equals to\n-200 and 01-1 respectively. The projection images\nof 1/2<111>and<100>dislocation loops\nwith different habit planes under different zone axis\nwere schematically shown. The solid circles are the\nloops appearing with contrast and the dashed cir-\ncles are the loops being extinct at this diffraction\ncondition. Both Fig.6a-b proved the existence of\nthe 1/2<111>and<100>type dislocation\nloops and the oxide particles in the irradiated re-\ngion. TheMoir ´efringes indicated that the oxides\nwere not amorphized. The diffraction patterns in\nFig.6c-d showed that the oxides were mainly YAP,\nwithαFe(0-11) corresponding to YAP(221) because\nthey have similar plane spacing. Fig.6c also showedanother relationship of αFe(001)//YAP(1-20) and\nαFe[100]//YAP[210].\nSong et al[38] studied the stability of oxide par-\nticles in ODS steels under ion-irradiation at 200 °C\nbased on the observation of Moir ´efringes, and re-\nported that the Y-Al-O oxides tended to become\namorphous under irradiation up to 8 dpa and dis-\nsolved thereafter. They suggested that the radia-\ntion tolerance of the oxide particles depended on\nboth the irradiation temperature and damage rate\nas well as total damage (dpa). In this study, un-\nder the ion-irradiation at 300 °C and almost the\nsame damage rate, the oxides were not amorphized,\nwhich means the Y-Al-O system oxides are rela-\ntively stable at this irradiation condition. It might\nbe also owing to the smaller dose used in this ex-\nperiment compared to the study of Song et al[38].\nThe average diameter and number density of dis-\nlocation loops were summarized in Table 2, where\nthe density of dislocation loops was adjusted ac-\ncording to the invisible criterion in TEM two beam\ndiffraction condition. The diameters of disloca-\ntion loops in SP12 and SP13 are 11 .6±2.0nm\nand 12.0±1.0nm, and the number densities are\n2.26±0.34×1022/m3and 1.84±0.85×1022/m3,\nrespectively.\n3.3. The nano-indentation hardness.\nThe profiles of nanoindentation hardness of ir-\nradiated and unirradiated FeCrAl ODS steels are\nshown in Fig.7. The features of the profiles include:\n1) the hardness decreases gradually along with in-\ndentation depth because of the indentation size ef-\nfect, 2) a reverse size effect in some tests before\n100nm occurred possibly because of initial contact\nvariance from surface roughness, grain boundaries\nand precipitates, but as the indent went deeper, the\nnormal size effect became dominant. 3) the irradi-\nated samples have elevated hardness than the unir-\nradiated ones indicating irradiation hardening. 4)\nthe hardening disappeared at an indentation depth\naround 2000 nm where the plastic deformation zone\nin the irradiated region took small fraction com-\npared to the unirradiated region.\nThe Nix-Gao hardness plots of both irradiated\nand unirradiated steels are shown in Fig.8. Before\nirradiation, the Nix-Gao plots were linear through\nthe entire exhibited range. In contrast, there is a\nclear shoulder of irradiated plots in the depth re-\ngion lower than 300 nm, which reflects the presence\nof layered structure in the intended region. The\n7bulk-equivalent hardness was estimated by the lin-\near fitting of the data between 100 nm 2000 nm\nin the unirradiated specimens. The hardness af-\nter irradiation was evaluated by data with different\nranges between 100 nm 350 nm of Nix-Gao plots.\nThe depth of damage limit at 1800 nm corresponds\nto about 5 times of the turning point at 350 nm.\nThe depth range selection for hardness evalua-\ntion of irradiation is not only dependent on the lin-\near correlation. This is because the profile of Nix-\nGao plots is usually not absolutely linear[39]. More-\nover, the surface roughness[40] and pile up[41] will\naffect the measured hardness not only increasing\nscattering but change the linear relationship. The\nbulk-equivalent nano-hardness evaluated by differ-\nent range of Nix-Gao plots were summarized in Ta-\nble 3. For Fe12Cr9Al and Fe15Cr9Al, as the se-\nlected range goes deeper, the evaluated hardness\nkeeps decreasing. Oppositely, the evaluated hard-\nness of Fe18Cr9Al increases with selected depth un-\ntil around 6 GPa. These are typical phenomenon\nin irradiated materials, where the surfaces are in-\nhomogeneous either because of irradiation induced\ndefects or surface roughness.\nIn this study, we chose the 100nm-300nm as the\nstandard range to evaluate bulk-hardness for ir-\nradiated materials, because in this range, the in-\ndentation deforming zone is fully within the irradi-\nated region. Fig.9 summarized the bulk-equivalent\nhardness of each nanoindentation of the irradiated\nand unirradiated steels. In unirradiated steels, the\nhardness linearly increases with Cr concentration.\nIn irradiated materials, Fe12Cr9Al and Fe15Cr9Al\nshowed similar high hardness while Fe18Cr9Al had\nthe lowest.\n4. Discussion\nFigure 10 summarized the irradiation harden-\ning in several FeCrAl ODS and non-ODS steels\nat similar irradiation conditions[13][15][23][26]. In\nthis study, the irradiation hardening exhibited Cr\ndependence, where a higher Cr content yielded a\nsmaller irradiation hardening. However, this trend\nis contradicted to the conventional understanding\nthat high Cr should generate more α′precipitate,\nthus yield a higher irradiation hardening. This\ntrend is also opposite to the hardening of FeCrAl\nnon-ODS steels which were subjected to neutron ir-\nradiation reported by Field et al[26] (Fig.10). There\nis a small successive decrease of the Al concentra-\ntion in the studied steels (Table ??), which might\nFigure 8: Nix-Gao plots of the irradiated and unirradiated\na) Fe12Cr9Al ODS steel (SP12), b) Fe15Cr9Al ODS steel\n(SP12) and c) Fe18Cr9Al ODS steel (SP14). Note that the\nmanually drawn lines are only an indicator to the shoulder\nfor linear fitting and do not correspond to the actual bulk\nequivalent hardness.\n8Figure 9: The bulk-equivalent hardness calculated by Nix-\nGao method with the data from 100nm to 1000nm of the\nunirradiated and from 100nm to 300nm of the irradiated\nmaterials.\nFigure 10: The summary of Cr dependent irradiation\nhardening in FeCrAl steels. The solid symbols stand\nfor ODS steels, and hollow symbols are non-ODS steels.\nThe neutron irradiation hardening measured by yield\nstress were converted to nanoindentation hardening by\nNH(GPa)=0.004891YS(MPa).affect the formation of Al-enrich β′precipitates,\nand consistent with the decreasing trend of irra-\ndiation hardening. However, the effect is doubtful\nbecause of the tiny difference of the Al concentra-\ntions (<1%).\nOne explanation might be that the α′was not\nprecipitate at all under current irradiation flux. Ke\net al[42] simulated the Cr precipitate in Fe-Cr bi-\nnary system based on phase-field theory. The re-\nsults showed that increasing dose rate will sup-\npress the formation of α′at 300 °C. The threshold\nflux ofα′disappearing was as low as 10−4dpa/s .\nThe experiments analysis by Zhao et al[43] on the\nprecipitates using APT demonstrated that α′will\ndissolve under 10−3dpa/s ion-irradiation at 300 °C.\nTherefore, it is reasonable to conclude that α′is\nnot the main factor in irradiation hardening at\nthe experiment condition in this study (dose rate\n10−410−3dpa/s ). Oppositely, in the neutron irra-\ndiated FeCrAl steels, the main contributor of hard-\nening was α′precipitates under the dose rate of\n8.1×10−7dpa/s , that the higher Cr content led to\nhigher hardening[26].\nThe hardening in FeCrAl ODS steels in this\nstudy was mainly owing to the dislocation loops.\nThe solution atoms of Cr could play an essen-\ntial role in the evolution of dislocation loops un-\nder irradiations[25]. Firstly, the solute element Cr\ncould impede the growth of dislocation loops. This\neffect will make loops grow into small sizes.\nSecondly, the Cr will hinder the migration of\n1/2<111>loops. The formation of <100>\nloops by two glissile 1 /2<111>reaction will be\nsuppressed[44], and the sessile <100>loops are\nconsidered as stronger obstacles for dislocation mi-\ngration than 1 /2<111>loops. Thirdly, the for-\nmation energy of <100>loops is much larger than\n1/2<111>loops, and the energy increasing much\nfaster with Cr concentration in <100>loops than\nthe latter[45]. Thus, the irradiation hardening will\nbe reduced by suppressing formation of dislocation\nloops with elevated Cr content.\nCottrell et al[46] developed a method to evalutate\nthe migration activation energy of dislocation loops\nwith respect to element content in steels. Here we\nsimplified this method to one equation as:\nEM(n)≈0.92n1/3·U8/9\n0·c4/9(2)\nWherenis the number of atomic spacing in a dis-\nlocation segment, U0is the binding energy of atom\nin the core of edge dislocation, c is the concentration\n9of alloying element. In the case of Cr, U0=0.032 eV.\nFor the typical value n=25, the activation energy\nby Cr atoms is 0.048 eV for Fe12Cr9Al, 0.053 eV\nfor Fe15Cr9Al, and 0.056 eV for Fe18Cr9Al ODS\nsteels, respectively. The activation energy is in-\ncreased with the Cr content; however, the increases\nare very small in comparison to Al (0.764 eV).\nThe examination of the dislocation loops was per-\nformed in Fe12Cr9Al and Fe15Cr9Al ODS steels.\nAs the samples are limited, only the information\nof total dislocation loops was compared (Table 2).\nGenerally, the dislocation loops in Fe12Cr9Al are\nslightly smaller and denser than in Fe15Cr9Cr ODS\nsteels, which is partially consistent with the above\nanalysis.\nThe simplified dispersed barrier hardening\n(DBH) model (equation 3) is used to evaluate the\nhardening induced by dislocation loops. In equation\n3,M= 3.06 is the Taylor factor for FCC and BCC\nmaterials. The coefficient α= 0.2 is a strength fac-\ntor. The shear modulus µis 82 GPa for FeCrAl\nODS steels. The Burgers vector b is 0.249 nm for\nglissile 1/2<111>dislocations. Nanddpresent\nfor the number density and diameter of loops, re-\nspectively.\n∆σloop=Mαµb√\nNd (3)\nThe estimated hardening by dislocation loops for\nSP12 and SP13 are 1.28 GPa and 1.18 GPa respec-\ntively. The measured hardening by nanoindenta-\ntion were 1.45±0.27 GPa and 1 .35±0.33 GPa for\nSP12 and SP13 (Table 2).\nOther factors which may influence the hardening\nare defect sink position including grain boundaries,\npre-existed dislocations, and oxides. In the solid-\nsolution strengthening analysis by Ukai et al[47],\nthe grain sizes of the same SP-series steels are mea-\nsured the same, and the dislocation densities are\nconsidered similar. Here we follow the same as-\nsumption. The oxides, however, may contribute to\nthe differences. On one hand, the surface of ox-\nides are effective annihilation sites for point defects\nsuch as interstitials and vacancies. On the other\nhand, atoms in large oxides may subject to knock-\nout effects, dissolute into matrix and reprecipitate\nas satellite clusters around original oxide[38]. This\nprogress might explain the decreasing trend of hard-\nening, with the increased number density of oxides,\nwhich offered larger surface area in total, and de-\ncreased diameter, which reduced the possibility of\ndissolution (Fig.3).Moreover, it seems reducing Al and adding Zr\nwill reduce the irradiation hardening, according to\nthe hardening results from Kondo et al[13] and Song\net al[15] (Fig.10). Although there are some differ-\nences in the irradiation condition in Fe15Cr4Al(Zr),\nwith lower temperature (30 °C) and damage dose (2\ndpa), the results are reasonable by the explanation\nthat the oxide density is much higher in steels with\n4wt%Al+Zr than with 9wt%Al, where irradiation\ndefects were annihilated by the larger oxide surface\narea.\nLower irradiation hardening usually indicates\nbetter irradiation resistance, though it is not ab-\nsolutely correct due to various assessment stan-\ndards. The irradiation hardening results in this\nstudy suggest the mechanism of Cr dependence in\nion-irradiation is different to neutron irradiation.\nThe current study in high Al FeCrAl steels will\nhelp to understand materials behavior at the irradi-\nation conditions. It may contribute to the FeCrAl\nmaterial design near the safe boundary of element\nconcentration.\n5. Conclusion\nThe Cr dependent irradiation hardening in Fe-\nCrAl ODS steels with high Al concentration was\nstudied. Three FeCrAl ODS steels, Fe12Cr9Al\n(SP12), Fe15Cr9Al (SP13), and Fe18Cr9Al (SP14),\nwere irradiated with 6.4 MeV Fe3+at 300 °C to\nnominal 3 dpa. Both 1 /2<111>and<100>\ndislocation loops formed after irradiation. No void\nappeared in the irradiated region. Oxides remained\ncrystalline after irradiation at experiment temper-\nature. The irradiation hardening was investigated\nby nanoindentation and TEM. The hardening de-\ncreases with increasing Cr in 9w% Al FeCrAl ODS\nsteels. Particularly, the Fe18Cr9Al showed the low-\nest irradiation hardening in the experiment con-\ndition. Due to the high dose rate in heavy ion-\nirradiations, α′should not be the main factor to ir-\nradiation hardening. The solute Cr atoms are con-\nsidered to hinder the growth of dislocation loops\nformation, that reduced the irradiation hardening.\nBesides, oxides might also influence the hardening.\nThe results will give reference for material design\nwith high Al in FeCrAl ODS steels.\n6. Acknowledgement\nWe gratefully acknowledge Prof. Kondo and Mr.\nHashitomi for their helping with the ion irradia-\n10tion in DuET, Kyoto University. ZXZ acknowl-\nedges Prof. Stuart A. Maloy in Los Alamos Na-\ntional Laboratory for the discussion ATF element\nselection. ZXZ acknowledges Prof. Kasada in To-\nhoku University for discussion on nanoindentation.\nZXZ would like to thank Prof. Akihiko Kimura in\nKyoto University for the supporting of the experi-\nment and the research communications.\nReferences\n[1] S. J. Zinkle, K. A. Terrani, J. C. Gehin, L. J. Ott, L. L.\nSnead, Accident tolerant fuels for LWRs: A perspective,\nJournal of Nuclear Materials 448 (2014) 374–379.\n[2] K. A. Terrani, Accident tolerant fuel cladding devel-\nopment: Promise, status, and challenges, Journal of\nNuclear Materials 501 (2018) 13–30.\n[3] A. Kimura, S. Ukai, M. Fujiwara, Development of fuel\nclad materials for high burn-up operation of SCPR,\nProc. GENES4/ANP2003, Paper 1198 (2003).\n[4] A. Kimura, R. Kasada, N. Iwata, H. Kishimoto,\nCH. Zhang, J. Isselin, P. Dou, JH. Lee, N. Muthuku-\nmar, T. Okuda, Super ODS steels R&D for fuel cladding\nof next generation nuclear systems 1) Introduction and\nalloy design, in: International Congress on Advances\nin Nuclear Power Plants 2009, ICAPP 2009, Atomic\nEnergy Society of Japan, 2009, pp. 2187–2194.\n[5] A. Kimura, R. Kasada, N. Iwata, H. Kishimoto,\nCH. Zhang, J. Isselin, P. Dou, JH. Lee, N. Muthuku-\nmar, T. Okuda, Development of Al added high-Cr ODS\nsteels for fuel cladding of next generation nuclear sys-\ntems, Journal of Nuclear Materials 417 (2011) 176–179.\n[6] SA. Maloy, E. Aydogan, O. Anderoglu, C. Lavender,\nY. Yamamoto, Viability of thin wall tube forming\nof ATF FeCrAl.; Los Alamos National Lab.(LANL),\nLos Alamos, NM (United States), Pacific Northwest\nNational Lab.(PNNL), Richland, WA (United States)\n(2016).\n[7] S. A. Maloy, T. A. Saleh, O. Anderoglu, T. J. Romero,\nG. R. Odette, T. Yamamoto, S. Li, J. I. Cole, R. Field-\ning, Characterization and comparative analysis of the\ntensile properties of five tempered martensitic steels and\nan oxide dispersion strengthened ferritic alloy irradiated\nat≈295 °C to≈6.5 dpa, Journal of Nuclear Materials\n468 (2016) 232–239. doi: 10.1016/j.jnucmat.2015.07.\n039.\n[8] S. Kobayashi, T. Takasugi, Mapping of 475 °C embrit-\ntlement in ferritic Fe–Cr–Al alloys, Scripta Materialia\n63 (2010) 1104–1107. doi: 10.1016/j.scriptamat.2010.\n08.015 .\n[9] D. Chen, A. Kimura, W. Han, H. Je, Age-hardening\nsusceptibility of high-Cr ODS ferritic steels and SUS430\nferritic steel, Fusion Engineering and Design 98–99\n(2015) 1945–1949. doi: 10.1016/j.fusengdes.2015.05.\n078.\n[10] B. C. Maji, S. Ukai, N. Oono-Hori, Microstructural sta-\nbility and intermetallic embrittlement in high Al con-\ntaining FeCrAl-ODS alloys, Materials Science and En-\ngineering: A 807 (2021) 140858. doi: 10.1016/j.msea.\n2021.140858 .\n[11] W. Sang, P. Dou, A. Kimura, Early-stage thermal age-\ning behavior of 12Cr, 12Cr–7Al and 18Cr–9Al ODSsteels, Journal of Nuclear Materials 535 (2020) 152164.\ndoi:10.1016/j.jnucmat.2020.152164 .\n[12] A. Kimura, W. Sang, W. Han, K. Yabuuchi, Z. Xin,\nJ. Luan, P. Dou, Twofold age-hardening mechanism of\nAl-added high-Cr ODS ferritic steels, Journal of Nu-\nclear Materials 575 (2023) 154223.\n[13] K. Kondo, S. Aoki, S. Yamashita, S. Ukai, K. Sakamoto,\nM. Hirai, A. Kimura, Ion irradiation effects on FeCrAl-\nODS ferritic steel, Nuclear Materials and Energy 15\n(2018) 13–16. doi: 10.1016/j.nme.2018.05.022 .\n[14] P. Song, D. Morrall, Z. Zhang, K. Yabuuchi, A. Kimura,\nRadiation response of ODS ferritic steels with different\noxide particles under ion-irradiation at 550 C, Journal\nof Nuclear Materials 502 (2018) 76–85.\n[15] P. Song, K. Yabuuchi, P. Sp¨ atig, Insights into harden-\ning, plastically deformed zone and geometrically neces-\nsary dislocations of two ion-irradiated FeCrAl (Zr)-ODS\nferritic steels: A combined experimental and simulation\nstudy, Acta Materialia 234 (2022) 117991.\n[16] J. Gao, Y. Yamasaki, P. Song, Y.-J. Huang, K. Yabu-\nuchi, A. Kimura, K. Sakamoto, S. Yamashita, Dose\ndependence of ion irradiation effects on 12Cr–6Al-ODS\nsteel with electron-beam weld line, Journal of Nuclear\nMaterials 528 (2020) 151858.\n[17] E. Getto, M. Johnson, M. Maughan, N. Nathan,\nJ. McMahan, B. Baker, K. Knipling, S. Briggs, K. Hat-\ntar, M. J. Swenson, Friction stir welding and self-\nion irradiation effects on microstructure and mechanical\nproperties changes within oxide dispersion strengthened\nsteel MA956, Journal of Nuclear Materials 567 (2022)\n153795. doi: 10.1016/j.jnucmat.2022.153795 .\n[18] E. Getto, N. Nathan, J. McMahan, S. Taller, B. Baker,\nUnderstanding radiation effects in friction stir welded\nMA956 using ion irradiation and a rate theory model,\nJournal of Nuclear Materials 561 (2022) 153530. doi: 10.\n1016/j.jnucmat.2022.153530 .\n[19] J. Ejenstam, M. Thuvander, P. Olsson, F. Rave, P. Sza-\nkalos, Microstructural stability of Fe–Cr–Al alloys at\n450–550 °C, Journal of Nuclear Materials 457 (2015)\n291–297. doi: 10.1016/j.jnucmat.2014.11.101 .\n[20] X. Zhou, L. Guo, Y. Wei, H. Wang, C. Chen, Y. Chen,\nW. Zhang, S. Liu, R. Liu, S. Mo, Effect of aluminum\ncontent on dislocation loops in model FeCrAl alloys,\nNuclear Materials and Energy 21 (2019) 100718.\n[21] E. R. Reese, N. Almirall, T. Yamamoto, S. Tumey,\nG. Robert Odette, E. A. Marquis, Dose rate depen-\ndence of Cr precipitation in an ion-irradiated Fe18Cr\nalloy, Scripta Materialia 146 (2018) 213–217. doi: 10.\n1016/j.scriptamat.2017.11.040 .\n[22] P. Edmondson, S. Briggs, Y.Yamamoto, R. Howard,\nK. Sridharan, K. Terrani, K. Field, Irradiation-\nenhancedα′precipitation in model FeCrAl alloys,\nScripta Materialia 116 (2016) 112–116. doi: 10.1016/j.\nscriptamat.2016.02.002 .\n[23] C. P. Massey, P. D. Edmondson, K. G. Field, D. T.\nHoelzer, S. N. Dryepondt, K. A. Terrani, S. J. Zinkle,\nPost irradiation examination of nanoprecipitate stabil-\nity andα′precipitation in an oxide dispersion strength-\nened Fe-12Cr-5Al alloy, Scripta Materialia 162 (2019)\n94–98.\n[24] D. Zhang, S. A. Briggs, P. D. Edmondson, M. N. Gus-\nsev, R. H. Howard, K. G. Field, Influence of welding\nand neutron irradiation on dislocation loop formation\nandα′precipitation in a FeCrAl alloy, Journal of Nu-\nclear Materials 527 (2019) 151784.\n11[25] K. S. Mao, C. P. Massey, Y. Yamamoto, K. A. Uno-\ncic, M. N. Gussev, D. Zhang, S. A. Briggs, O. Karakoc,\nA. T. Nelson, K. G. Field, Improved irradiation re-\nsistance of accident-tolerant high-strength FeCrAl al-\nloys with heterogeneous structures, Acta Materialia 231\n(2022) 117843.\n[26] K. G. Field, K. C. Littrell, S. A. Briggs, Precipitation\nofα′in neutron irradiated commercial FeCrAl alloys,\nScripta Materialia 142 (2018) 41–45.\n[27] K. G. Field, X. Hu, K. C. Littrell, Y. Yamamoto, L. L.\nSnead, Radiation tolerance of neutron-irradiated model\nFe–Cr–Al alloys, Journal of Nuclear Materials 465\n(2015) 746–755.\n[28] E. Aydogan, J. S. Weaver, S. A. Maloy, O. El-Atwani,\nY. Q. Wang, N. A. Mara, Microstructure and mechani-\ncal properties of FeCrAl alloys under heavy ion irradia-\ntions, Journal of Nuclear Materials 503 (2018) 250–262.\n[29] S. Ukai, K. Sakamoto, S. Ohtsuka, S. Yamashita,\nA. Kimura, Alloy Design and Characterization of\na Recrystallized FeCrAl-ODS Cladding for Accident-\nTolerant BWR Fuels: An Overview of Research Ac-\ntivity in Japan, Journal of Nuclear Materials (2023)\n154508.\n[30] A. Kohyama, Y. Katoh, M. Ando, K. Jimbo, A new\nMultiple Beams–Material Interaction Research Facility\nfor radiation damage studies in fusion materials, Fusion\nengineering and design 51 (2000) 789–795.\n[31] J. F. Ziegler, M. D. Ziegler, J. P. Biersack, SRIM–The\nstopping and range of ions in matter (2010), Nuclear\nInstruments and Methods in Physics Research Section\nB: Beam Interactions with Materials and Atoms 268\n(2010) 1818–1823.\n[32] ASTM E521-96 e1, Standard Practice for Neutron Ra-\ndiation Damage Simulation by Charged Particle Radi-\nation (2009).\n[33] B. N. Lucas, W. C. Oliver, Indentation power-law\ncreep of high-purity indium, Metallurgical and mate-\nrials Transactions A 30 (1999) 601–610.\n[34] N. Oono, S. Ukai, S. Hayashi, S. Ohtsuka, T. Kaito,\nA. Kimura, T. Torimaru, K. Sakamoto, Growth of oxide\nparticles in FeCrAl- oxide dispersion strengthened steels\nat high temperature, Journal of Nuclear Materials 493\n(2017) 180–188. doi: 10.1016/j.jnucmat.2017.06.018 .\n[35] W. D. Nix, H. Gao, Indentation size effects in crys-\ntalline materials: A law for strain gradient plastic-\nity, Journal of the Mechanics and Physics of Solids\n46 (1998) 411–425.\n[36] K. Yabuuchi, Y. Kuribayashi, S. Nogami, R. Kasada,\nA. Hasegawa, Evaluation of irradiation hardening of\nproton irradiated stainless steels by nanoindentation,\nJournal of nuclear materials 446 (2014) 142–147.\n[37] J. T. Busby, M. C. Hash, G. S. Was, The relation-\nship between hardness and yield stress in irradiated\naustenitic and ferritic steels, Journal of Nuclear Ma-\nterials 336 (2005) 267–278.\n[38] P. Song, A. Kimura, K. Yabuuchi, P. Dou, H. Watan-\nabe, J. Gao, Y.-J. Huang, Assessment of phase stability\nof oxide particles in different types of 15Cr-ODS ferritic\nsteels under 6.4 MeV Fe ion irradiation at 200 °C, Jour-\nnal of Nuclear Materials 529 (2020) 151953.\n[39] P. Hauˇ sild, Methodological comment on the nanoinden-\ntation of ion-irradiation hardened materials, Journal of\nNuclear Materials 551 (2021) 152987.\n[40] C. Walter, C. Mitterer, 3D versus 2D finite element\nsimulation of the effect of surface roughness on nanoin-dentation of hard coatings, Surface and Coatings Tech-\nnology 203 (2009) 3286–3290.\n[41] P. Zhu, Y. Zhao, S. Agarwal, J. Henry, S. J. Zinkle, To-\nward accurate evaluation of bulk hardness from nanoin-\ndentation testing at low indent depths, Materials &\nDesign 213 (2022) 110317.\n[42] J.-H. Ke, E. R. Reese, E. A. Marquis, G. R. Odette,\nD. Morgan, Flux effects in precipitation under irradia-\ntion – Simulation of Fe-Cr alloys, Acta Materialia 164\n(2019) 586–601. doi: 10.1016/j.actamat.2018.10.063 .\n[43] Y. Zhao, A. Bhattacharya, C. Pareige, C. Massey,\nP. Zhu, J. D. Poplawsky, J. Henry, S. J. Zinkle, Ef-\nfect of heavy ion irradiation dose rate and temperature\nonα′precipitation in high purity Fe-18%Cr alloy, Acta\nMaterialia 231 (2022) 117888. doi: 10.1016/j.actamat.\n2022.117888 .\n[44] J. C. Haley, S. A. Briggs, P. D. Edmondson, K. Sridha-\nran, S. G. Roberts, S. Lozano-Perez, K. G. Field, Dis-\nlocation loop evolution during in-situ ion irradiation of\nmodel FeCrAl alloys, Acta Materialia 136 (2017) 390–\n401. doi: 10.1016/j.actamat.2017.07.011 .\n[45] Y. Zhang, Z. Xiao, X.-M. Bai, Effect of Cr Concentra-\ntion on1\n2<111>to<100>Dislocation Loop Transfor-\nmation in Fe-Cr alloys, Journal of Nuclear Materials 543\n(2021) 152592. doi: 10.1016/j.jnucmat.2020.152592 .\n[46] G. A. Cottrell, S. L. Dudarev, R. A. Forrest, Immobi-\nlization of interstitial loops by substitutional alloy and\ntransmutation atoms in irradiated metals, Journal of\nNuclear Materials 325 (2004) 195–201. doi: 10.1016/j.\njnucmat.2003.12.001 .\n[47] S. Ukai, Y. Yano, T. Inoue, T. Sowa, Solid-solution\nstrengthening by Al and Cr in FeCrAl oxide-dispersion-\nstrengthened alloys, Materials Science and Engineer-\ning: A 812 (2021) 141076. doi: 10.1016/j.msea.2021.\n141076 .\n12"    },    {        "title": "1811.03314v1.Quasistatic_oscillations_in_subwavelength_particles__Can_one_observe_energy_eigenstates_.pdf",        "content": " \n1 \n QUASISTATIC OSCILLATIONS IN SUBWAVELENGTH PARTICLES: CAN ONE \nOBSERVE ENERGY EIGENSTATES? \n \nE. O. Kamenetskii \n \nMicrowave Magnetic Laboratory, Dep artment of El ectrical and Com puter Engineering  \nBen Gurion University of the Negev, Beer Sheva, Israel \n \nNovember 6, 2018    \nAbstract  \nIn increasing the capabilities of  the optical and microwave tec hniques further into the \nsubwavelength regime, quasistatic  resonant structures has attra cted considerable interest. \nElectromagnetic responses of elect rostatic (ES) plasmon resonan ces in optics and magnetostatic   \n(MS) magnon resonances in microw aves give rise to a strong enha ncement of local fields near the \nsurfaces of subwavelength particle s. In the near-field regions of subwavelength pa rticles one can \nonly measure the electric or the magnetic field with accuracy. Such uncertainty in definition of \nthe electric or magnetic field components raises the question o f energy eigenstates of quasistatic \noscillations. The energy eigenstate problem can be properly for mulated when potential functions, \nused in the quasistatic-resonance problems, are introduced as s calar wave functions. In this case, \none should observe quasistatic-wave retardation effects still s taying in frames of the quasistatic \ndescription of oscillations in a subwavelength particle. In thi s paper, we analyze the problem of \nenergy quantization of ES resona nces in subwavelength optical m etallic structures with plasmon \noscillations and MS resonances in subwavelength microwave ferri te particles with magnon \noscillations. We show that in a case of MS-potential scalar wav e function one can observe \nquasistatic retardation effect s and obtain a proper formulation  of the energy eigenstate problem.  \n  \nI. INTRODUCTION \n \nThe optical responses of metal particles arise from collective oscillations of their conduction \nelectrons. The microwave responses of ferrite particles arise f rom collective oscillations of their \nprecessing electrons. These electromagnetic responses, consider ing, respectively, as plasmon and \nmagnon resonances, give rise to a strong enhancement of local f ields near the particle surfaces. In \nincreasing the capabilities of t he optical and microwave techni ques further into the subwavelength \nregime, subwavelength resonant s tructures has attracted conside rable interest. The ability of metal \nnano structures to support and concentrate electromagnetic ener gy to spots much smaller than a \nwavelength arises from the fact that at plasmon oscillations, o ptical fields are almost purely \nelectric whereas the magnetic field component is small. From th e other side, the ability of ferrite \nstructures to support and concen trate electromagnetic energy to  spots much smaller than a \nwavelength arises from the fact that at magnon oscillations, mi crowave fields are almost purely \nmagnetic whereas the electric field component is small. Convent ionally, we will call plasmon \noscillations in optical subwavele ngth resonant structures as el ectrostatic (ES) resonances and \nmagnon oscillations in microwave subwavelength resonators as ma gnetostatic (MS) resonances. \n     In the case of ES resonances i n small metallic samples, on e neglects a magnetic displacement \ncurrent and an electric field is expressed via an electrostatic  potential, E\n[1]. Analogously, \nthe MS-resonance problem is considered as zero-order approximat ion of Maxwell’s equations \nwhen one neglects the electric displacement current and express es a magnetic field is via a \nmagnetostatic potential, H\n[2]. Fundamentally, subwavelength sizes of the particles \nshould eliminate any electromagne tic retardation effects. For a n electromagnetic wavelength   \nand particle of size a, quasistatic approximation 21a means the transition to a small phase.  \n2 \n What kind of the time-varying field structure one can expect to  see when an electric or magnetic \ndisplacements currents are neglected and so the electromagnetic -field symmetry (dual symmetry) \nof Maxwell equations is broken?           When one neglects a displacement current (magnetic or elec tric) and considers the scalar-\nfunction, \n(,)rt or (,)rt, solutions, one becomes faced with important questions, whethe r there \ncould be the propagation behavio rs inherent for the quasistatic  wave processes and, if any, what \nis the nature of these retardation effects. In a case of ES res onances, the Ampere-Maxwell law \ngives the presence of a curl ma gnetic field. With this magnetic  field, however, one cannot define \nthe power-flow density of propaga ting electrostatic-resonance w aves. Certainly, from a classical \nelectrodynamics point of view [3], one does not have a physical  mechanism describing the effects \nof transformation of a curl ma gnetic field to a potential elect ric field. In like manner, one can see \nthat in a case of MS resonances, the Faraday law gives the pres ence of a curl electric field. With \nthis electric field, one cannot define the power-flow density o f propagating magnetostatic-\nresonance waves since, from a classical electrodynamics point o f view, one does not have a \nphysical mechanism describing the effects of transformation of a curl electric field to a potential \nmagnetic field [3].      In the subwavelength resonators with ES or MS oscillations , measurements of optical or \nmicrowave energies become uncertain since we can measure with a ccuracy only, respectively, the \nelectric or magnetic field. Thus, an evident questions arise: D o the modes of ES resonances \nactually diagonalize the total energy of a metal subwavelength particle and, similarly, do the \nmodes of MS resonances actually diagonalize the total energy of  the subwavelength ferrite \nparticle? In this connection, the associated question is: Can o ne formulate the energy eigenstate \nproblems for ES modes in metal n ano structures as well as for M S oscillations in ferrite particles \nbased on the Schrödinger-like e quation written, respectively, f or an ES-potential scalar wave \nfunction  \n and a MS-potential scalar wave function ?  \n     In this paper, we analyze the problem of energy quantizati on of ES resonances in \nsubwavelength optical metallic structures with plasmon oscillat ions and MS resonances in \nsubwavelength microwave ferrite  particles with magnon oscillati ons. We start with a comparative \nstudy of these two types of quasi static resonances. We show tha t with a formal assumption of \nexistence of quasistatic retardation effects , caused by long range dipol e-dipole correlations, one \ncan clarify the notions of energy and currents (fluxes) for ES and MS waves and write the \nSchrödinger-like equati ons both for the ES and MS scalar wave f unctions. Initially stating that in \nsubwavelength structures made of  strongly dispersive materials the long range dipole-dipole \ncorrelation can be treated in terms of collective excitations o f the system as a whole, we argue \nthat between the electrostatic (with neglect of magnetic energy ) and magnetostatic (with neglect \nof electric energy) eigenvalue  problems there is a fundamental  difference. We show that in a case \nof MS-potential scalar wave function  one can observe quasistatic retardation effects  and obtain \na proper formulation of the ener gy eigenstate problem based on the Schrödinger-like equation. \nWe show that in near-field regions of a MS-resonance ferrite pa rticles there exist so-called \nmagnetoelectric fields. Such quantiz ed fields are distinguished  by unique topological structures. \n \nII. QUASI-ELECTROSTATIC AND QUAS I-MAGNETOSTATIC RESONANCES IN \nSUBWAVELENGTH STRUCTURES \n \nA. Quasi-electrostatic resonances i n subwavelength optical metalli c structures \n \nFor quasi-electrostatic resonan ces in subwavelength optical met allic structures, the electrostatic \nresults are derived from an orde r expansion of Maxwell’s equati ons. In this analysis, the problem \nis solved by expanding the dielect ric constant of the metal nan oparticle ()m at the resonance  \n3 \n frequency res in terms of the wave number in a host material hhkc  times the \ncharacteristic size of the nanoparticle a as [1, 4, 5] \n \n                                          (0) (1) 2 (2)( ) ( ) ( ) ...mr e s m h m h m ak ak                                                     (1) \n \nWith this expansion, one can ide ntify the relative importance o f the electromagnetic-field \ncomponents in the electrostatic  eigenvalue problem. The zeroth order term (0)\nm describes the \ninteraction between the electric fields and the dielectrics, wh ich results in the electrostatic \nformulation ( c ). In this case, the boundary value problems can be written in terms of ES-\npotential scalar function . This function must be continuous and differentiable with resp ect to \nthe normal to the boundary surface (Neumann-Dirichlet boundary conditions). The problem can \nbe solved based on the electrostatic surface integral approach [4, 6, 7]. With formulation of \nproper boundary conditions for sur face charges or surface dipol es over the metal-particle surface, \nfor two eigenvalues (0)\nmi   and (0)\nmk  one obtains the orthogonality r elations for electric-fields \neigenfunctions iE\n and kE\n. The electric permittivity of the metal and the surrounding \n(background) medium are related  to the spectral eigenvalue ()\n()mh\nmh, where the frequency \n is introduced as a parameter [4]. This technique is considered  as being instrumental for \ndevelopment of an efficient numerical algorithm in an analysis of the coupling of plasmon \nresonance modes to the incident electromagnetic fields. Based o n such a mathematical approach \none can greatly simplify the eigenvalue problem. \n     Another way to solve the problem in the electrostatic form ulation ( c ) for plasmon \nresonances in a subwavelength structure is to solve the Poison’ s equation [8 – 11]: \n \n                                                        ,, 0rr   .                                                        (2)  \n    \nHere the frequency  is also introduced as a parameter. The mode expansion relies o n the \nexistence of an orthogonal and co mplete set of real electric-fi eld eigenfunctions nE\n a n d  \neigenvalues n. For a composite consisting of the metal component with the pe rmittivity ()m \nand the ambient dielectric with the permittivity h, the effective permittivity is calculated as  \n \n                                                   ,1 1m\nh\nhrr          ,                                              (3) \n \nwhere ()r is the characteristic function equal to 1 for r in the metal component and 0 for r in \nthe dielectric. The eigenmodes ()nr satisfy a generalized eigenproblem equation [9, 12, 13]:    \n \n                                                        2() () ()nn n rr s r    ,                                                 (4) \n \nwhere  () ()nh h ms  . With use of Green function for Laplace equation \n  23,Grr r r     , one can solve Eq. (4). Taking into account the Dirichlet-Neum ann \nboundary conditions, we have the orthogonality relation   \n4 \n                                           \n                                                *3()nm n m\nVrd r      .                                                           (5)  \n \nThe eigenmodes are normalized over a volume V of a system:23() 1n\nVrd r  . Conventionally, \nthe eigenmode normalization is 23() 1n\nVEr d r . The spectral parameter can be represented also \nas 23()nn\nVsr E r d r.    \n     It was shown [4] that in the expansion (1), the first-orde r correction to the to the dielectric \nconstant at the resonance is zero, (1)0m. At the same time, with the second-order term in the \nexpansion, (2)\nm, one corrects the electrostatic resonance modes by electromagn etic retardation. \nThis term represents the electric induction created by the time -varying magnetic field, which \ninteracts back on the surface char ges. It means that a role of the magnetic field in plasmonic \noscillations in metal nanoparticle becomes appreciable only whe n in an eigenvalue problem one \ndeviates from the electrostatic approximation to the full-Maxwe ll-equation description.  \n     The statements that first-ord er term of Eq. (1) is zero an d that the magnetic field becomes \nappreciable only beyond the frame s of the electrostatic approxi mation are questioned, however, \nin some works. It is inferred [1, 14, 15] that in an analysis o f some effects one can use the first-\norder term (1)\nm in electrostatic equations to predict magnetic fields. At a sa me time, it is assumed \nthat this magnetic field, in itself, does not affect the electr ostatic result. This statement is strongly \nmisleading. First of all, with electrostatic equations one cann ot derive the conductivity electric \ncurrents created by the oscillati ng charge distributions and th u s  u s e  t h e  B i o - S a v a r t  l a w  f o r  \nderivation of the magnetic field  [14, 15]. The electrostatics a nd magnetostatics constitute two \ndifferent parts of the electromagnetic theory and their interac tion can be considered only in the \nframes of the full-Maxwell-equation description [3]. On the oth er hand, consideration of the \nmagnetic field created by the electric displacement current (as sociated with the oscillating \nelectric dipole moment) is also beyond a physical meaning in an  analysis of electrostatic \nresonances. This becomes evident from the following analysis [1 6].  \n     In a small (with sizes much less than a free-space electro magnetic wavelength) sample of a \ndielectric material with strong temporal dispersion (due to the  plasmon resonance), one neglects \na time variation of magnetic energ y in comparison with a time v ariation of electric energy. In \nthis case, the electromagnetic duality is broken and we have a system of three differential \nequations for the electric and magnetic fields       \n                                                                  \n0D\n,                                                                 (6)                          \n \n                                                                  0E\n,                                                                (7)                          \n \n                                                                  DHt ,                                                             ( 8)                \n      \nIn frames of the quasielectros tatic approximation, we introduce  electrostatic-potential   function \n(,)rt excluding completely the magnetic displacement current: 0B\nt\n. At the same time, from  \n5 \n the Maxwell equation (the Ampere-Maxwell law), DHt \n, we write that 2\n2HD\ntt \n. If \na sample does not possess any magnetic anisotropy, we have2\n20D\nt\n. From this equation it \nfollows that the electric field in small resonant objects vary linearly with time. This leads, \nhowever, to arbitrary large fields at early and late times, and  is excluded on physical grounds. An \nevident conclusion suggests itse lf at once: the electric field in electrostatic resonances is a constant \nquantity. Such a conclusion contra dicts the fact of temporally d i s p e r s i v e  m e d i a  a n d  t h u s  a n y  \nresonant conditions. Thus, it b ecomes clear that the curl magne tic field appearing in plasmonic \noscillations due to the Ampere-M axwell law, not does not affect  the electrostatic result. For this \nreason, such a magnetic field is a non-observed  quantity.  \n     The fact that for small metal particles the problem takes a mathematical form identical to that \nin electrostatics greatly simplifies the eigenvalue problem. Ho wever, this is only a mathematical \napproach. The quasielectrostatic model with neglecting any reta rdation effects, cannot accurately \npredict measured physical properties.  \nB. Quasi-magnetostatic resonances in subwavelength microwave ferri te structures \n \nFormally, one can see a certain resemblance between the electro static and magnetostatic \nresonances. For quasi-electrosta tic resonances in subwavelength  metal structures characterised by \nnon-homogeneous scalar permittivity, Eq. (2) can be rewritten a s  \n \n                                               210r     .                                                       (9) \n \nAt the same time, for quasi-magnetostatic resonances in subwave length microwave ferrite \nstructures with tensor permeability , one has [2]: \n  \n                                             2\n00 I      \n.                                                    (10) \n \nSolutions of both these equations  are harmonic fu nctions. Never theless, it appears that in spite of \na certain similarity between Eqs . (9) and (10), the physical pr operties of the oscillation spectra are \nfundamentally different in many aspects.      Alike to the ES resonances, MS  resonances can be described  by integral equation approaches. \nThe integral equation approaches for MS resonances are applied with use of eige nvalue functions \nof magnetization [17, 18]. In a f errite structure characterised  by time-varying magnetization \n,mrt, magnetostatic resonances are described by Poison’s equation d erived from the two \nequations 0 BH m   \n and H\n:  \n \n                                                             2\nM ,                                                                 (11) \n \nwhere  \n                                                           \nM m.                                                                     (12)         \n6 \n  \nThe general solution for time-varying magnetic field is written  as an integral transformation                       \n3 ˆ ,, ,\nVHr t r r mrtd r     G  of the magnetization with the tensorial kernel operator ˆ,rrG , \ncalled a tensorial magnetostatic Green’s function. The formal e xpression for the tensorial Green’s \nfunction ˆ,rrG  is obtained by calculating spatial derivatives from the conven tional \n‘‘Coulombs’’ kernel [2]. The dynamical magnetization of the mag netic structure can be \ndecomposed in series of spin wave eigenmodes  ,,nit\nnn\nnmrt a m rt e , where na a r e  t h e  \namplitudes of the spin wave eigenmodes and on are their eigenfr equencies. The quantized \nfrequencies n of magnetostatic eigenmodes can be found from the solution of the integral \nequation  3 ˆ,nn n\nVmr r r mrd r      G , where nmr are the n-eigenmode spatial profile. The \nspin wave eigenfrequencies n on of a magnetic element are the  simple functions of the discr ete \neigenvalues n of the Fredholm integral with the symmetric magnetostatic kern el ˆ,rrG . The \nset of the derived eigenfunctions nmr and eigenfrequencies n is a complete solution of the \nproblem of MS spin waves in a single magnetic element. The prob lem, however, does not have a \ndefinite analytical solution since the boundary conditions for variable magnetization at the edges \nof the pattern elements are not well defined. It is known that the usual electrodynamic boundary \nconditions leave the amplitude of dynamic magnetization at the boundaries of a sample undefined \n[2, 17, 18].        Together with integral equation approaches, one can formul ate the spectral problem for MS \nresonances, also based on differential operators using MS-poten tial functions as eigenvalue \nfunctions. The spectral solutions are obtained from the second- order differential equation (10) – \nthe Walker equation [2]. The MS wave function \n,rt is constructed in accordance with basic \nsymmetry considerations for the sample geometry. There could be , for example, simple sine MS \nwaves, Fourier–Bessel MS modes, and Fourier–Legendre MS modes. However, in this way of the \nspectral problem solution for MS  resonances, application of pro per boundary conditions appears \nas a very nontrivial question as well. It is known that in solv ing a boundary-value problem, which \ninvolves the eigenfunctions of a differential operator, the bou ndary conditions should be in \ndefinite correlation with the type of this differential operato r [19, 20]. When we employ expansion \nin terms of orthogonal functions, we have to use the homogeneou s Dirichlet-Neumann boundary \nconditions. For the fields expre ssed by MS-potential functions,  this demand to have continuity of \nthe functions together with their first derivatives on the samp le boundaries (the Dirichlet-\nNeumann boundary conditions) can be different from the electrod ynamic boundary conditions. \nThe latter are expressed by the conditions of continuity of  and a normal component of \nBH   . For  \n \n                                                            00\n0\n00 1a\nai\ni\n   \n  \n  ,                                                 (13) \n \nthe Walker equation in Cartesian coordinates is     \n7 \n                                                              22 2\n22 20xy z    .                                             (14) \n \n Evidently, the Walker equation does not contain the off-diagona l component of the permeability \ntensor. At the same time, the off-diagonal component \na can appear in a boundary conditions for \na normal component of B\n.   \n     The boundary conditions for dynamic magnetization and it d erivatives are not the \nelectrodynamic boundary conditions. On the other hand, because of magnetic gyrotropy, \nelectrodynamic boundary conditions for the -function solutions are not Dirichlet-Neumann \nboundary conditions. These aspects may question the validity of  the boundary-value-problem \nsolutions written in terms of MS-potential scalar function. The  question on quasistatic magnonic \neigenproblem with compl ete-set eigenstates becomes essentially crucial when we are talking \nabout combination of a microwave cavity and a subwavelength YIG  ferromagnet specimen. Such \na microwave structure represents a promising path towards the u ltrastrong-coupling regime of \nQED. MS oscillations in YIG sphe res were observe d and analysed long ago [21, 22] . While for a \nferrite sphere one sees a few broad absorption peaks, the MS re sonances in a quasi-2D ferrite disk \nare presented with the spectra of multiresonance sharp peaks. T here are very rich  spectra of both, \nFano and Lortenzian, types of the peaks. A thin-film ferrite di sk with MS oscillations embedded \nin a microwave waveguide or microwave cavity appears as an open  hi-Q resonator [23 – 25]. In \nour further analysis of MS resona nces, we will consider mainly the quasi-2D ferrite disk samples. \n \nIII. ENERGY AND CURRENTS (FLUXES) OF ES AND MS MODES  \n \nThe effects of quantum coherenc e involving a macroscopic degree  of freedom, and occurring in \nsystems far larger than individual atoms are one of the topical  fields in modern physics [26]. \nBecause of material dispersion, a phenomenological approach to macroscopic quantum \nelectrodynamics, where no canonical formulation is attempted, i s used. There is an evidence that \nmacroscopic systems can under appropriate conditions, be in qua ntum states, which are linear \nsuperpositions of states with di fferent macroscopic properties.  For subwavelength structures made \nof strongly dispersive materials  long range dipole-dipole corre lation can be treated in terms of \ncollective excitations of the system as a whole. At such an occ asion, potential functions, used in \nthe quasistatic-resonance spectra l problem analysis, can at som e cases, be introduced as scalar \nwave  functions.  \n     Recent years we have witnessed of development of a new fie ld of optics – quantum plasmonics \n– which combines the advantages of plasmonics and quantum elect ronics [27]. Considering a \nmetamaterial structure composed by plasmon-resonance metal nano particles embedded in a \ndielectric host material, Bergma n and Stockman introduced a not ion of a quantum generator for \nsurface plasmon quanta  – the spaser [9, 12, 13]. In the spaser, nanoscale resonators are employed \nfor controlling stimulated emission regimes, where the near-fie ld feedback replaces traveling \nphase behavior in a photon cavity. In a quasistatic approximati on used for the spaser analysis, it \nis assumed that the surface-plasmon (SP) eigen modes are non-pr opagating modes. This \napproximation means that there i s zero current carried by any e igenmode. Quantiz ation of the SP \nsystem is obtained based on the Hamiltonian used for a temporal ly dispersive dielectric medium \n  3, 1,,42dr dH Er Er drTd    [12, 28].  In the quasielectrostatic regime [for \n(,) (,)Ert rt], the electric field operator is  expanded in a series of the e igenstates ()nr:      \n8 \n  \n                                                          † ˆˆˆ() ( )nn n n\nnE Ar a a    ,                                                  (15) \n \nwhere nA is the mode amplitude and †ˆna and ˆna are, respectively, the cr eation and annihilation \noperators of the state ()nr. The validity of the expansion is relayed on an assertion that  the \neigenmodes ()nr satisfy a generalized eigenproblem equation (4). It is stated that with this \nexpansion, the quantized Hamilt onian takes the standard harmoni c oscillator form [12, 13, 29].   \n     It is known that the quantized form of the SP oscillations  are bosons and the structure of the \ntotal electromagnetic energy  of surface plasmon polaritons hav e a harmonic oscillator form.  The \nfields of these SPs are quantized by the association of a quant um mechanical oscillator for each \nmode wave number  [27]. The quantum harmonic oscillator is the quantum mechanica l analog of \nthe classical harmonic oscillator. For a sinusoidal driving for ce, an analogy of such an oscillator \nis RLC circuits (resistor-inducto r-capacitor). However, the que stions arise: Whether the SPs can \nbe considered as the bosons in the electrostatic  representation? Does the quantized electrostatic  \nHamiltonian take the standard har monic-oscillator form for eige nmodes with zero mode wave \nnumbers? The SP resonances are d riven by external electric fiel ds. In a quasistatic description, \nused in the Bergman-Stockman model, zero currents carried by ei genmodes are assumed. Thus, \nto an approximate extent, we have a system which is similar to a resistor–capacitor circuit (RC \ncircuit) driven by an external voltage. Definitely, this is not  a model of a classical harmonic \noscillator.       The spaser concept paves the way for the creation of stron g coherent plasmonic fields at the \nnanoscale. A significant number of generating spasers have been  reported in recent experiments \n[30 – 32]. Nevertheless, the que stion arises whether the Bergma n-Stockman quasistatic  theory is \nsufficient for explanation of the  observed spaser effects. In s pasers, nanoscale resonators are \nemployed for controlling stimulated emission regimes, where the  electromagnetically near-field \nfeedback replaces traveling phase behavior in a photon cavity. Is it correct that in the theory, such \na near-field feedback lacks any retardation behavior? In litera ture, we can see a certain criticism \nof the quasistatic model of spasers with pointing out the neces sity to extend the electrostatic limit \nby the electromagnetic radiation correction. It is discussed th at quasistatic approach is inherently \nunsuitable due to consideration only one decay channel for the resonance through resistive losses \nin the metal [33, 34].      How can one include retardation effects still staying in f rames of the quasistatic description \nof oscillations in a subwavelengt h particle? The fact that the electromagnetic retardation effects \nin the plasmonic or magnonic oscillations appear only when the particle sizes are comparable \nwith the free-space electromagnetic wavelength raises the quest ion on the possibility of existence \nof non-Maxwellian propagation-wave behaviors for the quasistati c-resonance processes. Such \nwave processes, if any, should be considered as currents (fluxe s) expressed by scalar wave \nfunctions \n(,)rt for ES waves and scalar wave functions (,)rt f o r  M S  w a v e s .  A  f o r m a l  \nanalysis given below clarifies t his question. It is shown that in this case, one has a possibility to \nformulate the energy eigenstat e boundary problem with scalar-wa ve eigenfunctions based on the \nSchrödinger-like equation.      In a functional analysis, a spectral theorem gives conditi ons for diagonalization of a linear \noperator. Suppose that for steady states of the system we have a time-independent equation \n \n                                                              ˆ ,                                                                      (16)                       \n   \n9 \n where ˆ is a Hermitian second-order differential operator,  is a certain scalar wave function \nand  is a real quantity. For a domain of volume V restricted by surface S, a double integration \nby parts gives    \n                                     \n** * ˆˆ ,\nVVSdV dV dS     .                                               (17) \n \nFor homogeneous boundary conditions, one has *,0\nSdS  and operator ˆ becomes a \nself-adjoint operator. If ˆ is a Laplace operator (2 ˆK , where K is a coefficient), the \nhomogeneous boundary conditions look as  **0\nSdS    . In this case, for two \neigenvalues ,mn  and, correspondingly, for  two eigenfunctions  ,mn one has \n \n                                 *2 * * 2 * *\nmn m n m nn m m nn m KK           \n .                (18) \n \nIntegration over the entire volume V gives the orthonormality conditions: \n \n                                                    *0mn m n\nVdV .                                                                (19) \n \n    In quantum mechanics, ˆ is the operator associated with  energy – the Hamiltonian – and   \nis an observable quantity of energy. The operation of the Hamil tonian on the scalar wave function \nis the time-independent Schrödinger equation . The wavefunction of an electron can be \ndecomposed with a complete set of scalar eigenfunctions, which obey the time-independent \nSchrödinger equation. The term **  \n  is associated with the quantum motion of the \ncharges. The form of the electron wave function determines the current \n, which is called the \nflow probability. In stationary s tates (the energy eigenstates) , the probability current is spatially \nuniform or zero. This means that in a stationary state, 0\n  [35]. The above the well-known \nprocedure can be formally used for other types of scalar wave f unctions – the scalar wave \nfunctions of the ES and MS resonant structures. As we will show , in a case of both ES and MS \nresonances one can introduce a certain notion of current \n, which is determined by the term \nlike **\n and has a meaning of the power flow density for the ES and MS waves.  \n     Let us assume that in a temporally dispersive dielectric m edium we have waves, which are \ndetermined by a scalar wave function (,)rt. These waves are pure electrostatic, without any \naccumulation of magnetic energy. A retardation process is due t o dipole-dipole interaction of \nelectric dipoles. Similarly, we assume that in a temporally dis persive magnetic medium the wave \nprocess, being pure magnetostatic, is determined by a scalar wa ve function (,)rt without any \naccumulation of electric energy. H ere have a retardation proces s is due to dipole-dipole interaction \nof magnetic dipoles. Suppose that in both cases, the waves prop agate in anisotropic media and the \nmedia do not contain any free ch arges and conductivity currents .  \n    Admitting that the media has small losses, we have the foll owing continuity equation for ES \nwaves propagating at frequency     \n                                               \n10 \n       1 1** * * *\n44el\nabsw iiDD D D D Dt                     .          (20) \n \nOn the right-hand side of this equation we have the average den sity of electric losses taken with \nan opposite sign. In derivation of Eq. (20) we used the followi ng relations: E\n, \nDE   , and 0D\n. The average density of electric losses is defined as \n \n                                              * 1\n2ah el\nabswiE Et  ,                                                        (21) \n \nwhere in the permittivity tensor  superscript ah means ‘anti-Hermitian’. The energy balance \nequation for monochromatic MS wave s in a lossy ferrite medium w e write as \n                            \n        1 1** * * *\n44mag\nabsw iiBB B B B Bt                     .         (22) \n \nIn derivation of Eq. (22) we used the following relations: H\n, BH    , and \n0B \n. The average density of magnetic losses is defined as \n \n                                              * 1\n2mag ah\nabswiH Ht  ,                                                    (23) \n \nwhere in the permeability tensor  superscript ah means ‘anti-Hermitian’. \n     With the above analysis, we can see that if in a anisotrop ic dielectric medium there exist the \nES waves described by a scalar wave function (,)rt,  the power flow density is viewed as a \ncertain current density: \n \n                                                          **\n4iDD\n\u0000 .                                                      (24) \n \nThis power flow can be observed because of dipole-dipole intera ction of electric dipoles. \nSimilarly, for MS waves in a ferrite medium, described by a sca lar wave function (,)rt, we \nhave the power flow density which can be viewed as a current de nsity: \n \n                                                         **\n4iB B \n\u0000 .                                                       (25) \n \nSuch a power flow can appear bec ause of dipole-di pole interacti on of magnetic dipoles.  \n     Let, in a particular case, both the dielectric and magneti c media be isotropic with the \nconstitutive relations   DE\n and B H\n. For ES and MS waves, we have, respectively,  \n \n                                                         **\n4i    \n\u0000                                                   (26)   \n11 \n  \nand   \n                                                        \n**\n4i      \n\u0000 .                                               (27) \n \n     Assume that using the Laplace operator and Dirichlet-Neuma nn boundary conditions in ES \nand MS spectral problems, we can decompose the wave functions (,)rt and (,)rt w i t h  a  \ncomplete set of scalar eigenfunctions, obeying the time-indepen dent Schrödinger-like equation. \nIt this case, we are able to rewrite the orthonormality relatio n (19) as \n \n                                                    *0mn m n\nVdV                                                                 (28) \nfor ES resonances and \n \n                                                    *0mn m n\nVdV                                                              (2 9) \nfor MS resonances. \n \nIV. MS MAGNONS IN FERRITE-DISK RESONATORS \n \nEqs. (24 – 29) were obtained in an assumption that in a subwave length specimen we have \npropagation of quasistatic bulk waves. This not the case of SP resonances in subwavelength \noptical metallic structures. In such structures, no retardation  processes characterized by the \nelectric dipole-dipole interacti on and described exclusively by  electrostatic wave function (,)rt \ntake place. There is no possibility to describe these resonance s by the Schrödinger-equation \nenergy eigenstate problem. Nevertheless, for MS resonances in f errite specimens we have bulk \nwave process, which are determined by a scalar wave function (,)rt [2, 28]. Due to retardation \nprocesses caused by the magnetic  dipole-dipole interaction in a  subwavelength ferrite particle, we \nhave a possibility to formulate the energy eigenstate boundary problem with scalar-wave \neigenfunctions (,)rt based on the Schrödinger-like equation. Such a behavior can be  obtained \ni n  a  f e r r i t e  p a r t i c l e  i n  a  f o r m  o f  a  q u a s i - 2 D  d i s k .  A s  w e  p o i n t ed out above, a ferrite disk is \ndistinguished from a ferrite sphere by multiresonance sharp-pea k spectra of MS oscillations. The \noscillations in a quasi-2D ferrite  disk, analyzed as spectral s olutions for the MS-potential scalar \nwave function (,)rt, has evident quantum-like attributes. Quantized forms of such matter \noscillations we call the MS magnons or the magnetic-dipolar-mod e (MDM) magnons. The \nmacroscopic nature of MDMs, invo lving the collective motion of a many-body system of \nprecessing electrons, does not destroy a quantum behavior. The long-range dipole-dipole \ncorrelation in positions of electron spins can be treated in te rms of collective excitations of a \nsystem as a whole.  \nA. Energy eigenstates of MS magnons \n \nWe analyse functions  within the space of square integ rable functions. For an open q uasi-2D \nferrite disk normally magnetized along the z axis, we can use separation of variables in the spectral \nproblem solution [36 – 38]. In cylindrical coordinate system (,, )zr, the solution is represented \nas   \n12 \n    \n                                                        ,, ,, ,, , () (, )pq pq pq q Az r      ,                                           (30) \n \nwhere ,,pqA is a dimensional amplitude coefficient, ,,()pqz  is a dimensionless function of the \nMS-potential distribution along z axis, and ,(, )qr  is a dimensionless membrane function. The \nmembrane function  is defined by a Bessel-function order  and a number of zeros of the Bessel \nfunction corresponding to a radial variations q. The dimensionless “thickness-mode” function \n()z  is determined by the axial-variation number p [36 – 38]. \n     Suppose that a mode number n holds a certain set of quantum numbers ,,qp . The solution \nfor the mode n is represented as  \n \n                                                              () (, )nn n nA zr   ,                                                   (31) \n \nIn a further analysis we will use the subscript  to denote differentiation over the in-plane ,r \ncoordinates and subscript || t o denote differentiation along th e disk axis  z. Also, we will apply \nsubscript for the vector and tensor components laying in the ,r plane. Using the separation \nof variables we write the Walke r equation (10) in the following  form: \n \n                                                             22\n|| 0    ,                                                        (32) \n \nwhere  is a diagonal component of the permeability tensor (13). An ax ial variation of a function \n()z  is defined by a solution of a boundary value problem with the function description inside a \nferrite as 1cos sinnn n\nnzz z \n\n,  o u t s i d e  a  f e r r i t e  a s  nz\nnze  ( w h e r e  \n1\nnn\nn\n\n), and with using the homogenious boundary conditions on the di sk surface planes \nz = 0 and z = d:  \n \n                                                              00 0 zznn\nzd zd\n\n ,                                                     \n \n \n                                                    \n00\n00nn\nzznn\nzd zzz\n\n\n        .                                          (33) \n \nFor the disk geometry, the energ y eigenvalue problem for MS mod es is defined by the differential \nequation [36 – 39] \n \n                                                                ˆ\nnn nGE ,                                                              (34)   \n \nwhere ˆGis a two-dimensional differential operator and nE is interpreted as density of \naccumulated magnetic energy of mode n. The operator ˆG and quantity nE are defined as    \n13 \n  \n                                                        2 0 ˆ\n4n\nngG,                                                                 (35) \n \n                                                         20\n4nn\nnzgE .                                                               (36) \n \nHere ng is a dimensional normalization coefficient for mode n and \nnzis the propagation constant \nof mode n along the disk axis z. The parameter n is to be regarded as an eigenvalue. Outside a \nferrite 1n. The operator ˆG is a self-adjoint operator only for negative quantities n in a \nferrite.  \n     For self-adjointness of operator ˆG, the membrane function (, )nr  must be continuous and \ndifferentiable with respect to the normal to lateral surface of  a ferrite disk. The homogeneous \nboundary conditions – the Neumann-Dirichlet boundary conditions  – for the membrane function \nshould be [36 – 41]:   \n                                                        \n 0nnrr                                                           (37) \n \nand  \n                                                      \n0nn\nrrrr\n     \n,                                             (38) \n \nwhere  is a disk radius. \n     MDM oscillations in a ferrite disk are described by real e igenfunctions: *\nn n . For \nmodes n and n, the orthogonality conditi ons are expressed as  \n \n                                            *\nccnn n nnn\nSSdS dS        .                                               (39) \n \nwhere cS is a circular cross section of a ferrite-disk region and nnis the Kronecker delta. \n     The spectral problem gives the energy orthogonality relati on for MDMs: \n \n                                                             *0\ncnn n n\nSEE d S   .                                               (40) \n \n     Since the space of square integrable functions is a Hilber t space with a well-defined scalar \nproduct, we can introduce a basis set. A dimensional amplitude coefficient in Eq. (30) we write \nas nnAca , where c is a dimensional unit coefficient and nais a normalized dimensionless \namplitude. The normalized scalar-wave membrane function  can be represented as \n \n                                                           nn\nna .                                                                     (41) \n  \n14 \n The amplitude is defined as \n \n                                                           2\n2 *\ncnn\nSad S ,                                                            (4 2) \n \nThe mode amplitude in Eq. (40) can  be interpreted as the probab ility to find a system in a certain \nstate n. Normalization of membrane function is expressed as  \n \n                                                               21n\nna .                                                                     (43) \n \n     The above analysis of discrete -energy eigenstates of the M S-wave oscillations, resulting from \nstructural confinement in a nor mally magnetized ferrite disk, w as based on a continuum model.  \nUsing the principle of wave–particle duality, one can describe this oscillating system as a \ncollective motion of quasiparticle s. These quasiparticles are c alled “light” magnons (lm). There \nare the MS magnons and the meaning of the term “light” arises f rom the fact that the effective \nmasses of these quasiparticles are much less, than the effectiv e masses of “real” (“heavy”) \nmagnons – the quasiparticles existing due to the exchange inter action. The spatial scale of the \nexchange interaction is much less than the MS-wave wavelength i n our structures and the \n“magnetic stiffness” is characte rized by the “weak” dipole-dipo le interaction [2, 37].  \n     An expression for the effective mass of the “light” magnon  we derive from the following \nconsideration. The MS-potential wavefunction  entirely defines the  MS-oscillation states of \na ferrite disk. Thereby, representation of this function in a c ertain time moment not only describes \nthe system behavior at the present moment, but defines the beha viour in all future time moments. \nIt means that at every time moment, a time derivative \nt\n should be defined by itself function \n at the same time moment. Moreover, because of the principle of  superposition this relation \nhas to be linear. In a general form, we can write that [35] \n \n                                                                       ˆiQt,                                                         (44) \n \nwhere ˆQ is a certain linear operator. From this equation it can be sho wn that for orthonormalized \nbasic vectors operator ˆQ is a self-conjugate differential operator. Thus, equation (44)  is a wave \nequation for complex scalar wavefunction [35]. \n     Let us represent the function  as a quasi-monochromatic wave propagating along a disk axis: \n \n                                                               max,,it zzt zt e ,                                           (45) \n  \nwhere a complex amplitude max,zt  is a smooth function of the l ongitudinal coordinate and \ntime, so that \n \n                                                                       max\n1m a x\nz\n                                                  (46) \n  \n15 \n and \n \n                                                                        max\n1m a x\nt\n  .                                            (47) \n \nThe situation of the quasi-monoc hromatic behavior can be realiz ed, in particular, by means of a \ntime-dependent bias magnetic field  slowly varying with respect to the Larmor frequency. In this \ncase, a spin-polarized ensemble will adiabatically follow the b ias magnetic field and the resulting \nenergy of interaction with a bia s field becomes time dependent.  \n     For a quasi-monochromatic wave, Eq. (44) can be written as  \n \n                                                                     2\n2it.                                                    (48) \n \nThe form of operator 2\n2ˆQi follows from the ‘stationary-state’ conditions. When we \ncompare Eq. (48) with the Schr ödinger equation for “free partic les” we get the expression for \nthe effective mass of the “light” magnon for a monochromatic MS  mode: \n \n                                                                      2\n()\n2lm n\neffnm\n.                                                  (49) \n \nExpression (49) looks very simila r to the effective mass of the  “heavy” magnon for spin waves \nwith a quadratic character of dispersion [2]. The MS “light” ma gnons can be considered as a free \nparticle with a mass: ()lm\neffnm. Hamiltonian of sich a free particle is 2\n2\n()ˆ\n2lm\neffnH\nm. For \nhomogeneous pressesion of m agnetization the energy is 0 E, where, for a thin cylinder, \n 0 2external\noo HM  . A surplus of energy 0 n E    can be interpreted as a magnon \npotential energy in a n external and demagnetization magnetic fi elds. In a quasi-2D disk, the MS \n“light” magnons are “flat-mode” quasiparticles at a reflexively -translational motion behavior \nbetween the lower ( z = 0) and upper ( z = d) planes of a ferrite disk. \n     It is important to note that while in quantum mechanics pr oblems, Schrödinger equation is \nwritten for 1D structure, in our case we have a 2D problem.  In the spectral problem solution for \nmembrane-function “flat modes” we use parameters obtained from the spectral problem solution \nfor “thickness modes”. However, in a case of a ferrite disk wit h a very small thickness/diameter \nratio, the spectrum of “thickness modes” is very rare compared to the dense spectrum of “flat \nmodes”. The entire spectrum of “flat modes” is completely inclu ded in the wavenumber region of \na fundamental “thickness mode”. This means that the spectral pr operties of a resonator can be \nentirely described based on cons ideration of only a fundamental  “thickness mode” and the \nproblem appears as a quasi one dimensional [38].  \nB. Power flow densities \n  \nWith use of separation of variables and taking into account a f orm of tensor  [see Eq. (13)], we \ndecompose a magnetic flux density ( BH    ) by two components:   \n16 \n  \n                                                                        || BBB\n.                                                            (5 0) \n \nThe component B\n are given as \n \n                                                () (, )nn n B Az r e                ,                         (51) \n \nwhere e is a unit vector laying in the ,r plane, and  \n                                       \n                                                     0a\nai\ni   .                                                             ( 52)                       \n \n For the component B\n we have  \n \n                                      0| | 0()(, ) en\nnn zzBA rz      ,                                                 (53)   \n \nwhere ez is a unit vector directed along the z axis. \n     The above representations allow considering, respectively,  two components of the power flow \ndensity (current density). For mode n, we can write Eq. (25) as   \n \n                                                         nnn \n \u0000 \u0000,                                                          (54)  \n \nwhere   **\n4nnnn niBB   \n\u0000  and   **\n4nnnn niBB      \n\u0000 . Along every of \nthe coordinates , ,  and rz , we have power flows (currents):   \n \n     *\n22 *\n0\n**\n22 **\n011\n4\n1           =4nn nn\nrn n n a n an\nnn nn\nnn n n a n niAi irr rr\niAirr r     \n                \n              \n   \u0000\n,re     (55) \n \n     *\n22 *\n0\n**\n22 **\n011\n4\n1           =4nn nn\nnn n a n an\nnn nn\nnn n n a n niAi irr rr\niAirr r       \n                 \n              \n  \u0000\n,\n           e\n      (56) \n   \n17 \n       *\n22 *\n04nn\nzn n n zniAezz       \u0000 ,                                                              (57) \n \nwhere re,e, and ze are the unit vectors.  \n     We can see that in in-plane coordinates, ,r, we have both real and imaginary power flows. \nThat is the radial and azimuth power flows are complex quantiti es:  rr r real imagi    and \n real imagi   . The imaginary parts of the flows shown in Eqs. (55), (56) are  due to \nthe material gyrotropy. In an electromagnetic theory, a reactiv e energy is related to the non-\npropagating (evanescent) fields. For the wave propagating along  a certain direction with a real \npower flow, the imaginary part of the Poynting vector indicates  a reactive power flux that \noscillates back and forth in t he transverse direction [3].  \n     Let a disk plane region 2Sr  be bounded by a circle 2L r , where 0r. For a two-\ndimensional vector field ,r \n\u0000 , the circulation-form Green's theorem is written in polar \ncoordinates as   \n \n                                    11r\nr\nSLrd s d r r drr r                                            (58) \n \nwhere dS rdrd . In a case of real power flows,  is a singlevalued function. Such a membrane \nfunction is an azimuthal standing wave: it has an integer numbe r of wavelengths around the circle. \nSo, a circulation of gradient  along contour L is equal to zero. In this instance, we have \n* . Using Eqs. (55) and (56), we can easily show that for real po wer flows, an integrand in \nleft-hand side of Eq. (58) is equal to zero. If such a double i ntegrand of a vector field ,r \n\u0000  \nis zero then this field is said to be irrotational. Since we ha ve  0rdr r d\n , no \ncirculation of a real pow er flow along contour L is presumed.  \n     For irrotational vector field ,r \n\u0000 , the 2D divergence theorem looks as     \n \n                                                         \nSLds ndl      ,                                                   (59) \n \nwhere n is the outwardly directed in-plane unit normal to the contour L. Following the known \nprocedure [3], we represent the power flow vector as  \n\u0000 , where  and  are arbitrary \nscalar fields. With such a representation, we have 2           and \nnr . Based on these expressions, we successively consider two case s: (a) , \n* and ( b) *,. After simple manipulation we obtain \n \n                                      ** 2 ** 2          .                                                (60) \n \nAs a result, we have a flux-form  Green's theorem for real power  flows:  \n18 \n  \n              *\n2* *2 *\nSLds dlrr             .                                    (61) \n \nFor a given mode n, the homogenous boundary conditions on internal circles and, f inally, the \nNeumann-Dirichlet boundary conditions (37), (38) on a circle 2  give the 2D divergence \nof a real-power-flow vector field \n\u0000 equal to zero. For two eigenvalues ,nnEE and, \ncorrespondingly, for two eigenfunctions  ,nn  one has the orthogonality relation (40) and thus \ncompleteness of eigenfunctions . In our case of MS-wa ve processes in a ferrite disk, we have a  \npossibility to formulate the energy eigenstate boundary problem  when real power flows, expressed \nby scalar wave functions , propagate along the radial coor dinate. As we noted above, for  the \nsignlevalued function  circulation of gradient  along contour 2L r  is equal to zero. So, \nno real power flows along the azimuth coordinate are assumed fo r such a signlevalued function. \nAt the same time, a reactive ener gy is related to the non-propa gating MS fields and the reactive \npower flux for membrane function , if any, should appear in the transverse direction, that is \nalong the azimuth coordinate. \n \nV. THE MAGNETOELECTRIC EFFECT \n \n     Taking into account both the real and imaginary parts of p ower flows we can see that the \nboundary conditions for complex vector \n\u0000 are different from the Ne umann-Dirich let boundary \nconditions (37), (38). On a circle 2  we have to have continuity of membrane function n \nand a radial component of the magnetic flux density 0nn\nranBr . These are the \nelectrodynamic boundary conditions expressed as: \n   \n                                                         0nnrr                                                         (62) \n \nand  \n                                   10nn n\na\nrrirr r            \n,                                     (63) \n  \nWith such boundary conditions it becomes evident the membrane f unction must be not only \ncontinuous and differentiable with  respect to th e normal to the  lateral surface, but, because of the \npresence of a gyrotropy term, be  also differentiable with respe ct to a tangent to the boundary \nsurface. The boundary conditions (37) and (38) are the so-calle d essential boundary conditions . \nWhen such boundary conditions are used, the MS-potential eigenf unctions of a differential \noperator form a complete basis in an energy functional space. T he boundary conditions (62) and \n(63) are the so-called natural boundary conditions  [19].  \n     To restore the Neumann-Dirichlet boundary conditions (37),  (38), and thus completeness of \neigenfunctions , we need introducing a certain surface magnetic current  ()m\nsjcirculating on a \nlateral surface of the disk. Thi s current should compensate the  term 1n\na\nrir \n\n in Eq. (63).   \n19 \n One can see that for a given direction of a bias magnetic field  (that is, for a given sign of a), \nthere are two, clockwise and counterclockwise, quantities of a circulating magnetic current. The \ncurrent ()m\nsjis defined by the velocity of an irrotational border flow. This  flow is observable via \nthe circulation integral of the gradient [39, 40, 42]  \n \n                                                         1\nre \n \n ,                                                       (64) \n \nwhere  is a double-valued edge wave function on contour 2 .  \n     On a lateral surface of a qua si-2D ferrite disk, one can d istinguish two different functions , \nwhich are the counterclockwise and clockwise rotating-wave edge  functions with respect to a \nmembrane function n. The spin-half wave-function  changes its sign when the regular-\ncoordinate angle  is rotated by 2.  A s  a  r e s u l t ,  o n e  h a s  t h e  e i g e n s t a t e  s p e c t r u m  o f  M S  \noscillations with topological phases accumulated by the edge wa ve function . A circulation of \ngradient \n along contour 2  gives a non-zero quantity when an azimuth number is a \nquantity divisible by1\n2. A line integral around a singular contour : \n2\n**\n01()  ()\nrid i d\n \n\n         \n  is an observable quantity. Because of the \nexisting the geometrical phase factor on a lateral boundary of a ferrite disk, MS oscillations are \ncharacterized by a pseudo-electric field (the gauge field) €\n. The pseudo-electric field €\n can be \nfound as ()m\n€ € \n. The field €\n is the Berry curvature. The corresponding flux of the \ngauge field €\n through a circle of radius  is obtained as: \n  () ( )2me\n€\nSK€ d S K d K q        \n , where ()e\n  are quantized fluxes of \npseudo-electric fields, K is the normalization coefficient. Each MS mode is quantized to  a  \nquantum of an emergent electric flux. There are the positive an d negative eigenfluxes. These \ndifferent-sign fluxes should be nonequivalent to avoid the canc ellation. It is evident that while \nintegration of the Berry curvatu re over the regular-coordinate angle  is quantized in units of 2\n, integration over the spin-coordinate angle  1\n2 is quantized in units of . The physical \nmeaning of coefficient K concerns the property of a fl ux of a pseudo-electric field. The  Berry \nmechanism provides a microscopic basis for the surface magnetic  current at the interface between \ngyrotropic and nongyrotropic media. Following the spectrum anal ysis of MS modes in a quasi-\n2D ferrite disk one obtains pse udo-scalar axion-like fields and  edge chiral magnetic currents [39]. \nThe anapole moment for every mode n is calculated as [39, 40, 42]: \n \n                                                   () ( )\n0()  d\nem\ns aj z d l d z\n \n .                                                     (65) \n  \n20 \n It follows that different orien tations of an electric moment ()ea (parallel or antiparallel with \nrespect to0H) correspond to different energy levels. The energy splitting b etween two cases, \n()\n00eaH and ()\n00eaH, is defined as the magnetoelectric (ME) energy [39, 40, 42]. T he ME \nenergy is the potential energy of a MS-mode ferrite disk in an external magnetic field. It is alike \nto another type of the potentia l energy of a magnetised body in  an external magnetic field – the \nZeeman energy.      With taking into account the ME energy, the MS-potential m embrane wave function is \nexpressed as: \n  rr   . For any mode n, the function n is a two-component sprinor \npictorially denoted by two arrows:  \n                                            \n                                             1\n2\n1\n2,,i\nn\nnn\ninerr\ne\n  \n\n\n \n                                                 (66) \n \nCirculation of gradient  along contour 2L r  is not equal to zero. So, we can observe the \nangular momentum due to the power-flow circulation: \n \n                                                             1\nzn\nLLr d lr  ,                                                    (67)   \n \nwhere \n \n                                      *\n22 *\n011()4nn\nnn a n nnAz еr                .                     (68) \n \nThe angular momentum zL\n is an intrinsic property of a ferrite-disk particle, unrelated  to any sort \nof motion in space. The direction of rotation is correlated wit h the direction of an anapole moment \nwith repect of a bias magnetic field. The rotational energy sho uld be equal to the ME energy. The \ncondition   \n                                                                   \nrotational MEE E                                                                    (69) \n \nis the necessary conditions to get a Hermitian Hamiltonial.  \n    With use of Eq. (57) we have now  \n               \n *\n22 *\n01(, )4nn\nzn n n zn n\nLiA re r d lzz r          \u0000 .              (70) \n                                                    \nThe first term in this momentum density is associated with the translational motion, whereas the \nsecond term is associated with circulated flow of energy in the  rest frame of the disk. For such a \njoint effect of the translationa l and circulating motions, the mebrane function n should be \nrepresented as a four-component s prinors described by a Hermiti an adjoint operator. \n  \n21 \n VI. CONCLUSION \n \nElectromagnetic responses of elect rostatic plasmon resonances i n optics and magnetostatic  \nmagnon resonances in microwaves give rise to a strong enhanceme nt of local fields near the \nsurfaces of subwavelength particles. Uncertainty in definition of the electric or magnetic field \ncomponents in the near-field regio ns of subwavelength particles  raises the question of energy \neigenstates of quasistatic oscill ations. In this paper, we argu e that staying in frames of the \nquasistatic description of oscillations in a subwavelength part icle, such an energy eigenstate \nproblem can be properly formul ated based on scalar-potential wa ve functions. In this case, one \nshould observe quasistatic-wave retardation effects caused by l ong range dipole-dipole \ncorrelations. We showed that in a  case of MS-pot ential scalar w ave function  one can observe \nsuch quasistatic retardation e ffects and obtain a proper formul ation of the energy eigenstate \nproblem based on the Schrödinger-like equation.       In literature, it is argued that the electron spin may be  regarded as an angular \nmomentum generated by a circulating flow of energy in the wave field of the electron [43, 44]. In \nthis paper, we showed that in a subwavelength ferrite-disk part icle one can observe the angular \nmomentum due to the power-flow circulation of double-valued edg e MS wave functions. For \nincident electromagnetic wave, this magnon subwavelength partic le emerges as a singular point \ncarrying quanta of angular momentum.  \nReferences  \n     \n[1] T.J. Davis and D.E. Góm ez, “Colloquium: An algebraic mode l of localized surface plasmons \nand their interacti ons”, Rev. Mod. Phys. 89, 011003 (2017). \n[2] A. G. Gurevich and G. A. Melkov, Magnetization Oscillations and Waves  (CRC Press, 1996). \n[3] J. D. Jackson, Classical Electrodynamics , 2nd ed. (Wiley, New York, 1975). \n[4] I. D. Mayergoyz, D. R. Fre dkin, and Z. Zhang, “Electrostati c (plasmon) resonances in \nnanoparticles,\" Phys. Rev. B 72, 155412 (2005). \n[5] T. G. Pedersen, J. Jung, T . Søndergaard, and K. Pedersen, “ Nanoparticle plasmon resonances \nin the near-static limit”, Opt. Lett. 36, 713 (2011). \n[6] J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. L.  Larsen, and B. B. Nielsen, \n“Electrostatic plasmon resonances of metal nanospheres in layer ed geometries”, Phys. Rev. B 81, \n125413 (2010). [7] Z. Zhang and I. D. Mayergoyz, “Numerical analysis of plasmo n resonances in metallic \nnanoshells”, IEEE Tran. Magn. \n43, 1689 (2007). \n[8] D. J. Bergman, “The dielectric constant of a composite mate rial—A problem in classical \nphysics”, Phys. Rep. 43, 377 (1978). \n[9] M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Localizat ion versus delocalization of \nsurface plasmons in nanosystems: Can one state have both charac teristics?,\" Phys. Rev. Lett. 87, \n167401 (2001). \n[10] V. Klimov, G.-Y. Guo, and M. Pikhota, “Plasmon resonances in metal nanoparticles with \nsharp edges and vertices: a material independent approach”, J. Phys. Chem. C 118, 13052 (2014). \n[11] R. Yu, L. M. Liz-Marzán, and F. J. Garcia de Abajo, ”Unive rsal analytical modeling of \nplasmonic nanoparticles”, Chem. Soc. Rev. 46, 6710 (2017). \n[12] D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplifi cation by Stimulated Emission \nof Radiation: Quantum Generati on of Coherent Surface Plasmons i n Nanosystems”, Phys. Rev. \nLett. 90, 027402 (2003). \n[13] M. I. Stockman, “The spaser as a nanoscale quantum generat or and ultrafast amplifier”, J. \nOpt. 12, 024004 (2010).   \n22 \n [14] T. J. Davis and E. Hendry, “Superchiral electromagnetic fi elds created by surface plasmons \nin nonchiral metallic nanostructures”, Phys. Rev. B 87, 085405 (2013). \n[15] T. J. Davis and D.E. Gómez,  “Interaction of localized sur face plasmons with chiral \nmolecules”, Phys. Rev. B 90, 235424 (2014). \n[16] K. T. McDonald, “An electro static wave,\" arXiv:physics/031 2025, 2003. \n[17] K. Y. Guslienko and, A. N. Slavin “Magnetostatic Green’s f unctions for the description of \nspin waves in finite rectangular magnetic dots and stripes”, J.  Magn. Magn. Mater. 323, 2418 \n(2011). [18] K. Yu. Guslienko, S. O. Demokritov, B. Hillebrands, and A.  N. Slavin,  “Effective dipolar \nboundary conditions for dynamic magnetization in thin magnetic stripes”, Phys. Rev. B \n66, \n132402 (2002). [19] S. G. Mikhlin, Variational Methods in  Mathematical Physics  (McMillan, New York, 1964) \n[20] M. A. Naimark, Linear Differential Operators  (F. Ung. Pub. Co, New York, 1967) \n[21] R. L. White and I. H. Solt, Jr., “Multiple ferromagnetic r esonance in ferrite spheres”, Phys. \nRev. \n104, 56 (1956).  \n[22] L. R. Walker, “Magnetostatic modes in ferromagnetic resona nce”, Phys. Rev. 105, 390 \n(1957). [23] J. F. Dillon Jr., “Magnetostatic modes in disks and rods”,  J. Appl. Phys. 31, 1605 (1960). \n[24] T. Yukawa and K. Abe, “FMR spectrum of magnetostatic waves  in a normally magnetized \nYIG disk”, J. Appl. Phys. \n45, 3146 (1974). \n[25] E. O. Kamenetskii, A. K. Saha, and I. Awai, \"Interaction o f magnetic-dipolar modes with \nmicrowave-cavity electromagnetic fields”, Phys. Lett. A 332, 303 (2004). \n[26] A. J. Leggett, “Macroscopic quantum systems and the quantu m theory of measurement”, \nProg. Theor. Phys. Suppl. 69, 80 (1980). \n[27] M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Ma ier, and M. S. Kim, “Quantum \nplasmonics”, Nature Phys. 9, 329 (2013).  \n[28] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media  (Pergamon Press, \nOxford, 1960). [29] M. I. Stockman “Spaser action, loss compensation, and stab ility in plasmonic systems with \ngain”, Phys. Rev. Lett. \n106, 156802 (2011). \n[30] M. A. Noginov et al, “Demonstration of a spaser-based nanolaser”, Nature 460, 1110 (2009). \n[31] R. F. Oulton et al, “Plasmon lasers at deep subw avelength scale”, Nature 461, 629 (2009). \n[32] R. A. Flynn et al, “A room-temperature semiconductor spaser operating near 1.5 μ m”, Opt. \nExpress 19, 8954 (2011).  \n[33] J. B. Pendry and S. A. Maie r, “Comment on “Spaser Action, Loss Compensation, and \nStability in Plasmonic Systems with Gain””, Phys. Rev. Lett. 107, 259703 (2011).  \n[34] S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Comment on “Spaser \nAction, Loss Compensation, and Stability in Plasmonic Systems w ith Gain””, Phys. Rev. Lett. \n107, 259701 (2011). \n[35] L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory , 3rd ed. \n(Pergamon, Oxford, 1977). [36] E. O. Kamenetskii, “Energy eigenstates of magnetostatic wa ves and oscillations”, Phys. Rev. \nE \n63, 066612 (2001). \n[37] E. O. Kamenetskii, R. Shavit, and M. Sigalov, \"Quantum wel ls based on magnetic-dipolar-\nmode oscillations in disk fe rromagnetic particles\", Europhys. L ett. 64, 730 (2003). \n[38] E. O. Kamenetskii, M. Sigal ov, and R. Shavit, \"Quantum con finement of magnetic-dipolar \noscillations in ferrite discs\", J. Phys.: Condens. Matter 17, 2211 (2005). \n[39] E. O. Kamenetskii, \"Vortices and chirality of magnetostati c modes in quasi-2D ferrite disc \nparticles\", J. Phys. A: Math. Theor . 40, 6539 (2007).  \n23 \n [40] E. O. Kamenetskii, R. Joffe, and R. Shavit, \"Microwave mag netoelectric fields and their role \nin the matter-field interaction,\" Phys. Rev. E 87, 023201 (2013). \n[41] E. O. Kamenetskii, M. Sigal ov, and R. Shavit, “Tellegen pa rticles and magnetoelectric \nmetamaterials”, J. Appl. Phys. 105, 013537 (2009). \n[42] E. O. Kamenetskii, “The anapole moments in disk-form MS-wa ve ferrite particles“, \nEurophys. Lett. 65, 269 (2004). [43] H. C. Ohanian, “What  is spin?”, Am. J. Phys. \n54, 500 (1986). \n[44] K. Mita, “Virtual probabil ity current associated with the spin”, Am. J. Phys. 68, 259 (2000).   \n                 \n \n                     "    },    {        "title": "0806.4974v1.Beam_Coupling_Impedance_Measurement_and_Mitigation_for_a_TOTEM_Roman_Pot.pdf",        "content": "arXiv:0806.4974v1  [physics.ins-det]  30 Jun 2008BEAM COUPLING IMPEDANCE MEASUREMENT AND MITIGATION\nFORATOTEM ROMAN POT\nM.Deile, F. Caspers, T. Kroyer, M.Oriunno,E. Radermacher, A.Soter\n(CERN, Geneva,Switzerland),F. Roncarolo (UniversityofM anchester, UK).\nAbstract\nThe longitudinal and transverse beam coupling\nimpedance of the first final TOTEM Roman Pot unit has\nbeenmeasuredinthelaboratorywiththewiremethod. For\nthe evaluation of transverse impedance the wire position\nhas been kept constant, and the insertions of the RP were\nmoved asymmetrically. With the original configuration\nof the RP, resonances with fairly high Q values were\nobserved. In order to mitigate this problem, RF-absorbing\nferrite plates were mounted in appropriate locations. As a\nresult, all resonanceswere sufficientlydampedto meet the\nstringentLHCbeamcouplingimpedancerequirements.\nTHE TOTEM ROMANPOTS\nThe LHC experiment TOTEM [1] is designed for mea-\nsuring the elastic pp scattering cross-section, the total p p\ncross-section and diffractive processes. These physics ob -\njectives require the detection of leading protons with scat -\nteringanglesofa few µrad,whichisaccomplishedusinga\nRomanPot(“RP”)systemwithstationsat147mand220m\nfrom the interaction point 5 where also CMS will be lo-\ncated. Each station is composedof two RP units separated\nbya few metresdependingonbeamequipmentintegration\nconstraints. Each RP unit consists of a vacuum chamber\nequippedwithtwoverticalinsertions(topandbottom)and\na horizontal one (Fig. 1). Each insertion (“pot”) contains\na package of 10 silicon detectors in a secondary vacuum.\nThepotscanbemovedintotheprimaryvacuumofthema-\nchine through vacuum bellows. In order to minimise the\ndistance of the detectors from the beam, and to minimise\nmultiple scattering, the wall thickness of the pot is locall y\nreducedtoa thinwindowfoil.\nThe lowimpedancebudgetofthe LHCmachine(broad-\nband longitudinal impedance limit Z/n≈0.1Ω) imposes\na tightlimit ontheRPs’ beamcouplingimpedance.\nFigure 1: Left: the vacuum chambers of a RP unit acco-\nmodating the horizontal and the vertical pots and a Beam\nPosition Monitor. Right: the potwith the thin windowand\na Ferritecollar(black).IMPEDANCEMEASUREMENT WITH\nTHE WIREMETHOD\nLongitudinalImpedance\nThe beam coupling impedance measurement was per-\nformed with the wire method like with the first RP pro-\ntotype in 2004 [2]. After pulling a 0.3mm thick wire\nthroughtheRP alongits beamaxis, a vectornetworkanal-\nyser wasusedto measurethecomplextransmissioncoeffi-\ncientS21(f,dx,dy)betweenthetwoendsoftheRP(Fig.2)\nas a function of the frequency fand of the horizontal and\nverticalpotdistances( dx,dy) fromthewire.\n/g0047\n/g004f/g0003/g0020/g0003/g0014/g0018/g0003/g0046/g0050/g0055/g0003/g0020/g0003/g0017/g0003/g0046/g0050\n/g0014/g0013/g0003/g0047/g0025/g0003/g0024/g0057/g0057/g0048/g0051/g0058/g0044/g0057/g0052/g0055/g0056/g0026/g0044/g004f/g004c/g0045/g0055/g0044/g0057/g004c/g0052/g0051\n/g0039/g0048/g0046/g0057/g0052/g0055/g0003/g0031/g0048/g0057/g005a/g0052/g0055/g004e\n/g0024/g0051/g0044/g004f/g005c/g0056/g0048/g0055/g0014 /g0015/g0039/g0048/g0055/g0057/g004c/g0046/g0044/g004f/g0003/g0033/g0052/g0057/g0056\n/g002b/g0052/g0055/g004c/g005d/g0052/g0051/g0057/g0044/g004f/g0003/g0033/g0052/g0057 /g0030/g0044/g0057/g0046/g004b/g004c/g0051/g004a/g0003/g0035/g0048/g0056/g004c/g0056/g0057/g0052/g0055\nFigure2: Setupofthe impedancemeasurements.\nFig. 3 shows the measurement result for all pots in re-\ntractedpositionandcomparesit with simulationsbasedon\ntwo different programs. While the simulations describe\nqualitatively all main structures seen in the data, the res-\nonances are shifted in frequency by up to 20%. This dis-\nagreement is attributed to the modelling of the bellows in\nthe simulations. An exact model requires a very dense\nmesh of the volume which compromises the simulation\nconvergence in an acceptable CPU time. Substituting the\nbellowswithalongersmoothcylinderofanequivalenttotal\nmetallic surfaceprovidesgoodagreementat the first mode\nfrequency( ∼500MHz),butdoesnotsucceedathigherfre-\nquencies. Improved numerical simulation models will be\nstudied.\nThe longitudinal impedance Zwas calculated with the\n“improvedlogformula”[3]\nZ(f,dx,dy) =\n=−2ZClnS21(f,dx,dy)\nSref\n21(f)\n1+ilnS21(f,dx,dy)\nSref\n21(f)\n4πlf/c\n,\n(1)-60-50-40-30-20-100\n0 0.5 1 1.5 2 2.5 3\nf [GHz]|S21| [dB]\n1a,1b\n-50-40-30-20-100\n0 0.5 1 1.5 2 2.5 3\nf [GHz]|S21| [dB]\nCST Microwave Studio\n-50-40-30-20-100\n0 0.5 1 1.5 2 2.5 3\nf [GHz]|S21| [dB]\nHFSS\nFigure 3: Comparison of the measured (top) and the sim-\nulated (middle and bottom) transmission coefficient |S21|\nwith all potsinretractedposition( dx=dy= 40mm).\n490500510520530540550560\n0 10 20 30 40\ndy [mm]f [MHz]\n1a1b\n0100200300400500600700800\n0 10 20 30 40\ndy [mm]Re Z [W]\n1a1b\nFigure4: Frequencyandimpedanceofthefirstdoubleres-\nonance as a function of the distance of the vertical pots\nfromthewire,withretractedhorizontalpot.\nwhereZC= 294Ω is the characteristic impedance of the\nunperturbed beam pipe and l= 15cm is the length of the\nperturbation (i.e. the diameter of the pot insertions). The\nmeasurement with all pots in retracted position served as\nreference measurement Sref\n21(f)after removal of all reso-\nnancesbyinterpolationinbothmodulusandphase.\nThe approximately Gaussian LHC bunch structure with\nσt= 0.25ns leads to a Gaussian envelope with σf=\n0.63GHz in the frequencydistribution of the LHC current\nwith harmonics every 40MHz. Hence the relevant reso-\nnancesliewellbelow1GHz. Fig.4showstheevolutionof\nfrequency and longitudinal impedance of the first double\nresonancepeakasafunctionoftheverticalpotposition dy(forthismeasurementthe topand thebottompotpositions\nwere symmetricalw.r.t. the wire). Theimpedancevalueof\n700Ωformode1b at dy= 0.5mmcorrespondsto Z/n=\n14mΩ, wheren=freson/fLHC= 555MHz /11kHz, or\nadissipatedpowerofabout200W,whichdemonstratesthe\nnecessity of mitigating hardware modifications. The latter\nwere realised in the form of a collar of ferrite tiles around\nthepotinsertions(Fig.1,right). Theyhadthedesiredeffe ct\nofsmearingoutallresonancesbeyondrecognition(Fig.5).\n-70-60-50-40-30-20-100\n0 200 400 600 800 1000 1200 1400\nf [MHz]|S21| [dB]dx=2mm\ndy=2mm without ferrites\nwith ferrites\nFigure 5: Frequency spectrum of the transmission coeffi-\ncient|S21|beforeandafterinstallationoftheferritetiles.\nTransverseImpedance\nThe transverse impedance was only measured for the\nconfiguration without ferrite tiles where resonances were\nvisible. Fortechnicalreasons,neitherthetwo-wiremetho d\nnoramovablewirewerepracticable. Instead,thetwoverti-\ncalpotsweremovedasymmetrically,keepingtheirrelative\ndistanceD– the jaw width – constant. Then the longitu-\ndinal impedancewas measured as a functionof the excen-\ntricityy, i.e. the position of the jaw centre with respect\nto the wire (Fig. 6, top and middle). After a parabolic fit\nZL(y) =z0+z1y+z2y2,whereideally z1= 0byvirtueof\nsymmetry, a combinationof vertical transverse impedance\nZTyand detuning impedance Zdetcan be obtained from\nthe curvature parameter z2, like in the moving wire tech-\nnique[4]:\nZTy+Zdet=c\n2πfz2. (2)\nSince there is only one horizontal pot, no analogous mea-\nsurement of the x-component ZTx−Zdetcould be made,\nwhich would have enabled the elimination of Zdet. How-\never,basedonthecalculationsinRef.[5]fordifferentape r-\nture geometries, the contributions ZTyandZdetcould be\napproximately disentangled. The result for the first group\nof resonances is shown in Fig. 6 (bottom) as a function of\nthe jawwidth D.\nTimeDomainStudies–theLoss Factor\nThebuilt-inFouriertransformationcapabilityofthenet-\nwork analyser facilitated a transmission study in the time\ndomain. Fig. 7 shows the transmission response to an in-\njected Gaussian pulse with σ=0.6ns for two different\nposition configurationsof the horizontal and vertical pots .0100200300400500600\n-20 -15 -10 -5 0 5 10 15 20\ny [mm]Re Z [W]1b\n1a\n1c\n110102103\n0 10 20 30 40 50 60 70 80\nD [mm]Re(ZT) [kW/m]\n1a1b1c\nFigure 6: Study of the transverse impedance of the first\nresonance group. Top: Frequency spectra around the first\nresonance group for a fixed vertical RP aperture width\nD=40mm and different excentricities yof this aperture\nwith respect to the wire; middle: longitudinal impedance\nas a function of the excentricity yfor the fixed aperture\nwidthD=40mm; bottom: dependence of the transverse\nimpedance on the aperture width D. For this entire study,\nthe horizontalpotwasinretractedposition.\nWhile without ferrites the resonant behaviour of the inser-\ntion cavities leads to oscillations extending beyond 25ns\nafter the main pulse, this “ringing” is suppressed by the\nferritesafterlessthan10ns.\nFocussing on the main pulse, the loss factor can be cal-\nculatedaccordingtothe formula[6]\nk(dx,dy) = 2ZC/integraltext\nIref(t)[Iref(t)−I(dx,dy,t)]dt\n/bracketleftbig/integraltext\nIref(t)dt/bracketrightbig2,\n(3)\nwherethetimeintegralextendsoverarangeof ±2σaround\nthe peak. Iref(t)is the reference pulse measured with all\npots in retracted position. As Fig. 8 shows, the loss factor\ndoesnotchangestronglywiththe additionofthe ferrites.-0.0200.020.040.060.080.10.120.14\n0 10 20 30 40\nt [ns]I/I0\nNo ferrites\nV at 3 mm, H at 40 mm\n-0.0200.020.040.060.080.10.120.14\n0 10 20 30 40\nt [ns]I/I0\nNo ferrites\nV at 40 mm, H at 3 mm\n-0.0200.020.040.060.080.10.120.14\n0 10 20 30 40\nt [ns]I/I0\nWith ferrites\nV at 3 mm, H at 40 mm\n-0.0200.020.040.060.080.10.120.14\n0 10 20 30 40\nt [ns]I/I0\nWith ferrites\nV at 40 mm, H at 3 mm\nFigure 7: Transmission of a Gaussian pulse of magnitude\nI0without (top) and with (bottom) ferrites for two differ-\nent combinationsof the horizonal (H) and vertical (V) pot\ndistancesfromthewire.\n10-310-210-1\n0 2.5 5 7.5 10 12.5 15 17.5 20\nd [mm]k [V/pC]\nNo ferrites; vertical pots approaching beam\nNo ferrites; horizontal pots approaching beam\nWith ferrites; vertical pots approaching beam\nWith ferrites; horizontal pots approaching beam\nFigure8: Lossfactorasafunctionofthepotdistancefrom\nthe wire with and without ferrites, distinguishing move-\nmentsofthe verticalandhorizontalpots.\nACKNOWLEDGEMENTS\nWe thank J. Noel, A.G. Martinsde Oliveira and S. Ran-\ngodfortheassemblyoftheRomanPot.\nREFERENCES\n[1] TOTEM,TechnicalDesignReport,CERN-LHCC-2004-002.\n[2] M. Deile et al., Tests of a Roman Pot Prototype for the\nTOTEM Experiment, Proceedings of PAC 2005, Knoxville,\nTennessee, pp.1701ff. arXiv:physics/0507080.\n[3] E.Jensen, PS-RFNote 2000-001, CERN2000.\n[4] T. Kroyer, F. Caspers, E. Gaxiola, Longitudinal and Tran s-\nverse Wire Measurements for the Evaluation of Impedance\nReductionMeasuresontheMKEExtractionKickers,CERN-\nAB-Note-2007-028.\n[5] H. Tsutsui, On single wire technique for transverse coup ling\nimpedance measurement, CERN-SL-Note-2002-034 AP.\n[6] M. Sands, J.Rees, SLACReport PEP-95,Aug. 1975."    },    {        "title": "1606.02469v1.A_method_to_decrease_the_harmonic_distortion_in_Mn_Zn_ferrite_PZT_and_Ni_Zn_ferrite_PZT_layered_composite_rings_exhibiting_high_magnetoelectric_effects.pdf",        "content": " \n1 \n A method to decrease the harmonic distortion in Mn -Zn ferrite/PZT and \nNi-Zn ferrite/PZT layered composite rings exhibiting h igh m agnetoelectric \neffect s.  \nV. Loyau1, V. Morin1, J. Fortineau2, M. LoBue1, and F. Mazaleyrat1 \n1SATIE UMR 8029 CNRS, ENS Cachan, Université Paris -Saclay, 61, avenue du président \nWilson, 94235 Cachan Cedex, France.  \n2 INSA Centre Val de Loire, Université François Rabelais , Tours,  GREMAN UMR 7347, \nCampus de Blois, 3 rue de la chocolaterie, CS 23410, 41034 Blois Cedex, France   \nAbstract .  \nWe have investigated the magnetoelectric ( ME) effect  in layered composite rings subjected to \ncircumferential AC magnetic fields and DC magnetic fields  in radial , axial or circumferential  \ndirection s. Bilayer  samples were obtained combining different grades of commercial Mn -Zn \nferrites or Ni -Zn ferrites with commercial  lead zirconate titanate (PZT). Mn-Zn ferrites with \nlow magnetostriction saturation (        ) and low magneto -crystalline anisotropy \nconstant s show high ME capabilities when associated with PZT  in ring structures . In certain \nconditions, these ME effects are higher than those obtained with Terfenol -D/PZT composite s \nin the same layered ring structure. Magnetostrictive and mechanical characterizati ons have \ngiven results that explain these high ME performances. Nevertheless, Mn -Zn ferrite/PZT  \ncomposites  exhibit voltages responses with low linearity  especially at high signal level . Based \non the particular structure of the ME device, a method to decrea se the nonlinear harmonic \ndistortion of the ME voltages is proposed. Harmonic d istortion analysis of ME voltage s \nmeasured in different configurations allows  us to explain the phenomenon .  \nI. INTRODUCTION  \nIn the field of magnetoelectric  (ME) materials, ME composites consisting in piezoelectric and \nmagnetostrictive phases mechanically coupled to each other have shown a great interest. The \nwide range of piezoelectric and magnetostrictive materials permits to obtain a large variety of \nME co mposites with different properties and application areas. Field and current sensors1, 2, 3, 4  \n(direct ME effect) , ME memories5, 6, and electrostatically tunable inductances7, 8 (converse \nME effect), are promising fields for ME composites. Concerning the current sensors, ME \ncomposites are well suited for manufacturing devices with low power consumption and \nsimplified electronic.  Among the different possible connectivities between  the two phases, \nonly two have shown great interests: 3 -3 (bulk composites9, 10, 11), and 2 -2 (laminated \ncomposites12, 13, 14). When fabricated, ME composites are characterized using a standardized \nset-up15: in case of direct ME effect measurements, ME sam ples are subjected to \nunidirectional AC and DC magnetic fields and the induced electric field across the \npiezoelectric layer is sensed . Obviously, ME samples optimized with respect to this method of \nmeasurement have high sensing capabilities when a AC fiel d with a radial direction is \nproduced by an external coil carrying AC currents. However, for current sensors there is a \nneed to measure currents flowing in a straight wire, producing circumferential magnetic  \n2 \n fields. In this case, the ME sample best geometr y is the ring configuration. In the literature, \nthere are few works reported on the subject of ME composites in such a structure. Dong et al. \n(see Ref. 1 and 2) have proposed ME rings in laminate configurations consisting in a PZT or \nPZN -PT ring sandwiched between two Terfenol -D rings. This configuration was named C -C \ncoupling mode because the Terfenol -D layers was magnetized in the circumferential direc tion \nand the piezoelectric layer was polarized in this same direction. Magnetic bias was produced \nby external permanent magnets. More recently, Leung et al. (see Ref. 3) have tailored a smart  \nME ring. The structure is based on two concentric layers. The ex ternal one is a bulk PZT ring \nbonded to an inner ring consisting in a Terfenol -D/Epoxy -matrix composite. Small NdFeB \npermanent magnets are included in the magnetostrictive phase for magnetic biasing. The PZT \nring was polarized in the radial direction, wher eas the magnetic field is circumferential.  \nIn a recent study4, we reported that optimized compositions of Co -substituted Ni -Zn ferrites \nmade by SPS (Spark Plasma Sintering) produce high ME effect in transversal mode when \nassociated with PZT in layered com posites. The ME performances are comparable to those \nobtained with Terfenol -D/PZT composites in the same structure. We demonstrated that the \nlow piezomagne tic coefficients of the ferrite  material (in comparison with Terfenol -D) are \ncounter balanced by a hi gh stiffness that permits to produce high mechanical stress. Secondly, \nwe have shown that the permeability of the magnetic layers, associated with the \ndemagnetizing factor, influences the ME response s. Using a new method of ME \ncharacterization, based on ME  samples in a ring structure submitted to a circumferential AC \nfield, the demagnetizing effect was overcame , and the intrinsic ME behavior was measured. It \nwas established  that low susceptibilities  (     )  (so high field penetrations) are needed to \nobtain high ME effect s when the AC magnetic field is produced by an external means \n(Helmholtz coils for example). In this case, Terfenol -D and nano -size grains Ni -Zn ferrites \nproduce the best ME effect.  But when a circumferential AC field is forced in a ri ng structure, \nit was shown that the ME response is not weakened by a high susceptibility, because the \ndemagnetizing effect does not exist.  \nStarting from the previous considerations, we have  show n, in the present paper , the potential \ninterest of ordinary h igh permeability Mn -Zn ferrites and Ni -Zn ferrites in ME layered \ncomposite ring structures subjected to circumferential AC magnetic field. In this work, we \nhave investigated ME effects in bilayered ME rings consisting in PZT rings pasted on \ncommercial  high permeability Mn -Zn ferrites and Ni -Zn ferrites rings. Those commercial \nferrites are commonly used to make inductors, transformers, and filters . To our best \nknowledge, those kinds of magnetic material s were never used in ME applications . The ME \ncharac terization set -up involves the use of circumferential AC field  and radial, axial or  \ncircumferential  DC magnetic fields.  Since the AC magnetic field is not subjected to \ndemagnetizing effect, the theory predict that the ME response is not weakened even for \nmagnetic materials exhibiting high permeability  such as Mn -Zn ferrites . For comparison, \nbilayered ME rings of the same structure made with high performance Terfenol -D or Ni -Co-\nZn ferrite (with nano -size grains) were characterized . Then, the different ME sa mples were \ntested in current sensor configuration s and their potential uses were discussed. We have \nfocused our work on a study of the ME voltage harmonic  distortion.  The level of  \n3 \n fundamental, second and third harmonics of ME voltages were analyzed for AC  magnetic \nfields increasing from 10 A/m up to 2000 A/m. A special configuration  of electrodes and \nelectric field measurement set -up ac ross the piezoelectric layer have  permitted to develop an \noriginal method to decrease the harmonic distortion of the ME vo ltage in ring structure s. \nLastly, exploiting the low magneto -crystalline anisotropies of Mn -Zn ferrites, we proposed a \nspecial configuration of ME current sensor s. The bias magnetic field was produced without \nexternal permanent magnets or external electromagnets.  This is a promising way to reduce the \nsize of ME sensors .   \nThe paper is organized in the following way. In Sec. II, a theoretical analysis of the ME \neffects, and the influence of the demagnetizing field in two different configurations of M E \nmeasurement is discussed. In Sec. III, the fabrication method of the ME samples is presented, \nand the ME characterization set -up is described. Characterization results are given in Sec IV. \nFirstly, ME measurements for small AC signal show that all sample s produce ME voltages in \nthe same range.  Magnetostrictive and mechanical characterizations were conducted on a Mn -\nZn ferrite ring. The measured parameters were used in a theoretical model of the ME \ncoefficient that fit well the experimental. In section V,  a study at higher levels of AC signal \ndemonstrates that Mn -Zn ferrites have piezomagnetic effects exhibiting low linearity in \ncomparison with Terfenol -D or Ni -Co-Zn ferrite. In order to overcome this problem, we have \nproposed a differential voltage measur ement method that increase the linearity of the ME \nresponse. A harmonic analysis of the distortion shows that this method permits to weaken the \nsecond harmonic components and it leads to a decrease of the global distortion of the ME \nsignal. Lastly, we have  studied a current sensor structure where the DC bias field was \nproduced without permanent magnets . \nII. THEORETICAL ANALYSIS  \nUsually, ME composites are characterized by applying a small external AC magnetic field (by \nmeans of Helmholtz coils) superimposed to a DC field15 in the same direction . The external \nAC field is measured by means of a hall probe or a search coil. When a DC bias field and a \nAC field     are applied in direction (1), producing an electric field    in the direction (3), the \ntransversa l coupling ME coefficient      (in quasi -static mode) is theoretically  given by4: \n      \n         \n                                                   \n                                                             (1)                                          \nwhere      and     ,     , and     , are zero field compliances, piezoelectric coefficient, and zero \nstress permittivity ,  respectively , for the piezoelectric material;      and      ,      and     , and \n  are zero field compliances,  intrinsic  piezomagnetic coefficients, and zero stress dynamic  \nsusceptibility , respect ively , for the magnetic material;   and    are the volume ratio  of the \nmaterials  and the radial demagnetizing factor respectively.  Note that for most of \npolycrystalline material s,                   . Furthermore, it must be noted that a perfect \n(but not realistic) mechanical coupling between the piezoelectric and piezomagnetic  layers is \nconsidered here  (without any  flexural strain ). Due to the demagneti zing effect , the level of the \ninternal AC field is divided by         with respect to the level of the external AC field. \nThe left hand term of Eq. 1, depending on the piezoelectric properties  and the mechanic al  \n4 \n properties of the magnetic and piezoelectric material s, can be regarded as constant s. The right \nhand term depends strongly on the bias field because the values of     ,     , and   are \ndependent on  the field. As a consequence , the ME curve is shaped b y the  right hand term.  \nA second method was recently proposed4 to characterized ME samples . The aim was to \novercome the demagnetizing effect and reach the intrinsic ME behavior.  A circumferential \nAC magnetic field is forced within the magnetic material by means of a coil wounded on the \nME ring (see Fig. 1 (a)). In this configuration, the value of the internal AC field       is \ndeduced from the measurement of the current flowing into the coil.  Obviously, in this case , \nthe demagnetizing factor    in Eq.  1 is equal to zero. This leads to the transversal coupling \nME coefficient       related to the circumferential AC field       in the (1,2) plane:  \n        \n          \n                                                                                                       (2) \nAs seen in Eq. 2, the dynamic susceptibility   has no influence on the amplitude of the ME \ncoefficient      . Nevertheless , the piezomagnetic coefficient,     , depends strongly on the \ninternal bias field    . In general, an applied bias field      is produced by an electromagnet \nand is measured by means of a Hall probe.  Then , the ME coefficient       is plotted as a \nfunction of the applied bias     . However,  this bias field is subjected to the demagnetizing \neffect  and the link between interna l and applied field s is given by : \n     \n                                                                                                                              (3)         \nwhere     is the static susceptibility. Thus , the demagnetizing effect has influence on the \nshape of the ME coefficient curve , shifting  it along the HDC axis.  \nWhen a AC field is applied by external source s (Helmholtz coils, for example), the \ndemagnetizing effect reduces the field penetration within the magnetic material. Eq. 1  clearly \ndemonstrates that, in this condition of measurement, magnetostrictive materials with low \nsusceptibilities   produce high ME  effects when associated with PZT . For example, in Ref. \n12, the transversal ME coefficient was 0.8V/A for Ni -Zn ferrite/PZT multilayers with \noptimized composition s. In Ref. 16, s imilar compositions of ME composites gave     \n          (trilayer sample)  and               (bilayer sample) . The differences in ME \ncoefficient s seem  to be due to  demagnetizing effects : the ferrite layers have thicknesses  with \ndifferent values . Usually ,          for polycrystalline Ni -Zn ferrites with nano -sized \ngrains, and         for Terfenol -D (at optimal bias) . It is obvious that in this case, \nmaterials with high susceptibilities such as Mn -Zn ferrites or Ni -Zn ferrites (with grain size  \nover 5µm ) cannot show exploitable ME effects. By opposition , when a circumferential field \n     is forced within the ferrite, these materials are not limited by their high susceptibilities  \n(see Eq. 2) . As a consequence, t he only condition that requires  a high ME effect is a high \nintrinsic piezomagnetic coefficient                   (where    is the magnetostriction \nmeasured is direction (1) for an internal field   ). Knowing the saturation magnetostriction    \nand the internal field    at this saturate d state, this coefficient can be estimated roughly by \napplying the formula:           . In a simple model17,    is directly linked to   , the  \n5 \n magneto -crystalline anisotropy constant of the second  order, and we can conclude that the \nintrinsic piezomagnetic coefficient      is proportional to the ratio      . The \nmagnetostriction and the magnetic anisotropy have the same origin, namely the spin-orbit \ncoupling.  Ferrite properties can be tailored by the chemical composition , so     and    can \nvary on a large span. B ut, in general, magnetostricti on and magneto -crystalline anisotropy \nchange in the same manner  (i.e. low magnetostriction is coupled with low anisotropy , whereas  \nhigh magnetostriction is coupled with high anisotropy).  We can expect that almost all ferrite \ncompositions ( Mn-Zn ferrites, Ni -Zn ferrites , Co-Zn ferrites  and substituted compositions) \nexhibit       ratios (and so , intrinsic piezomagnetic coefficients     ) within  the same order \nof magnitude.  Optimized compositions of Ni -Zn ferrites have much lower piezomagnetic \ncoefficients in comparison with Terfenol -D. But it was demonstrated that this weakness is \ncounter balanced by  a low compliance , so high ME ef fects were obtained in layered ME \ncomposites4. Comparable phenomenon can be expected with Mn-Zn ferrites  in layered ME \nstructures , even for compositions exhibiting very low  saturation  magnetostriction .  \nIII. SAMPLES FABRICATION AND MEASUREMENT SET -UP  \nCommercial f errite rings were purchased from Ferroxcube : two Mn-Zn ferrites  exhibiting  \nlow magnetostriction , 3E6, and 3E8,  and a Ni -Zn ferrite , 4A11 . All of them  were machined to \nreduce their thicknesses to 2  mm. To form ME bilayer samples, each ferrite ring was pasted \nwith silver e poxy (Epotek E4110) on a PZT ring  (PIC255, 10 mm  outer diameter, 5 mm \ninternal diameter, 1 mm thickness , polarized in direction (3) ). For comparison, two ME \nbilayer sample s were fabricated  using the same techn ique with materials known to produce \nhigh ME effect: a Terfenol -D (TFD) ring purchased from Etrema , and a Ni-Zn ferrite (FNCZ) \nring made by reactive  Spark Plasma S intering  (SPS) in our laboratory with the initial \ncomposition (mixture of precursor oxides)   (Ni 0.973Co0.027)0.75Zn0.25Fe2O4 (see Ref. 4 for \ninformation on the synthesis process) . The final composition after the SPS stage was \nmeasured using EDX chemical analysis ( Hitachi S -3400N SEM ) and it is very close to the \ninitial one. This is due to the very short time duration (25 minutes) of the SPS stage . This \ncomposition of ferrite was chosen because it produce s high ME effect s when a circumferential \nAC magnetic field is applied. The characteristics of all the magnetic material are summarized \nin Table 1 . Lastly , five bilayer ed ME samples were fabricated : 3E6/PIC255, 3E8/PIC255, \n4A11/PIC255,  FNCZ/PIC255,  and TFD/PIC255.  \nThe ME characterization  procedure is  based on an 8 turns coil wounded on the ME ring that \nforce s a circumferential AC magnetic field within the magnetic layer. The internal magnetic \nfield      in the (1,2) plane is related to the AC current      flowing into the coil:       \n       , where     is the number of turns and L is the mean length of the circular magnetic \npath.  When the  DC magnetic field is applied in the (radial) direction (1) by the means of an \nelectromagnet (see Fig. 1(a)), the measurement configuration is named CRA (Circumferential \nAC field, Radial DC field, Axial electric field). In this case, two opposite voltages V and V’ \nare induced on each halve s electrodes on the top of  the PZT layer (the top electrode was split \nby two strokes of file in the same direction (1 )). When the  DC magnetic field is applied in the \n(axial) direction (3) (see Fig. 1(b)), the measurement configuration is named CAA \n(Circumferential AC field, Axial DC field, Axial electric field).  Lastly, when the AC and DC  \n6 \n magnetic field s are forced  in the circumferential direction (see Fig. 1(c )), the measurement \nconfiguration is named CCA (Circumferential AC field, Circumferential  DC field, Axial \nelectric field).  It must be noted that the electric field is always in the (axial) direction (3).  A \nlock-in amplifier measures the voltage V on a half electrode at each DC magnetic field . For all \nthose working points, the ME coefficient is deduced from                , where   \n     is the thickness of the PZT layer, and       is the internal AC field deduced from the \nmeasurement of the cur rent     flowing into the coil.  \nIV. ME CHARACTERIZATION .  \nA. ME coefficient measurements  in CRA configuration . \nThe ME coefficients in CRA configuration  were measured and plotted in Fig. 2 for the ME \nsamples made with ferrites and in Fig. 3 for the ME sample made with T erfenol -D. The \nmagnitude of the AC magnetic field is around 1.5 A/m at 80 Hz (to avoid any resonance \nphenomenon). Concerning the ferrite/PI C255 samples, t he maximum ME effect s occur  at low \nbias magnetic fields between  8 kA/m and 25 kA/m. This fact confirms that the ferrite \nmaterials  (due to high permeability ) are easily magnetized  in comparison to the T erfenol -D: \nthe TFD/PIC255 sample exhibit  a maximum ME effect at             .  On the other \nhand, it is clearly seen that all the ferrite/PIC255 samples have better ME effects (          \n           ) than the ME sample fabricated with Terfenol -D (             ). Note that \nthe ME curve of the 3E6/PIC255 sample exhibits two peaks: a small peak at low DC field \n(           ) and a bigger one at higher DC field (            ). The reason of this \nbehavior will be explained later in the paper . The high ME effect obtained with Mn -Zn \nferrites is not obvious and it can be explained by low compliance s (two times lower than the \nPZT compliances , see Table 2 ) associated to  relatively high intrinsic piezomagnetic \ncoefficient s, according Eq. 2.  \nB. ME coefficient measurements in CAA configuration.  \nA second configuration  to measure a ME coupling  is investigated : the DC magnetic  field is  \napplied in the direction (3) when the circumferential AC magnetic field is in t he (1,2) plane of \nthe ME sample . Result s are plotted in Fig. 4 for 3E8/PIC255 and TFD/PIC255 ME samples.  \nThe two curves show ME effects roughly 10 times lower in comparison to the previous \nconfiguration measurement. Since  the demagnetizing effect do not exist for the AC magnetic \nfield, this discrepancy of the ME effect s can be explained by a lowering of the piezomagnetic \ncoefficients  when the applied DC field is perpendicular to the  AC field . In fact, when a bias \nfield is applied in direction (3), the magnetization is roughly forced in this d irection. So, the \nAC field, which is applied in a perpendicular direction, has difficulties to turn the \nmagnetization, and  consequently the piezomagnetic  effect is low.  Moreover, due to higher \ndemagnetizing effect s (which exist for the DC magnetic field) p eaks of curves are shifted at \nhigher bias fields. Note that for the TFD/ PIC255 sample there are two peaks at      \n         and         . \nC. Correlation with m agnetostriction measurement on 3E6 material.   \n7 \n High permeability Mn -Zn ferrites can produce ME effects (when associated with PZT) \ncomparable to those obtained with Terfenol -D. This good performance should be explained \nby measuring the piezomagnetic and elastic properties.  It is known that high susceptibility \nMn-Zn ferrites exhibit low magnetostriction, in the range of      (in relative ) at saturation. \nThis value is too low to be measured by means  of metal strain gauge, and piezoresistive \ngauges are very sensitive to thermal drift . So we have chosen an interferom etry method that \npermits strain measurement under     . Magnetostriction measurement was conducted on a \n3E6 ring. Four turns of wire were  wounded on the ring and a current (1.2 A peak) at 1kHz \nwas applied. This current forces a 200A/m peak magnetic field within the ring, which is \nsufficient to reach the saturation of the magnetic material. The velocity, at the surface of the \nring along a radial direction, was measured by means of a veloc imeter ( Polytec Laser Surface \nVelocimeter ). The displacement, and then the strain, was deduced by an integration of the \nvelocity . Magnetostriction c urve versus internal magnetic field is plotted in Fig. 5. A well \nknown butterfly shape is obtained.  Note tha t the velocimeter was used at its lowest frequency \nlimit (1kHz) and the curve may be a little bit distorted . The magnetostriction is very low, \n          , but it is obtained for a very low internal field:          . We can estimate \nan intrinsic piezomagnetic coefficient:                            at the optimal bias \n          . Velocity wave measurement of ultrasonic pulses (20MHz  center frequency ) \nalong the thickness of the ring permits us to deduce the       and       compliances of the 3E6 \nmaterial.  The pulse -echo technique for longitudinal and shear waves leads to:            \n(longitudinal) and            (transversal). This yields to:                  and \n                   . If we assume that the po lycrystalline ferrite is not textured, we \nhave:           and          . Using Eq. 2 and the data given in Table 2, we have calculated \nthe magnetoelectric  response of the sample # 3E6/PIC255. We obtain theoretically: \n              , and experime ntally the value is               (at optimal bias) , which is \nlower.  Eq. 2  has been developed assuming that the strain in the magnetic layer,    , and the \nstrain in the piezoelectric layers,    , are the same. That is definitely a rough approximation . \nTo try to better describe the reel system we introduce a ratio of strain  , taking into account \nthe differential strain between the two layers:               (in average).  So Eq. 2 \nbecomes4: \n        \n            \n                                                                                                      (4) \nThe ratio    depends on the composite structure. The lower value is obtained for staked \nPZT/ferrite bilayer  structures when the PZT layer is stressed on only one face. When the PZT \nlayer is stressed on its both faces (in case of ferrite/PZT/ferrite trilayers  or more ) the value of \n  is increased4. Moreover ,  in case of concentric PZT/ferrite discs19, the mechanical coupling \nis enhanced . In the present case of a staked  bilayer ring, the hole can influence the mechanical \ncoupling between the layers , and consequently,  the value of   is affected.  So the influence on \nthe ME response of the composite  ring structure  (that affect s the mechanical coupling)  is \nincluded in  . It is difficult to measure or to calculate the value of the ratio of strain  . \nNevertheless, using        in Eq.  4, the theoretical value of the ME coefficient ,      , fits \nthe experimental one.  This value of   is in the range of a value already measured for a ME  \n8 \n bilayer of the same kind4.  Note that the magnetostriction curve given i n Fig. 5 shows two \nlocal extrema at           (local maximum) and          (local minimum). It may be \ndue to a special shape of the domain structure near the demagnetized state. This local \nbehavior at low field can explain the first small peak of the ME curve (see Fig. 2) for the \n3E6/PIC255 sample.  The previous magnetostriction loop measurement method developed for \nthe 3E6 ring cannot be applied to Ni-Zn ferrites (4A11 and FNCZ) or Terfenol -D rings.  In \nfact, due to their high magneto -crystalline anisotropies , very high level currents (      ) in \nthe coil s are needed to saturate the materials. Nevertheless, the intrinsic piezomagnetic \ncoefficient can be roughly estimated using  the approximated formula:           , where    \nis the saturation magnetostriction, and    is the internal field needed to saturate the material.  \nThe saturation magnetostriction values were measured on disc samples (see method in  Ref. 4) \nusing strain gauges and we obtained:           (FNCZ) and             (Terfenol -\nD). The correspond ing internal saturation fields were  deduced from virgin magnetization \ncurves  (corrected in demagnetizing fields)  measured by means of a Vibrating Sample \nMagnetometer  (Lakeshore 7404) . We obtained:                (FNCZ) and    \n        (Terfenol -D). So, the estimated intrinsic piezomagnetic coefficient s are:          \n         (FNCZ) , and                  (Terfenol -D). Using the same rough \ncalculation  method for the 3E6 material, we obtained:                          (see \nFig. 5  for    and    values ). The approximated piezomagnetic coefficients of 3E6 and FNCZ \nmaterials are in the same range. This fact is confirmed by results in Fig. 2: th e two materials \nproduce ME responses with the same level. Although  the Terfenol -D material have a \npiezomagnetic coefficient roughly ten times higher in comparison to the previous materials , \nthe ME responses is in the same range (           . In the case of Terfenol -D,  the high \npiezomagnetic coefficient is counter balanced by its high compliance. (see Ref. 4).  \nV. STUDY OF CURRENT SENSOR APPLICATIONS.  \nA. ME samples used in CRA  configuration .  \nWe have investigated the potential use of those ferrite/PZT bilayer ME samples in a  current \nprobe application. The set -up is describe d in Fig. 1 (a), where the DC field  was applied along \nthe direction (1 ) and the AC field in the (1,2) plane was produced by a 8 turns coil wounded \non the ME ring  (CRA configuration) . A 55  mA peak , triangle waveform  current  at 1kHz was \napplied to  the coil . It correspond to a medium level AC field of about  18A/m.  In each case, \nthe DC field was set to obtain the highest ME voltage with good linearity. The time variation \nof the  applied  current  was deduced from the voltage produced by a 1Ω resistor connected in \nseries  with the coil . The ME voltage was sensed directly by a passive      voltage probe \n(10 MΩ input impedance) and recorded by an oscilloscope (Lecroy Waverunner 44Xi) . The \nresults are given in Fig. 6 . All the ME  samples show good linearity, except the FNCZ sample. \nFor this medium level AC field, the voltage levels produce by the ME samples are consistent \nwith the ME coefficient measurements (Fig. 2 and Fig. 3), except for the 4A11/PIC255 \nsample, for which the vol tage at medium excitation is two times higher with respect to the \nME coefficient measurement. Note that as expected, the TFD/PIC255 sample shows the \nlowest voltage response  (but with the best linearity) .   \n9 \n For AC field over 5 0 A/m, high distortions on ME vo ltages appear for 3E6/PIC255, \n3E8/PIC255,  and 4A11/PIC255 samples. It means that these sample s are suitable only for low \nAC magnetic field (or low AC current) detection.  On the other hand,  ME samples made with \nTFD or FNCZ materials show  relevant ME coefficients in large bias field ranges (see Fig. 2 \nand Fig. 3). In these  cases, we can expect good linearity even when high AC magnetic field s \nare applied. Experiments were conducted on ME composites made with TFD and FNCZ \nmaterials  under lar ge excitation:  a 3 A peak, triangle waveform current at 1kHz was applied \nin the 8 turns coils ( the AC field is about 1200 A/m peak) . The ME waveforms are given in \nFig. 7 . In each case, the bias field was tuned with the goal of getting a good linearity  of the \nME voltage . This is obtained when the bias field is over the DC field giving the maximum \nME voltage . But,  it conducts to a significant de crease of the ME response level. This is  \nespecially true concerning the  FNCZ/PIC255  sample  for which the ME co efficient is reduced \nto                at              (three times lower than the low signal ME \ncoefficient  at optimal bias ). This effect is less pronounced for the TFD/PIC255 sample for \nwhich the ME coefficient  at high level signal,                 at              , is \ncloser to t he value obtained at low AC level  in Fig. 3 .  \nWhen a ferrite material is subjected at the same time to a circumferential AC magnetic field \nand an unidirectional bias field (see Fig. 1 (a)), two opposite strains occur in each half part of \nthe material  because the radial components of the AC field are opposite for radial ly opposed \npoints . This effect produces two opposite electric fields in the corresponding parts of the \npiezoelectric layer. Theoretically, the ME coefficient can be doubled when  the voltage is \nmeasured between the two hal ves electrodes on the top of the piezoelectric layer.  Figure 8 \nshows an example of the two voltages V and V’ sensed on each part of the  FNCZ/PIC255 \nsample. A 300 mA  peak current (1kHz) with triangular waveform was applied to  the coil. The \ntwo voltages waveforms  (dotted and dashed lines), measured by two passive voltage probes, \nare almost symmetrical: they have opposite phases, but the voltage levels are slightly \ndifferent . This difference can be explain ed if we suppose that the piezomagnetic and the \npiezoelectric properties are not perfectly homogeneous in the materials.  The differential ME \nvoltage measured  with only one voltage probe  connected between  the two  halve s electrodes  is \ngiven in Fig. 8 (thick solid line). As expected, the voltage is twice higher and it is seen that  \nthe linearity is  enhanced.  \nB. Harmonic distortion analysis  in CRA  configuration . \nNonlinear effect  is a recent subject of study in the field of ME devices , and some applications \nhave been developped20, 21, 22. As seen before  in the present paper,  the linearity of the ME \nresponse is enhanced when the voltage i s measured between the two halve s electrodes.  To \nunderstand this effect, we have analyzed and compared the harmonic content s of the ME \nresponses when the  voltages are measured on a halves  electrode  (direct voltage)  and between \nthe two halves  electrodes  (differential voltage).  Experiments  were performed using  sinusoidal  \nAC magnetic field from 10 A/m up to 2000 A/m at 1kHz. The ME voltages were recorded by \nan oscilloscope  (and a passive 1  10 voltage probe)  and a Fast Fourrier Transform (FFT) was \nperformed . In Fig . 9, fundamental s (1kHz), second harmonic s (2kHz), and third harmonic s \n(3kHz)  are plotted as function of the AC field for the ME sample # 3E8/PIC255 . It is worth  \n10 \n noting  that the DC bias field was set to obtain (relatively) low distortion at high AC field. So, \nthe ME sensit ivity is lower than the best value for this sample.  Fig. 9  shows that when a \ndifferential voltage measurement is done, the fundamental and the third harmonic amplitudes \nare roughly doubled (+6dB) with respect to the direct voltage measurement. In an opposite \nway, the second harmonic is highly weakened  (-18dB at        A/m), leading to a \ndecrease of the global distortion of the signal. The same experimen t was conducted on the \nsample # FNCZ/PIC255  and result s are displayed in Fig. 10 : here again , the differential \nvoltage measurement leads to a decrease of the second harmonic amplitude , and this effect \noccurs for all even harmonics . The second harmonic  compensation indicates that the secon d \nharmonic voltages on each halves  electrode s are in phase, whereas the third harmonic \nvoltages are in opposition . The second harmonic generation is mainly due to the quadratic \ncomponent of the magnetostriction λ versus H field  behavior,      . In this case, the two \nhalve s parts of the magnetic ma terial are alternative ly strain ed in phase with same  amplitude . \nAssuming that the related voltages are well balanced, the second harmonic component can \ntheoretically be cancelled.  Lastly, the same harmonic distortion measurement s were  made for \nthe sample # TFD/PIC255, and results are displayed in Fig. 11 .  The bias field was chosen to \nproduce the high est ME voltage and the lowest distortion.  It can be seen that the fundamental \ncomponent of the voltage increases linearly with Hac and the second harmonic is always 50dB \nlower.  But for this sample , the effect of second harmonic compensation do es not occur and \nthe rea son remains unclear. The third harmonic amplitude is roughly constant (~ -60dBm) \nfrom      A/m up to 100A/m  and,  consequently, at low AC field (       A/m) the ME \nvoltage is highly distorted.  For this  sample, i t is clearly seen that the best  ME performance  \nare obtained when      is over 100 A/m  because in this region, the harmonic distortion is low \n(the ME coefficient is 1.4 V/A in the differential mode). Due to the second harmonic \ncompensation effect, t he sample #  FNCZ/PIC255, display s low distortion for Hac between 40 \nA/m and 2 00 A/m (in the differential mode) . This range defines its best working region for \nwhich the ME coefficient is around 1.75 V/A. These findings demonstrate that, in a useful \nrange of  Hac, nickel -cobalt -zinc ferrites can have performances comparable to those obtained \nwith Terfenol -D.  \nC. ME sample used in CCA configuration .  \nIn most of case s, ME devices need a DC magnetic bias field to reach the optimal  working \npoint (where the ME coefficient is maximum). Bias fields can be produced by permanent \nmagnets4 (barium ferrite magnets for example) but this techn ique leads to some limitations: \n(i) permanent magnets increase the size of the ME devices; (ii) magne tic lea kage can \ninfluence other devices in the surrounding environment,  (iii) the working point is not tunable. \nBut from  Fig. 6, it is apparent that Mn -Zn ferr ites reach optimal piezomagnetic coefficients at \nlow internal magnetic field (in the range of 50 A/m). This low bias field can easily be \nproduced by an additional coil wounded on the ME ring and carrying a DC current. So we \nhave conducted the following exp eriment on the 3E8/PIC255 sample. An additional coil \n(     turns) was wounded on the ME sample, carrying a DC current provided by a tunable \ncurrent source (with high input impedance) made using a LM317 integrated circuit.  This \nconfiguration is sketched Fig. 1(c) (CCA configuration).  The IDC current can be set from 0 to  \n11 \n 0.5A.  The AC magnetic field was produced by a 50mV rms, 1kHz, sinus waveform  current \nflowing inside a 8 turns coil wounded on the ME ring. The ME voltage was measured using \nan oscilloscope , and has been analyzed by FFT . In Fig. 12, fundamental and second -harmonic \ncomponents have been plotted as function of the DC current ×turns product. Seeing t he curve \nof the fundamental component, we find that the maximum voltage is obtained for a DC \ncurrent as low as          (          ).  At this working point, the ME coefficient \nreaches        . This high ME effect can be explained by an ideal configuration where both \nthe AC and DC magnetic fiel ds are circumferential, and so parallel to each other. Obviously, \nthe second -harmonic component is maximum at zero bias field. It is attributed to the \nfrequency doubling effect due to the quadratic behavior of the magnetostriction at low field. \nIncreasing the DC field, the second -harmonic amplitude decreases and reaches a minimum \nnear the optimal working point.  In conclusion, the feasibility of a highly sensitive tunable \nME device, without  permanent magnets, was demonstrated.  \n \nVI. CONCLUSION  \nWe have demonstrated that commercial Mn -Zn ferrites exhibiting low magnetostriction have \npotential interest in ME applications. A layered ring configuration with a circumferential \nmagnetic excitation is needed to meet high ME effects. The reason for this performan ce is a \ncombination of three factor s: (i) the forced AC magnetic field i s free of demagnetizing effect; \n(ii) the intrinsic piezomagnetic coefficient  of the Mn-Zn ferrite s is relatively high; and (iii) the \ncompliance of ferrites is low.  The present  study co ncerning Mn -Zn ferrites in ME composites \nis not exhaustive. Such ferrites are widely used in electronic devices and a large amount of \ngrades are available with various properties. We expect  that various compositions with high \nintrinsic piezomagnetic properties  could produce ME effect s of potential interest . The ME \nring structure is suitable for current sensing in straight cables, and  it was shown that Mn-Zn \nferrites  are the best candidates when we need to sense  low level signal s. At high level signal s, \nthe non linear harmonic distortion limits the performances of the ME device. This problem is \npartially overcome when using the differential voltage measurement method proposed in the \npaper. Harmonic distortion analysis have shown that a second harmonic compensation occurs.  \n  \n \n \n \n \n \n \n  \n12 \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n13 \n REFERENCES  \n1S. Dong, J. G. Bai, J. Zhai, J.F. Li, G.Q. Lu, D. Viehland, S. Zhang, T.R. Shrout, Appl. Phys. \nLett. 86, 182506 (2005).  \n2S. Dong, J -F Li, and D. Viehland, J. Appl. Phys. 96, 3382 (2004).  \n3C. M. Leung,  S. W. Or, and S. L.  Ho, J. Appl. Phys. 115, 17A933 (201 4). \n4V. Loyau, V. Morin, G. Chaplier, M. LoBue, and F. Mazaleyrat, J. Appl. Phys. 117, 184102 \n(2015 ). \n5T. Wu et al.  Appl. Phys. Lett. 98, 012504 (2011 ). \n6J. H. Kim, K. S. Ryu, J. W. Jeong , and S. C. Shin, Appl. Phys. Lett. 97, 252508 (2010 ). \n7G. Liu, X. Cui, and S. Dong, J. Appl. Phys. 108, 094106 (2010).  \n8J. Lou, D. Reed, M. Liu, and N. X. Sun, J. Appl. Phys. 94, 112508 (2009).  \n9R. A. Islam, V. Bedekar, N. Poudyal, J. P. Liu, and S. Priya , J. Appl. Phys. 104, 104111 \n(2008)  \n10Y. Liu, X. Ruan, B. Zhu, S. Chen, Z. Lu, J. Shi, and R. Xiong,  J. Am. Soc., 94[6] 1695 -1697 \n(2011).  \n11G. Srinivasan, C. P. DeVreugd, C. S. Flattery,  V. M. Laletsin, and N. Paddubnaya,  Appl. \nPhys. Lett. 85, n. 13, 2550 (2004).  \n12G. Srinivasan, E.T. Rasmussen, and R. Hayes, Phys. Rev. B 67, 014418 (2003).  \n13M.I. Bichurin, V.M. Petrov, G. Srinivasan, Phys. Rev. B 68, 054402 (2003).  \n14G. Srinivasan, E.T. Rasmussen, J. Gallegos, R. Srinivasan, Y.I. Bokhan, V.M. Laletin,  Phys. \nRev. B 64, 214408 (2001).  \n15G.V. Duong, R. Groessinger, M. Schoenhart, D. Bueno -Basques, J. Magn. Magn. Mater. \n316, 390 -393 (2007).  \n16N. Zhang, D. Liang, T. Schneider, an d G. Srinivasan, J. Appl. Phys. 101 , 083902 (2007 ). \n17S. Chikaz umi, Physics of magnetism, pp 260 -263, John Wiley & Sons, INC (1964).  \n18 See http://piceramic.com/  for piezoelectric and physical properties of Pic255 piezoceramic.  \n19L. Li, Y. Q. Lin, and X. M. Chen, J. Appl. Phys. 102 , 064103 (2007 ). \n20H. Xu, Y. Pei, D. Fang, and P. W ang, Appl. Phys. Lett. 105, 012904 (2014 ). \n21 Y. Shen, J. Gao, Y. Wang, P. Finkel, J. Li, and D. Viehland, Appl. Phys. Lett. 102, 172904 \n(2013 ).  \n14 \n 22L.  Shen et al. , J. Appl. Phys. 110, 114510 (2011).  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n15 \n  \n \n \n \n \n \n \n \n \nMaterial   # Outer  diameter  \n(mm)  Internal diameter  \n(mm)  Initial permeability  \n(in relative)  Material type  \n3E6 9.5 4.8 12000  Mn-Zn ferrite  \n3E8 9.5 4.8 18000  Mn-Zn ferrite  \n4A11  10 6 850 Ni-Zn ferrite  \nFNCZ  10 4 400 Ni-Co-Zn ferrite  \nTFD  10 4 40 Terfenol -D \n \nTABLE 1 . Characteristics of the magnetic rings.  Characteristics of 3E6, 3E8, and 4A11 materials are \ncited from Ferroxcube.  All the magnetic rings have 2 mm thickness.  \n \n \n \n \n \n \n \n \n \n \n \n  \n16 \n  \n \n \n \n \n \n \n \n \n \n      \n(pC/N)       \n(nm/A)       or      \n(m2/N)      or      \n(m2/N) µT or      \n(in relative ) \nPic255  -180                      2400  \n3E6 f errite   3                    12000  \n \nTABLE  2 : Material properties for Pic255 (cited from  Physik Intrumente18), and 3E6 ferrite.  \n \n \n \n \n \n \n \n \n \n \n \n \n  \n17 \n FIGURE  CAPTIONS  \nFIG.1.  Sketch es of three configurations of  ME measurement . (a): the circumferential AC \nmagnetic field is forced in the (1,2) plane (the coil is not represented) and the DC magnetic \nfield is applied in the (radial) direction (1) (CRA). (b):  the circumferen tial AC magnetic field \nis forced in the (1,2) plane  and the DC magnetic field is applied in the (axial) direction (3) \n(CAA). (c):  both AC and DC magnetic fields are forced in the circumferential direction \n(CCA). In all case, the electric field is measured in the (axial) direction (3).  \nFIG. 2. Transversal magnetoelectric coefficients under radial DC field (CRA configuration). \nDashed line: 3E8/PIC255 sample. Dotted line: 3E6/PIC255 sample. Solid line: 4A11/PIC255 \nsample. Dashed -dotted line: FerriteNiCoZn/PIC255.  \nFIG. 3. Transversal magnetoelectric coefficient under radial DC field  (CRA configuration)  for \nthe TFD/Pic255 sample.  \nFIG. 4 . Magnetoelectric coefficients when the DC field is applied in (axial) direction (3) and \nthe AC field is in the (1,2) plane (CAA configuration). Dashed line: 3E8/Pic255 sample. Solid \nline: TFD/Pic255 sample.  \nFIG. 5. Longitudinal magnetostristion curve versu s internal magnetic field measured on a 3E6 \nring excited at 1kHz.  \nFIG. 6. ME voltages when a 55mA peak triangle current flows in the  8 turns coil (CRA \nconfiguration).  Red line: TFD/PIC255 sample. Black line: FNCZ/PIC255 sample. Green line: \n3E6/PIC255 sam ple. Blue line: 3E8/PIC255. Purple line: 4A11/PIC255.  \nFIG. 7. ME voltages when a 3A peak triangle current (1kHz) flows in the 8 turns coil (CRA \nconfiguration). Dotted line: TFD/PIC255 sample. Dashed line: FNCZ/PIC255 sample. Solid \nline: voltage obtained wi th a commercial active current probe (sensitivity: 0.5 V/A).  \nFIG. 8. ME voltages when a 300mA peak triangle waveform current (1kHz) flows in the 8 \nturns coil wounded on the  FNCZ/PIC255 sample (CRA configuration). Thin solid line: \nvoltage obtained with a c ommercial active current probe (sensitivity: 0.5 V/A). Dotted line : \nvoltage V on a half electrode. Dashed line: voltage V’ on the other half electrode. Thick solid \nline: differential voltage between the two electrodes.  \nFIG. 9.  3E8/PIC255 sample: fundamental (circles), second -harmonic (squares), and third -\nharmonic (triangles) of ME voltages versus AC field (1kHz) amplitude (CRA configuration). \nThe thin lines correspond to voltages measured on a half electrode. The thick lines correspond \nto voltages  measured between the two halve electrodes (differential voltages).  \nFIG. 10.  FNCZ/PIC255 sample: fundamental (circles), second -harmonic (squares), and third -\nharmonic (triangles) of ME voltages versus AC field (1kHz) amplitude (CRA configuration). \nThe thin lines correspond to voltages measured on a half electrode. The thick lines correspond \nto voltages measured between the two halve electrodes (differential voltages).   \n18 \n FIG. 11.  TFD/PIC255 sample: fundamental (circles), second -harmonic (squares), and third -\nharmonic (triangles) of ME voltages versus AC field (1kHz) amplitude (CRA configuration). \nThe thin lines correspond to voltages measured on a half electrode. The thick lines correspond \nto voltages measured between the two halve electrodes (differential voltag es).  \nFIG. 12.  3E8/PIC255 sample: fundamental (solid line) and second -harmonic (dotted line)  \nME voltages in CCA configuration. The ampere -turns are  produced by a 30 turns coil \nwounded on the ME ring and carrying a DC current.    \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n19 \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFIG.1.  Sketch es of three configurations of  ME measurement . (a): the circumferential AC \nmagnetic field is forced in  the (1,2) plane (the coil is not represented) and the DC magnetic \nfield is applied in the (radial) direction (1) (CRA). (b):  the circumferential AC magnetic field \nis forced in the (1,2) plane  and the DC magnetic field is applied in the (axial) direction ( 3) \n(CAA). (c):  both AC and DC magnetic field s are forced  in the circumferential direction \n(CCA).  In all case , the electric field is measured in the (axial) direction (3).  \n \n      (1) (2) (3) \n            V        \n       \n              \n     \n(c) (a)               V V’        \n(1) (2) (3) \n     \n(b)      \n       (1) (2) (3) \n            V        \n      \n20 \n  \n \n \n \n \n \n \n \n \n \n \nFIG. 2. Transversal magnetoelectric coefficients  under radial DC field  (CRA configuration) . \nDashed line: 3E8/P IC255 sample. Dotted line: 3E6/P IC255 sample. Solid line: 4A11/P IC255 \nsample.  Dashed -dotted line: Ferrite NiCo Zn/PIC255 . \n \n \n \n \n \n \n \n \n \n \n \n \nFIG. 3 . Transversal magnetoelectric coefficient under radial DC field  (CRA configuration)  for \nthe TFD/Pic255 sample.  \n \n \n21 \n  \n \n \n \n \n \n \n \n \n \n \nFIG. 4 . Magnetoelectric coefficients when the DC field is applied in (axial) direction (3) and \nthe AC field is in the (1,2) plane  (CAA configuration) . Dashed line: 3E8/Pic255 sample. Solid \nline: TFD/Pic255 sample.  \n \n \n \n \n \n \n \n \n \n \n \nFIG. 5. Longitudinal magnetostristion curve versus internal magnetic field measured on a 3E6 \nring excited at 1kHz.  \n \n \n22 \n  \n \n \n \n \n \n \n \n \n \nFIG. 6 . ME voltages when a 55mA peak triangle current flows in the  8 turns coil  (CRA \nconfiguration) .  Red line: TFD/PIC255 sample. Black line: FNCZ/PIC255 sample. Green line: \n3E6/PIC255 sample. Blue line: 3E8/PIC255. Purple line: 4A11/PIC255.  \n \n \n \n \n \n \n \n \n \n \n \nFIG. 7 . ME voltages when a 3A peak triangle current (1kHz) flows in the 8 turns coil  (CRA \nconfiguration) . Dotted line: TFD/PIC255 sample. Dashed line: FNCZ/PIC255 sample. Solid \nline: voltage obtained with a commercial active current probe (sensitivity: 0.5 V/A).  \n \n \n \n23 \n  \n \n \n \n \n \n \n \n \n \nFIG. 8 . ME voltages when a 300mA peak triangle waveform current (1kHz) flows in the 8 \nturns coil wounded on the  FNCZ/PIC255 sample  (CRA configuration) . Thin solid line: \nvoltage obtained with a commercial active current probe (sensitivity: 0. 5 V/A). Dotted line : \nvoltage V on a half electrode. Dashed line: voltage V’ on the other half electrode. Thick solid \nline: differential voltage between the two electrodes . \n \n \n \n \n \n \n \n \n \n \nFIG. 9 . 3E8/PIC255 sample: f undamental (circles), second -harmonic (squares), and third -\nharmonic (triangles) of ME voltages versus AC field  (1kHz) amplitude  (CRA configuration) . \nThe thin lines correspond to voltages measured on a half electrode. The thick lines correspond \nto voltages measured between the two hal ve electro des (differential voltages).  \n \n \n24 \n  \n \n \n \n \n \n \n \n \n \nFIG. 10 . FNCZ/PIC255  sample: fundamental (circles), second -harmonic (squares), and third -\nharmonic (triangles) of ME voltages versus AC field (1k Hz) amplitude  (CRA configuration) . \nThe thin lines correspond to voltages measured on a half electrode. The thick lines correspond \nto voltages measured between the two hal ve electrodes (differential voltages).  \n \n \n \n \n \n \n \n \n \n \nFIG. 11 . TFD/PIC255 sample: fundamental (circles), second -harmonic (squares), and third -\nharmonic (tr iangles) of ME voltages versus AC field (1kHz) amplitude  (CRA configuration) . \nThe thin lines correspond to voltages measured on a half electrode. The thick lines correspond \nto voltages measured between the two hal ve electrodes (differential voltages).  \n \n \n25 \n  \n \n \n \n \n \n \n \n \nFIG.12.  3E8/PIC255 sample: fundamental (solid line) and second -harmonic  (dotted line)  ME \nvoltages  in CCA configuration . The ampere -turns are  produced by a 30 turns coil wounded \non the ME ring and  carrying a DC current  \n \n \n \n \n \n \n \n"    },    {        "title": "2309.15680v1.On_the_potential_of_hard_ferrite_ceramics_for_permanent_magnet_technology____a_review_on_sintering_strategies.pdf",        "content": "Journal of Physics D: Applied Physics\nJ. Phys. D: Appl. Phys. 54(2021) 303001 (13pp) https://doi.org/10.1088/1361-6463/abfad4\nTopical Review\nOn the potential of hard ferrite ceramics\nfor permanent magnet technology—a\nreview on sintering strategies\nCecilia Granados-Miralles1and Petra Jenuš2\n1Electroceramic Department, Instituto de Cer ´amica y Vidrio, CSIC, Madrid, Spain\n2Department for Nanostructured Materials, Jožef Stefan Institute, Ljubljana, Slovenia\nE-mail:c.granados.miralles@icv.csic.es\nReceived 26 November 2020, revised 12 March 2021\nAccepted for publication 22 April 2021\nPublished 14 May 2021\nAbstract\nA plethora of modern technologies rely on permanent magnets for their operation, including\nmany related to the transition towards a sustainable future, such as wind turbines or electric\nvehicles. Despite the overwhelming superiority of magnets based on rare-earth elements in\nterms of the magnetic performance, the harmful environmental impact of the mining of these\nraw materials, their uneven distribution on Earth and various political conflicts among countries\nleave no option but seeking for rare-earth-free alternatives. The family of the hexagonal ferrites\nor hexaferrites, and in particular the barium and strontium M-type ferrites (BaFe 12O19and\nSrFe12O19), are strong candidates for a partial rare-earth magnets substitution, and they are\nindeed successfully implemented in multiple applications. The manufacturing of hexaferrites\ninto dense pieces (i.e. magnets) meeting the requirements of the specific application (e.g.\nmagnetic and mechanical properties, shape) is not always straightforward, which has in many\ncases hampered the actual substitution at the industrial level. Here, past and on-going research\non hexaferrites sintering is reviewed with a historical perspective, focusing on the challenges\nencountered and the solutions explored, and correlating the sintering approaches with the\nmagnetic performance of the resulting ceramic magnet.\nKeywords: permanent magnets ,hexaferrites ,SrFe12O19,ceramic magnets ,sintered ferrites ,\nrare-earth-free ,substitution\n(Some figures may appear in colour only in the online journal)\n1 . Introduction\nRare-earth elements (REEs), often referred to as simply rare-\nearths, are the basis of both well-implemented and emerging\nOriginalcontentfromthisworkmaybeusedundertheterms\nof theCreative Commons Attribution 4.0 licence . Any fur-\ntherdistributionofthisworkmustmaintainattributiontotheauthor(s)andthe\ntitle of the work, journal citation and DOI.modern technologies [ 1]. Although REEs are not as scarce as\ntheir name suggests, they are very scattered, and their mining\niscostlyandcontaminant[ 2].Furthermore,depositswhichare\nworth mining (with sufficient concentrations) are not evenly\ndistributed throughout the globe, with China being the world-\nleading REE-producer and processor by far, accounting for\nmore than 70% of the total produced [ 3]. China has already\nused its dominant position in the past, when they limited the\nexports in 2009 and 2010, and raised the prices in 2011 [ 4].\nAfter this event, great powers such as Japan, the EU or the US\n1361-6463/21/303001+13$33.00 1 © 2021 The Author(s). Published by IOP Publishing Ltd Printed in the UKJ. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nhave made great efforts to reduce REE-consumption and min-\nimize the dependence on China [ 5–7]. Considering the ongo-\ning US–China trade conflict and the current global COVID-\n19 crisis [ 8], the situation threatens to become critical again.\nSome have anticipated that the Chinese could take revenge on\nthe US by restricting the REE-supply, especially when even\nChina itself is expecting to be affected by shortage [ 9]. Per-\nmanent magnets (PMs) make a textbook example of techno-\nlogy stricken with the REE-problem [ 10].\nOwing to their ability to interconvert between motion and\nelectricity, devices which operation relies on PMs are nearly\ninnumerable. Some examples are: microphones and speak-\ners of everyday electronic devices (mobile phones and com-\nputers),harddiskdrivesandotherinformationstoragedevices,\nmotors and generators of electric vehicles, machinery to har-\nvest renewable energy sources (e.g. wind or underwater tur-\nbines) or household appliance, small motors and sensors in\ncars (windscreen wipers and power windows motors, steering\nwheel position sensors) [ 11]. For many of these applications,\nreducing the weight is either beneficial or adds value to the\nproduct(miniaturizationishighlyappreciatedinourhigh-tech\ntimes). The better the magnetic performance of a magnet, the\nless amount of magnetic material is required to develop a spe-\ncific magnetic work. Thus, mass/volume of the devices may\nbe reduced by employing better magnets [ 12].\nAt present, Nd–Fe–B magnets are the best known PMs,\nby virtue of the REE Nd [ 13]. This intermetallic phase was\nsimultaneously discovered in 1984 by Croat (General Motors\nResearch Laboratories, US) [ 14] and M Sagawa (Sumitomo\nSpecial Metals Company, Japan) [ 15], and it meant a break-\nthrough in the field of PMs. Although magnets based on the\nSm–Co alloy were already well-developed at the time [ 16],\nthey were produced in very small quantities (and still are),\nonly reserved to very specific applications, as a consequence\nof the elevated price of the material [ 17]. In these REE-based\nintermetalliccompounds,thetransitionmetal(Fe,Co)ensures\na high magnetization while the REE (Nd, Sm) is responsible\nfor a very high magnetocrystalline anisotropy, which in turn\nproduces a large coercivity, Hc[18]. As a result, REE-based\nmagnetshaveanoutstandingmagneticperformance,withvery\nhigh energy products ( BHmax), typically above 200 kJ m−1\n[3,19] Unfortunately, as mentioned earlier, REEs are sub-\nject to irregular market fluctuations and intermittent shortage,\nwhichleadstoahighdependencyonexternalfactorsthatmag-\nnetmanufacturesandend-usersareveryinterestedinavoiding.\nTwo main options are currently being explored in order\nto overcome this problem: (a) REE-recycling and (b) REE-\nsubstitution.Themoststraightforwardapproachhasbeenrais-\ning awareness and implementing strategies towards the recyc-\nling and reuse of REEs [ 10,13,20]. However, this can only\nfunction as a short-term solution. Positively preventing the\ncriticality of raw materials from hindering further technolo-\ngical advances unarguably requires giving consideration to\nthe full (or at least partial) substitution of REE-based mag-\nnets. This is undoubtedly a more laborious process but shall\nbe worthy if outlined as a long-term solution.\nAlthough REE-magnets are indispensable in some high-\nperformance devices, there are many others not requiring somuch magnetic power but where Nd–Fe–B magnets are still\nemployed, since the just-below alternatives are considerably\nworse in performance and cannot meet the requirements [ 21].\nIn many of these scenarios, subtle changes on the engineer-\ning of the device, such as reinventing the magnets assembly\nand/or rethinking the device design, allow for a smaller mag-\nnetic power demand, which automatically makes substitution\npossible [ 22–24]. There are also quite some cases for which a\nmoderate betterment of the magnetic properties would allow\nreplacing REEs by lower-grade magnets without exceeding\nthe mass limitation. Thus, great efforts are devoted to shrink-\ning the gap between REE-containing and REE-free magnets,\neither by finding new REE-free alternatives or by optimizing\nthe performance of known magnetic phases [ 25].\nHexagonal ferrites have long been considered as plaus-\nible ‘gap magnets’ for REE-substitution, as a consequence of\ntheir relatively good magnetic properties coming along with a\nremarkably high stability and high Curie temperature, all this\nat a very low price compared to REE magnets [ 26]. However,\nmanufacturing dense hexaferrite pieces (i.e. hexaferrite mag-\nnets) with high enough densities while maintaining the good\nmagneticpropertiesofthepowdershasprovennotstraightfor-\nward, which in many cases has hampered a marketable REE\nsubstitution by ferrites. The technical difficulties encountered\nduring the densification of hard ferrites over the years and the\nnumerousstudiesaddressingthistopicstandasthemotivation\nfor the present review.\n2. Hexagonal ferrites\n2.1. Generalcharacteristicsand properties.Whyhexagonal\nferrites?\nHexagonal ferrites, also known as hexaferrites or simply hard\nferrites, were first announced as PM materials in 1952 by van\nOosterhout and co-workers at the Philips Research Laborat-\nories (Eindhoven, The Netherlands) [ 27,28], based on the\nformer work on magnetic oxides performed by Snoek, also\nat Philips [ 29]. This family of compounds are ternary or qua-\nternary iron oxides that crystallize in a hexagonal lattice with\nconsiderably long c-dimension (23.03–84.11 Å) [ 30]. Among\nall hexaferrites, the so-called M-type are particularly interest-\ning for PMs applications, owing to the large magnetocrystal-\nlineanisotropyalongthecrystallographic c-axis,derivedfrom\ntheir atomic structure. The strong uniaxial anisotropy causes\nthe M-type ferrites to have fairly large theoretical maximum\nHc, making them very robust against demagnetization (mag-\nnetically hard) and therefore very useful as PMs.\nThe M-type hexaferrites have general formula MFe12O19,\nM=Ba2+or Sr2+, and are typically abbreviated as BaM\nand SrM. They crystallize in a hexagonal magnetoplumbite\nstructure ( P63/mmc) with two formula units per unit cell. The\ncrystal lattice has very anisotropic dimensions ( a=5.892 Å,\nc=23.18 Å for BaM and a=5.884 Å, c=23.05 Å for\nSrM) and the crystallographic (theoretical) densities are 5.30\nand 5.10 g cm−3, respectively. [ 31,32] The lattice can be\ndivided into two alternating structural blocks stacked along\nthec-direction (cubic S and hexagonal R block, respectively)\n2J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nFigure 1. Representation of the crystal and magnetic structure of\nthe M-type hexaferrites, i.e. BaFe 12O19and SrFe 12O19. The black\nspheres represent the alkaline earth metals (Ba, Sr) while the colored\npolyhedra represent the five different Fe crystallograpic sites. The\narrows represent the magnetic spins of the Fe atoms. Oxygen atoms\nare found at all the vertices of the Fe polyhedra. Reproduced from\n[35] with permission from the Royal Society of Chemistry.\n[33]. The basic unit cell is composed of two R- and two S-\nblocks, RSR∗S∗, where∗denotes a 180◦rotation around the\nc-axis,andcontainstwoformulaunits(64atomsintotal)[ 33].\nThe Ba2+(or Sr2+) and O2−are arranged in a close-packed\nmanner, while the smaller Fe3+ions are located at interstitial\npositions [ 30,33,34]. The crystal (and magnetic) structure of\nM-type hexaferrites is shown in figure 1.\nTheintrinsicmagneticparametersofBaMandSrMarelis-\nted in table 1and they will be discussed below. The net mag-\nneticmomentofM-typehexaferritesarisesfromtheantiferro-\nmagneticalignmentoftheindividualFe3+magneticmoments\n(seearrowsinfigure 1),resultinginatheoretical(at0K)mag-\nneticmomentof20 µBpermoleculeofBaFe 12O19and20.6 µB\nfor SrM [ 30,36]. This translates into rather high maximum\n(saturation) values of mass-magnetization, Ms, and magnetic\nfluxdensityormagneticinduction(perunitvolume), Bs.Their\nCurie temperature, TC, is outstanding compared to most mag-\nnets, including REE-based. Thus, the TCof BaM or SrM is\nmore than 150◦C higher than that of Nd 2Fe14B.\nBothcompoundshaverelativelyhighanisotropyconstants,\nK1, which gives them a rather large magnetocrystalline aniso-\ntropy, HA, along the c-axis (see table 1) [37–39]. In a single-\ncrystalform,themaximum Hcvaluesreportedare594kAm−1\nfor BaM and around 533–597 kA m−1for SrM [ 28,33,37,\n38]. However, when in a polycrystalline form, the coercivity\nof M-hexaferrites largely depends on the particle size and it is\nusuallymuchsmallerthanthetheoreticalvalue[ 28,30,33].As\na side note, the coercivity of BaM and SrM display an inter-\nesting behaviour with temperature: for both compounds, Hc\nincreases with temperature up to a certain value (for polycrys-\ntallineBaM,thepeakisreachedatapproximatelly250◦CwithHcof 380 kA m−1) [28,33]. Beyond this certain value, Hc\ndecreaseswithincreasingtemperature,whichisthebehaviour\nusually found in ferrimagnetic materials.\nDespite the overwhelming magnetic superiority of Nd-\nbasedmagnets,hexaferriteshavebeenwidelyusedinthePMs\nindustry since their discovery. They are still of great research\ninterest as evidenced by the record number of publications on\nthe topic [ 30], and even today, hexaferrites continue to be the\nmostproducedmagneticmaterial[ 40].Thehegemonyofhard\nferrites compared to REE-magnets, despite the superior per-\nformance of the latter, rely on their decent performance at a\nvery low price. For instance, in 2013 hexaferrites accounted\nfor 85 wt% of the PMs sales, although they only represented\n50% of the billing [ 18]. The cost of a raw material is gener-\nally related to the abundance of the elements in the Earth’s\ncrust, and the elemental constituents of hexagonal ferrites are\nwidely available. Fe is the fourth most abundant element in\nEarth’s crust, and the indisputable first among the magnetic\nelements [ 39]. In particular, Fe is more than a thousand times\nmore abundant than Nd [ 41], and a thousand times cheaper\n[40]. Oxygen is the most abundant element while Ba and Sr\nare in 14th and 15th positions, respectively [ 41]. Apart from\nthe price, hexaferrites present other advantages compared to\nREE-based magnets. They have an outstanding chemical sta-\nbility and resistance to corrosion, and their high TCis very\nconvenient when utilized in motors or other devices that tend\nto acquire temperature during operation.\nLike for any other functional material, the magnetic prop-\nertiesofM-typehexagonalferritesdonotonlydependontheir\nstructureandchemicalcomposition[ 38],orthetemperatureof\noperation [ 37]. They are also highly influenced by the method\nusedforthesynthesisofthemagneticpowders[ 30,42–50],as\nwell as by the strategies followed to consolidate the powders\n[30,33,51–55], and very importantly, by the magnetic align-\nment or orientation of the densified piece [ 28,33,56,57].\nThe last one is particularly interesting here, as the particles\nof the M-type hexaferrites have a tendency to acquire a plate-\nlike shape, with the platelet plane perpendicular to the c-axis\n(see figure 2) [58,59]. This shape favors a crystallographic\nalignment during compaction under a uniaxial pressure, dur-\ningwhichtheplate-likeparticleswillhaveatendencytospon-\ntaneously lay on their larger surface side, just as a deck of\ncards would. This shape-induced orientation implicitly entails\na magnetic alignment, as the easy magnetization axis lies par-\nalleltothe c-axis(perpendiculartotheplateletplane)[ 52,58],\nvanishingtheneedforanexternalmagneticfieldappliedprior\nor during compaction, which considerably simplifies manu-\nfacturing the magnetic piece. Preparation methods and mag-\nnetic properties of M-type ferrites in the powder shape are\nextensively reviewed in another article of the present issue\n[26], while aspects related to consolidation and magnetic ori-\nentation of the powders are addressed here.\n2.2. Generalaspects on consolidation and typicalproblems\nencountered\nInordertobeanintegralpartofanydevice,magneticpowders\nneed to be conformed into dense pieces (i.e. magnets) with\n3J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nTable 1. Basic intrinsic magnetic properties of BaFe 12O19and SrFe 12O19, along with those of Nd 2Fe14B for comparison. All\ntemperature-sensitive parameters are room temperature values [ 33,37–39].\nMs(Am2kg−1) Bs(T) TC(◦C) K1(MJ m−3) HA(MA m−1)\nBaFe12O19 72 0.48 467 0.32–0.33 1.34–1.35\nSrFe12O19 74.5 0.48 473 0.35–0.36 1.47–1.59\nNd2Fe14B 165 1.61 315 4.9 6.13\nFigure 2. Illustration of the shape-induced orientation occurring during compaction of M-type platelets under uniaxial pressure. The\nmagnetic easy axis (i.e. the net magnetization direction) lies parallel to the crystallographic c-axis.\nspecific shapes and dimensions. Like with any other material,\nagooddensityisrequiredtoensuregoodmechanicalperform-\nance of the component. But this is even more crucial in the\ncase of magnetic materials, given that the magnetic figure of\nmerits ( BHmax) scales with the density. Simplistically speak-\ning, the densification of powders is generally carried out by\neithersimultaneousorconsecutiveapplicationofpressureand\ntemperature. This single- or multiple-step consolidation pro-\ncess is known as sintering, and in particular, when applied\nto ceramic materials such as ferrites, it may be referred to as\nceramic sintering [ 60].\nIn the consolidation of functional materials, which are\noptimized in the powders shape, it is crucial that the mater-\nial properties remain unaltered after sintering. In fact, great\nefforts are devoted to either adapt the conventional routes or\ndevelop new sintering strategies which are optimized for each\nspecific material, so that the damage is minimized [ 60]. As a\nmatter of fact, sintering of hexaferrites often ends up in a loss\nof magnetic attributes [ 61]. A frequent problem when sinter-\ning hexaferrites is the appearance of secondary phases, many\ntimes the highly stable iron oxide α-Fe2O3(hematite), which\nantiferromagneticcharacterdiminishesthesaturationmagnet-\nization. Luckily, when the starting powders are stoichiomet-\nrically pure and the thermal treatment is complete, this is gen-\nerally not an issue, and the Msvalues attained experimentally\nareusuallyaround70Am2kg−1,indeedclosetothemaximum\ntheoretical values [ 30].\nSubstantially more difficult to avoid is the damage to the\nHcresulting from the elevated temperatures required to attain\ngooddensitiesinthesinteredpiece.Hexaferritesaregenerally\nsintered between 1100◦C and 1350◦C [30], and these high\ntemperaturestriggeranexaggeratedgraingrowthwhichtrans-\nlates into a dramatic loss in coercivity [ 62]. Thus, while for\nhexaferritepowders, Hcvaluesclosetothesingle-crystalmax-\nima have been reported (487–525 kA m−1) [49,63–65], the\nstandard ceramic methods usually yield much lower values of\naround (<300 kA m−1), as a consequence of the grain growth\nduring the process [ 30,61]. Thus, the BHmaxvalues obtainedafter consolidation of BaM and SrM powders is generally\nfar below the theoretical maximum of 45 kJ m−3predicted\nfor these compounds [ 17]. Different strategies are pursued to\nretain Hcaftersintering,suchasfine-tuningthethermalcycles\ninordertomaximizethedensitywhileminimizingthetemper-\nature [66–68], or including different additives to hinder grain\ngrowth [ 69–71].\nAnother common strategy to minimize the Hcloss is\nmixing the magnetic powders with a polymer matrix and\nmanufacturing the mixture to obtain a dense piece or bon-\nded magnet [ 73,74]. The presence of the polymer reduces\nMscompared to a pure ceramic magnet, and the maximum\noperating temperature in the applications may be limited by\nthe glass transition or the viscosity temperature of the poly-\nmer (mechanical softening), but in return, bonded magnets\ncan be easily made into any desired shape, widening the spec-\ntrum of applications of ferrites (sintered pieces are generally\nlimited to simple shapes). Regarding the mechanical prop-\nerties, bonded ferrites are generally better in terms of flex-\nuralstrength(moreductile),whileceramicshavemuchhigher\nhardness. The details on bonded ferrites are out of the scope\nof this review and are gathered elsewhere [ 75–81]. Here, dif-\nferent ceramic sintering techniques applied to hexaferrites are\nreviewed, analyzing the problems encountered, the proposed\nsolutions and the main advances introduced during the last\ndecades. The quality of the obtained ceramic magnets is eval-\nuated in terms of the density and the magnetic performance.\n3. Sintered hexaferrites\nSintering is one of the key procedures in manufacturing and\nprocessing of ceramics. It is the step responsible for the trans-\nformationofparticulatestonet-shapedbodieswiththedesired\nproperties. The material densification during sintering occurs\nas a consequence of matter transport to or around pores,\ntriggered by appropriate conditions of temperature, pressure\nand atmosphere [ 82–84]. Sintering is usually accompanied by\n4J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nFigure 3. SEM micrographs and schematic representation of iso- and anisotropic sintered hexaferrite magnets. Reprinted by permission\nfrom Springer Nature Customer Service Centre GmbH: Springer Nature, Journal of Materials Science: Materials in Electronics [ 72],\nCopyright 2013.\nchanges in the microstructure, such as reduction in the con-\ntent and size of pores and grain growth. Although sintering\nitself is an ancient process that has been carried out for thou-\nsands of years, the scientific investigation on the phenomena\ntakingplaceduringsinteringhasmostlybeeninprogressfrom\nthe 1950s [ 84]. Besides continues optimization of the conven-\ntional ceramic methods, a plethora of new sintering methods\nhave been explored in the last decades, aiming at facing new\nchallenges such as microstructure preservation after sintering\n[60]. This is no exception for ferrites.\nThe history of sintered ferrites started almost 100 years\nago with Takei and Kato from Tokyo Institute of Techno-\nlogy (Japan) and their patent on production of soft magnetic\nzinc-ferrite cores [ 85], which led to the TDK Corporation\nand with that, to the commercialization of ferrites. Shortly\nafter, European researchers from Philips Research Laboratory\n(The Netherlands) also started investigating ferrites. They ini-\ntially focused on soft ferrites but they later went into hard fer-\nrites too, and in 1952 Philips came out to announce the first\ncommercial hard ceramic magnet, which was composed of\nhexagonal Ba-ferrite and to which they referred as Ferroxdure\n[27,28].Sincethen,therehasbeen,andstillis,alotofresearch\nfocused on the consolidation of hexaferrites, in a quest to pro-\nduce ferrite PMs with improved magnetic properties [ 86].\nFor PM materials, the important properties are the coerciv-\nity,Hc, and the remanent induction (or simply remanence),\nBr, targeting the highest possible maximum energy product,\nBHmax. The coercivitystrongly depends on the microstructure\nof the sintered material, and especially on the grain size. If\nthe grains contain a single magnetic domain, the demagnet-\nization through domain wall motion is not possible (as there\nare no domain walls in a single-domain body) and therefore,\nthe demagnetization of the piece can only occur by domain\nrotation, which is fairly difficult in a dense material, which inturn results in a high Hc[18,19,30,33]. In most ferrites, the\nparticles/grains are in a single domain state when their size\ndoes not exceed one micron [ 33]. On the other hand, the key\nparameters determining the remanence are the chemical com-\nposition,thedensityandthedegreeofgrainorientationwithin\nthe sintered magnet, i.e. the purest, the denser and the more\nmagnetically-oriented, the higher the Brvalue of the magnet.\nAtpresent,BaMandSrMmagnetsarecommerciallyavail-\nableinboththeirnon-oriented(isotropic)andoriented(aniso-\ntropic) forms, and the difference in Br(and therefore BHmax)\nbetweenthemisremarkable.Whilecommercialisotropic(ran-\ndomly oriented) ferrite magnets display energy products up\nto about 10 kJ m−1[3,87,88] anisotropic (magnetically\noriented) magnets reach up to 33.0–41.8 kJ m−3[87–90].\nHigher values (up to 44 kJ m−3) are found for La- and Co-\nsubstituted ferrites [ 91,92]. Scanning electron microscopy\n(SEM) images of both types of sintered hexaferrite magnets\nare shown figure 3, along with the corresponding schematic\nrepresentation of both cases.\nAlthough sintered ferrite magnets available on the market\nare consolidated by the conventional method, optimization of\nthe traditional ceramic routes is still an active research topic.\nBesides, the application of novel sintering techniques, such as\nmicrowave or spark plasma sintering (SPS), to ferrites is also\na rich and interesting field. In the following sections, the most\nrelevantadvancesonM-typeferritessinteringarehighlighted.\n3.1. Conventionalsintering\nThe original Ferroxdure phase reported by Went et alin\n1952 was an isotropic Ba-ferrite with a high coercive force\n(≈240kAm−1)andarelativelylowremanentinduction(0.2–\n0.21 T), which resulted in a maximum energy product of\n6.8 kJ m−3[27,28]. Although these first two papers about\n5J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nFerroxdure presented its magnetic properties in detail, they\ndid not describe the preparation procedure and the condi-\ntions used for sintering. In the following paper on Ferroxdure,\nauthored by Stuijts et althe development of anisotropic Ba-\nhexaferritemagnetswithenergyproductsupto28kJm−3was\nannounced[ 93].Toprepareananisotropicferritemagnet,they\nused randomly oriented non-aggregated Ba-ferrite powder,\nwhich was pressed-formed as an aqueous sludge under an\napplied external magnetic field. The excess water was then\nremoved by drying followed by the sintering of the pre-forms.\nThis process developed in Philips Research Laboratories in\n1950s is, with some modifications, still in use for the prepara-\ntion of commercial sintered ferrite magnets.\nStuijts et altested sintering temperatures ranging from\n1250◦Cto1340◦C,andtheyfoundoutthatincreasingthesin-\ntering temperature yields a higher degree of orientation [ 93].\nThus, an almost fully anisotropic magnet was obtained at the\nhighest sintering temperature (1340◦C). On the contrary, the\ncoercivity was the lowest (<20 kA m−1) at this temperature.\nThey also found out that the grain growth occurring during\nsintering enhances the magnetic anisotropy, but at the same\ntime, it limits the BHmaxdue to the decrease in coercivity. In\nthe same paper, they calculated the maximum value of BHmax\nfor a Ba-ferrite single crystal, assuming a 100% degree of ori-\nentation,resultinginaremanenceof0.42Tandconsequently,\naBHmaxof 35 kJ m−3.\nThe coercivity of ferrite magnets largely depends on their\ngrain size. Namely, the highest coercivities are reached when\nthe grain size is in the narrow region around the limit of the\nsingle domain [ 27,38,94]. The final stages of sintering are\ngenerally accompanied by an (extensive) grain growth, which\nis even more pronounced when powders with small particle\nsizes are densified [ 84,95,96]. As an example, the study\nby El Shater et albrings out the pronounced damage to the\ncoercivity caused by the elevated temperatures and prolonged\ntimeswhensinteringnano-sizedBaM[ 61].Thus,pelletsmade\nout of the same batch of powders sintered at 1000◦C and\n1300◦C presented coercivity values of 271 and 56 kA m−1,\nrespectively.\nThe densification of final stages is not at all unwanted, as\nthe remanence of a magnet increases linearly with the dens-\nity, so the optimal sintering method should ensure a trade-off\nbetweenacontrolledgraingrowthandagooddensification.In\na quest for the suppression of grain growth during final stages\nofsinteringwithouthamperingdensification,varioussintering\nadditives have been used, SiO 2being one of the most widely\nexplored [ 57,71,94,97–100]. In 1985, Kools concluded that\nthe highest Hcwere obtained for SiO 2concentrations within\nthe range 0.36–1.44 wt% and he put forward a mechanism\nfor the grain growth impediment [ 97,98]. In 1991, Beseni ˇcar\nandDrofenikstudiedthesinteringoffineSrMparticleswitha\nsmall addition (0.5 wt%) of SiO 2[99]. They found out that\nSiO2does not only suppress grain growth, but it also pro-\nmotes rearrangement of Sr-ferrite particles during sintering\nleading to highly anisotropic magnets with elevated density\n(97% of the theoretical value). These values were achieved at\n1260◦C with a holding time of only 3 min at the final temper-\nature, and yield a remanence of ≈0.39 T and a coercivity of≈340kAm−1(graphicallyestimatedfromfigure5in[ 99]).In\n2013, Kobayashi et alconcluded that to improve the coerciv-\nity, the amount of added SiO 2is preferably 1–1.8 wt%, while\nadditionshigherthan1.8wt%undesirablylowerthecoercivity\n[100].\nWhile small additions of SiO 2suppress ferrite grain\ngrowth, the addition of CaO promotes densification and con-\nsequently increases the remanence [ 57,94,100]. The down-\nside of the addition of CaO is the extensive grain growth,\nwhich negatively affects the coercivity (and also BHmax).\nHowever, a combination of the two additives in the right\namounts has shown good results [ 101,102]. In 1999, Lee\net alobtained an enhanced coercivity of 281 kA m−1by sin-\ntering SrM mixed with 0.6 wt% SiO 2and 0.7 wt% CaO at\n1200◦C for 4 h [ 101]. However, the orientation was not so\nhigh,whichyieldonlymoderatevaluesofremanence(0.36T)\nandBHmax(29.4 kJ m−1[3]). In 2005, Töpfer et alinvest-\nigated the effect of simultaneous addition of SiO 2and CaO\non the microstructure and magnetic properties of sintered Sr-\nferrite [102]. They found out that a Sr-ferrite powder mixed\nwith 0.5 wt% of SiO 2and CaO in a 1:1 ratio, and sintered\nat 1280◦C for a short period of time, resulted in a dense Sr-\nferrite magnet (98%) with refined microstructure and good\nmagnetic properties ( Br=0.42 T, Hc=282 kA m−1, and\nBHmax=32.6 kJ m−3). In 2018, Huang et altested the sim-\nultaneous addition of CaCO 3and SiO 2together with Co 3O4\n[70]. By conventionally sintering a mixture of SrM powders\nwith 1.1 wt% CaCO 3, 0.4 wt% SiO 2, 0.3 wt% Co 3O4, and\n0.5 wt% of a dispersant, they managed to manufacture a\n99% dense piece with remarkably good magnetic properties\n(Br=0.44 T, Hc=264 kA m−1, andBHmax=38.7 kJ m−3).\nBesides the use of sintering additives, other approaches\nhave been explored to overcome the grain growth problem.\nFollowing a two-step sintering method proposed by Chen and\nWang in 2000 which offered good results on nanosized Y 2O3\n[95], Du et alrecently presented a two-step sintering pro-\nfile adapted to Sr-ferrite [ 66]. In this work, the green body is\nfirst heated to a higher temperature for a short time (1200◦C\nfor 10 min) and then immediately cooled to an intermedi-\nate temperature, at which it remains to continue sintering\nfor a prolonged time (1000◦C for 2 h). Such a procedure\nresulted in a fully dense Sr-ferrite magnet with a reman-\nence of 0.44 T, a coercivity of 328 kA m−1, and a BHmax\nof 37.6 kJ m−3.\n3.2. Microwavesintering\nWhile in the majority of cases microwaves (MW) are used as\na synthesis aid [ 30,46,47,57,103,104], there are also some\nreports on MW sintering of hexaferrites [ 72,105,106]. For\nmicrowave sintering, the powders are generally cold-pressed\ninto relatively dense pieces (green bodies) which are then\nsintered by electromagnetic radiation in the GHz region MW\noven [60]. The preliminary tests carried out by Binner et alin\n1999, suggested that it was possible to MW-sinter nano-sized\nferrite powders without inducing much grain growth as long\nas the starting powders were not agglomerated [ 105]. Unfor-\ntunately, most of the dense pieces they produced contained\n6J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nFigure 4. SEM images or SrFe 12O19microwave sintered for 10 min\nat (a) 1000◦C, (b) 1050◦C, (c) 1100◦C, and (d) 1150◦C.\nReprinted from [ 107], Copyright 2002, with permission from\nElsevier.\ncracks after the sintering. In 2009, Yang et alprepared 97%\ndenseBaMmagnetsbymicrowavesintering[ 106].Theycould\navoid the presence of α-Fe2O3as an impurity while redu-\ncing the sintering temperature considerably compared to the\nconventional ceramic methods. However, in this case, they\ncould not avoid grain growth, yielding to a very low Hc\n(<50 kA m−1).\nMuchmorepromisingresultswerepresentedbyKanagesan\net alin 2013 [ 72]. They used sol-gel synthesized Sr-ferrite,\nwhich was uniaxially pressed and sintered by microwave\nsintering. Figure 4shows SEM images of the microwaved\nsintered samples obtained at temperatures between 1000◦C\nand 1150◦C, with a heating rate of 50◦C min−1, and with a\nholding time at the maximum temperature of only 10 min. At\nthe highest sintering temperature tested (1150◦C), they could\nmakeafairlydenseSrMmaterial(95%)withveryacompetit-\niveHcof 445 kA m−1, although the Brwas not so high in this\ncase.\n3.3. Sparkplasma sintering\nWith the start of the new millennium, a densification tech-\nnique called SPS started to gain more and more interest in\nmaterial science, and also in the field of ferrite magnets.\nIn SPS, a powder sample is introduced in a sintering die,\ngenerally made of graphite. The powders are subjected to a\nuniaxial pressure while an electrical current is run through\nthe sample to heat it up by Joule effect (see figure 5for\na typical SPS setup). This heating modes enables fast heat-\ning rates, lower sintering temperatures and shorter sintering\ntimes compared to the conventional and microwave sintering\n[108,109]. All this features posed a viable option for a dens-\nification of materials with no, or with a limited grain growth\nFigure 5. Typical spark plasma sintering experimental setup.\nReprinted from [ 51], Copyright 2014, with permission from\nElsevier.\n[109], which would positively affect the coercivity and con-\nsequently also the maximum energy product of ferrite mag-\nnets.Ontheotherhand,apositiveeffectonthemagneticprop-\nerties (especially on the remanence) could also have a direct\napplication of uniaxial pressure during densification by SPS,\nby causing the preferential orientation of hexagonally shaped\ngrains. So, SPS studies including various M-type hexafer-\nrites and composites based (mainly) on Ba- or Sr-hexaferrite\nwere presented in the last 20 years or so [ 35,51–53,55,58,\n64,110,107,111–115], and some of them will be discussed\nbelow.\nIn 2002, Obara et alpresented results of SPS sintered\nLa, Co-doped SrM ferrite fine particles (1.0 wt% La 2O3and\n0.1 wt% Co 3O4) [107]. With a final temperature of 1100◦C, a\nholdingtimeofonly5minandanappliedpressureof50MPa,\ntheypreparedfullydensesamples(density =5.15gcm−1[3])\nwith a remanence of 0.32 T, a coercivity of 325 kA m−1, and\naBHmaxof 18.3 kJ m−1[3]. In 2006, Zhao et alSPS sintered\na textured BaM powder (nanorods) [ 110]. Although the sin-\ntering temperature was rather low (800◦C), the Hcvalue was\nnot stunning (112 kA m−1). In 2011, Mazaleyrat et alcarried\nout several SPS tests on pure BaM nanoparticles (< 100 nm)\nobtaining high Hcvalues [53]. By limiting the growth of the\nnanoparticles during SPS, they managed to achieve a coerciv-\nity of 390 kA m−1for the dense material. This value is even\nhigherthantheobtainedbyObarafortheLa,Co-dopedmater-\nial [107]. However, the magnet was not so dense in this case\n(88% of the theoretical density), and therefore, the resulting\nBHmax, was considerably lower, i.e. 8.8 kJ m−3.\nIn 2014, Ovtar et alevidenced the notable smaller sizes\nobtained after SPS of nanosized BaM powders compared to\n7J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nFigure 6. SEM images of the inside of (a) an BaM pellet SPS\nsintered at 900◦C and (b) the same powder conventionally sintered\nat 1350◦C. Reproduced from [ 58] with permission of The Royal\nSociety of Chemistry.\nthe same material sintered conventionally (see figure 6) [51].\nTheystudiedthepartialdecompositiontakingplaceduringthe\nSPS process and additionally, they noticed that the impurity\nphases segregate within the sintered material, resulting in the\nformation of a magnetite or hematite layer at the surface of\nthe sintered pellets while the inside remained Ba-rich. They\ndemonstrated that the protective layer placed between the\npowders and the graphite die has an influence on the decom-\nposition. After testing different materials (boron nitride, gold,\nalumina), they obtained their best results using alumina pro-\ntectivediscs,yieldingan82%densepelletwithacoercivityof\n350 kA m−1.\nIn 2015, Stingaciu et altested a ball milling procedure a\nmicro-sized commercial SrM powder aimed at reducing the\nparticle size of the powders prior to SPS [ 55]. The method\nwas not fully successful as the amorphous phases generated\nduringmillingtransformedintosecondaryphasesduringSPS.\nAlthough the sintered densities were well above 90% of the-\noretical density, the magnetic properties were highly affected\nby the formation of these secondary phases, which signific-\nantly lowered the BHmaxvalues of the sintered magnets (val-\nues reported were in the range of 3.5–4.6 kJ m−3). Later, the\nBHmaxcould be improved to some extent (up to 9.6 kJ m−3)\nby an additional heat treatment. Thus, it follows that not only\npre-treatment of powders used for the consolidation, but also\nsintering by SPS itself can pose a risk for the decomposition\nof Ba- or Sr-ferrites.\nIn 2016, Jenuš et alpresented a study on the SPS sintering\nof hard-soft composites based on hydrothermally (HT) syn-\nthesized Sr-ferrite [ 115]. Out of all the samples reported by\nJenuš, only the SPS sintering of Sr-ferrite alone is considered\nhere. All sintered SrM samples had densities higher than 90%\nof the theoretical value, regardless of sintering temperature\n(700◦C–900◦C) or holding time (1 or 5 min). The best pure\nSrMpelletfromthisstudywassinteredat900◦C,withahold-\ning time of 5 min and an applied pressure of 92 MPa, and\ndisplayed remanence Mrof 65.8 Am2kg−1, a coercivity of\n167 kA m−1and a high BHmaxof 21.9 kJ m−3. Although\ntheHcvalue is not particularly high in this case, the BHmax\nvalueisratherlargecomparedtootheroldstudies,andthiscan\nbe explained by the highly anisotropic morphology of the HT\nsynthesized SrM particles used. The anisotropic shape favors\nthe SrM particles to lie on their basal plane when pressed,this is, with the magnetization pointing out of the pellet plane,\nwhich translates in a pronounced magnetic alignment ( Mr/Ms\nratio3=0.90) and consequently a high BHmax.\nIn the same year, Saura-M ´uzquiz et alpublished another\nSPS study where the starting SrM powders were HT-\nsynthesized hexagonal platelets with very small sizes (e.g. for\nsome samples the platelet thickness was only slightly over the\ndimension of one unit cell) [ 58]. By tuning the SPS routine,\nthey managed to minimize the grain growth during sintering,\nwith which the resulting pellets had a relatively large coerciv-\nity of 301 kA m−1. High-resolution powder x-ray diffraction\ndataweremeasuredontheSrMpowdersbeforeandaftercom-\npaction and Rietveld analysis on those data was carried out to\nextract quantitative information. Figure 7(a) shows the meas-\nured diffraction patterns and Rietveld models of the powders\nprior to compaction (red) and the densified SPS pellet (blue).\nBoth patterns correspond to the same crystallographic phase,\nSrM,however,therelativeintensitiesofthepeaksareverydif-\nferent, as a consequence of the crystalline orientation. While\nthe powders present a random orientation of the crystallites,\na pronounced crystalline alignment (texture) is observed for\nthepellet.Thiscrystallinealignmentwasfurtherstudiedusing\nx-ray pole figures on different Bragg reflections, confirming\nthe preferential orientation along the c-crystallographic dir-\nection (see figure 7(b)). This crystalline alignment translates\nin a pronounced magnetic alignment ( Mr/Msratio=0.89),\nwhich combined with the high coercivity results in an even\nhigher BHmaxvalue of 26 kJ m−3. As explained above, and\ngraphically represented in figure 2, the alignment of thin SrM\nplatelets occurs due to the uniaxial pressure applied during\nthe SPS procedure. Furthermore, this spontaneous crystallo-\ngraphic alignment is very convenient from the magnet manu-\nfacturing point of view, as the resulting dense pieces exhibit\na high magnetic alignment without the need for an externally\napplied field prior or during compaction, this way avoiding a\nwhole step in the fabrication chain [ 111]. This characteristic\nalignment has also been seen to have an effect on the thermal\nconductivity (much higher along the in-plane than the out-\nof-plane direction), which opens an opportunity for effective\ncooling [ 52].\nFurther investigations based on both ex situandin situ,\nx-ray and neutron powder diffraction measurements, have\nallowed to optimize the preparation method (HT syn-\nthesis +SPS), with which a BHmaxof 30 kJ m−3could be\nachieved by SPS [ 48,112,113,116]. Applying a magnetic\nfield prior to sintering showed an improvement on the tex-\nture ( Mr/Msratio=0.95), but this came at the cost of a\nreduced coercivity (133 kA m−1), and the BHmaxbetterment\nwas not significant (29 kJ m−3)[114]. Instead, subsequent\npost-annealing of the SPS pellet (4 h at 850◦C) did allow\na great enhancement of the squareness of the hysteresis loop\n(Mr/Msratio=0.93), reaching a BHmaxof 36 kJ m−3, which\n3The common parameter used to estimate the degree of magnetic orientation\nis the remanence-to-saturation ratio in mass units ( Mr/Ms), as the maximum\npossible remanence, Mr(100% oriented magnet) is set by the corresponding\nsaturation value, Ms, of the measured M-Hhysteresis curve [ 19].\n8J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nFigure 7 . (a) Powder x-ray diffraction data along with the corresponding Rietveld models of a hydrothermally-synthesized SrM powder (red\nline) and a dense SPS pellet fabricated out of those powders (blue line). (b) X-ray pole figure measurements of the SPS pellet. Reproduced\nfrom [58] with permission from the Royal Society of Chemistry.\nwould approximately correspond to a ‘Y36’ in Chinese stand-\nards [88,90]. Similar sintering routes have been tested on\nSrM powders with different morphology, including commer-\ncial powders and powders synthesized following a conven-\ntional sol-gel method and a modified sol-gel method [ 35,64].\nHowever, the resulting alignment was not as exaggerated as\nfor the thin SrM platelets obtained HT.\nInsummary,consolidationofhexaferritesbySPSisfollow-\ning trends valid also for other (ceramic) materials. Namely,\nthe method uses lower sintering temperatures and much\nshorter sintering times than conventional sintering, and thus\nthe particles’ growth is limited. With limited grain growth,\nthe consolidation of nano-sized hexaferrites is effectively\nresulting in smaller changes in the coercivity when com-\npared to the conventionally sintered magnets, in which grain\ngrowth is substantial, as retaining nano-sized particles in the\nsinteredsampleusuallyresultsinhighercoercivities.Theuni-\naxial pressure applied during the process positively affects\nthe density and it also promotes texturing (see figure 2).\nWhendealingwithmagneticmaterials,highdensityandmag-\nnetic alignment lead to an increase in remanence. Thus, a\nhigher degree of texturing is reflected in the higher square-\nness of the hysteresis loops, which together with high reman-\nence and high coercivity leads to better maximum energy\nproduct. Although SPS provides several advantages when it\ncomes to the consolidation of M-type ferrite (nano)powders,\nthere is also a drawback of this method, which needs to\nbe taken into an account. If graphite dies with protectinggraphite sheets are used, a chemical reduction of the material\natthesurfacesmayoccur.Dependingonthereductiondegree,\nthe magnetic properties of the sintered piece can deteriorate\nsubstantially.\n3.4. Other options toexploreand futurework\nTheinnovationinthefieldofsinteringduringthelast10years\nhas been considerable [ 60], and several new sintering tech-\nnologies have been brought into the picture, including cold\nsintering processes [ 117,118], flash sintering [ 119,120], and\nmodified SPS methodologies [ 121,122]. This widens the\nrange of options for sintering ferrites with optimized micro-\nstructureandmagneticproperties.Recently,Serrano et alhave\nmanaged to produce dense SrM ceramic magnets with com-\npetitive magnetic properties using cold sintering routes that\nrequire much lower temperatures and reduce the energy con-\nsumption (>25%) [ 67,68]. However, to the best of our know-\nledge, none of these other new sintering methods have been\ntested on hard hexagonal ferrites yet, which leaves plenty of\nroom for an improvement in the research field analyzed in the\npresent review.\n4. Conclusions and perspectives\nHexagonal ferrites, in particular the M-type (BaFe 12O19,\nSrFe12O19), are well-established PM materials, and they show\n9J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\ngreat potential as gap magnets, in the run for substitution of\nrare-earthsinsomePMapplications.Theproblemsecountered\nin the consolidation of hexaferrites are outlined, and literature\non the sintering of M-type ferrites is reviewed and discussed\nin the context of the density and magnetic properties of the\nresulting material.\nThe sintered magnets available in the market are prepared\nby traditional/conventional sintering methods. The conven-\ntional approaches require prolonged times and elevated tem-\nperatures, which promote an exagerated growth of the ferrite\ngrains which damages the coercivity of the densified piece.\nHowever, after years of investigation on the topic, addition\nof sintering aids has proven satisfactory in controlling this\ngrowth, yielding dense pieces with good magnetic properties.\nDespite the good results of conventional sintering, great\nefforts have been and still are dedicated towards finding new\nor modified ways of densification of ferrite magnets, e.g.\nmicrowave sintering, SPS, flash sintering, cold sintering. This\ninnovative methods reduce the sintering times and temperat-\nures and/or the energy consumption by using faster and more\nefficient heating processes (MW, Joule heating) or experi-\nmental setups that allow for simultaneous application of pres-\nsure and temperature. Ferrite magnets sintered using these\nnoveltechniquesarealreadyyieldinggooddensitiesandcom-\npetitive magnetic properties, but the continuous development\nof the sintering technologies leaves space for further investig-\nations in the field.\nThe latter is of the greatest importance since already small\nimprovements in ferrites could lead to substitution of rare-\nearth-based magnets for a large number of applications, as in\nmotors and generators even a mild remanence enhancement\ncan lead to an increased power output, therefore paving the\nway to a cheaper, and more importantly, greener electrific-\nation. It is worth noting that the European Union wishes to\nreach climate neutrality by 2050 [ 123], and environmentally\nfriendly technologies are vital for accomplishing this, giving\na head start to magnets with less or no rare-earths. In addi-\ntion, oxides as they are, ferrites are easily recyclable materi-\nals, providing a good starting point for a circular economy of\nsuch PMs.\nData availability statement\nNo new data were created or analysed in this study.\nAcknowledgments\nThis work is supported by the European Commission through\ntheH2020projectwithGrantagreementH2020-NMBP-2016-\n720853 (AMPHIBIAN) and by the Spanish Ministerio de\nCiencia, Innovación y Universidades (RTI2018-095303-A-\nC52). C G M acknowledges financial support from Spanish\nMinisterio de Ciencia e Innovación (MICINN) through the\n‘Juan de la Cierva’ Program (FJC2018-035532-I). Financial\nsupport from the Slovenian Research Agency (research core\nfunding No. P2-0087) is acknowledged.ORCID iDs\nCecilia Granados-Miralles https://orcid.org/0000-0002-\n3679-387X\nPetra Jenuš https://orcid.org/0000-0002-1926-479X\nReferences\n[1]Leader A, Gaustad G and Babbitt C 2019 The effect of\ncritical material prices on the competitiveness of clean\nenergy technologies Mater. Renew. Sustain. Energy\n88\n[2]Gupta C K and Krishnamurthy N 1992 Extractive metallurgy\nof rare earths Int. Mater. Rev. 37197–248\n[3]U.S. Geological Survey 2019 Mineral Commodity\nSummaries U.S. Department of the Interior ( https://doi.\norg/10.3133/70202434 )\n[4]Jones N 2011 Materials science: the pull of stronger magnets\nNature 47222–23\n[5]Vekasi K 2019 Politics, markets, and rare commodities:\nresponses to Chinese rare earth policy Japan. J. Political\nSci.202–20\n[6]Goodenough K M et al2016 Europe’s rare earth element\nresource potential: an overview of REE metallogenetic\nprovinces and their geodynamic setting Ore Geol. Rev.\n72838–56\n[7]Sandalow D U.S. Department of Energy Office of Policy and\nInternational Affairs (PI) 2011 Critical Materials Strategy\nDOE/PI-0009 U.S. Department of Energy\n[8]The editorial board 2020 The dangers of a US-China\nfinancial war (Financial Times) ( https://www.ft.com/\ncontent/85bca04a-9529-11ea-abcd-371e24b679ed ) (14\nMay 2020)\n[9]Li X Y, Ge J P, Chen W Q and Wang P 2019 Scenarios of\nrare earth elements demand driven by automotive\nelectrification in China: 2018–2030 Resour. Conserv.\nRecycl. 145322–31\n[10]Chen Y and Zheng B 2019 What happens after the rare earth\ncrisis: a systematic literature review Sustainability 111288\n[11]Jimenez-Villacorta F and Lewis L H 2014 Advanced\npermanent magnetic materials Nanomagnetism ed\nJ M G Estevez (Cheshire: One Central Press) pp 161–89\n[12]Gutfleisch O, Willard M A, Brück E, Chen C H, Sankar S G\nand Liu J P 2011 Magnetic materials and devices for the\n21st century: stronger, lighter, and more energy efficient\nAdv. Mater. 23821–42\n[13]Yang Y et al2017 REE recovery from end-of-life ndfeb\npermanent magnet scrap: a critical review J. Sustain.\nMetall. 3122–49\n[14]Croat J J, Herbst J F, Lee R W and Pinkerton F E 1984 Pr-Fe\nand Nd-Fe-based materials: a new class of\nhigh-performance permanent magnets (invited) J. Appl.\nPhys. 552078–82\n[15]Sagawa M, Fujimura S, Togawa N, Yamamoto H and\nMatsuura Y 1984 New material for permanent magnets on\na base of Nd and Fe (invited) J. Appl. Phys. 552083–7\n[16]Strnat K 1970 The recent development of permanent magnet\nmaterials containing rare earth metals IEEE Trans. Magn.\n6182–90\n[17]Coey J M D 2011 Hard magnetic materials: a perspective\nIEEE Trans. Magn. 474671–81\n[18]Lewis L H and Jiménez-Villacorta F 2013 Perspectives on\npermanent magnetic materials for energy conversion and\npower generation Metall. Mater. Trans. A442–20\n[19]Coey J M D 2012 Permanent magnets: plugging the gap Scr.\nMater. 67524–9\n10J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\n[20]Is ¸ıldar A, Van Hullebusch E D, Lenz M, Du Laing G,\nMarra A, Cesaro A, Panda S, Akcil A, Kucuker M A and\nKuchta K 2019 Biotechnological strategies for the\nrecovery of valuable and critical raw materials from waste\nelectrical and electronic equipment (WEEE)—a review J.\nHazard. Mater. 362467–81\n[21]Pavel C C, Thiel C, Degreif S, Blagoeva D, Buchert M,\nSchüler D and Tzimas E 2017 Role of substitution in\nmitigating the supply pressure of rare earths in electric\nroad transport applications Sustain. Mater. Technol.\n1262–72\n[22]Cai H, Guan B and Xu L 2014 Low-cost ferrite PM-assisted\nsynchronous reluctance machine for electric vehicles\nIEEE Trans. Ind. Electron. 615741–8\n[23]Fasil M, Mijatovic N, Jensen B B and Holboll J 2015\nPerformance variation of ferrite magnet PMBLDC motor\nwith temperature IEEE Trans. Magn. 511–6\n[24]Pedersen J R, Speiermann M and Zamany J 2019 Flywheel\nsystems and flywheel bearing modules WO2019076419A1\n[25]Skomski R and Coey J M D 2016 Magnetic anisotropy—how\nmuch is enough for a permanent magnet? Scr. Mater.\n1123–8\n[26]De Juli ´an Fern ´andez C, Sangregorio C, De La Figuera J,\nBelec B, Makovec D and Quesada A 2021 Topical review:\nprogress and prospects of hard hexaferrites for permanent\nmagnet applications J. Phys. D: Appl. Phys. 54153001\n[27]Went J J, Rathenau G W, Gorter E W and van\nOosterhout G W 1952 Hexagonal iron-oxide compounds\nas permanent-magnet materials Phys. Rev. 86424–5\n[28]Went J J, Rathenau G W, Gorter E W and van Oosterhout G\n1952 Ferroxdure, a class of new permanent magnet\nmaterials Philips Tech. Rev. 13194\n[29]Snoek J L 1949 New Developments in Ferromagnetic\nMaterials 2nd edn (Amsterdam: Elsevier)\n[30]Pullar R C 2012 Hexagonal ferrites: a review of the\nsynthesis, properties and applications of hexaferrite\nceramics Prog. Mater. Sci. 571191–334\n[31]Obradors X, Collomb A, Pernet M, Samaras D and\nJoubert J C 1985 X-ray analysis of the structural and\ndynamic properties of BaFe 12O19hexagonal ferrite at\nroom temperature J. Solid State Chem. 56171–81\n[32]Obradors X, Solans X, Collomb A, Samaras D, Rodriguez J,\nPernet M and Font-Altaba M 1988 Crystal structure of\nstrontium hexaferrite SrFe 12O19J. Solid State Chem.\n72218–24\n[33]Smit J and Wijn H P J 1959 Ferrites: Physical Properties of\nFerrimagnetic Oxides in Relation to Their Technical\nApplications (Eindhoven: Philips’ Technical Library)\n[34]Cullity B D and Graham C D 2009 Introduction to Magnetic\nMaterials 2nd edn (New York: Wiley)\n[35]Saura-M ´uzquiz M, Eikeland A Z, Stingaciu M,\nAndersen H L, Granados-Miralles C, Avdeev M, Luzin V\nand Christensen M 2020 Elucidating the relationship\nbetween nanoparticle morphology, nuclear/magnetic\ntexture and magnetic performance of sintered SrFe 12O19\nmagnets Nanoscale 129481–94\n[36]Chikazumi S 1997 Physics of Ferromagnetism 2nd edn, ed\nS Chikazumi and C D Graham Jr (Oxford: Oxford\nUniversity Press)\n[37]Shirk B T and Buessem W R 1969 Temperature dependence\nof Msand K 1of BaFe 12O19and SrFe 12O19single crystals\nJ. Appl. Phys. 401294–6\n[38]Jahn L and Müller H G 1969 The coercivity of hard ferrite\nsingle crystals Phys. Status Solidi 35723–30\n[39]Coey J M D 2001 Magnetism and Magnetic Materials\n(Cambridge: Cambridge University Press)\n[40]Expert Magnet Research 2020 Global Permanent Magnets\nMarket Report and Forecast 2020–2025\n[41]Abalakin Victor 2006 Abundance of elements in the earth’s\ncrust and in the sea CRC Handbook of Chemistry andPhysicsInternet Version ed D R Lide (Boca Raton, FL:\nTaylor and Francis) pp 14–17\n[42]Dang T M H, Trinh V D, Bui D H, Phan M H and\nHuynh D C 2012 Sol–gel hydrothermal synthesis of\nstrontium hexaferrite nanoparticles and the relation\nbetween their crystal structure and high coercivity\nproperties Adv. Nat. Sci.: Nanosci. Nanotechnol.\n3025015\n[43]Primc D, Makovec D, Lisjak D and Drofenik M 2009\nHydrothermal synthesis of ultrafine barium hexaferrite\nnanoparticles and the preparation of their stable\nsuspensions Nanotechnology 20315605\n[44]Drofenik M, Kristl M, Žnidarši ˇc A, Hanžel D and Lisjak D\n2007 Hydrothermal synthesis of Ba-hexaferrite\nnanoparticles J. Am. Ceram. Soc. 902057–61\n[45]Kaczmarek W A, Idzikowski B and Müller K H 1998 XRD\nand VSM study of ball-milled SrFe 12O19powder J. Magn.\nMagn. Mater. 177–181 921–2\n[46]Grindi B, Beji Z, Viau G and BenAli A 2018\nMicrowave-assisted synthesis and magnetic properties of\nM-SrFe 12O19nanoparticles J. Magn. Magn. Mater.\n449119–26\n[47]Molinari F, Maignan A, Marinel S and Savary E 2017 Fast\nsynthesis of SrFe 12O19hexaferrite in a single-mode\nmicrowave cavity Ceram. Int. 434229–34\n[48]Granados-Miralles C, Saura-M ´uzquiz M, Bøjesen E D,\nJensen K M Ø, Andersen H L and Christensen M 2016\nUnraveling structural and magnetic information during\ngrowth of nanocrystalline SrFe 12O19J. Mater. Chem. C\n410903–13\n[49]Guzm ´an-Mínguez J C, Moreno-Arche L,\nGranados-Miralles C, López-S ´anchez J, Marín P,\nFern´andez J F and Quesada A 2021 Boosting the\ncoercivity of SrFe 12O19nanocrystalline powders obtained\nusing the citrate combustion synthesis method J. Appl.\nPhys. 54014002\n[50]Gjørup F H, Saura-M ´uzquiz M, Ahlburg J V, Andersen H L\nand Christensen M 2018 Coercivity enhancement of\nstrontium hexaferrite nano-crystallites through\nmorphology controlled annealing Materialia\n4203–10\n[51]Ovtar S, Le Gallet S, Minier L, Millot N and Lisjak D 2014\nControl of barium ferrite decomposition during spark\nplasma sintering: towards nanostructured samples with\nanisotropic magnetic properties J. Eur. Ceram. Soc.\n34337–46\n[52]Volodchenkov A D, Ramirez S, Samnakay R, Salgado R,\nKodera Y, Balandin A A and Garay J E 2017 Magnetic\nand thermal transport properties of SrFe 12O19permanent\nmagnets with anisotropic grain structure Mater. Des.\n12562–68\n[53]Mazaleyrat F, Pasko A, Bartok A and LoBue M 2011 Giant\ncoercivity of dense nanostructured spark plasma sintered\nbarium hexaferrite J. Appl. Phys. 10907A708\n[54]Shishkovskii I V, Kuznetsov M V and Morozov Y G 2003\nNew methods for development of three-dimensional\nceramics based on barium hexaferrite with chromium\nadditives Glass Ceram. 60174–8\n[55]Stingaciu M, Topole M, McGuiness P and Christensen M\n2015 Magnetic properties of ball-milled SrFe 12O19\nparticles consolidated by spark-plasma sintering Sci. Rep.\n514112\n[56]Zhang T et al2017 Structural, magnetic and electromagnetic\nproperties of SrFe 12O19ferrite with particles aligned in a\nmagnetic field J. Alloys Compd. 690936–41\n[57]Goldman A 2006 Modern Ferrite Technology (Berlin:\nSpringer)\n[58]Saura-M ´uzquiz M, Granados-Miralles C, Stingaciu M,\nBøjesen E D, Li Q, Song J, Dong M, Eikeland E and\nChristensen M 2016 Improved performance of SrFe 12O19\n11J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\nbulk magnets through bottom-up nanostructuring\nNanoscale 82857–66\n[59]Lisjak D and Mertelj A 2018 Anisotropic magnetic\nnanoparticles: a review of their properties, syntheses and\npotential applications Prog. Mater. Sci. 95286–328\n[60]Biesuz M, Grasso S and Sglavo V M 2020 What’s new in\nceramics sintering? A short report on the latest trends and\nfuture prospects Curr. Opin. Solid State Mater. Sci.\n24100868\n[61]El Shater R E, El-Ghazzawy E H and El-Nimr M K 2018\nStudy of the sintering temperature and the sintering time\nperiod effects on the structural and magnetic properties of\nM-type hexaferrite BaFe 12O19J. Alloys Compd.\n739327–34\n[62]Dho J, Lee E K, Park J Y and Hur N H 2005 Effects of the\ngrain boundary on the coercivity of barium ferrite\nBaFe12O19J. Magn. Magn. Mater. 285164–8\n[63]Dufour J, Latorre R, Negro C, Alcal ´a E M, Formoso A and\nLópez-Mateos F 1997 Protocol for the synthesis of\nBa-hexaferrites with prefixed coercivities J. Magn. Magn.\nMater. 172308–16\n[64]Eikeland A Z, Stingaciu M, Mamakhel A H,\nSaura-M ´uzquiz M and Christensen M 2018 Enhancement\nof magnetic properties through morphology control of\nSrFe12O19nanocrystallites Sci. Rep. 87325\n[65]Hölscher J, Saura-M ´uzquiz M, Ahlburg J, Mørch M,\nGrønseth D K and Christensen M 2020 Controlling\nstructural and magnetic properties of SrFe 12O19\nnanoplatelets by synthesis route and calcination time J.\nPhys. D: Appl. Phys. 53474002\n[66]Du J, Zhou T, Lian L, Liu Y and Du Y 2019 Two-step\nsintering of M-type strontium ferrite with high coercivity\nCeram. Int. 456978–84\n[67]Serrano A, García E, Fern ´andez J F, Granados-Miralles C\nand Quesada A 2020 Procedimiento de obtención de un\nim´an permanente de cer ´amica magnéticamente anisótropo\ny denso P202030112\n[68]Serrano A, García-Martín E, Granados-Miralles C, Gorni G,\nLópez-S ´anchez J, Ruiz-Gómez S, Pérez L, Quesada A and\nFern´andez J F Hexaferrite-based permanent magnets with\nupper magnetic properties by cold sintering process via a\nnon-aqueous solvent Acta Mater. under review\n[69]Özkan O T, Erkalfa H and Yildirim A 1994 The effect of\nB2O3addition on the direct sintering of barium hexaferrite\nJ. Eur. Ceram. Soc. 14351–8\n[70]Huang C C, Jiang A H, Hung Y H, Liou C H, Wang Y C,\nLee C P, Hung T Y, Shaw C C, Kuo M F and Cheng C H\n2018 Influence of CaCO 3and SiO 2additives on magnetic\nproperties of M-type Sr ferrites J. Magn. Magn. Mater.\n451288–94\n[71]Guzm ´an-Mínguez J C, Vicente-Arche L M,\nGranados-Miralles C, Fern ´andez J F and Quesada A 2021\nImprovement of the magnetic properties of SrFe 12O19\nceramics by tailored sintering with SiO 2addition J. Alloys\nCompd. 860157890\n[72]Kanagesan S, Hashim M, Jesurani S, Kalaivani T, Ismail I\nand Ahmod C S 2013 Effect of microwave sintering on\nmicrostructural and magnetic properties of strontium\nhexaferrite using sol–gel technique J. Mater. Sci. Mater.\nElectron. 243881–4\n[73]Coey J M D and O’Donnell K 1997 New bonded magnet\nmaterials (invited) J. Appl. Phys. 814810–5\n[74]Gonz ´alez-Gutiérrez J, Stringari G B and Emri I 2012 Powder\ninjection molding of metal and ceramic parts Some\nCritical Issues for Injection Molding ed J Wang (London:\nInTech) 65–88\n[75]Hung Y C, Ko W S, Tung M J, Chen L K and Chang W C\n1989 Effects of additives on the orientation and strength of\nplastic ferrite magnet IEEE Trans. Magn. 253287–9[76]Zlatkov B S, Nikolic M V, Aleksic O, Danninger H and\nHalwax E A 2009 Study of magneto-crystalline\nalignment in sintered barium hexaferrite fabricated by\npowder injection molding J. Magn. Magn. Mater.\n321330–5\n[77]El-Sayed A H, Hemeda O M, Tawfik A and Hamad M A\n2015 Remarkable magnetic enhancement of type-M\nhexaferrite of barium in polystyrene polymer AIP Adv.\n5107131\n[78]Murillo N, Gonz ´alez J, Guraya C, Gutiérrez M and Seco F\n1999 Structural and magnetic properties of sintered\nSr-ferrites fabricated by powder injection molding J.\nMagn. Magn. Mater. 203165–8\n[79]Lee S H and Jeung W Y 2001 Anisotropic injection molding\nof strontium ferrite powder using a PP/PEG binder system\nJ. Magn. Magn. Mater. 226–230 1400–2\n[80]Zlatkov B S, Nikolic M V, Zeljkovic V, Obradovic N,\nPavlovic V B and Aleksic O 2011 Analysis and modeling\nof sintering of Sr-hexaferrite produced by PIM technology\nSci. Sinter. 439–20\n[81]Drummer D and Messingschlager S 2014 Material\ncharacterization of strontium ferrite powders for\nproducing sintered magnets by ceramic injection molding\n(magnetPIM) Adv. Mater. Sci. Eng. 20141–8\n[82]Averback R S, Höfler H J, Hahn H and Logas J C 1992\nSintering and grain growth in nanocrystalline ceramics\nNanostruct. Mater. 1173–8\n[83]Saptono R 2012 Solid state sintering of nanostructured\nceramics Proc. Eng. 50369–80\n[84]Bansal N P and Boccaccini A R 2012 Ceramics and\nComposites Processing Methods ed N P Bansal and\nA R Boccaccini (Hoboken, NJ: Wiley) ( https://doi.org/\n10.1002/9781118176665 )\n[85]Kato Y and Takei T 1932 Production Method of Magnetic\nCore Mainly Made of Metal Oxides 98844\n[86]Mahmood S and Abu-Aljarayesh I 2016 Hexaferrite\nPermanent Magnetic Materials vol 4 Materials Research\nFoundation (Millersville, PA: Materials Research Forum\nLLC) (https://doi.org/10.21741/9781945291074 )\n[87]IMA - Ingeniería Magnética Aplicada S.L.U. Ferrite Magnets\n(available at: www.imamagnets.com/en/ferrite-magnets/ )\n(Accessed 6 May 2021)\n[88]BUNTING Magnetics Group Grades of ferrite (available at:\nhttps://e-magnetsuk.com/ferrite-magnets/grades-of-\nferrite/) (Accessed 6 May 2021)\n[89]ITALFIT MAGNETI S.R.L. Ferrite Discs (available at:\nwww.italfitmagneti.com/products/ferrite-permanent-\nmagnet-alnico-smco/ferrite-discs ) (Accessed 6 May 2021)\n[90]Eclipse Magnetics Ltd Ferrite Magnets/Ceramic Magnets\nDatasheet (available at: https://www.eclipsemagnetics.\ncom/site/assets/files/2418/ferrite_ceramic_\ndatasheet.pdf ) (Accessed 6 May 2021)\n[91]TDK Corporation Ferrite magnets (available at: https://\nproduct.tdk.com/info/en/catalog/datasheets/\nmagnet_fb_summary_en.pdf ) (Accessed 6 May 2021)\n[92]Hitachi Metals, Ltd Ferrite Magnets ( https://www.hitachi-\nmetals.co.jp/e/products/auto/el/p03_05.html ) (Accessed 6\nMay 2021)\n[93]Stuijts A L, Rathenau G W and Weber G H 1954 Ferroxdure\nII and III, anisotropic permanent-magnet materials Philips\nTech. Rev. 16141–7\n[94]Ghate B B and Goldman A 2006 Ferrimagnetic ceramics\nMaterials Science and Technology (New York: Wiley)\n681–706\n[95]Chen I W and Wang X H 2000 Sintering dense\nnanocrystalline ceramics without final-stage grain growth\nNature 404168–71\n[96]Groza J R 1999 Nanosintering Nanostruct. Mater.\n12987–92\n12J. Phys. D: Appl. Phys. 54(2021) 303001 Topical Review\n[97]Kools F 1985 The action of a silica additive during sintering\nof strontium hexaferrite part I: preparation and\nexamination of sintered materials, the chemical action of\nsilica, grain growth inhibition by precipitate drag Sci.\nSinter. 1749–62\n[98]Kools F 1985 Reaction-induced grain growth impediment\nduring sintering of strontium hexaferrite with silica\naddition Solid State Ion. 16251–9\n[99]Beseni ˇcar S and Drofenik M 1991 High coercivity Sr\nhexaferrites J. Magn. Magn. Mater. 101307–9\n[100]Kobayashi Y, Hosokawa S and Oda E 2013 Sintered ferrite\nmagnet and its production method EP 2 881 956 B1\n[101]Lee J W, Cho Y S and Amarakoon V R W 1999\nImproved magnetic properties and growth anisotropy of\nchemically modified Sr ferrites J. Appl. Phys.\n855696–8\n[102]Töpfer J, Schwarzer S, Senz S and Hesse D 2005 Influence of\nSiO2and CaO additions on the microstructure and\nmagnetic properties of sintered Sr-hexaferrite J. Eur.\nCeram. Soc. 251681–8\n[103]Kanagesan S, Jesurani S, Sivakumar M, Thirupathi C and\nKalaivani T 2011 Effect of microwave calcinations on\nbarium hexaferrite synthesized via sol-gel combustion J.\nSci. Res. 3451–6\n[104]Dong S, Lin C and Meng X 2019 One-pot synthesis and\nmicrowave absorbing properties of ultrathin SrFe 12O19\nnanosheets J. Alloys Compd. 783779–84\n[105]Binner J G P, Caro I and Firkins J 1999 Microwave sintering\nof nanometer and micrometer ferrite powders J. Microw.\nPower Electromagn. Energy 34131–6\n[106]Yang Q, Zhang H, Liu Y and Wen Q 2009 Microstructure\nand magnetic properties of microwave sintered M-type\nbarium ferrite for application in LTCC devices Mater. Lett.\n63406–8\n[107]Obara G, Yamamoto H, Tani M and Tokita M 2002 Magnetic\nproperties of spark plasma sintering magnets using fine\npowders prepared by mechanical compounding method J.\nMagn. Magn. Mater. 239464–7\n[108]Munir Z A, Anselmi-Tamburini U and Ohyanagi M\n2006 The effect of electric field and pressure on the\nsynthesis and consolidation of materials: a review of the\nspark plasma sintering method J. Mater. Sci.\n41763–77\n[109]Kirchner R FAST—field assisted sintering technology basics,\nstate of the art and future aspects presentation at Technical\nUniversity (TU) of Darmstadt International Spring School\non Field Assisted Sintering Technique (https://\nwww.mawi.tu-darmstadt.de/media/fast/vortrge_2/\n07_Kirchner_FCT_Systeme_-_Progress_in_\nFAST_equipments.pdf ) (20–26 March 2011)\n[110]Zhao W Y, Zhang Q J, Tang X F, Cheng H B and Zhai P C\n2006 Nanostructural M-type barium hexaferritesynthesized by spark plasma sintering method J. Appl.\nPhys. 9908E909\n[111]Christensen M, Saura-M ´uzquiz M and Stingaciu M\n2015 A permanent magnetic material WO2015000491\n[112]Eikeland A Z, Stingaciu M, Granados-Miralles C,\nSaura-M ´uzquiz M, Andersen H L and Christensen M 2017\nEnhancement of magnetic properties by spark plasma\nsintering of hydrothermally synthesised SrFe 12O19\nCrystEngComm 191400–7\n[113]Saura-M ´uzquiz M, Granados-Miralles C, Andersen H L,\nStingaciu M, Avdeev M and Christensen M 2018\nNanoengineered high-performance hexaferrite magnets by\nmorphology-induced alignment of tailored nanoplatelets\nACS Appl. Nano Mater. 16938–49\n[114]Stingaciu M, Eikeland A Z, Gjørup F H, Deledda S and\nChristensen M 2019 Optimization of magnetic properties\nin fast consolidated SrFe 12O19nanocrystallites RSC Adv.\n912968–76\n[115]Jenuš P, Topole M, McGuiness P, Granados-Miralles C,\nStingaciu M, Christensen M, Kobe S and Žužek\nRožman K 2016 Ferrite-based exchange-coupled hard-soft\nmagnets fabricated by spark plasma sintering J. Am.\nCeram. Soc. 991927–34\n[116]Granados-Miralles C, Saura-M ´uzquiz M, Stingaciu M,\nAndersen H L and Christensen M Monitoring the\nconsolidation of anisotropic SrFe 12O19nanoparticles\nin a DAC using in situpowder diffraction (in\npreparation)\n[117]Guo J, Guo H, Baker A L, Lanagan M T, Kupp E R,\nMessing G L and Randall C A 2016 Cold sintering: a\nparadigm shift for processing and integration of ceramics\nAngew. Chem., Int. Ed. 5511457–61\n[118]Grasso S, Biesuz M, Zoli L, Taveri G, Duff A I, Ke D,\nJiang A and Reece M J A 2020 Review of cold sintering\nprocesses Adv. Appl. Ceram. 119115–43\n[119]Yu M, Grasso S, Mckinnon R, Saunders T and Reece M J\n2017 Review of flash sintering: materials, mechanisms and\nmodelling Adv. Appl. Ceram. 11624–60\n[120]Biesuz M and Sglavo V M 2019 Flash sintering of ceramics\nJ. Eur. Ceram. Soc. 39115–43\n[121]Muche D N F, Drazin J W, Mardinly J, Dey S and\nCastro R H R 2017 Colossal grain boundary strengthening\nin ultrafine nanocrystalline oxides Mater. Lett.\n186298–300\n[122]De Beauvoir T H, Sangregorio A, Cornu I, Elissalde C and\nJosse M 2018 Cool-SPS: an opportunity for low\ntemperature sintering of thermodynamically fragile\nmaterials J. Mater. Chem. C62229–33\n[123]European Comission A European Green Deal: Striving to be\nthe first climate-neutral continent (available at: https://\nec.europa.eu/info/strategy/priorities-2019-2024/european-\ngreen-deal_en ) (Accessed 6 May 2021)\n13"    },    {        "title": "1611.02225v2.Second_order_perturbed_Heisenberg_Hamiltonian_of_Fe3O4_ultra_thin_films.pdf",        "content": " \n1 \n Second order perturbed Heisenberg Hamiltonian of Fe 3O4 ultra-thin films \nP. Samarasekara \nDepartment of Physics, University of Peradeniya, Pe radeniya, Sri Lanka \n \nAbstract \nDue to the wide range of applications, theoretical models of Fe 3O4 films are found to be \nimportant. Ultra thin Fe 3O4 films with ferrite structure have been theoretical ly investigated using \nsecond order perturbed modified Heisenberg Hamilton ian. Matrices for ultra thin films with two \nand three spin layers are presented in this manuscr ipt. Total magnetic energy was expressed in \nterms of spin exchange interaction, magnetic dipole  interaction, second order magnetic \nanisotropy and stress induced magnetic anisotropy. Magnetic properties were observed for films \nwith two spin layers and variant second order magne tic anisotropy. For the film with three spin \nlayers, second order anisotropy constant was fixed to avoid tedious derivations. Magnetic easy \naxis rotates toward the in plane direction as the n umber of spin layers is increased from two to \nthree because the stress induced anisotropy energy dominates at higher number of spin layers. \nAccording to some other experimental data, the magn etic easy axis of thin films rotates toward \nthe in plane direction as the thickness is increase d. For ferrite film with two spin layers, magnetic \neasy and hard directions can be observed at 0.75 an d 1.2 radians, respectively, when the ratio of \nstress induced anisotropy to the long range dipole interaction strength is 3.9. For ferrite film with \nthree spin layers, magnetic easy and hard direction s can be observed at 2.4 and 2.3 radians, \nrespectively, when the ratio of stress induced anis otropy to the long range dipole interaction \nstrength is 4.2. \nKeywords:  Heisenberg Hamiltonian, spinel ferrites, Fe 3O4, ultra thin films, easy direction  \n2 \n 1. Introduction: \nMagnetite (Fe 3O4) and maghemite ( γFe 2O3) are the most popular natural oxides. Fe 3O4 finds \npotential applications in magnetic storage, industr ial catalysts, water purification and drug \ndelivery. Fe 3O4 is a ferrite with inverse spinel structure. Spinel  structure with tetrahedral and \noctahedral sites can be found in detail in some pre vious publications [1, 2, 3, 4, 5]. Five of Fe 3+  \nions occupy tetrahedral sites. Other five Fe 3+  ions and four Fe 2+  ions occupy octahedral sites. \nBecause magnetic moments of Fe 3+  in tetrahedral and octahedral sites cancel each ot her, the net \nmagnetic moment of Fe 3O4 is completely due to the magnetic moments of four Fe 2+  ions. \nTherefore, the theoretical net magnetic moment of F e 3O4 is 4 Bohr magnetons. However, \nexperimental value of net magnetic moment is approx imately 4.1 Bohr magnetons. The spinel \nstructure of this ferrite is represented by Fe 3+( Fe 2+ Fe 3+) O4. The magnetic moments of Fe 2+  and \nFe 3+  are 4 µB and 5 µB, respectively.  \nCation distribution of ferrite like compounds has b een found using Rietveld method [1, 2]. \nSurface spin waves in CsCl type ferrimagnet with a (001) surface has been studied by combining \nGreen function theory with the transfer matrix meth od [6]. Anisotropy of ultrathin ferromagnetic \nfilms and the spin reorientation transition have be en investigated using Heisenberg Hamiltonian \nwith few terms [7]. In addition, the surface magnet ism of ferrimagnet thin films has been studied \nusing Heisenberg method [8]. The surface spin wave spectra of both the simple cubic and body \ncentered ferrimagnets have been theoretically studi ed using Heisenberg Hamiltonian [9]. The \ncation distribution and oxidation state of Mn-Fe sp inel nanoparticles have been systematically \nstudied at various temperatures by using neutron di ffraction and electron energy loss \nspectroscopy [4]. The crystal structure of spinel t ype compounds has been found using single \ncrystal X-ray diffraction data [3]. The lattice par ameter, anion parameter and the cation inversion  \n3 \n parameter of spinel structures have been presented [5]. Surface spin waves on the (001) free \nsurface of semi-infinite two lattice ferrimagnets o n the Heisenberg model with nearest neighbor \nexchange interactions has been investigated [10].    \nFerromagnetic ultra-thin and thick films have been investigated using second order perturbed \nHeisenberg Hamiltonian by us [11]. Previously ferro magnetic ultra thin and thick films have \nbeen studied using third order perturbed Heisenberg  Hamiltonian [12, 13].  Furthermore, ferrite \nultra-thin and thick films have been investigated u sing second order perturbed Heisenberg \nHamiltonian by us [14, 15]. Ferrite ultra-thin and thick films have been investigated using third \norder perturbed Heisenberg Hamiltonian [16, 17]. In  this manuscript, the spinel structure of \nFe 3O4 was used to find the magnetic properties of Fe 3O4 ultra thin films.      \n2. Model: \nClassical Heisenberg Hamiltonian of a thin film can  be written as following. \nH= -∑ ∑∑ − − +\n≠ n m mz\nm\nn mmn n mn mn m\nmn n m\nn m S D\nrSrrS\nrSSSSJ\nm\n,2 ) 2 (\n5 3 )( )).)( .( 3 .( .λ ωrrrrrrrr\n  \n            ∑−\nmm sSin K θ2                                                                                                                                        (1)  \n            Here J,  ω, θ,  ,,) 2 (\ns mK D  m, n and N are  spin exchange interaction, strengt h of long range \ndipole interaction, azimuthal angle of spin, second  order anisotropy constant, stress induced \nanisotropy constant, spin plane indices and total n umber of spin layers in film, respectively. \nWhen the stress applies normal to the film plane, t he angle between m th  spin and the stress is θm.   \n4 \n             The cubic cell was divided into 8 spin layers with alternative Fe 2+  and Fe 3+  spins layers \n(Sickafus et al. 1999). The spins of Fe 2+  and Fe 3+  will be taken as 1 and p, respectively. While \nthe spins in one layer point in one direction, spin s in adjacent layers point in opposite directions. \nA thin film with (001) spinel cubic cell orientatio n will be considered. The length of one side of \nunit cell will be taken as “a”. Within the cell the  spins orient in one direction due to the super \nexchange interaction between spins (or magnetic mom ents). Therefore, the results proven for \noriented case in one of our early report [15] will be used for following equations. But the angle  θ \nwill vary from  θm to  θm+1  at the interface between two cells.   \nFor a thin film with thickness Na, \nSpin exchange interaction energy=E exchange = N(-10J+72Jp-22Jp 2)+8Jp ∑−\n=+−1\n11 ) cos( N\nmm m θ θ  \nDipole interaction energy=E dipole  \n∑ ∑\n=−\n=+ + + + − + + −=N\nmN\nmm m m m m dipole p E\n11\n11 1 )] cos( 3) [cos( 41 . 20 )2cos 31 ( 415 . 48 θ θ θ θ ω θ ω  \nHere the first and second term in each above equati on represent the variation of energy within \nthe cell and the interface of the cell, respectivel y.  \nTotal energy  \nE= N(-10J+72Jp-22Jp 2)+8Jp ∑−\n=+−1\n11 ) cos( N\nmm m θ θ  \n      ∑ ∑\n=−\n=+ + + + − + + −N\nmN\nmm m m m m p\n11\n11 1 )] cos( 3) [cos( 41 . 20 )2cos 31 ( 415 . 48 θ θ θ θ ω θ ω   \n5 \n        ∑\n=−N\nmm mD\n12 ) 2 (] cos [ θ∑\n=− −N\nmm sK p\n1]2sin [) 1 ( 4 θ                                                            (2)  \nHere the anisotropy energy term and the last term h ave been explained in our previous report for \noriented spinel ferrite [15]. If the angle is given  by θm=θ+εm with perturbation  εm, after taking \nthe terms up to second order perturbation of ε only , \nThe total energy can be given as E( θ)=E 0+E( ε)+E( ε2) \nHere \nE0= -10JN+72pNJ-22Jp 2N+8Jp(N-1)-48. 415ωΝ -145.245ωΝ cos(2 θ) \n      +20.41 ωp[(N-1)+3(N-1)cos(2 θ) ] θ θ 2sin ) 1 ( 4 cos \n1) 2 ( 2\nsN\nmm NK p D − − −∑\n=                   (3)   \n∑ ∑−\n= =+ − =1\n1 1) ()2sin( 23 . 61 )2sin( 5 .290 ) (N\nmn mN\nmm p E ε ε θ ω ε θ ω ε  \n         ∑\n=+N\nmm mD\n1) 2 (2sin ε θ ∑\n=− −N\nmm sKp\n12cos ) 1 ( 8 εθ                                                            (4)  \n∑ ∑ ∑−\n= =−\n=− − + − −=1\n1 121\n12 2 2) ( 2 . 10 )2cos( 5 .290 ) ( 4 )(N\nmN\nmmN\nmn m m n p Jp E ε ε ω ε θ ω ε ε ε  \n           ∑−\n=+ −1\n12) ()2cos( 6 . 30 N\nmm n p ε ε θ ω  ∑\n=− −N\nmm mD\n12 ) 2 ( 2 2) cos (sin ε θ θ  \n             )[ 1(8 p− + ] 2sin \n12∑\n=N\nmm sK εθ                                                                                    (5)   \n6 \n The sin and cosine terms in equation number 2 have been expanded to obtain above equations. \nHere n=m+1. \nUnder the constraint ∑\n==N\nmm\n10 ε , first and last terms of equation 4 are zero.  \nTherefore, E (ε)= εαrr. \nHere θ θ εα 2sin ) ( ) (Brr=  are the terms of matrices with \n) 2 (46 .122 )(λ λ ω θ Dp B + −=                                                                                                   (6)  \nAlso εε εrr. .21)(2C E = , and matrix C is assumed to be symmetric (C mn =C nm ). \nHere the elements of matrix C can be given as follo wing, \nCm, m+1 =8Jp+20.4 ωp-61.2p ωcos(2 θ) \nFor m=1 and N,  \nCmm = -8Jp-20.4 ωp-61.2p ωcos(2 θ)+581 ωcos(2 θ) ) cos (sin 22 2θ θ− −) 2 (\nmD  \n      )] 2sin( )[ 1 (16 θsKp− +                                                                                             (7)  \nFor m=2, 3, ----, N-1 \nCmm = -16Jp-40.8 ωp-122.4p ωcos(2 θ)+581 ωcos(2 θ) ) cos (sin 22 2θ θ− −) 2 (\nmD  \n      )] 2sin( )[ 1 (16 θsKp− +     \n7 \n Otherwise, C mn =0 \nTherefore, the total energy can be given as \nE( θ)=E 0+εαrr.+ εεrr. .21C=E 0 α αrr..21+− C                                                                                 (8)  \nHere C + is the pseudo-inverse given by \nNECC −=+1 . .                                                                                                                       (9)  \nHere E is the matrix with all elements E mn =1.  \n \n \n3. Results and discussion: \nA film with two spin layers (N=2) will be considere d first. If the anisotropy constants vary \nwithin the film, then C 12 =C 21  and 22 11 C C≠ .   \nThen \n) ( 22\n21 22 11 21 22 12 11 \nC CCC CC C\n−+= −=+ + and  \n) ( 222 11 2\n21 11 21 22 21 \nCC CC CC C\n−+= −=+ +. \nHence,  ) ( ) ( ..112 221 2 1 α α α α α α+ + +− − = C C Crr  \nThen   \nC11 = -8Jp-20.4 ωp-61.2p ωcos(2 θ)+581 ωcos(2 θ) )2(cos 2 θ +) 2 (\n1D +16(1-p)K ssin(2 θ) \nC22 = -8Jp-20.4 ωp-61.2p ωcos(2 θ)+581 ωcos(2 θ) ) 2(cos 2 θ +) 2 (\n2D +16(1-p)K ssin(2 θ)  \n8 \n C12 =8Jp+20.4 ωp-61.2p ωcos(2 θ) \nα1=[-122.46 ωp+D 1(2) ]sin(2 θ) \nα2=[-122.46 ωp+D 2(2) ]sin(2 θ) \nE( θ)=E 0-2) ( ) (112 221 2 1 α α α α+ +− − C C \n E0= -20J+144pJ-44Jp 2+8Jp-96.83 ω-290.5 ωcos(2 θ)+20.41 ωp[1+3cos(2 θ) ] \n      ] [ cos ) 2 (\n2) 2 (\n12D D + − θ -4(1-p)NK ssin(2 θ) \nHere D 1(2) and D 2(2)  were taken as the anisotropy constants of first an d second spin layers of the \nFe 3O4 film, respectively.  \nBecause the magnetic moments of Fe 2+  and Fe 3+  are 4 µB and 5 µB, respectively, \np=5/4=1.25. \nThen \nC11 = -10J-25.5 ω+504.5ω cos(2 θ) )2(cos 2 θ +) 2 (\n1D -4K ssin(2 θ) \nC22 = -10J-25.5 ω+504.5 ωcos(2 θ) ) 2(cos 2 θ +) 2 (\n2D -4K ssin(2 θ) \nC12 =10J+25.5 ω-76.5 ωcos(2 θ) \nE0= 101.25J-71.32 ω-214 ωcos(2 θ) ] [ cos ) 2 (\n2) 2 (\n12D D + − θ +2K ssin(2 θ)  \n9 \n Figure 1 shows the 3-D plot of ωθ) (E versus θ and  ωsK, for 5 ,10 ) 2 (\n2) 2 (\n1= = =ω ω ωD DJ. Minima \nof this 3-D plot can be observed at ωsK=2.9, 3.9, 7, ------ etc. Maxima of this 3-D plot ca n be \nobserved at 1.9, 4.0, 4.9, ------- etc. According t o this graph, film can be easily oriented in some \nparticular directions by applying a stress. The tot al energy of this ferrite ultra thin film is much \nsmaller than the total energy of thick ferromagneti c films implying that total energy increases \nwith the number of spin layers [12]. However, this graph is similar to the 3-D graph of ωθ) (E \nversus θ and  ωsK obtained for nickel ferrite [15]. Figure 2 shows th e graph of ωθ) (E versus angle \nfor ωsK=3.9. One minimum and a consecutive maximum of this  graph can be observed at 0.75 \nand 1.2 radians, respectively. Energy minima and ma xima correspond to magnetic easy and hard \ndirections, respectively. Changing the value of ωsK didn’t change this graph of energy versus \nangle considerably. In addition, several less space d peaks can be observed in this case compared \nto thick ferromagnetic films [12]. However, the spi kes observed in energy versus angle graph of \nthin ferromagnetic films with two layers don’t appe ar in this graph [13].  \n10 \n 0246810 \n0510 -2 -1 012x 10 9\nKs/ ωangle θ(radians) E( θ)/ ω\n \n  \nFigure 1: 3-D plot of energy versus angle and stres s induced anisotropy for N=2.  \n11 \n 0 1 2 3 4 5 6 7-2 -1 01234x 10 8\nangle θ(radians) E( θ)/ ω\n \nFigure 2: Graph of energy versus angle for ωsK=3.9 and N=2.    \nFor N=3, the each C +\nnm  element found using equation 9 is consist of more than 20 terms. To \navoid this problem, matrix elements were found usin g C.C +=1. Then C +\nmn  is given by  \nCcofactorC Cnm mn det =+. Under this condition, 0 .=αrr\nE , and the average value of first order \nperturbation is zero. The second order anisotropy c onstant is assumed to be an invariant for the \nconvenience.      \nThen C 11 =C 33 , C 12 =C 21 =C 23 =C 32 , C 13 =C 31 =0, α1=α2=α3. \nC11 =C 33 = -10J-25.5 ω+504.5ω cos(2 θ) )2(cos 2 θ +) 2 (\nmD -4K ssin(2 θ)  \n12 \n C22 = -20J-51 ω+428ω cos(2 θ) ) 2(cos 2 θ +) 2 (\nmD -4K ssin(2 θ) \nTherefore, 33 \n11 2\n32 22 2\n11 2\n32 22 11 11 \n2+ +=\n−−= C\nCC CCC CCC , 31 \n11 2\n32 22 2\n11 2\n32 13 \n2+ +=\n−= C\nCC CCCC  \n32 23 21 \n11 2\n32 22 2\n11 11 32 12 \n2+ + + += = =\n−−= C C C\nCC CCCCC ,\n11 2\n32 22 2\n11 2\n11 22 \n2 CC CCCC\n−=+ \nThe total energy can be found using the following e quation. \nE( θ)=E 0-0.5[C +\n11 (2 α12)+C +\n32 (4α 12)+C +\n31 (2α 12)+ α12C+\n22 ]  \nHere E 0= 156.875J-94.22 ω-282.66 ωcos(2 θ) ] [ cos ) 2 (\n3) 2 (\n2) 2 (\n12D D D + + − θ  +3K ssin(2 θ) \nFigure 3 shows the 3-D plot of ωθ) (E versus θ and  ωsK, for 10 ) 2 (\n= =ω ωmDJ. Maxima of this \ngraph can be observed at ωsK=5.2, 8.2, ---- etc. Minima of the graphs can be ob served at \nωsK=4.2, 6.2, 8.2, -----etc. The total energy of ferri te thin films with three layers obtained using \nthird order perturbation is comparable to the total  energy in this case [16]. The total energy of \nthick ferrite films obtained using third order pert urbed Heisenberg Hamiltonian is higher than \nthat of this ultra thin ferrite film [17]. Figure 4  shows the graph of ωθ) (E versus angle for \nωsK=4.2. Nearest maxima and minima of this graph can b e observed at 2.3 and 2.4 radians, \nrespectively. In this case, the magnetic hard and e asy directions are 2.3 and 2.4, respectively. The  \n13 \n position of minima and maxima of these graphs don’t  change considerably with ωsK. The shape \nof energy versus angle graph of ferrite thin films with three layers obtained using third order \nperturbation is different from the same graph in th is case [16]. Some spikes observed in energy \nversus angle graph of ferromagnetic films with five  layers don’t appear in this graph. According \nto our previous experimental data of ferrite thin f ilms, the coercivity and the magnetic anisotropy \ndepend on the stress of the film [18]. \n0246810 \n0510 500 1000 1500 2000 2500 3000 \nKs/ ωangle θ(radians) E( θ)/ ω\n \nFigure 3: 3-D plot of energy versus angle and stres s induced anisotropy for N=3. \n \n  \n14 \n 0 1 2 3 4 5 6 7-3000 -2000 -1000 01000 2000 3000 4000 5000 6000 \nangle θ(radians) E( θ)/ ω\n \nFigure 4: Graph of energy versus angle for ωsK=4.2 and N=3.    \nAccording to figures 2 and 4, the first magnetic ea sy direction can be observed at 0.25 and 0.75 \nradians for two and three spin layers, respectively . Therefore, the magnetic easy axis rotates \ntoward the in plane direction as the number of laye rs is increased. According to the equation of \ntotal energy, only the E 0 term depends on the number of layers (N). Only ter m with N is the \nstress induced anisotropy. Because 1-p is negative for most of the spinel ferrites, the energy of \nstress induced anisotropy increases with the number  of layers. As the thickness is increased, \nstress induced anisotropy dominates spin exchange i nteraction, second order magnetic anisotropy \nand magnetic dipole interaction. The domination of stress induced anisotropy is the possible \nreason for the rotation of easy direction with the number of layers. The same phenomenon was  \n15 \n observed for thick ferromagnetic films using second  order and third order perturbed Heisenberg \nHamiltonian by us. According to some experimental d ata, the easy axis of magnetic thin films \nrotates toward the in plane direction, as the numbe r if layers is increased [19, 20]. In addition, the  \nmagnetic easy direction of thin films depends on th e deposition temperature. The variation of \neasy axis with deposition temperature can be explai ned using spin reorientation coupled with \nHeisenberg Hamiltonian [11, 21, 22].                 \n4. Conclusion: \nTotal magnetic energy, magnetic easy direction and magnetic hard direction were determined for \nfilms with two and three spin layers by plotting 3- D graphs of energy versus stress induced \nanisotropy and angle, and graphs of energy versus a ngle. Minimum of energy of 3-D plot can be \nobserved at several values of stress induced anisot ropy. For two spin layers, consecutive \nminimum and maximum can be observed at 0.75 and 1.2  radians, respectively for ωsK=3.9. For \nthree spin layers, consecutive minimum and maximum can be observed at 2.4 and 2.3 radians, \nrespectively for ωsK=4.2. According to the first minima of 2-D plots of  two and three layers, the \nmagnetic easy axis gradually rotates toward the in plane direction of the film as the number of \nspin layers is increased. The possible reason for t he rotation of magnetic easy axis is the \ndomination of stress induced magnetic anisotropy. T his theoretical data qualitatively agree with \nsome experimental data of magnetic thin films.  \n  \n16 \n References: \n1. I. S. Ahmed Farag, M. A. Ahmed, S.M. Hammad and A.M. Moustafa (2001). Study of cation   \n       distribution in Cu 0.7 (Zn 0.3-xMg x)Fe 1.7 Al 0.3 O4 by X-ray diffraction using Rietveld method.   \n       Egyptian Journal of Solids  24(2) : 215-225. \n2. I. S. Ahmed Farag, M.A. Ahmed, S.M. Hammad and A .M. Moustafa (2001). Application of  \n       Rietveld method to the structural characteri stics of substituted copper ferrite compounds.   \n       Crystal Research & Technology  36(1) : 85-92. \n3. V. Kahlenberg, C.S.J. Shaw and J.B. Parise (2001 ). Crystal structure analysis of synthetic Ca 4 \n            Fe 1.5 Al 17.67  O32 : A high-pressure, spinel-related phase. American Mineralogist  86 : 1477-  \n       1482.  \n4. Z. John Zhang, L. Zhong Wang, Bryan C. Chakoumak os and Jin S. Yin. (1998). Temperature  \n      dependence of cation distribution and oxidati on state in magnetic Mn-Fe ferrite   \n      nanocrystals.   Journal of the American Chemical Society  120(8):  1800-1804.  \n5. E. Sickafus Kurt, John M. Wills and Norman W. Gr imes. (1999). Structure of spinel. Journal  \n    of  the American Ceramic Society  82(12) : 3279-3292.  \n6. S.T. Dai and Z.Y. Li (1990). Surface spin waves in a semi-infinite ferrimagnet. Physics Letters  \n    A 146 : 450-456.  \n7. K.D. Usadel and A. Hucht (2002). Anisotropy of u ltrathin ferromagnetic films and the spin   \n    reorientation transition. Physical Review B  66 : 024419. \n8. Ding Ze-Nong, D.L. Lin and Libin Lin (1993). Sur face magnetism in a thin film of   \n    Heisenberg Ferrimagntes. Chinese Journal of Physics  31(3) : 431-440.  \n17 \n 9. D.H. Hung, I. Harada and O. Nagai (1975). Theory  of surface spin-waves in a semi-infinite   \n       ferrimagnet. Physics Letters A  53(2) : 157-158. \n10. H. Zheng and D.L. Lin (1988). Surface spin wave s of semi-infinite two sublattice   \n      ferrimagnets. Physical Review B  37(16):  9615-9624.   \n11. P. Samarasekara and N.H.P.M. Gunawardhane (2011 ). Explanation of easy axis orientation    \n     of ferromagnetic films using Heisenberg Hamilt onian. Georgian electronic scientific  \n     journals: Physics  2(6) : 62-69. \n12. P. Samarasekara (2008). Influence of third orde r perturbation on Heisenberg Hamiltonian of  \n      thick ferromagnetic films. Electronic Journal of Theoretical Physics  5(17):  227-236. \n13. P. Samarasekara and William A. Mendoza (2010). Effect of third order perturbation on    \n      Heisenberg Hamiltonian for non-oriented ultra -thin ferromagnetic films. Electronic Journal  \n      of Theoretical Physics  7(24) : 197-210. \n14. P. Samarasekara (2010). Determination of Energy  of thick spinel ferrite films using   \n      Heisenberg Hamiltonian with second order pert urbation” Georgian electronic scientific  \n      journals: Physics  1(3) , 46-52. \n15. P. Samarasekara, M.K. Abeyratne and S. Dehipawa lage (2009). Heisenberg Hamiltonian    \n      with Second Order Perturbation for Spinel Fer rite Thin Films. Electronic Journal of  \n     Theoretical Physics  6(20):  345-356. \n \n  \n18 \n 16. P. Samarasekara and William A. Mendoza (2011). Third Order Perturbed Heisenberg   \n      Hamiltonian of Spinel Ferrite Ultra-thin film s.  Georgian Electronic Scientific Journals:    \n      Physics  1(5) : 15-24. \n17. P. Samarasekara (2011). Investigation of Third Order Perturbed Heisenberg Hamiltonian of   \n      Thick Spinel Ferrite Films. Inventi Rapid: Algorithm Journal  2(1) : 1-3. \n18. P. Samarasekara and F.J. Cadieu (2001). Polycry stalline Ni ferrite films deposited by RF  \n      sputtering techniques. Japanese Journal of Applied Physics  40 , 3176-3179.  \n19. J. Araya-Pochet, C.A. Ballentine and J.L. Erski ne (1988). Thickness and temperature   \n     dependent spin anisotropy of ultrathin epitaxi al Fe films on Ag(100). Physical Review B    \n     38(11) : 7846-7849 \n20. U. Parlak, M.E. Akoz, S. Tokdemir Ozturk and M.  Erkovan (2015). Thickness dependent   \n         magnetic properties of polycrystalline nic kel thin films. Acta Physica Polonica  A 127(4) :   \n        995-997.  \n21. P. Samarasekara and Udara Saparamadu (2012). In vestigation of Spin Reorientation \n      in Nickel Ferrite Films. Georgian electronic scientific journals: Physics  1(7):  15-20.  \n22. P. Samarasekara and Udara Saparamadu (2013). In  plane oriented Strontium   \n      ferrite thin films described by spin reorient ation.  Research & Reviews: Journal  \n      of Physics-STM journals  2(2) : 12-16. \n  "    },    {        "title": "1910.10948v1.Zero_Field_Cooled_Exchange_Bias_Effect_in_Nano_Crystalline_Mg_Ferrite_Thin_Film.pdf",        "content": "1 \n Zero Field Cooled Exchange Bias Effect in Nano -Crystalline Mg -Ferrite \nThin Film  \n \nHimadri Roy Dakua  \nDepartment of physics, Indian Institute of Technology Bombay, Mumbai, India 400076  \nEmail: hroy89d@gmail.com   \n \n \nAbstract  \nI report, Zero Field Cooled (ZFC) E xchange  Bias (EB) effect in a single phase  nanocrystalline \nMg-ferrite thin film , deposited on an amorphous quartz substrate using pulsed laser ablation \ntechnique. The film show ed a high ZFC EB shift (HE~ 190 Oe) at 5 K. The ZFC EB  shift \ndecreased  with increasing  tempera ture and disappeared  at higher temperature s (T > 70 K). This \nMg-ferrite thin film also showed  Conventional Exchange Bias (CEB)  effect, but unlike many \nCEB systems, the  film showed decrease in the co ercivity (H C) under  the Field Cooled (FC) \nmeasurements. The film also showed training effect in ZFC measurements  which followed the \nfrozen spin relaxation  behaviour . The observed exchange bias could be attributed to the pinning \neffect of the surface spins of frozen glassy states at the interface of large ferrimagnetic grains.  \n \nI. Introduction  \nMeiklejohn and Bean  discovered the Exchange Bias  (EB)  effect  in the Ferromagnetic (FM) \nCo and A ntiferromagnetic (AFM) CoO core-shell heterostructures .1 The exchange bias effect \nwas characterized by a horizontally (along the field axis) off -centred M -H loop of the Field \nCooled (FC) core -shell heterostructure.  Since then, a  lot of research have  been carried out  on \ndifferent  exchange bias systems due to their applicability in many magnetic devices  such as \ndata storage device s, spin valve devices and  voltage control magnetic devices etc .2-6  \nApart from these  Conventional Exchange Bias (CEB) systems , Wang et al.  reported an \nunusual exchange bias effect in the Ni 50Mn 50-xInx (x = 11 -15) bulk Heusler alloys  in 2011 .7 \nHere, unlike the CEB systems, the sample  showed a large shift in the M -H loops even in the \nZero F ield Cooled (ZFC) measurements . Subsequently, Nayak et al. also reported ZFC \nExchange Bias (EB) effect in bulk Heusler alloy Mn 2PtGa .8 Recently, some other groups also 2 \n reported ZFC EB effect in few more  bulk materials .9-11 All these studies had broadly pointed \nout that a unidirectional anisotropy is introduced  to the system  during the initial magnetization \nprocess.  While, the microscopic origin of the ZFC EB effect is not yet fully understood.  \nThis paper focuses on  the exchange bias  effect in Mg -ferrite nanocrystalline thin film.  The \ncubic spinel ferrites such as Mg, Ni, Mn –ferrites are well known magnetic materials for the \nhigh frequency applications.12, 13 The ferrimagnetic ordering in these ferrite systems is mainly  \ndue to the anti -parallel alignment of cation spins at  the tetrahedral (A) and the octahedral (B)  \nsites. The chemical formula of these cubic spinel ferrites is expressed as (M 1-xFex)A(MxFe2-\nx)BO4 based on their cation occupancy .14 In Mg -ferrite bulk sample, a (x  = ~ 0.89) faction of \nFe3+ ions occupy the A sites while other (2 -x) in the B sites and this leads to the ferrimagnetic \nordering in it.14, 15 However, i t is to be noted that the se single phase bulk spinel ferrite s \n(MFe 2O4, M = Mg, Mn, Co, Ni) do not show exchange bias effect. Though , there are few \nreports on  conventional exchange bias effect  in thin film s of some ferrites . Like, Venzke et \nal.16 observed the CEB effect in as deposited Ni -ferrite thin films. Alaan et al. also reported \nexchange bias effect in MnZn  - ferrite thin films .17, 18 While in case of Mg -ferrite thin films,  \nsome inconsistent  and self-contradicting  data on exchange bias effect were  also reported \nearlier .19, 20 Therefore, the details and true behaviour of the exchange bias effect in Mg -ferrite \nthin films a re still unknown. Here,  I have presented the detail study of the exchange effect in \nMg-ferrite thin film. The data presented in this paper, shows some distinguishably deferent \nfeatures compared to the CEB effect. These features are compared with the other exchange bias  \nsystems a nd discussed in this paper.  \n \n \nII. Experimental d etails  \na. Details of the thin film growth conditions  \nNanocrystalline M g-ferrite thin film  was deposited using pul sed laser ablation technique. A \nsingle phase high density  Pulsed Laser Deposition (PLD)  target was prepared through solid \nstate reaction route.  The film was deposited using a Nd:YAG pulsed laser with energy density \n2 Joule/cm2. The pulsed laser repetition rate was kept at 10 shots/sec and the film was deposited  \non quartz substrate using 1800 0 pulsed laser shots. The clean amorphous  quartz substrate was \nkept 4.5 cm away from the PLD target and was heated to 500  °C while taking the deposition. \nThe deposited film was ex-situ annealed  at 250  °C for 2 hrs in air and cooled down to room 3 \n temperature  (RT)  through atmospheric cooling in closed furnace. All the measurements were \nperformed using this annealed film.  \n \nb. Magnet ization loops (M -H) measurement  details  \nThe field dependence of magnetization (M -H) of the film was measured using two protocols, \nZFC and FC. For the ZFC measurements , the film was cooled down in zero magnetic field \nfrom RT. The ZFC M-H loops were collected by sweeping the magnetic field in two different \nways . In the first way  (p-type), the field was swept from 0 Oe →  +50 kOe → -50 kOe  → +50 \nkOe . In the second way (n-type) , the field was swept from 0 Oe → -50 kOe → +50 kOe → -\n50 kOe. In these measurements the initial 0 Oe → ±50 kOe, magnetization curve is termed as \nvirgin M -H curve.  \nThe FC M -H loops were collected by cooling the film in an applied  field HFC, from RT and \nthe M -H loops were measured by sweeping the field as H FC → -50 kOe → + 50 kOe. Prior to \nall the measurements the film was subjected to a damped oscillating magnetic field (centred at \n0 Oe ) which gradually becomes zero at RT. This process ensure d the zero magnetization state \nof the film  at RT . All the measurements were performed by applying the magnetic field along \nthe film’s plane.  \n \n \nIII. Results  \na. Structural and elemental properties of the film  \nFig. 1 shows the GIXRD data of the film measured at room temperature with an incident \nangle 0.5 °.  4 \n \n30 40 50 60 70(220)\n(440)(511)(422)(400)Intensity (arb. unit)\n2 (Degree)Mg-ferrite thin film(311)Fig. 1. GIXRD of the magnesium ferrite thin film, deposited at T S = 500 °C and annealed \nat 250 °C for 2 hours  \n \nThe GIXRD  of the film shows  diffraction peaks correspond  to the cubic spinel structure of \nMg-ferrite of space group Fd3m. The observed peaks are identifie d and indexed in the \nFig. 1. \n \n \n \n \n \n \n \n \n \n \n \nFig. 2 . Planner FEG -SEM image of the Mg -ferrite thin film  100 nm  \n01020304050Count (arb. unit)\nSize (nm)5 \n  \nFig. 2 shows the FEG -SEM image of the film surface. The FEG -SEM shows nano  size \ngrains . The size of these grains  were  measured and the histogram of the size distribution is \nshown in the inset of the Fig.  2. The  grain  size varies from few nanometre t o ~ 40  nm with a  \ndistribution  peak at ~ 17 nm . The thickness of the film was around 135 nm.  \nThe elemental analysis of the film was performed using X -ray Photoelectron Spectroscopy \n(XPS) data. Fig. 3 (a) shows the XPS survey profile of the film.  The observed peaks can be \nidentified due to th e Magnesium (Mg), Iron (Fe), Oxygen (O)  and surface absorbed C arbon (C)   \nXPS and Auger peaks. The observed peaks are indexed in the figure . The survey spectra do not \nshow an y additional peak correspond to alien element s, which confirm s the elemental purity of \nthe deposited film. Fig. 3 (b), (c) and (d) show  the high resolution  core level XPS spectra of \nMg 1s, Fe 2p and O 1s respectively. The Mg 1s  core level spectra shows peak at 1303.08  eV \nwhich is similar to that observed in MgFe 2O4 system by Mittal et al .21 \n1200 1000 800 600 400 200 0 1305 1300 1295\n740 735 730 725 720 715 710 705 540 535 530 525 520 (a) Mg 1s\nOAugerOAuger\nFe 2p\nO 1s\nMgAuger\nMg KLL\nMg 2s\nFe 3p\nMg 2p O 2s\n  Intensity (arb. unit)MgFe2O4 thin film\nC 1sMg2+\n (b)\n  \n Mg 1s\nFe3+ satellite2p1/22p3/2 (c)\n  Intensity (arb. unit)\nBE (eV) Fe 2p O 1sSurface oxygen(d)\n  \nBE (eV)  O 1s\n \nFig. 3. (a) XPS survey spe ctroscopy of the film, (c) Mg 1s, (c) Fe 2p and (d) O 1s  high \nresolution core level spectra.  6 \n  \nThe Fe 2p core level spectra  shows two satellite peaks at 719.5  eV and ~733.6  eV. The se \nsatellite peak s confirm  the presence of Fe3+ ionic state  in the system.  A similar Fe  2p spectra \nwas also obtained for Fe3+ ions by other research groups.21-23 The oxygen 1s  core level spectra \nshows two peaks (at 530.2  eV and 532.3  eV) correspond to surface  absorbed oxygen (532.3 \neV)24 and 1s core level spectra  (530.2  eV) of oxygen s of the MgFe 2O4. The GIXRD , FEG -\nSEM  and the XPS results suggest that the film is single phase nano -crystalline  and impurity \nfree MgFe 2O4.  \n \nb. Zero field Cooled (ZFC) and Field Cooled Exchange Bias effect  \nThe Mg -ferrite thin film showed Exchange Bias (EB) effect even in Zero Field Cooled (ZFC) \nmeasurements. Here I present the detail features of this ZFC EB effect. Fig. 4 (a) shows the p-\ntype ZFC M -H loop of the film, measured at 10 K. The open circle data represent the virgin \nM-H curve . Fig. 4 (b) shows the zoomed  view of the  Fig. 4 (a). This figure clearly shows that \nthe ZFC M -H loop is shifted towards the negative field axis. The observed shift is termed as \nZFC Exchange Bias (EB) shift (or field) and measu red as HE = |(HC1 + H C2)/2| , where HC1 \nand HC2 are the two intercept s of the magnetization curve with t he field axis as shown in \nFig. 4 (b).  The average coercivity of the M -H loop is measured as HC = │H C1 – HC2│/2. It was \nalso observed that in this p -type ZFC M -H loop, the value of the remanence magnetization \n|Mr1| (= 73.4 emu/cc) on positive y -axis is smaller than that of the negative y -axis, |Mr2| (= 81.6 \nemu/cc). The average remanence magnetizations is expressed  as Mr=|Mr2|+|Mr1|\n2. \nAnother distinguishable feature is observed in the virgin magnetization curve of the ZFC M -\nH loop.  The Fig. 4 (a) clearly shows that a portion of virgin magnetization curve (open circle) \nis outside the M -H loop. This curve exited  the loop at a magnetic field H' and merged with the \nM-H data at a magnetic field H''. A similar behaviour of the virgin magnetization curve was \nalso reported in  some  bulk ZFC EB systems.7, 8 25 This behaviour was speculated due to a field \ninduced ordering in the system.7, 9 \nHere one need to note  that t he shifted  asymmetric  M-H loops were also observed not only \ndue to the exchange bias effect but also due to minor loop and experimental arte facts.26 A minor \nM-H loop generally shows vertical shift, open loop and non -saturation.26 In case of this film,  it \nwas observed  that the  magnitude of the  high field magnetizations ( |M+50 kOe | and |M-50 kOe |) of 7 \n the M -H loop are equal  and also t he hysteresis in the M -H loop disappeared in the high field \nregion ( |H| > 30 kOe).  These confirmed  that this  M-H loop is not a minor loop of the film.   \n-40 -20 0 20 40-200-150-100-50050100150200\n-3 -2 -1 0 1 2 3-100-50050100\nH'H'' Virgin curve\n M-H loopM (emu/cc)\nH (kOe) (a)\nMr2Mr1\nH'\nHC2HC1 Virgin curve\n M-H loopM (emu/cc)\nH (kOe) (b)\nFig. 4 . (a) 10 K ZFC p -type M -H loop. The virgin M -H curve is shown in red  open circle . (b) \nShows the zoomed  view of the figure (a).  \n \nThe possibility of measurement arte facts in the ZFC EB effect was checked by measuring \nthe ZFC p -type and n -type M -H loops. Previously, similar procedure was also followed by \ndifferent grou ps to check the measurement arte facts in EB effect. 7, 25 \n-3 -2 -1 0 1 2 3-100-50050100\n-50-25 02550-1500150M (emu/cc)\nH (kOe)  p-type\n  n-type5 K, ZFC\n \n  \n \nFig. 5. K ZFC p -type and  n-type M-H loops, plotted within the field range ±3 kOe. Inset shows \nthese ZFC p-type and n -type loops within the field range ±50 kOe.  \n 8 \n Fig. 5 shows the p-type and n -type ZFC M -H loops along with the corresponding virgin \nmagnetization curves of the film, measured at 5 K.  The high field magnetizations  (both |M+50 \nkOe| and |M-50kOe|) of the film remain same  irrespective of these two different measurements . \nBut the shift al ong the magnetic field axis has  changed. The p-type M -H loop shifted along the \nnegative field axis  (HE = 190 Oe) , whereas, the n-type M -H loop shifted along the positive field \naxis (HE = 198 Oe) . The exchange bias shift observed in the  both p-type and n -type \nmeasurements were found to be equivalent and opposite. Moreover, the value of │H'│ for both \nthe p-type (H' = 912 Oe)  and n-type (H' = -947 Oe) loops were found to be similar. These \nresults indicate  that the observed EB effect is due to Zero Field Cooled  Mg-ferrite film  and not \ndue to any experimental arte facts.7, 25   \nI have also studied the Conventional Exchange Bias (CEB) effect in this Mg-ferrite thin film. \nFig. 6  shows the ZFC p-type and FC M -H loops measured at 10 K. The F C measurements  were  \nperformed after cooling down the film in presence of  a field, HFC, (here H FC = 50 kOe ). Similar \nto the ZFC p -type M -H loop, the FC M -H loop also showed exchange bias shift along the \nnegative field axis.  \n-3 -2 -1 0 1 2 3-100-50050100\n-40 -20 020 40-1500150M (emu/cc)\nH (kOe) ZFC Virgin curve\n ZFC M- H\n FC M-H\n10 K\nFig. 6. ZFC p -type and FC M -H loops, measured at 10 K, the loops are enla rged within ±3  kOe. \nInset : full range (±  50 kOe) ZFC and FC M -H loops measured 10  K. The open circles are virgin \nM-H curve of the ZFC measurement.  \n 9 \n The FC EB shift was found to be HE = 110 Oe  for H FC = 50 kOe,  which is lower than the ZFC \nEB field , HE = 177  Oe. The coercivity ( HC =750 Oe ) of this  FC M -H loop is also smaller than \nthe ZFC HC (= 100 0 Oe). One need s to note that this behaviour is not common in CEB systems. \nThe CEB systems generally show an enhancement in the coercivity of the field cooled M -H \nloops .27, 28  \nFig. 6 also shows  that the values of the | Mr1| (= 108  emu/cc ) and | Mr2| (= 96 emu/cc ) of the  \n50 kOe  FC M -H loop are higher than th at of the  |Mr1| (= 73 emu/cc)  and |Mr2| (= 82 emu/cc ) of \nZFC p -type M -H loop, respectively. Whereas, the high field (± 50 kOe) magnetization of both \nthe FC and ZFC M -H loops were same. The increase in remanence magnetization of FC M -H \nloops of CEB systems is also reported but it often associated with an equiv alent change in high \nfield magnetization too .29-32 \nThe temperature and cooling field (H FC) dependence of the exchange bias shift of the Mg -\nferrite thin film was also studied. Fig. 7 (a) shows the temperature dependence of the exchange \nbias field , HE, for H FC = 0 Oe and 50 kOe.  Fig. 7 (b) shows the temperature dependence of \ncoercivity  (HC) for H FC = 0 and 50 kOe.  The film showed higher va lue of HE for H FC = 0 Oe \n(ZFC)  than that of the H FC = 50 kOe . The ZFC and the  50 kOe  FC exchang e bias shift decreased \nwith increasing temperature.  10 \n \n01020304050607080050100150200\n010203040506070806007008009001000\n0 10 20 30 40 50160180200220240260280\n0 10 20 30 40 50600700800900  ZFC\n  +50 kOe FC \n T (K)(a)\n   HE (Oe)  ZFC\n  +50 kOe FC(b)\n  HC (Oe)\nT (K)\nT = 5 K\n   HE(Oe)\nHFC (kOe)(d)(c) HC (Oe)\nHFC (kOe)T = 5 K \nFig. 7 . (a) Temperature dependence change in ZFC (open circle), FC (open Tringle) exchange \nbias field  HE (b) Temperature dependent coercivity of the ZFC and FC M -H loops.  The cooling \nfield (H FC) dependent (c) exchange bias shift ( HE) and (d) coercivity ( HC) at 5 K.  Lines are \nguide to eyes.  \n \nThe coercivity  HC, of the ZFC M -H loops decreased almost monotonically as the temperature \nincreased  (except the 5 K data) . While , the coercivity ( HC) of the 50 kOe FC M-H loops  showed  \na small er value than that of the ZFC M -H loops at low temperature and it increased with the \nincreasing temperature. The HC of the +50 kOe FC M-H loops showed a maximum  value  at \n~25 K before merging with the ZFC  HC value as the temperature increased .   \nFig. 7 (c) and (d ) show the cooling field (H FC) dependence of the  exchange bias shift ( HE) \nand the coercivity ( HC) of the film, measured at 5 K.  The exchange bias shift showed a large \nincrease for H FC = 5 kOe as compare d to the ZFC value.  However as H FC increas ed beyond \n5 kOe, the exchange bias field ( HE) decreased almost monotonically and a lower than ZFC EB 11 \n shift w as observed for H FC = 50 kOe. While t he coercivity ( HC) of the film decreased rapidly \nwith the increasing cooling field for HFC ≤ 10 kOe  and as the H FC increased beyond 10 kOe it \nshows almost a constant value . Previously, Wang et al.7 and Nayak et al.8 had also showed  that \nthe coercivity of the bulk ZFC EB system s decreased in the FC measurements. However, it is \nknown that in  CEB systems the coercivity generally increased in the FC measurements.28 \n \nc. Zero Field Cooled (ZFC)  training e ffect  \nAnother important feature of the exchange bias effect is training effect. Th e training effect \nis extensively used to understand the exchange coupling behaviour at the interface of the \nconventional exchange bias systems.31, 33-35 I have also studied the training effect in this Mg -\nferrite thin film  to understand the origin of the ZFC EB effect in the system . Here unlike the \nCEB systems (in CEB systems, training effect is studied in Field cooled mode), t he film was \ncooled down  to 10 K from RT wi thout a magnetic field. The n consecutive training M-H loops \nwere collected  by sweeping the magnetic field at 10 K . Fig. 8 (a) shows low field part these M -\nH loops. The complete M -H loops  are shown in the inset of Fig. 8  (a). The Fig. 8  (a) clearly \nshows th at the exchange bias shift (H E) and  coercivity (H C) of the M -H loops decrease as a \nresult of consecutive M-H loop iterations  (loop number ‘ n’). Similar behaviour is also observed \nin Conventional Exchange B ias (CEB)  systems.30, 36 Though the CEB systems necessarily \nrequire  to field cool be fore the training measurements.30, 36 It is also interesting to note that the \nremanence magnetizations (both |M r1| and |M r2|) of the film  increased with the increasing ‘n’. \nWhereas  in case of the CEB systems , the training effect of the M -H loop  (that shifted along \nnegative field axis ), generally shows  a decrease in  the |M r1| value with increasing ‘n’.32, 34, 37, 38 \nWhile  the |M r2| has both decreasin g and increasing tendencies depending on the CEB syst ems. \n34, 37-39 \nThe decrease in the exchange bias field  (HE) of the training M -H loops were extensively \nstudied in different  CEB systems30, 33, 36 and most of them follow an empirical power law \nrelation  \nHE−HE∞=KE\n√n                                   (1) \n Where, H E is the exchange bias field for the nth M -H loop, H E∞ is the EB field for n  = ∞ \nand K E is a proportionality constant. This behaviour was attributed to the thermodynamic \nrelaxation of the interfacial spins and it is found that most of the CEB systems obey  this 12 \n behaviour for n > 1. 32, 40 The H C and the M E (=|Mr2|−|Mr1|\n2) of the training M -H loops of these \nCEB systems also show similar trend for n >1. 30 40, 41 \nMishra et al.35 had proposed another mechanism for the training effect. They had considered \nthe frozen spin relaxation and the spin rotation at the interface of the CEB systems during \ntraining effect measurements  and the exchange bias shift was formulated as  35 \n𝐻𝐸=𝐻𝐸∞+𝐴𝑓𝑒−𝑛\n𝑃𝑓+𝐴𝑖𝑒−𝑛\n𝑃𝑖                       (2) \nWhere, A f and Pf are the parameters related to the frozen spin relaxation, A i and P i are the \nparameters related to the spin rotation. The A factors are the weight factor and have the \ndimension of magnetic field, the P is a dimensionless parameter related to rela xation rate. 35, 40, \n42, 43 \nThe exchange bias field  (HC) and coercivity (H C)  of the Mg -ferrite thin film are plotted as a \nfunction of the training loo p index number ‘n’ in the Fig. 8 (b). Fig. 8  (c) and (d) show the M E \nand average M r of the film with ‘n’ , respectively . The exchange bias field (HE) can be  fitted \nwith the equation 1 for n > 1 .Whereas  the H E of the film shows good fitting with only one \nexponent of  equation 2 for all ‘n’. Similar to the H E, the H C, M E and M r of the film are also \nfitted with the equation 1 for n > 1 and with  one exponent of  equation 2 for all ‘n’. The \ndimension and notation of the parameters of the equations 1 and 2 are changed accor dingly  for \nthe fitting of H C, M E and M r. Table 1 shows th e parameters obtained from the  fittings  of \nexchange bias field , HE. The fitting with equation 1 for H E yield H E∞ = -50 Oe. Here one need s \nto note that, previously t he negative H E∞ was also obtained  in Fe3O4 film.40 However,  the sign \nchange in EB shift was not observed even after large number of M -H loop iterations.  Therefore, \nthe sign change in this Mg-ferrite thin film is also not anticipated and rather it is likely that  the \nM-H loop might be come  symmetric after a large number of loop iterations  since the loop shift \nbecome very small (H E ~ 20 Oe) for n = 6 . This indicates that the thermal relaxation of the \ninterfacial spins might  not be a feasible explanation of the ZFC training effect of Mg -ferrite \nthin film. On the other hand, the fitting with one exponent of equation  2 provide the ‘P’ factor \n(P = 0.845) value similar to the relaxation rate of the frozen spins (P f) obtained in different \nCEB systems.35, 43  This indicate s that the ZFC training effect of the film  is most likely to be \ndominated by the relaxation of the frozen spins at the interface of the grain boundary. \nNevertheless, a good fitting with one exponent of the equation 2 for the training H C, M E and \nMr of the film also support the frozen spin relaxation behaviour .  13 \n \n-3 -2 -1 0 1 2 3-100-50050100\n-40 0 40-1500150\n1 2 3 4 5 6050100150200\n4006008001000\n1 2 3 4 5 6707274767880\n1 2 3 4 5 61234\n  M (emu/cc)\nH (kOe) 1st virgin\n 1st\n 2nd\n 3rd\n 4th\n 5th\n 6th(a)\n  \n  HE (Oe)\nLoop no. (n)   HE\n  HE Fit, Equ- 1\n  HE Fit, Equ- 2(b)\nHC (Oe)   HC\n  HC Fit, Equ- 1\n  HE Fit, Equ- 2ME (emu/cc)\nLoop no. (n) Mr\n  Equ 1  \n  Equ 2(d)\nMr (emu/cc) \nLoop no. (n) ME\n Equ - 1\n Equ - 2(c) \nFig. 8 . (a) Zoomed view of the ZFC training M -H loops at 10 K. Inset: Full M -H loops (for n \n= 1 and 6). (b ) Exchange bias Field  (HE) and coercivity (H C) as a function o f training M -H loop \niteration number  n. Both H E and H C are fitted with equation 1 and 2.  (c) M E and (d ) M r with n.  \n \n \nTable 1. Parameters obtained from the fitting of training effect  \nFrom equation (1)  From equation (2) \nKE (Oe) HE∞ (Oe)  HE∞ (Oe) Af (Oe) Pf \n159 -50  20 503 0.845  \n \n \n 14 \n  \n \n \nIV. Discussion  \nThe conventional exchange bias effect is generally attributed to the exchange coupling  \nbetween the interfacial spins of two magnetic materials such as ferromagnetic ( FM) –\nAntiferromagnetic ( AFM )1, 36, FM - spin glass44, 45, FM – Ferrimagnetic ( FIM)46, 47 etc. \nThere are also some sin gle phase (c rystallographic phase) materials that show CEB \neffect.30, 41, 48 However, th ese single phase materials show  coexistence of different magnetic  \norders within them and the e xchange coupling at the interface of these magnetic orders \nresulted in  exchange bias effect.30, 41, 48 The XRD  of our  thin film shows single phase of \nMg-ferrite cubic spinel  structure . The XPS data also support ed it, since no impurity element \nwas found . Therefore to understand the exchange bias phenomenon in this film one need s \nto know the magnetic orderings  within it . The thermomagnetic measurements were  \nperformed to address this. Fig. 9  (a) and (b)  show the t hermomagnetic  data (M-T) of the \nfilm. The M -T were  measured in both Zero Field Cooled (ZFC) and Field Cooled (FC) \nmode s (in Fig. 9 (a)) . We can see tha t the ZFC M -T data deviates from the FC M -T data at \nTirr (indicated with arrow in the Fig. 9 (a) ).  \n \n \n \n \n \n \n \nFig. 9.  (a) ZFC and FC M -T data of the Mg -ferrite thin film. Inset: T irr vs H2/3, the line \nrepresents Thouless  and de Almeida fitting. (b) High field FC M -T data. The b lue dashed \nlines are the fitted data using Bloch’s law  for ferrimagnetic sample and red lines are due to \ncoexistence of ferrimagnetic and SPM grains in the film.  \n0 50 100 150125150175200\n  M (emu/cc)\nT (K) 10 kOe\n 20 kOe\n 30 kOe\n 40 kOe\n 50 kOe\n Bloch Law\n Bloch law + SPM\nTd(b)\n0 100 200 300050100150200250\n0 1000 20000100200300(a)\nTirrFC\nZFC10 kOe\n5 kOe 1 kOe\n  M (emu/cc)\nT (K)500 Oe  Fit\n  Tirr (K)\nH2/3 (Oe2/3)15 \n This behaviour is generally attribut ed to the freezing of the moments of smaller grains.45, 49  \nBelow T irr the spin of the smaller nanocrystalline grains fr ozen to the random direction as the \ncrystalline anisotropy of the grains overcome the thermal fluctuation.49 The value of Tirr \ndecreases  as the applied magnetic field increase s. The decrease of T irr with the increasing \nmagnetic field followed the famous Thouless and de Almeida line50, 51 (Tirr ∝ H2/3) for spin \nglass systems,  shown in the inset of the Fig. 9  (a).  \nThe high field FC M-T data is shown in the Fig. 9  (b). These FC M -T data shows good fit \nwith the Bloch’ s law52 (M(T)= M0(1−BT3\n2)), for temperature dependence magnetization \nof a ferrimagnetic system , above T d (indicated by arrow) . As temperature decreased below T d, \nan upturn in the magnetization is observed. It is also observed that the value of T d increased \nwith the applied magnetic field. I assumed that this behaviour is  due to the coexistence  of \nferrimagnetic and superpa ramagnetic  (SPM)  grains  in the film (formulated as M(T)=\n M0∗(1−BT3\n2)+∁∗/T, where M0∗=(1−x)M0 and ∁∗\nT=xCH\nT, where ‘x’ is the volume fraction \nof the superparamagnetic state, C is the Currie constant of the superparamagnetic state ). The  \n10 – 30 kOe FC M -T data show good fit with this assumption. However , as the field increased \n(above 30 kOe), the low temperature data shows a tendency towards saturation as compared to \nthe fitted data. This behaviour could be due to a weak ordering of the  SPM grains under \napplication of high magnetic field. The  similar  field induced ordering of the SPM grains were \nalso predicted in different ZFC EB systems .7, 25 Therefore, it is likely that the smaller grains of \nthis Mg -ferrite nanocrystalline thin film were frozen into a spin glass like state as the \ntemperature decreased much below the T irr. The pinning effect of the surface  spins of these \nfrozen  glass y states at the interface of f errimagnetic grains could possibly  leads to  the observed \nexchange bias effect. Earlier, exchange bias effect was also reported in different single phase \nferrite thin films such as Ni -ferrite, MnZn -ferrite  thin films .16-18 The observed EB effect in \nthese systems was also speculated due to the pinning effect  of the surface spins of a disordered \nstate (glassy states/super paramagnetic (SPM) states) at the interface of the ferrimagnetic \ngrains. Howeve r, softening (decrease of H C) of the FC M -H loops  could be associated with the \nfield induce d weak ordering of th e SPM grains. The ordering within these SPM grains reduced \nthe net anisotropy of the system. I speculate  similar effect in the training effect  measurements , \nhere the frozen SPM grains relaxed towards an ordered state and decrease d the anisotropy of \nthe sy stem . This  reduced anisotropy leads to a square  trained M-H loop  (or increase in |M r1| \nand |M r2|) as compared to the initial ZFC M -H loop.  16 \n  \nV. Conclusion  \nA single layer Mg -ferrite thin film  was deposited  on amorphous quartz substrate using pulsed \nlaser ablation technique. This film showed ZFC EB effect along with the ZFC training effect. \nThe f ilm also showed CEB effect in  field cool ed measurements. The observed exchange bias \neffect is attributed to the pinning effect of the surface spin s of frozen glassy state s at the \ninterface of ferrimagnetic grains. The decrease in the coercivi ty of the field cooled M -H loop  \nis speculated due to a weak field induce ordering of the superparamagnetic grains.  \n \n \n \nAcknowle dgements  \nI thank Prof. Shiva Prasad and Prof. N. Venkataramani for the lab facilities. I also thank SAIF \nand IRCC of IIT Bombay for the VSM, XRD, ESCA and  FEG -SEM facilities.  \n \n \nReferences  \n1. W. H. Meiklejohn and C. P. Bean, Physical Revie w 105 (3), 904 (1957).  \n2. M. Kiwi, Journal of Magnetism and Magnetic Materials 234 (3), 584 -595 (2001).  \n3. R. Stamps, Journal of Physics D: Applied Physics 33 (23), R247 (2000).  \n4. S. Gider, B. -U. Runge, A. Marley and S. Parkin, Science 281 (5378), 797 -799 (1998).  \n5. B. Park, J. Wunderlich, X. Martí, V. Holý, Y. Kurosaki, M. Yamada, H. Yamamoto, A. Nishide, J. \nHayakawa and H. Takahashi, Nature materials 10 (5), 347 -351 (2011).  \n6. S. M. Wu, S. A. Cybart, P. Yu, M. D. Rossell, J. X. Zhang, R. Ramesh and R. C.  Dynes, Nat Mater \n9 (9), 756 -761 (2010).  \n7. B. Wang, Y. Liu, P. Ren, B. Xia, K. Ruan, J. Yi, J. Ding, X. Li and L. Wang, Physical review letters \n106 (7), 077203 (2011).  \n8. A. Nayak, M. Nicklas, S. Chadov, C. Shekhar, Y. Skourski, J. Winterlik and C. Felser , Physical \nreview letters 110 (12), 127204 (2013).  \n9. J. K. Murthy, K. Chandrasekhar, H. Wu, H. Yang, J. Lin and A. Venimadhav, Journal of Physics: \nCondensed Matter 28 (8), 086003 (2016).  \n10. B. Wang, Y. Liu, B. Xia, P. Ren and L. Wang, Journal of Applied Physics 111 (4), 043912 (2012).  \n11. P. Liao, C. Jing, X. Wang, Y. Yang, D. Zheng, Z. Li, B. Kang, D. Deng, S. Cao and J. Zhang, Applied \nPhysics Letters 104 (9), 092410 (2014).  \n12. M. Pardavi -Horvath, Journal of Magnetism and Magnetic Materials 215–216, 171 -183 (2000).  \n13. M. Sugimoto, Journal of the American Ceramic Society 82 (2), 269 -280 (1999).  \n14. B. D. Cullity and C. D. Graham, Introduction to magnetic materials . (IEEE/Wiley, Hoboken, N.J, \n2009).  \n15. H. R. Dakua, N. Venkataramani and S. Prasad, AIP Advances 6 (5), 055919 (2016).  17 \n 16. S. Venzke, R. Van Dover, J. M. Phillips, E. Gyorgy, T. Siegrist, C. Chen, D. Werder, R. Fleming, R. \nFelder and E. Coleman, Journal of materials research 11 (5), 1187 -1198 (1996).  \n17. U. Alaan, G. Sreenivasulu, K. Yu, C. Jenkins, P. Shafer, E. Arenholz, G. Srinivasan and Y. Suzuki, \nJournal of Magnetism and Magnetic Materials 405, 129 -136 (2016).  \n18. U. Alaan, F. Wong, A. Grutter, J. Iwata -Harms, V. Mehta, E. Arenholz and Y. Suzuki, Journal of \nApplied Physics 111 (7), 07A337 (2012).  \n19. K. Mallick and P. Anil Kumar, Journal of Applied Physics 124 (5), 053901 (2018).  \n20. H. R. Dakua, arXiv preprint arXiv:1910.10120v1 (2019).  \n21. V. Mittal, P. Chandramohan, S. Bera, M. Sriniv asan, S. Velmurugan and S. Narasimhan, Solid \nstate communications 137 (1), 6 -10 (2006).  \n22. S. Gota, E. Guiot, M. Henriot and M. Gautier -Soyer, Physical Review B 60 (20), 14387 -14395 \n(1999).  \n23. M. C. Biesinger, B. P. Payne, A. P. Grosvenor, L. W. Lau, A. R. Gerson and R. S. C. Smart, Applied \nSurface Science 257 (7), 2717 -2730 (2011).  \n24. V. Datsyuk, M. Kalyva, K. Papagelis, J. Parthenios, D. Tasis, A. Siokou, I. Kallitsis and C. Galiotis, \nCarbon 46 (6), 833 -840 (2008).  \n25. J. Krishna Murthy and A. Venimadh av, Applied Physics Letters 103 (25), 252410 (2013).  \n26. J. Geshev, Journal of Magnetism and Magnetic Materials 320 (3-4), 600 -602 (2008).  \n27. R. L. Stamps, Journal of Physics D: Applied Physics 33 (23), R247 (2000).  \n28. M. D. Stiles and R. D. McMichael, P hysical review B 63 (6), 064405 (2001).  \n29. L. Del Bianco, D. Fiorani, A. M. Testa, E. Bonetti and L. Signorini, Physical Review B 70 (5), \n052401 (2004).  \n30. S. Giri, M. Patra and S. Majumdar, Journal of Physics: Condensed Matter 23 (7), 073201 (2011).  \n31. C. Binek, Physical Review B 70 (1), 014421 (2004).  \n32. A. Hochstrat, C. Binek and W. Kleemann, Physical Review B 66 (9), 092409 (2002).  \n33. D. Paccard, C. Schlenker, O. Massenet, R. Montmory and A. Yelon, physica status solidi (b) 16 \n(1), 301 -311 (1966).  \n34. R. Zheng, G. Wen, K. Fung and X. Zhang, Physical Review B 69 (21), 214431 (2004).  \n35. S. Mishra, F. Radu, H. Dürr and W. Eberhardt, Physical review letters 102 (17), 177208 (2009).  \n36. J. Nogués and I. K. Schuller, Journal of Magnetism and Magnetic Mat erials 192 (2), 203 -232 \n(1999).  \n37. Z. Tian, S. Yuan, L. Liu, S. Yin, L. Jia, P. Li, S. Huo and J. Li, Journal of Physics D: Applied Physics \n42 (3), 035008 (2009).  \n38. S. Karmakar, S. Taran, E. Bose, B. Chaudhuri, C. Sun, C. Huang and H. Yang, Physical Rev iew B \n77 (14), 144409 (2008).  \n39. X. Zhang, J. Yuan, Y. Xie, Y. Yu, F. Kuang, H. Yu, X. Zhu and H. Shen, Physical Review B 97 (10), \n104405 (2018).  \n40. P. M. Shameem and M. S. Kumar, Journal of Magnetism and Magnetic Materials 458, 241 -252 \n(2018).  \n41. Y.-k. Tang, Y. Sun and Z. -h. Cheng, Physical Review B 73 (17), 174419 (2006).  \n42. I. Fita, A. Wisniewski, R. Puzniak, P. Iwanowski, V. Markovich, S. Kolesnik and B. Dabrowski, \nPhysical Review B 95 (13), 134428 (2017).  \n43. H. Khurshid, P. Lampen -Kelley, Ò. Iglesias, J. Alonso, M. -H. Phan, C. -J. Sun, M. -L. Saboungi and \nH. Srikanth, Scientific reports 5, 15054 (2015).  \n44. M. Ali, P. Adie, C. H. Marrows, D. Greig, B. J. Hickey and R. L. Stamps, Nature Materials 6 (1), \n70-75 (2007).  \n45. M. Gruyters, Physi cal Review Letters 95 (7), 077204 (2005).  \n46. Q. K. Ong, A. Wei and X. -M. Lin, Physical Review B 80 (13), 134418 (2009).  \n47. M. Kaur, J. S. McCloy and Y. Qiang, Journal of Applied Physics 113 (17), 17D715 (2013).  \n48. A. K. Nayak, M. Nicklas, S. Chadov, P. Khuntia, C. Shekhar, A. Kalache, M. Baenitz, Y. Skourski, \nV. K. Guduru and A. Puri, Nature materials 14 (7), 679 -684 (2015).  18 \n 49. Q. Chen and Z. J. Zhang, Applied Physics Letters 73 (21), 3156 -3158 (1998).  \n50. J. De Almeida and D. J. Thouless, Journal of Ph ysics A: Mathematical and General 11 (5), 983 \n(1978).  \n51. M. Vafaee, S. Finizio, H. Deniz, D. Hesse, H. Zabel, G. Jakob and M. Kläui, Applied Physics \nLetters 108 (7), 072401 (2016).  \n52. S. Blundell, Magnetism in condensed matter . (Oxford University Press I nc., New York, 2001).  \n \n \n \n \n "    },    {        "title": "1407.1798v1.Multiferroic_hexagonal_ferrites__h_RFeO__3___R_Y__Dy_Lu___an_experimental_review.pdf",        "content": "arXiv:1407.1798v1  [cond-mat.mtrl-sci]  7 Jul 2014Multiferroic hexagonal ferrites (h-RFeO 3, R=Y, Dy-Lu): an\nexperimental review\nXiaoshan Xu1and Wenbin Wang2\n1Department of Physics and Astronomy,\nUniversity of Nebraska-Lincoln, Lincoln, NE 6858, USA\n2Department of Physics, Fudan University, Shanghai 200433, China\n(Dated: July 8, 2014)\nAbstract\nHexagonal ferrites (h-RFeO 3, R=Y, Dy-Lu) have recently been identified as a new family of\nmultiferroic complex oxides. The coexisting spontaneous e lectric and magnetic polarizations make\nh-RFeO 3rare-case ferroelectric ferromagnets at low temperature. Plus the room-temperature mul-\ntiferroicity and predicted magnetoelectric effect, h-RFeO 3are promising materials for multiferroic\napplications. Here wereview the structural, ferroelectri c, magnetic, and magnetoelectric properties\nof h-RFeO 3. The thin film growth is also discussed because it is critical in making high quality\nsingle crystalline materials for studying intrinsic prope rties.\n1Contents\nI. Introduction 2\nA. Structure 3\nB. Ferroelectricity 4\nC. Magnetism 5\n1. Single ion anisotropy 6\nII. Stabilization of RFeO 3in hexagonal structure 7\nIII. Thin film growth in hexagonal structure 9\nA. Epitaxial orientations 10\nB. Strain at the interface 13\nIV. Ferroelectricity 15\nV. Magnetism 19\nVI. Magnetoelectric couplings 24\nVII. Conclusion 25\nAcknowledgments 25\nA. Structural Stability in RFeO 3 25\nReferences 29\nI. INTRODUCTION\nIn the quest for energy-efficient and compact materials for inform ation processing and\nstorage, magnetoelectric multiferroics stand out as promising can didates.[1, 2] In particular,\nironbased oxide materials areanimportant categorybecause of th e strong magnetic interac-\ntions of the Fe sites. For example, BiFeO 3is arguably the most studied multiferroic material\nduetothecoexistence offerroelectricity andantiferromagnetis maboveroomtemperature.[3]\nBaO-Fe 2O3-MeO ferrites of hexagonal structure (Me=divalent ion such as Co , Ni, and Zn;\n2Ba canbesubstituted by Sr) exhibit room-temperaturemagnetoe lectric effect.[4–6] LuFe 2O4\nisa unique ferrimagnetic material with antiferroelectricity originate dfromchargeorder.[7, 8]\nSpontaneous electric and magnetic polarizations occur simultaneou sly in hexagonal ferrites\nh-RFeO 3(R=Y, Dy-Lu) at low temperature;[9–13] the antiferromagnetism and ferroelec-\ntricity is demonstrated to persists above room temperature.[13]\nIn this review, we focus on hexagonal ferrites h-RFeO 3, which is isomorphic to hexago-\nnal RMnO 3. Although the stable structure of free-standing RFeO 3are orthorhombic, the\nhexagonal structure can be stabilized using various methods.[9–31 ] Similar to hexagonal\nRMnO 3(space group P6 3cm), h-RFeO 3exhibit ferroelectricity and antiferromagnetism.[10,\n11, 13, 32, 33] What distinguishes h-RFeO 3from RMnO 3is the low temperature weak fer-\nromagnetism and the higher magnetic transition temperature due t o the stronger exchange\ninteraction between the Fe3+sites; the spontaneous magnetization can be magnified by the\nmagnetic R3+sites.[10, 12] The theoretically predicted reversal of magnetizatio n using an\nelectric field is another intriguing topic in h-RFeO 3.[34] We will review the experimental\naspects of the h-RFeO 3, including their structural, ferroelectric, magnetic, and magneto -\nelectric properties. Since h-RFeO 3is a metastable state of RFeO 3, the growth of materials\ninvolve special treatment; we will discuss the stability of h-RFeO 3and emphasize especially\non the thin film growth. In addition to a summary of the existing exper imental work, we\nalso included some new analysis, representing the current underst anding of the authors.\nA. Structure\nThe structure of the h-RFeO 3at room temperature belongs to a P6 3cm space group with\na six-fold rotational symmetry, as shown in Fig. 1.[24] The unit cell ca n be divided into\nfour layers: two RO 2layers and two FeO layers. The arrangements of the atoms follow\nroughly the ABC hexagonal stacking [Fig. 4(c)]. The Fe atoms occup y the two dimensional\ntriangular lattice in the FeO layer. Every Fe atom is surrounded by fiv e oxygen atoms (three\nin the same FeO layer and one above and one below the FeO layer), for ming a FeO 5trigonal\nbipyramid [Fig. 1(d)]. Each R atom is surrounded by eight oxygen atom s (six in the same\nRO2layer, one above and one below the RO 2layer), forming a RO 8local environment. Note\nthat the FeO 5is slightly rotated along the [120] crystal axis; this rotation causes the broken\ninversion symmetry of the h-RFeO 3structure, allowing for the ferroelectricity.[32, 34]\n3FIG. 1: (Color online) Structure of the h-RFeO 3. (a) Viewed along the c-axis. (b) Viewed along\nthea-axis. (c) Viewed in terms of the ABC stacking. (d) FeO 5as the local environment of Fe\natoms.\nB. Ferroelectricity\nFIG. 2: (Color online) The illustration of the three phonon m odes (Γ−\n2, K1and K 3) related to\nthe P6 3/mmc to P6 3cm structural transition. We use the coordinate system of P6 3cm structure\nhere (and throughout the review) for the a,bandcaxis. The rods connecting atoms are not to\nindicate chemical bonds, but to highlight the structural sy mmetry.\nHexagonal transition metal oxides have a P6 3/mmc structure at high temperature\n(TC≈1000 K, Fig. 2) and a P6 3cm structure at room temperature (Fig. 1). In the\ntransition from the P6 3/mmc structure to the P6 3cm structure, three structural changes\noccur, which can be viewed as the frozen phonon modes Γ−\n2, K1and K 3, as shown in Fig.\n42. The Γ−\n2mode corresponds to the uneven displacement of the atoms along t hec-axis; this\ngenerates the spontaneous electric polarization (ferroelectricit y). The K 3mode corresponds\nto a collective rotation of the FeO 5trigonal bipyramids; it turns out to be the driving force\nfor the structural transition that causes the none-zero displac ement of the Γ−\n2modes.[32, 34]\nAs shown in Fig. 2, the direction of the FeO 5rotation actually decides whether the majority\nof the R atoms are above or below the minority in the RO 2layers, which in turn decides the\ndirection of the spontaneous electric polarization.\nC. Magnetism\nFIG. 3: (Color online) Four (Γ 1to Γ4) independent 120-degree antiferromagnetic orders of the\nspins on the Fe sites in h-RFeO 3. The blue and green arrows represent the spins in z= 0 and\nz=c\n2FeO layers viewed along the c-axis. The four spin structures come from the combination\nof twoφangles and two relative alignments of the spins between the t wo FeO layers (parallel or\nantiparallel). Only Γ 2allows for spontaneous magnetic polarizations.\nThe Fe site in h-RFeO 3are trivalent and carry magnetic moments. The magnetic mo-\nments on Fe come approximately from the electronic spins (for conv enience, we use spin\nand magnetic moments interchangeably for the Fe sites to describe the magnetic order).\nThe strongest magnetic interaction between the Fe sites is expect ed to be the exchange\ninteraction within the FeO layer, which can be written as:\n5Hab\nex=/summationdisplay\nij,nJab\ni,j/vectorSnc\n2\ni·/vectorSnc\n2\nj, (1)\nwhere/vectorSnc\n2\niis the spin on the ith Fe site in the z=nc\n2FeO layer,nis an integer, and Jab\ni,jis\nthe exchange interaction strength between the ith andjth sites in the same FeO layer. Due\nto the two dimensional triangular lattice and antiferromagnetic inte raction between Fe sites,\nthis interaction is frustrated if the spins are along the c-axis. On the other hand, if the spins\nare within the FeO plane, the frustration is lifted, generating the so -called the 120 degree\norders, as shown in Fig. 3. In the 120-degree antiferromagnetic o rders, the moments in the\nsame FeO layer can collectively rotate within the a-b plane, correspo nding to the degree of\nfreedomφ(Fig. 3).\nAs shown in Fig. 1, there are two FeO layers in the unit cell of h-RFeO 3. The interlayer\ninteractions determine the magnetic order along the c-axis, which can be written as:\nHc\nex=/summationdisplay\ni,j,nJc\ni,j/vectorSnc\n2\ni·/vectorSj(n+1)c\n2, (2)\nwhereJc\ni,jis the exchange interaction strength between the ith andjth sites in the\nneighboring FeO plane. By combining the two independent directions o f the spins in one\nFeO layer ( φ=0 orφ=90 degrees) and the two different alignments between the spins in t he\ntwo neighboring FeO layers (parallel or antiparallel), one can constr uct four independent\nmagnetic orders (Γ 1to Γ4), as shown in Fig. 3. For h-RFeO 3, the spins follow one of the\norders in Γ 1to Γ4or a combination.\n1. Single ion anisotropy\nThe key for the 120-degree magnetic orders is that the spins on th e Fe sites lie in the a-b\nplane. This spin orientation is affected by the single ion anisotropy, wh ich can be written\nas:\nHSIA=/summationdisplay\niaz(/vectorSi·/vector c)2+(/vectorSi·ˆn)2, (3)\nwhere the sign of azdetermines whether the c-axis is an easy axis or a hard axis and\nanand ˆndetermine the preferred value of the angle φ. Ifazhas a large negative value,\n6the electronic spins tend to point along the c-axis, corresponding to a magnetic frustration\nbecause of the antiferromagnetic interactions between the Fe sit es; which suppresses the\nmagnetic order temperature. In the limit of the Ising model (spins m ust be along c-axis),\nno long-range order can be formed. Therefore, the single ion aniso tropy is an important\nparameters that affects the magnetic ordering.\nIf the magnetic order is Γ 2or Γ3, the Dzyaloshinskii-Moriya (DM)[35, 36] interaction will\ncause a canting of the spins on the Fe sites toward the c-axis; this generates the non-zero\ncomponents of the spins along the c-axis. The DM interaction can be written as:\nHDM=/summationdisplay\ni,j,n/vectorDi,j·(/vectorSnc\n2\ni×/vectorSnc\n2\nj), (4)\nwhereDi,jisthevectorinteractionstrength. Inparticular,intheΓ 2magneticorder, the c-\naxis component of thespins onallFesites areparallel; thisgenerate s a net magneticmoment\nalong thec-axis, causing a spontaneous magnetic polarization (weak ferroma gnetism).\nII. STABILIZATION OF RFEO 3IN HEXAGONAL STRUCTURE\nAlthough Fe3+and Mn3+have almost identical radius, RFeO 3is stable in orthorhombic\nstructuer, while RMnO 3is stable in hexagonal structure. According to the discussion in A,\nthe stability of the hexagonal manganites is a special case, while the stability orthorhombic\nstructure for RFeO 3follows closer to the trend of other rare earth transition metal ox ides.\nNevertheless, the metastable hexagonal structure in RFeO 3can be achieved using special\nmaterial preparation methods. These methods are: 1) wet-chem ical method,[14, 15, 20, 23,\n25, 37] 2) under-cooling from a melt,[16, 18, 19, 21, 24, 38] 3) thin film growth on substrates\nwith trigonal symmetry,[9, 10, 10–13, 17, 26, 28, 29, 31, 39] and 4 ) doping either in the R\nsite or in the Fe site.[24, 30] In the method 1)-3), interface energy between the crystalline\nphase and the liquid (or amorphous phase) is the key; in the method 4 ), the reduction of\nthe Gibbs free energy of the crystalline phase itself is employed.\nAlthough the orthorhombic structure is the ground state struct ure for RFeO 3, the hexag-\nonal structure is an intermediate metastable state between the liq uid (amorphous) and the\ncrystalline orthorhombic state. Consider a transition from a liquid (a morphous) phase to\na crystalline phase, the nucleation of the crystalline phase generat es an interface between\nthe two phases. The competition between the energy gain in forming the crystalline phase\n7and the energy loss in forming the interface results in a critical size o f the nucleation for the\ngrowth of the crystalline phase; this critical size corresponds to a n energy barrier:\n∆G∗=16πσ3v2\nc\n3∆µ2, (5)\nwhereσis the surface energy, vcis the molar volume, ∆ µis the molar change of chemical\npotential.\nBecause the orthorhombic phase is the stable crystalline phase, th e ∆µ2is larger for\nthe liquid →orthorhombic transition. On the other hand, if the interface ener gyσbetween\nthe liquid and hexagonal phase is smaller, ∆ G∗can be smaller for the liquid →hexagonal\ntransition in a certain temperature range, considering that ∆ µdecrease as temperature\nincreases. In fact, the symmetry of hexagonal phase is higher th an that of the orthorhom-\nbic phase, which suggests a smaller entropy change between the liqu id and the hexagonal\nphase, or a smaller interface energy. A simulation on the energy sho ws that below a certain\ntemperature, the energy barrier for forming hexagonal phase c an be lower than that for\nforming orthorhombic phase.[16] The temperature range becomes narrower for larger R3+\nand diminishes in LaFeO 3.\nThis model has been corroborated by experimental observations . First, hexagonal fer-\nrites are formed in an undercooled melt (from above 2000 K by laser- heating) of RFeO 3.\nFor YFeO 3, the hexagonal phase exists as a transient state, while for LuFeO 3, the hexago-\nnal phase persist even down to the room temperature.[16, 18] Sec ond, using wet-chemical\nmethod, amorphous YFeO 3, EuFeO 3and YbFeO 3are first created; after annealing to above\n750◦C, nanoparticles (10-50 nm diameter) of hexagonal phase were ge nerated; further an-\nnealing converts the hexagonal phase into the orthorhombic phas e.[14]\nTherefore, the smaller σat the liquid/hexagonal interface (compared to that at the liq-\nuid/orthorhombic interface) is the key in making the hexagonal pha se metastable during\nthe liquid →crystalline solid transition. On the other hand, as the size of the hex agonal\ncrystalline phase grow (3 dimensionally), the interface energy beco mes less important; this\nis why the hexagonal phase exists in the form of nanoparticles or in t he form of impurity\nphase (or even transient phase) in bulk samples. To maximize the effe ct of interface en-\nergy in stabilizing the hexagonal phase, epitaxial thin film growth emp loys the substrate\nsurface of trigonal or hexagonal symmetry which enlarges the co ntrast between the σof the\nsubstrate/hexagonal and substrate/orthorhombic interface s.\n8In the epitaxial growth of thin films, the material grows along only on e dimension (per-\npendicular to the surface), which makes the interface energy bet ween the film material and\nthe substrate much more important. Here the total Gibbs free en ergy of the substrate and\nthe film is\nG=A(σ+gd), (6)\nwhereg=µ\nvcis the Gibbs free energy per unit volume of the film, Aanddare the surface\narea and film thickness.\nThe difference of the Gibbs free energy between the substrate/h exagonal and sub-\nstrate/orthorhombic combinations is\n∆G=A(∆σ+∆gd), (7)\nTherefore, if the a substrate of trigonal or hexagonal symmetr y is used to minimize the\nsubstrate/hexagonal interface energy σ, the combination of the hexagonal phase and the\nsubstrate actually can be the stable state. In other words, below a critical thickness\ndc=−∆σ\n∆g, (8)\nthe hexgonal phase is more energy favorable. For d > dc, the hexagonal phase will remain\nmetastable because the energy barrier for forming the hexagona l phase will always be lower\nthan that for the forming the orthorhombic phase if the underlaye r is hexagonal. The\nthicknessoftheh-RFeO 3filmintheliteratureistypicallylessthan100nmonYSZandAl 2O3\nsubstrates. Recently a growth of 200 nm h-LuFeO 3on YSZ using oxide molecular-beam\nepitaxy is reported.[31] However, a systematic study on the critica l thickness to investigate\nthe dependence on the substrate and the type of R3+is still needed.\nIII. THIN FILM GROWTH IN HEXAGONAL STRUCTURE\nThe epitaxial growth of thin films depends greatly on the processes , which may generate\nthe stable and metastable states of the substrate/film heterost ructures. Here, we will not\n9consider the growth dynamics and growth methods and ignore the m orphology of the epi-\ntaxial thin films. Instead, we focus on the equilibrium state of the ep itaxy, assuming the\nstoichiometry of the epilayer is correct.\nA. Epitaxial orientations\nTheepitaxial growthofathinfilmontopofasubstrateischaracter izedbytheparallelism\nofthecontactplane(textureorientation)andtheparallelismofth ecrystallographicdirection\n(azimuthal orientation). The epitaxial orientationisdetermined by theminimum freeenergy\nconditions, which relate to the bonding across the substrate-epila yer interface and the lattice\nmisfit.\nAccording to the Royer’s rules[40] for epitaxial growth of ionic crys tals, the crystal planes\nincontactmust havethesamesymmetry. Therefore, ifthesurfa cesymmetry ofthesubstrate\nis triangular, the epilayer of RFeO 3is either h-RFeO 3(0001) or o-RFeO 3(111) in the pseudo\ncubic coordinates, depending on the interfacial energy which is det ermined by the difference\ninstructures and thelattice misfit. Forexample, if SrTiO 3(111)is used asthe substrate, the\no-RFeO 3will be the favorable structural of the epilayer because o-RFeO 3share the similar\n(perovskite) structure and the similar lattice constants ( ∼2% misfit); this is actually a case\nclose to homoepitaxy.[41] On the other hand, the lack of substrate of similar structure to h-\nRFeO3makesthehomoepitaxyverydifficult. Inmostcaseoftheepitaxialg rowthofh-RFeO 3\nfilms, although the substrates have triangular symmetry, the str ucture and lattice constants\nare very different from h-RFeO 3, which certainly falls into the category of heteroepitaxy.[41]\nTABLE I: The structures of the substrates and epitaxial orie ntations with h-RFeO 3. The lattice\nconstants of the h-LuFeO 3are a=b=5.9652 ˚A and c=11.7022 ˚A. [24]\nSubstrate Structure Lattice ConstantsLattice ConstantEp itaxial Orientation\n(Bulk, in ˚A) (In-plane, in ˚A)(substrate ∝bardblh-LuFeO 3)\nAl2O3(0001)R¯3c(167)a=4.7602, c=12.9933 a=b=4.7602 (0001) ∝a\\gbracketleft100∝a\\gbracketright||(0001)∝a\\gbracketleft100∝a\\gbracketright\nYSZ(111)Fm ¯3m(225) a=5.16(2) a=b=7.30 (111) ∝a\\gbracketleft11-2∝a\\gbracketright||(0001)∝a\\gbracketleft100∝a\\gbracketright\nPt(111) Fm ¯3m(225) a=3.9231 a=b=5.548 (0001) ∝a\\gbracketleft1-10∝a\\gbracketright||(0001)∝a\\gbracketleft100∝a\\gbracketright\nEpitaxial h-RFeO 3thin films have been deposited on various substrates including Al 2O3\n10FIG. 4: (Color online) RHEED Pattern of the substrates and th e overlayer of h-LuFeO 3.\nFIG. 5: (Color online) The possible interfacial layers of th e substrates and h-RFeO 3. The red\n(orange) color of the oxygen indicates that the atoms are abo ve (below) the center of mass along\nthe surface normal. The lattices of h-RFeO 3, Al2O3, and YSZ are in the same scale. The multiple\noxygen atoms on the same site indicates the uncertainty of th e oxygen positions in YSZ. The\nprojection of the edges of the bulk unit cells of the structur es are indicated by the thin lines. The\noxygen networks are highlighted by the connection between t he oxygen atoms with the yellow rods.\n(0001), yttrium stabilized zirconium oxide (YSZ) (111) and Al 2O3(0001) buffered with Pt\n(111) layers.[9, 10, 10–13, 17, 26, 28, 29, 31, 39] All the epitaxial growth is along the c-axis\nof h-RFeO 3, to satisfy the matching triangular symmetry.\nAs shown in Table I, there is no obvious lattice match between the h-R FeO3and Al 2O3,\n11YSZ, or Pt. On the other hand, the epitaxial growth can be obtaine d, as shown in Fig.\n4 as an example using the pulsed laser deposition. The in-plane epitaxia l orientations is\nnormally studied using x-ray diffraction. Nevertheless, the reflect ion high energy electron\ndiffraction (RHEED) provides an in-situ, time-resolved characteriz ation of the in-plane epi-\ntaxial orientation too. As shown in Fig. 4, one can calculate the in-pla ne lattice constants\nfrom the separation of the RHEED patterns and determine the orie ntation of the overlayer\nwith respect to the substrates. The resulting epitaxial orientatio ns are shown in Table I.\nIt appears that the key in growing epitaxial h-RFeO 3films is the substrate with a surface\nof triangular symmetry. On the other hand, the in-plane 2-dimensio nal lattice constants\nbetween h-RFeO 3and the substrates do not show obvious match. For Al 2O3, the in-plane 2-\ndimensional latticeconstants area=b=4.7602 ˚A, which hasalattice misfit greater than25%.\nIf one considers the super cell match (four times of lattice consta nt of h-LuFeO 3v.s. five\ntimes of lattice constant of Al 2O3), the lattice misfit is -0.25%, which falls into the category\nof coincident lattices.[41] There is also a large (-18%) lattice misfit bet ween h-LuFeO 3(0001)\nand YSZ (111), if we take YSZ [1-10] as the direction of in-plane 2-dim ensional basis. Using\na super-cell scheme (five times of lattice constant of h-LuFeO 3v.s. four times of lattice\nconstant of YSZ), the lattice misfit is 2%. It turns out that the in-p lane epitaxial orientation\nbetween the h-LuFeO 3and YSZ substrates is ∝a\\gbracketleft100∝a\\gbracketrightof h-LuFeO 3|| ∝a\\gbracketleft11−2∝a\\gbracketrightof YSZ, which\ndoes not follow the super-cell scheme, but involves a 30 degree rot ation from that, which\nis similar to the observed epitaxy of YMnO 3(0001) on YSZ (111).[42, 43] After the 30\ndegree rotation, the lattice point of [1-21] of YSZ is close to the latt ice point of [020] of\nh-LuFeO 3, with a misfit of -5.6%, as shown in Fig. 4. For the growth of h-LuFeO 3on\nPt (111), the lattice misfit between h-LuFeO 3(0001) and Pt (111) is -7.5%, if we take Pt\n[1-10] as the direction of in-plane 2-dimensional basis. The growth t urns out to have the\nepitaxial orientation of ∝a\\gbracketleft100∝a\\gbracketrightof h-LuFeO 3∝bardbl ∝a\\gbracketleft11−2∝a\\gbracketrightof Pt, despite the large misfit, which\nis understandable because the 30 degree rotation will generate on ly a much larger misfit.\nSince the azimuthal epitaxial orientations of h-LuFeO 3films cannot be explained simply\nby the lattice misfit, the detailed interfacial structure must be res ponsible. As shown in\nFig. 6 (also in Fig. 1), there are two types of layers in h-RFeO 3: the LuO 2layer and the\nFeO layer. The common part of the LuO 2and FeO layers are the plane of oxygen network\nwith triangluar connectivity. The YSZ and Al 2O3structures also contain plane of oxygen\ntriangular lattice. It appears that the epitaxial orientations of th e h-LuFeO 3films on YSZ\n12(111) and Al 2O3(0001) aligns the oxygen networks. In particular, the rotation of YSZ in-\nplane axis by 30 degree is explained: after the rotation, the oxygen networks of h-LuFeO 3\n(0001) and YSZ (111) may match at the interface with a -5.6% misfit. The share of the\noxygen network at the interface reduces the total energy, whic h may be responsible for the\nobserved azimuthal epitaxial orientation. The better match of th e oxygen networks between\nthe h-LuFeO 3(0001) and YSZ (111) in comparison with Al 2O3(0001) also indicates that\nthe interfacial bonding of h-LuFeO 3(0001)/YSZ(111) is stronger. If the key in the epitaxy is\nthe share of oxygen network, one can infer that it is more energet ically favorable to have the\nLuO2layer (instead of the FeO layer) at the interface with the YSZ and Al 2O3substrates,\nwhich means that the surface of the h-LuFeO 3films will have FeO layer as the termination.\nB. Strain at the interface\nFIG. 6: (Color online) A spectrum of the effective in-plane lat tice constants (in ˚A) of different\nsurfaces. For the corundummaterials (Al 2O3, Fe2O3, and Cr 2O3), the values are 5/4 of the original\nin-plane lattice constant; for spinel (MgAl 2O4and Fe 3O4), the values are 1/2 of the in-plane lattice\nconstant; for the hexagonal material (6H-SiC, GaN, AlN, BN, ZnO, YAlO 3, LuBO 3, and YBO 3),\nthe values are the in-plane lattice constant with a 30-degre e rotation; for YSZ, the values are 1/2\nthe in-plane lattice constant after a 30-degree rotation.\nEpitaxial strain is an extremely important issue in epitaxial thin film gro wth, because the\nstrain may change the properties of the epilayer, offering opportu nities of material engineer-\ning. Here we discuss the possibility of straining the h-RFeO 3film, although no systematic\nwork on the strain effect has been reported on these films.\nBesides the epitaxial orientations discussed above, the interfacia l structure is another key\nproperty of the epitaxy. Depending on the relative strength betw een the interfacial bonding\n13(ψs−e) and the bonding in the epilayer ( ψe) and the lattice misfit, the interfacial structure\ncan be divided as the following categories, assuming the substrate is rigid (bonding in the\nsubstratesψs=∞). 1) When the ψs−eis much weaker than ψe, the interface is a vernier of\nmisfit.[41] The substrate and the epilayer maintain their structures ; there is minimal strain\nontheepilayer. 2)When the ψs−eismuch stronger than ψe, the interfacehas ahomogeneous\nstrain. The epilayer follows the structural of the substrates; th e epitaxy is pseudomorphic.\n3) When the ψs−eis comparable to ψe, the misfit is accommodated by a mixture of locally\nhomogeneous strain and dislocations. Over all, the epitaxy is called mis fit dislocation with\nperiodic strain. Ideally, the category 2), the homogeneous strain is desirable for material\nengineering. However, the category 3), misfit dislocations, corre sponding to a gradient\nof strain along the out-of-plane direction, also causes a change of material properties. On\naverage, the lattice parameter of the epitaxial film with misfit disloca tions will be in between\nthe value of the substrate and the bulk value of the film material, whic h can be consider as\npartially strained.\nA qualitative criteria for the homogeneous stain can be discussed us ing a one-dimensional\nmodel, in which the substrate is parameterized using a sinusoidal pot ential (period as,\namplitudeW), and the epilayer is parameterized as a chain of particles connecte d by springs\nof natural length aeand spring constant k; the misfit is defined as f=ae−as\nas.[41] The\nmaximum misfit allowed for a homogeneous strain was found as fs=2\nπλ, whereλ=/radicalBig\nka2e\n2W.\nAssuming that multiple epilayers can be described simply by replacing kwithnk, wheren\nis the number of epilayers, one can find the maximum number of epilaye rs that allows for\nhomoegeneous strain as n= (2\nfπλ)2. The bottom line of this model is that the homogeneous\nstain occurs only when the misfit is small and the interfacial bonding is strong.\nBased on this qualitative model, one can discuss the possible homogen eous strain in h-\nRFeO3films. Forthe Al 2O3(0001)substrates, the lattice mismatch of the super cell is small;\nbut the huge misfit of the lattice constant suggests weak interfac ial bonding. For YSZ (111)\nsubstrate, the similar oxygen network suggests strong interfac ial bonding. But the large\nmisfit (∼5%) makes the homogeneous strain more difficult. Therefore, the h omogenous\nstrain in h-RFeO 3on these substrates will have a very small critical thickness.\nPartially strained films have been reported for epitaxial growth of Y MnO3(0001) on\nYSZ (111).[43] In contrast, the strain effect of h-LuFeO 3(0001) on YSZ (111) is minimal. A\npossible model in terms of the difference in the electronic structure of RMnO 3and h-RFeO 3\n14has been proposed to account for the observation.[17] In this mod el, high flexibility of the\nRMnO 3lattice is hypothesized based on the 3d4configuration of Mn3+. In contrast, the\n3d5configuration of Fe3+makes the h-RFeO 3lattice more rigid. So the ψeand the effective\nspring constant kin h-RFeO 3are large, making these materials more difficult to strain and\nthe critical thickness is small. Note also that the lattice misfit betwee n RMnO 3(0001) and\nYSZ (111) is about half of that between h-RFeO 3(0001) and YSZ (111), which may also be\nan important factor of increased critical thickness in RMnO 3/YSZ, according to the model\ndiscussed above.\nFig. 6 shows a spectrum of the effective in-plane lattice constants o f surfaces of triangular\nsymmetry, calculated from the corresponding bulk structure. Ep itaxial growth of h-RFeO 3\non most of the materials as substrates have not been reported, w hich can be explained by\nthe lack of good lattice match. If a substrate of RMnO 3is used, the homogeneous strain\nmay be possible because the lattice mismatch is small and the interfac ial bonding is strong\ndue to the same P6 3cm lattice structure.\nIV. FERROELECTRICITY\nFIG. 7: (Color online) Structure of the h-RFeO 3at room temperature (a), (b) with P6 3cm\nsymmetry and at high temperature (c), (d) with P6 3/mmc symmetry. (e) The possible routes of\nstructure transitions. After Wang et. al. 2013.[13]\nThe transition from the high temperature paraelectric phase to th e ferroelectricity phase\n15FIG. 8: (Color online) Structural characterization of the h -LuFeO 3films. (a) A RHEED image\nof the h-LuFeO 3film at 300 K with an electron beam along the h-LuFeO 3[100] direction. (b)\nIntensities of the RHEED (100) peak and XRD (102) peak as func tions of temperature. After\nWang et. al. 2013.[13]\nFIG. 9: (Color online) Piezoelectric polarization of h-LuF eO3films. (a) PFM response displaying\nsquare-shaped hysteresis loop. The amplitude and phase are shown in the insets. (b) Schematic of\nwritten domain pattern with DC voltage ( V= 20 V dc). (c) PFM image of the same region without\nDC voltage. After Wang et. al. 2013.[13]\nin h-RFeO 3involves change of structure, including the symmetry and size of th e unit cell.\nAs shown in Fig. 7, from the high temperature P6 3/mmc structure to the low temperature\nP63cm structure, there are three possible routes, involving different intermediate structures.\nIn route (i), K 1mode freezes first, followed by the freezing of Γ−\n2and K 3; this generates an\nintermediate non-polar structure with trippled unit cell. In route (ii) , Γ−\n2mode freezes first,\nfollowed by the freezing of K 3; this generates an intermediate ferroelectric structure with\nthe same unit cell size as the high temperature structure. In rout e (iii), Γ−\n2and K 3freeze\nsimultaneously, with no intermediate state.\nThe structural transition of h-LuFeO 3has been studied up to 1150 K using x-ray and\n16electron diffraction.[13] As shown in Fig. 8, the room temperature RH EED pattern shows\nintense diffraction streaks separated by weak streaks, which can be understood in terms of\nthe detailed structure of h-LuFeO 3. The freezing of K 3mode corresponds to a√\n3×√\n3\nreconstruction in the a-b plane (tripling the unit cell). The RHEED pat tern is in perfect\nagreement with the√\n3×√\n3 reconstruction in the a-b plane. From the streak separation,\nthe in-plane lattice constants of the h-LuFeO 3films were estimated as to be consistent with\nthe value of the bulk P6 3cm structure. Hence, the indices of the diffraction streaks can be\nassigned using a P6 3cm unit cell, as indicated in Fig. 8(a). By measuring the diffraction\nintensities of the(102) peakof XRDand(100)peak ofRHEED as afu nction oftemperature,\nthe structural transition at which the trippling of unit cell disappea rs, was determined to\noccur at 1050 K. The piezoelectric reponse has been demonstrate d in h-LuFeO 3films, as\nshown in Fig. 9, using piezoforce microscopy (PFM).[13] Switching of t he polarization\ndirection at room temperature is also achieved using a conducting tip on a h-LuFeO 3film\ngrown on Al 2O3(0001) buffer with Pt. Combining the PFM study and the structural\ncharacterization, one may conclude that 1) the h-LuFeO 3films are ferroelectricity at room\ntemperature; 2) the polar structure and the trippling of unit cell p ersist at least up to 1050\nK.\nAnotherevidence oftheferroelectricity oftheh-LuFeO 3filmsgrownonPt-bufferedAl 2O3\n(0001) substrate, are in the temperature dependence of the ele ctric polarization, measured\nbetween300and650K.[11]Acleartransitionwasobservedat560K, whichwasattributedas\nthe Curie temperature of the ferroelectricity, because a dielectr ic anomaly was also observed\nat the same temperature. The electric polarization at 300 K was det ermined as 6.5 µC/cm2,\nwhich is comparable to that of YMnO 3.\nThese experimental observations are consistent with the theore tical calculations. It has\nbeen shown by the density functional calculations that the origin of ferroelectricity in h-\nLuFeO 3is similar to that in YMnO 3.[34] In other words, the instability of the Γ−\n2mode\nis induced by the frozen K 3mode. So h-LuFeO 3is intrinsically antidistortive, extrinsically\nferroelectric (improperly ferroelectric).\nThe ferroelectric properties in h-YbFeO 3have been studied on films grown on Al 2O3\n(0001) buffered with Pt by measuring the electric polarization.[10] Th e polarization-electric\nfield loop was demonstrated to verify the ferroelectricity of h-YbF eO3(Fig. 10(a). The most\ninteresting finding in h-YbFeO 3is the two-step transition in the temperature dependence\n17FIG. 10: (Color online) Charcterization of the ferroelectr icity in h-YbFeO 3films. a) Polarization-\nelectric field loop measured at two different temperatures. b) Temperature dependence of the\nelectric polarization. After Jeong et. al. 2012.[10]\nof the electric polarization. As shown in Fig. 10 (b), the ferroelectr ic polarization becomes\nnon-zero below 470 K and a second transition occurs at 225K; the lo w-temperature electric\npolarization was determined to be 10 µC/cm2. A two-step structural transition sequence is\nproposed as P6 3/mmc→P63mc→P63cm, based on the two observed transitions in the\nelectric polarizations. This sequence corresponds to route ii) in Fig. 7. The most intriguing\ninference here is that h-YbFeO 3is properly ferroelectric with a P63mc structure at room\ntemperature, which is difference from that of RMnO 3. On the other hand, reconstruction-\nfashioned3-foldperiodicitywasobservedinelectrondiffractionpat ternatroomtemperature,\nindicating a trippling of the unit cell (compared with that of P6 3/mmc) in h-YbFeO 3, which\ncontradicts the proposed P6 3mc structure at room temperature.[12] Direct observation of\nthe structural transition has not been demonstrated to occur a t the transition of electric\npolarization. Other indication of the polar structure at room tempe rature is indicated by\nthe optical second harmonic generation (SHG).[12] In particular, a transition in the SHG\nsignal was observed at 350 K. Dielectric anomaly was also observed in h-YbFeO 3at this\ntemperature, indicating ferroelectricity.\nAlthough it is a consensus that the ferroelectric transition in h-RFe O3is accompanied by\na structural transition, there is significant controversy in the lite rature about the symmetry\nof the structures and the transition temperature, which may be d ue to the sample-sample\nvariation. A study on the structural and ferroelectricy transitio n of the same samples should\nbe helpful in clarifying this issue.\n18V. MAGNETISM\nAs discussed in Section IB, the low temperature structure of h-RF eO3has the same space\ngroup P6 3cm as that of RMnO 3. This plus the assumption that the magnetic unit cell is\nthe same as the structural unit cell, result in the four possible magn etic structures shown\nin Fig. 3, same as those in RMnO 3. The distinction of h-RFeO 3compared with RMnO 3\nis following: 1) The spins of Fe3+are canted slightly out of the FeO plan, causing a weak\nferromagnetism in theΓ 2spin structure; thisis reported forall the h-RFeO 3regardless of the\nR3+site.[9–11, 11–13, 31] 2) When the R3+sites are magnetic, the moment of R3+will be\naligned by the field of Fe3+sites, generating a large magnetic moment at low temperature;\nthe moment per formular unit (f.u.) is close to that of the R3+.[10, 12] 3) The higher spin\nof Fe3+and the stronger exchange interactions between the Fe3+sites (compared with those\nof the Mn3+) suggests higher magnetic ordering temperature TN.[34]\nThe weak ferromagnetism in h-LuFeO 3was first reported in films grown using metal-\norgannic chemical vapor deposition (MO-CVD) and confirmed later o n in films grown using\npulsed laser deposition and molecular beam epitaxy.[9, 11, 13, 31] The origin of the weak\nferromagnetism is attributed to the canting of magnetic moment of Fe3+because Lu3+has\nno magnetic moment. An important issue of the magnetism of h-LuFe O3films is the sto-\nichiometry dependence. A non-stoichiometric h-LuFeO 3film may contain LuFe 2O4, Fe3O4\nand Lu 2O3phases. These impurity phasese, particularlly LuFe 2O4and Fe 3O4may coexist\nepitaxially with the h-LuFeO 3structure, which can introduce confusion in the magnetic\ncharacterization since both are ferrimagnetic (the Neel tempera ture are 240 K and 860\nK for LuFe 2O4and Fe 3O4respectively). Indication of magnetic impurities was observed\nin Fe-rich h-LuFeO 3films as the two-step transitions in the temperature dependence o f the\nmagnetization.[31] The transition at lower temperature is expected to be from h-LuFeO 3be-\ncause the higher transition is consistent with the formation of ferr imagnetism in h-LuFe 2O4.\nAn important observation is that the weak ferromagnetism of h-Lu FeO3occurs at higher\ntemperature when the Fe concentration is higher and saturate wh en the Fe and Lu ratio are\nclose to one.\nFigure 11 shows the temperature and magnetic field dependence of the magnetization\nof a nominally stoichiometric h-LuFeO 3film.[31] From the M−Trelation, the critical\ntemperature for the weak ferromagnetism ( TW) is determined as approximately 147 K, and\n19FIG. 11: (Color online) Weak ferromagnetism of a nominally s toichiometric h-LuFeO 3film. (a)\nTemperature dependence ( M−T) of the magnetization in both field cool (FC) and zero field coo l\n(ZFC) processes; the magnetic field is along the c-axis. (b) M−Tin both FC ZFC; the magnetic\nfield is perpendicular to the c-axis. (c) The field depdendence of ( M−H) when the magnetic field\nat different magnetic field directions and temperatures. Afte r Moyer et. al. 2014.[31]\nthe out-of-plane component of the Fe3+moment is 0.018 µB/formula unit. From the low\ntemperature M−Hrelations, the coercive field of h-LuFeO 3is found as approximately 25\nkOe at 50 K. Therefore, there is a huge anisotropy in the magnetic m oment of h-LuFeO 3;\nthec-axis is the easy axis. The sharp change of magnetization at 25 kOe in Fig. 11 indicate\nthat the magnetic moments in h-LuFeO 3areIsing-like, which isconsistent thecanting model\nfor the origin of the weak ferromagnetism. Even in the nominally stoic hiometric h-LuFeO 3\nfilms, there appears to be a second magnetic component that pers ist beyond 350 K; this\ncomponent also show anisotropy according to the M−Trelations. The true nature of\nthis second component is however difficult to determine from the mag netometry in Fig. 11\nbecause of the limited temperature range of the measurement.\n20FIG. 12: (Color online) Ferrimagnetism in h-YbFeO 3films. (a) Magnetic-field dependence of the\nmagnetization at various temperatures (after Jeong et. al. 2012).[10] (b) Temperature dependence\nof the high-field magnetization. The dots are the experiment al magnetization values taken from\n(a) at 10000 Oe. The lines are simulations.\nWhentheR3+sitearemagnetic(R=Dy-Yb),thetotalmagneticmomentofh-RFe O3have\ncontributions frombothFe3+and R3+sites. It turns out that the total moment of h-YbFeO 3\nalong thec-axis can be much larger than that of h-LuFeO 3.[10, 12] As shown in Fig. 12(a),\nthe magnetization of h-YbFeO 3at 3 K in 10000 Oe is close to 4 µBper formular unit, the\nmagnetic moment of free Yb3+. Therefore, the measured magnetization in Fig. 12(a) should\ncome mainly from the moment of Yb3+. According to the temperature dependence of the\nhigh-field magnetization [see Fig. 12(b)], the Yb3+sites show paramagnetic-like behavior.\nOn the other hand, the onset of the field-cool magnetization sugg ests a correlation between\nthe magnetization of the Yb3+sites with that of theFe3+sites. Below, we model the effect of\nthe magnetization of the Fe3+sites on that of the Yb3+sites, assuming that the interaction\nbetween the Yb3+sites are weak enough to be ignored.\nThe Yb3+can be polarized by an effective magnetic field Beff, which is a combination\nof the external field Hand the molecular field from Fe3+sites:\nBeff=µ0H+γMFe, (9)\nwhereMFeis the magnetization of the Fe3+sites andγrepresents the strength of the\ninteractionbetween Yb3+andFe3+sites. SincetheYb3+sitesareassumedtobeisolated, the\naverage projection of the magnetic moment along the c-axis,∝a\\gbracketleftµYb∝a\\gbracketright, follows the paramagnetic\nbehavior described by the Langevin function:\n∝a\\gbracketleftµYb∝a\\gbracketright=µYbL(µYbBeff\nkBT), (10)\n21whereLis the Langevin function, µYbis the magnetic moment of Yb3+,kBis the Boltzmann\nconstant, and Tis temperature. Note that MFeis temperature dependent; here we assume\nMFe=M0\nFecos(π\n2T\nTW) forT <T W, andMFe= 0 forT >T W.\nBy fitting the experimental data in Fig. 12(b) at H= 10000 Oe using Eq. (10)\nwith parameters TW= 120 K and M0\nFe= 0.02µB/f.u, we found µ0\nYb= 4.3µBand\nγ= 200T/(µB/f.u.); this corresponds to a molecular field of 4 T for MFe=0.02µB/f.u.\nThe simulated magnetization (same as ∝a\\gbracketleftµYb∝a\\gbracketrightinµB/f.u.) at 10000 Oe is displayed in\nFig. 12, using the parameters found from the fitting. A simulation as suming no molecular\nfield from Fe3+site (γ=0) is also shown for comparison. It is clear that the moments of\nYb3+sites are significantly polarized by the molecular field of Fe3+. In other words, the\nweak spontaneous magnetization from the Fe3+sites are magnified by the existence of large,\nisolated Yb3+moments, which generates a huge residual magnetization at low tem perature,\nas displayed in Fig. 12(a).\nFIG. 13: (Color online) Indication of high-temperature ant iferromagnetism in h-LuFeO 3films.\nTemperature dependence of the intensities of the (100) (a) a nd (102) (b) peaks of the neutron\ndiffractions. (c) The FC and ZFC magnetization along the c-axis as a function of temperature. (d)\nScan of diffraction peak (300) in reciprocal lattice unit (r.l .u.) at 4 and 450 K. After Wang et. al.\n2013.[13]\nAs discussed in Section IC, the magnetic orders in h-RFeO 3areessentially 120-degree an-\ntiferromagnetic. Amongthefourpossiblemagneticstructures, t heDMinteractioncoefficient\n22/vectorDi,jis non-zero only for Γ 2and Γ3. The alignment between neighboring FeO layers are ferro-\nmagnetic and antiferomagnetic in Γ 2and Γ3respectively. Therefore, the Γ 2structure can be\ndetermined using magnetometry because of the non-zero sponta neous magnetization, which\ncorresponds to the weak (parasitic) ferromagnetism discussed a bove. On the other hand, the\nother antiferromagnetic structures are more difficult to identify u sing magnetoemtry alone,\nparticularly in thin film samples which contain small amount of materials.\nNeutron diffraction offers a way of measuring the magnetic orders w ithout the need for a\nnet magnetization, which is more suitable for antiferromagnetic mat erials.[44] In addition,\ndifferent selection rules of different diffraction peaks may provide mo re information on the\nmagnetic structures.\nBecause the crystallographic and magnetic structure of h-RFeO 3have the same unit cell,\nin general, the intensities of the neutron diffraction peaks have con tributions from both nu-\nclear and magnetic interactions between the atoms and the neutro n beams. However, the\nintensity could be dominated by nuclear or magnetic diffraction becau se of the difference\nbetween the two kinds of interactions: 1) all the sites contribute t o the nuclear diffraction\nwhile only magnetic sites (Fe3+in the case of h-LuFeO 3) contribute to the magnetic diffrac-\ntion; 2) the selection rules are different for the two interactions. O ne way to identify the\ncontribution of the intensities is to examine the temperature depen dence of the peak inten-\nsities and compare with that of the x-ray and electron diffraction wh ich are not expected to\nreflect the magnetic interactions. As shown in Fig. 13(a) and (b), d iffraction peaks (100)\nand (102) show transitions at 130 and 440 K respectively. These tr ansitions do not occur\nin x-ray and electron diffraction,[13, 45] indicating that the magnetic diffraction contributes\nsignificantly in the (100) and (102) peak intensities. In particular,th e 130 K is also the crit-\nical temperature of the weak ferromagnetism TWin h-LuFeO 3[see Fig. 13(c)], indicating\na transition of spin structure at TW. In contrast, the neutron diffraction intensities do not\nchange significantly for (300) peaks in the temperature range 4 K < T <450 K, which is\nsimilar to the behavior of the peaks in electron and x-ray diffractions (Fig. 8). Therefore,\nthe diffraction intensity of the (300) peak is dominated by the nuclea r contributions.\nThe intensity of the magnetic diffraction of a neutron beam follows:[44 ]\nI∝ |/summationdisplay\nipi/vector qiei2π/vectorh·/vector ri|2, (11)\nwhere/vector qi=/vectorh(/vectorh·/vector mi)−/vector mi,piis the isotope specific factor for each site, /vector miis the unit\n23vector of the magnetic moment and /vectorhiis the unit vector perpendicular to the atomic planes\ninvolved in the diffraction. Because the factor /vector qithat depends on the orientations of the\nmagnetic moments, does not play a role in the nuclear diffraction, new selection rules are\ngenerated. In short, only Γ 1and Γ3contributes to the (100) magnetic diffraction intensities.\nThe contribution to diffraction intensities from the Fe3+sites of the z=1/2 andz=0 layers\nare cancelled out for Γ 2and Γ 4magnetic structures. This cancellation does not occur for\n(102) magnetic diffraction because the factors introduced by the differentzpositions; for\nthe (102) peak, the diffraction intensity is non-zero for all the spin structures Γ 1through\nΓ4.\nTherefore, the combination of the significant intensity of the (100 ) neutron diffraction\npeak and the weak ferromagnetism below TWindicates that the magnetic structure in h-\nLuFeO 3is a mixture of Γ 1and Γ 2. AboveTW, the (100) peak diminishes while (102) peak\npesists up to 440 K; this suggests a antiferromagnetic order betw een 130 K and 440 K,\nmost probably with a Γ 4magnetic structure.[13] The coexistence of the antiferromagnet ic\norder and ferroelectricity above room temperature in h-LuFeO 3, makes this material room-\ntemperature multiferroic. To date, the high-temperature antife rromagnetic order has not\nbeen confirmed using other method of characterization, which may be because of the ex-\nperimental difficulty in determining antiferromagnetism, particularlly in thin film samples.\nNevertheless, this high temperature antiferromagnetism is an ess ential issue in h-RFeO 3. If\nthe room-temperature antiferromagnetism does exist, then the transition at TWis a spin\nreorientation, which may be adjusted by tuning the structure of h -RFeO 3; this may lead to\nthe simultaneous ferroelectricity and weak ferromagnetism above room temperature in the\nsingle phase h-RFeO 3.\nVI. MAGNETOELECTRIC COUPLINGS\nOne of the most interesting topic in h-RFeO 3is the possible coupling between the elec-\ntric and magnetic degrees of freedom. This coupling may be manifest ed as a change of\nelectric (magnetic) properties in a magnetic (electric) field or at a ma gnetic (ferroelectric)\ntransition. There has been some evidence of magnetoelectric coup ling reported in the liter-\nature. For example, it was observed that the dielectric constant in h-YbFeO 3is sensitive at\na ferroelectric transition temperature.[10] The optical second ha rmonic generation increases\n24below theTW.[12] More importantly, the desirable property of switching the spon taneous\nmagnetization in h-RFeO 3using an electric field has been predicted theoretically.[34] Due to\nthe improper nature of both ferroelectricity and ferromagnetism in h-RFeO 3, the structural\ndistortion may mediate the coupling between the ferroelectric and m agnetic orders;[45] this\nmay cause a reversal of magnetization of h-RFeO 3in a electric field.[34]\nVII. CONCLUSION\nIn conclusion, h-RFeO 3is an intriguing family of materials in terms of multiferroic prop-\nerties. Despite the similarity with the RMnO 3family, the uniqueness of the coexisting\nspontaneous electric and magnetic polarization suggests promising application potentials.\nOn the other hand, a great deal of investigations still need to be do ne, because even the\nfundamental properties, such as structure, ferroelectricity, and magnetism are under debate.\nIn addition, the magnetoelectric couplings in h-RFeO 3, as extremely appealing properties\npredicted by theory, are yet to be studied in different aspects. We expect to learn more\nexciting physics from the material family h-RFeO 3in the future.\nAcknowledgments\nX.S.X. acknowledges the support from the Nebraska EPSCoR.\nAppendix A: Structural Stability in RFeO 3\nRFeO3(R=La-Lu, Y) is known to crystallize in two structure families. The st able struc-\nture for bulk stand-alone RFeO 3is orthorhombic (orthoferrite).[89] In contrast, the stable\nstructure for manganites are hexagonal for R of small ionic radius (R=Ho-Lu, Y, Sc)[46].\nIn order to understand the structural stability of RFeO 3, we take an overview of the ABO 3\ncompounds of different A and B sites. Table II displays the stable str ucture of selected\nABO3compound, where A sites include rare earth, Y, and Sc, and B sites in clude Sc-Ni.\nThe stable structures of most of the compounds are orthorhomb ic. For small A site (Sc),\nthe bixbyite structure is stable. When the radius is large for A site an d small for B site, the\nrhombohedral structure becomes stable.\n25TABLE II: Stable structure type of the selected ABO 3compounds at ambient temperature and\npressure, where A=Sc, Y, La-Lu, and B=Sc-Ni. The radii (in pm ) of the trivalent ion are in the\nparenthesis. The atoms are sorted according to their ionic r adii. The structures are abbreviated:\no for orthorhombic, r for rhombohedral, b for bixbiyte, and h for hexagonal.\nA\\B Site Sc(74.5) Ti(67) Mn(64.5) Fe(64.5) V(64)Cr(61.5) Co( 61)Ni(60)\nLa (103.2) o[47, 48] o[49]o[50, 51] o[52] o[53, 54] o[47, 55] r[56] r[57]\nCe (101) o[58] o[59] o[53, 54]\nPr(99) o[47, 48] o[49] o[51] o[52] o[47, 54] o[47] o[60]o[57 , 61]\nNd (98.3)o[47, 48, 62]o[49] o[51] o[52] o[47, 54] o[47] o[63 ] o[57]\nSm (95.8) o[48, 62] o[49] o[51] o[52] o[54] o[47] o[63]o[57, 64]\nEu (94.7) o[48, 65] o[51, 66] o[52] o[63]o[64, 67]\nGd (93.8)o[47, 48, 62]o[49] o[68] o[52, 69] o[47, 54] o[47]\nTb (92.3) o[48, 70] o[49] o[71] o[72] o[54] o[60] o[63]\nDy (91.2) o[48, 62] o[49]o[51, 73] o[72] o[54] o[74] o[60]\nHo (90.1) o[48] o[49] h[75] o[72] o[76] o[77] o[60]\nY (90) o[47] o[49]h[33, 75]o[52, 78] o[54] o[47]\nEr (89) o[49] h[75] o[72] o[54] o[79] o[60]\nTm (88) o[49] h[75] o[72] o[80] o[60]\nYb (86.8) o[49]h[75, 81] o[72] o[54] o[82] o[60]\nLu (86.1) o[49]h[75, 83] o[72] o[54] o[84] o[60]\nSc (74.5) b[85] b[86]h[33, 75] b[87] b[88]\nIn general, the stability of a crystal structure is related to the ion ic radius. If the ionic\nradius of A and B atoms ( rAandrBrespectively) are very different, the stable structure\ncontains two very different sites for metal ions. A good example is th e perovskite structure\n(see Fig. 14 (a)). The relation between the ionic radius can be found from the geometry as\nt=rA+rO√\n2(rB+rO)= 1, (A1)\nwheretis called tolerance factor and rOis the ionic radius of O2−.[46] Here the A ions\nhave 12 oxygen neighbor while B ions have only 6 neighbor, correspon ding to the large\n26FIG. 14: (Color online) The structures in TABLE II for ABO 3compounds. The perovskite\nstructure contains BO 6octahedra and AO planes. The psedo-cubic ABO 3fractions are indicated\nin the rhombohedral and othorhombic structures. The orthor hombic structure can be viewed as\nthe perovskite structure with rotated BO 6octahedra. The rhombohedral structure can be viewed\nas the perovskiste structure distorted along the [111] diag onal direction, in which the A atoms\nmove out of the AO planes. In the bixbyite structure, the A and B atoms are not distinguished by\nthe atomic sites they occupy.\ndifference between the two kinds of ionic radii . On the other hand, p erfect satisfaction\nof Eq. (A1) is rare, which is why perfect perovskite structure is ra re. Iftdecreases from\n1 (the radii of A and B ions become less different), a structural dist ortion to reduce the\ncoordination of the A ions occurs while keeping the coordination of th e B ions as 6; this is\nachieved by either moving A ions out of the AO plane or by rotating the BO6octahedra. As\nshown in Fig. 14, in the distorted structures (rhombohedral or or thorhombic), the A ions\nmove closer to some O2−but away from other O2−, reducing the coordination for A ions.\nWhen the radii of A and B sites are close, the stable structure is bixb yite in which the A\nand B ions occupy the similar sites.[90]\nOn the other hand, the stability of the hexagonal manganites cann ot be understood using\nthe argument of atomic radius discussed above. More specifically, t he structures for RFeO 3\nand RMnO 3(for R= Ho-Lu, Sc, Y) are very different, while the radii of Fe3+and Mn3+are\n27identical (see Table II). Therefore, the electronic structure mu st play an important role in\nthe stability of the hexagonal manganites. Below, we propose a mod el to explain why some\nmanganites are stable in hexagonal structure in terms of the elect ronic structure of Mn3+.\nFIG.15: (Coloronline)Acrystal-fieldenergymodelforthes tability ofhexagonalmanganites. The\nelectronic configuration of the Mn3+(3d4) in octahedral environment (left) and trigonal bipyramid\n(right). The adoption of the MnO 5local environment may reduce the total energy and stabilize d\nthe hexagonal structure.\nFig. 15 displays the electronic configuration in the local environment of orthorhombic\nand hexagonal structures respectively. In the orthorhombic st ructure, the energy level of\nthe 3d electrons in the 6-coordinated Mn3+is split into t2gandeglevels. Only one eglevel\nis occupied while all the t2glevels are singly occupied in Mn3+with a 3d4configuration,\ngenerating a degeneracy. In the hexagonal structure, the ene rgy level of the 3d electrons in\nthe5-coordinatedMn3+issplitinto e′′,e′, anda′\n1levels. Thereisnoelectronicdegeneracyfor\nMn3+in this case because the highest level a′\n1is not degenerate. According to the evolution\nof the 5 3d orbitals (xx-yy, zz, xy, yz, zx), the electronic configu ration can be treated as\nthe splitting of t2gandeglevels due to the MnO 6to MnO 5distortion. If we assume that\nthe distortion does not change the total energy of the electronic levels (i.e.Exx−yy+Ezzand\nExy+Eyz+Ezxare both conserved), the total energy of the electronic configu ration in MnO 5\nis lower than that in MnO 6. This scenario is only true for Mn3+with 3d4configuration\nbecause of the electronic degeneracy. In contrast, for other t rivalent ions (Sc to Ni), the\nhexagonal structure will not be stable, because the5-coordinat edlocal environment does not\nreduce the energy. At the same time, the distortion to hexagonal structure must decrease\nthe ionic bonding energy because of the reduced coordination. The competition between\nthe two effects stabilized the hexagonal structure for small A ions (Ho-Lu, Sc, Y).\n28[1] D. Khomskii, Physics 2, 20 (2009).\n[2] N. A. Spaldin, S. W. Cheong, and R. Ramesh, Physics Today 63, 38-43 (2010).\n[3] G. Catalan, & J. F. Scott, Advanced Materials 21, 2463 (2009).\n[4] R.C. Pullar, Progress in Materials Science, 57, 1191 (2012).\n[5] Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamu ra, & T. Kimura. Nature Mate-\nrials,9, 797 (2010).\n[6] M. Soda, T. Ishikura, H. Nakamura, Y. Wakabayashi, & T. Ki mura, Physical Review Letters,\n106, 087201 (2011)\n[7] A.D. Christianson, M.D. Lumsden, M. Angst, Z. Yamani, W. Tian, R. Jin, E.A. Payzant, S.E.\nNagler, B.C. Sales, and D. Mandrus, Phys. Rev. Lett. 100, 107601 (2008).\n[8] J. de Groot, T. Mueller, R.A. Rosenberg, D.J. Keavney, Z. Islam, J.-W. Kim, and M. Angst,\nPhys. Rev. Lett. 108, 187601 (2012).\n[9] A.R. Akbashev, A.S. Semisalova, N.S. Perov, and A.R. Kau l, Appl. Phys. Lett. 99, 122502\n(2011).\n[10] Y.K. Jeong, J. Lee, S. Ahn, S.-W. Song, H.M. Jang, H. Choi , and J.F. Scott, J. Am. Chem.\nSoc.134, 1450 (2012).\n[11] Y.K. Jeong, J.-H. Lee, S.-J. Ahn, and H.M. Jang, Chem. Ma ter.24, 2426 (2012).\n[12] H. Iida, T. Koizumi, Y. Uesu, K. Kohn, N. Ikeda, S. Mori, R . Haumont, P.-E. Janolin, J.-M.\nKiat, M. Fukunaga, and Y. Noda, J. Phys. Soc. Japan 81, 024719 (2012).\n[13] W. Wang, J. Zhao, W. Wang, Z. Gai, N. Balke, M. Chi, H.N. Le e, W. Tian, L. Zhu, X. Cheng,\nD.J. Keavney, J. Yi, T.Z. Ward, P.C. Snijders, H.M. Christen , W. Wu, J. Shen, and X. Xu,\nPhys. Rev. Lett. 110, 237601 (2013).\n[14] H. Walitzki, H. Rath, J. Feffle, S. Pahlke, O. Yamaguchi, H . Takemura, and M. Yamashita,\nJ. Electrochem. Soc. 138, 1492 (1991).\n[15] Y. Mizoguchi, H. Onodera, and H. Yamauchi, Mater. Sci. E ng. AA217/A218 , 164 (1996).\n[16] K. Nagashio and K. Kuribayashi, J. Am. Ceram. Soc. 85, 2550 (2002).\n[17] A.A. Bossak, I.E. Graboy, O.Y. Gorbenko, A.R. Kaul, M.S . Kartavtseva, V.L. Svetchnikov,\nand H.W. Zandbergen, Chem. Mater. 16, 1751 (2004).\n[18] K. Nagashio, K. Kuribayashi, M.S. Vijaya Kumar, K. Niwa ta, T. Hibiya, a. Mizuno, M.\n29Watanabe, and Y. Katayama, Appl. Phys. Lett. 89, 241923 (2006).\n[19] K. Kuribayashi, K. Nagashio, K. Niwata, M.S. V Kumar, an d T. Hibiya, Rev. Adv. Mater.\nSci.18, 444 (2008).\n[20] J. Li, U.G. Singh, T.D. Schladt, J.K. Stalick, S.L. Scot t, and R. Seshadri, Chem. Mater. 20,\n6567 (2008).\n[21] M.S. V Kumar, K. Nagashio, T. Hibiya, K. Kuribayashi, an d M.S. Vijaya Kumar, J. Am.\nCeram. Soc. 91, 806 (2008).\n[22] M.S. Vijaya Kumar, K. Kuribayashi, and K. Kitazono, J. A m. Ceram. Soc. 92, 903 (2009).\n[23] S. Hosokawa, H.-J. Jeon, S. Iwamoto, and M. Inoue, J. Am. Ceram. Soc. 92, 2847 (2009).\n[24] E. Magome, C. Moriyoshi, Y. Kuroiwa, A. Masuno, and H. In oue, Jpn. J. Appl. Phys. 49,\n09ME06 (2010).\n[25] S. Hosokawa, H.-J. Jeon, and M. Inoue, Res. Chem. Interm ed.37, 291 (2011).\n[26] V. V. Pavlov, a. R. Akbashev, a. M. Kalashnikova, V. a. Ru sakov, a. R. Kaul, M. Bayer, and\nR. V. Pisarev, J. Appl. Phys. 111, 56103 (2012).\n[27] A.R. Akbashev, V. V. Roddatis, A.L. Vasiliev, S. Lopati n, A.S. Semisalova, N.S. Perov, V. a.\nAmelichev, and A.R. Kaul, CrystEngComm 14, 5373 (2012).\n[28] A. R. Akbashev, V. V Roddatis, a L. Vasiliev, S. Lopatin, V. a Amelichev, and a R. Kaul,\nSci. Rep. 2, 672 (2012).\n[29] V. V. Roddatis, A.R. Akbashev, S. Lopatin, and A.R. Kaul , Appl. Phys. Lett. 103, 112907\n(2013).\n[30] A. Masuno, A. Ishimoto, C. Moriyoshi, N. Hayashi, H. Kaw aji, Y. Kuroiwa, and H. Inoue,\nInorg. Chem. 52, 11889 (2013).\n[31] J. a. Moyer, R. Misra, J. a. Mundy, C.M. Brooks, J.T. Hero n, D. a. Muller, D.G. Schlom, and\nP. Schiffer, APL Mater. 2, 012106 (2014).\n[32] C. J. Fennie and K. M. Rabe, Physical Review B 72, 100103 (2005).\n[33] A. Munoz, J. A. Alonso, M. J. Martinez-Lope, M. T. Cassis , J. L. Martinez, and M. T.\nFernandez-Diaz, Physical Review B 62, 9498 (2000).\n[34] H. Das, A.L. Wysocki, Y. Geng, W. Wu, and C.J. Fennie, Nat Commun 5, 2998 (2014).\n[35] I. Dzyaloshinsky, Journal of Physics and Chemistry of S olids4, 241 (1958).\n[36] F. J. Morin, Physical Review 78, 819 (1950).\n[37] L.J. Downiea, R.J. Goffa, W. Kockelmannb, S.D. Forderc, J .E. Parkerd, F.D. Morrisona, P.\n30Lightfoota, L.J. Downie, R.J. Goff, W. Kockelmann, S.D. Forde r, J.E. Parker, F.D. Morrison,\nand P. Lightfoot, J. Solid State Chem. 190, 52 (2012).\n[38] M.V. Kumar, K. Kuribayashi, J. Yu, J.T. Okada, and T. Ish ikawa, J. Am. Ceram. Soc. 96,\n995 (2013).\n[39] W. Wang, H. Wang, X.X. Xu, L. Zhu, L. He, E. Wills, X. Cheng , D.J. Keavney, J. Shen, X.\nWu, and X. Xu, Appl. Phys. Lett. 101, 241907 (2012).\n[40] L. Royer, Bull. Soc. Fr. Mineralog. Crystallogr. 51, 7 (1928).\n[41] Markov, I. V. Crystal Growth for Beginners: Fundamenta ls of Nucleation, Crystal Growth\nand Epitaxy. Singapore ; River Edge, N.J. : World Scientific ( 2003).\n[42] C. Dubourdieu, G. Huot, I. Gelard, H. Roussel, O.I. Lebe dev, and G. Van Tendeloo, Philos.\nMag. Lett. 87, 203 (2007).\n[43] K.H. Wu, H.-J. Chen, Y.T. Chen, C.C. Hsieh, C.W. Luo, T.M . Uen, J.Y. Juang, J.-Y. Lin,\nT. Kobayashi, and M. Gospodinov, Europhysics Lett. 94, 27006 (2011).\n[44] S. W. Lovesey, Theory of Neutron Scattering from Conden sed Matter (Clarendon Press, Ox-\nford, 1984).\n[45] H. Wang;, I. V. Solovyev;, W. Wang;, X. Wang;, P. Ryan;, D .J. Keavney;, J.-W. Kim;, T.Z.\nWard;, L. Zhu;, X.M. Cheng;, J. Shen;, L. He;, X. Xu;, and X. Wu ;, arXiv:1312.6984 (2014).\n[46] The ionic radius in an oxide depends on the coordination (number of oxygen neighbors) and\nvalence. In this paper, we assume 3+ for the valence and 6 oxyg en neighbors. The radius of\n6-coordinate O2−is 140 pm.\n[47] S. Geller, Acta Crystallogr. 10, 243 (1957).\n[48] R.P. Liferovich and R.H. Mitchell, J. Solid State Chem. 177, 2188 (2004).\n[49] H.D. Zhou and J.B. Goodenough, J. Phys. Condens. Matter 17, 7395 (2005).\n[50] F. Moussa, M. Hennion, J. Rodriguez-Carvajal, H. Moudd en, L. Pinsard, and A. Revcolevschi,\nPhys. Rev. B 54, 15149 (1996).\n[51] B. Dabrowski, S. Kolesnik, A. Baszczuk, O. Chmaissem, T . Maxwell, and J. Mais, J. Solid\nState Chem. 178, 629 (2005).\n[52] S. Geller and E. a. Wood, Acta Crystallogr. 9, 563 (1956).\n[53] H.C. Nguyen and J.B. Goodenough, J. Solid State Chem. 119, 24 (1995).\n[54] S. Miyasaka, Y. Okimoto, M. Iwama, and Y. Tokura, Phys. R ev. B68, 100406 (2003).\n[55] T. Hashimoto, N. Tsuzuki, A. Kishi, K. Takagi, K. Tsuda, M. Tanaka, K. Oikawa, T.\n31Kamiyama, K. Yoshida, H. Tagawa, and M. Dokiya, Solid State I onics132, 183 (2000).\n[56] L.B. Sis, J. Appl. Phys. 44, 5553 (1973).\n[57] J.L. Garcia-Munoz, J. Rodriguez-Carvajal, P. Lacorre , and J.B. Torrance, Phys. Rev. B 46,\n4414 (1992).\n[58] J.E. Sunstrom, S.M. Kauzlarich, and M.R. Antonio, Chem . Mater. 5, 182 (1993).\n[59] M. Robbins, G.K. Wertheim, A. Menth, and R.C. Sherwood, J. Phys. Chem. Solids 30, 1823\n(1969).\n[60] J. a. Alonso, M.J. Martinez-Lope, C. de la Calle, and V. P omjakushin, J. Mater. Chem. 16,\n1555 (2006).\n[61] P. Lacorre, J.B. Torrance, J. Pannetier, A.I. Nazzal, P .W. Wang, and T.C. Huang, J. Solid\nState Chem. 91, 225 (1991).\n[62] B. Velickov, V. Kahlenberg, R. Bertram, and M. Bernhage n, Zeitschrift Fur Krist. 222, 466\n(2007).\n[63] G. Demazeau, M. Pouchard and P. Hagenmuller, J. Solid St ate Chem., 9, 512 (1974).\n[64] S. Rosenkranz, M. Medarde, P. Lacorre, F. Fauth, and V. T rounov, Phys. Rev. B 57, 456\n(1998).\n[65] V. Kahlenberg, D. Maier, and B. Velikov, Acta Crystallo gr. Sect. E. Struct. Rep. Online 65,\ni8 (2009).\n[66] Y. Tadokoro, Y.J. Shan, T. Nakamura, and S. Nakamura, So lid State Ionics 108, 261 (1998).\n[67] J.A. Alonso, J.L. Garcia-Munoz, M.T. Fernandez-Diaz, M.A.G. Aranda, M.J. Martinez-Lope,\nand M.T. Casais, Phys. Rev. Lett. 82, 3871 (1999).\n[68] T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A.P. Ramirez , Phys. Rev. B 71, 224425 (2005).\n[69] S. Geller, J. Chem. Phys. 24, 1236 (1956).\n[70] B. Velickov, V. Kahlenberg, R. Bertram, and R. Uecker, A cta Crystallogr. Sect. E-Structure\nRep. Online 64, I79 (2008).\n[71] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, a nd Y. Tokura, Nature 426, 55\n(2003).\n[72] M. Marezio, J.P. Remeika, and P.D. Dernier, Acta Crysta llogr. Sect. B Struct. Crystallogr.\nCryst. Chem. 26, 2008 (1970).\n[73] T. Mori, K. Aoki, N. Kamegashira, T. Shishido, and T. Fuk uda, Mater. Lett. 42, 387 (2000).\n[74] I.B. Krynetskii and V.M. Matveev, Phys. Solid State 39, 584 (1997).\n32[75] H.L.J. Yakel, W.C. Koehler, E.F. Bertaut, and E.F. Forr at, Acta Crystallogr. 16, 957 (1963).\n[76] M. Sikora, C. Marquina, M.R. Ibarra, a. a. Nugroho, and T .T.M. Palstra, J. Magn. Magn.\nMater.316, e692 (2007).\n[77] B. Tiwari, M.K. Surendra, and M.S.R. Rao, J. Phys. Conde ns. Matter 25, 216004 (2013).\n[78] H. Kawano, H. Yoshizawa, and Y. Ueda, J. Phys. Soc. Japan 63, 2857 (1994).\n[79] M. Kanekot, S. Kuritaz, and K. Tsushimat, J. Phys. C Soli d State Phys 10, 1979 (1977).\n[80] K. Yoshii, Mater. Res. Bull. 47, 3243 (2012).\n[81] M. Isobe, N. Kimizuka, M. Nakamura, and T. Mohri, ACTA Cr ystallogr. Sect. C-CRYSTAL\nStruct. Commun. 47, 423 (1991).\n[82] N. Kojima, I. Tsujikawa, H. Hori, H. Nishimura, M. Date, and K. Tsushima, J. Phys. Soc.\nJapan53, 2875 (1984).\n[83] B.B. Van Aken, A. Meetsma, and T.T.M. Palstra, Acta Crys tallogr. Sect. E Struct. Reports\nOnline57, i101 (2001).\n[84] J.P. van der Ziel and L.G. van Uitert, J. Appl. Phys. 40, 997 (1969).\n[85] S. Geller, P. Romo, and J.P. Remeika, ZEITSCHRIFT FUR Kr ist. Krist. Krist. Krist. 124,\n136 (1967).\n[86] S.P. Shafi, B.C. Hernden, L.M.D. Cranswick, T.C. Hansen , and M. Bieringer, Inorg. Chem.\n51, 1269 (2012).\n[87] M. Li, U. Adem, S.R.C. Mcmitchell, Z. Xu, C.I. Thomas, J. E. Warren, D. V Giap, H. Niu,\nX. Wan, R.G. Palgrave, F. Schiffmann, F. Cora, B. Slater, T.L. B urnett, M.G. Cain, A.M.\nAbakumov, G. Van Tendeloo, M.F. Thomas, M.J. Rosseinsky, an d J.B. Claridge, J. Am.\nChem. Soc. 134, 3737 (2012).\n[88] J.A. Alonso, M.T. Casais, and M.J. Martnez-Lope, Dalto n Trans. 9, 1294 (2004).\n[89] N. P. Cheremisinoff, Handbook of Ceramics and Composites (M. Dekker, New York, 1990).\n[90] When the raius of the A and B ions are small, a corundum-li ke structure will be stable (e.g.\nFe2O3and FeTiO 3).\n33"    },    {        "title": "1607.05689v1.Synthesis_of_strontium_ferrite_iron_oxide_exchange_coupled_nano_powders_with_improved_energy_product_for_rare_earth_free_permanent_magnet_applications.pdf",        "content": "1 \n Synthesis of strontium ferrite/ iron o xide exchange coupled  nano -powders  with improved \nenergy product  for rare earth free  permanent magnet applications  \nA. D. V olodchenkov  1,2, Y . Kodera  1,2 and J. E. Garay  1,2,3 \n1Advanced Materials Processing and Sythesis ( AMPS) Laboratory  \n2Materials Science and Engineering Program, Mechanic al Engineering Department  \nUniversity of California, Riverside  \n3Materials Science and Engineering Program, Mechanical and Aeronautical Engineering \nDepartment  \nUniversity of California, San Diego  \nAbstract  \nWe present a simple , scalable  synthes is route for producing exchange coupled soft/hard \nmagnetic composite  powder that outperforms  pure soft and hard phase constituents. Importantly, \nthe composites is  iron oxide based (SrFe 12O19 and Fe 3O4) and contain no rare earth or precious \nmetal. The two step synthesis process  consists of f irst precipitating, an Iron oxide/hydroxide \nprecursor  directly  on top of SrFe 12O19 nano -flakes, ensuring a very fine degree of mixing between \nthe hard and the soft magne tic phases. We then use a second step that serves to re duce the precursor \nto create the proper soft magnetic phase and create the intimate interface necessary for exchange \ncoupling . We establish a clear  processing window ; at temperatures  below this window the desired \nsoft phase is not produced , while higher temperatures  result in deleterious reaction at the soft/hard \nphase interfaces , causing an improper  ratio of soft to hard phases.  Improvements of Mr, M s, and \n(BH) max are 42%, 29% and 37% respectively  in the SrFe 12O19/Fe 3O4 composite  c ompared to pure \nhard phase (SrFe 12O19). We provide evidence of coupling (exchange spring behavior) with \nhysteresis c urves, first order reversal c urve (FORC)  analysis and recoil measurements.  \n \n2 \n Introduction and Background  \nPerma nent magnets (PMs) are essential to an amazing variety of current and future devices, \ncausing widespread  interest in improving PM performance. Magnets with high rare earth (RE) \ncontent such as Nd-Fe-B (typically with compositi on Nd2Fe14B), and Sm -Co (typic ally SmCo 5) \nare currently the state of the art PMs. One approach to increasing PM performance is the exchange \nspring concept which has been predicted  to yield  huge gains in energy product , (BH) max (figure of \nmerit for PM performance )1. This promise  has inspired  successful pioneering research  in RE based \nexchanged -couple d PMs2-6 as well as  in Fe -Pt based PMs7, 8. For example Lyubinya et al 6 showed \nevidence of exchange coupling in Fe -Pt powders while Liu and Davies8 showed exchange in RE -\niron melt spun alloys.  \nA natural extension of the exchange spring concept is to replace expen sive and threatened \nmagnetic  phases (such as RE or Pt based materials) with much more abundant and accessible \nmaterials.  Along these lines, Debangsu et al 9 were abl e to synthesize  all ferrite materials with \nexchange spring behavior.   In this work we chose  strontium  ferrite (SrFe 12O19) as a hard phase \nand Fe3O4 as a soft phase. SrFe 12O19, hence forth to be referred to as SFO, is mostly Fe and O \nwhich are two of the mo st abundant elements on earth. This makes SFO a popular PM material in \na host of consumer devices .1,10 While the coercivity  of SFO  cannot compete with that of  RE based \nhard magnets , the complete elimination  of REs and expensive elements  is an enticing compromise . \nThe soft phase  is composed of  only Fe  and O and thus is extremely inexpensive and abundant. \nCubic Fe 3O4 has a saturation magnetization o f 84 emu/g  2, higher than pure SFO (42  emu/g)  which \ncan potentially lead to exchange coupled SFO/Fe 3O4 composite that out performs pure SFO.  \nIn addition  to using earth abundant, low co st elements, PM material implementation would \nbenefit  tremendously  from  low cost , scalable synthesis  procedure s. A particular benefic iary would \nbe PM s for motors and generators since  kilogram quantities  are necessary for these  applications .7   \nExchange coupling relies heavily on a high interaction  area between the  hard phase and the soft \nphase , requiring the grains of soft and h ard material  to be in the sub-micrometer/nanometer range \nand well intermixed3. The combination of nano -grains, good mixing, as well as clean interfaces \nmake  synthesizing exchange coupled PM using a scalable and economical synthesis procedure \nchalleng ing. 3 \n Among the  many different approaches t o synthesize powder, the hom ogeneous precipitation \n(HP) method is one of the most common approaches used in inorganic chemistry for lab oratory  \nand industrial scales11, 12. HP generally provides good morphology  and crystal phase control \nwithout the need for extreme conditions/ systems, such as rapid heating/cooling, high vacuum, high \npressure, etc.  There  have been previous successful  soft chemi stry routes13 for obtaining  exchange \ncoupled particles , although  these  pioneering  cases did not lead to improved  (BH)max.   Our con cept \nfor synthesizing  composite PM s is a twostep  process , shown schematically in Figure 1 . First we  \nuse HP to  precip itate a Fe-O/Fe-O-H precursor  directly  on top of SFO nano -flakes , ensuring a very \nfine degree of mixing between the hard and the soft magnetic phases.  We then use a  second s tep \nthat serve s to reduce the precursor to create the proper soft magnetic phase and create  the intimate \ninterface necessary for coupling . The result is a simple , inexpensive synthesis route for exchange \ncouple d PM composite powder that outperform s pure SFO.  \n \nFigure 1 . Schematic of hard -soft composite synthesis.  \nExperimental procedure  \na. Material synthesis  \nPrecipitation by decomposition of urea was chosen as the method of depositing  Fe \noxide/hydroxide ( Fe-O/Fe -O-H as the precursor of the soft phase ) onto SFO powder (SrFe 12O19, \nNanostructured & Amorphous Materials Inc). The SFO powder consists of high aspect ratio flake \nlike particles with average diameter  of 1.12 μm and thickness of 0.16 μm.  As starting materials \nfor Fe oxide/hydroxide  precipitation , 28.7  mmol of Fe(NO 3)3 (Sigma Aldrich >98%) and 167 \nmmol of CO(NH 2)2(Urea ; Sigma Aldri ch >99.5%  )were mixed into 150 ml of H2O. The mixture \nwas then titrated into a slurry of 1.58 mmol of SFO and 50 ml of H 2O. The temperature was \n4 \n maintained at 90 oC for 2 hours. The resulting composite powder was cooled quickly to prevent \nfurther particle g rowth.  \nIn order to understand the Fe-O/Fe -O-H precipitation process  (phase and morphology  \ndevelopment during the process)  we also did experiments without the SFO (soft phase only) in \nwhich no titration is used. The s ame amount of  Fe(NO 3)3 and 167 mmol of  Urea were mixed into \n150 ml of H2O and held at 90 oC for 2 hours. The resulting homogeneous precipitation creates \nnano -scale particles of the soft magnetic phase precursor.  \nIn both the composite and soft phase cases, the resulting particles were centrifu ged, washed \nwith ultra -high pure water and centrifuged again. The powder and liquid was separated by \ndecantation . The powder was dried at 80 oC in a vacuum furnace for 24 hours to ensure no moisture \nremains after which the dried agglomerates are broken by mortar and pestle. The powders were \nthen treated in a tube furnace under forming gas (5% H 2, 95 % N 2) at temperatures ranging from \n300oC to 500oC with 1 hour ramp and no hold time. The resulting powder was handled in Argon \natmosphere to avoid oxidation.  \n The yield of Fe -O precipitation was obtained by the gravimetric analysis based method. \nThe collected liquid  from decantation  was dried and calcined at 800 oC for 6 h in air atmosphere.  \nThe residue remaining after calcination was -Fe2O3 single phase which was confirmed by X -ray \ndiffraction analysis. The amount of -Fe2O3 was used to calculate the yield of the precipitation \nprocess.  \nb. Structural and microstructural characterization  \nThe phase composition was characterized with X -ray diffraction (XRD) (PANalytical \nEmpyrean Diffractometer with Cu Kα X -ray source λ Kα1=1.54056 Å λ Kα2=1.54440 Å using \n0.01313o step size).  In order to provide a simplified estimate of phase composition ratio, XRD \npeak intensities ratio was calculated by ta king the highest intensity peak of one phase and dividing \nit by the sum of the highest intensity peaks of all detectable phases and multiplying by 100. The \nparticle morphology was characterized by Scanning Electron Microscopy (SEM) (Philips XL30).  \n \n 5 \n c. Ma gnetic measurements  \nMagnetic properties were measured using a Vibrating Sample Magnetometer (VSM) \n(Lakeshore 7400 Series) at room temperature. Hysteresis loop measurements using field values of \nup to 1.7 T were obtained in order mass normalized magnetizat ion, σ [emu/g] vs. applied field, H \n[Oe]. We refer to these measurements as customary hysteresis loops. Coercivity, Hc [Oe], \nremanence magnetization Mr [emu/g] and saturation magnetization Ms [emu/g] was extracted from \nthe σ vs. H hysteresis curves. In cal culating Ms, the non -saturating slope (due to SFO and Fe 3O4 \nbeing ferrimagnetic) was subtracted. Energy product, (BH) max [MGOe] was calculated assuming \nfull density of SFO , .  \n First order reversal curve (FORC) measurements were done by ramping the field t o 0.6 T  \nthen decreasing the magnetic field to a reversal field with value of Ha and ramping back up to 0.6 \nT through field values, Hb with a step size of 200 Oe. Magnetization as a function of Ha and Hb, \nM(Ha,Hb), is recorded. This procedure was repeated i n order to measure a collection of first order \nreversal curves for reversal fields in 200 Oe intervals from 5800 Oe to -6000 Oe. FORC \ndistribution,  is calculated using the relation5:  \n𝜌(𝐻𝑎,𝐻𝑏)=−𝜕2𝑀(𝐻𝑎,𝐻𝑏)\n𝜕𝐻𝑎𝜕𝐻𝑏    (1) \nFORCinel was used to calculate the FORC distribution and plot it, traditionally, a s Hc vs.  Hu where \nHc = (Hb-Ha)/2 and Hu = (Ha+H b)/2 14.  \nRecoil loop measurements were done by first ramping magnetic field to 1.7 T in order to \nbring the sample to saturation (ignoring the non -saturating component due to SFO and Fe 3O4 being \nferrimagnetic). A Reversal field, Ha, was applied, removed (field taken to 0 Oe) and reapplied \n(field taken back to Ha). Ha values were varied from 100 Oe to 1400 Oe in 100 Oe increments. \nMeasurements of mag netization, σ, were taken from Ha to 0 Oe, forming the recoil magnetization \ncurve, and likewise from 0 Oe back to Ha, forming the recoil demagnetization curve. The area \nbetween recoil magnetization and recoil demagnetization curves was calculated using num erical \nmethods. Normalized recoil loop area was calculated by dividing the area between recoil \nmagnetization and recoil demagnetization curves by one half of the total area of the sample’s \ncustomary hysteresis loop area (also calculated using numerical met hods). Mrecoil is the value of 6 \n magnetization with 0 Oe field applied following recoil magnetization from Ha to 0 Oe. Recoil \nremanence ratio Mrecoil/Mr was calculated by taking the Mrecoil, values and dividing it by the \nmagnetic remanence Mr (from the custo mary loop obtained as described above).  \nResults and Discussion  \nSynthesis of soft magnet phase  \nWe start by discussing the Fe-based soft magnet powders  (Fe-O/Fe -O-H) i.e. materials  \nwithout the hard SFO phase . Althou gh many different approaches have  been repo rted for \nsynthesizing iron  hydroxide/ oxide s11, 12, 15, it is important to understand the  detail of synthesis and \nreduction behavior  of iron hydroxide/oxide in our experimental condition s in order to achieve our \ngoal of obtaining  soft-hard composites with controlled properties . The precursor was synthesize d \nthrough precipitation by thermal decomposition of urea in iron nitrate solution12,16. There are \nseveral reports on the synthesis of iron hydroxide/oxide and oxide using iron sa lt and urea as \nreactant that produce  fine nano -particles and high y ields16-19.   We chose i ron nitrate and urea as \nreactant s in this particular study  because of the  simplicity of the removal of ammonium nitrate  \n(formed as byproduct) in the process.  \nFigure 2 shows XRD patterns of the as -precipitated powder from iron nitrate and urea \nsolution heated at 90  oC. The XRD confirm s that the product is mixture of α-Fe2O3 and α -FeO(OH) \nand low crystallinity which  agree s with previous results20.  The h igh back ground  intensity  at low \nangles suggests the presence of  low crystallinity /amorphous  phase . \nIn order to achie ve the desired  soft phase  (Fe 3O4) the dried as -precipitated powder was then \nthermally treated in 95%  N2: 5% H2 gas flow. The XRD in Fig 2 shows the influence of treating \ntemperature  on the reduction of  the precipitated  α-Fe2O3/α-FeO(OH). Increasing tempera ture \ncauses decomposition of α -FeO(OH) and reduction of hexagonal Fe 2O3 to cubic Fe 3O4 and \nsubsequently reduction of Fe 3O4 to metal -Fe at higher temperature. These observations agree \nwith previous studies21-24. FeO was not detected during the reduction process because the \nprocessing temperature was kept below 570 ̊C25. The phase evolution is  more easily appreciated \nin Figure  3 showing  XRD peak intensity ratio vs. reduction tempe rature.  At the process ing \ntemperat ure of  300 oC, all of the as -precipitated phase s are converted to Fe3O4.  The metal -Fe \nappear s at 350 oC and  its relative amount  increases  with temperature , however it is not the major 7 \n component until reduction temperature is increased to 450 oC.  The co nversion ratio reaches  over \n80% at 500  oC based on simplified estimation from XRD intensity ratio .   \n \nFigure 2: X-ray diffraction pattern s for the soft phase after precipitation as well as at reduction \ntemperatures 300 -500oC. \n8 \n Figure 3: XRD peak intensity  ratios at various reduction temperatures.  The peak intensity ratio \nis the ratio of the most intense  peak of a particular phase to the sum of the intensities of  the most \nintense peaks of  all identifiable phases. The most intense peaks for α-Fe, Fe 3O4, α-Fe2O3 and α -\nFeO(OH) are from  the (110), (311), (104) and (101) planes, respectively.  \n Figure 4  show s SEM  micrographs  of as -precipitated powder  as well as heat treated ones. \nThe as-precipitated particles exhibit  morphology with low aspect rat io and small grain size (tens \nof nm). Also the micrographs suggested that the low degree of aggregation of particles . These \nmorphological characteristics contribute  to the ease of reduction.  \nThe SEM micrographs of sample reduced  at 400  °C shows significan t change in surface \nroughness and evidence of grain growth. Considering  this result and the reduction mechanism, we \nassume about 70% of  Fe3O4 remain s as a core that is surrounded by  -Fe (about 30%) as a shell \nat 400 oC. Despite the clear grain growth, these soft phases did remain in the nanoscale which  is \nvery important for obtaining an exchange coupled PM.  \n9 \n  \nFigure 4: ( a), (b ): SEM micrographs of as -precipitated  soft phase powder. ( c), (d ): SEM \nmicrographs soft phase powder reduced at 400oC. \nSynthesis of soft/ hard magnet composites  \nFigure 5  shows XRD of  SFO powders after having undergone  the precipitation  of sof t \nphase precursor. Also shown in  Figure  5 are the XRD pattern s of the sof t/hard composites powders \nafter reduction at various temperatures . The a s-precipitated sample show s XRD patterns identical  \nto as as -received  SFO (not shown here)  and no significant peak f rom precipitate except  small peak \nat 33  degree s corresponding  to α-Fe2O3.  This result suggests that there is no significant damage \nof SFO during the precipitation process.  Figure 6  shows XRD peak intensity ratio vs. reduction \ntemperature. At 300 °C,  the intensity of α -Fe2O3 peak s increas e and the peaks of Fe 3O4 appear.   By \ncontrast, t he soft phase only results ( Figure 3 ) show  the full conversion  of precursor  to Fe 3O4 at \nsame temperature  (300 °C). In the case of non -composite system, the entire  surface of particle, \nexcept point contacts between particles, is exposed to atmosphere, on the other hand, in the \ncomposite case ( Figure 6), - Fe2O3 particles  are precipitated on the SFO meaning at least one \n10 \n side of particles is not exposed to  atmosphere;  this should slow  down reduction kinetics of Fe 3O4 \nformation  \nFigure 5 X -ray diffraction patterns for the SFO -(Fe-O) composite after precipit ation procedure \nas well as at reduction temperatures 300 -500oC. \n11 \n  \nFigure 6: XRD peak intensities ratios at varying reduction temperatures. The peak intensity ratio \nis the ratio of the most intense peak  of a particular phase to the sum of the intensities o f the most \nintense peaks of all identifiable phases. The most intense peaks  for Fe 3O4, α-Fe2O3 and SFO are \nfrom the (311), (104) and (107) planes, respectively.  \nIn addition to reaction of the precipitated layer the decay of SFO was simultaneously \nobserved by XRD. At 500 °C, the Fe 3O4 peaks bec ome more intense than the  SFO peaks . This \nsugge sts that the reaction between the deposite d layer and SFO is taking place. This  reaction is \nmore intense at higher  temperature.  Based on the results of the soft phase study in (Figure 3), the \nheat required to reduce iron oxide to metal α-Fe is enough to ca use significant reaction between \nSFO and soft magnet phase. In other words , too low a temperature  produces SFO/-Fe2O3 \ncomposites instead of the desired SFO/Fe 3O4 composites , while too high  a temperature  destroys \nthe SFO phase , resulting in a composite wit h too much soft phase . This  data clearly show that there \nis a limited processing temperature  window  that produces the  desired phases . \n12 \n Figure 7  shows SEM micrographs of samples  of the as-received  SFO powder as well as \ncomposite powders after the precipitati on step and after the reduction s tep at various \nmagnifications. The As-received SFO (Figure 7 a-c) exhibits hexagonal facets which correspond  \nto its crystal structure.  When the precursor is precipitated in SFO suspension, there are “clouds ” \nof particles d eposited on the surface and at th e intersections of SFO grains  (Figure  7 d-f). The \nhigher magnification image s confirm that those  particles size are tens o f nanome ters.  \nThe calculated yield of the precipitated material was 62%.  When precipitated the Fe b ased \nsoft phase forms only Fe 3O4 (e.g. the sample reduced at 400 °C), the volume ratio of hard / soft \nphase ( SFO / Fe3O4) is 55/45. Therefore, the estimated thickness of Fe 3O4 coating is  calculated to \nbe 37 nm on the surface of SFO assuming a hexagonal plate -like particle as shown in Figure 1 . \nThe dimensions used for this estimate are the average sizes measured for SFO (diameter of 1.12 \nμm and thickness of 0.16 μm).  \nAfter reducing composites at 400 °C, there is not significant change in  low magnification \nimag es and there are still relatively sharp corner/edge  of SFO composite grains. This suggests  that \nsintering and grain gro wth of SFO composite is not significant  at this temperature. However, high \nmagnification  images ( compare between Figure 7 a, d and g)) reveal a clear change in the surface \nmorphology of SFO composite. The SFO  composite grains show  agglomerated round  shape d \nparticles (tens of nano meters ) with curved edges and many pores. This is caused by the reduction \nof precursor and sintering of Fe 3O4 during the reduction process. First, both decomposition and \nreduction reduc e the number of atoms in the compound and create  voids and pores. Then , sintering \nforms neck and causes grain growth. Therefore , those voids and pores are segregated from  the \nmatrix  to form the microstructure  we can see in Figure 7i .   \nThere is a clear contrast between the soft phase  only and composite  powders  in the degree \nof grain growth .  When the samples  are treated at 400  oC, the soft magnet shows significant grain \ngrowth, on the o ther hand, the  composite (soft phase  on SFO ) does not show such a drastic growth \n(see Figure 4c  and Figure 7i ).  In order to have sufficient significant grain growth, two conditions \nare required: 1. There  needs to be sufficient atomic mobility for grain gr owth . 2. There need s to \nbe sufficient  material to form coarse grain s with large r volume. Since the soft phase  results ( Figure \n4) show significant  grain growth there is sufficient  thermal energy  at 400 oC required for mobility 13 \n indic ating that there  simply  is not enough soft phase  on the surface of SFO to form large grain  in \nthe composite case.    \nThese structural  and morphological  characterizations  confirm that we successful in  \nsynthesizing  SFO/Fe3O4 nanocomposites  by precipitation of precursor  on the SFO  followed by a \nreduction process.  \n \nFigure 7: ( a), (b), (c ): SEM micrographs of single phase  SFO powder . (d), (e ), (f): SEM \nmicrographs of composite powder after precipitation procedure . (g), (h), (i ): SEM micrographs \nof composite powder after reduction at 400  oC.  \nMagnetic Properties  \nMagnetic saturation , Ms taken from the measured hysteresis  loops of soft phase powder s is \ndisplayed in Figure 8 . Post precipitation, (0  oC in Figure 8) the powder h as very low Ms as   \nexpected for a powder composed of α-Fe2O3 and α-FeO(OH) (see XRD results ( Figure 2)). Both  \nα-Fe2O3 and α -FeO(OH) are antiferromagnetic . As we reduce the powder at 300  oC the hexagonal \nα-Fe2O3 becomes mostly cubic Fe3O4 with saturation magnetization of 93 emu/g.  Ms increases \nfurther after 400  oC as the  composition of α-Fe increases and cubic Fe3O4 decreases. After \n14 \n reduction at 500  oC the powder has a  very high Ms = 147 emu/g as expected for a powder that is \nmostly -Fe.  \n \nFigure 8: Saturation magnetization of the soft phase at various reduction tempera tures.  \nMagnetic properties of the as received SFO and composite powder are displayed in Figure \n9. The  single phase  SFO powder has coercivity, Hc, remanence  magnetization , Mr, saturation \nmagnetization,  Ms and energy product, (BH)max values of 967 Oe, 18.3 emu/g, 42 emu/g and 0.1 65 \nMGOe .  The  (BH) max values were  values  calculated   assuming full density  of 5.1 g/cm3 for SFO26. \nThese values provide bench mark values i.e. the main  goal of the study is to achieve  a composite \nPM with (BH)max higher  than 0. 165. It should be no ted that it is possible to produce  SFO magnets \nwith highe r (BH) max, but optimization of magnetic  performance  typically require s grain  alignment \nto achieve highest coercivity. Here we are comparing random (unaligned) magnetic powders in \nboth the composites and pure SFO cases.  \n15 \n After initial precip itation, the composite powder s show a decrease  in  magneti c properties  \nThis is not surprising because the addition volume of  antiferromagnetic  α-Fe2O3 dilutes SFO’s \nremanence, saturation and energy product. The magnetic properties are improved with reduction \nhowever; Figure 9  also shows that magnetic properties have a clear dependence on the reduction \ntemperature.  16 \n  \nFigure 9: SFO/ (Fe-O) composite magnetic properties (coercivity, remnant magnetization, \nsaturation m agnetization, energy product).  \n17 \n As the reduction temperature increases, the magnetic properties impro ve significantly , at \nintermediate  temperatures  (250 - 400 oC) and decrease again  at 45 0 oC. This “optimal” temper ature \nfinding  mirrors the processing window effect shown for the phase evolution ( Section  IIIb) and can  \nbe explained  as follows. At low tempera tures  the soft phase  has not been fully converted  to the \ndesired soft ferrimagnetic  Fe3O4.  At reduction temperatures higher than 400  oC there is too much \nreaction between the SFO  and the precipitated phase, causing there to be too much soft \nferrimagnetic phase relative to hard f errimagnetic phase . The maximum (BH) max is achieved by \nreducing the composite at  400 oC. Notably , all magnetic properties, except coercivity, of this  \nnanocomposite powder surpass those of the  pure SFO powder . Improvements in Mr, M s, and \n(BH) max are 42%, 29% and 37% respectively.  As noted earlier, it is likely that the (BH) max of these \ncomposites can be further increased by aligning the magnetic  phases. This should be facilitated  by \nthe flake -like nature of our SFO and composites phas es. Further studies in this direction are \nunderway.  \nFigure 10  compares hysteresis loops of the  pure SFO and SFO/Fe 3O4 composite  reduced \nat 400  oC. The smooth hysteresis  curve for the composite  is indicative of  single phase behavior  \nand therefore is eviden ce that the hard and soft phases are  exchange  coupled27.  If the composite  \nwas decoupled , the curve would have  a clear kink resulting from the hard -soft phases acting  \nindependently . 18 \n  \nFigure 10: SFO/Fe 3O4 composite (reduced at 400oC) hysteresis loop compared to single phase  \nSFO. \nFORC diagrams are useful for gauging particle interactions of magnetic particles.  Figure \n11 shows the FORC  diagram  for SFO/Fe 3O4 composite  (Figure 11b) as well as pure SFO hard \nphase  (Figure  11a). Comparison of the two diagrams shows clear differences. The maximum value \nfor the FORC distribution is 65 × 10-9 for the composite material and 19 ×10-9 for the SFO . \nGenerally , a higher maximum value indicates more ferromagnetic interactions28, 29, which we \nattribute to the existence of the soft phase in the composite.  \nThere  is also a larger  spread of Hu data, suggesting  more  particle interactions (larger mean \nintera ction field) in the composite material.  The location of the density distribution peak i.e. \n‘density hotspot’  can also help interpret the nature of interactions. A hot spot located below the Hu \n= 0 axis further indicates interacting particles30 and is characteristic of an exchange style \n19 \n interaction28. The hots pot peak is shifted to Hu = -236 Oe for the composite which strongly \ncorroborates the hysteresis curve results ( Figure 10) demonstrating exchange coupling.  \n \nFigure 11: First order reversal curve (FORC) diagrams  for (A) single phase  SFO and (B) \nSFO/Fe 3O4 composite  (reduced at 400oC). \nTo further confirm the existence  of coupling in our composites, we did recoil loop \nmeasurements ; recoil loop analysis  has been used previously to evaluate coupling in \nnanocomposite  permanent magnets31-33.  Figure 12  shows recoil loop measurements for \nSFO/Fe 3O4 composite as well as pure SFO hard phase, along with the recoil loop areas and recoi l \nremanence for both SFO/Fe 3O4 composite and pure SFO.  \nIn a single phase (or ver y well couple d) magnet, one would expect closed loops i.e. little \nto no area between the magnetization  and demagnetization curves . Open recoil loop are often \nattributed to par tial or total decoupling of the soft phase and hard phases in nanocomposite magnets \n34  Although not typically expected in a single composition magnet, the pure SFO exhibits open \nrecoil loops ( Figure 12a ). Open recoil loops have been reported  before in  nano -scale single \ncomposition  magnets and attributed to inhomogeneity in magnetic anisotropy35, thermal \nfluctuation36 and intergranular exchang e interactions37. We believe that one or more of these cause  \nopen loops in pure SFO.  Comparison of the ‘openness’ of the curves in Figure 12 a and 12b \nreveals a  very similar recoil be havior  in SFO/Fe 3O4 composite and SFO.  \n20 \n A more quantitative comparison  of the  recoil loop area can be achieved  by normalizing the \nrecoil lo op are  by ½ of the total hysteresis loop area. The data for SFO/Fe 3O4 composite in \ncomparison to pure SFO is plotted in Figure 12c . The fact that the open area is almost  identical  \nmeans that the addition of the soft phase  Fe3O4 is not increasing the degree of dec oupling of the \ncomposite compared to SFO. This is not surprising in light of the hysteresis  curve and  FORC \nanalysis discussed above , showing that  the SFO/Fe 3O4 composites behave  as exchanged coupled  \nmagnets.  \nFrom a permanent magnet development point of view, the  primary reason one wants an \nexchange spring behavior is to increase the energy product (BH)max as we s how here.  Another very \nimportant  benefit  is to increase the magn et’s resistance  to demagnetization. A measure of \nresistance to demagnetization  can be obtained by calculating the ratio  of the remanence  value \nmeasured  during a recoil measurement , Mrecoil (see experimental  procedure for details) to the Mr \nmeasured du ring a standard hysteresis loop . This ratio is plotted for the nanocomposite and SFO \nin Figure 12d . An exchange coupled nanocomposite magnet with optimal microstructure has a \npartially reversible demagnetization curve38, meaning that at low  Ha values,  the Mrecoil/Mr ratio is \nnear 1. We see that this is the case for the recoil remanence ratio ( Figure 12d ) of the \nnanocomposi tes. The data also reveal that the Mrecoil/Mr values are  higher for the SFO/Fe 3O4 \ncomposite  that the pure SFO at all applied magnetic fields, demonstrating that the composites are \nmore resistant to demagnetization and providing further evidence of exchange  coupling.   21 \n  \nFigure 12 : (A) Single phase  SFO recoil loop measurement. (B) SFO/Fe 3O4 composite  (reduced \nat 400oC) recoil loop measurement . (C) Normalized recoil loop areas (normalized by ½ full \nhysteresis area) for pure SFO and SFO /Fe 3O4 composite  (reduced  at 400  oC). (D) Recoil \nremanence ratio for pure SFO and SFO /Fe 3O4 composite  (reduced at 400  oC). \nSummary  \nIn summary, we have presented a synthesis and processing procedure for the production of \nSFO/Fe 3O4 exchange  coupled nanocom posites that contain  no rar e earth or precious metals . Our \nprocedure is a simple scalable procedure that relies on a precipitation  step followed by a reaction \nstep. The precipitation  step ensures  intimate  contact  and good intermixing  of the two phases . The \nreaction  step allows  for the conversion of the as -precipitated  precursor  to convert  to the desired \nmagnetic soft phase (Fe 3O4). The  data presented, clearly show that there is a limited processing \ntemperature window that produces the desired phase. Magnetic measurements  reveal  that the \n22 \n (BH)max of the SFO/Fe 3O4 composite  powders is 37% higher that the pure SFO hard phase, \nconfirming   that evasive goal of a rare earth free PM material can be realized  using the procedure \npresented here.  \nAcknowledgments  \nWe thank Ms. S. Inoue, Mr.  M. Manuel and  Mr. R.  Shah  for help with sample synthesis and \npreparation. The support of this work from the Office of Naval Research with Dr. H. S. Coombe \nas program manager is most gratefully acknowledged.  \n \nReferences  \n1. N. Poudyal and J. P. Liu, J Phys D Appl Phys , 2013, 46. \n2. M. I. Dar and S. A. Shivashankar, Rsc Adv , 2014, 4, 4105 -4113.  \n3. N. Jones, Nature , 2011, 472, 22-23. \n4. H. Unuma, S. Kato, T. Ota and M. Takahashi, Adv Powder Technol , 1998, 9, 181 -190. \n5. C. R. Pike, Phys Rev B , 2003, 68. \n6. J. Lyubina, I. Opahle, K. H. Muller, O. Gutfleisch, M. Richter, M. Wolf and L. Schultz, J \nPhys -Condens Mat , 2005, 17, 4157 -4170.  \n7. H. Zeng, J. Li, J. P. Liu, Z. L. Wang and S. H. Sun, Nature , 2002, 420, 395 -398. \n8. Z. W. Liu and H. A. Davies, J Phys D Appl Phys , 2009, 42. \n9. D. Roy, C. Shivakumara and P. S. A. Kumar, J Magn Magn Mater , 2009, 321, L11 -L14. \n10. K. J. Strnat, P Ieee , 1990, 78, 923 -946. \n11. E. Matijevic, Langmuir , 1986, 2, 12-20. \n12. E. Matijevic, Chemistry of Materials , 1993, 5, 412-426. \n13. A. H. Lu, E. L. Salabas and F. Schuth, Angew Chem Int Edit , 2007, 46, 1222 -1244.  \n14. R. J. Harrison and J. M. Feinberg, Geochem Geophy Geosy , 2008, 9. \n15. M. Ocana, M. P. Morales and C. J. Serna, J Colloid Interf Sci , 1995, 171, 85-91. \n16. M. O cana, M. P. Morales and C. J. Serna, J Colloid Interf Sci , 1999, 212, 317 -323. \n17. K. M. Parida and J. Das, J Mater Sci , 31, 2199 -2205.  \n18. K. Parida and J. Das, J Colloid Interf Sci , 1996, 178, 586 -593. \n19. S. Bakardjieva, V. Stengl, J. Subrt and E. Vecer nikova, Solid State Sci , 2005, 7, 367 -374. \n20. R. M. Cornell, R. Giovanoli and W. Schneider, J Chem Technol Biot , 1989, 46, 115 -134. \n21. G. Munteanu, L. Ilieva and D. Andreeva, Thermochim Acta , 1997, 291, 171 -177. \n22. O. J. Wimmers, P. Arnoldy and J. A. Mo ulijn, J Phys Chem -Us, 1986, 90, 1331 -1337.  \n23. H. Y. Lin, Y. W. Chen and C. P. Li, Thermochim Acta , 2003, 400, 61-67. \n24. O. E. Lebedeva and W. M. H. Sachtler, J Catal , 2000, 191, 364 -372. \n25. W. K. Jozwiak, E. Kaczmarek, T. P. Maniecki, W. Ignaczak and W . Maniukiewicz, Appl \nCatal a -Gen, 2007, 326, 17-27. \n26. L. K. Lagorce and M. G. Allen, J Microelectromech S , 1997, 6, 307 -312. \n27. X. Q. Liu, S. H. He, J. M. Qiu and J. P. Wang, Appl Phys Lett , 2011, 98. 23 \n 28. D. Roy and P. S. A. Kumar, Aip Adv , 2015, 5. \n29. I. D. Mayergoyz, in Mathematical Models of Hysteresis and Their Applications , Elsevier \nScience, New York, 2003, pp. 65 -147. \n30. C. R. Pike, A. P. Roberts and K. L. Verosub, J Appl Phys , 1999, 85, 6660 -6667.  \n31. Y. Choi, J. S. Jiang, J. E. Pearson, S. D. B ader and J. P. Liu, J Appl Phys , 2008, 103. \n32. D. Goll, M. Seeger and H. Kronmuller, J Magn Magn Mater , 1998, 185, 49-60. \n33. C. L. Harland, L. H. Lewis, Z. Chen and B. M. Ma, J Magn Magn Mater , 2004, 271, 53-\n62. \n34. J. P. Liu, in Nanoscale Magnetic Mater ials and Applications , eds. P. J. Liu, E. Fullerton, \nO. Gutfleisch and D. J. Sellmyer, Springer US, Boston, MA, 2009, DOI: 10.1007/978 -0-\n387-85600 -1_11, pp. 309 -335. \n35. Y. Choi, J. S. Jiang, J. E. Pearson, S. D. Bader and J. P. Liu, Appl Phys Lett , 2007, 91. \n36. C. Rong, Y. Liu and J. P. Liu, Appl Phys Lett , 2008, 93. \n37. C. B. Rong and J. P. Liu, Appl Phys Lett , 2009, 94. \n38. E. F. Kneller and R. Hawig, Ieee T Magn , 1991, 27, 3588 -3600.  \n "    },    {        "title": "0802.2915v1.Electric_field_induced_spin_flop_in_BiFeO3_single_crystals_at_room_temperature.pdf",        "content": "Electric-\feld-induced spin-\rop in BiFeO 3single crystals at\nroom-temperature\nD. Lebeugle,1D. Colson,1A. Forget,1M. Viret,1A. M. Bataille,2and A. Gukasov2\n1Service de Physique de l'Etat Condens\u0013 e,\nCEA Saclay, F-91191 Gif-Sur-Yvette\n2Laboratoire Leon Brillouin, CEA Saclay, F-91191 Gif-Sur-Yvette\nAbstract\nBismuth ferrite, BiFeO 3, is the only known room-temperature 'multiferroic' material. We\ndemonstrate here, using neutron scattering measurements in high quality single crystals, that the\nantiferromagnetic and ferroelectric orders are intimately coupled. Initially in a single ferroelectric\nstate, our crystals have a canted antiferromagnetic structure describing a unique cycloid. Under\nelectrical poling, polarisation re-orientation induces a spin \rop. We argue here that the coupling\nbetween the two orders may be stronger in the bulk than that observed in thin \flms where the\ncycloid is absent.\n1arXiv:0802.2915v1  [cond-mat.mtrl-sci]  20 Feb 2008Electricity and magnetism are properties which are closely linked to each other. This link\nis dynamic in essence, as moving charges generate a magnetic \feld and a changing magnetic\n\feld produces an electric \feld. This forms the basis of Maxwell's equations. In a solid,\na similar coupling was \frst considered by Pierre Curie [1] between the magnetization M\nand electric polarization P. This magneto-electric (ME) e\u000bect was recently understood to\nbe potentially important for applications because in information technology, it would allow\nmagnetic information to be written electrically (with low energy consumption) and to be\nread magnetically. The ME e\u000bect was demonstrated and studied in the 1960s in Russia [2]\nand since then, many so called 'multiferroic' materials have been identi\fed [3]. However, so\nfar the magnitude and operating temperatures of any observed ME coupling have been too\nsmall for applications. In fact, the only known multiferroic material of potential practical\ninterest is bismuth ferrite, BiFeO 3which is actually antiferromagnetic below TN\u0019370 °C\n[2] and ferroelectric with a high Curie temperature: Tc\u0019820 °C [4]. As a result, in recent\nyears, there has been a resurgence in the research conducted on this material. Moreover,\nepitaxial strain in BiFeO 3thin \flm has been described as a unique means of enhancing\nmagnetic and ferroelectric properties [5]. It is actually unclear whether this is indeed the\ncase and in order to clarify this point, the intrinsic properties of the bulk material need to\nbe better understood. It is stunning that although BiFeO 3has been extensively studied\nover the past 50 years, some of its most basic properties are still not fully known. For\ninstance, it is only in 2007 that its spontaneous polarisation at room-temperature has been\nmeasured to be in excess of 100 \u0016C=cm2[6]. Moreover, in the bulk, the coupling between\nmagnetic and ferroelectric orders has never been fully clari\fed. This property has only been\nmeasured in thin \flms [7] very recently. This lack of accurate data stems from the di\u000eculty\nin making high quality single crystals. We have recently been able to grow such single\ncrystals below their ferroelectric Curie temperature using the \rux technique [6, 8]. They\nare usually produced in the form of platelets 40-50 microns thick and up to 3 mm2in area.\nPolarised light imaging and P(E) measurements [8] indicate that the as-grown crystals are\ngenerally in a single ferroelectric/ferroelastic domain state. We report here on a neutron\nstudy of the coupling between magnetic and ferroelectric orders in two of these crystals.\nOurBiFeO 3single crystals are rhombohedral at room temperature with the space group\nR3c and a pseudo-cubic cell with apc= 3:9581 \u0017A,\u000bpc= 89:375 °(ahex= 5:567(8) \u0017A,\nchex= 13:86(5) \u0017Ain the hexagonal setting), in perfect agreement with previous reported\n2data [9]. No ferroelastic twinning was observed and the elongated rhombohedral direction,\nwhich is parallel to the polarisation, is indexed as (111). Fe3+ions are ordered antiferro-\nmagnetically (G-type) and their moments describe a cycloid with a period of 62 nm, as has\nbeen established by early neutron di\u000braction data on sintered samples [10, 11]. Because of\nthe rhombohedral symmetry, there are three equivalent propagation vectors for the cycloidal\nrotation:~k1= (\u000e0\u0000\u000e),~k2= (0\u0000\u000e\u000e) and~k3= (\u0000\u000e\u000e0) where\u000e= 0:0065. In powder neu-\ntron di\u000braction, the di\u000berent equally populated ~kdomains lead to a splitting of magnetic\npeaks along three directions. Thus, as has been pointed out recently [11], the determination\nof modulated magnetic ordering is not unique because elliptical cycloids and Spin Density\nWaves (SDW), give the same di\u000braction pattern. The exact nature of the periodic struc-\nture is an important parameter for antiferromagnetic ferroelectrics since recent models of\nmagnetoelectric coupling give a non-vanishing electric polarization for cycloids and elliptic\nordering and zero polarization for a SDW [11, 12]. It is possible to eliminate this ambigu-\nity by measuring high-resolution scans around the strongest magnetic re\rections of a single\ncrystal. This is however a di\u000ecult experimental challenge because the long period imposes\nan extremely high angular resolution. The di\u000bractometre used in this work is 'Super 6T2'\nin the 'Laboratoire L\u0013 eon Brilloin' in Saclay (France), where a resolution of 0 :15 °vertically\nand 0:1 °horizontally can be achieved. We have measured the intensity distribution of the\nas-grown crystals around the four antiferromagnetic Bragg re\rections (1\n2;\u00001\n2;1\n2), (1\n2;1\n2;1\n2),\n(1\n2;1\n2;\u00001\n2) and (\u00001\n2;1\n2;1\n2). The peak splitting only occurs along one of the three symmetry\nallowed directions as shown for the (1\n2;1\n2;1\n2) re\rection in Fig. 1-a. Therefore, the modulated\nstructure has a unique propagation vector ~k1= (\u000e0\u0000\u000e) with\u000e= 0:0064(1) corresponding\nto a period of 64 nm. The elongated shape of the measured sattelites is due to the better\nresolution in the horizontal direction (along (10-1)) but also possibly because of a slight\nwarping of the sample induced by the silver epoxy electrodes apposed on both sides of the\ncrystals (corresponding to the (010) plane) for electric poling.\nThe spin rotation plane can also be determined because the magnetic scattering amplitude\ndepends on the component of magnetic moments perpendicular to the scattering vector. A\nquantitative analysis of the integrated intensities of 10 theta/two-theta magnetic re\rections\n(see table I) allows us to conclude unambiguously that the moments lie in the plane de\fned\nby~k1= (\u000e0\u0000\u000e) and the polarisation vector ~P==[111] (\fg. 1-b).\nThe structure re\fnement also con\frms that the periodic structure is indeed a circular\n3cycloid with antiferromagnetic moments \u0016Fe= 4:11(15)\u0016B. Using a SDW model, or in-\ntroducing a 20% ellipticity, deteriorates signi\fcantly the agreement factor of the \ft. A\nconsequence of the single ~kvector of the cycloid is that the crystal symmetry is lowered.\nIndeed, the ternary axis is lost and the average symmetry becomes monoclinic with the\nprincipal direction along ~k=(110) [13].\nNo electric \feld e\u000bect on the magnetic order has ever been reported in bulk BiFeO 3. Here,\nwe analyse the e\u000bect of poling in the (010) direction perpendicular to the platelet. Because\npolarisation changes force charges to re-organise, the polarisation state of the sample can be\nmonitored by measuring the current in the circuit. As the \frst coercive \feld was reached,\nwe measured a signi\fcant decrease in the (1\n2;\u00001\n2;1\n2) neutron re\rection intensity, indicating\na redistribution of the average rhombohedral distortion. After reaching a multidomain\nstate with< P >\u00190, several neutron di\u000braction scans were performed. When trying to\nmap precisely the intensity distribution around the antiferomagnetic Bragg positions, we\nfound that the vertical resolution used for the crystal in its virgin state (in \fg. 1) was\nnot su\u000ecient. Indeed, in the multi-domain state, ferroelastic distortions twin the crystal\nand complicate the di\u000braction patterns. In order to obtain a meaningful measurement, we\nhad to reach 0.1 °of resolution in both horizontal and vertical directions, which pushes the\nexperimental conditions to the limit of what can be done with these instruments. Figure\n2-b shows the (3D) reciprocal space mapping of the crystal. Yellow (111) type re\rections\nare purely nuclear in origin while the red (1\n2;1\n2;1\n2) are purely magnetic. (111) and (1-11)\nre\rections are split along the long diagonals (dashed lines), which indicates the presence\nof two domains with di\u000berent reticular distances. These are two rhombohedral twins with\npolarization axes along (111) and (1-11), roughly 50% \u000050% in volume. The other (-111)\nand (11-1) re\rections are also split, but along the (101) direction. This is due to a buckling\nof the crystal schematically shown in \fg. 2-a, which slightly changes the angles ful\flling the\nBragg conditions. This is fully consistent with polarised optical microscope images taken on\nsimilar crystals (\fg. 2-a) indicating that the multi-domain state consists of stripe regions\nwith two di\u000berent polarisation directions.\nThe purely antiferromagnetic peaks have been analysed in more details. The strongest\n(1\n2;\u00001\n2;1\n2) re\rection is shown in the zoomed region of \fg. 2-b to be composed of four spots.\nThese result from two simultaneous splits, one due to the ferroelectric distortion (already\nevidenced in the nuclear peaks) and one of magnetic origin. A projection of the zoomed area\n4is represented in \fgure 3 on with the expected re\rections from P111andP1\u000011domains are\nshown as green spots. The magnetic satellites are also indicated as black spots for the cycloid\nin the original (-101) direction and white spots for the other two symmetry allowed ones. The\ndomains with the original P111direction of polarisation lead to the pattern in the lower half\nof the \fgure, while those where the polarisation rotated by 71 °(P1\u000011) are in the upper half.\nIn the latter domain, the expected satellites are not in a regular rhombohedral symmetry\nbecause they do not belong to the (111) di\u000braction plane of the \fgure. However, were they\npresent, these satellites would still appear because the \fgure is a projection. Figure.3 shows\nthat in both domains, the splitting is only in the horizontal direction. Hence, the original\n(\u000e0\u0000\u000e) propagation direction of the cycloid in the virgin state was retained everywhere.\nThe rotation planes of the AF vectors in the two domains can again be determined using\nthe integrated intensities of the magnetic re\rections (table II). These can be well accounted\nfor by considering that 55% of the crystal volume has switched its polarisation by 71 °, and\nbrought with it the rotation plane of the Fe moments. Thus, in each domain, AF moments\nare rotating in the plane de\fned by ~k1and~Pas represented in \fg.4. Hence, the electric\n\feld induced change of polarisation direction produces a spin \rop of the antiferromagnetic\nsublattice.\nThese measurements unambiguously demonstrate that the magnetic Fe3+moments are\nintimately linked to the polarisation vector. This negates the common belief that in bulk\nBiFeO 3magneto-electric coupling must be weak because the cycloid cancels linear ME ef-\nfects [14, 15, 16, 17]. Although hMi= 0 imposes a zero global linear ME e\u000bect in the bulk,\nthe atomic coupling between ~Mand~Pstill exists. The underlying relevant microscopic\nmechanism is the (generalised) Dzyaloshinskii-Moriya (DM) [20] interaction which has re-\ncently been re-addressed starting from electronic Hamiltonians including spin-orbit coupling\n[18, 19]. Katsura et al. [18] describe in terms of spin currents the polarisation induced by a\ncycloidal spin arrangement, which can be written as ~P/~ eij\u0002(~Si\u0002~Sj), with~Si;jthe local\nspins and~ eijthe unit vector connecting the two sites. The interaction of this polarisation\nwith a coexisting internal polarisation produces a magneto-electric term in the total energy\n[18]:EDM= (~P\u0002~ eij):(~Si\u0002~Sj). This ME interaction, which can also be obtained from\nsymmetry considerations [12, 17], was held responsible for the cycloidal spin arrangement in\nBiFeO 3[17]. This coupling energy induces the canting of Fe moments which exactly com-\npensates for the loss in exchange energy (neglecting the anisotropy energy): E=\u0000Ak2. A\n5ME energy density of \u00003:107J=m3can be inferred from the value of the period of the cycloid\nand the exchange constant ( A= 3:10\u00006J=m). Importantly, the coupling energy is zero when\n~Pis perpendicular to the local moments and maximum when it lies in the cycloid rotation\nplane. This explains the antiferromagnetic \rop we observe when ~Pchanges direction. This\nalso explains why the two crystals we measured had their cycloids in the same direction ~k1.\nIndeed, this minimises the components of the magnetic spins parallel to the depolarisation\n\feld (normal to the platelets surface), which lowers the cost in DM energy.\nWhen in thin \flm form, BiFeO 3is a very di\u000berent system because epitaxial strain sup-\npresses the cycloid and induces a weak magnetic moment [21]. Locally, the magnetic struc-\nture consists of canted spins with angles changing sign between neighbours, which makes\nthe moments add. If this magnetic con\fguration were to generate a local polarisation, its\ndirection would alternate from site to site. Therefore, in order for a global polarisation to\ncoexist with weak ferromagnetism, it is better if the spins are in a plane perpendicular to the\npolarisation direction, a con\fguration for which the DM based interactions are zero. This is\nexactly what is observed in BiFeO 3\flms [5]. The magnitude of this ME coupling is more\ndi\u000ecult to estimate than that in the bulk, but because it originates from the frustration of\nthe DM interactions, it is likely to be weaker. Interestingly, canting angles are only about\n0.2 °(the weak ferromagnetic moment being 0 :02\u0016B=atom [21]), to be compared with 2.25 °in\nthe bulk. This underlines the ME origin of the cycloid and also hints at a stronger coupling\nin the bulk since the interaction between ~Pand~Mis directly linked to canting.\nIn order to make a useful device with BiFeO 3, we suggest to use the exchange bias inter-\naction between a thin ferromagnetic layer and a BiFeO 3substrate, i.e. with its cycloid. It\nshould be possible to vary electrically the exchange bias interaction using the antiferromag-\nnetic \rop observed here. Indeed, it is known that in conventional exchange bias systems, a\nnon-compensated antiferromagnetic surface is not a prerequisite to obtain a large exchange\n\feld. Hence, it is likely that the cycloid may not signi\fcantly a\u000bect the bias, while optimising\nthe coupling between the antiferromagnetic and ferroelectric orders.\nWe would like to aknowledge fruitfull discussions with Hans Schmid, Alexander Zhdanov\nand Daniil Khomskii as well as funding from the 'Agence Nationale de la Recherche' through\nthe contract 'FEMMES'. We also thank X. Le Go\u000b for X-ray measurements on single crystals\nas well as Gustau Catalan, Neil Mathur and Manuel Bib\u0012 es for their critical reading of the\n6manuscript.\n[1] P. Curie, J. Phys. 3, 393 (1894).\n[2] G. Smolenskii and I. Chupis, Sov. Phys. Uspekhi 25, 475 (1982). Y. Venevtsev and V. Gagulin,\nFerroelectrics 162, 23 (1994), and references therein.\n[3] M. Fiebig, J. Phys. D 38, R123 (2005). W. Eerenstein, N. D. Mathur, and J. F. Scott, Nature\n442, 759765 (2006).\n[4] R. Smith et al., J. Appl. Phys. 39, 70 (1968).\n[5] J. Wang et al. Science 299, 1719 (2003).\n[6] D. Lebeugle et al., Appl. Phys. Lett. 91, 022907 (2007). V.V. Shvartsman et al., Appl. Phys.\nLett. 90, 172115 (2007).\n[7] T. Zhao et al. Nature Materials 5, 823 (2006).\n[8] D. Lebeugle et al., Phys. Rev. B 76, 024116 (2007).\n[9] F. Kubel and H. Schmid, Acta Crystallographica B 46, 698 (1990).\n[10] I. Sosnowska, T. Peterlin-Neumaier, and E. Steichele, J. Phys. C: Solid State Phys. 15, 4835\n(1982).\n[11] R. Przenioslo, M. Regulski, and I. Sosnowska, J. Phys. Soc. Jpn. 75, 084718 (2006).\n[12] M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006).\n[13] H. Schmid, private communication.\n[14] C. Tabares-Munoz et al., Jpn. J. Appl. Phys. 24, 1051 (1985).\n[15] Y. F. Popov et al., JETP Lett. 57, 69 (1993).\n[16] J. Scott and D. Tilley, Ferroelectrics 161, 235 (1994).\n[17] A. Kadomtseva et al., JETP Letters 79, 571 (2004).\n[18] H. Katsura, N. Nagaosa, and A. V. Balatsky, Phys Rev Lett. 95, 057205 (2005).\n[19] I. Sergienko and E. Dagotto, Phys. Rev. B 73, 094434 (2006).\n[20] I. Dzyaloshinskii, Sov. Phys. JETP 10, 628 (1959). T. Moriya, Phys. Rev. 120, 91 (1960).\n[21] H. Bea et al., Appl. Phys. Lett. 87, 072508 (2005). H. Bea et al., Phil. Mag. Lett. 87, 165\n(2007).\n7Figures\n0.988 0.994 11.006 1.012 \n-0.012 -0.006 0 0.006 0.012 \n(ξ,0,−ξ) ξ,0,−ξ) ξ,0,−ξ) ξ,0,−ξ) (ξ,0,ξ) (ξ,0,ξ) (ξ,0,ξ) (ξ,0,ξ) k1= [δδ δδ0-δδ δδ]k2= [0 δδ δδ-δδ δδ]\na* c* b* \nk3= [-δδ δδ δδ δδ0] \nλ= 640 Ǻ[10-1] [111] \nP(a) \n(b) \nFIG. 1: (a) Neutron intensity around the (1\n2;\u00001\n2;1\n2) Bragg re\rection in the single domain state.\nThe two di\u000braction satellites indicate that the cycloid is along the (10-1) direction. (b) Schematics\nof the magnetic con\fguration of antiferromagnetic vectors in the 64 nmperiodic circular cycloid.\n8[11-1] [-11-1] \nc* a* b* [111] [-111] \nP[111] \n(a) \n(b) FIG. 2: Mapping of the neutron intensity in reciprocal space. Two sets of splitting appear for the\nnuclear intensity (yellow spots) consistent with the presence of two ferroelastic domains (see (a)):\none because of the presence of two rhombohedral distortions along [111] and [1-11], and the second\nbecause of a physical buckling of the crystal induced by the twinning. Magnetic peaks are further\nsplit because of the cycloids. Note that because the splitting is small, the scale has been magni\fed\nby a factor of 10 on each peak position.\n90.988 0.994 11.006 1.012 \n-0.012 -0.006 0 0.006 0.012 \n(ξ,0,−ξ) ξ,0,−ξ) ξ,0,−ξ) ξ,0,−ξ) (ξ,0,ξ) (ξ,0,ξ) (ξ,0,ξ) (ξ,0,ξ) \n71°\nq1= [ δδ δδ0-δδ δδ]q2= [0 δδ δδ-δδ δδ]\na* c* b* \nq3= [- δδ δδ δδ δδ0] q1= [ δδ δδ0-δδ δδ]\n0°FIG. 3: Neutron intensity around the (1\n2;\u00001\n2;1\n2) Bragg position in the multidomain state. Theo-\nretical positions are indicated by the black and white spots. Di\u000braction satellites are visible in the\n0 °(bottom half) and 71 °(top half) domains of polarisation. The di\u000berence in vertical spot shape\nlikely originates from the position of reversed domains at opposite ends of the sample because of\na prefered nucleation near the the edges. Any warping of the sample splits the new (1-11) peak\nwhile recovering an improved resolution for the original domain located near the center.\n10P [111]\nP [1-11]k1EFIG. 4: Schematics of the planes of spin rotations and cycloids ~k1vector for the two polarisation\ndomains separated by a domain wall (in grey).\n11Tables\nBragg peak ~P;~k1~P;~k2~P;~k3Iobs\n(1\n2;\u00001\n2;1\n2)189 122 122 198(8)\n(1\n2;1\n2;1\n2)100 100 100 99(6)\n(\u00001\n2;1\n2;1\n2)122 122 189 116(6)\n(1\n2;1\n2;\u00001\n2)122 189 122 114(6)\n(1\n2;\u00003\n2;1\n2)113 71 71111(11)\n(3\n2;\u00001\n2;\u00001\n2)71 71 113 83(8)\n(\u00001\n2;\u00001\n2;3\n2)71 113 71 83(8)\n(\u00001\n2;\u00003\n2;\u00001\n2)71 61 61 78(9)\n(3\n2;1\n2;1\n2)61 61 71 52(6)\n(1\n2;1\n2;1\n2)61 71 61 56(7)\nTABLE I: Intensity measured around the magnetic Bragg positions compared to that expected for\na cycloid with magnetic vectors in the di\u000berent allowed ( ~P;~k) planes.\nBragg peak ~P0;~k1~P71;~k0\n1~P71;~k0\n2~P71;~k0\n3Iobs Icalc\n(1\n2;\u00001\n2;1\n2)189 100 100 100 158(7) 150\n(1\n2;1\n2;1\n2)100 189 122 122 145(6) 139\n(\u00001\n2;1\n2;1\n2)122 122 122 189 120(8) 122\n(1\n2;1\n2;\u00001\n2)122 122 189 122 112(9) 122\nTABLE II: Intensity measured around the magnetic Bragg positions compared to that expected for\na cycloid with magnetic vectors in the di\u000berent allowed planes. Calculated values are obtained with\n55% of domains having switched their polarisation by 71 °and kept the same propagation vector.\n12"    },    {        "title": "1111.4361v1.Microwave_near_field_helicity_and_its_role_in_the_matter_field_interaction.pdf",        "content": "Microwave near-field helicity and its role in the m atter-field interaction  \n \nE.O. Kamenetskii, R. Joffe, and R. Shavit \n \nDepartment of Electrical and Computer Engineering, \nBen Gurion University of the Negev, Beer Sheva, Isr ael \n \nNovember 16, 2011 \n \nAbstract \n \nIn the preceding paper, we have shown analytically that in a source-free subwavelength region of \nmicrowave fields there exist the field structures w ith local coupling between the time-varying \nelectric and magnetic fields differing from the ele ctric-magnetic coupling in regular free-space \nelectromagnetic waves. As a source of such near fie lds, there is a small quasi-2D ferrite disk with \nthe magnetic-dipolar-mode (MDM) spectra. The near f ields originated from a MDM ferrite \nparticle are characterized by topologically distinc tive structures of power-flow vortices, non-zero \nhelicity, and a torsion degree of freedom. In this paper, we present numerical and experimental \nstudies on the microwave near-field helicity and it s role in the matter-field interaction. We show \nthat one can distinguish different microwave near-f ield-helicity parameters for different \npermittivities of dielectric samples loading a ferr ite-disk sensor. We analyze a role of topological \nstructures of the fields on the helicity properties . We demonstrate dependence of the MDM \nspectra and the near-field-helicity parameters from  the enantiomeric properties of the loading \nsamples.     \n \nPACS number(s): 41.20.Jb; 76.50.+g; 84.40.-x; 81.05 .Xj \n \n \nI. Introduction \n \nThe well known possibility of electrostatic (plasmo n) resonances in metallic nanoparticles to \nexhibit strong localization of electric fields in a  subwavelength region was used recently for \nultrasensitive characterization of biomolecules [1] . In these experiments, the enhanced sensitivity \nof a chiroptical measurement was obtained owing to the chiral asymmetry of the metallic \nstructures. Such a special geometry of nanoparticle s can produce so-called superchiral \nelectromagnetic fields which have a high rate of op tical excitation of small chiral molecules [2].    \n    The results shown in Refs. [1, 2] are related t o optical studies and can hardly be applied to \nmicrowave frequencies, since plasmonic oscillations  in metallic structures are ineffective at \nmicrowaves. There is, however, another way for subw avelength localization and chiral \nasymmetry of the fields in microwaves. Recent studi es of interaction between microwave \nelectromagnetic fields and small ferrite particles with magnetic-dipolar-mode (MDM) \noscillations evidently demonstrate that such partic les are origin of topological singularities of the \nmicrowave near fields, which are characterized by P oynting vector vortices and symmetry \nbreakings [3]. In contrast to small plasmon-resonan ce particles with the electric-field \nlocalization, in small ferrite particles with MDM r esonances one has subwavelength localization \nof both the electric and magnetic fields. At the re sonance frequencies, power flows of \npropagating electromagnetic waves are strongly attr acted by the MDM vortices at their \nvicinities. Coupled states of electromagnetic field s with vortices of MDM oscillations – the \nMDM-vortex polaritons – are physical entities with symmetry properties distinguished from \nsymmetry properties of the regular electromagnetic near-field configurations [4]. In Ref. [5], it  2has been shown analytically that microwave near fie lds of a MDM ferrite disk are characterized \nby the helicity factor and a torsion degree of free dom. These symmetry properties of the \nmicrowave near fields could appear as very intrigui ng factors in general problems of the field-\nmatter interaction. With use of the MDM near-field structures one acquires an effective \ninstrument for local microwave characterization of properties of matter. In microwave \nexperiments [6], it was shown, for the first time, that there is a transformation of the MDM \nspectrum due to dielectric samples abutting to the surface of a ferrite disk. Such a dielectric \nloading results in shifts of the MDM resonance peak s without evident destroying the shape of \nthe spectrum peaks. The value of the peak shifts de pends on the permittivity of dielectric \nsamples [6]. Use of subwavelength microwave fields with localization and chiral asymmetry \nopens a perspective for unique applications. Becaus e of the helicity structure of the MDM near-\nfields, one can predict carrying out a precise spec troscopic analysis of natural and artificial chiral  \nstructures at microwaves. This will pave, in partri cular, the way to creating pure microwave \ndevices for separation of biological and drug enant iomers. This also may give an answer to a \ncontroversial issue whether or not microwave irradi ation can exert a non thermal effect on \nbiomolecules [7]. In a view of these discussions, i t is worth noting that in biological structures, \nmicrowave radiation can excite certain rotational t ransitions, which cannot be explained as \nclassical heating effects [7]. One can predict that  rotating microwave near fields originated from \nMDM ferrite particles [3, 4] can be used to explain  such extraordinary effects in biological \nstructures.  \n    In this paper, we analyze numerically the symme try properties of microwave subwavelength \nfields originated from a quasi-2D ferrite disk with  MDM oscillations. Based on a commercial \nfinite-element based electromagnetic solver (HFSS, Ansoft), we confirm the helicity properties \nof the MDM near fields predicted analytically in Re f. [5]. We present results of numerical and \nexperimental studies of interaction of the microwav e near field with the helicity properties with \ndielectrics characterized by different permittivity  parameters. We demonstrate dependence of the \nnear field helicity parameters on the enantiomeric properties of the loading samples. We discuss \npossibility for implementation of the shown effects  in near field microwave microscopy for \nsensitive characterization of materials with chiral  enantiomeric properties.       \n \nII. Helicity density of the MDM near fields \n \nIn the preceding paper [5] we have shown analytical ly that in a near-field region abutting to a \nquasi-2D ferrite disk with the MDM oscillations, th ere should exist a non-zero parameter which \nwe call as the helicity density of the MDM fields. For a real electric field, this parameter is \nwritten as (contrarily to Ref. [5] we use here the SI system of units): \n \n                                                              0\n2F E E ε≡ ⋅∇× r r \n .                                                           (1) \n \nFor time-harmonic fields, we can calculate this par ameter as  \n \n                                                           ( ){}*0Im 4F E E ε= ⋅ ∇× r r r \n|.                                                   (2) \n \nWe can also calculate a space angle between the vec tors Er\n and E∇× r r \n as \n  3                                                            ( ){}*Im \ncos E E \nE E α⋅ ∇× \n=\n∇× r r r \nr r .                                                (3 ) \n  \n    Distinct parameters of helicity density of the MDM fields become evident from numerical \nstudies based on a commercial finite-element electr omagnetic solver (HFSS, Ansoft). For a \nnumerical analysis in the present paper, we use the  same disk parameters as in Refs. [3, 4, 8, 9]: \nthe yttrium iron garnet (YIG) disk has a diameter o f3=Dmm and the disk thickness is \n05. 0=tmm; the disk is normally magnetized by a bias magnet ic field  49000=HOe; the \nsaturation magnetization of the ferrite is  1880 4=sMπ G. Our analysis starts with a structure \nwhere a ferrite disk is placed inside a 10TE-mode rectangular X-band waveguide symmetrically \nto its walls so that the disk axis is perpendicular to a wide wall of a waveguide. The waveguide \nwalls are made of a perfect electric conductor (PEC). For be tter understanding the field \nstructures we use a ferrite disk with very small losses : the linewidth of a ferrite is 0.1 Oe H∆ = . \nFig. 1 shows the module of the reflection (the 11 S scattering-matrix parameter) coefficient. The \nresonance modes are designated in succession by numbe rs n = 1, 2, 3… An insert in Fig. 1 shows \ngeometry of the structure. One can clearly see that, s tarting from the second mode, the coupled \nstates of the electromagnetic fields with MDM vortices demonstrate split-resonance states. The \nproperties of these coalescent resonances, denoted in Fig. 1 by single and double primes, were \nanalyzed in details in Ref. [4].  \n    In Refs. [3, 4], we studied general properties of th e microwave near fields originated from a \nferrite disk with MDM resonances. Here we calculate num erically the helicity parameter of these \nnear fields based on Eqs. (2) and (3). For demonstration of the helicity parameter distribution in \nthe near-field regions of a ferrite disk, we use a cross-s ection plane which passes through the \ndiameter and the axis of the disk. Fig. 2 shows the h elicity density parameter F, calculated for the \n1st MDM based on numerically obtained electric near fields . For the 2 nd  mode (the resonance 2\"), \nparameter F is shown in Fig. 3. For the resonances denoted by si ngle primes (the resonances \n2, 3,′ ′ etc.) in Fig. 1, as well for non-resonance frequencies , one has zero parameter F (see Fig. \n4). As it follows from Figs. 2 and 3, there are reg ions with positive and negative quantities of the \nhelicity parameter.  \n    As we showed in Ref. [5], the helicity properti es of the near fields are strongly related to the \nmagnetization distribution of MDMs. The present stu dies of the helicity factor F give evidence \nfor the relations between distributions of magnetiz ation inside a ferrite disk and the helicity \nproperties of the fields outside a disk. Fig. 5 ( a), (b) show the numerical solutions for \nmagnetization for the 1st and 2 nd  (the resonance 2\") MDMs. These numerical results a re in a good \ncorrespondence with the analytical solutions shown in Fig. 5 (c), (d). In the pictures in Fig. 5, we \nmarked specific topological regions – the vortices – of magnetization. At the time variation, \nthese vortices of magnetization, characterizing by positive and negative topological charges, \nrotate about a disk axis. There can be clockwise or  counterclockwise rotation, depending on a \ndirection of a bias magnetic field. One can see tha t while for the 1 st MDM, the vortices of \nmagnetization exist in peripheral regions of a ferr ite disk, for the 2 nd  MDM, these vortices of \nmagnetization are shifted to a center of a disk. In  Figs. 2 and 3, we marked the positions of these \nmagnetization vortices. It is worth noting that the  magnetization vortices are situated near the \nregions where parameter F is zero. A maximum of parameter F is at a center of a ferrite disk, \nbetween the magnetization vortices. It is also wort h noting that the regions where parameter F is \nmaximal correspond to the regions where there is a maximal electric field of MDM oscillations \n[3, 4, 8, 9].   4    In paper [5], we noticed that the electric fiel ds originated from the MDMs cannot by related to \nthe electric-polarization effects both inside a fer rite and in abutting dielectrics outside a ferrite.  \nHowever, when the dielectrics are polarized by the external (DC or RF) electric fields, one \nshould observe the influence of the dielectric prop erties on the oscillation spectra due to the \n\"spin\" and \"orbital\" angular momentums of the MDM e lectric fields. Based on numerical studies, \nin the present paper, we verify this statement and show what is a role of dielectric loadings in the \nspectral characteristics and helicity properties of  the MDM fields. We start with a structure of a \nferrite disk loading symmetrically with two dielect ric cylinders. The structure is placed inside a \nrectangular waveguide (Fig. 6). The dielectric cyli nders (every cylinder is with the diameter of 3 \nmm and the height of 2 mm) are electrically polariz ed by the RF electric field of the 10TE mode \npropagating in a waveguide. The frequency character istics of a module of the reflection \ncoefficient for the 1 st MDM at different dielectric parameters of the cyli nders are shown in Fig. \n7. One can see that at dielectric loadings there ar e coalescent resonances (the resonances 1′ and \n1′′). Fig. 8 shows the Poynting vector distributions a bove a ferrite disk at the frequencies related \nto the resonance 1 of an unloaded (without dielectr ic cylinders) ferrite disk and the resonances \n1′′ of a ferrite disk with dielectric loadings. These pictures, corresponding, evidently, to the \nknown Poynting vector distributions of the 1 st MDM [3, 4, 8, 9], clearly show that dielectric \nloadings do not destroy the entire MDM spectrum, bu t cause, however, the frequency shifts of \nthe resonance peaks.   \n    One of the main features of the frequency chara cteristics of a structure with the symmetrical \ndielectric loadings, shown in Fig. 7, is the fact t hat the resonances of the 1 st MDM become \nshifted not only to the lower frequencies, but appe ar to the left of the Larmor frequency of an \nunloaded ferrite disk. For a normally magnetized fe rrite disk with the pointed above quantities of \nthe bias magnetic field and the saturation magnetiz ation, this Larmor frequency (calculated as \n1\n2H if H γπ=, where γ is the gyromagnetic ratio  and iH is the internal DC magnetic field) is \nequal to 8,456 GHz Hf= . When a ferrite disk is without dielectric loading s, the entire spectrum \nof MDM oscillations is situated to the right of the  Larmor frequency Hf. Since dielectrics do not \ndestroy the entire MDM spectrum, one can suppose th at the Larmor frequency of a structure with \ndielectric loadings is lower than the Larmor freque ncy of an unloaded ferrite disk. We clarify this \nstatement based on the following analysis.  \n    The electric field of MDMs has both the \"spin\" and \"orbital\" angular momentums. As we \ndiscussed in Ref. [5], the electric fields originat ed from a MDM ferrite disk cannot cause the \nelectric polarization of a dielectric material. How ever, due to the MDM electric fields one can \nobserve the mechanical torque exerted on a given el ectric dipole. This mechanical torque is \ndefined as a cross product of the MDM electric fiel d r\nE and the electric moment of the dipole \npr[5]: \n \n                                                                 p= × r r rNE.                                                                 (4) \n \nThe dipole pr appears because of the electric polarization of a dielectric by the RF electric field \nof a microwave system (the electric field of the 10TE mode in a rectangular waveguide, in \nparticular). This dipole is perpendicular to a ferr ite disk. At the same time, as it was shown in \nRef. [5], the MDM electric field r\nE is the field precessing in a plane parallel to a f errite-disk \nplane. When a dielectric sample is placed above a f errite disk, the electric field r\nE affects on the \nelementary dipole moments of a dielectric, causing precession of these dipole momenta. The \ntorque exerting on the electric polarization due to  the MDM electric field should be equal to  5reaction torque exerting on the magnetization in a ferrite disk. Because of this reaction torque, \nthe precessing magnetic moment density of the ferro magnet will be under additional mechanical \nrotation at a certain frequency Ω. For the magnetic moment density of the ferromagne t, Mr\n, the \nmotion equation acquires the following form (see Ap pendix B in Ref. [5]): \n \n                                                              dM M H dtγγ  Ω=− × −     rr r \n,                                                 ( 5) \n \nThe frequency Ω is defined based on both, \"spin\" and \"orbital\", mo mentums of the fields of \nMDM oscillations. One can see that at the dielectri c loadings, the magnetization motion in a \nferrite disk is characterized by an effective magne tic field \n \n                                                                     effH H γΩ= − r r \n.                                                         (6) \n \nSo, the Larmor frequency of a structure with dielec tric loadings is at lower frequencies in \ncomparison with such a frequency in an unloaded fer rite disk. When we put a dielectric loading \nabove or (and) below a ferrite disk and apply to th is structure an external electric field oriented \nalong a disk axis, we have two (or three) capacitan ces connected in series. The capacitance of a \nthin-film ferrite disk is much bigger than the capa citances of dielectric samples. Thus, the surface \nelectric charges on ferrite-disk planes will be mai nly defined by the permittivity and geometry of \ndielectric samples. As a result, one has the MDM sp ectrum transformation dependable on \nparameters of the dielectric samples.  \n    The effective helicity of the fields in a diele ctric is due to the helicity of the MDM near field \nin vacuum and associated motion of the electric pol arization. The recoil torque of the fields in a \ndielectric loading on a ferrite disk should be dire ctly proportional to the refractive index of the \ndielectric. The helicity densities in dielectrics w ere calculated numerically based on Eq. (2). In \nFig. 9, we can see the helicity density distributio ns in the cross-section plane passed through the \ndiameter and the axis of the disk for different die lectric parameters of cylinders. The frequencies \ncorrespond to the 1 st  MDM. In Fig. 10 one can see the helicity paramete r distributions when the \ncross-section planes are parallel to the ferrite-di sk plane and are placed at different distances \nfrom the ferrite surface. Since amplitude of the el ectric field strongly reduces with increase of a \ndistance from the ferrite surface, it will be more interesting to analyze the properties of the near-\nfield structures when the helicity factor is normal ized on the field amplitudes. The normalized \nhelicity factor, represented as the cosine of a spa ce angle between vectors Er\n and E∇× r r \n, was \ncalculated numerically based on Eq. (3) and is show n in Fig. 11 for a cross-section plane passing \nthrough the diameter and the axis of a ferrite disk . \n    As one can see from Figs. 9 – 11, the dielectri c loadings not only reduce the quantity of the \nhelicity factor, but result in strong modification of the near-field structure. A special attention \nshould be paid to a case of a sufficiently big diel ectric constant of the loading material ( 50 rε=, \nin our case). In this case, there are singular poin ts on an axis of a structure [points A and B in Fig. \n11 (c)] where the helicity of the near fields changes it s sign. To clarify these properties more in \ndetails, we illustrate in Fig. 12 the electric and magnetic fields in a structure of a ferrite disk wi th \nloading dielectrics ( 50 rε=). These field distributions, shown at a certain ti me phase, are \ncharacterized by \"spin\" and \"orbital\" rotations. Fo r a comparative analysis, we illustrate initially \nthe field structures inside a ferrite without loadi ng dielectrics [Fig. 12 ( a)] and inside a ferrite \nwith loading dielectrics [Fig. 12 ( b)]. There are evident differences between these fie ld \nstructures. Figs. 12 ( c) and (d) show the field structures in a dielectric above a  ferrite disk. As we  6can see in Fig. 12 ( c), in a central region of a cutting plane placed be low a singular point A, a \nspace angle between the electric and magnetic field s is about 180 o. This gives a negative helicity \nfactor. When, however, a cutting plane is placed ab ove a singular point A [Fig. 12 (d)], a space \nangle between the electric and magnetic fields in a  central region is about 0o. This results in a \npositive helicity factor . Such specific properties of the helicity distribut ions, observed in a \ndielectric cylinder with a sufficiently big dielect ric constant, can be explained from the fact that, \nbecause of the depolarization field, the electric p olarization inside such a dielectric cylinder will \nbe strongly nonhomogeneous. So, precession of the e lectric polarization (due to the MDM \nelectric field r\nE) will be nonhomogeneous as well. This results in p eculiar distribution of phases \nof the fields along an axis of a system. \n    As one can see from Figs. 2, 3, 9, 11, for the patterns symmetrical with respect to a normal \naxis, there are antisymmetrical distributions of th e helicity. For the near field structure, a plane o f \na thin-film ferrite disk (where the electric field changes its direction [8], [9]) is a plane of a twi st. \nThe uniqueness of the observed properties of the fi elds in dielectric cylinders (with 50 rε=) is \nthe presence of additional planes (which pass throu gh points A and B, above and below a ferrite \ndisk) of a twist for the near fields. In these pane s the magnetic field changes its direction. It \nbecomes evident that an entire structure of the nea r fields shows the torsion degree of freedom. It \nis also worth noting here that in Fig. 11( a), a picture of the normalized helicity factor has a slight \ninclination from a normal axis. Such an inclination  (well observed, when no dielectric loading \nexist) can appear as a result of an interaction of two electromagnetic-wave power flows: one is \ndue to propagation of a waveguide mode and another – due to the near-field power-flow vortex \nof the MDM. When one changes the ports of a wavegui de, a picture of the normalized helicity \nfactor inclines from a normal axis to an opposite s ite. \n    When a sample of a ferrite disk with a dielectr ic loading is nonsymmetric with respect to a \nnormal axis, a structure of helicity of the near fi eld becomes nonsymmetrical as well. Such a \nsample, placed inside a 10TE-mode rectangular X-band waveguide, is shown in Fig . 13. The \nfrequency characteristics of a module of the reflec tion coefficient for the 1 st MDM at different \nparameters of a nonsymmetrical dielectric loading a re shown in Fig. 14. The helicity density \ndistributions [calculated numerically based on Eq. (2)] are represented in Fig. 15 for the cross-\nsection plane passed through the diameter and the a xis of the disk. It is evident that a loading by \none dielectric cylinder results in a nonsymmetrical  helicity density of the near fields. It is also \nevident that for different dielectric parameters of  a loading cylinder, the picture of the helicity \ndistribution inside a dielectric is strongly differ ent from to the above results for a sample with \nsymmetrical dielectric loadings. A more detailed an alysis of the helicity properties of the near \nfields in a nonsymmetrical ferrite/dielectric patte rn is beyond a frame of the present paper.    \n \nIII. The near-field characterization of dielectric parameters and enantiomeric properties of \nmatter \n \nThe shown helicity parameters of the near fields re flect exclusive properties of the MDM \noscillations, which can find applications for the n ear-field characterization of materials at \nmicrowaves. For this purpose, it is more preferable  to use an open-access microstrip structure \nwith a ferrite-disk sensor, instead of a closed wav eguide structure studied above. Fig. 16 \nrepresents the frequency characteristic of a module  of the transmission (the 21 S scattering-matrix \nparameter) coefficient for a microstrip structure w ith a thin-film ferrite disk. Geometry of a \nstructure is shown in an insert. In a discussed abo ve waveguide structure with an enclosed ferrite \ndisk, the main features of the MDM spectra are evid ent from the reflection characteristics. \nContrarily, in the shown microstrip structure, the most interesting are the transmission \ncharacteristics. In Fig. 16, one can see the 1 st and 2 nd  resonances of the radial variation. The  7frequencies of these eigenmode resonances are in a good correspondence with the frequencies of \nthe 1st and 2 nd  resonances shown in Fig. 1 for a waveguide structu re. Between the 1 st and 2 nd  \nresonances of the radial variations, in Fig. 16 one  can see the resonance of the azimuth mode. \nThis resonance appears because of the azimuth nonho mogeneity of a microstrip structure. A \ndetailed classification of the radial- and azimuth- variation MDMs in a ferrite disk can be found \nfrom the analytical studies in Ref. [10]. The helic ity density distribution for the 1 st radial-\nvariation resonance in a microstrip structure with a ferrite disk is shown in Fig. 17 ( a). Due to a \nmetallic ground plane and dielectric properties of a substrate in a microstrip structure, there is \nslight nonsymmetry of the helicity distribution wit h respect to a disk plane. It is worth noting that \nthe helicity properties of the near fields appear o nly at the MDM resonances. At non-resonance \nfrequencies, there is zero helicity of the field st ructure [see Fig. 17 ( b)].  \n    Fig. 18 shows the spectrum transformation due t o a dielectric placed above a ferrite disk. In \nthere numerical studies of a loading of a ferrite d isk in a microstrip structure, we used dielectric \ncylinders with the same parameters as above: the di ameter of 3mm and the height of 2 mm; the \ndielectric constants of 30 rε= and 50 rε=. We can see shifts of the peaks depending on the \ndielectric properties of a sample. It is evident th at for the 1 st radial-variation MDM resonance in \na microstrip structure, there is a sufficiently goo d correspondence of the peak positions with the \nresults in a waveguide structure shown in Fig. 14.   \n    Our numerical studies of the microwave field he licity and its role in the matter-field \ninteraction open a perspective for the experimental  near-field characterization of material \nparameters. An experimental microstrip structure is  realized on a dielectric substrate (Taconic \nRF-35, 3.52 rε=, thickness of 1.52 mm). Characteristic impedance o f a microstrip line is 50 \nOhm. For dielectric loadings, we used cylinders of commercial microwave dielectric (non \nmagnetic) materials with the dielectric permittivit y parameters of 30=rε (K-30; TCI Ceramics \nInc) and 50=rε (K-50; TCI Ceramics Inc). The experimental results  for characterization of \ndielectric properties of materials are shown in Fig . 19. One can see a sufficiently good \ncorrespondence between the numerical and experiment al results. It is necessary to note here that \ninstead of a bias magnetic field in numerical studi es (04900 H=Oe), in the experiments we \napplied lower quantity of a bias magnetic field: 04708 H=Oe. Use of such a lower quantity \n(giving us the same positions of the non-loading-fe rrite resonance peak in the numerical studies \nand in the experiments) is necessary because of non -homogeneity of an internal DC magnetic \nfield in real ferrite disks. A more detailed discus sion on a role of non-homogeneity of an internal \nDC magnetic field in the MDM spectral characteristi cs can be found in Refs. [10, 11]. \n    With use of the MDM near-field structures one m ay acquire an effective instrument for local \ncharacterization of special topological properties of matter. This, in particular, will allow \nrealization of microwave devices for precise spectr oscopic analysis of materials with chiral \nstructures such, for example, as biological and dru g enantiomers. In Ref. [5] we showed \nanalytically that the helicity density F above and below a ferrite disk should have differe nt signs \nfor different orientations of a normal bias magneti c field. The present numerical results confirm \nthis prediction. Fig. 20 shows the F-factor distributions for a ferrite disk (without a  loading \ndielectric) in a microstrip structure at opposite d irections of a normal bias magnetic field [in a \ncase of a ferrite disk in a waveguide, one has the same change of a sign of parameter F when a \ndirection of a normal bias magnetic field changes].  This confirms that the near-field structure of \nthe MDM electric field is characterized by the spac e and time symmetry breakings. Based on \nnumerical studies, we show how these properties of the MDM near fields can be applied for \ncharacterization of enantiomers. For this purpose, we use a special chiral sample. This is a \ndielectric disk with a chiral-structure metal coati ng. Fig. 21 (a) shows the sample structure. Fig \n21 (b) represents the helicity -parameter distribution in a dielectric disk ( 30 rε=) when magnetic  8bias is up. This is the distribution with evident l ack of azimuth symmetry. On a chiral-structure \nmetal coating the helicity parameter is zero. When this sample is placed on a surface of a ferrite \ndisk, one obtains evident distinction of the MDM sp ectra at different orientations of a bias \nmagnetic field. This is illustrated in Fig. 22 for a transmission coefficient of a microstrip \nstructure with a thin-film ferrite disk. \n \nIV. Conclusion \n \nSmall quasi-2D ferrite disks with the magnetic-dipo lar-oscillation spectra are sources of peculiar \nmicrowave near fields. These fields, studied analyt ically in the preceding paper [5], are \ncharacterized by topologically distinctive power-fl ow vortices, non-zero helicity, and a torsion \ndegree of freedom. The numerical and experimental s tudies shown in the present paper confirm \nmain statements of the theory in Ref. [5].  \n    Among a series of interesting properties of the  microwave near fields, originated from quasi-\n2D ferrite disks with the magnetic-dipolar-oscillat ion spectra, there are interactions of such near \nfields with matter. Transformation of the MDM spect rum due to dielectric samples abutting to \nthe surface of a ferrite disk was observed experime ntally, for the first time, in Ref. [7]. In the \npresent studies, we showed that the transformation of the MDM spectrum due to dielectric \nsamples is strongly related to the helicity propert ies of the MDM near fields. We also showed \nthat in virtue of the near-field helicity one can e ffectively observe at microwaves the \nenantiomeric properties of the samples. Use of subw avelength MDM fields with energy \nlocalization and symmetry breakings opens a perspec tive for unique microwave applications. \nPresently, the precise spectroscopic analysis of na tural and artificial chiral structures is \nconsidered as one of the very important aspects in material characterization. Because of the \nhelicity structure of the MDM near-fields, one can predict carrying out a precise spectroscopic \nanalysis of natural and artificial chiral structure s at microwaves. \n \nReferences \n \n[1] E. Hendry, T. Carpy, J. Johnston, M. Popland, R . V. Mikhaylovskiy, A. J. Lapthorn, S. M. \nKelly, L. D. Barron, N. Gadegaard, and M. Kadodwala , Nature Nanotechnol. 5, 783 (2010). \n[2] Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104 , 163901 (2010). \n[3] E. O. Kamenetskii, M. Sigalov, and R. Shavit, P hys. Rev. A 81 , 053823 (2010). \n[4] E. O. Kamenetskii, R. Joffe, and R. Shavit, Phy s. Rev A 84 , 023836 (2011). \n[5] E. O. Kamenetskii, preceding paper. \n[6] M. Sigalov, E. O. Kamenetskii, and R. Shavit, J . Appl. Phys. 104 , 053901 (2008). \n[7] A. de la Hoz, A. Diaz-Ortiz, and A. Moreno, Che m. Soc. Rev. 34 , 164 (2005). \n[8] M. Sigalov, E. O. Kamenetskii, and R. Shavit, J . Phys.: Condens. Matter 21 , 016003 (2009).  \n[9] E. O. Kamenetskii, M. Sigalov, and R. Shavit, J . Appl. Phys. 105 , 013537 (2009). \n[10] E. O. Kamenetskii, M. Sigalov, and R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005). \n[11] T. Yukawa and K. Abe, J. Appl. Phys. 45 , 3146 (1974). \n \n \n \n \n \n \n \n \n  9Figure captions  \n \nFig. 1. Frequency characteristics of a module of th e reflection coefficient for a rectangular \nwaveguide with an enclosed thin-film ferrite disk. The resonance modes are designated in \nsuccession by numbers n = 1, 2, 3… The coalescent r esonances are denoted by single and double \nprimes. An insert shows geometry of a structure. \n \nFig. 2. The helicity  parameter for the 1 st MDM (a ferrite disk is inside a rectangular wavegu ide).  \n \nFig. 3. The helicity  parameter for the 2 nd  (the resonance 2'') MDM (a ferrite disk is inside a \nrectangular waveguide). \n \nFig. 4. The helicity  parameter for non-resonance frequencies (a ferrite disk is inside a rectangular \nwaveguide). \n \nFig. 5. Magnetization distributions in a ferrite di sk at the MDM resonances. ( a) and (b)  \nnumerical results for the 1 st and 2 nd  (the resonance 2\") MDMs, respectively; ( c) and (d) analytical \nresults for the 1 st and 2 nd  MDMs, respectively, obtained based on the models i n Refs. [8, 9]. The \ndistributions are shown for a certain time phase.  \n \nFig. 6. A sample of a ferrite disk with two loading  dielectric cylinders placed inside a 10TE-mode \nrectangular waveguide.  \n \nFig. 7. Frequency characteristics of a module of th e reflection coefficient for the 1 st MDM at \ndifferent parameters of a symmetrical dielectric lo ading. Frequency 8,456 GHz Hf=  is the \nLarmor frequency of an unloaded ferrite disk. \n \nFig. 8. Poynting vector distributions above a ferri te disk (on the plane parallel to the ferrite-disk \nplane and at distance 75 microns above a disk). The  frequencies correspond to the resonance 1 of \nan unloaded (without dielectric cylinders) ferrite disk and the resonances 1′′ of a ferrite disk with \ndielectric loadings.  \n \nFig. 9. Numerically calculated helicity-parameter d istributions for the 1 st MDM at different \ndielectric constants of loading cylinders. The dist ributions are shown on the cross-section plane \nwhich passes through the diameter and the axis of t he ferrite disk. \n \nFig. 10. The helicity parameter distributions for t he 1 st MDM at different dielectric constants of \nloading cylinders. The cross-section planes are par allel to the ferrite-disk plane and are at \ndifferent distances from the ferrite surface: (a) 2 5 mkm, (b) 75 mkm, (c) 150 mkm. \n \nFig. 11. Space angle between vectors Er\n and E∇× r r \n for the 1 st MDM at different dielectric \nconstants of loading cylinders. ( a) 1rε=; (b) 30 rε=; (c) 50 rε=. Points A and B are singular \npoints in dielectrics, where the helicity of the ne ar fields changes its sign. \n \nFig. 12. The electric and magnetic fields (at a cer tain time phase) in a structure of a ferrite disk \nwith loading dielectrics. ( a) and (b)  the electric and magnetic fields inside a ferrit e disk for \ndielectric loadings of 1rε= and 50 rε=, respectively;  ( c)  the electric and magnetic fields in a \ndielectric ( 50 rε=) on a plane 0.75 mm above a surface of a ferrite d isk (the plane is below a  10 singular point A); (d) the electric and magnetic fields in a dielectric (50 rε=) on a plane 1.7 mm \nabove a surface of a ferrite disk (the plane is abo ve a singular point A). \n \nFig. 13. A sample of a ferrite disk with one loadin g dielectric cylinder placed inside a 10TE-mode \nrectangular waveguide.  \n \nFig. 14. Frequency characteristics of a module of t he reflection coefficient for the 1 st MDM at \ndifferent parameters of a dielectric cylinder.   \n \nFig. 15. Numerically calculated helicity parameter distributions for the 1 st MDM at different \ndielectric constants of a loading cylinder. The dis tributions are shown on the cross-section plane \nwhich passes through the diameter and the axis of t he ferrite disk. \n \nFig. 16. Frequency characteristic of a module of th e transmission coefficient for a microstrip \nstructure with a thin-film ferrite disk. An insert shows geometry of a structure. \n \nFig. 17. The helicity  parameter for a microstrip structure with a ferrite  disk. (a) For the 1 st radial-\nmode resonance frequency; (b) at non-resonance freq uencies.  \n \nFig. 18. Transformation of the MDM spectrum due to a dielectric loading in a microstrip \nstructure (numerical results). \n \nFig. 19. Transformation of the MDM spectrum due to a dielectric loading in a microstrip \nstructure (experimental results). \n \nFig. 20. The helicity  parameter for the 1 st radial mode at opposite directions of a normal bia s \nmagnetic field. A ferrite disk is placed in a micro strip structure without a loading dielectric. ( a) \nMagnetic bias is up; ( b) magnetic bias is down. \n \nFig. 21. A chiral sample. ( a) Sample structure; ( b) the helicity  parameter distribution in a \ndielectric disk when magnetic bias is up. \n \nFig. 22. Measuring of chirality with use of opposit e directions of a DC magnetic field (numerical \nresults). An insert shows the position of a chiral sample in a microstrip structure. \n \n \n \n \n \n \n \n \n \n \n \n \n \n  \n  11 \n \nFig. 1. Frequency characteristics of a module of th e reflection coefficient for a rectangular \nwaveguide with an enclosed thin-film ferrite disk. The resonance modes are designated in \nsuccession by numbers n = 1, 2, 3… The coalescent r esonances are denoted by single and double \nprimes. An insert shows geometry of a structure. \n \n \n \n  \n  \n \nFig. 2. The helicity  parameter for the 1 st MDM (a ferrite disk is inside a rectangular wavegu ide).  \n \n  12 \n \n \n \nFig. 3. The helicity  parameter for the 2 nd  (the resonance 2'') MDM (a ferrite disk is inside a \nrectangular waveguide). \n \n \n \n \nFig. 4. The helicity  parameter for non-resonance frequencies (a ferrite disk is inside a rectangular \nwaveguide). \n \n \n  13      \n      \n \n                                     ( a)                                                                        ( b) \n                                                           \n \n     \n  \n                                   ( c)                                                                          ( d) \n \nFig. 5. Magnetization distributions in a ferrite di sk at the MDM resonances. ( a) and (b)  \nnumerical results for the 1 st and 2 nd  (the resonance 2\") MDMs, respectively; ( c) and (d) analytical \nresults for the 1 st and 2 nd  MDMs, respectively, obtained based on the models i n Refs. [8, 9]. The \ndistributions are shown for a certain time phase.  \n \n      \n \n  14 \n \n \nFig. 6. A sample of a ferrite disk with two loading  dielectric cylinders placed inside a 10TE-mode \nrectangular waveguide.  \n \n \n \n \n \nFig. 7. Frequency characteristics of a module of th e reflection coefficient for the 1 st MDM at \ndifferent parameters of a symmetrical dielectric lo ading. Frequency 8,456 GHz Hf=  is the \nLarmor frequency of an unloaded ferrite disk. \n \n         15 \n \n \n                      8.52256  res f GHz =          8.451485 res f GHz =         8.38578 res f GHz =  \n \nFig. 8. Poynting vector distributions above a ferri te disk (on the plane parallel to the ferrite-disk \nplane and at distance 75 microns above a disk). The  frequencies correspond to the resonance 1 of \nan unloaded (without dielectric cylinders) ferrite disk and the resonances 1′′ of a ferrite disk with \ndielectric loadings.  \n \n                                                                                            \n \n \n                                8.52256  res f GHz =           8.451485 res f GHz =               8.38578 res f GHz =  \n \nFig. 9. Numerically calculated helicity-parameter d istributions for the 1 st MDM at different \ndielectric constants of loading cylinders. The dist ributions are shown on the cross-section plane \nwhich passes through the diameter and the axis of t he ferrite disk. \n \n \n  16                          8.52256  res f GHz =              8.451485 res f GHz =                8.38578 res f GHz =  \n \n                 (a) \n \n \n                            8.52256  res f GHz =          8.451485 res f GHz =                8.38578 res f GHz =  \n \n                 (b) \n \n \n                            8.52256  res f GHz =          8.451485 res f GHz =              8.38578 res f GHz =  \n    \n                 (c) \n \nFig. 10. The helicity parameter distributions for t he 1 st MDM at different dielectric constants of \nloading cylinders. The cross-section planes are par allel to the ferrite-disk plane and are at \ndifferent distances from the ferrite surface: (a) 2 5 mkm, (b) 75 mkm, (c) 150 mkm.  \n \n  17 \n \n                            ( a)                                       ( b)                                      ( c) \n \n                   8.52256  res f GHz =          8.451485 res f GHz =           8.38578 res f GHz =  \n \nFig. 11. Space angle between vectors Er\n and E∇× r r \n for the 1 st MDM at different dielectric \nconstants of loading cylinders. ( a) 1rε=; (b) 30 rε=; (c) 50 rε=. Points A and B are singular \npoints in dielectrics, where the helicity of the ne ar fields changes its sign. \n \n \n   \n  \n    \n                                                              (a) \n \n  \n  \n \n \n                                                                          ( b) \n  18 \n      \n  \n \n                                                                            ( c) \n \n \n     \n      \n                      \n                                                                      (d) \n \nFig. 12. The electric and magnetic fields (at a cer tain time phase) in a structure of a ferrite disk \nwith loading dielectrics. ( a) and (b)  the electric and magnetic fields inside a ferrit e disk for \ndielectric loadings of 1rε= and 50 rε=, respectively;  ( c)  the electric and magnetic fields in a \ndielectric ( 50 rε=) on a plane 0.75 mm above a surface of a ferrite d isk (the plane is below a \nsingular point A); (d) the electric and magnetic fields in a dielectric (50 rε=) on a plane 1.7 mm \nabove a surface of a ferrite disk (the plane is abo ve a singular point A). \n \n  19 \n \n \nFig. 13. A sample of a ferrite disk with one loadin g dielectric cylinder placed inside a 10TE-mode \nrectangular waveguide.  \n \n \n \n \n \nFig. 14. Frequency characteristics of a module of t he reflection coefficient for the 1 st MDM at \ndifferent parameters of a dielectric cylinder.   \n \n  20 \n \n   \n                   8.52283 res f GHz =           8.515816 res f GHz =         8.513436 res f GHz =  \n \nFig. 15. Numerically calculated helicity parameter distributions for the 1 st MDM at different \ndielectric constants of a loading cylinder. The dis tributions are shown on the cross-section plane \nwhich passes through the diameter and the axis of t he ferrite disk. \n \n \n \n \n \n \nFig. 16. Frequency characteristic of a module of th e transmission coefficient for a microstrip \nstructure with a thin-film ferrite disk. An insert shows geometry of a structure. \n \n  21 \n \n \nFig. 17. The helicity  parameter for a microstrip structure with a ferrite  disk. (a) For the 1 st radial-\nmode resonance frequency; (b) at non-resonance freq uencies.  \n \n \n \n \n \nFig. 18. Transformation of the MDM spectrum due to a dielectric loading in a microstrip \nstructure (numerical results). \n  22 \n \n \nFig. 19. Transformation of the MDM spectrum due to a dielectric loading in a microstrip \nstructure (experimental results). \n \n \n \n                             ( a)                                                                     (b) \n \nFig. 20. The helicity  parameter for the 1st radial mode at opposite directions of a normal bia s \nmagnetic field. A ferrite disk is placed in a micro strip structure without a loading dielectric. ( a) \nMagnetic bias is up; ( b) magnetic bias is down. \n \n \n  23 \n    \n             \n \n                                           ( a)                                                                       (b)   \n \n \nFig. 21. A chiral sample. ( a) Sample structure; ( b) the helicity  parameter distribution in a \ndielectric disk when magnetic bias is up. \n \n \n   \n \n \n \nFig. 22. Measuring of chirality with use of opposit e directions of a DC magnetic field (numerical \nresults). An insert shows the position of a chiral sample in a microstrip structure. \n \n "    },    {        "title": "2201.08249v2.A_Nanomechanical_Testing_Framework_Yielding_Front_Rear_Sided__High_Resolution__Microstructure_Correlated_SEM_DIC_Strain_Fields.pdf",        "content": "A Nanomechanical Testing Framework Yielding Front&Rear-sided,\nHigh-resolution, Microstructure-correlated SEM-DIC Strain Fields\nT. Vermeija, J.A.C. Verstijnena, T.J.J. Ramirez y Cantadora, B. Blaysatb, J. Neggersc, J.P.M.\nHoefnagels*a\naDept. of Mechanical Engineering, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands\nbUniversit\u0013 e Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, F-63000 Clermont-Ferrand, France\ncUniversit\u0013 e Paris-Saclay, ENS Paris-Saclay, CentraleSup\u0013 elec, CNRS, LMPS, 91190, Gif-sur-Yvette, France\nAbstract\nThe continuous development of new multiphase alloys with improved mechanical properties requires quan-\ntitative microstructure-resolved observation of the nanoscale deformation mechanisms at, e.g., multiphase\ninterfaces. This calls for a combinatory approach beyond advanced testing methods such as microscale\nstrain mapping on bulk material and micrometer sized deformation tests of single grains. We propose a\nnanomechanical testing framework that has been carefully designed to integrate several state-of-the-art test-\ning and characterization methods, including: (i) well-de\fned nano-tensile testing of carefully selected and\nisolated multiphase specimens, (ii) front&rear-sided SEM-EBSD microstructural characterization combined\nwith front&rear-sided in-situ SEM-DIC testing at very high resolution enabled by a recently developed InSn\nnano-DIC speckle pattern, (iii) optimized DIC strain mapping aided by application of SEM scanning artefact\ncorrection and DIC deconvolution for improved spatial resolution, (iv) a novel microstructure-to-strain align-\nment framework to deliver front&rear-sided, nanoscale, microstructure-resolved strain \felds, and (v) direct\ncomparison of microstructure, strain and SEM-BSE damage maps in the deformed con\fguration. Demon-\nstration on a micrometer-sized dual-phase steel specimen, containing an incompatible ferrite-martensite\ninterface, shows how the nanoscale deformation mechanisms can be unraveled. Discrete lath-boundary-\naligned martensite strain localizations transit over the interface into di\u000buse ferrite plasticity, revealed by the\nnanoscale front&rear-sided microstructure-to-strain alignment and optimization of DIC correlations. The\nproposed testing and alignment framework yields front&rear-sided aligned microstructure and strain \felds\nproviding 3D interpretation of the deformation and opening new opportunities for unprecedented validation\nof advanced multiphase simulations. DOI: https://doi.org/10.1007/s11340-022-00884-0\nKeywords: nano SEM-DIC, interface mechanics, nano tensile testing, microstructure strain alignment\nHighlights\n•Close integration of state-of-the-art nanomechanical testing, EBSD, and ultra-high resolution SEM-DIC\n•Extensive alignment framework of 8 independent data sets yields microstructure-correlated strain maps\n•Front&rear-sided EBSD of microspecimens yields approx. microstructure over full 3D specimen volume\n•Forward-deformed strains & microstructure mapped to post-mortem BSE damage maps, at both sides\n•Challenging test case: unraveling of nano-deformation mechanisms at martensite-ferrite phase boundary\n\u0003Corresponding author\nEmail address: j.p.m.hoefnagels@tue.nl (J.P.M. Hoefnagels*)\nPreprint submitted to Experimental Mechanics August 31, 2022arXiv:2201.08249v2  [physics.app-ph]  30 Aug 20221. Introduction\nIn materials science and engineering, the design and manufacturing of new materials and alloys is in-\ncreasingly important to adhere to the ever more demanding requirements for materials, such as increased\nstrength, ductility and toughness, for automotive and other industries. Many of these new materials, of-\nten metal alloys, have a multiphase microstructure in which, for instance, a hard phase is combined with\na soft phase to retrieve favourable global properties that re\rect a combination of the individual phases\n[1, 2, 3, 4, 5, 6]. The further development of these materials is limited by our understanding of the governing\ndeformation mechanisms at the micro- and nanoscale and the ability to cast this knowledge into numerical\nmodels for prediction of mechanical behaviour at the engineering scale. Such understanding can only be\nunlocked by means of detailed experimental analysis of the mechanics of these alloys. However, whereas\nalmost all studies so far have focused on the contribution of the individual phases to the alloy's mechanics,\nrecent works have shown that micro- and nanoscale deformation mechanisms at phase and grain boundaries\nmay govern the material behaviour, in cases of early failure by interface damage [4, 7, 8, 9] or increased\nductility by deformation transfer over the phase interfaces and grain boundaries [10, 11, 12]. Therefore,\nobservation and quanti\fcation of plasticity (and subsequent damage) at these interfaces, at high resolution\nand in-situ during deformation, is crucial. Such studies are obviously challenging, but are often further\ncomplicated when one of the phases (such as martensite or bainite) has a \fne and complex microstructure\nand a resulting complex (jagged) interface [9], thereby leading to nanoscale microstructural and mechanistic\nfeatures at the interfaces.\nThrough recent advances in experimental mechanics, ( in-situ ) mechanical characterization of polycrys-\ntalline and multiphase metals at small scales is increasingly more accessible. Particularly, the development\nof Digital Image Correlation (DIC) patterning methods for in-situ Scanning Electron Microscopy based\nDIC (SEM-DIC) has lead to the capability of observing plastic deformation mechanisms from micrometer\nto nanometer scales [13, 14, 15, 16, 17, 18]. In practice, SEM-DIC testing of these metals is commonly\nperformed on bulk samples that are (mechanically) polished, of which the microstructure is characterized\n(with, e.g., Electron Backscatter Di\u000braction (EBSD)), that are subsequently decorated with a DIC speckle\npattern, and are \fnally tested by means of in-situ SEM-DIC, resulting in plastic strain \felds over a cer-\ntain millimeter or micrometer sized area in the microstructure [10, 11, 15, 19, 20, 21, 22, 23, 24, 25, 26].\nSuch approaches have provided valuable insights into plasticity mechanisms in the microstructure, strain\npartitioning between phases [19, 20], how plasticity leads to damage [15, 23, 25], and on qualitative defor-\nmation patterns at multiphase interfaces [11, 24]. However, these experiments have severe limitations, as\ninformation on the subsurface 3D microstructure and on the true local stresses and boundary conditions\nare often unknown. Moreover, as said above, almost all studies focus on the deformation of the individual\nphases, whereas the quantitative interaction between the phases can strongly in\ruence the individual re-\nsponse of the phases, thus requiring more detailed investigations. Aspects that complicate such experiments\nare (i) the inherent complexity and small scale of the microstructure, especially when complex phases such\nas martensite and bainite are involved, leading to a highly complex, intangible combination of deformation\nmechanisms near and at the interfaces and (ii) the inherent nanoscale dimensions of these microstructures\nand their mechanisms (e.g. individual slip traces and substructure sliding [27]), requiring nanoscale spatial\nstrain resolution and high-resolution microstructure to strain alignments [25].\nIn contrast to these microscale SEM-DIC experiments on \"bulk\" materials, a di\u000berent class of small-scale\nmechanical testing techniques exists that is particularly suitable for single phases and single grains. Well-\nde\fned micro-pillar compression, micro- or nanotensile testing, and micro-bending experiments o\u000ber unique\ninsights into the stress-strain behaviour and slip system activity of individual phases, when performed on\nindividual grains or bi-crystals [28, 29, 30, 31, 32, 33]. Fabrication of microscopic specimens by Focused\nIon Beam milling (FIB), the use of dedicated nanometer and nano-force resolution testing rigs, and careful\npre-test alignment yields deformation tests with a well-known stress-strain state and crystallography, while\nallowing in-situ and/or post-mortem identi\fcation of individual slip systems or crack paths. However, mul-\ntiphase, or even polycrystalline, specimens are rarely studied with these methods, with some exceptions for\nlamellar metals [34, 35]. Moreover, singular multiphase interfaces have yet to be tested on these scales, to\nthe best of our knowledge. The main challenges in conducting these micro-testing techniques on polycrys-\n2talline and multiphase specimens, speci\fcally when the focus lies on interface mechanics, include (i) the\nselection and extraction of specimens that contain (only) the most interesting feature (e.g. an individual\ninterface) [36], (ii) measurement of the nanoscale deformation \felds, with high-resolution SEM-DIC, during\nthese micro-tests, which is currently only achieved by a small number of research groups [35, 37, 38] and\n(iii) attribution of deformations to microstructure features and subsequent identi\fcation of their character,\nwhich requires data collection of two (or more) sides of the specimen and careful data alignment.\nIn this work, we present a new nanomechanical testing framework that addresses all these challenges\nas this framework allows to combine, for the \frst time, such a large number of state-of-the-art micro-\nmechanical testing and microscopic characterization tools to enable highly detailed investigation of nanoscale\ndeformation mechanisms. These tools include (i) nano-tensile testing of \"1D\" (3 :5\u00032:5\u000310µm) specimens\n[32], isolated from the bulk microstructure at speci\fc regions of interest, (ii) multi-modal microstructure\nmeasurements at the front and rear of the micro-specimens, (iii) front&rear-sided SEM-DIC yielding very\nhigh-resolution strain maps by (iv) application of a recently proposed nanoscale DIC speckle patterning\ntechnique [16, 25], (v) SEM scanning artefact correction [39] and (vi) DIC deconvolution correction [40],\nwhile (vii) all of this front&rear-sided data is aligned using a novel data alignment framework. We will\ndemonstrate that the combination of all these measurement modalities will yield front&rear-sided nanoscale\nand microstructure-resolved strain \felds that push the limits of SEM-DIC. A particularly interesting type\nof specimen is investigated in which an incompatible (i.e. high crystallographically misoriented) ferrite-\nmartensite interface reveals a sharp transition from discrete (martensite) to di\u000buse (ferrite) plasticity. It\nwill be shown that the nanoscale spatial strain resolution and the alignment framework are crucial to\ndetermine how the (near-)interface behaviour evolves, while the correlated front&rear-sided microstructure\nand strain \felds allow interpretation in 3D of both microstructure and deformation. A parameter study\nthat includes the DIC subset size, DIC deconvolution and strain \feld calculation method reveals how both\ndiscrete (martensite) and di\u000buse (ferrite) plasticity can be identi\fed, which is crucial for complex multiphase\nspecimens. This specimen, and a second specimen produced in the same way, will be used to explain\nthe nanomechanical testing framework in Section 2. Finally, the aligned data allows assessment of the\ndeformation in the (ampli\fed) forward deformed con\fguration, which eases interpretation and analysis of\nthe micro-mechanics at and near the multiphase interfaces.\nIn Section 2, the details of the nanomechanical testing framework will be provided based on its 4 pillars:\n(I) specimen selection and fabrication, (II) characterization and nano-DIC patterning, (III) nanoscale testing\nand DIC, and (IV) data alignment. Subsequently, in Section 3, the capabilities of the framework will be\ndemonstrated on a nano-tensile specimen containing a single and clean martensite-ferrite interface. To this\nend, a commercial DP600 grade (0.092C-1.68Mn-0.24Si-0.57Cr wt.%) has been heat-treated (20 minutes\naustenization at 1000 °C, followed by a cool down to 770 °C in 50 minutes, 30 minutes inter-critical anneal at\n770°C, and water quenching to room temperature) to produce a coarse ferrite-martensite microstructure with\nmartensite volume fraction of 70 \u00065% that allows for selection and fabrication of nano-tensile specimens with\na single, continuous and straight ferrite-martensite interface that runs from the top surface to the bottom\nsurface. Finally, discussion and conclusions follow in Section 4.\n2. Nanomechanical Testing Framework\n2.1. Methodology Part I: Specimen Selection and Fabrication\nThe specimen fabrication and characterization methods are based on the work of Du et al. [32] and\nare optimized and automated further in this work. Figure 1a-d shows the di\u000berent steps of the sample\npreparation, specimen selection and specimen fabrication. A 12 \u00029\u00021 mm piece of material is mechanically\nground and electropolished to create a 4 °wedge with a deformation-free, high-quality surface at both sides\nof the micrometer-thin tip of the wedge (Figure 1a) [32].\nFigure 1b illustrates the three-sided SEM characterization of the wedge tip (here done using a Tescan\nMira 3) for identi\fcation of viable specimen locations on the 6 mm long section of the wedge tip, which\nis highlighted in Figure 1a by the red rectangle and in Figure 1b by the yellow dashed lines. Long phase\nboundaries, perpendicular to the wedge tip, are \frst identi\fed on the rear surface using channelling contrast\n3in SEM BackScattered Electron (BSE) images. Then, SEM Secondary Electron (SE) images of the tip are\nused to spatially align the front and rear microstructure, after which a viable specimen location can be\ndetermined, see the red rectangle in Figure 1b.\nThe FIB milling procedure (done here with a FEI Nova Nano FIB-SEM Dual Beam) for specimens\nfabrication on the wedge tip is schematically shown in Figure 1c, where we employ the same FIB milling\nprocedure as Du et al. [32], with an added \fnal parallel FIB polishing step for improved EBSD quality.\nInitially, a wider nano-tensile specimen is fabricated, centered around the identi\fed location. The reason\nfor this is that during the FIB thinning on the front side of the wedge tip to create a parallel front and rear\nsurface, the material removal causes the frontside to change for a \"non-columnar microstructure\", which\nprevents precise identi\fcation of the \fnal specimen location before FIB thinning. This problem is addressed\nby leaving a wider (parallel) specimen after the frontside thinning, from which the \fnal, narrower specimen\nlocation is selected using BSE (and if necessary EBSD) imaging. For an optimal con\fguration of the ferrite-\nmartensite boundary/interface, since the martensite is stronger than the ferrite, it is crucial to obtain the\nphase boundary along the full length of the specimen, in order to obtain \"parallel\" loading of both the ferrite\nand martensite phase, and to prevent early necking over a full ferrite cross-section [41]. The specimen is\n\fnished with a \fne parallel FIB milling step. A \fnished specimen (Figure 1d) typically has a gauge section\nof 10\u00023:5\u00022:5µm (Length\u0002Width\u0002Thickness ), however dimensions may vary in order to obtain the\ndesired microstructure.\n2.2. Methodology Part II: Characterization and Nano-DIC Patterning\nSEM characterization is performed on the front and rear surfaces (colored blue and red respectively, in\nFigure 1) of the \fnished nano-tensile specimen. After FIB thinning, the microstructures on both sides of the\nspecimen are more similar, but never 100% the same. Therefore, microstructure information from both sides\nof the specimen is needed to estimate the full 3D microstructure for interpretation of the through-thickness\nplastic behavior and for potential comparisons to 3D simulations.\nFigure 1e) shows BSE images which are used to determine the arrangement of phases in the microstruc-\nture and the morphology of the F/M interface, requiring optimization of SEM parameters for electron\nchanneling contrast imaging [9]. While electropolishing induces a surface roughness that results in BSE\nedge e\u000bects and decreases the channeling contrast quality, especially at the phase boundaries, FIB milling\non the front surface removes this topography and thereby allows more accurate identi\fcation of the location\nof the interface. However, since BSE electrons originate from a larger interaction volume, deeper inside\nthe material, these images are ill-suited for identi\fcation of topography and of the exact location of the\ngauge edges and corners. Such information is required for (i) determination of the specimen geometry for\ncalculation of global stress levels during the experiment and (ii) for several alignment steps in Section 2.4.\nTherefore, SE images (Figure 1e) are captured, during the same scan as BSE, for assured data alignment,\nwith optimized contrast and brightness settings for localization of the gauge edges and corners. Additionally,\nthe specimen thickness is measured on SE images taken from the side and under an angle (not shown here).\nSE and BSE images acquired directly after FIB milling will, in the rest of this work, be referred to as the\nMicrostructure dataset.\n4Figure 1: General overview of the sample preparation and characterization. (a) Wedge production process, detailing\nmechanical grinding and electropolishing for a deformation free, high quality, wedge tip. (b) Secondary Electron (SE)\nand BackScattered Electron (BSE) SEM images, used to identify possible specimen locations. The yellow dashed line\nindicates the wedge edge and the red areas indicates a viable specimen position. Viewing directions are indicated\non the \fnished wedge in (a). (c) Schematic overview of Focused Ion Beam (FIB) milling steps used for specimen\nfabrication. From left to right: rough contouring, rough thinning, \fne contouring, \fne thinning [32]. (d) A schematic\nof a \fnished specimen and its general dimensions. (blue = front, red = rear). (e) front&rear-sided microstructure and\nEBSD crystallographic orientations (normal direction inverse pole \fgure) of a \fnished specimen, with insets showing\nthe quality increase owing to Spherical Indexing with EMSphInx [42] compared to standard indexing. All rear maps\nare \ripped over the horizontal axis to allow easy comparison to the front. The reference image shows an overlay of\nin-beam SE (IB-SE) and BSE images after the DIC pattern is applied. (f) Experimental data with proper alignment\n(yellow) and without proper alignment (red, only rigid body movement). The green circles in the zoom annotate the\nsame triple junction of the EBSD data.\n5EBSD measurements are performed (with an Edax Digiview 2 camera) on both front and rear sides of the\nspecimen, with the raw EBSD patterns saved for subsequent o\u000fine indexing. The spherical cross-correlation\nindexing algorithm \"EMSphInx\" [42] is employed for robust indexing of noisy (martensite) EBSPs, improv-\ning indexing of martensite and F/M interfaces considerably, as compared to traditional Hough transform\nbased indexing. The Normal Direction Inverse Pole Figure (ND IPF) of specimen S1 is shown in Figure 1e,\nwith insets highlighting the di\u000berence in quality between Hough indexing and Spherical indexing. This\nimprovement of EBSD quality will turn out to be crucial for the alignment steps based on microstructural\nfeatures. As will be demonstrated in future work, the resulting EBSD map of the crystallographic orien-\ntations can be used for quanti\fcation of slip systems, orientation relationships and plastic compatibility\n[43, 44, 45]. Furthermore, Con\fdence Index (CI) and Image Quality (IQ) are EBSD quality metrics that\ncan be used for identi\fcation of lath boundaries and phases, as lath martensite has signi\fcantly higher\ndislocation densities than ferrite, thereby producing lower quality EBSD patterns [46]. In this work, the\ncrystallographic orientation, CI and IQ maps will be referred to as the EBSD dataset.\nSubsequently, to enable strain measurements at the nanoscale, a scaleable and dense nano-DIC speckle\npattern was applied using a recently developed novel patterning method, involving a single-step sputter\ndeposition of a low temperature solder alloy that forms nanoscale islands during deposition [16, 25]. The\nsolder alloy In52Sn48 was sputtered at 18 mA, 1 E\u00002 mbar, 25 °C, 120 s, at\u001880 mm from the sputter\ntarget, resulting in a dense, random, high-quality pattern with features of \u001820\u000050 nm in size as shown\nin Figure 2a. The patterning parameters deviate slightly from (c) in Table 1 of Hoefnagels et al. [16], in\norder to acquire a slightly \fner nano-DIC pattern (20 \u000050 nm vs 20\u0000100 nm), which also reduce the\nInSn thickness for improved BSE imaging. For the \frst time in literature, this nano-DIC pattern is applied\nto both the front and rear of the nano-tensile specimen surfaces, in separate patterning steps, allowing\nfor front&rear-sided SEM-DIC, albeit that for the rear side SEM-DIC can only be applied on the images\ncaptured before and after the test (not in-situ ).\nAfter nano-DIC patterning, the specimens are again subjected to SEM characterization with high accel-\neration voltage (20 keV) for correlation of the DIC pattern with the exact underlying microstructure. The\nhigh acceleration voltage creates an interaction volume which penetrates through the nanometer thickness\nDIC speckle pattern, allowing for in-beam BSE (IB-BSE) and regular BSE imaging of the underlying mi-\ncrostructure [25]. Despite the large interaction volume, in-beam SE (IB-SE) and regular SE images still\nprovide representative images of the nano-DIC speckle pattern as these signals mainly originate from the\ntop surface. The high voltage (IB-)SE and (IB-)BSE images, acquired after application of the DIC speckle\npattern, will, for the rest of this work, be referred to as the Reference dataset. This dataset is used as\nthe baseline onto which all other data will be warped and aligned, as it can be easily correlated to all other\ndatasets. An overlay of IB-SE and BSE data is provided in the bottom row of Figure 1e, illustrating the\ncorrelation between speckle pattern and underlying microstructure.\n2.3. Methodology Part III: Nanoscale Testing and DIC\nForin-situ mechanical loading of the microscopic specimens, many types of testing setups can be used,\nsuch as an in-situ nano-indentation stage for micro-compression or micro-bending tests (e.g. using a Hysitron\nPicoindenter). Requirements for the stage include: (i) the capability for in-situ SEM at low acceleration\nvoltages, and (ii) the ability to mount the wedge, and to load the specimens that are fabricated on the tip, to\nenable precise (axial) loading under one-sided in-situ SEM observation. Additionally, the rear (opposite the\nin-situ measured) surface nano-DIC pattern requires measurement ex-situ , i.e. before and after performing\nthein-situ test.\nIn this work, the nano-tensile testing procedure of Refs. [32, 47] has been extended to in-situ SEM-DIC\nby integrating the Nano-Tensile Stage (NTS) into the SEM (in this case a Tescan Mira 3). In addition,\na procedure for sequential in-situ SEM-DIC testing of multiple nano-tensile specimens (located on the\nsame wedge), without recurring optical alignment, was developed. All nano-tensile specimens on a single\nwedge are produced parallel to the rear surface, however, as the wedge tip may not be perfectly straight\nand specimens on the wedge may be produced during multiple FIB sessions, small relative misorientations\nmay be present between the specimens, which must be known to allow sequential in-situ SEM-DIC testing\nof multiple specimens without breaking vacuum. Therefore, before the wedge is mounted in the NTS for\n6mechanical testing, optical pro\flometry and SEM imaging are employed to measure, respectively, the relative\ntilt and relative in-plane misorientation of all specimens. The wedge is then mounted in the NTS and a\nsingle specimen is aligned, along the two rotational axes that are perpendicular to the loading axis, using\noptical microscopy and optical pro\flometry, following the procedure of Bergers et al. [47] and Du et al. [32],\nyielding near perfect uniaxial tension alignment, resulting in less than 0.5% bending stress at the start of\nthe test. After a tensile test has been \fnished, the next specimen can be aligned inside the SEM with similar\naccuracy based on the previously measured relative misorientation with respect to the previous specimen.\nAll specimens can be tested individually without a\u000becting the others, since they are su\u000eciently separated\non the wedge tip.\nIn-situ SEM-DIC uniaxial nano-tensile experiments (Figure 2a) are performed on the aligned specimens.\nAt pre-determined global stress levels, the loading is paused for IB-SE and SE imaging of the front surface\nwith a low acceleration voltage (5 kV) at a low working distance (3 :5 mm), limiting the interaction volume\nas much as possible for optimal contrast and spatial resolution of the nano-DIC pattern (inset of Figure 2a).\nNote that this low working distance, which was chosen after careful optimization of the nano-DIC pattern\nimaging resolution and quality, is not a hard requirement for the method. Two images with orthogonal\nscanning directions (by applying 90\u000escan rotation for the second scan) are acquired at each stress level and\nare \"combined\", using a recently developed tool to correct for SEM scanning artefacts, i.e. the so-called\n\"Scan Corr\" GUI developed by Neggers et al. [39, 48]. This correction algorithm assigns translation\ndegrees of freedom to each scan line of the two orthogonal scans in order to \fnd the best match between\nthe scans in a dedicated DIC framework, whereafter these two adjusted images are combined into a single\ncorrected image. This is based on the assumption that the fast scanning direction, i.e. the scan lines, in\nSEM images contain considerably fewer artefacts than the slow scanning direction, wherein drift and line\njumps are prone to distort the SEM image [49, 50]. Figure 2b shows a deformation-free strain \feld without\nand with SEM artefact correction applied, supplemented by a schematic overview of the correction method.\nThe strain \feld after correction shows a decrease in the overall noise level and, more importantly, fewer\nsystematic line artefacts, which could be mistaken as e.g. slip activity. These line artefacts were likely\nintroduced by line jumps and minor vibrations during testing. Further details and examples of the SEM\nartefact correction method are described by Neggers et. al. in Ref. [39]. An overview of the di\u000berent SEM\nand EBSD imaging parameters are provided in Table 1.\nDuring the in-situ test, we aim to acquire images at several increments with increasing plastic defor-\nmation, without fracture of the specimen, as imaging of the deformed rear surface is only possible af-\nter un-mounting the wedge from the tensile stage, here called the Post-mortem dataset. By avoiding\nfracture, SEM-DIC can be performed on the full rear surface (for the last deformation step), providing\nvaluable information regarding the presence or absence of continuity of plasticity through the thickness.\nLocal DIC is employed to correlate the artefact-corrected SEM-DIC images to retrieve the displacement\n\feld ~ u. For noise reduction, a gaussian \flter with a standard deviation of 3 datapoints is applied to\nthe displacement data. Thereafter, the displacement gradient tensor ~r0~ uis calculated by taking the di-\nrect (nearest-neighbours) spatial gradient of ~ uand is used to compute the Green-Lagrange strain tensor:\nE=1\n2[(~r0~ u)T+~r0~ u+(~r0~ u)T\u0001~r0~ u]. To simplify the analysis and the plotting of local strains, we employ the\n2D equivalent von Mises strain measure, which has been shown to be a reliable indicator for local plasticity\n[20, 25]: Eeq=p\n2\n3q\n(Exx\u0000Eyy)2+E2xx+E2yy+ 6E2xy. The DIC reference image and displacement/strain\n\felds as described here, are, for the rest of this section, referred to as the SEM-DIC dataset. In this section\nall artefact-corrected SEM-DIC images have been correlated using the commercial DIC package \"MatchID\",\nusing a pixel size of 7 nm, subset size of 29 pixels and a step size of 1 pixel (see also Table 2). In the case\nstudy in Section 3, we will study the in\ruence of a di\u000berent subset size and a di\u000berent strain calculation\nmethod, employing a home-built DIC code that can be executed with and without applying so-called \"de-\nconvolution\" [40], to demonstrate (i) the high spatial resolution of the strain \feld that can be achieved and\n(ii) the capability to identify both di\u000buse and discrete slip through di\u000berent DIC strategies.\nFigure 2c shows an example of the resulting SEM-DIC displacement (U and V) and equivalent strain\n\felds ( Eeq) of specimen S1 for the second-to-last increment, n\u00001, where this specimen has not fractured yet.\nSeveral slip bands can be discerned in both displacement and strain \felds. Since S1 did fracture, specimen\n7S2 is used to illustrate the rear displacement and strain \felds in Figure 2d. In the case study of S2 in\nSection 3, we will showcase how the front and rear strain \felds can be interpreted for a full 3D view of the\ndeformation mechanisms. It is clear from the strain \felds in Figure 2c-d that we need a proper alignment\nfrom the Microstructure ,EBSD andSEM-DIC data sets to the Reference , to be able to relate the\nmicrostructure-resolved strain \felds to the (complex) nanoscale deformation mechanisms.\nFigure 2: SEM-DIC nano-tensile testing. (a) Example of a specimen with an inset showing the nanoscale DIC pattern.\nThe blue squares in the left image represent the gripper \"arms\" with speci\fed loading direction that is precisely aligned\nto the specimen axis resulting in clean uniaxial tension [32, 47]. (b) Deformation-free equivalent strain \felds without\nand with scanning artefact correction applied [39], with a schematic drawing of the correction to illustrate the concept\nof the correction method. (c) Front side SEM-DIC displacement and equivalent strain \felds for increment n\u00001, i.e.\nsecond-to-last increment, of specimen S1 and (d) rear side SEM-DIC displacement and equivalent strain \felds for the\n\fnal (unloaded and post-mortem) increment nof specimen S2.\n8Table 1: SEM parameters used during acquisition of the Microstructure ,EBSD ,Reference ,SEM-DIC andPost-\nmortem data sets (HV = high voltage, i.e. the SEM acceleration voltage, BI = beam intensity (a Tescan beam current\nmeasure), WD = working distance, FOV = \feld of view, BW = bandwidth for spherical indexing using EMSphInx\n[42]). All data is captured with a Tescan Mira 3; when SEMs from other manufactures would be used, these settings\nmay have to be adjusted slightly.\nData set: Microstructure EBSD Reference SEM-DIC Post-Mortem Unit\nDetector BSE EBSD (IB-)SE+BSE IB-SE+SE BSE -\nSEM Mode Depth Depth Depth Resolution Depth -\nHV 20 20 20 5 20 kV\nBI 18 18 16 7 16 -\nWD 10.5 20 8.8 3.5 8.8 mm\nTilt 0 70 0 0 0 °\nDwell time 32 8000 32 8 32 µs/pix\nFOV 15 - 21.5 21.5 21.5 µm\nResolution 2048 \u00022048 - 3072 \u00023072 3072\u00023072 3072\u00023072 pix\u0002pix\nBinning - 8 \u00028 - - - pix \u0002pix\npixel size 7.3 30 7 7 7 nm\nBW (EMSphInx) - 88 - - - -\nTable 2: Local DIC (MatchID) correlation parameters used in Section 2\nParameter Value Unit\nSoftware MatchID\nImage \fltering Gaussian; std 0.67 pix\nSubset size 29 pix\nStep size 1 pix\nMatching criterion ZNSSD\nInterpolant Bicubic Spline\nStrain window 3x3\nVirtual Strain gauge size [51] 41 pix\nSubset Shape function A\u000ene\n2.4. Methodology Part IV: Alignment of All Front and Rear Data\nThrough the ( in-situ ) experiments, several datasets are acquired, yet a precise relation between the\ncoordinate systems is missing. In general, errors between two SEM datasets are only induced by rigid body\nmotion (RBM), i.e. translation and (minor) rotation, whereas the EBSD dataset is often severely warped\nand has inaccuracies of the absolute crystal orientations [52]. Indeed, when the EBSD dataset is aligned to\ntheMicrostructure dataset using translations only, it is observed that the EBSD grain boundaries will\nnever precisely correspond to the microstructure, as shown in Figure 1f with the red boundaries.\nA novel data alignment framework is introduced, which is schematically shown in Figure 3, that will\nreduce the misalignments between the datasets tremendously by not only correcting for translations and\nrotations, but also image warping, while simultaneously retrieving the correct absolute crystal orientations.\n9Before the alignment framework with its di\u000berent modules is explained, the improvements in alignment when\nusing the framework is demonstrated for specimen S1 can be observed in Figure 1f (by comparing the red\nboundaries to the yellow ones). For emphasis, a single, arbitrary, triple junction is highlighted (Figure 1f,\ngreen circle) for both red and yellow boundaries, showing a decrease in misalignment of several hundreds\nof nanometers. For this specimen, the alignment framework made it possible to reduce the misalignment\nbetween the EBSD dataset and Reference dataset to 50 nm on average (close to the spatial resolution of\nEBSD), the Microstructure dataset and Reference dataset to below 50 nm, and the SEM-DIC datasets\nand the Reference dataset to as little as 15 nm. The framework also reduces the inaccuracies of the crystal\norientations through an EBSD orientation correction step.\nThe data alignment framework is developed with Matlab using the MTex toolbox [53, 54] and is optimized\nforin-situ SEM-DIC nano-tensile experiments of specimens with a heterogeneous microstructure. Three\nself-contained modules are employed for alignment and correction (Figure 3): EBSD orientation correction ,\npoints-based alignment (PBA) and edge-based alignment (EBA). This modular design allows for application\nto the front and rear datasets, providing \rexibility in alignment strategy, also for other types of experiments\n(e.g. single-sided SEM-DIC tests, e.g. on bulk material). In the upcoming description, the di\u000berent\nalignment steps will be demonstrated for the more challenging front surface (of specimen S1), as FIB milling\nreduces the topographical contrast on this side of the specimen, complicating the alignment compared\nto the rear surface. Another important note is that successful alignment of the front surface is more\nvaluable than alignment of the rear, as strain evolution can only be measured on the front surface during\nin-situ SEM-DIC nano-tensile experiments. Finally, as illustrated on the bottom of Figure 3, we also\nperform a points-based alignment in the (\fnal) deformed con\fguration, between the DIC-based forward-\ndeformed Reference and the post-mortem BSE images (taken at high eV to penetrate through the nano-\nDIC pattern). The Matlab code of the full alignment framework will be available on GitHub ( https:\n//github.com/Tijmenvermeij/NanoMech_Alignment_Matlab ).\n2.4.1. EBSD Orientation Correction\nIn these experiments, the front&rear-sided EBSD measurements allow us to assess the EBSD orientation\naccuracy by comparing the orientation of through thickness ferrite grains on front and rear sides. Figure 4a\nshows the uncorrected EBSD maps of the front and rear surface (\ripped over the vertical to allow easy\ncomparison to the front), wherein the cyan and yellow ferrite grains appear to di\u000ber in their IPF color (e.g.,\nas indicated by the white crosses). Indeed, the initial crystallographic misorientation between the front\nand rear EBSD dataset is measured to be, in so-called \"axis-angle\" representation [55], 4 :1o(\u00000:88~ ex\u0000\n0:08~ ey+ 0:48~ ez). For other specimens, similar initial misalignments have been observed. Several sources\nof this misalignment can be identi\fed, including the wedge and specimen production process (e.g. wedge\ncurvature) as well as alignment errors (of, e.g., the wedge orientation and EBSD detector alignment) [32, 52].\nIn this case, the rotation axis has large ~ exand~ ezcomponents, indicating that most of the misalignment\narises, respectively, from tilt and in-plane rotation. While the magnitude of absolute misorientation is mostly\nnot being discussed in literature, it is clearly important to correct these to enable accurate identi\fcation\nof deformation mechanisms and slip activity. The EBSD orientation correction module of the alignment\nframework employs 3 steps to reduce the error of the absolute crystallographic orientations: (a,b) for each\nside of the specimen separately, alignment of (a) tilt and (b) in-plane rotation to the tensile direction, by\nmeans of, respectively, points-based and edge-based alignment of the tilted SE scan at 70 °to the \rat SE\nscan at 0 °, as shown in Figure 4b, and (c) to determine the real crystallographic orientation, which is de\fned\nas the \"averaged\" orientation between the front and rear EBSD data. The mismatch in tilt and rotation\nare measured on SE images as these show sharp edges and corners, allowing for detection of corners (points)\nand edges, and have relatively low drift-induced artefacts, as compared to the EBSD data, as acquisition\ntimes are much lower.\n10Figure 3: Schematic representation of all experimental datasets and alignment steps (EBSD = Electron backscatter\ndi\u000braction, MSF=R = Microstructure (front/rear), REF = Reference, DIC = SEM-DIC, PM = Post-Mortem, EBSD\norientation correction, PBA = Points-based alignment, EBA = edge-based alignment). Most datasets include a zoom\n(green border) of the same 1\u00031µm area. Red borders indicate data manipulation without performing any spatial\nalignment resulting in altered data on the same grid. The alignment of the rear data is performed using the same\nsteps (indicated by (1) to (4)) as shown in this \fgure for the frontside. The bottom-right of the \fgure also shows\nalignment in the deformed con\fguration, where a PM image is aligned to the forward-deformed REF con\fguration,\nwhich in turn is obtained by applying the DIC displacement \feld to each pixel (purple arrows).\nFor the \"tilt correction\" (a), the change in gauge length is determined between \rat and tilted con\fgu-\nration, for the left and right gauge edges, by selecting the gauge's vertices, indicated with the red and blue\nmarkers in Figure 4b. For specimen S1, the \"true tilt\" of the front and rear EBSD data was measured to\nbe 66 :7o(~ ex) and 72 :4o(~ ex) respectively, resulting in tilt corrections of 3 :3o(~ ex) and\u00002:4o(~ ex) respectively.\nNext, the in-plane rotation mismatch (b) is found by measuring the misalignment of the specimen gauge\nedges, between tilted and \rat SE scans. Canny edge detection and subsequent \ftting of a line over the\ngauge edges (red dotted line in Figure 4b) results in an average in-plane misalignment, which was 0 :95o(~ ez)\nand\u00001:43o(~ ez) for the front and rear of S1 respectively. Now, the front and rear EBSD data are corrected\nfor these misalignments, using the tools available in MTex.\nWith the orientation errors in both front and rear EBSD data sets minimized separately, a \fnal \"com-\nbined\" correction (c) of front and rear is performed. Here, the assumption is made that a single through-\nthickness ferrite grain has the same crystallographic orientation on both sides of the specimen. In practice,\nnot all grains (e.g. in martensite) are identi\fable through the thickness, making it impossible to perform\nthis correction on all grains individually. Instead, the complete front and rear EBSD datasets are corrected\nbased on the misorientation of a single large, through-thickness grain (indicated with the white cross in\nFigure 4a) between front and rear. The required correction for specimen S1 is 2 :1o(0:15~ ex+ 0:97~ ey\u00000:20~ ez)\nand is performed by applying the rotation from original towards averaged grain orientation, for front and\nrearEBSD data on the complete maps. This leads to an upper limit of the uncertainty (i.e. mismatch)\non the crystallographic orientation of \u00061:05o, which is well below the generally accepted absolute EBSD\naccuracy of\u00062o[52]. The corrected ND IPFs of front and rear EBSD are shown in Figure 4c, thresholded\natCI > 0:2.\n11Figure 4: Overview of the EBSD orientation correction: (a) normal direction (ND) inverse pole \fgure (IPF) maps\nof the specimen, before correction, of the front and rear side. The white crosses indicates the same through-thickness\ngrain, which has slightly di\u000berent IPF colors on the front and rear side, (b) tilt and in-plane misalignment correction,\nby assessment of the length and gauge edge direction of the specimen, in tilted (left) and \rat (right) con\fguration,\nwith the markers showing homologous points and the red dotted lines showing the results of edge detection and \ftting.\n(c) Front and rear ND IPF after all EBSD correction steps; note the same IPF colors of the front and rear ferrite\ngrain, for both ferrite grains.\n2.4.2. Alignment of the EBSD toMicrostructure Datasets\nFor all specimens in this work, direct alignment of the EBSD dataset to the Reference dataset is\ninhibited by the poor channeling contrast of small micro-structural features in the Reference (IB-)BSE\nimages, which is caused by the InSn DIC speckle pattern obscuring the BSE signal and by the \rat topography\nafter FIB milling. Therefore, the EBSD data will \frst be warped, aligned and put on the same grid as the\nMicrostructure data, which has better channelling contrast, using the points-based alignment module of\nthe alignment framework (step (2) in Figure 3). Afterwards, The Microstructure (with EBSD ) data will\nbe aligned to the Reference data during step (3) \"MS to REF\", see Figure 3.\nSeveral distinct points can be identi\fed in the EBSD ND IPF with CI overlay and Microstructure\nSE/BSE overlay in Figure 5a, in which pairs of homologous selection points, i.e. features on the specimen\nthat can be identi\fed in both datasets, are connected with dashed red lines. The connection lines are\nnot parallel, nor of equal length, indicating that the EBSD data is severely warped with respect to the\nMicrostructure data.\nFor all pairs of selection points the misalignments are calculated ( ~U=~ xREF\u0000~ xEBSD ) and used to\n\ft a polynomial displacement \feld needed to align the EBSD data to the Microstructure data. The\npolynomial order, individually determined for each alignment step, should be chosen as low as possible, as\nunnecessary high polynomial orders may introduce large errors [56]. Alignment and warping of the EBSD\ndata to the Microstructure data is performed using the polynomial displacement \felds:\n8\n>>>>>><\n>>>>>>:Ux=nX\nk=0akxiyj;\nUy=nX\nk=0bkxiyj;\ni+j\u0014k;(1)\nwith nconstituting the polynomial order. For a total of N degrees of freedom (DOFs), e.g. N= 6 in\nthe case of a \frst order polynomial,N\n2selection points are required, at a minimum, to (uniquely) describe\n12the polynomial displacement \felds, as each selection point yields both an x and y coordinate. The use of\nmore selection points is recommended, as it results in least-squares \ftting of the polynomial \feld, thereby\nminimizing errors that result from erroneous selection points. For specimen S1, 11 selection points could\nbe identi\fed and were used for \ftting of a \frst order (a\u000ene) polynomial. Thereafter, the EBSD data is\naligned, warped, linearly interpolated to the same grid as that of the Microstructure data.\nThe results of this alignment step are displayed in Figure 5b, where an SE/BSE overlay of Microstruc-\nture with aligned EBSD grain boundaries is shown. Overall, the a\u000ene displacement \felds provide good\nalignment of the EBSD data to the Microstructure data. Alignment accuracy is measured at several\ndistinct points, not used in the \ftting routine, resulting in a misalignment below 100 nm (not shown).\nDespite the large (non-linear) warping in the EBSD data, alignment to the Microstructure data\nusing a\u000ene (\frst order) displacement \felds was found to yield the best (global) alignment results for these\nspecimens. Several tests were performed using higher order polynomials, which resulted in a marginal (and\nvery localized) error reduction around the selection points, with larger mis\fts between the EBSD grain and\nMicrostructure BSE boundaries away from the selection points, see the zoom \fgures in Figure 5b. Based\non these test results with few available homologous markers, the \frst order polynomial order works best,\nhowever, if many more homologous markers are available in the EBSD map, then second order warping\nmay further improve the results.\nFigure 5: Alignment of EBSD toMicrostructure data sets, demonstrated for specimen S1. (a) shows the EBSD ND\nIPF with 50% transparent CI overlay and the SE/BSE overlay data from the Microstructure dataset, with selected\nhomologous points in both datasets. The dashed red lines connect corresponding selection points. (b) Microstructure\nBSE/SE overlay with aligned (and warped) EBSD grain boundaries plotted as overlay. A small area with a clear\nF/M interface (manually drawn over the BSE image with an orange dashed line) shows the alignment results (aligned\ngrain boundaries in black lines) for 1st, 2nd and 3rd order polynomial displacement \felds, using the same set of\nhomologous selection points.\n2.4.3. Alignment of the Microstructure andSEM-DIC toReference Datasets\nBoth the Microstructure andSEM-DIC data sets are aligned, warped and interpolated to the grid of\ntheReference dataset using the points-based alignment module. Figure 6a shows 8 connected homologous\npoints (a combination of geometrical features, microstructural features and gauge topography) between an\nBSE/SE overlay of the Microstructure data and a BSE/IB-SE overlay of the Reference data. Addition-\nally, individual InSn DIC speckles are employed as (10) homologous points between SEM-DIC (IB-SE)\nand IB-SE Reference data, as demonstrated in Figure 6b. It can be observed that the displacement \felds\nare described (almost purely) by RBM, as connection lines are closely parallel and of equal length for both\ncombinations. An a\u000ene displacement \feld is therefore used for both alignments, as it is capable of correcting\nfor RBM (including small rotations) and may also correct for any minor warping which might be present\ndue to, for example, sample drift.\nThe results of the SEM-DIC toReference alignment step can be seen in Figure 6c, showing an\noverlay of the EBSD grain boundaries over the SEM-DIC equivalent strain data. Note that the EBSD\ngrain boundaries are aligned to the Reference dataset using indirect alignment via Microstructure ,\n13therefore, the misalignment of EBSD grain boundaries to the Microstructure data is superimposed on\nthe misalignment of the current step.\nForSEM-DIC toReference alignment, many more DIC speckles are available that could be used to\nenhance the alignment accuracy, which is estimated to be half a speckle or 15 nm. Alternatively, alignment\ncould be performed through global DIC, since both datasets show the same speckle pattern, although at\ndi\u000berent brightness and contrast. Such an approach could result in sub-pixel ( <7 nm) alignment accuracy.\nFigure 6: Alignment of Microstructure andSEM-DIC data sets to Reference data set, demonstrated for specimen\nS1. (a) Connected homologous points between Microstructure BSE/SE overlay and Reference IB-SE/BSE overlay\ndata and (b) connected selection points between SEM-DIC IB-SE and Reference IB-SE, with insets illustrating how\nindividual points are selected. (c) SEM-DIC toReference alignment results, shown by plotting of the equivalent\nstrain \feld with EBSD grain boundary overlay.\n2.4.4. Alignment of Rear to Front\nAfter all front and rear data sets are aligned in the, respective, front or rear Reference dataset con\fg-\nuration, the rear Reference data must be aligned to the front Reference data. Despite careful specimen\nselection and production, through-thickness changes in the microstructure will always be present, preventing\ncorrelation of the front and rear Reference datasets based solely on micro-structural features. Therefore,\nalignment is performed using the edge-based alignment module. For nano-tensile specimens, edge-based\nalignment relies on the edges of the T shaped specimen, which are visible on both sides of the specimen,\nto determine a theoretically identical alignment point (Figure 7a). These edges are considered to be at the\nsame in-plane position, as they were created in the same FIB milling step.\nCanny edge detection is employed to create a (binary) edge image from the Reference SE image, which\nis used to identify the gauge edges (solid green lines) and the gripper contact surfaces (solid red lines) for the\nfront and rear (Figure 7b). The gauge edges and contact surfaces are averaged to determine the gauge center\n(dashed green lines) and average contact surface (dashed red lines), respectively. The theoretically identical\nalignment point, i.e. the intersection of the gauge center and gripper contact surface, is identi\fed in both\ndatasets (white marker) and is used to determine the translational misalignment between the front and rear\nReference datasets. Rotational misalignment is determined using the relative angle between the two gauge\ncenter lines. The RBM displacement \feld necessary for alignment of the rear Reference dataset to the\nfront Reference dataset is constructed by superimposing the translational and rotational misalignments.\nThe rear Reference dataset, with all other rear datasets included, is aligned with the front Reference\n14dataset by applying the RBM displacement \felds resulting in the alignment shown in Figure 7d.\nFigure 7: Alignment of rear to front Reference datasets, illustrated for specimen S1. (a) Schematic representation of\nedge-based alignment. The solid green lines indicate the two sides of the gauge section and are used to determine the\ngauge center line (dashed green line). The solid red lines indicate the gripper contact surface, from which the average\ncontact surface (dashed red line) is derived. (b) SE images of the Reference dataset of both front and rear. The\ntheoretically identical alignment point is indicated with the white marker. (c) Grain boundaries of front (black) and\nrear (red) data sets in one graph, visualizating the original misalignment between the datasets. (d) After alignment,\nzoom of the gauge with front (black) and rear (red) EBSD grain boundaries and the respective gauge edges (dashed\nlines), extracted from the Reference SE binary edge image.\n2.4.5. Alignment of Post-Mortem BSE to forward-deformed Reference\nUp to this point, all data used in the alignment framework was considered to be in the undeformed\ncon\fguration, such that only translation, rotation or (minor) warping were required for alignment. However,\nPost-Mortem images, or in-situ images besides those used for DIC, may also require alignment to the\nmicrostructure and strain \felds, e.g., to investigate the evolution of microstructure-resolved strain \felds\ninto cracks and/or damage [25]. Therefore, as illustrated schematically in Figure 3 (bottom-right), the\nReference dataset is \frst forward transformed to the deformed-con\fguration, updating its position \feld by\nadding the (aligned) DIC displacement \feld values to the position vector values (purple arrows in Figure 3).\nThereafter, the Post-Mortem image is aligned to this Forward-Deformed Reference using point-based\nalignment, such that all data can be plotted in the deformed con\fguration.\n3. Case Study: Incompatible Martensite-Ferrite Interface\nThe capabilities and results of the full nanomechanical testing framework will be demonstrated here on\nspecimen S2, which contains a single ferrite-martensite interface with high crystallographic misorientation\nalong the full gauge-length. A full overview of all aligned data of specimen S2, in deformed and ampli\fed-\ndeformed con\fguration, will illustrate how the specimen deforms and how the plasticity occurs in the\nmicrostructure on two sides of the specimen. Subsequently, we employ a custom DIC code with varying DIC\nsubset sizes, with and without \"deconvolution\" (explained below), on two smaller areas, employing di\u000berent\nstrain calculation methods to highlight the highest achievable spatial strain resolution and to identify both\ndi\u000buse ferrite plasticity and discrete martensite plasticity. Finally, we utilize the aligned front&rear-sided\nstrain and microstructure data \felds to interpret the 3D and through-thickness deformation behaviour.\n153.1. Overall Microstructure and Deformation\nAll the steps of the framework, as described in Section 2, are applied to specimen S2 and result in the\naligned data sets as shown in Figure 8, in which all plotting (except for the SE image in (a)) is done in\nthe deformed con\fguration, which is hardly visible by eye due to the small global strain of \u00180:02. Figures\n8b,c show the aligned EBSD phase map (martensite-ferrite identi\fed by thresholding of the EmSphInx\nCon\fdence Index (CI)) and ND IPF map respectively, with an overlay of phase, grain and lath boundaries,\nas described in the legend. The specimen predominantly consists of a single through-thickness ferrite grain\non the top side, with several martensite variants on the bottom side. The ferrite-martensite interface is\nstraight and runs through-thickness, at an angle, from front to rear, resulting in more martensite on the\nrear than on the front. The location of the nano-tensile specimen on the wedge was carefully selected\nto contain the harder martensite along the full length of the specimen gauge, to assure that deformation\ncrosses the phase boundary under global tension. According to theory, misorientations between laths are\nalmost zero [57], inhibiting easy identi\fcation with EBSD. This explains why in BSE channeling contrast\nimaging (Figure 8d) clearly more boundaries are visible than the few boundaries identi\fed by EBSD. These\nadditional low-misorientation boundaries, which are most likely lath boundaries, are drawn by hand in red\nover the BSE image, in addition to the EBSD based grain and phase boundaries (Figure 8d), and can also\nbe used as an overlay for all other data sets since these are all aligned. The channeling contrast quality on\nthe rear side is lower than that on the front, due to the topography caused by electropolishing (which was\nmilled away by FIB on the front). Therefore, to prevent misidenti\fcation, lath boundaries are only drawn\non the front side.\nThe microstructure-correlated strain maps of front and rear in Figure 8f, with overlay of all boundaries,\nindicate that plasticity is discrete in martensite and di\u000buse in ferrite, with a sharp transition at the ferrite-\nmartensite interface. The plasticity protrusions from martensite into the ferrite would likely evolve into the\nso-called \"near-interface damage\" in bulk material, which has been studied in detail by Liu et al. [9]. In\nmartensite, slip bands clearly align with the lath and variant boundaries, which are in turn parallel to the\nmartensite habit plane trace, as checked with a prior austenite grain reconstruction, discussed further in\nSection 3.3. In the ferrite away from the interface, plasticity spreads out into multiple directions and appears\nto be rather di\u000buse, inhibiting robust trace identi\fcation. In Figure 8e, we also show the global stress-strain\ncurve of the nano-tensile test (global strain calculated by averaging of the DIC strain data) and equivalent\nstrain \felds at several increments, as indicated in the stress-strain curve. In increment 2, plasticity initializes\nin the ferrite, which is expected since ferrite is the softer phase. Subsequently, in increment 3, plasticity\nin ferrite and localization in martensite occur concurrently, which is expected, considering that the ferrite\nand martensite need to deform roughly in parallel, which means strong plasticity on one side (e.g. the soft\nside) needs to be followed by the other side. The fact that the deformation pattern in both ferrite and\nmartensite is very similar between increments 3 and 4, with only a di\u000berence in strain amplitude, underlines\nthe robustness of the SEM-DIC strain measurement. To study the strain accuracy in more detail, two small\nnear-interface areas are marked in Figure 8f (orange and red dashed rectangles), which will be subject to a\nfurther high-resolution investigation in Figure 10, with a focus on DIC parameters, deconvolution and strain\ncalculation methods. The orange area is also used in Figure 8e. Finally, the post-mortem BSE images in\nFigure 8g clearly shows several sharp localizations in the martensite on the front, which correspond exactly\nto the strongest strain bands in the martensite. On the rear, the localizations are not as clearly visible in\nthe BSE contrast, due to the signi\fcant topography of the specimen, however, comparison with the strain\nmap con\frms that the slip bands closely align with the substructure boundaries. Moreover, these post-\nmortem BSE images, which are carefully aligned to the forward-deformed microstructure and strain \felds\n(see Section 2.4.5), are well suited for the identi\fcation of damage and to study any preceding plasticity\nmechanisms at the same position [25].\n16Figure 8: Overview of front (left, blue background) and rear (right, red background) aligned data of specimen S2 in the\nforward-deformed (except for (a)) con\fguration. (a) SE images of the gauge in undeformed con\fguration, with the\ngreen rectangle outlining the ROIs used for the rest of the sub\fgures, wherein DIC data is available, (b) EBSD phase\nmap indicating the presence of ferrite or martensite, (c) EBSD ND IPF map, (d) BSE microstructure maps showing,\nthrough channeling contrast, \fne microstructure morphology such as lath boundaries, which are manually drawn over\nthe front datasets with red lines. Also includes EBSD grain and phase boundary overlay. (e) Global stress-strain\ncurve with equivalent strain \felds (on a small area on the front side marked in orange in (f)) at 4 increments as\nindicated. (f) Equivalent strain \felds on the front (at 850 MPa) and the rear (unloaded after 850 MPa), with overlaid\nBSE-derived lath boundaries (front) and EBSD grain and phase boundaries (front and rear). The front strain \feld\nshows two smaller areas that are shown in more detail in (e) and in Figure 10. (g) Post-mortem high eV BSE images,\nwith phase, grain and lath boundary overlay, showing signs of cracks and localizations at high strain positions at lath\nboundaries.17The alignment of microstructure and DIC displacement data also allows plotting of all data in an \"am-\npli\fed\" forward-deformed con\fguration, as illustrated in Figure 9. This is achieved by multiplying the\ndisplacement \feld values with an \"ampli\fcation factor\", after which this ampli\fed displacement \feld is\nadded to the undeformed position \feld for plotting. An ampli\fcation factor of 10 was employed in Fig-\nure 9a,b,c for plotting of IPF, BSE microstructure and equivalent strain \feld respectively, for front and\nrear, illustrating how the deformation occurs. This allows a direct comparison to simulations, wherein this\n\"ampli\fed\" forward-deformed con\fguration is common practice. Some interesting observations include: (i)\nthe smoothness of the ferrite edge versus the rather discrete steps on the martensite edge denote di\u000buse\nversus discrete plasticity; (ii) the necking behaviour, without any signi\fcant in-plane shear deformation,\nsuggests partly out-of-plane deformation; and (iii) a \"double\" necking can be observed on the front side,\nlikely caused by the small martensite islands on the top that partially blocks the ferrite plasticity near the\nedge.\nFigure 9: 10X-ampli\fed forward-deformed maps of front and rear of specimen S2, for visual interpretation of the\ndeformation. The initial (undeformed) shape of the area of interest was the same rectangle as in Figure 8. (a) EBSD\nND IPF maps, (b) BSE microstructure maps and (c) equivalent strain maps. The legend of the maps is that of\nFigure 8.\n3.2. High-resolution DIC Study\nNext, we will highlight both the accurate microstructure-to-strain alignment and the high spatial strain\nresolution, which will be pushed to the limit through optimized DIC, \"deconvolution\" and strain calculation\nmethods. In martensite, the exact location of the discrete plasticity needs to be determined, while in ferrite,\nwe want to unravel the di\u000buse slip bands. Improvements of the spatial strain resolution in SEM-DIC may be\nachieved by: (i) decreasing the nano-DIC speckle pattern size, (ii) decreasing the subset size, (iii) employing\nthe recently proposed method of \"deconvolution\" of the DIC displacement \felds [40], (iv) optimizing strain\ncalculation methods and/or (v) application of advanced DIC algorithms such as subset splitting [58, 59].\nAlthough the InSn nano-DIC speckle pattern size [16] could be decreased further for future experiments, we\nchoose to focus here on points (ii), (iii) and (iv), while (v) subset splitting requires distinct slip steps that\nare clearly not present in ferrite. As such, we performed local DIC (see Table 3 for all the parameters) on\nthe front side using a varying subset size of 17, 29 and 41 pixels (119 nm, 203 nm and 287 nm, respectively).\nNext, deconvolution was performed according to the approach proposed by Grediac et al. [40]. This\ndeconvolution algorithm relies on the fact that DIC displacements correspond, when omitting the e\u000bect of\nthe pattern [60], to the physical displacement convoluted with a Savitzky-Golary kernel [61, 62], which can\n18be directly related to the subset size, shape and order. The deconvolution consists of correcting the higher\norder spatial derivative terms, which are computed by di\u000berentiation. These derivatives are calculated in\nthe frequency domain, and a low-pass \flter is introduced to avoid the ampli\fcation of high frequencies,\ne.g. arising from measurement noise, remaining SEM scanning artefacts, and potential pattern bias, with\nthe threshold set to fmax = 1=pmin, wherein pminis the minimum wavelength of a signal that can be\npicked up by the deconvolution. The deconvolution is applied to the displacement \felds resulting from the\ndi\u000berent subset sizes, using pminvalues of 25, 39 and 55 pixels for the data with subset size 17, 29 and\n41 pixels, respectively. Additionally, we consider two strain calculation methods: (i) computation of the\ndisplacement gradient tensor ~r0~ uthrough the direct (central di\u000berences) spatial gradient of ~ ufrom both\nthe (i a) regular and (i b) the deconvoluted displacement \felds (after applying a gaussian \flter with standard\ndeviation of 3 pixels) and (ii) determination of the displacement gradient tensor ~r0~ ufrom the correlated\na\u000ene subset shape functions inside each subset (i.e. at each pixel position, since the step size was 1), which\nwe call \"Subset Internal Strains\". No \fltering is applied here. For both methods, Green-Lagrange and 2D\nequivalent strains are computed according to the equations given in Section 2.3.\nTable 3: Custom local DIC code correlation parameters\nParameter Value Unit\nSoftware Home made\nImage \fltering -\nSubset size 17 / 29 / 41 pix\nDeconvolution: pmin 25 / 39 / 55 pix\nStep size 1 pix\nMatching criterion SSD\nInterpolant Cubic Spline\nStrain window 3x3 pix\nVirtual Strain Gauge size [51] 19 / 31 / 43 pix\nSubset Shape function A\u000ene\nFor the evaluation of the results of these correlations, we focus on two smaller areas on the front side\n(indicated in Figure 8f), as shown in Figure 10, which mainly comprises of an area with martensite activity\nin Figure 10a,b,c,d,e, with a minor focus on ferrite in Figure 10f. For the martensite area, Figure 10a\nand 10b show BSE images of the undeformed (without nano-DIC pattern) and deformed (with nano-DIC\npattern) con\fguration respectively. Two strong localizations can be clearly observed (indicated by the red\narrows) near and on top of a lath boundary. While clearly visible in the (high-eV) post-mortem BSE image,\nthe localizations are not so apparent in the SEM-DIC images (Figure 10b 1,b2), since IB-SE and low-eV\nimaging was performed such that only the nano-DIC pattern was imaged. Therefore, the localizations do\nnot signi\fcantly hinder the DIC correlation, so that they can still be observed in the strain maps as sharp\nstrain bands in Figure 10c,d,e, where each row of sub\fgures shows strain \felds computed with a certain\nsubset size, and each column corresponds to one of the three strain calculation methods. The martensite\nstrain localizations are clearly more narrow for smaller subset sizes, although the noise in the strain level\nincreases at the same time. For this discrete plasticity, the deconvolution does not seem to improve the\nspatial resolution, likely due to the limiting factor of the pminvalue, which needed to be rather high here\nto avoid ampli\fcation of noise in the DIC results. However, the Subset Internal Strain \felds show a clear\nimprovement of spatial strain resolution as compared to the other strain calculation methods, which could\nbe due to the fact that no \fltering was applied. The advantage of the deconvolution however is quite clear\nfor the small ferrite area in Figure 10f, with the deconvoluted strain \feld showing the di\u000buse ferrite strain\nbands, likely due to plastic slip, most clearly, as indicated by the black dashed lines in Figure 10f 2. This\n19improvement for di\u000buse strains (as opposed to discrete strains) can likely be explained by the inherently\nlower spatial frequency of these di\u000buse bands, whereby the deconvolution is not inhibited by the pmin(or\nequivalently fmax) values. Note that these clear strain bands, clari\fed through deconvolution, are only\napparent in the strain data of a subset size of 41 pixels, likely because this provides a more stable correlation\nthat is less sensitive to noise. In all, the analysis in Figure 10 shows that by selecting the most appropriate\nDIC strain calculation method and subset size, di\u000berent features of the deformation can be exposed.\nNext, we assess the microstructure-to-strain alignment accuracy by considering the localization which\noccurs exactly at the lath boundary (indicated by the red arrow in Figure 10 on the right side). In all\nstrain maps of this area (Figure 10c,d,e) the strain localization is centered on this martensite lath boundary,\nwhich proves that the microstructure-to-strain alignment is good enough to related speci\fc plasticity events\nto features in the \fne lath martensite microstructure. Indeed, in this case, we can likely classify this\nspeci\fc strain localization event as substructure boundary sliding, which has been shown to be an important\nplasticity mechanism in lath martensite [63, 41] and dual-phase steel [9]. The localization event marked by\nthe left red arrow appears to fall exactly between 2 lath boundaries, which is especially clear on the strain\n\feld with small subsets. Therefore, this strain localization appears to be either intra-lath slip along the\nhabit plane [64] or substructure boundary sliding over a lath boundary that is not clearly visible in the BSE\nimages. This will be investigated in future work [44].\nFinally, it is interesting to note that in the ferrite area in Figure 10f the clear transition over the\ninterface from discrete martensite plasticity to di\u000buse ferrite plasticity. While there is some connection\nbetween martensite and ferrite plasticity, as shown by the brown dashed lines at the bottom of Figure 10f,\nthese do not connect well to the ferrite slip bands, which is likely due to the plastic incompatibility between\nferrite and martensite [45].\n20Figure 10: High-resolution investigation of the e\u000bect of strain calculation methods, DIC deconvolution and varying\nDIC subset sizes on small area 1 (a-e), which focuses on martensite deformation, and area 2 (f), focused on ferrite\ndeformation. Both areas are indicated on the front strain \feld in Figure 8f. For area 1, (a 1) shows undeformed\nBSE microstructure with overlay of phase, grain and lath boundaries, (a 2) post-mortem high-eV BSE scan, showing\nstrong localizations (local nano-damage) as indicated by the red arrows, and (b 1;2) low-eV IB-SE images, as used for\nSEM-DIC correlation, in the (b 1) undeformed and (b 2) \fnal deformed state. (c 1;2;3, d1;2;3, e1;2;3, f1;2;3) equivalent\nstrain \felds of the two areas, computed with a subset size (in pixels) of (c) 17, (d) 29 and (e,f) 41. The columns show\nstrain \felds computed through (c 1, d1, e1, f1) direct (nearest neighbour) gradient of the displacements, (c 2, d2, e2,\nf3) direct (nearest neighbour) gradient of the deconvoluted displacements and (c 3, d3, e3, f3) subset internal strain,\nfor which the strain tensor is derived from the values of the degrees of freedom of the a\u000ene subset shape functions,\nfor each subset (at each pixel) individually. In (f2) we mark several clear slip traces in ferrite with black dashed lines\nand the martensite localizations that cross the interface with brown dashed lines. Note that the scale bar in (f) is\ndi\u000berent from that in the rest of the \fgure. All strain \felds also contain overlays of phase, grain and lath boundaries.\n213.3. front&rear-sided microstructure resolved strain \felds\nSince both front and rear strain \felds are available and are aligned with respect to each other and with\nrespect to the microstructure, we can now attempt to link the deformations on both sides, with the aim of\ninferring how the deformation occurs in 3D. In Figure 11a,c the front and rear strain \felds are shown, while\nFigure 11b contains a side-view of the specimen after deformation, in which several slip bands are clearly\nobserved, as indicated by the arrows and dashed lines. Judging from the strain \felds alone, one can already\ninfer that the deformation mechanisms have the same character on front and rear: discrete (and vertical) in\nmartensite and di\u000buse in ferrite. Moreover, the most prominent martensite strain localizations on front and\nrear can be followed over the side of the specimen, see the red and orange arrows, which means that these\nlocalizations run completely through the thickness, under an angle, as expected. On the ferrite side-view of\nthe specimen, no discrete slip bands could be found (not shown), which agrees well with the large di\u000berence\nbetween front and rear for ferrite, which is also an indication that cross-slip is dominant in ferrite.\nWhile the martensite slip bands align with the lath boundaries on front and rear, the lath boundaries\nare not visible on the side of the specimen. However, before deformation, we performed EBSD scans on\na larger area around the specimen, which was used to perform a Prior Austenite Grain reconstruction\n[65] (not shown), through which the habit plane was determined. In lath martensite, lath boundaries are\npredominantly aligned with the habit plane, such that it can be used to estimate the 3D orientation of the\nlath boundary planes. For the current specimen, the habit plane aligns well with the martensite slip traces\non the front, side and rear surfaces. This is a strong indication of martensite plasticity along the laths and/or\ntheir boundaries. For further veri\fcation of the 3D lath boundary con\fguration, specimen characterization\nof future specimens could be extended to include BSE and EBSD imaging of the sides of the specimens.\n22Figure 11: Interpretation of the 3D martensite deformation of specimen S2 by assessment of (a) front equivalent strain\n\feld, (b) post-mortem SE side view and (c) rear equivalent strain \feld. The red and orange arrows both follow a\nmartensite localization band that appears to be connected from the front, over the side, to the rear. The yellow dotted\nlines and arrows indicate two more slip traces on the side that are less visible. The strain \feld colorbar is equal to\nthat in Figure 10.\n4. Conclusions\nAdvancement in the understanding of complex nanoscale multiphase interface and grain boundary me-\nchanics requires measurement of nanoscale deformation mechanisms on targeted microstructure con\fgu-\nrations, a challenge that requires combination of two state-of-the-art methods: (i) well-de\fned micro-\ndeformations tests of carefully chosen specimens and (ii) measurement of nanoscale resolution microstructure-\nresolved strain \felds. In this work, we presented a nanomechanical testing framework that addresses this\nchallenge by integrating the following state-of-the-art testing and characterization methods:\n•(I) specimen selection and fabrication: fabrication of micron-sized \"1D\" specimens that were isolated\nfrom the bulk microstructure at speci\fc regions of interest;\n•(II) characterization and nano-DIC patterning: front&rear-sided microstructure characterization and\nfront&rear-sided application of a recently developed ultra\fne nano-DIC speckle pattern on the micro-\nspecimens;\n23•(III) nanoscale testing and DIC: front&rear-sided high-resolution SEM-DIC strain mapping, under\nuniaxial loading conditions, aided by SEM scanning artefact correction and DIC deconvolution cor-\nrection;\n•(IV) data alignment: alignment of all microstructure and strain data using a novel data alignment\nframework.\nA case study on a particularly interesting type of dual-phase steel specimen with an incompatible (i.e.\nhigh crystallographically misoriented) ferrite-martensite interface showed how the very high spatial strain\nresolution (after optimization of DIC and application of deconvolution) and the careful microstructure-to-\nstrain alignment gives insight into the martensite, ferrite and (near-)interface deformation mechanisms at\nthe nanoscale. Moreover, the front&rear-sided and aligned strain \felds, in combination with the well-de\fned\nand isolated state of the multiphase specimen, gives opportunities to unravel the 3D deformations while only\nhaving access to in-plane strain \felds. Additionally, the high degree of alignment between microstructure\nand strain \felds allow plotting of microstructure and strain \felds into an \"ampli\fed\" deformed con\fguration,\nwhich eases interpretation of the general deformation of the specimen.\nThe ferrite-martensite interface specimen presented in this work shows how discrete martensite plasticity\nprotrudes through the interface into the ferrite and transits further in the ferrite into di\u000buse plasticity.\nThrough analysis of the SEM-DIC nanoscale strain \felds, EBSD-based habit plane identi\fcation in the\nmartensite and multi-sided observation, all aligned with the here-proposed data alignment framework, the\nmartensite plasticity is identi\fed to be aligned with the lath boundaries, con\frming previous observations\nof soft habit plane martensite plasticity.\nThe isolated nature of these tests, under well-de\fned loading conditions, combined with front&rear-sided\nfull-\feld knowledge of microstructure-resolved displacement and strain \felds, provides ample opportunities\nfor more extensive and more quantitative comparison to complex multiphase numerical simulations than\nwas possible so far. Yet, even without simulation, identi\fcation of the slip systems in complex phases such\nas martensite and bainite, and identi\fcation of nanoscale interface deformation mechanisms, is feasible after\napplication of the here-presented nanomechanical testing framework.\nAcknowledgements\nThe authors acknowledge Marc van Maris, Chaowei Du, Lei Liu, Marc Geers and Ron Peerlings for\ndiscussions and (experimental) support. This research was carried out under project number S17012b in\nthe framework of the Partnership Program of the Materials innovation institute M2i (www.m2i.nl) and the\nTechnology Foundation TTW (www.stw.nl), which is part of the Netherlands Organization for Scienti\fc\nResearch (http://www.nwo.nl). B. Blaysat is grateful to the French National Research Agency (ANR) and\nto the French government research program \"Investissements d'Avenir\" for their \fnancial support (ICAReS\nproject, N ANR-18-CE08-0028-01 & IDEX-ISITE initiative 16-IDEX-0001, CAP 20-25).\nDeclarations\nThe authors state that regarding the research and writing of the manuscript, there are no con\ricts of\ninterest and that all the authors consent to the content of the manuscript.\nCode & Data availability\nThe Matlab code for the full data alignment framework, together with a small example, will be avail-\nable on GitHub ( https://github.com/Tijmenvermeij/NanoMech_Alignment_Matlab ). The full dataset is\navailable upon request.\n24References\n[1] M. S. Rashid, Dual phase steels, Annual Review of Materials Science 11 (1981) 245{266.\n[2] J. PJ, E. Girault, A. Mertens, B. Verlinden, J. Van Humbeeck, F. Delannay, The developments of cold-rolled trip-assisted\nmultiphase steels. al-alloyed trip-assisted multiphase steels, ISIJ international 41 (2001) 1068{1074.\n[3] A. Mortensen, J. Llorca, Metal matrix composites, Annual Review of Materials Research 40 (2010) 243{270.\n[4] C. Tasan, M. Diehl, D. Yan, M. Bechtold, F. Roters, L. Schemmann, C. Zheng, N. Peranio, D. Ponge, M. Koyama,\nK. Tsuzaki, D. Raabe, An overview of dual-phase steels: Advances in microstructure-oriented processing and microme-\nchanically guided design, Annual Review of Materials Research 45 (2015) 391{431.\n[5] B. E. Carroll, T. A. Palmer, A. M. Beese, Anisotropic tensile behavior of ti{6al{4v components fabricated with directed\nenergy deposition additive manufacturing, Acta Materialia 87 (2015) 309{320.\n[6] Z. Li, K. G. Pradeep, Y. Deng, D. Raabe, C. C. Tasan, Metastable high-entropy dual-phase alloys overcome the strength{\nductility trade-o\u000b, Nature 534 (2016) 227{230.\n[7] C. Landron, O. Bouaziz, E. Maire, J. Adrien, Characterization and modeling of void nucleation by interface decohesion\nin dual phase steels, Scripta Materialia 63 (2010) 973{976.\n[8] J. Hoefnagels, C. Tasan, F. Maresca, F. Peters, V. Kouznetsova, Retardation of plastic instability via damage-enabled\nmicrostrain delocalization, Journal of Materials Science 50 (2015) 6882{6897.\n[9] L. Liu, F. Maresca, J. Hoefnagels, T. Vermeij, M. Geers, V. Kouznetsova, Revisiting the martensite/ferrite interface\ndamage initiation mechanism: The key role of substructure boundary sliding, Acta Materialia 205 (2021) 116533.\n[10] A. Orozco-Caballero, D. Lunt, J. D. Robson, J. Quinta da Fonseca, How magnesium accommodates local deformation\nincompatibility: A high-resolution digital image correlation study, Acta Materialia 133 (2017) 367{379.\n[11] S. Wei, G. Zhu, C. C. Tasan, Slip-twinning interdependent activation across phase boundaries: An in-situ investigation\nof a ti-al-v-fe ( \u000b+\f) alloy, Acta Materialia 206 (2021) 116520.\n[12] M. E. Harr, S. Daly, A. L. Pilchak, The e\u000bect of temperature on slip in microtextured Ti-6Al-2Sn-4Zr-2Mo under dwell\nfatigue, International Journal of Fatigue 147 (2021) 106173.\n[13] A. D. Kammers, S. Daly, Small-scale patterning methods for digital image correlation under scanning electron microscopy,\nMeasurement Science and Technology 22 (2011) 125501.\n[14] F. Di Gioacchino, J. Quinta da Fonseca, Plastic strain mapping with sub-micron resolution using digital image correlation,\nExperimental Mechanics 53 (2012) 743{754.\n[15] D. Yan, C. Tasan, D. Raabe, High resolution in situ mapping of microstrain and microstructure evolution reveals damage\nresistance criteria in dual phase steels, Acta Materialia 96 (2015) 399{409.\n[16] J. P. M. Hoefnagels, M. P. F. H. L. van Maris, T. Vermeij, One-step deposition of nano-to-micron scalable, high-quality\ndigital image correlation patterns for high strain in-situ multi-microscopy testing, Strain (2019).\n[17] C. Montgomery, B. Koohbor, N. Sottos, A robust patterning technique for electron microscopy-based digital image\ncorrelation at sub-micron resolutions, Experimental Mechanics 59 (2019) 1063{1073.\n[18] S. Shafqat, J. Hoefnagels, Cool, dry, nano-scale dic patterning of delicate, heterogeneous, non-planar specimens by\nmicro-mist nebulization, Experimental Mechanics 61 (2021) 917{937.\n[19] C. Tasan, J. Hoefnagels, M. Diehl, D. Yan, F. Roters, D. Raabe, Strain localization and damage in dual phase steels inves-\ntigated by coupled in-situ deformation experiments and crystal plasticity simulations, International Journal of Plasticity\n63 (2014) 198{210.\n[20] C. Tasan, M. Diehl, D. Yan, C. Zambaldi, P. Shanthraj, F. Roters, D. Raabe, Integrated experimental{simulation analysis\nof stress and strain partitioning in multiphase alloys, Acta Materialia 81 (2014) 386 { 400.\n[21] J. Stinville, N. Vanderesse, F. Bridier, P. Bocher, T. Pollock, High resolution mapping of strain localization near twin\nboundaries in a nickel-based superalloy, Acta Materialia 98 (2015) 29{42.\n[22] Z. Zhang, D. Lunt, H. Abdolvand, A. Wilkinson, M.P., F. Dunne, Quantitative investigation of micro slip and localization\nin polycrystalline materials under uniaxial tension, International Journal of Plasticity 108 (2018) 88 { 106.\n[23] A. Kumar, A. Dutta, S. K. Makineni, M. Herbig, R. Petrov, J. Sietsma, In-situ observation of strain partitioning and\ndamage development in continuously cooled carbide-free bainitic steels using micro digital image correlation, Materials\nScience and Engineering: A 757 (2019) 107{116.\n[24] X. Li, C. Li, L. Lu, J. Huang, S. Luo, Interactions between slip bands and interfaces in a compressed duplex stainless\nsteel, Materials Science and Engineering: A 818 (2021) 141325.\n[25] T. Vermeij, J. P. M. Hoefnagels, Plasticity, localization, and damage in ferritic-pearlitic steel studied by nanoscale digital\nimage correlation, Scripta Materialia 208 (2021).\n[26] M. Charpagne, J. Stinville, A. Polonsky, M. Echlin, T. Pollock, A multi-modal data merging framework for correlative\ninvestigation of strain localization in three dimensions, JOM (2021) 1{9.\n[27] C. Du, J. Hoefnagels, R. Vaes, M. Geers, Plasticity of lath martensite by sliding of substructure boundaries, Scripta\nMaterialia 120 (2016) 37 { 40.\n[28] G. Dehm, B. Jaya, R. Raghavan, C. Kirchlechner, Overview on micro- and nanomechanical testing: New insights in\ninterface plasticity and fracture at small length scales, Acta Materialia 142 (2018) 248{282.\n[29] H. Ghassemi-Armaki, R. Maa\u0019, S. Bhat, S. Sriram, J. Greer, K. Kumar, Deformation response of ferrite and martensite\nin a dual-phase steel, Acta Materialia 62 (2014) 197{211.\n[30] C. Motz, T. Sch oberl, R. Pippan, Mechanical properties of micro-sized copper bending beams machined by the focused\nion beam technique, Acta Materialia 53 (2005) 4269{4279.\n[31] D. Kiener, W. Grosinger, G. Dehm, R. Pippan, A further step towards an understanding of size-dependent crystal\nplasticity: In situ tension experiments of miniaturized single-crystal copper samples, Acta Materialia 56 (2008) 580 { 592.\n25[32] C. Du, J. P. M. Hoefnagels, L. I. J. C. Bergers, M. G. D. Geers, A uni-axial nano-displacement micro-tensile test of\nindividual constituents from bulk material, Experimental Mechanics 57 (2017) 1249{1263.\n[33] C. Tian, D. Ponge, L. Christiansen, C. Kirchlechner, On the mechanical heterogeneity in dual phase steel grades: Activation\nof slip systems and deformation of martensite in DP800, Acta Materialia 183 (2020) 274{284.\n[34] M. Ekh, N. Larijani, E. Dartfeldt, M. Kapp, R. Pippan, Prediction of the mechanical behaviour of pearlitic steel based\non microcompression tests, micromechanical models and homogenization approaches, European Journal of Mechanics -\nA/Solids 67 (2018) 272{279.\n[35] T. E. J. Edwards, F. Di Gioacchino, A. J. Goodfellow, G. Mohanty, J. Wehrs, J. Michler, W. J. Clegg, Transverse\ndeformation of a lamellar tial alloy at high temperature by in situ microcompression, Acta Materialia 166 (2019) 85{99.\n[36] C. Du, R. Petrov, M. Geers, J. Hoefnagels, Lath martensite plasticity enabled by apparent sliding of substructure\nboundaries, Materials & Design 172 (2019) 107646.\n[37] F. Di Gioacchino, W. J. Clegg, Mapping deformation in small-scale testing, Acta materialia 78 (2014) 103{113.\n[38] T. E. J. Edwards, X. Maeder, J. Ast, L. Berger, J. Michler, Mapping pure plastic strains against locally applied stress:\nRevealing toughening plasticity, Science Advances 8 (2022) eabo5735.\n[39] J. Neggers, E. Heripre, S. Hallais, A. Tanguy, M. Bonnet, D. Boivin, E. Rouesne, F. Gaslain, D. Loisnard, A. E. Sabbagh,\nS. Roux, Correcting sem scanning artifacts using orthogonal scans, Submitted for publication (2022).\n[40] M. Grediac, B. Blaysat, F. Sur, A robust-to-noise deconvolution algorithm to enhance displacement and strain maps\nobtained with local dic and lsa, Experimental Mechanics 59 (2019) 219{243.\n[41] C. Du, R. Petrov, M. Geers, J. Hoefnagels, Lath martensite plasticity enabled by apparent sliding of substructure\nboundaries, Materials & Design 172 (2019) 107646.\n[42] W. Lenthe, S. Singh, M. D. Graef, A spherical harmonic transform approach to the indexing of electron back-scattered\ndi\u000braction patterns, Ultramicroscopy 207 (2019) 112841.\n[43] T. Vermeij, R. Peerlings, M. Geers, J. Hoefnagels, Crystallographic slip activity \felds identi\fed automatically from dic\ndata, even for intersecting, di\u000buse and cross slip, arXiv preprint arXiv:2207.12814 (2022).\n[44] T. Vermeij, R. L. A. Kerkhof, J. P. M. Hoefnagels, Favorable lath martensite plasticity mechanisms in dual-phase steel:\nsubstructure boundary sliding and habit plane slip (working title), Under Preparation (2022).\n[45] T. Vermeij, J. A. C. Verstijnen, J. P. M. Hoefnagels, Compatibility of plasticity between ferrite and lath martensite in\ndual-phase steels (working title), Under Preparation (2022).\n[46] S. Wright, M. Nowell, Ebsd image quality mapping, Microscopy and microanalysis : the o\u000ecial journal of Microscopy\nSociety of America, Microbeam Analysis Society, Microscopical Society of Canada 12 (2006) 72{84.\n[47] L. Bergers, J. Hoefnagels, M. Geers, On-wafer time-dependent high reproducibility nano-force tensile testing, Journal of\nPhysics D Applied Physics 47 (2014) 495306.\n[48] H. Teyssedre, S. Roux, G. R\u0013 egnier, A. Tracz, Filtering out slow-scan drifts in atomic force microscopy images, The Journal\nof Strain Analysis for Engineering Design 46 (2011) 361{367.\n[49] M. A. Sutton, N. Li, D. Garcia, N. Cornille, J.-J. Orteu, S. McNeill, H. Schreier, X. Li, A. P. Reynolds, Scanning electron\nmicroscopy for quantitative small and large deformation measurements part ii: experimental validation for magni\fcations\nfrom 200 to 10,000, Experimental Mechanics 47 (2007) 789{804.\n[50] S. Maraghechi, J. Hoefnagels, R. Peerlings, O. Roko\u0014 s, M. Geers, Correction of scanning electron microscope imaging\nartifacts in a novel digital image correlation framework, Experimental mechanics 59 (2019) 489{516.\n[51] I. D. I. C. Society, E. M. C. Jones, M. A. Iadicola (Eds.), A good practices guide for digital image correlation (2018).\n[52] G. Nolze, Image distortions in sem and their in\ruences on ebsd measurements, Ultramicroscopy 107 (2007) 172{183.\n[53] R. Hielscher, H. Schaeben, A novel pole \fgure inversion method: speci\fcation of the MTEX algorithm, Journal of Applied\nCrystallography 41 (2008) 1024{1037.\n[54] F. Bachmann, R. Hielscher, H. Schaeben, Texture analysis with mtex { free and open source software toolbox, in: Texture\nand Anisotropy of Polycrystals III, volume 160 of Solid State Phenomena , Trans Tech Publications Ltd, 2010, pp. 63{68.\ndoi:10.4028/www.scientific.net/SSP.160.63 .\n[55] J. Diebel, Representing attitude: Euler angles, unit quaternions, and rotation vectors, Matrix 58 (2006) 1{35.\n[56] M. D. Atkinson, J. M. Donoghue, J. Q. da Fonseca, Measurement of local plastic strain during uniaxial reversed loading\nof nickel alloy 625, Materials Characterization 168 (2020) 110561.\n[57] S. Morito, X. Huang, T. Furuhara, T. Maki, N. Hansen, The morphology and crystallography of lath martensite in alloy\nsteels, Acta Materialia 54 (2006) 5323{5331.\n[58] J. Poissant, F. Barthelat, A novel \\subset splitting\" procedure for digital image correlation on discontinuous displacement\n\felds, Experimental mechanics 50 (2010) 353{364.\n[59] F. Bourdin, J. C. Stinville, M. P. Echlin, P. G. Callahan, W. C. Lenthe, C. J. Torbet, D. Texier, F. Bridier, J. Cormier,\nP. Villechaise, T. M. Pollock, V. Valle, Measurements of plastic localization by heaviside-digital image correlation, Acta\nMaterialia 157 (2018) 307 { 325.\n[60] F. Sur, B. Blaysat, M. Gr\u0013 ediac, On biases in displacement estimation for image registration, with a focus on photome-\nchanics, Journal of Mathematical Imaging and Vision (2021) 1{30.\n[61] A. Savitzky, M. J. Golay, Smoothing and di\u000berentiation of data by simpli\fed least squares procedures., Analytical\nchemistry 36 (1964) 1627{1639.\n[62] H. W. Schreier, M. A. Sutton, Systematic errors in digital image correlation due to undermatched subset shape functions,\nExperimental Mechanics 42 (2002) 303{310.\n[63] C. Du, J. Hoefnagels, R. Vaes, M. Geers, Plasticity of lath martensite by sliding of substructure boundaries, Scripta\nMaterialia 120 (2016) 37{40.\n[64] K. Ryou, S. Nambu, T. Koseki, E\u000bect of carbon content on selection of slip system during uniaxial tensile deformation of\n26lath martensite, Materials Science and Engineering: A 777 (2020) 139090.\n[65] R. Hielscher, T. Nyyss onen, F. Niessen, A. A. Gazder, The variant graph approach to improved parent grain reconstruction,\nMaterialia 22 (2022) 101399.\n27"    },    {        "title": "2402.15338v1.Effect_of_temperature_and_copper_doping_on_the_heterogeneous_Fenton_like_activity_of_Cu__x_Fe___3_x__O__4__nanoparticles.pdf",        "content": "Effect of  temperature and copper dop ing on the heterogeneous Fenton -like \nactivity of 𝑪𝒖 𝒙𝑭𝒆 𝟑−𝒙𝑶𝟒 nanoparticles   \nNahuel Nuñez1,2,3*, Enio Lima Jr.1,2, Marcelo Vásquez  Mansilla1,2, Gerardo F. Goya4,5, Álvaro Gallo -\nCordova6, María del Puerto Morales6, Elin L. Winkler1,2,3* \n1 Laboratorio de Resonancias Magnéticas, Gerencia de Física, Centro Atómico Bariloche, Av. \nBustillo 9500, (8400) S. C. de Bariloche (RN), Argentina.  \n2 Instituto d e Nanociencia y Nanotecnología (CNEA -CONICET), Nodo Bariloche, Av. Bustillo 9500, \n(8400) S. C. de Bariloche (RN), Argentina.  \n3 Instituto Balseiro, CNEA -UNCuyo, Av. Bustillo 9500, (8400) S. C. de Bariloche (RN), Argentina  \n4 Dept. Física de la Materia Conden sada, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009, \nZaragoza, Spain  \n5 Instituto de Nanociencia y Materiales de Aragón, CSIC -Universidad de Zaragoza, C/ Mariano \nEsquillos S/N , 500 18, Zaragoza, Spain  \n6 Instituto de Ciencia de Materiales de Madrid, ICM M/CSIC, C/  Sor Juana Inés de la Cruz 3, 28049, \nMadrid, Spain  \n *Corresponding authors  : nahuel.nunez@ib.edu.ar   \nKeywords: copper doped iron oxide nanoparticles; Heterogeneous Fenton reaction; free radicals ; \nmagnetic catalyst ; organic dyes  \n  Abstract  \nFerrite nanoparticles serve as potent heterogeneous Fenton -like catalysts, producing reactive \noxygen species (ROS) for decomposing organic pollutants. We investigated the impact of \ntemperature and copper content on the catalytic activity of nanoparticles w ith different oxidation \nstates of iron. Via solvothermal synthesis, we fabricate d copper -doped magnetite (Cu xFe3-xO4) with \na Fe2+/Fe ratio ~0.33 for the undoped system. Using a microwave -assisted method, we produced \ncopper -doped oxidized ferrites, yielding  a Fe2+/Fe ratio of ~0.11 for the undoped nanoparticles. \nThe ROS generated by the catalyst were identified and quantified by electron paramagnetic \nresonance, while optical spectroscopy allowed us to evaluate its effectiveness for the degradation \nof a model  organic dye. At room temperature, the magnetite nanoparticles exhibited the most •OH \nradical production and achieved almost 90% dye discoloration in 2 hours. This efficiency \ndecreased with increasing Cu concentration, concurrently  with a decrease in •OH g eneration. \nConversely, above room temperature, Cu -doped nanoparticles significantly enhance the  dye \ndegradation, reaching 100% discoloration at 90°C. This enhancement is accompanied by a \nsystematic increase in the kinetic constants, obtained  from reaction equations, with Cu doping. \nThis study highlights the superior stability and high -temperature catalytic advantages of copper \nferrite holding promise for enhancing the performance of nanocatalysts for decomposing organic \ncontaminants.  \n \n \n \n \n \n 1. Introduction  \n \nEnvironmental remediation process es based on the catalytic activity of m agnetic nanoparticles \nhave gained considerable attention in recent years.1–3 One promising example on this is the use \nof iron oxide nanoparticles as heterogeneous catalysts in the Fenton  reaction s that generates \nreactive oxygen species (ROS) .4,5 These species allow s the degradation of various organic \npollutants  through an advanced oxidation process .6 In the homogeneous  Fenton reaction, •OH and \n•OOH radicals are generated by soluble Fe2+ and Fe3+ ions through  the following reactions : Fe2++\nH2O2→Fe3++•OH+OH− (kcat=63 M−1 s−1) and  \n Fe3++H2O2→Fe2++•OOH +H+ (kcat=0.001  M−1 s−1).7 In the literature this second equation \nis known as Fenton -like reaction, bei ng the limiting reaction due to  the lower rate constant .8,9 These \nfree radicals oxidize  organic molecules and pollutants, reducing their toxicity. Compared to the \nhomogeneous Fenton reaction, the use of heterogeneous catalysts offers several advantages, \nsuch as increased stability, recyclability, and reduced secondary pollution .10 It is expected that in  \nhomogeneous catalysis , the solubility of catalyst ions is the process limiting factor , while in the \nheterogeneous one, the adsorption steps as well as the diffusion of the reactive species in the \nmedium are dominant .11 Therefore, heterogeneous  catalysis provides  greater degrees of freedom \nto tune and gain control over  the subsequent advanced oxidation reaction .  \nLike any thermally activated process, the kinetics of th e Fenton reaction is accelerated by \ntemperature .12 For this reason, numerous studies aimed to design multifunctional nanoparticles \ncapable of inducing local heating to enhance its catalytic activity.13,14 This provi des an additional \nparameter to control and optimize the efficiency of catalysts in Fenton processes. In fact, studies \nfocused on decontaminating landfill leachate using copper catalysts concluded that the optimum \ntemperature for the reaction was 70 °C.15   \nWhile it is true that increasing the temperature of the system can elevate the cost of wastewater \ntreatment, in some instances, the waste is already above room temperature, condition that can be \nleveraged to enhance the efficiency of the nanocata lyst. For example, it was reported that the temperature of effluents from textile wet processing is in the range of 30°C to 60°C .16 Similarly, \nvinasse, a byproduct of bioethanol distillation, is generated at high temperatures, approximately \naround 90°C.17,18 Another example is the paper industry, whe re the chemical treatment of  wood \ngenerates a black liquor residue at about  60-70°C .19 On the other hand, w hile increasing the \ntemperature accelerates the kinetics of th e reaction, improving the catalyst's efficiency, it may also \nproduce undesirable effects The thermally accelerated decomposition of hydrogen peroxide can \ndecrease the degradation efficiency by Fenton  and Fenton -like processes .20 Moreover , it has been \ndemonstrated that Fe3O4 nanoparticles undergo a transformat ion into γ-Fe2O3 after continuous \nFenton reaction due to the different kcat of Fe2+ and Fe3+ ions,  resulting in a subsequent loss of \ntheir catalytic activity .21 This oxidation of iron catalysts  also could be promoted by increasing the \ntemperature. Therefore, various effects of the operating temperature must be taken into account \nwhen the optimal working temperature for wastewater treatment is defined.  \nTo optimize the  catalytic efficiency of iron oxide nanoparticles  in advanced oxidation reactions , \nvarious ions have been incorporated in to the ferrite lattice in order to modify their  surface \nreactivity .7,22,23 Among them, copper has received special attention due to its strikingly similar redox \nproperties like iron.24–32 Both the monovalen t Cu+ and divalent Cu2+ oxidation states easily react \nwith H2O2 analogous to the Fe2+/H2O2 and Fe3+/H2O2 systems, the reaction constants of these \nFenton -like process es are kcat=104 M−1 s−1 and kcat=4.6 ∗102 M−1 s−1, respectively .7 Due to \nits enhanced activity, copper nanocatalysts have been previously  employed to efficient ly degrade \ncontaminants like phenols ,33 insecticides ,34 pharmaceuticals35–37  and also as antibacterial agent.38 \nMoreover, a synergistic effect was observed when copper was introduced into a mesoporous iron \noxide catalyst for the Fenton -like process .15,26,39,40 In this case, t he proposed mechanism for the \ngood performance of copper -iron catalysts is the regeneration of Fe2+ ions through the reaction \nFe3++Cu1+→Fe2++Cu2+. An other interesting capability of copper catalysts is  its good \nperformance after recycling . Hussain et al. found that zirconia -supported copper catalysts \nmaintained their activity when recycled, unlike iron catalysts wh ose activity diminished .40 For these reasons  copper catalysts are interesting materials to be tested in Fenton -like processes at high \ntemperature reactions.  \nIn this context, in the present work we investigate the heterogeneous Fenton -like catalytic activity \nof copper -doped  iron oxide nanoparticles with the aim of studying  the role played by the surface \nactive ions in the generation of ROS, and determine the proper doping condition  and surface \noxidation state  for different working temperature in wastewater treatment .  For this , copper -doped \nmagnetite and maghemite nanoparticles  were synthesized by two different polyol method s: \nsolvothermal and microwave -assisted, respectively . The as -synthesized nanoparticles were \ncharacterized by various techniques, including X -ray diffraction  (XRD) , transmission electron \nmicroscopy  (TEM)  and X -ray photoelectron spectroscopy  (XPS)  in order to determine their \ncrystal line structur e, morpholog y and composition. Subsequently,  the production of free radicals \ncatalyzed by each sample was identified and quantified by means of electron paramagnetic \nresonance (EPR) spectroscopy assisted with a spin trap molecule . Finally , the catalytic \nperformance of the nanoparticles was evaluated by measuring their degradation efficiency of \nmethylene blue (M B) at different reaction temperatures using optical spectroscopy . These results \ndemonstrate th at, while the magnetite is most efficient nanocatalyst at room temperature, it \noxidizes and los es its activity at higher temperature s; copper doping  being  essential  to maintain, \nand even surpass, its performance at higher temperature s. \n \n2. Materials and methods  \n2.1. Materials  \nThe reagents used in this work are: iron (III) nitrate nonahydrate ( Fe(NO 3)3.9H2O, 98% Sigma -\nAldrich ), copper (II) sulfate pentahydrate ( CuSO4.5H2O, 99% Merk ), triethylene glycol  (99% Sigma -\nAldrich) , diethylene glycol  (99% Sigma -Aldrich) , ethan ol (96%) , methylene blue  (>82% Sigma -\nAldrich) , 5,5 -dimethyl -1-pyrroline N -oxide (DMPO , >97%  Cayman ), dimethyl sulfoxide (DMSO, \n>99%) and H 2O2 aqueous solution (30% Sigma -Aldrich).  2.2. Synthesis of the catalysts  \nFor this study we synthesized two series of copper doped iron oxide nanoparticles. The first one \nis co mposed of almost stoichiometric copper ferrite nanoparticles ( Cu𝑥2+Fe1−𝑥2+Fe23+O4). It was \nobtained by the solvothermal method using a polyol as solvent. The second batch was obtained \nby the microwave assisted method, also using a polyol as solvent. In this case the nanoparticles \nwere overoxidized by adding water into the synthesis rea ctor.  \nSolvothermal synthesis : In this method  4 mmol of metals were dissolved in 40 mL of triethylene \nglycol. The  proportions of the precursors Fe(NO 3)3.9H2O and CuSO4.5H2O were adjusted \naccording to the required stoichiometry  by the relations: 𝑚𝐹𝑒(𝑁𝑂 3)3=(3−𝑥)∗241 .86 mg and \n𝑚𝐶𝑢𝑆𝑂 4=𝑥∗249 .68 mg, where x determines the Cu content of atoms in a molecule (Cu xFe3-xO4). \nThe solution was heated at 100 °C for 1 h to evaporate the water from the system and then \ntransferred to a 100 mL teflon autoclave and k ept at 260 °C for 4 h. Once the synthesis is finished, \nthe obtained material was repeatedly washed by magnetic separation with ethanol and then dried \nat 70 °C. The nanoparticle samples were named STX, w here X= 0, 1, 2 an d 3 represents  the \nnominal conce ntration x= 0, 0.1, 0.2 and 0.3 , respectively.  \nMicrowave -assisted synthesis : In this synthesis method , the microwave oven Monowave 300 \n(Anton Paar GmbH, Graz, Austria) with a built -in magnetic stirrer  was used to synthesize  the \ncatalysts,  working at 2.45 GH z and following a protocol similar to that presented by Gallo -Cordova \net al41. Briefly , 1.75 mmol of metals were dissolved in a solution of diethyle ne glycol (18.3 mL) and \nwater (0.7 mL), adjusting the proportions of precursors Fe(NO 3)3.9H2O and CuSO4.5H2O2 \naccording to the required stoichiometry  following  the relationship previously mentioned in the \nsolvothermal synthesis method. The solution was tra nsferred to a 30 mL vial and the temperature \nwas raised to 230 °C with a ramp of 5.25 °C/m in, where it was maintained for 2 h and then cooled \nabruptly. It is important to mention that the  pressure increases due to  the presence of water that \nlowers the boiling point of the solvent mixture (170 ºC) , reaching up to 30 Bar in some cases. After \nthe synthesis, the nanoparticles were repeatedly washed  by magnetic separation  with alcohol and redispersed in water. In this case, the nanoparticle samples were name d MWX, where X= 0, 1, 2, \n3 and 4 represents  the nominal concentration x= 0, 0.1, 0.2, 0.3 and  0.4, respectively.  \n2.3. Characterization of the samples and evaluation of catalytic activity  \nThe crystal structure of the synthesized samples was characterized by X -ray diffraction (XRD) \nusing the Bruker Advance D8 diffractometer (Cu -Kα radiation, λ=0.15406 nm). The incorporation \nof copper ions into the structure of the nanoparticles was verified by inductively coupled plasma \noptical emission spectroscopy  (ICP-OES) using  a Perkin Elmer apparatus (OPTIME  2100 DV ) and \nthe organic content quantified by thermogravimetric analysis (TGA) in a ATD/DSC/TG, Q600 from \nTA Instruments . X-ray photoelectron spectroscopy (XPS) was used to analyze the oxidation state \nof iron ions in the n anoparticles, employing the Kratos AXIS Supra . The values of Fe2+ and Fe3+ for \neach sample w ere obtained by fitting each XPS spectrum with the peaks of the Fe2+ (lower binding \nenergy) and Fe3+ (higher binding energy) multiple ts using the software CASA XPS. The size and \nmorphology of the NPs were studied by transmission electron microscopy (TEM)  in a Philips CM -\n200 microscope operating at 200 kV. The DC magnetization of the samples was studied with a \nLakeShore 7300 vibrating sample magnetometer (VSM). Magneti zation versus applied field  (M(H))  \ncycles w ere acquired at room temperature with the VSM up to  an applied field of  ±10 kOe. \nThe generation of free radicals by the catalysts was studied by electron paramagnetic resonance \n(EPR) working in the X -band (9.5 GHz ) at room temperature with a BRUKER ELEXSYS II -E500 \nspectrometer  using the nitrone -based DMPO as a spin trap . Measurements were performed with \na modulation signal of 100 kHz and 3 G of amplitude , and using the resonance of Mn2+ impurities \nin a MgO crystal as a pattern signal to normalize the free radical production of each sample .21 In \nthese experiments, 0.1 mg/mL of catalyst  was dispersed in 100 mM acetate buffer  at pH=5 , then \n50 μL of a 1 mg:6 mL s olution of DMPO:DMSO were added . Then 5 μL of 30% H2O2 aqueous \nsolution were added and EPR spectra were taken at intervals of no more than 10 minutes . About \n90 μL of the reaction solution was contained in a quartz tube  and the height of the measured region \nwas 30 mm . To evaluate the efficiency of the synthesiz ed nanoparticles for degrading organic compounds, \ncolorimetric experiments were performed with methylene blue dye . The methylene blue \nconcentration was selected from previous works42, and the catalyst and hydrogen peroxide dosage \nwere fixed in common values reported for Fenton and Fenton -like processes43,44. A pH=5 was \nchosen, acid ic enough to favor the Fenton reaction45, but no t so low to avoid leaching, which is \ndrastically enhanced for pH<5 .46,47 \nIn these experiments, 1 mg/mL of nanoparticles and 100 ppm of dye were dispersed in a pH= 5 \n100 mM acetate buffer , and the system was kept under agitation for two hours to ensure adsorption \nof the dye onto the nanoparticles' surface. Then, 10 μL/mL of 30% H2O2 aqueous mixture  were \nadded to the solution, and the degradation efficiency was determined by measuring the \nabsorbance at 663 nm at different time intervals (5 , 15, 30, 60 and 120 min) and considering a \ncalibration curve absorbance vs  MB concentration . These experiments were carried out in 2 mL \nreactors, using different reactors for each time (six in total for a complete measurement).  \nMeasurements were taken at room temperature , at 60 °C and at 90°C using the NUMAK 721 UV -\nVis spectrophotometer.   \n3. Results and discussion  \n3.1. Nanocatalysts characterization  \nXRD  patterns of the copper doped iron oxide  nanoparticles synthe sized by the solvothermal and \nmicrowave -assisted method are shown in Fig.1a and Fig.1b , respectively. The main XRD \ndiffraction peaks observed can be  assigned to the Fd3m spinel structure, characteristic of copper \nferrite. Noticeably, the XRD pattern of the  x=0 microwave -assisted sample shows  also additional \npeaks at 32° and 34°, besides the ones indexed with the spinel structure mentioned above , which \nare characteristic of  the ordering of cation vacancies in the maghemite structure .48 This result \nconfirms  a higher degree of oxidation of  the samples fabricated by microwave -assisted method  in \ncomparison to those prepared by  the solvothermal one , attributed  to the presence of the water \nadded in the synthesis. The intensity of the mentioned peaks decreases as copper is introduced into the structure and almost disappears for x=0.2, which could be  explained by the copper \noccupancy of cation vacancies into the maghemite structure.  Minority m etallic copper segreg ation \nwas observed for the largest copper substitution , this occurs for x>0.3 and x>0.4 for nanoparticles \nfabricated by solvothermal and microwave -assisted method s, respectively. Due to the metallic \nphase segregation, this study was restricted to x ≦0.3 and x ≦0.4 for nanoparticles synthesized by \nsolvothermal and microwave route, respectively. The XRD pattern s of the solvothermal sample s \nshow a low intensity peak at 24°, attributed to the presence of iron hydroxide  traces  (JCPDS 00 -\n046-1436)  49. Additionally,  narrow peaks at 17° and 23° were observed in the x=0 sampl e which \nare ascribed to polymerized (poly -) ethylene glycol.50,51  \n \nFig.1: X-ray diffractogram of the copper -incorporated iron oxide nanoparticles obtained by : (a) the \nsolvothermal method and (b) the microwave –assisted method . \n \nThe incorporation of copper in the structure was measured by ICP -OES , and the results are \npresented in Table1 , where a systematic increase of Cu -concentration was determined, although \nslightly smaller than the nominal doping  for both methods.  The oxidation state of iron for all the \nnanoparticles system s was evaluated by XPS measurements.  Notice that although the XPS is a \nsurface sensitive technique, in this case it provides  information of almost the whole nanoparticle \nas the measuring range technique is about 4 nm.  From the XPS spectra (shown in Figs. S1 and \nS2 of the Supplementary Informat ion) the Fe2+/Fe ratio was determined for all the samples and the \nresults are presented in Table1 . In the solvothermal samples, the Fe2+/Fe ratio obtained by XPS \nis similar to the one expected for the stoichiometric  CuxFe3−xO4 nanoparticles, where x \ncorresponds  to the value determined by ICP -OES.  On the other hand, microwave -assisted \nsamples present much lower Fe2+/Fe ratio than the theoretical one, confirming that these samples \nare overoxidized. This result is consist ent with the maghemite phase detected by the XRD patterns.  \n \nMethod  Solvothermal  Microwave -assisted  \nSample  ST0 ST1 ST2 ST3 MW0  MW1  MW2  MW3  MW4  \n𝐱𝐧𝐨𝐦𝐢𝐧𝐚𝐥  0 0.1 0.2 0.3 0 0.1 0.2 0.3 0.4 \n𝐱𝐈𝐂𝐏 0 0.08 0.15 0.23 0 0.09 0.17 0.24 0.32 \nFe2+/Fe \nnominal  0.333  0.315  - 0.278  0.333  0.313  0.293  0.286  0.253  \nFe2+/Fe  \nby XPS  0.33 0.32 - 0.26 0.11 0.16 0.18 0.12 0.16 \n𝐝𝐓𝐄𝐌 (nm)  13(3)  12(3)  10(2)  9(2) 11(2)  12(2)  11(2)  12(4)  11(3)  \n(𝐦𝐍𝐏𝐬\n𝐦𝐬𝐚𝐦𝐩𝐥𝐞)𝐓𝐆𝐀 0.81 0.84 0.83 0.86 0.96 0.97 0.96 0.96 0.95 𝐌𝐬 by VSM \n(emu/g)  66(1)  67(1)  64(1)  62(1)  76(1)  74(1)  68(1)  51(1)  50(1)  \nTable1:  Results of the 𝐶𝑢𝑥𝐹𝑒3−𝑥𝑂4 nanoparticles characterization: Cu incorporation degree \ndetermined by ICP -OES ( 𝐱𝐈𝐂𝐏), Fe2+/Fe ratio determined by XPS measurements and theoretically \nby taking in account the copper incorporation obtained by ICP -OES, size obtained by TEM ( 𝐝𝐓𝐄𝐌), \nmass percentage of nanoparticles in the samples as obtained by TGA (𝐦𝐍𝐏𝐬\n𝐦𝐬𝐚𝐦𝐩𝐥𝐞), and the  saturation \nmagnetization (M s) obtained from the M(H) curves at room temperature.  \n \nTo study the size and morphology of the nanoparticles we performed TEM measurements of all \nsamples, which are presented in Fig.2  along with the corresponding size distributi on histogram \n(measured as diameter due to the spherical -like shape of the particles)  and fitted to a lognormal \nfunction . Solvothermal samples exhibit a slight dependence of size with copper content, ranging \nfrom 13(3) nm for x=0 to 9(2) nm for x=0.3  and irregular shape  (see Table1 ). In contrast, no size \ndependence with copper content was observed in microwave -assisted samples , all with rather \nspherical shape and  sizes between 11 - 12 nm , probably due to the higher pressure synthesis \ncondition.  \n  \nFig.2: Representative TEM images of the MWX and STX CuxFe3−xO4 nanoparticles and their \ncorresponding size distribution  histogram fitted with lognormal distribution.  \n \nThe DC field dependence of the magnetization, measured at room temperature, shows a reversible \nbehavior for all the samples, in agreement with a superparamagnetic regime of the nanoparticles \nat these conditions. Figures  3a and 3b show  the MvsH curves for the solvothermal and \nmicrowave -assisted samples, respectively . The sample ´s magnetization was corrected by \nconsidering the proportion of the organic compound in the as -made nanoparticles, determined \nfrom TGA measurement, as reported in Table1. \n \n \nFig.3: (a)  M vs H cycle of the solvothermal nanoparticles. The inset shows the  fit using the \nLangevin model  for the ST1 sample . (b) M vs H cycle of the Microwave -assisted nanoparticles. \nThe inset shows the fit using the Langevin model for the MW1 s ample.  \n \nThe M(H) curve can be fitted with a Langevin model for all the samples, in agreement with a \nsuperparamagnetic behavior . From the fitting, the corresponding saturation magnetization ( Ms) \ncan be determined. Table1  presents the values  of Ms obtained  for bo th the solvothermal and \nmicrowave -assisted samples. In both systems it is observed a decreases of Ms when the copper \nconcentration  increases  in the ferrite , as expected when the Fe2+ (~4B) is replaced by an ion \nwith smaller magnetic moment such as Cu2+ (~1B) and in agreement with previous results .52,53 \nFrom this results  it is also notice d that the microwave -assisted nanoparticles  (MW)  have larger \nmagne tization than those prepared by solvothermal method  (ST). This is striking considering that \nthe crystalline structure of MW nanoparticles corresponds to the maghemite oxidized phase with \nlower Ms than magnetite, i.e.   Ms(γ-Fe2O3)=74 emu/g   and Ms(Fe3O4)=84 emu/g  for bulk materials .54 \nThe origin of this result may be due to the higher pressure attained in the microwave synthesis \nthat improve the crystallinity of the nanoparticles,  reducing  magnetic disorder , and also due t o the \noverestimation of the magnetite  mass  because of the presence of iron hydroxide  impurities  in \nsolvothermal samples . At this point we would like to highlight  that these  system s show promising \nproperties to test their potential as magnetic catalysts. On one hand, the nanoparticles ' \nsuperparamagnetic behavior at room temperature reduces the  agglomeration and facilitates the \nnanoparticles dispersion in the solution; and on the other hand, their relative large magnetization, \ni.e. Ms=50-70 emu/g, would enable the nanoparticles magnetic ally-assisted harvesting from \nsolution after catalytic reactions, both properties particularly relevant for the design of magnetic \nnanocatalyst s for environmental remediation applications.  \n \n3.2. Catalytic evaluation  In order to  evalu ate the Fenton -like activity  of these nano catalysts, we performed EPR \nmeasurements of the nanoparticles dispersed in acetate buffer solution at pH=5, containing H 2O2 \nand using DMPO as spin trap. These measurements allow the  identif ication  and quantification of  \nthe free radicals produced in the reaction. Figure 4a  shows a representative EPR spectrum along \nwith its corresponding fitting curve.  The fitting curve results to the superposition of the resonance \nlines of the different free radicals generated in the rea ction. According to the NIEHS Spin -Trap \ndatabase,55  from the spectrum features and the fitting parameters, the resonance of four different \nfree radicals can be clearly recognized: •OH, •OOH, •CH 3, and •N. According to the Fenton -like \nreaction, the •OH and •OOH radicals were produc ed by  Fe2+/ Cu+ and  Fe3+/ Cu2+, respectively; \nwhile the •CH 3 signal comes from a secondary reaction between •OH and the DMSO  used to \ndissolve DMPO .23 Also, a small nitrone radical  signal is observed. However, this last one  is also \nobserved in the solution withou t the nanoparticles, being not resulting from oxidation process \nduring the studied reactions, so it was not considered in the analysis.23,56 All the spectra also shows \nthe resonance  corresponding to the MgO : Mn2+ sample used as a pattern to normalize the EPR \nintensity .   \nFig.4:  (a) Representative measurement of the free radicals generated by the catalysts, along with  \nthe spectrum fitting and  the corresponding deconvoluted spectra . Kinetic curves of the free radicals  \ncatalyzed  by the  Cu-doped oxidi zed nanoparticles fabricated by microwave -assisted method  (b-\nc); and, (d-f) by the cu -doped magnetite nanoparticles fabricated by  solvothermal  method .  \nThe kinetic reaction was followed by acquiring the EPR spectra for each set o f samples  as a \nfunction of the time . The quantity of radicals is directly proportional to the area of the EPR \nabsorption curve , which can be determined by the double integral of the measured spectrum.56 \nThe kinetic  of radical generation by  the Cu-doped magnetite  samples , ST0, ST1, and ST3 is shown \nin Figs.4d -f. From these figures it is notice that the •OH and •CH 3 are the main species  produced , \nwith a systematic decrease  of their concentration for increas ing copper content. Assuming that \nCu2+ replaces Fe2+ within the spinel structure, this result suggests  that Fe2+ ions have the highest \ncatalytic activity  at room temperature . On the other hand, the Cu-doped  oxidized samples , i.e. the \nbatch  fabricated by mi crowave assisted method;  produce at least ten times fewer  radicals than the  \nCu-doped magnetite , as depicted  in Figs.4b -c. This result is in agreement with the lower Fe2+/Fe \nratio in this set of samples measured by XPS, as compared with the Cu -doped magneti te. \nConsistently, a lower ROS concentration is expected due to the lower rate constant of Fe3+ than \nthat of Fe2+ in the Fenton reaction. Notice that, besides the  •OH and •CH 3, microwave -assisted \nsamples also produce an appreciable amount of •OOH radicals, as shown in Figs.4b -c. Actually, \nin sample MW4 the •OOH intensity exceeds that of the hydroxyl radical after 1 h of reaction time. \nThis response is attributed to the predomin ance of Fe3+ oxidation state of iron .13,23 Overall, the \nEPR measurements provide valu able insights into the mechanisms of free radicals generation by \nthe copper ferrite nanoparticles, highlighting the importance of Fe2+ ions and the impact of copper \nincorporation on the Fenton catalytic activity of the nanoparticles at room temperature.  \nIn order t o evaluate the ability of the synthesized nanoparticles to degrade organic compounds , \nwe conducted colorimetric  experiments using a  MB cationic dye . In these experiments the \nnano catalyst s and the MB were dis persed in a pH=5 acetate buffer and,  to ensure adsorption of \nthe dye onto the nanoparticles surface , the system was kept under agitation for two hours before \nadding  H2O2. Furthermore, control experiments, or blanks tests, were conducted for each condition \nto quantify MB degradation by hydrogen p eroxide alone, in absence of cat alyst. Figures 5 a and \n5b show  the MB discoloration  curves measured at room temperature using the nanocatalyst \nfabricated by  solvothermal and microwave -assisted method s, respectively. Nanoparticles \nfabricated by solvothermal route showed the  great performance for degrading MB, since the \nmagnetite ST0 sample exhibited a percentage of discoloration up to 80% in the first 15 minutes \nand up to 90% in 2 h. For this set of samples  the activity decreases with the copper incorporation,  \nfor example the ST3 nanoparticles  only exhibited an efficiency of 24% in 2 h. The activity observed \nat room temperature for this family of samples  can be attributed to the Fe2+ active ions at the \nnanoparti cle surface and, accordingly , the efficiency decreased with the substitution of iron by \ncopper. The EPR measurement s support this result as the Fe2+ was identified as the principal \nresponsible of  the free radical production at room temperature . On the othe r hand, none of the Cu -doped oxidized nanoparticles, fabricated b y microwave -assisted method,  were efficient for \ndegrading MB at room temperature  (Fig. 5b ). Resul t in agreement with the low Fe2+/Fe ratio \nobtained by XPS for these  samples  and the low free radical production measured by  EPR \nexperiments .  \n \n \nFig.5 : Methylene blue degradation experiments by solvothermal samples  measured  (a) at room \ntemperature with an adsorption time of t=2h;  (c) at T=60°C and adsorption time of t=2h ; and (e) at \nT=60°C with an  adsorption time of t=24h. Methylene blue degradation experiments by m icrowave -\nassisted samples measured (b) at room temperatur e with an adsorption time of t=2h; (d) at T=60°C \nwith an adsorption time of t=2h;  and (f) at T=90°C with an adsorption time of t=2h.  Control \nexperiments, indicated by dashed lines in each graph, were performed to quantify MB degradation \nby hydrogen peroxide alone, without the catalysts.  \n \nIt is well known that the catalytic reaction rate increases with the increasin g temperature due to \nthe higher kinetic energy of the molecules. Besides, a s mentioned at the introduction, different \nresidual effluents are produced above room temperatures, as it is the case of textile and paper \nindustries  16–19 Therefore, it is interesting to take advantage of this additional kinetic energy pr esent \nin some waste water  to increase the performance of the nanocatalysts to decompose organic \ncontaminants.  To anal yze the temperature dependence o n the reactions  and the stability of the \nmaterials , we performed colorimetric experiments up to 9 0°C with a similar protocol to the one \nmentioned above.  \n \nFigure 5 c shows t he MB oxidation experiments at 60°C using solvothermal samples . Surprisingly, \nthe MB  degradation  is lower at 60°C than the obtained at room temperature for the ST0 sample.  \nThis result can be explained by considering the accelerated oxidation from Fe2+ to Fe3+ as a \nconsequence of the  temperature , which  decreases the kinetic rate for the ROS production . For the \nST3 sample a slight increase of activity was observed at higher temperature , attributed to the \ncombined effect of iron oxidation and kinetic promotion of Cu catalyzed degradation pathways, \nexpected to rapidly increase with increasing temperature . This assumption  was confirmed  by \nrepeating the discoloration curve after  incubati ng the nanoparticles for  24 h at 60°C, to comple te \nthe surface oxidation  (Fig.5e). In this case the efficiency of ST0 sample was even lower than the \npresented in Figs. 5a and 5c, consistent ly with the lower kinetic of Fe3+ to catalyze the H 2O2 \ndecomposition in ROS . On the other hand, the ST3 activity remained almost the same  for both of \nthe adsorption times tested , suggesting a better response  and stability of copper  doped \nnanoparticles  to high temperature condition s.  \nThis observation is clearly confirmed by the discoloration experiments using the Cu -doped \nmaghemite  nanoparticles  (samples fabricated by microwave route) above room temperature. Figure 5d  shows the experiments carried out at 60°C, where it is observed that almost all the \nsamp les showed catalytic activity to degrade MB and its efficiency increased with the copper \ncontent.  When the MB oxidation experiment  is running at 90°C  the response of the nanocatalysts \nimproves significantly , reaching up to 90% percentage of MB discoloratio n in the first 30 minutes \nand almost 100% in 2 h. This result shows that the copper ferrite exhibits superior thermal stability \nand catalytic performance under elevated temperature conditions, maintaining its catalytic activity \nwithout significant degradat ion or loss of performance. It is noteworthy that increasing the \ntemperature in reactions mediated by iron -based catalyst is not always beneficial, and it is crucial \nto know the chemical kinetic of the active ions involved in the ROS generation, for the de sign of \nproper nanocatalys for specific work conditions.   The key role of co pper ions in enhancing the \ncatalytic activity of oxidized nanoparticles can be elucidated through an examination of the \nelectronic properties of Cu -doped maghemite. Employing Densi ty Functional Theory (DFT) \nalongside  with the functional Perdew, Burke and Ernzerhof (PBE) 57, Pires et al. 58 calculated th e \nelectronic density map of -Fe2O3 and Cu/-Fe2O3  at the (311) surface plane. These computations \nrevealed a lower electronic density at Cu sites, these more positive region exhibit heightened \nsusceptibility to interact with hydrogen peroxide molecules, thereby facilitating the generation of \n•OH radicals. Despite the advancements achieved through computational methods, a \ncomprehensive investigation of the electron transfer process at interfaces is still lacking to fully \nunderstand the peroxidase decomposi tion mechanism at the nanocatalyst's surface.59  \n \nNanocatalyst stability is also an important property desired in materials for environmental \napplications. With the aim to evaluate the stability of the samples with time, the free radical \nproduction  was followed by EPR  after different storage conditions .  Figure S3 of the \nSupplementa ry Information shows the •OH radical s produced by Cu 0.1Fe2.9O4 (MW1) and \nCu0.4Fe2.6O4 (MW4) nanoparticles upon synthesis and after 4 mon ths of storage in air and water. \nThe •OH production in the as -made samples decreases with the copper content due to copper \nsubstituting the most active  Fe2+ ion. For powder samples stored in air condition, Fe2+ oxidized to Fe3+, decreasing MW1's activity. Conversely, MW4, already highly oxidized and copper -activity \nreliant, retains its •OH production after 4 months in air. This effect is amplified in water storage, \nwhere after four months, the trend reverses, and •OH production increases with copper content . \nThese results signal that the Fe2+-dependent catalysts would become less efficient upon reuse, \nwhile copper -dependent catalysts are expected to maintain their efficiency  for longer times .  \nOn the other hand, the stability of the catalysts before and after the MB degradation experiments, \nwere conducted by evaluating the changes in the structure and morphology of the nanoparticles. \nThe degradation was carried out under the most efficient conditions for each catalyst, i.e. room \ntemperature for magnetite (ST0) and high temperature (60°C) for Cu 0.4Fe2.6O4 (MW4 ). Figure S4 -\na and c, included in the Supplementa ry Information , illustrate the diffractograms comparison  before \nand after catalysis for samples ST0 and MW4, respectively. For ST0, the spinel phase \ncharacteristic peaks remain  unchanged. Also it is observed that the  peaks at 17° and 23° ascribed \nto polymerized ethylene glycol are no longer observed after reaction, likely due to the high solubility \nof the ethylene glycol in water. Additionally, the pea k at 24° , attributed to traces of iron hydroxide , \nvanishes  as expected , given its lower stability compared to the ferrite structure of the nanoparticles. \nNo structural changes are observed in the MW4 sample after the reaction , according to the X -ray \ndiffra ctograms. TEM micrographs of samples ST0 and MW4 after catalysis are presented in Fig. \nS4-b and d, respectively , along with their corresponding size distribution pre - and post -catalysis. \nThe size distributions for ST0 and MW4 before and after catalysis show no significant differences, \nsuggesting minimal or no leaching during the process.  \n \nThe Fenton -like reaction assumes that the free radicals produced in the nanoparticles' surface \nreact with the organic molecules adsorbed on t he surface of the nanocatal yst. Th is oxidation \nreaction can be described by the nth -order equation:  \n𝑑𝐶\n𝑑𝑡=−𝑘𝑛𝐶𝑛 \nwhere C represent s the organic molecu les concentration, kn is the reaction constant and n is the \norder of the reaction.  Usually , the Fenton -like oxidation follows a pseudo -second order dependence  𝐶0/𝐶=𝑘2𝐶0𝑡+1  , i.e. the kinetic depends on the pollutant or dye concentrations .60,61 \nOn the contrary, if the reaction is independent of the  substrates concentration,  the kinetics follow s \na pseudo -first order dynamics 𝑙𝑛(𝐶0\n𝐶)=𝑘1𝑡.8,62 Figures S5 and S6 in the Supplementary \nInformation include the analysis of the resul ts, adjusted with the pseudo -first order and pseudo -\nsecond order models, respectively; and the corresponding fitting parameters are reported in Table \n2.  At room temperature, the system with higher pseudo -first order kinetic rate is the magnetite  \n(ST0) , reaching k1=0.07(2) min-1 value, while in the doped samples the activity is negligible. \nInstead, the constant rate of the MB degradation by over oxidized MWX samples at 90 °C, \nsystematically increases with the Cu concentration up to k1= 0.10(2) min-1 for the sample MW4 \n(Cu0.4Fe2.6O4). The obtained k1 values confirm the good response of the materials to degrade MB \ncompared to the previous reports of heterogeneous Fenton and Fenton -like catalysts which are \nreported in the k1 =0.0053 min-1- 0.1455 min-1 range. 63–68 In the case of the adjustment with a \nsecond order equation, similar trends are obtained, with k2=0.0020(3) min-1mg-1L for the magnetite \nat room temperature, and k2=0.0039(4) min-1mg-1L for the sample Cu0.4Fe2.6O4 (MW4) m easured \nat 90  °C.  \nThe regression coefficients  obtained from the fitting, R2, are in the range R2=0.82-0.991 for the \npseudo -first order reaction, and R2=0.95 -0.99997 for the  pseudo -second order reaction model,  \nwhich signal t hat the kinetic is better described with the pseudo -second order reaction equation . \nThis result suggests that the amount of MB molecules adsorbed on the catalyst depends on its \ninitial  concentration and determines the kinetic of the reaction.9 \n \nSample  ST0 ST3 MW1 MW2 MW4 \nTemp.  RT 60°C RT 60°C 60°C 90°C 60°C 90°C 60°C 90°C \nPFO k1 \n(min-1) 0.07(2)  0.010(1)  0.009(1)  0.0032(2)  0.0028(7)  0.032(4)  0.0044(5)  0.065(9)  0.009(1)  0.10(2)  \nR2 0.85 0.97 0.94 0.991 0.82 0.96 0.97 0.94 0.96 0.91 PSO k2 \n(min-1 \nmg-1L) 0.0020(3)  0.00011(1)  0.00017(3)  0.000034(2)  0.000029(8)  0.000047(4)  0.00010(1)  0.00049(2)  0.00159(7)  0.0039(4)  \nR2 0.95 0.9994  0.9990  0.99997  0.9995  0.998 0.9998  0.996 0.9993  0.97 \n \nTable 2. Reaction constants for methylene blue degradation: Data fitted using Pseudo -First-Order \n(PFO) and Pseudo -Second -Order (PSO) models. The table also includes the corresponding \nregression coefficients for each fit.  \n \n4. Conclusions  \nWe have evaluated the catalytic efficiency of Cu doped  magnetite and maghemit e nanoparticles \nwith average size of  11 nm, obtained from solvothermal and microwave -assisted methods, \nrespectively. We found t hat the magnetite nanoparticles present an excellent performance for \noxidizing the organic dye methylene blue at room temperature, producing up to a 90% of \ndiscoloration  in 2 h. The catalytic activity was attributed to Fe2+ centers  that generate •OH in the  \nheterogeneous Fenton reaction , which are the main specie s responsible for the MB oxidation.  This \ndegradation efficiency decreased notably with increasing Cu content. Consistently, th e •OH  \nspecie s is systematic ally reduced when the  Cu concentration  increases . However, a bove room \ntemperature, the magnetite loss es its  efficiency as nanocatalyst due to the surface oxidation and \nbecause of the low rate constant of the Fe3+/Fe2+ redox cycle  in the Fenton reaction. In this \ncondition the role of copper bec ame relevant, with the samples with the highest percentage of \ncopper being those that presented a better efficiency as catalysts. In fact, at 90°C the CuₓFe ₃₋ₓO₄ \nwith x=0.4 produce a 90% of MB discoloration in the first 30 minutes and a complete discolorat ion \nin less than 2 h.  \nThese results show that the nanoparticle composition and the oxidation state of the surface active \nions, determine the nanoparticle reactivity and the nature of the free radicals produced, providing a tool to engineering more efficien t nanocatalyst s. In particular,  we have demonstrate d that while \nmagnetite nanocatalyst is effective to degrade dyes at room temperature, it is also highly unstable \ncompound, easily prone to oxidation under normal conditions, and particularly at high \ntemperatures. Instead, copper ferrite has an advantage over magnetite in terms of stability being \na superior alternative for catalytic applications  at higher temper ature. Given that many industrial \nresidual effluents are produced above  room temperatures, as observed in textile and paper \nindustries, leveraging this additional kinetic energy becomes interesting for enhancing the \nperformance of nanocatalysts in decomposing organic contaminants. In summary, our research \ncontributes valuable  insights that could pave the way for the development of more efficient \nnanocatalysts, with practical applications in addressing environmental challenges associated with \nindustrial effluents.  \n \n5. Declaration  of interest  \nThe authors declare that they have no known competing financial interests or personal \nrelationships that could have appeared to influence the work reported in this paper.  \n6. CRediT authorship contribution statement  \nNahuel Nuñez: Writing – Original Draft , Conceptualization, Investigation, Visualization. Enio  Lima \nJr.: Investigation. Marcelo Vásquez Mansilla:  Investigation . Gerardo F. Goya:  Funding \nacquisition , Project administration.  Álvaro Gallo -Cordova:  Investigation. Maria del Puerto \nMorales:  Supervisi on, Resources. Elin L. Winkler:  Writing – Review & Editing,  Conceptualization, \nSupervision, Resources. The manuscript was written through contributions from all authors. All \nauthors have given approval to the final version of the manuscript.  \n7. Acknowledgemen t The authors thank  to the Argentine government agency ANPCyT for providing financial support for \nthis work through Grants No. PICT -2019 -02059, as well as to UNCuyo for their support through \nGrant No. 06/C029 -T1. Additionally, this research received partia l funding from Project PDC2021 -\n12109 -I00 (MICRODIAL) MCIN/AEI/10.13039/501100011033 through the European Union \n“NextGenerationEU/PRTR” . Furthermore, the authors acknowledge the support of Project H2020 -\nMSCA -RISE -2020 (NESTOR) PROJECT Nº 101007629, funded by the EU -commission.  \n \n8. References  \n(1)  Mohammed, L.; Gomaa, H. G.; Ragab, D.; Zhu, J. Magnetic Nanoparticles for \nEnvironmental and Biomedical Applications: A Review. Particuology  2017 , 30, 1–14. \nhttps://doi.org/ 10.1016/j.partic.2016.06.001.  \n(2)  Mapossa, A. B.; Mhike, W.; Adalima, J. L.; Tichapondwa, S. Removal of Organic Dyes \nfrom Water and Wastewater Using Magnetic Ferrite -Based Titanium Oxide and Zinc Oxide \nNanocomposites: A Review. Catalysts  2021 , 11 (12). \nhttps://doi.org/10.3390/catal11121543.  \n(3)  Goya, G. F.; Mayoral, A.; Winkler, E.; Zysler, R. D.; Bagnato, C.; Raineri, M.; Fuentes -\nGarcía, J. A.; Lima, E. Next Generation of Nanozymes: A Perspective of the Challenges to \nMatch Biological Performance. J. Appl . Phys.  2021 , 130 (19), 190903. \nhttps://doi.org/10.1063/5.0061499.  \n(4)  Rahim Pouran, S.; Abdul Raman, A. A.; Wan Daud, W. M. A. Review on the Application of \nModified Iron Oxides as Heterogeneous Catalysts in Fenton Reactions. J. Clean. Prod.  \n2014 , 64, 24–35. https://doi.org/10.1016/j.jclepro.2013.09.013.  \n(5)  Thomas, N.; Dionysiou, D. D.; Pillai, S. C. Heterogeneous Fenton Catalysts: A Review of \nRecent Advances. J. Hazard. Mater.  2021 , 404 (PB), 124082. https://doi.org/10.1016/j.jhazmat.2020.124082.  \n(6)  Xu, M.; Wu, C.; Zhou, Y. Advancements in the Fenton Process for Wastewater Treatment. \nIn Advanced Oxidation Processes - Applications, Trends, and Prospects ; IntechOpen, \n2020; Vol. 11, p 13. https://doi.org/10.5772/intechopen.90256.  \n(7)  Bokare, A. D.; Choi,  W. Review of Iron -Free Fenton -like Systems for Activating H2O2 in \nAdvanced Oxidation Processes. J. Hazard. Mater.  2014 , 275, 121 –135. \nhttps://doi.org/10.1016/j.jhazmat.2014.04.054.  \n(8)  Mitsika, E. E.; Christophoridis, C.; Fytianos, K. Fenton and Fenton -like Oxidation of \nPesticide Acetamiprid in Water Samples: Kinetic Study of the Degradation and \nOptimization Using Response Surface Methodology. Chemosphere  2013 , 93 (9), 1818 –\n1825. https://doi.org/10.1016/j.chemosphere.2013.06.033.  \n(9)  Quadrado, R. F. N.; Fajardo, A. R. Fast Decolorization of Azo Methyl Orange via \nHeterogeneous Fenton and Fenton -like Reactions Using Alginate -Fe2+/Fe3+ Films as \nCatalysts. Carbohydr. Polym.  2017 , 177 (June), 443 –450. \nhttps://doi.org/10.1016/j.carbpol.2017. 08.083.  \n(10)  Jain, B.; Singh, A. K.; Kim, H.; Lichtfouse, E.; Sharma, V. K. Treatment of Organic \nPollutants by Homogeneous and Heterogeneous Fenton Reaction Processes. Environ. \nChem. Lett.  2018 , 16 (3), 947 –967. https://doi.org/10.1007/s10311 -018-0738 -3. \n(11)  Díaz-Ufano, C.; Gallo -Cordova, A.; Santiandreu, L.; Veintemillas -Verdaguer, S.; Sáez, R.; \nTorralvo Fernández, M. J.; Morales, M. del P. Maximizing the Adsorption Capacity of Iron \nOxide Nanocatalysts for the Degradation of Organic Dyes. Colloids Surfa ces A \nPhysicochem. Eng. Asp.  2023 , 658. https://doi.org/10.1016/j.colsurfa.2022.130695.  \n(12)  Zazo, J. A.; Pliego, G.; Blasco, S.; Casas, J. A.; Rodriguez, J. J. Intensification of the \nFenton Process by Increasing the Temperature. Ind. Eng. Chem. Res.  2011 , 50 (2), 866 –870. https://doi.org/10.1021/ie101963k.  \n(13)  Gallo -Cordova, A.; Castro, J. J.; Winkler, E. L.; Lima, E.; Zysler, R. D.; Morales, M. del P.; \nOvejero, J. G.; Streitwieser, D. A. Improving Degradation of Real Wastewaters with Self -\nHeating Magne tic Nanocatalysts. J. Clean. Prod.  2021 , 308 (October 2020), 127385. \nhttps://doi.org/10.1016/j.jclepro.2021.127385.  \n(14)  Yan, B.; Shi, Z.; Lin, J.; Zhang, L.; Han, L.; Shi, X.; Yang, Q. Boosting Heterogeneous \nFenton Reactions for Degrading Organic Dyes vi a the Photothermal Effect under Neutral \nConditions. Environ. Sci. Nano  2022 , 9 (2), 532 –541. \nhttps://doi.org/10.1039/D1EN00874A.  \n(15)  Hussain, S.; Aneggi, E.; Trovarelli, A.; Goi, D. Removal of Organics from Landfill Leachate \nby Heterogeneous Fenton -like Oxidation over Copper -Based Catalyst. Catalysts  2022 , 12 \n(3), 338. https://doi.org/10.3390/catal12030338.  \n(16)  Yaseen, D. A.; Scholz, M. Textile Dye Wastewater Characteristics and Constituents of \nSynthetic Effluents: A Critical Review ; Springer Berlin Hei delberg, 2019; Vol. 16. \nhttps://doi.org/10.1007/s13762 -018-2130 -z. \n(17)  Lodi, A.; Modesto, M. Analysis of the Thermal Exploitation of the Vinasse from Sugarcane \nEthanol Production through Different Configurations of an Organic Rankine Cycle. Chem. \nEng. Tr ans. 2018 , 65, 619 –624. https://doi.org/10.3303/CET1865104.  \n(18)  Niz, M. Y. K.; Fuentes, L.; Etchebehere, C.; Zaiat, M. Sugarcane Vinasse Extreme \nThermophilic Digestion: A Glimpse on Biogas Free Management. Bioprocess Biosyst. \nEng. 2021 , 44 (7), 1405 –1421 . https://doi.org/10.1007/s00449 -021-02517 -7. \n(19)  Covinich, L.; Felissia, F.; Massa, P.; Fenoglio, R.; Area, M. C. Kinetic Modeling of a \nHeterogeneous Fenton -Type Oxidative Treatment of Complex Industrial Effluent. Int. J. \nInd. Chem.  2018 , 9 (3), 215 –229. https://doi.org/10.1007/s40090 -018-0151 -6. (20)  Hashemian, S. Fenton -like Oxidation of Malachite Green Solutions: Kinetic and \nThermodynamic Study. J. Chem.  2013 , 2013 . https://doi.org/10.1155/2013/809318.  \n(21)  Dong, H.; Du, W.; Dong, J.; C he, R.; Kong, F.; Cheng, W.; Ma, M.; Gu, N.; Zhang, Y. \nDepletable Peroxidase -like Activity of Fe3O4 Nanozymes Accompanied with Separate \nMigration of Electrons and Iron Ions. Nat. Commun.  2022 , 13 (1). \nhttps://doi.org/10.1038/s41467 -022-33098 -y. \n(22)  Hussa in, S.; Aneggi, E.; Goi, D. Catalytic Activity of Metals in Heterogeneous Fenton -like \nOxidation of Wastewater Contaminants: A Review. Environ. Chem. Lett.  2021 , 19 (3), \n2405 –2424. https://doi.org/10.1007/s10311 -021-01185 -z. \n(23)  Moreno Maldonado, A. C.; W inkler, E. L.; Raineri, M.; Toro Córdova, A.; Rodríguez, L. M.; \nTroiani, H. E.; Mojica Pisciotti, M. L.; Mansilla, M. V.; Tobia, D.; Nadal, M. S.; Torres, T. E.; \nDe Biasi, E.; Ramos, C. A.; Goya, G. F.; Zysler, R. D.; Lima, E. Free -Radical Formation by \nthe Peroxidase -Like Catalytic Activity of MFe 2 O 4 (M = Fe, Ni, and Mn) Nanoparticles. J. \nPhys. Chem. C  2019 , 123 (33), 20617 –20627. https://doi.org/10.1021/acs.jpcc.9b05371.  \n(24)  Wang, D.; Wu, H.; Wang, C.; Gu, L.; Chen, H.; Jana, D.; Feng, L.; Liu, J.; Wa ng, X.; Xu, \nP.; Guo, Z.; Chen, Q.; Zhao, Y. Self -Assembled Single -Site Nanozyme for Tumor -Specific \nAmplified Cascade Enzymatic Therapy. Angew. Chemie - Int. Ed.  2021 , 60 (6), 3001 –\n3007. https://doi.org/10.1002/anie.202008868.  \n(25)  Xia, F.; Shi, Q.; Nan, Z . Improvement of Peroxidase -like Activity and Application for \nDetection of H2O2 and Dopamine for SDBS -Cu-CuFe2O4. Surfaces and Interfaces  2021 , \n24 (December 2020), 101109. https://doi.org/10.1016/j.surfin.2021.101109.  \n(26)  Bao, C.; Zhang, H.; Zhou, L.; Sh ao, Y.; Ma, J.; Wu, Q. Preparation of Copper Doped \nMagnetic Porous Carbon for Removal of Methylene Blue by a Heterogeneous Fenton -like \nReaction. RSC Adv.  2015 , 5 (88), 72423 –72432. https://doi.org/10.1039/C5RA12621E.  (27)  Chen, Y.; Wei, A.; Ma, X.; Tianyu , W.; Chen, A. Copper -Incorporated Dendritic \nMesoporous Silica Nanospheres and Enhanced Chemical Mechanical Polishing (CMP) \nPerformance via Cu2+/H2O2 Heterogeneous Fenton -like System. Appl. Surf. Sci.  2022 , \n601 (July), 154262. https://doi.org/10.1016/j.aps usc.2022.154262.  \n(28)  Khan, A.; Valicsek, Z.; Horváth, O. Comparing the Degradation Potential of Copper(II), \nIron(II), Iron(III) Oxides, and Their Composite Nanoparticles in a Heterogeneous Photo -\nFenton System. Nanomaterials  2021 , 11 (1), 1 –18. https://do i.org/10.3390/nano11010225.  \n(29)  Zhou, Z.; Liu, T.; Wu, J.; Li, H.; Chu, S.; Zhu, X.; Zhang, L.; Lu, J.; Ivanets, A.; Davronbek, \nB.; Ma, K.; Su, X. Preparation of Copper -Based Catalysts from Electroplating Sludge by \nUltrasound Treatment and Their Antibiot ic Degradation Performance. Environ. Res.  2023 , \n216 (P2), 114567. https://doi.org/10.1016/j.envres.2022.114567.  \n(30)  Huang, X.; Du, W.; Chen, R.; Chen, F. Adsorption -Enhanced Catalytic Wet Peroxide \nOxidation of Aromatic Compounds on Ionothermally Synthesised Copper -Doped \nMagnetite Magnetic Nanoparticles. Environ. Chem.  2020 , 17 (6), 426. \nhttps://doi.org/10.1071/EN19245.  \n(31)  Twinkle; Singh, K.; Bansal, S. A.; Kumar, S. Graphene Oxide (GO)/Copper Doped \nHematite (α -Fe2O3) Nanoparticles for Organic Pollutants Degradation Applications at \nRoom Temperature and Neutral PH. Mater. Res. Express  2019 , 6 (11), 0 –11. \nhttps://doi.org /10.1088/2053 -1591/ab4459.  \n(32)  Yang, J.; Huang, R.; Cao, Y.; Wang, H.; Ivanets, A.; Wang, C. Heterogeneous Fenton \nDegradation of Persistent Organic Pollutants Using Natural Chalcopyrite: Effect of Water \nMatrix and Catalytic Mechanism. Environ. Sci. Pollu t. Res.  2022 , 29 (50), 75651 –75663. \nhttps://doi.org/10.1007/s11356 -022-21105 -0. \n(33)  Brillas, E.; Garcia -Segura, S. Benchmarking Recent Advances and Innovative Technology \nApproaches of Fenton, Photo -Fenton, Electro -Fenton, and Related Processes: A Review on the Relevance of Phenol as Model Molecule. Sep. Purif. Technol.  2020 , 237 \n(November 2019), 116337. https://doi.org/10.1016/j.seppur.2019.116337.  \n(34)  Wang, Y.; Zhao, H.; Li, M.; Fan, J.; Zhao, G. Magnetic Ordered Mesoporous Copper \nFerrite as a Heteroge neous Fenton Catalyst for the Degradation of Imidacloprid. Appl. \nCatal. B Environ.  2014 , 147, 534 –545. https://doi.org/10.1016/j.apcatb.2013.09.017.  \n(35)  Lyu, L.; Zhang, L.; Hu, C. Enhanced Fenton -like Degradation of Pharmaceuticals over \nFramework Copper Species in Copper -Doped Mesoporous Silica Microspheres. Chem. \nEng. J.  2015 , 274, 298 –306. https://doi.org/10.1016/j.cej.2015.03.137.  \n(36)  Liu, C.; Lu, J.;  Hu, J.; Liu, L.; An, W.; Liang, Y.; Cui, W. Dual Reaction Centers Promote \nAdsorption -Photo Fenton Synergistic Efficient Removal of Tetracycline by Reduced \nGraphene Oxide/CuFe2O4 -Oxygen Vacancies. Appl. Surf. Sci.  2022 , 606 (September), \n154890. https://doi .org/10.1016/j.apsusc.2022.154890.  \n(37)  Ding, R. R.; Li, W. Q.; He, C. S.; Wang, Y. R.; Liu, X. C.; Zhou, G. N.; Mu, Y. Oxygen \nVacancy on Hollow Sphere CuFe2O4 as an Efficient Fenton -like Catalysis for Organic \nPollutant Degradation over a Wide PH Range. Appl. Catal. B Environ.  2021 , 291 (March), \n120069. https://doi.org/10.1016/j.apcatb.2021.120069.  \n(38)  Liu, Y.; Guo, Z.; Li, F.; Xiao, Y.; Zhang, Y.; Bu, T.; Jia, P.; Zhe, T.; Wang, L. Multifunctional \nMagnetic Copper Ferrite Nanoparticles as Fenton -like Rea ction and Near -Infrared \nPhotothermal Agents for Synergetic Antibacterial Therapy. ACS Appl. Mater. Interfaces  \n2019 , 11 (35), 31649 –31660. https://doi.org/10.1021/acsami.9b10096.  \n(39)  Tian, X.; Jin, H.; Nie, Y.; Zhou, Z.; Yang, C.; Li, Y.; Wang, Y. Heterog eneous Fenton -like \nDegradation of Ofloxacin over a Wide PH Range of 3.6 –10.0 over Modified Mesoporous \nIron Oxide. Chem. Eng. J.  2017 , 328, 397 –405. https://doi.org/10.1016/j.cej.2017.07.049.  \n(40)  Hussain, S.; Aneggi, E.; Trovarelli, A.; Goi, D. Heterogeneous Fenton -like Oxidation of Ibuprofen over Zirconia -Supported Iron and Copper Catalysts: Effect of Process Variables. \nJ. Water Process Eng.  2021 , 44 (June), 102343. \nhttps://doi.org/10.1016/j.jwpe. 2021.102343.  \n(41)  Gallo -Cordova, Á.; Espinosa, A.; Serrano, A.; Gutiérrez, L.; Menéndez, N.; del Puerto \nMorales, M.; Mazarío, E. New Insights into the Structural Analysis of Maghemite and (MFe \n2 O 4 , M = Co, Zn) Ferrite Nanoparticles Synthesized by a Mic rowave -Assisted Polyol \nProcess. Mater. Chem. Front.  2020 , 4 (10), 3063 –3073. \nhttps://doi.org/10.1039/D0QM00460J.  \n(42)  Bandala, E. R.; Peláez, M. A.; García -López, A. J.; Salgado, M. de J.; Moeller, G. \nPhotocatalytic Decolourisation of Synthetic and Real T extile Wastewater Containing \nBenzidine -Based Azo Dyes. Chem. Eng. Process. Process Intensif.  2008 , 47 (2), 169 –\n176. https://doi.org/10.1016/j.cep.2007.02.010.  \n(43)  Gallo -Cordova, A.; Veintemillas -Verdaguer, S.; Tartaj, P.; Mazarío, E.; Morales, M. del P.;  \nOvejero, J. G. Engineering Iron Oxide Nanocatalysts by a Microwave -Assisted Polyol \nMethod for the Magnetically Induced Degradation of Organic Pollutants. Nanomaterials  \n2021 , 11 (4), 1052. https://doi.org/10.3390/nano11041052.  \n(44)  Yang, X.; Chen, W.; Hua ng, J.; Zhou, Y.; Zhu, Y.; Li, C. Rapid Degradation of Methylene \nBlue in a Novel Heterogeneous Fe3O4 @rGO@TiO2 -Catalyzed Photo -Fenton System. \nSci. Rep.  2015 , 5 (1), 10632. https://doi.org/10.1038/srep10632.  \n(45)  Vasquez -Medrano, R.; Prato -Garcia, D.; Vedr enne, M. Ferrioxalate -Mediated Processes. \nIn Advanced Oxidation Processes for Waste Water Treatment ; Elsevier, 2018; pp 89 –113. \nhttps://doi.org/10.1016/B978 -0-12-810499 -6.00004 -8. \n(46)  Clotilde Apua, M.; Madiba, M. S. Leaching Kinetics and Predictive Mode ls for Elements \nExtraction from Copper Oxide Ore in Sulphuric Acid. J. Taiwan Inst. Chem. Eng.  2021 , \n121, 313 –320. https://doi.org/10.1016/j.jtice.2021.04.005.  (47)  Granath, T.; Mandel, K.; Löbmann, P. The Significant Influence of the PH Value on Citrate \nCoordination upon Modification of Superparamagnetic Iron Oxide Nanoparticles. Part. \nPart. Syst. Charact.  2022 , 39 (3), 534 –545. https://doi.org/10.1002/ppsc.202100279.  \n(48)  Haneda, K.; Morrish, A. H. Vacancy Ordering in γ -Fe2O3 Small Particles. Solid Stat e \nCommun.  1977 , 22 (12), 779 –782. https://doi.org/10.1016/0038 -1098(77)90067 -9. \n(49)  Galloni, M. G.; Campisi, S.; Marchetti, S. G.; Gervasini, A. Environmental Reactions of Air -\nQuality Protection on Eco -Friendly Iron -Based Catalysts. Catalysts  2020 , 10 (12), 1415. \nhttps://doi.org/10.3390/catal10121415.  \n(50)  Jayaramudu, T.; Raghavendra, G. M.; Varaprasad, K.; Reddy, G. V. S.; Reddy, A. B.; \nSudhakar, K.; Sadiku, E. R. Preparation and Characterization of Poly(Ethylene Glycol) \nStabilized Nano Silver Particles by a Mechanochemical Assisted Ball Mill Process. J. Ap pl. \nPolym. Sci.  2016 , 133 (7), n/a -n/a. https://doi.org/10.1002/app.43027.  \n(51)  Barron, M. K.; Young, T. J.; Johnston, K. P.; Williams, R. O. Investigation of Processing \nParameters of Spray Freezing into Liquid to Prepare Polyethylene Glycol Polymeric \nParticles for Drug Delivery. AAPS PharmSciTech  2003 , 4 (2), 1 –13. \nhttps://doi.org/10.1208/pt040212.  \n(52)  Latiff, H.; Kishimoto, M.; Sharmin, S.; Kita, E.; Yanagihara, H. Effect of Copper \nSubstitution on Fe3O4 Particles Prepared via Coprecipitation and Flux M ethods. IEEE \nTrans. Magn.  2017 , 53 (1), 5 –8. https://doi.org/10.1109/TMAG.2016.2596291.  \n(53)  Nakhjavan, B.; Tahir, M. N.; Panthöfer, M.; Gao, H.; Schladt, T. D.; Gasi, T.; Ksenofontov, \nV.; Branscheid, R.; Weber, S.; Kolb, U.; Schreiber, L. M.; Tremel, W. Synthesis, \nCharacterization and Functionalization of Nearly Mono -Disperse Copper Ferrite \nCuxFe3−xO4 Nanoparticles. J. Mater. Chem.  2011 , 21 (19), 6909. \nhttps://doi.org/10.1039/c0jm04577b.  (54)  O’Handley, R. C. Modern Magnetic Materials: Principles and App lications ; 1999.  \n(55)  National Institute of Environmental Health Sciences -NIEHS, U. Spin Trap Database . \nhttps://tools.niehs.nih.gov/stdb/index.cfm).  \n(56)  Raineri, M.; Winkler, E. L.; Torres, T. E.; Vasquez Mansilla, M.; Nadal, M. S.; Zysler, R. D.; \nLima , E. Effects of Biological Buffer Solutions on the Peroxidase -like Catalytic Activity of \nFe 3 O 4 Nanoparticles. Nanoscale  2019 , 11 (39), 18393 –18406. \nhttps://doi.org/10.1039/C9NR05799D.  \n(57)  Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Ap proximation Made Simple. \nPhys. Rev. Lett.  1996 , 77 (18), 3865 –3868. https://doi.org/10.1103/PhysRevLett.77.3865.  \n(58)  Pires, M. D. S.; Nogueira, F. G. E.; Torres, J. A.; Lacerda, L. C. T.; Corrêa, S.; Pereira, M. \nC.; Ramalho, T. C. Experimental and Theore tical Study on the Reactivity of Maghemite \nDoped with Cu 2+ in Oxidation Reactions: Structural and Thermodynamic Properties \ntowards a Fenton Catalyst. RSC Adv.  2016 , 6 (84), 80830 –80839. \nhttps://doi.org/10.1039/C6RA11032K.  \n(59)  Nørskov, J. K.; Abild -Peder sen, F.; Studt, F.; Bligaard, T. Density Functional Theory in \nSurface Chemistry and Catalysis. Proc. Natl. Acad. Sci.  2011 , 108 (3), 937 –943. \nhttps://doi.org/10.1073/pnas.1006652108.  \n(60)  Díaz-Ufano, C.; Gallo -Cordova, A.; Santiandreu, L.; Veintemillas -Verdaguer, S.; Sáez, R.; \nTorralvo Fernández, M. J.; Morales, M. del P. Maximizing the Adsorption Capacity of Iron \nOxide Nanocatalysts for the Degradation of Organic Dyes. Colloids Surfaces A \nPhysicochem. Eng. Asp.  2023 , 658 (December 2022). \nhttps://doi.org/1 0.1016/j.colsurfa.2022.130695.  \n(61)  Wang, S. A Comparative Study of Fenton and Fenton -like Reaction Kinetics in \nDecolourisation of Wastewater. Dye. Pigment.  2008 , 76 (3), 714 –720. https://doi.org/10.1016/j.dyepig.2007.01.012.  \n(62)  Ivanets, A.; Prozorovich, V.; Roshchina, M.; Grigoraviciute -Puroniene, I.; Zarkov, A.; \nKareiva, A.; Wang, Z.; Srivastava, V.; Sillanpaa, M. Heterogeneous Fenton Oxidation \nUsing Magnesium Ferrite Nanoparticles for Ibuprofen Removal from Wastewater: \nOptimiza tion and Kinetics Studies. J. Nanomater.  2020 , 2020 . \nhttps://doi.org/10.1155/2020/8159628.  \n(63)  Wang, Q.; Tian, S.; Ning, P. Degradation Mechanism of Methylene Blue in a \nHeterogeneous Fenton -like Reaction Catalyzed by Ferrocene. Ind. Eng. Chem. Res.  \n2014 , 53 (2), 643 –649. https://doi.org/10.1021/ie403402q.  \n(64)  Qin, Q.; Liu, Y.; Li, X.; Sun, T.; Xu, Y. Enhanced Heterogeneous Fenton -like Degradation \nof Methylene Blue by Reduced CuFe 2 O 4. RSC Adv.  2018 , 8 (2), 1071 –1077. \nhttps://doi.org/10.1039/C7RA12488K . \n(65)  Choquehuanca, A.; Ruiz -Montoya, J. G.; La Rosa -Toro Gómez, A. Discoloration of \nMethylene Blue at Neutral PH by Heterogeneous Photo -Fenton -like Reactions Using \nCrystalline and Amorphous Iron Oxides. Open Chem.  2021 , 19 (1), 1009 –1020. \nhttps://doi.or g/10.1515/chem -2021 -0077.  \n(66)  Shi, G.; Zeng, S.; Liu, Y.; Xiang, J.; Deng, D.; Wu, C.; Teng, Q.; Yang, H. Efficient \nHeterogeneous Fenton -like Degradation of Methylene Blue Using Green Synthesized \nYeast Supported Iron Nanoparticles. Ecotoxicol. Environ. S af. 2023 , 263, 115240. \nhttps://doi.org/10.1016/j.ecoenv.2023.115240.  \n(67)  Michálek, J.; Domnina, K.; Kvorková, V.; Šefčovičová, K.; Mončeková, K.; Soldán, M. \nHeterogeneous Fenton -Like Oxidation of Methylene Blue Using Alternative Catalysts. Res. \nPap. Fac.  Mater. Sci. Technol. Slovak Univ. Technol.  2021 , 29 (48), 91 –97. \nhttps://doi.org/10.2478/rput -2021 -0009.  (68)  Gao, W.; Zhang, G.; Zhang, X.; Zhou, S.; Wang, Z. Degradation of Methylene Blue in the \nPhoto -Fenton -Like Process with WO3 -Loaded Porous Carbon N itride Nanosheet Catalyst. \nWater  2022 , 14 (16), 2569. https://doi.org/10.3390/w14162569.  \n    \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Supplementary Information  \nEffect of the temperature and copper doping on the heterogeneous Fenton \nactivity of 𝑪𝒖 𝒙𝑭𝒆 𝟑−𝒙𝑶𝟒 nanoparticles  \nNahuel Nuñez1,2,3*, Enio Lima Jr.1,2, Marcelo Vásquez Mansilla1,2, Gerardo F. Goya4,5,  \nÁlvaro Gallo -Cordova6, María del Puerto Morales6, Elin L. Winkler1,2,3*  \n \n1 Resonancias Magnéticas, Gerencia de Física, Centro Atómico Bariloche, Av. Bustillo 9500, (8400) S. C. \nde Bariloche (RN), Argentina.  \n2 Instituto de Nanociencia y Nanotecnología (CNEA -CONICET), Nodo Barilo che, Av. Bustillo 9500, (8400) \nS. C. de Bariloche (RN), Argentina.  \n3 Instituto Balseiro, CNEA -UNCuyo, Av. Bustillo 9500, (8400) S. C. de Bariloche (RN), Argentina  \n4 Dept. Física de la Materia Condensada, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009,  Zaragoza, \nSpain  \n5 Instituto de Nanociencia y Materiales de Aragón, CSIC -Universidad de Zaragoza, C/ Mariano Esquillos \nS/N, 50018, Zaragoza, Spain  \n6 Instituto de Ciencia de Materiales de Madrid, ICMM/CSIC, C/ Sor Juana Inés de la Cruz 3, 28049, Madrid, \nSpain  \n *Corresponding authors : nahuel.nunez@ib.edu.ar  \n \n \n \n \n XPS characterization.  We p erformed XPS measurements of the Fe 2 P3/2 absorption of  \nsolvothermal and microwave -assisted samples , which are presented in Fig.S1  and Fig.S2  \nrespectively. The spectra obtained were fitted with two multiplets related to Fe2+ and Fe3+ \nrespectively, as done by Grosvenor et al.45, and the fitting parameters are presented in TableS1 .  \n \nFig.S1: XPS spectra and fit of the Fe 2 P3/2 absorption in the solvothermal samples. Peaks p1, p2 \nand p3 are from Fe2+ ion; peaks p4, p5, p6 and p7 are from Fe3+ ion. The peaks position for each \nof the 3 peaks related to the 𝐅𝐞𝟐+ and 4 peaks related to the 𝐅𝐞𝟑+ were extr acted from reference \n45 \n \n \nFig.S2: XPS spectra and fit of the Fe 2 P3/2 absorption in the microwave -assisted samples. Peaks \np1, p2 and p3 are from Fe2+ ion; pea ks p4, p5, p6 and p7 are from Fe3+ ion. The peaks position \nfor each of the 3 peaks related to the 𝐅𝐞𝟐+ and 4 peaks related to the 𝐅𝐞𝟑+ were extracted from \nreference . 45 \n \nIdentificat\nion 𝐅𝐞𝟐+ 𝐅𝐞𝟑+ Satellite  \n peak  p1 p2 p3 p4 p5 p6 p7 LE HE \nBE (eV)  708.50\n(2) 709.50\n(3) 710.40\n(1) 710.30\n(2) 711.30\n(2) 712.60\n(3) 714.00\n(4) 707.1\n(2) 718.9\n(5) \nSample  Area  𝐅𝐞𝟐+/\nFe \nratio  \nST0 583 600 209 984 895 636 305 662 3579  0.33 \nST1 125 129 45 218 199 141 67 0 2066  0.32 \nST3 406 419 146 954 868 617 295 0 1997  0.26 \nMW0  106 110 38 689 627 446 213 0 2555  0.11 \nMW1  334 344 120 1435  1306  928 444 0 5040  0.16 \nMW2  270 278 97 996 906 644 308 595 3754  0.18 \nMW3  85 87 30 540 491 349 167 0 2359  0.12 \nMW4  78 81 28 351 319 227 108 0 1350  0.16 Table S1:  Parameters used for the fitting of the XPS spectra. The peaks position for each of the 3 \npeaks related to the 𝐅𝐞𝟐+ and 4 peaks related to the 𝐅𝐞𝟑+ were extracted from reference 45. The \nrelationship between the area of the peaks of each multiplet  was fixed. Peaks LE and HE \ncorresponds to low and high energy satellites.  \n \n \nStability analysis.  We investigated the aging stability of selected catalysts under various \nconditions, as well as the structural changes in the materials after the catalytic reac tion. \nSpecifically, using EPR, we quantified the •OH free radicals production in the as made MW1 and \nMW4 samples, and again after four months of storage in air and water. These results are detailed \nin Fig.S3 . Additionally, we examined the structural altera tions of ST0 and MW4 samples post -\ncatalysis. TEM images of samples ST0 and MW4 after 6 hours of continuous catalysis are \npresented in Figs.S4 -b and -d, respectively. Correspondingly, Figs.S4 -a and -c show  a \ncomparative analysis of the X -ray diffraction pat terns before and after the catalytic reaction.  \n \nFig. S3:  Normalized •OH production, determined by EPR, of samples MW1 and MW4 in different \nconditions: as made (black) and after 4 months stored in air (red) and water (blue).  \n \nFig. S4:  (a) XRD patterns of ST0 before and after 6 hours of continuous catalysis. (b) TEM of ST0 \npost-catalysis with comparative size distributions before and after catalysis. (c)  XRD patterns of \nMW4  before and after 6 hours of continuous catalysis. (d) TEM of MW4  post-catalysis with \ncomparative size distributions before and after catalysis.  \nKinetic modelling. From the methylene blue degradation curves depicted in Fig.5 , different \nreaction kinetics models were explored. Specifically, the experimental data were fitted  to pseudo -\nfirst-order ( ln (𝐶0\n𝐶)=𝑘1𝑡) and pseudo -second -order (𝐶0\n𝐶=𝑘2𝐶0𝑡+1) reaction models. Fig.S5  \nillustrates the linearized pseudo -first-order fits for the various catalysts used under different \nexperimental conditions. The linearized pseudo -second -order fits are shown in Fig.S6. Table  2 \npresents the 𝑘1 and 𝑘2 constants derived from each model, along with their corresponding \nregression coefficients  𝑅2. \n \nFig.S5: Pseudo -First-Order kinetics for methylene blue degradation at different experimental \nconditions: (a) ST samples at room temperature (RT), (b) MW samples at 60°C, (c) ST samples \nat 60°C, and (d) MW samples at 90°C.  \n \nFig.S6: Pseudo -Second -Order kinetics for  methylene blue degradation at different experimental \nconditions: (a) ST samples at room temperature (RT), (b) MW samples at 60°C, (c) ST samples \nat 60°C, and (d) MW samples at 90°C.  \n"    },    {        "title": "2312.05314v1.Strontium_Ferrite_Under_Pressure__Potential_Analogue_to_Strontium_Ruthenate.pdf",        "content": "Strontium Ferrite Under Pressure: Potential Analogue to Strontium Ruthenate\nAzin Kazemi-Moridani,1, 2, aSophie Beck,2Alexander Hampel,2A.-M. S. Tremblay,3, bMichel C ˆot´e,1, cand Olivier Gingras2, d\n1D´epartement de Physique, Universit ´e de Montr ´eal, 1375 ave Th ´er`ese-Lavoie-Roux, Montr ´eal, Qu ´ebec H2V 0B3, Canada\n2Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA\n3D´epartement de Physique, Institut quantique, Universit ´e de Sherbrooke, Sherbrooke, Qu ´ebec J1K 2R1, Canada\n(Dated: December 12, 2023)\nDespite the significant attention it has garnered over the last thirty years, the paradigmatic material strontium\nruthenate remains the focus of critical questions regarding strongly correlated materials. As an alternative plat-\nform to unravel some of its perplexing characteristics, we propose to study the isostructural and more correlated\nmaterial strontium ferrite. Using density functional theory combined with dynamical mean-field theory, we at-\ntribute the experimentally observed insulating behavior at zero pressure to strong local electronic correlations\ngenerated by Mott and Hund’s physics. At high pressure, our simulations reproduce the reported insulator-to-\nmetal transition around 18GPa. Along with distinctive features of a Hund’s metal, the resulting metallic state is\nfound to display an electronic structure analogous to that of strontium ruthenate, suggesting that it could exhibit\nsimilar low-energy properties.\nThe unconventional superconductivity of strontium ruthen-\nate (Sr 2RuO 4, SRO) still fuels debates almost thirty years af-\nter its discovery [1–3]. It was the first layered perovskite su-\nperconductor to be discovered after the cuprates. However,\ncontrarily to the cuprates, SRO does not necessitate doping\nto exhibit superconductivity, which allows for investigations\nin high-quality single crystals. This distinction has motivated\nextensive studies aimed at characterizing both its normal and\nsuperconducting states.\nTheoretically, the normal state is nowadays understood as a\ncorrelated Hund’s metal [4, 5] with important spin-orbit cou-\npling. Only the t2gelectrons of the ruthenium atom play a\nfundamental role and interactions can be considered local,\nmodelled by the Kanamori Hamiltonian [6–8]. Indeed, the\ncombination of density functional theory (DFT) and dynami-\ncal mean-field theory (DMFT) has yielded impressive agree-\nment with experiments, reproducing for example the Fermi\nsurface [9] and the magnetic susceptibility [10]. Additionally,\nit captures expected hallmarks of Hund’s metals such as or-\nbital selective mass renormalizations [11, 12] and a crossover\nfrom a bad metal to a Fermi liquid [13, 14]. The supercon-\nducting state, however, remains enigmatic. The debates per-\nsist because thermodynamic measurements supported by the-\nory suggest a one-component order parameter [15–20], while\nother experiments observed evidence of a two-component or-\nder parameter [21–23]. New knobs to turn could help unravel\nkey additional information regarding SRO.\nOne such knob is simply to study a different, yet similar\nmaterial. In this regard, our focus turns to strontium ferrite\n(Sr2FeO 4, SFO) for which the ruthenium atom (Ru) is re-\nplaced with an isoelectronic iron atom (Fe). This substitution\nresults in an increased on-site Coulomb repulsion due to the\nmore localized nature of Fe’s 3d-shell compared to Ru’s 4d-\nshell, along with a decreased spin-orbit coupling due to the\nsmaller nuclear charge of Fe compared with that of Ru. Our\nstudy of SFO is driven by a dual purpose: first, to investi-\ngate the distinctive behaviors and electronic properties exhib-\nited by a material with an identical crystal structure to SRO,\nand second, to harness SFO as a potential source of deeper in-sights into the elusive physics of SRO’s superconducting state.\nThis strategy has been previously successful to shed light on\nHund’s physics and the role of van Hove singularities by com-\nparing SRO to Sr 2MoO 4[8].\nWhile only a few experiments have been performed, SFO\nhas hardly been studied and in particular no electronic struc-\nture calculation has been reported to our knowledge. Ex-\nperiments report that SFO is an antiferromagnetic insulator\nwith a N ´eel temperature around 60Kelvin [24–26]. Also, a\nroom-temperature insulator-to-metal transition has been de-\ntected around 18GPa [27, 28]. Thus, applying pressure to\nSFO could be a way to suppress the antiferromagnetic order\nfor the benefit of superconductivity, as is observed in many\nunconventional superconductors [29–32].\nIn this paper, we explore the correlated electronic structure\nof unstrained and strained SFO in its normal state above the\nN´eel temperature and compare it to experiments. Starting with\nDFT, we find that the electronic structure of SFO differs from\nthat of SRO. In SFO, both the egand the t2gorbitals cross\nthe Fermi energy and are partially occupied, whereas in SRO\ntheegstates are empty while the t2gorbitals are partially oc-\ncupied. Then, by incorporating dynamical local correlations\nwithin DMFT, we explore the rich phase diagram generated\nby the on-site Coulomb repulsion Uand Hund’s coupling J.\nWe argue that the phase most consistent with experiment is\nfound around U≥2.5eV and J <0.7eV . This value of Uis\nslightly above the one predicted using the constrained random\nphase approximation (cRPA). In this phase, the egstates are\npushed above the Fermi energy, while the remaining electrons\nin the t2gshell become Mott insulating. We show that this\nphase undergoes an insulator-metal transition around 18GPa\nof isotropic pressure, consistent with experiments. By com-\nparing the band structure, the Fermi surface and the mass en-\nhancements of this metallic phase with that of SRO, we reveal\nan exciting similarity between the two, suggesting SFO as an\nalternative platform to understand SRO.\nDFT electronic structure. — SFO (SRO) crystallizes in a\nbody-centered tetragonal structure with Fe (Ru) at the center\nof FeO 6(RuO 6) octahedra. The crystal field generated by thearXiv:2312.05314v1  [cond-mat.str-el]  8 Dec 20232\nFIG. 1. Comparison of the open d-shell orbital character on the band structure of (a) SRO, and (b) SFO under 40GPa of isotropic pressure.\nThedxy,dyz/zx ,dz2anddx2−y2orbital characters are shown in red, green, blue and orange, respectively. The horizontal line at zero marks\nthe Fermi energy. The egorbitals are unoccupied in SRO while the dx2−y2orbital is slightly metallic in SFO at 40GPa.\np-orbitals of the surrounding oxygen atoms splits the five-fold\ndegeneracy of the Fe d-shell into an egdoublet ( dx2−y2and\ndz2orbitals) and a t2gtriplet ( dxy,dzxanddyzorbitals).\nFigure 1 presents the band structures of both (a) SRO\nand (b) SFO at 40 GPa obtained using DFT. The details of\nthe calculations can be found in the Supplemental Materials\n(SM) [33]. We show the projection of the wave function onto\nthed-orbitals of the transition metal element, along with the\norbital selective densities of states (DOS). Note that the elec-\ntronic structure of SFO without pressure is qualitatively simi-\nlar to the one at 40 GPa [33]. In SRO, the band dispersion re-\nveals an overlap between the egandt2gorbitals, but only the\nt2gorbitals are partially filled and cross the Fermi level while\ntheegorbitals remain completely unoccupied. Thus, as was\ndone in most theoretical studies of SRO [6–10, 12, 14, 18–20],\none can focus solely on the t2gorbitals.\nHowever, in the case of SFO, both the t2ganddx2−y2or-\nbitals are active at the Fermi level, necessitating a minimal\nmodel that includes the egorbitals to describe the low-energy\nphysics accurately.\nIn short, although the non-interacting band structure of SFO\nis similar to SRO’s, the presence of egelectrons at the Fermi\nlevel is a massive distinction. Moreover, we have been ne-\nglecting so far the role of strong electronic correlations. In\nSRO, although important, they do not significantly affect the\nFermi surface itself [34]. In contrast, experiments on SFO ob-\nserve an insulating state rather than a metallic one. We now\ninvestigate whether the correlation effects among the Fe d-\nelectrons can be responsible for this discrepancy with DFT.\nStrong correlations. — Because of the localized nature of\n3dorbitals, SFO is expected to be affected by strong electronic\ncorrelations. This is reinforced by the disagreement between\ntheab initio prediction of a metallic state and the experimen-\ntal observation of an insulating state. We now incorporate the\nmissing local electronic correlations from DFT using DMFT.\nThis is done by projecting the DFT Kohn-Sham wave function\nonto a downfolded model considering only the five 3dorbitals\nof the Fe atom and constructed using the Wannier90 pack-\nage. The correlations are obtained by iteratively solving the\nimpurity model using DMFT, with the interactions modelledby the full rotationally invariant Slater Hamiltonian (including\nnon-density-density terms) which depends on two parameters:\nthe strength of the electronic Coulomb repulsion Uand the\nHund’s coupling J. Details about the downfolding, the nu-\nmerical calculations and the Slater Hamiltonian parametriza-\ntion can be found in the SM [33].\nWe explore possible electronic states of SFO by investigat-\ning the U−Jparameter space of the full Slater Hamiltonian.\nThe phase diagram in Fig. 2 summarizes our findings for a\ntemperature of 146K (1/kBT= 80 eV−1). Based on ob-\nservables such as the spectral function [33] and the resulting\norbital occupations, we classify the phases using three types\nof colored markers: the blue triangles, red squares and green\nstars, corresponding to the t 2gorbitals being metallic, being\ninsulating due to correlations, or being orbital-selectively in-\nsulating, respectively. For the first two classes (triangles and\nsquares), a filled (empty) symbol represents metallic (band\ninsulating) egorbitals, while a half-filled symbol indicates\nthat only the dx2−y2orbital is metallic. For the third class\n(stars), the dxyandegorbitals are found metallic, while the\ndzx/yz ones are Mott insulating. We call this phase the orbital-\nselective Mott phase (OSMP).\nWe now discuss the different phases and physical mecha-\nnisms leading to the phase diagram shown in Fig. 2. Addi-\ntional information can be found in the SM [33]. In the low\nUand low Jregime depicted by half-filled blue triangles, we\nfind the DFT solution shown in Fig. 1 (b) where only the dz2\norbital is empty. As mentioned before, experimental obser-\nvations suggest SFO to be a small gap insulator at zero pres-\nsure [24–26]. We find the phase that best reproduces these ob-\nservations at larger U: the phase marked by open red squares\nwhere all orbitals are insulating. This phase emerges by in-\ncreasing the cost of double occupancy Ubecause it suppresses\ncharge fluctuations and constrains the Fe atoms to host four lo-\ncalized electrons. Due to the crystal field splitting generated\nby the oxygen atoms surrounding the Fe atom, the dxyorbital\nhas the lowest on-site energy and is getting fully filled, the\negorbitals have the highest on-site energies and are pushed\nabove the Fermi level making them band insulating, and the\ndyz/zx orbitals have to share two electrons which make them3\nFIG. 2. Phase diagrams of SFO in the space of the interaction\nparameters at T= 146 K for three pressures. Here, the Hund’s cou-\npling Jand on-site Coulomb repulsion Uare expressed in the Slater\ndefinition. The red squares distinguish Mott insulating t2gorbitals,\nwhereas the blue triangles correspond to metallic t2gorbitals. The\nfilling of the markers reflects whether both egorbitals are partially\noccupied (full), only the dx2−y2is partially occupied (half-filled), or\nnone are (empty). The narrow region with green stars corresponds\nto an orbital-selective Mott phase (OSMP) with dxyandegmetallic,\nanddzx/yz Mott insulating. On the right, a selected region is com-\npared for three different pressures: 0,20, and 40GPa. It highlights\nthe insulator-to-metal transition observed around 18GPa [27, 28] for\nU∼2.5 eV , where the resulting metallic states have empty egor-\nbitals.\nMott insulating.\nThis phase, most consistent with experimental observations\nat zero pressure, is found roughly in the parameter regime\nU≥2.5eV and J <0.7eV . Using the cRPA to calculate the\nscreened interaction parameters [33], we find the static values\n(zero frequency limit) to be UcRPA, JcRPA= 1.5eV ,0.5eV .\nAlthough these numbers are outside of the region deemed re-\nalistic, it is known that cRPA overestimates screening effects,\nleading to underestimated Uvalues [35, 36]. Considering this\nfact,UcRPA appears reasonably close to the empty red square\nregion. Now, to attain a deeper understanding of the physical\nmechanisms at play and guide possible fine tuning, we con-\ntinue analysing the full phase diagram.\nIf again we start from the small Uand small Jregion, but\nthis time go along the direction of increasing Jinstead of U,\nwe see that the occupancies of the egorbitals start to increase.\nThis happens because of the Hund’s rule, which states that J\nfavors spin-alignment and thus spreads the orbital occupation\nthroughout the entire d-shell, making all orbitals metallic at\nsome point. Eventually at very large J, there is enough occu-\npation transfer from the t2gto the egorbitals so that a Mott\ngap opens up in t2gwhile egremains metallic: first, the Mottgap opens in the less occupied dyz/zx orbital (leading to the\ngreen star phase), and then in the dxyorbital, resulting in the\nt2ginsulating and egmetallic phase (full red square phase).\nFinally, another remarkable result from the phase diagram\nof Fig. 2 is the empty blue triangle phase, which has band-\ninsulating egand partially filled t2gorbitals. This configura-\ntion is analogous to that of SRO and could offer an alternative\nroute to study the physics of this important system. Since this\nmetallic phase is on the border with the realistic insulating\nphase, we believe isotropic pressure might actually allow to\nrealize this metallic phase.\nIsotropic pressure. — In this section, we explore the\ninsulator-to-metal transition of SFO under pressure and show\nthat the metallic phase can be fine-tuned to have a similar band\nstructure and Fermi surface to that of SRO. The insulator-\nto-metal transition observed experimentally happens around\n18GPa at room temperature [27, 28]. Our results natu-\nrally predicts that this critical pressure should be temperature-\ndependent, which can be tested experimentally. To investigate\nthis insulator-to-metal transition, we restricted our simulation\nto a window near the phase transition between the insulating\n(the empty red square phase) and the metallic phases. The\nright panels of Fig. 2 present this evolution for three pressures:\n0,20, and 40GPa. We preserve the original crystalline sym-\nmetry, in agreement with experiments that confirmed this up\nto30GPa [27, 28, 37].\nIncreasing pressure increases the propensity of electrons\nto hop from site to site t, i.e., it increases the bandwidth\nof the d-shell without significantly affecting the Coulomb\nrepulsion U. Consequently, the effective Coulomb repul-\nsionU/t decreases. This effect results in the expansion of\nthe metallic state within the parameter space as shown on\nthe right of Fig. 2, while also providing a clear explanation\nfor the insulator-to-metal transition observed in experiments.\nMoreover, this effect suggests that the boundary between the\nmetallic and insulating regions should move with temperature,\nleading to a temperature-dependent critical pressure for the\ninsulator-to-metal transition. Experiments could already be\nperformed to test this prediction.\nWe now focus on the region where both egorbitals are\nempty, which we observe also grows with pressure. This is\nlikely due to the modified competition between the crystal\nfield and Hund’s coupling J. Indeed, applying pressure on the\nmaterial increases the crystal field splitting which favors low-\nspin states and pushes the egorbitals further away in energy.\nIn contrast, Jfavors a high-spin state and spreads the orbital\noccupations. Thus, with increasing pressure, a larger Jis re-\nquired to occupy the egorbitals. Therefore the empty blue\ntriangle region that represents a metallic phase with empty eg\norbitals expands.\nIn order to compare the three-orbital metallic phase of SFO\nfound under pressure with SRO, we present their respective\ncorrelated band structures, DOSs and Fermi surfaces in Fig. 3.\nWhat is meant by these correlated objects is detailed in the\nSM [33]. In (a), we display the 40GPa phase of SFO to high-\nlight a case at higher pressure, and we selected U= 2.5eV4\nFIG. 3. Correlated band structure on the left, DOS in the middle\nand Fermi surface on the right of (a) 40GPa SFO in the three orbital\nmetallic phase and (b) SRO, both at T= 146 K. The DFT result is\nrepresented by the black lines. Clearly, correlations push egorbitals\naway from the Fermi level. The Fermi surfaces are labeled α, β, γ\nin part (b). The parameters for the calculations are on top of the\nFermi surfaces. Although calculations for both of the materials rely\non the Slater Hamiltonian, SRO’s parameters are presented in the\nKanamori convention to ease the comparison with previous studies.\nThe corresponding values of SRO in Slater are U= 1.66eV and\nJ= 0.56eV . See Eqs (S30, S31) of the SM for conversion relations\nbetween Slater and Kanamori values.\nandJ= 0.45eV as an example that reproduces the exper-\nimental observations with physically relevant parameters. In\nthe first panel, we contrast the correlated band structure with\nthe one obtained using DFT and one clearly sees that corre-\nlations have pushed the egorbitals away from the Fermi level\ncompared to Fig. 1 (b).\nComparing the corresponding quantities for both systems,\nwe argue that SFO in this particular phase is analogous to\nSRO. Both are metals with four t2gelectrons, three similar\nFermi sheets and comparable DOSs with a van Hove singu-\nlarity in the vicinity of the Fermi energy. There are, however,\ntwo important differences between the two, which can be re-\ngarded as opportunities: First, even with pressure, the band-\nwidth of SFO remains smaller, implying stronger electronic\ncorrelations than in SRO. Since higher pressure should bring\nit to a value similar to that of SRO, this represents an opportu-\nnity to study continuously a more correlated version of SRO.\nThis increased strength of interaction should lead to stronger\nmagnetic fluctuations which can promote a magnetic order, or\npossibly superconductivity.\nSecond, the γsheet of the Fermi surface of SFO is more\nsquare-like than that of SRO. While the calculations presented\nhere do not include spin-orbit coupling, it should not have\nan important impact on SFO because of the small charge ofFe’s nuclei. As a result, the squareness of the γsheet pre-\nsented for SFO in Fig. 3 (a) should remain similar, leading\nto a larger nesting than in SRO. Nesting itself leads to an in-\ncreased strength of the spin fluctuations. More studies need to\nbe performed on these speculations.\nIn addition to the observables presented above, we demon-\nstrate that the three-orbital metallic phase that we find for SFO\ndisplays distinctive features of Hund’s metals [4, 5, 12]. This\nis highlighted by inspecting the effect of Hund’s coupling Jon\nthe orbital-selective effective mass enhancementsm∗\nmDFT\f\f\f\nland\non the scattering rates Γl. These quantities measure the degree\nof electronic correlations missing from DFT and captured by\nDMFT. They are reported in the SM [33]. Indeed, three points\nstand out: First, we find that the mass enhancements and the\nscattering rates all increase with J. Second, the effective mass\nof the xyorbital increases faster than those of the yz/zx or-\nbitals. Third, the larger J, the lower we have to go in tem-\nperature before the effective masses saturate. This last point\nhighlights that it is increasingly challenging to reach the co-\nherent regime where quasi-particles are well defined, that is\nthe Fermi liquid regime. The considerable increase in correla-\ntion, orbital differentiation due to Jand pushing of the Fermi\nliquid scale to lower temperatures due to Jare all hallmarks\nof Hund’s metals [4, 5]. They are also observed in SRO [12],\nthus supporting further the analogy between SFO and SRO.\nWe note that reaching the coherent regime at large Jis es-\npecially challenging for five orbital systems, thus we plan on\nextracting the effective masses that would be measured exper-\nimentally in future works.\nConclusion. — We studied the correlated electronic struc-\nture of strontium ferrite, Sr 2FeO 4, using the combination of\ndensity functional theory and dynamical mean-field theory.\nCorrectly capturing correlation effects of the Fe d-electrons is\nessential to reproduce the experimentally observed insulating\nstate of Sr 2FeO 4. We find such a state for interaction strengths\nU > 2.5eV , where only the t2gorbitals are occupied. More-\nover, we are able to reproduce the experimentally observed\ninsulator-to-metal transition in Sr 2FeO 4under pressure. The\nmetallic state of Sr 2FeO 4at40GPa with U > 2.5eV dis-\nplays the distinctive features of Hund’s metals and offers a\npromising analogue state to Sr 2RuO 4, for which correlations\ncould be tuned with additional pressure. Indeed, both these\nstates are metals with four electrons in their t2gshells with\nsimilar band structures, density of states and Fermi surfaces.\nThe difference is that the effective mass enhancement is gen-\nerally larger in SFO, and the nesting of its Fermi surface is\nsuggestive of enhanced magnetic fluctuations that may lead to\nsuperconductivity.\nAcknowledgments. — We are grateful for discussions\nwith Antoine Georges, Andrew J. Millis, Olivier Parcollet and\nDavid S ´en´echal. Support from the Canada First Research Ex-\ncellence fund is acknowledged. The Flatiron Institute is a di-\nvision of the Simons Foundation.5\namohaddeseh.kazemi.moridani@umontreal.ca\nbandre-marie.tremblay@usherbrooke.ca\ncMichel.Cote@umontreal.ca\ndogingras@flatironinstitute.org\n[1] Y . Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita,\nJ. G. Bednorz, and F. Lichtenberg, Superconductivity in a lay-\nered perovskite without copper, Nature 372, 532 (1994).\n[2] A. P. Mackenzie, R. K. W. Haselwimmer, A. W. Tyler,\nG. G. Lonzarich, Y . Mori, S. Nishizaki, and Y . Maeno, Ex-\ntremely Strong Dependence of Superconductivity on Disorder\nin Sr 2RuO 4, Phys. Rev. Lett. 80, 161 (1998).\n[3] A. P. Mackenzie, T. Scaffidi, C. W. Hicks, and Y . Maeno,\nEven odder after twenty-three years: the superconducting or-\nder parameter puzzle of Sr 2RuO 4, npj Quantum Materials 2, 40\n(2017).\n[4] A. Georges, L. d. Medici, and J. Mravlje, Strong Correlations\nfrom Hund’s Coupling, Annual Review of Condensed Matter\nPhysics 4, 137 (2013).\n[5] L. de’ Medici, J. Mravlje, and A. Georges, Janus-Faced Influ-\nence of Hund’s Rule Coupling in Strongly Correlated Materials,\nPhys. Rev. Lett. 107, 256401 (2011).\n[6] T. Mizokawa and A. Fujimori, Unrestricted Hartree-Fock\nstudy of transition-metal oxides: Spin and orbital ordering in\nperovskite-type lattice, Phys. Rev. B 51, 12880 (1995).\n[7] M. Zingl, J. Mravlje, M. Aichhorn, O. Parcollet, and\nA. Georges, Hall coefficient signals orbital differentiation in the\nHund’s metal Sr 2RuO 4, npj Quantum Materials 4, 35 (2019).\n[8] J. Karp, M. Bramberger, M. Grundner, U. Schollw ¨ock, A. J.\nMillis, and M. Zingl, Sr 2MoO 4and Sr 2RuO 4: Disentangling\nthe Roles of Hund’s and van Hove Physics, Phys. Rev. Lett.\n125, 166401 (2020).\n[9] A. Tamai, M. Zingl, E. Rozbicki, E. Cappelli, S. Ricco, A. de la\nTorre, S. M. Walker, F. Y . Bruno, P. D. C. King, W. Meevasana,\nM. Shi, M. Radovic, N. C. Plumb, A. S. Gibbs, A. P. Macken-\nzie, C. Berthod, H. Strand, M. Kim, A. Georges, and F. Baum-\nberger, High-resolution photoemission on Sr 2RuO 4reveals\ncorrelation-enhanced effective spin-orbit coupling and domi-\nnantly local self-energies, Physical Review X 9, 021048 (2019),\narXiv: 1812.06531.\n[10] H. U. R. Strand, M. Zingl, N. Wentzell, O. Parcollet, and\nA. Georges, Magnetic response of Sr 2RuO 4: quasi-local spin\nfluctuations due to Hund’s coupling, Physical Review B 100,\n125120 (2019), arXiv: 1904.07324.\n[11] C. Bergemann, J. S. Brooks, L. Balicas, A. P. Mackenzie, S. R.\nJulian, Z. Q. Mao, and Y . Maeno, Normal state of the unconven-\ntional superconductor Sr 2RuO 4in high magnetic fields, Phys-\nica B: Condensed Matter Proceedings of the Sixth International\nSymposium on Research in High Magnetic Fields, 294–295 ,\n371 (2001).\n[12] J. Mravlje, M. Aichhorn, T. Miyake, K. Haule, G. Kotliar, and\nA. Georges, Coherence-Incoherence Crossover and the Mass-\nRenormalization Puzzles in Sr 2RuO 4, Physical Review Letters\n106, 096401 (2011).\n[13] N. E. Hussey, A. P. Mackenzie, J. R. Cooper, Y . Maeno,\nS. Nishizaki, and T. Fujita, Normal-state magnetoresistance\nof Sr 2RuO 4, Physical Review B 57, 5505 (1998), publisher:\nAmerican Physical Society.\n[14] F. B. Kugler, M. Zingl, H. U. R. Strand, S.-S. B. Lee, J. von\nDelft, and A. Georges, Strongly Correlated Materials from\na Numerical Renormalization Group Perspective: How the\nFermi-Liquid State of Sr 2RuO 4Emerges, Physical Review Let-ters124, 016401 (2020), publisher: American Physical Society.\n[15] E. Hassinger, P. Bourgeois-Hope, H. Taniguchi, S. Ren ´e de\nCotret, G. Grissonnanche, M. S. Anwar, Y . Maeno, N. Doiron-\nLeyraud, and L. Taillefer, Vertical Line Nodes in the Super-\nconducting Gap Structure of Sr 2RuO 4, Phys. Rev. X 7, 011032\n(2017).\n[16] Y .-S. Li, M. Garst, J. Schmalian, S. Ghosh, N. Kikugawa, D. A.\nSokolov, C. W. Hicks, F. Jerzembeck, M. S. Ikeda, Z. Hu, B. J.\nRamshaw, A. W. Rost, M. Nicklas, and A. P. Mackenzie, Elas-\ntocaloric determination of the phase diagram of Sr 2RuO 4, Na-\nture607, 276 (2022).\n[17] Y .-S. Li, N. Kikugawa, D. A. Sokolov, F. Jerzembeck, A. S.\nGibbs, Y . Maeno, C. W. Hicks, J. Schmalian, M. Nicklas,\nand A. P. Mackenzie, High-sensitivity heat-capacity measure-\nments on Sr 2RuO 4under uniaxial pressure, Proceedings of\nthe National Academy of Sciences 118, e2020492118 (2021),\nhttps://www.pnas.org/doi/pdf/10.1073/pnas.2020492118.\n[18] O. Gingras, R. Nourafkan, A.-M. S. Tremblay, and M. C ˆot´e,\nSuperconducting Symmetries of Sr 2RuO 4from First-Principles\nElectronic Structure, Physical Review Letters 123, 217005\n(2019).\n[19] O. Gingras, N. Allaglo, R. Nourafkan, M. C ˆot´e, and A.-\nM. S. Tremblay, Superconductivity in correlated multiorbital\nsystems with spin-orbit coupling: Coexistence of even- and\nodd-frequency pairing, and the case of Sr 2RuO 4, Phys. Rev.\nB106, 064513 (2022).\n[20] J. B. Hauck, S. Beck, D. M. Kennes, A. Georges, and\nO. Gingras, Competition between d-wave superconductiv-\nity and magnetism in uniaxially strained Sr 2RuO 4(2023),\narXiv:2307.10006 [cond-mat.supr-con].\n[21] S. Benhabib, C. Lupien, I. Paul, L. Berges, M. Dion, M. Nar-\ndone, A. Zitouni, Z. Q. Mao, Y . Maeno, A. Georges, L. Taille-\nfer, and C. Proust, Ultrasound evidence for a two-component\nsuperconducting order parameter in Sr 2RuO 4, Nature Physics\n17, 194 (2021).\n[22] S. Ghosh, A. Shekhter, F. Jerzembeck, N. Kikugawa, D. A.\nSokolov, M. Brando, A. P. Mackenzie, C. W. Hicks, and B. J.\nRamshaw, Thermodynamic evidence for a two-component su-\nperconducting order parameter in Sr 2RuO 4, Nature Physics 17,\n199 (2021).\n[23] V . Grinenko, S. Ghosh, R. Sarkar, J.-C. Orain, A. Nikitin,\nM. Elender, D. Das, Z. Guguchia, F. Br ¨uckner, M. E. Bar-\nber, J. Park, N. Kikugawa, D. A. Sokolov, J. S. Bobowski,\nT. Miyoshi, Y . Maeno, A. P. Mackenzie, H. Luetkens, C. W.\nHicks, and H.-H. Klauss, Split superconducting and time-\nreversal symmetry-breaking transitions in Sr 2RuO 4under\nstress, Nature Physics 17, 748 (2021).\n[24] S. Dann, M. Weller, and D. Currie, The synthesis and structure\nof Sr 2FeO 4, Journal of Solid State Chemistry 92, 237 (1991).\n[25] S. E. Dann, M. T. Weller, D. B. Currie, M. F. Thomas,\nand A. D. Al-Rawwas, Structure and magnetic properties of\nSr2FeO 4and Sr 3Fe2O7studied by powder neutron diffraction\nand M ¨ossbauer spectroscopy, J. Mater. Chem. 3, 1231 (1993).\n[26] P. Adler, Properties of K 2NiF 4-Type Oxides Sr 2FeO 4, Journal\nof Solid State Chemistry 108, 275 (1994).\n[27] G. R. Hearne, M. P. Pasternak, and R. D. Taylor, Selected stud-\nies of magnetism at high pressure, Il Nuovo Cimento D 18,\n145–161 (1996).\n[28] G. K. Rozenberg, A. P. Milner, M. P. Pasternak, G. R. Hearne,\nand R. D. Taylor, Experimental confirmation of a p−pintra-\nband gap in Sr 2FeO 4, Phys. Rev. B 58, 10283 (1998).\n[29] R. Brusetti, M. Ribault, D. J ´erome, and K. Bechgaard, Insulat-\ning, conducting and superconducting states of (TMTSF)2AsF6\nunder pressure and magnetic field, Journal de Physique 43,6\n801–808 (1982).\n[30] N. Mathur, F. Grosche, S. Julian, I. Walker, D. Freye, R. Hasel-\nwimmer, and G. Lonzarich, Magnetically mediated supercon-\nductivity in heavy fermion compounds, Nature 394, 39 (1998).\n[31] S. Lefebvre, P. Wzietek, S. Brown, C. Bourbonnais, D. J ´erome,\nC. M ´ezi`ere, M. Fourmigu ´e, and P. Batail, Mott transition, anti-\nferromagnetism, and unconventional superconductivity in lay-\nered organic superconductors, Phys. Rev. Lett. 85, 5420 (2000).\n[32] N. Doiron-Leyraud, P. Auban-Senzier, S. Ren ´e de Cotret,\nC. Bourbonnais, D. J ´erome, K. Bechgaard, and L. Taillefer,\nCorrelation between linear resistivity and T cin the Bechgaard\nsalts and the pnictide superconductor Ba(Fe 1−xCox)2As2,\nPhys. Rev. B 80, 214531 (2009).\n[33] See Supplemental Material at online link for the computational\ndetails, the classification and mechanisms found in the phase di-\nagram, the band structure of Sr 2FeO 4under pressure, the con-\nnection between Slater and Kanamori Hamiltonians, the corre-\nlated band structure, and the quasi-particle Fermi surface. The\nSupplemental Material includes Refs. [35, 36, 38–68].\n[34] G. Zhang, E. Gorelov, E. Sarvestani, and E. Pavarini, Fermi\nSurface of Sr 2RuO 4: Spin-Orbit and Anisotropic Coulomb In-\nteraction Effects, Phys. Rev. Lett. 116, 106402 (2016).\n[35] M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake,\nA. J. Millis, and S. Biermann, Low-energy models for corre-\nlated materials: Bandwidth renormalization from coulombic\nscreening, Phys. Rev. Lett. 109, 126408 (2012).\n[36] C. Honerkamp, H. Shinaoka, F. F. Assaad, and P. Werner, Lim-\nitations of constrained random phase approximation downfold-\ning, Phys. Rev. B 98, 235151 (2018).\n[37] P. Adler, A. F. Goncharov, K. Syassen, and E. Sch ¨onherr, Opti-\ncal reflectivity and Raman spectra of Sr 2FeO 4under pressure,\nPhys. Rev. B 50, 11396 (1994).\n[38] P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas,\nPhysical Review 136, B864 (1964), publisher: American Phys-\nical Society.\n[39] W. Kohn and L. J. Sham, Self-Consistent Equations Including\nExchange and Correlation Effects, Physical Review 140, A1133\n(1965).\n[40] W. Kohn, A. D. Becke, and R. G. Parr, Density Functional The-\nory of Electronic Structure, The Journal of Physical Chemistry\n100, 12974 (1996).\n[41] G. Pizzi, V . Vitale, R. Arita, S. Bl ¨ugel, F. Freimuth,\nG. G ´eranton, M. Gibertini, D. Gresch, C. Johnson, T. Koret-\nsune, J. Iba ˜nez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand,\nA. Marrazzo, Y . Mokrousov, J. I. Mustafa, Y . Nohara, Y . No-\nmura, L. Paulatto, S. Ponc ´e, T. Ponweiser, J. Qiao, F. Th ¨ole,\nS. S. Tsirkin, M. Wierzbowska, N. Marzari, D. Vanderbilt,\nI. Souza, A. A. Mostofi, and J. R. Yates, Wannier90 as a com-\nmunity code: new features and applications, Journal of Physics:\nCondensed Matter 32, 165902 (2020).\n[42] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dy-\nnamical mean-field theory of strongly correlated fermion sys-\ntems and the limit of infinite dimensions, Rev. Mod. Phys. 68,\n13 (1996).\n[43] K. Held, Electronic structure calculations using dynamical\nmean field theory, Advances in Physics 56, 829 (2007).\n[44] G. Kotliar, S. Y . Savrasov, K. Haule, V . S. Oudovenko, O. Par-\ncollet, and C. A. Marianetti, Electronic structure calculations\nwith dynamical mean-field theory, Rev. Mod. Phys. 78, 865\n(2006).\n[45] X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet,\nJ.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet,\nN. Brouwer, F. Bruneval, G. Brunin, T. Cavignac, J.-B. Char-\nraud, W. Chen, M. C ˆot´e, S. Cottenier, J. Denier, G. Gen-este, P. Ghosez, M. Giantomassi, Y . Gillet, O. Gingras, D. R.\nHamann, G. Hautier, X. He, N. Helbig, N. Holzwarth, Y . Jia,\nF. Jollet, W. Lafargue-Dit-Hauret, K. Lejaeghere, M. A. L. Mar-\nques, A. Martin, C. Martins, H. P. C. Miranda, F. Naccarato,\nK. Persson, G. Petretto, V . Planes, Y . Pouillon, S. Prokhorenko,\nF. Ricci, G.-M. Rignanese, A. H. Romero, M. M. Schmitt,\nM. Torrent, M. J. van Setten, B. Van Troeye, M. J. Verstraete,\nG. Z ´erah, and J. W. Zwanziger, The Abinit project: Impact, en-\nvironment and recent developments, Computer Physics Com-\nmunications 248, 107042 (2020).\n[46] A. H. Romero, D. C. Allan, B. Amadon, G. Antonius, T. Ap-\nplencourt, L. Baguet, J. Bieder, F. Bottin, J. Bouchet, E. Bous-\nquet, F. Bruneval, G. Brunin, D. Caliste, M. C ˆot´e, J. Denier,\nC. Dreyer, P. Ghosez, M. Giantomassi, Y . Gillet, O. Gingras,\nD. R. Hamann, G. Hautier, F. Jollet, G. Jomard, A. Mar-\ntin, H. P. C. Miranda, F. Naccarato, G. Petretto, N. A. Pike,\nV . Planes, S. Prokhorenko, T. Rangel, F. Ricci, G.-M. Rig-\nnanese, M. Royo, M. Stengel, M. Torrent, M. J. van Setten,\nB. Van Troeye, M. J. Verstraete, J. Wiktor, J. W. Zwanziger,\nand X. Gonze, ABINIT: Overview and focus on selected capa-\nbilities, The Journal of Chemical Physics 152, 124102 (2020).\n[47] P. E. Bl ¨ochl, Projector augmented-wave method, Physical Re-\nview B 50, 17953 (1994).\n[48] M. Torrent, F. Jollet, F. Bottin, G. Z ´erah, and X. Gonze, Im-\nplementation of the projector augmented-wave method in the\nABINIT code: Application to the study of iron under pressure,\nComputational Materials Science 42, 337 (2008).\n[49] F. Jollet, M. Torrent, and N. Holzwarth, Generation of Projector\nAugmented-Wave atomic data: A 71 element validated table\nin the XML format, Computer Physics Communications 185,\n1246 (2014).\n[50] M. van Setten, M. Giantomassi, E. Bousquet, M. Verstraete,\nD. Hamann, X. Gonze, and G.-M. Rignanese, The pseudodojo:\nTraining and grading a 85 element optimized norm-conserving\npseudopotential table, Computer Physics Communications 226,\n39 (2018).\n[51] A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards,\nS. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and\nK. A. Persson, Commentary: The materials project: A materi-\nals genome approach to accelerating materials innovation, APL\nMaterials 1, 011002 (2013).\n[52] O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko,\nL. Messio, and P. Seth, TRIQS: A toolbox for research on inter-\nacting quantum systems, Computer Physics Communications\n196, 398 (2015).\n[53] J. Kanamori, Electron Correlation and Ferromagnetism of Tran-\nsition Metals, Progress of Theoretical Physics 30, 275 (1963).\n[54] M. Aichhorn, L. Pourovskii, P. Seth, V . Vildosola, M. Zingl,\nO. E. Peil, X. Deng, J. Mravlje, G. J. Kraberger, C. Martins,\nM. Ferrero, and O. Parcollet, TRIQS/DFTTools: A TRIQS ap-\nplication for ab initio calculations of correlated materials, Com-\nputer Physics Communications 204, 200 (2016).\n[55] P. Werner, A. Comanac, L. de’ Medici, M. Troyer, and A. J.\nMillis, Continuous-time solver for quantum impurity models,\nPhys. Rev. Lett. 97, 076405 (2006).\n[56] E. Gull, P. Werner, S. Fuchs, B. Surer, T. Pruschke, and\nM. Troyer, Continuous-time quantum monte carlo impurity\nsolvers, Computer Physics Communications 182, 1078 (2011).\n[57] P. Seth, I. Krivenko, M. Ferrero, and O. Parcollet,\nTRIQS/CTHYB: A continuous-time quantum Monte Carlo hy-\nbridisation expansion solver for quantum impurity problems,\nComputer Physics Communications 200, 274 (2016).\n[58] L. Boehnke, H. Hafermann, M. Ferrero, F. Lechermann,\nand O. Parcollet, Orthogonal polynomial representation of7\nimaginary-time Green’s functions, Phys. Rev. B 84, 075145\n(2011).\n[59] M. E. Merkel, A. Carta, S. Beck, and A. Hampel, solid dmft:\ngray-boxing DFT+DMFT materials simulations with TRIQS,\nJournal of Open Source Software 7, 4623 (2022).\n[60] G. J. Kraberger, R. Triebl, M. Zingl, and M. Aichhorn, Maxi-\nmum entropy formalism for the analytic continuation of matrix-\nvalued Green’s functions, Phys. Rev. B 96, 155128 (2017).\n[61] R. N. Silver, D. S. Sivia, and J. E. Gubernatis, Maximum-\nentropy method for analytic continuation of quantum Monte\nCarlo data, Phys. Rev. B 41, 2380 (1990).\n[62] J. E. Gubernatis, M. Jarrell, R. N. Silver, and D. S. Sivia, Quan-\ntum Monte Carlo simulations and maximum entropy: Dynam-\nics from imaginary-time data, Phys. Rev. B 44, 6011 (1991).\n[63] M. Jarrell and J. Gubernatis, Bayesian inference and the an-\nalytic continuation of imaginary-time quantum Monte Carlo\ndata, Physics Reports 269, 133 (1996).\n[64] F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Bier-\nmann, and A. I. Lichtenstein, Frequency-dependent local inter-\nactions and low-energy effective models from electronic struc-\nture calculations, Phys. Rev. B 70, 1 (2004).\n[65] K. Nakamura, Y . Yoshimoto, Y . Nomura, T. Tadano, M. Kawa-\nmura, T. Kosugi, K. Yoshimi, T. Misawa, and Y . Motoyama,\nRESPACK: An ab initio tool for derivation of effective low-\nenergy model of material, Computer Physics Communications\n261, 107781 (2021).\n[66] L. Vaugier, H. Jiang, and S. Biermann, Hubbard U and Hund\nexchange J in transition metal oxides: Screening versus local-\nization trends from constrained random phase approximation,\nPhys. Rev. B 86, 1 (2012).\n[67] P. Seth, P. Hansmann, A. Van Roekeghem, L. Vaugier, and\nS. Biermann, Towards a First-Principles Determination of Ef-\nfective Coulomb Interactions in Correlated Electron Materials:\nRole of Intershell Interactions, Phys. Rev. Lett. 119, 1 (2017).\n[68] E. S ¸as ¸ıo ˘glu, C. Friedrich, and S. Bl ¨ugel, Effective coulomb in-\nteraction in transition metals from constrained random-phase\napproximation, Phys. Rev. B 83, 121101 (2011).8\nSupplemental Material\nto\nStrontium Ferrite Under Pressure: Potential Analogue to Strontium Ruthenatg\nAzin Kazemi-Moridani,1,2,aSophie Beck,2Alexander Hampel,2A.-M. S. Tremblay,3,bMichel C ˆot´e,1,cand Olivier Gingras2,d\n1D´epartement de Physique, Universit ´e de Montr ´eal, 1375 ave Th ´er`ese-Lavoie-Roux, Montr ´eal, Qu ´ebec H2V 0B3, Canada\n2Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA\n3D´epartement de Physique, Institut quantique, Universit ´e de Sherbrooke, Sherbrooke, Qu ´ebec J1K 2R1, Canada\nThe content of this Supplemental Material is as follows:\nSection one is devoted to the computational details of the\ncalculations performed on SFO and SRO, employing density\nfunctional theory, Wannier90, dynamical mean-field theory,\nand constrained random-phase approximation methods. In\nsection two, we explain the classification and potential mech-\nanisms found in the phase diagram of SFO. The band struc-\ntures of SFO obtained by DFT, both strained and unstrained,\nare displayed in section three. Section four derives the rela-\ntionship between Slater and Kanamori Hamiltonians. Sections\nfive provides the definitions for correlated band structure and\nquasi-particle Fermi surface. Finally in section six, we report\nthe mass enhancement and scattering rate of SFO as a function\nof Hund’s coupling.\nComputational details\nIn this section, we present the computational details of the\ndensity functional theory (DFT) [1–3], construction of the\ndownfolded models using Wannier90 [4], dynamical mean-\nfield theory (DMFT) [5–7] and constrained random-phase ap-\nproximation (cRPA) calculations of both SFO and SRO.\nDFT\nWe calculated the DFT electronic structures of SFO and\nSRO using the ABINIT package [8, 9] version 9.6.2. We used\nthe local density approximation (LDA) functional and the pro-\njector augmented-wave (PAW) pseudo-potentials [10, 11] ver-\nsion JTH v1.1 obtained from Pseudo-Dojo [12, 13]. The\ninitial crystal structures were obtained from the Materials\nproject [14] in the body-centered tetragonal unit cell (space\ngroup I4/mmm #139) and were then relaxed. The Brillouin\nzone was sampled using a 8 ×8×8 Monkhorst-Pack k-point\ngrid with a smearing of 0.001 Ha based on Fermi-Dirac statis-\ntics.\nFor SFO, we used a wave function energy cutoff of\n33 Hartrees. At zero pressure, we kept 37 electronic bands\nand obtained the following lattice parameters for the relaxed\nstructure: a=b= 3.44˚A and c= 11.71˚A. At 40 GPa, the\nrelaxation was performed using the stress tensor functionalityof ABINIT. We kept 45 electronic bands and obtained the fol-\nlowing lattice parameters: a=b= 3.27˚A and c= 10.98˚A.\nFor SRO, we used a wave function energy cutoff of\n28 Hartrees. We kept 45 electronic bands and obtained the\nfollowing lattice parameters for the relaxed structure: a=\nb= 3.60˚A and c= 11.77˚A.\nFIG. S1. The band structure of SFO at zero pressure obtained from\nWannier90 Hamiltonian (thick line) within the localized subspace is\nin complete agreement with that obtained from DFT (thin line). This\nexample serves to highlight that such agreement persists across all of\nour other cases.\nWannier90\nFrom the Kohn-Sham wave functions obtained from DFT,\nthe Wannier90 package allowed us to construct a downfolded\nmodel of only the active dorbitals of the correlated atom, iron\nin SFO and ruthenium in SRO.\nThis is done by constructing local Wannier orbitals and\nmaximally localizing them while still preserving the elec-\ntronic dispersion of the bands near the Fermi level. Figure S1\nshows the agreement between SFO’s band structure obtained\nfrom DFT and the downfolded one obtained from Wannier90.\nFor SFO, we constructed a minimal model involving all\nthe five iron 3dorbitals ( t2gandeg). At zero pressure, the\nWannier orbitals were constructed within the disentanglement\nenergy window [4.5, 12] eV with the Fermi energy being9\naround 6.66 eV . Under 40 GPa, the values were [5, 16] eV ,\nand 8.82 eV respectively.\nFor SRO, only the t2gorbitals are partially occupied and\nare needed for the minimal model. However, to have a fair\ncomparison to SFO with its whole d-shell partially occupied,\nwe constructed the five Wannier-like t2gandegorbitals of\nSRO in the disentanglement energy window [3, 16] eV with\nthe Fermi energy around 7.81 eV .\nDMFT\nWe calculate the effects of the local interactions due to\nCoulomb repulsion by solving an impurity model within\nthe DMFT framework using the TRIQS packages [15].\nThe second-quantized interacting Hamiltonian responsible of\nthese effects is expressed in a set of local orbitals with cre-\nation and annihilation operators given by doσwhere oandσ\nare the orbital and spin labels. It is expressed, in the general\nform, as\nHint=X\noo′o′′o′′′Uoo′o′′o′′′c†\noc†\no′co′′′co′′ (S1)\nwere the matrix elements Uoo′o′′o′′′are explicitly written in\nEqs (S11, S12, S23, S24).\nIn the Kanamori formulation which typically used for\nsystems with only degenerate t2gorbitals, the interacting\nKanamori Hamiltonian reads [16]\nHint,K=UKX\noˆno↑ˆno↓+U′\nKX\no̸=o′ˆno↑ˆno′↓\n+ (U′\nK−JK)X\no<o′,σˆnoσˆno′σ (S2)\n−JKX\no̸=o′d†\no↑do↓d†\no′↓do′↑+JKX\no̸=o′d†\no↑d†\no↓do′↓do′↑\nwhere UKis the intra-orbital Coulomb repulsion term, JK\nis the Hund’s coupling and U′\nKis the inter-orbital inter-spin\nCoulomb repulsion, usually given by U′\nK=UK−2JKin\nthe rotationnally invariant formulation. The definition of the\nSlater UandJand their relation with UKandJKcan be\nfound around Eqs (S30, S31).\nNow the non-interacting Hamiltonian depends on the\nchoice of these local orbitals. The construction of these or-\nbitals is detailed in the previous section about Wannier90. The\ninterface between Wannier90 and TRIQS is done using DFT-\nTools [17] and the impurity is solved using the continuous-\ntime quantum Monte Carlo in the hybridization expansion for-\nmulation [18, 19] with the CT-HYB solver [20]. The CT-HYB\nsolver computes the Green’s function in the domain of imagi-\nnary time. The Green’s function can be represented in a more\ncompact basis by transforming it into the Legendre basis [21].\nWe used the solid dmft wrapper [22] to launch these calcu-\nlations. Rather than performing full charge-self-consistent\nDFT+DMFT calculations, we performed so-called ”one-shot”DFT+DMFT calculations. In this case, DMFT is used sim-\nply as a post-processing tool within solid dmft to solve the\nHubbard-like Hamiltonian. To obtain the real frequency prop-\nerties of the materials such as the density of states, we use the\nTRIQS application MaxEnt [23] to perform the analytic con-\ntinuation of the Green’s functions and self-energies [24–26].\ncRPA\nTo determine the appropriate interaction parameters for\nDMFT, we used the constrained random phase approxima-\ntion (cRPA) [27] as implemented in the RESPACK code [28],\nwhich allows the calculation of the effective partially screened\nCoulomb interaction by separating the electronic structure\ninto a subspace near the Fermi level and the rest of the system.\nFormally, this means the separation of the total electronic po-\nlarizability P=Psub+Prestwhere Psubis the polarizability\nfor the correlated subspace and Prestis for the rest of the sys-\ntem. Then, the screened Coulomb tensor can be calculated in\na local basis from the bare Coulomb interaction tensor V, as\nU(ω) =V/[1−VPrest(ω)]. We used the same well-localized\ncorrelated subspace basis for cRPA as used within DMFT, i.e.\ncontributions to the polarizability for the target space are re-\nmoved via their overlap with the Kohn-Sham states [29] and\nthe screened and bare Coulomb integrals are then evaluated in\nthe maximally localized Wannier orbitals basis set of the cor-\nrelated subspace treated in DMFT. Here, we limit ourselves to\nthe static limit U(ω= 0) of the screened interaction.\nTo derive an effective symmetrized interaction tensor that\ncan be efficiently handled by the impurity solver within\nDMFT, we compute the spherical average of the full four-\nindex screened-Coulomb interaction tensor Uijklto obtain\ntheU:=F0Slater parameter, and its corresponding ex-\nchange interaction parameter J:= (F2+F4)/14assuming\nF4/F2= 0.625.\nWhile our cRPA calculations give us an estimate as to the\nappropriate Ufor the studied systems, these values are not\nguaranteed to be quantitatively accurate for all materials prop-\nerties [30, 31], and often tend to overestimate screening, i.e.\nresulting in too low Coulomb interaction parameters.\nClassification and mechanisms found in the phase diagram\nIn this section, we explain how we have classified the differ-\nent phases found in the phase diagram Fig. 2 of the main text.\nThe classification is based on the partial densities of states ob-\ntained by analytically continuing the self-energy of the con-\nverged solutions of the phase diagram. We also present poten-\ntial mechanisms that explain this phase diagram by carefully\nanalyzing the dominant spin configurations present in each of\nthese phases.10\nFIG. S2. Example of the partial density of states, or orbitally-\nresolved spectral functions Al(ω), obtained in each different phase\nof the phase diagram in Fig. 2 of the main text.\nDensity of states\nThe classification of phases is done based on the orbitally-\nresolved spectral functions (or partial densities of states\n(PDOSs)) obtained at every point of the phase diagram. These\nPDOSs provide information on which orbitals are metal-\nlic, band insulating or insulating due to correlations. The\norbitally-resolved spectral functions can be computed using\nAl(ω) =−1\nπImGll(ω), (S3)\nwhere Gll(ω)is the Green’s function on the real-frequency\naxis corresponding to the propagation of an electron in the or-\nbitall. Since the Green’s functions that we obtain from DMFT\nprocedure are computed on the imaginary-axis, we used the\nMaxEnt code [23, 25] to perform the analytic continuation of\nthe impurity Green’s function, giving as a result G(ω).\nBased on these definitions, we find a total of six distinct\nphases in the phase diagram of SFO at zero pressure. In\nFig. S2, we showcase the PDOSs of one representative point\nin each phase of the phase diagram. We also show the one ob-\ntained for U= 0,J= 0 eV corresponding to the DFT case,\nalthough it is not explicitly included in the phase diagram.\nSpin configurations\nFrom the many-body density matrix, we extracted the\neigenstates of the impurity Hamiltonian with the highest oc-\ncurrence probabilities. Since we are dealing with the Fe d-\nshell which has 10 orbitals, there are in total 210= 1024 pos-\nsible states. We present in Fig. S3 the states with the highest\nprobabilities at three different points in the phase diagram:\n1. In the low UandJregime corresponding to the bottom-\nleft corner of the blue triangle phase in Fig. 2, the num-\nber of Fe electrons on the impurity can vary between\nN= 3,4, or5. It means the electrons are able to hop\naround, corresponding to a metallic state. These threecases are distinguished in Fig. S3 with different colors:\ngreen (light grey) for N= 3, orange (medium grey)\nforN= 4, and purple (dark grey) for N= 5. In this\nregime, the crystal field is dominant and mostly the t2g\norbitals are active. For N= 3, Hund’s coupling fa-\nvors the spreading of electrons on different orbitals. For\nlarger N, it is preferable to first doubly filled the xyor-\nbital which has the lowest on-site energy, and then one\nof the yz/zx orbitals.\n2. Increasing Utowards the bottom right corner where the\nempty red square phase dominates, charge fluctuations\nget suppressed, allowing only N= 4electrons on each\ncorrelated site rather than two sites to have N= 3 and\n5electrons. Again because of the strong crystal field, it\nis more favorable to doubly occupy the xyorbital.\n3. Moving to the top of the phase diagram where Jhas\nlarge values, the egshell becomes more occupied. In\nthis region, we find the Hund’s metal regime, where\na larger Uis required to drive the system to the Mott\nphase. Thus there is once again inter-site charge fluctu-\nations leading to N= 3 andN= 5 states. However,\nthe strong Hund’s coupling now favors different total\nspin|ms|values.\nFIG. S3. Rearrangement in spin configurations of Fe d-electrons as\na result of increasing UandJ. The strength of UandJgoes from\n0.5 to 5 eV and from 0.15 to 0.94 eV respectively.\nBand structure of Sr 2FeO 4under pressure\nIn Fig. S4, we present the band structure of SFO a) at zero\npressure on the left and b) under 150 GPa of pressure on the\nright. The bandwidth of SFO under pressure becomes broader\nand the egorbitals are pushed up in energy. However, the\ndx2−y2band is still touching the Fermi energy.11\nFIG. S4. Comparison of the open d-shell orbital character on the band structure of SFO a) under no pressure, and b) under 150 GPa of\nisotropic pressure. The dxy,dyz/zx ,dz2anddx2−y2orbital characters are shown in red, green, blue and orange, respectively. The horizontal\nline at zero marks the Fermi energy. The dx2−y2orbital is slightly metallic at zero pressure and almost tangent to the Fermi level at 150 GPa.\nSlater and Kanamori formulations of the local Coulomb\nrepulsion\nIn this section, we derive the effective Slater and Kanamori\nHamiltonians for a specific electronic shell of orbitals, start-\ning from the on-site Coulomb interaction ˆU=P\ni̸=j1\n|ri−rj|.\nTo do so, this interaction is first expanded in a basis of local\nstates, as\nˆU=1\n2X\nii′jj′X\nnpn′p′Uiji′j′\nnpn′p′d†\nind†\njpdj′p′di′n′ (S4)\nwhere d†\nin(din) creates (annihilates) an electron on the lo-\ncal site iwith other quantum numbers n. Note the the bare\nCoulomb interaction does not depend on the spin of the elec-\ntrons, so those are not written explicitly. Now, the coefficients\nof the Coulomb interaction in that basis are given by\nUiji′j′\nnpn′p′=⟨in;jp|ˆU|i′n′;j′p′⟩ (S5)\n=Zdr1dr2\n|r1−r2|¯ψin(r1)¯ψjp(r2)ψj′p′(r2)ψi′n′(r1).\nIn this derivation, we only consider the local part of this\ninteraction where i=i′=j=j′. We remove these\nindices from now on. Moreover, it is useful to derive\nthe Coulomb interaction in the basis of spherical harmon-\nicsψnlm(r) = Rnl(r)Yl\nm(θ, ϕ)which solve the hydrogen\natom, where n, l, m are the principal, total angular momen-\ntum and projected angular momentum quantum numbers re-\nspectively. The position is expressed in spherical coordinates\nr=rsinθcosϕx+rsinθsinϕy+rcosθzandR, Y are the\nradial and angular parts of the spherical harmonics. From now\non, we only consider a single electronic shell, so this basis has\nfixed nandl, and the only varying quantum number is m.\nIn this basis, we can write\n1\n|r1−r2|=∞X\nk=0rk\n<\nrk+1\n>4π\n2k+ 1kX\nq=−kYk\nq(Ω2)¯Yk\nq(Ω1)(S6)\nwhere Ω≡(θ, ϕ)is a solid angle, r<(r>) is the smaller\n(larger) of r1andr2, and ¯Y≡Y∗. We insert this expressionin Eq. (S5) and find\nUm1m2m3m4=2lX\nk=0ak(m1m3;m2m4)Fk (S7)\nwhere we defined the Slater integrals\nFk≡Z\ndr1dr2r2\n1r2\n2R2\nnl(r1)rk\n<\nrk+1\n>R2\nnl(r2) (S8)\nand the angular integrals given by\nak(m1m2;m3m4)\n4π≡kX\nq=−kGk\nq(m1, m2)\u0002\nGk\nq(m4, m3)\u0003∗\n2k+ 1\n(S9)\nwith the Gaunt coefficients for ldefined as\nGk\nq(m, m′)≡Z\ndΩ¯Yl\nm(Ω)Yk\nq(Ω)Yl\nm′(Ω). (S10)\nThe most important components of the Coulomb interac-\ntion are the direct ( Umm′mm′) and exchange ( Umm′m′mwith\nm̸=m′) integrals, which we write as\nUmm′mm′≡Umm′=2lX\nk=0bk(m, m′)Fk (S11)\nUmm′m′m≡Jmm′=2lX\nk=0ck(m, m′)Fk. (S12)\nIt can be shown that they are positive and that Umm′≥Jmm′.\nIn this basis, one can show that Ummm′m′≡Kmm′=\nUmm′δmm′. Neglecting the other terms, the Coulomb in-\nteraction Eq. (S4) in the local approximation becomes, with12\nnmσ≡d†\nmσdmσ,\nˆUloc=1\n2X\nmm′X\nσUmm′nmσnm′−σ (S13)\n+1\n2X\nm̸=m′X\nσ(Umm′−Jmm′)nmσnm′σ (S14)\n+1\n2X\nm̸=m′X\nσJmm′d†\nmσd†\nm′−σdm−σdm′σ (S15)\n+1\n2X\nm̸=m′X\nσKmm′d†\nmσd†\nm−σdm′−σdm′σ.(S16)\nWe now expressed this interaction in terms of the average\nCoulomb parameters in the basis of spherical harmonics, de-\nfined as\nUavg=1\n(2l+ 1)2X\nmm′Umm′and (S17)\nUavg−Javg=1\n2l(2l+ 1)X\nmm′(Umm′−Jmm′).(S18)\nNow in materials, real harmonics (that we now call orbitals)\nare normally used, because they are better eigenstates of the\ncrystal fields. They are defined as follow:\nyl0≡Yl\n0, ylm≡1√\n2\u0000\nYl\n−m+ (−1)mYl\nm\u0001\nand (S19)\nyl−m≡i√\n2\u0000\nYl\n−m−(−1)mYl\nm\u0001\n,form > 0. (S20)\nIn this orbital basis, we use the letter oto denote a real spher-\nical harmonic. We define\nJavg=1\n2l(2l+ 1)X\no̸=o′Joo′ (S21)\nand one can show that in the l= 2 case corresponding to\nd-orbitals,\nJavg=5\n7Javg. (S22)\nMoreover, in this basis, the terms Koo′are non-vanishing for\noff-diagonal elements.\nWe now look specifically at delectrons with a total angular\nmomentum l= 2. The basis of real spherical harmonics (or-\nbitals) is chosen as {dxy, dyz, dz2, dzx, dx2−y2}. In this basis,\ntheUoo′part of the Coulomb interaction is given as\nUoo′= (S23)\nU0 U0−2J1U0−2J2U0−2J1U0−2J3\nU0−2J1 U0 U0−2J4U0−2J1U0−2J1\nU0−2J2U0−2J4 U0 U0−2J4U0−2J2\nU0−2J1U0−2J1U0−2J4 U0 U0−2J1\nU0−2J3U0−2J1U0−2J2U0−2J1 U0\n,while the Joo′=Koo′parts are given as\nJoo′=Koo′=\nU0J1J2J1J3\nJ1U0J4J1J1\nJ2J4U0J4J2\nJ1J1J4U0J1\nJ3J1J2J1U0\n. (S24)\nIn these expressions,\nU0=F0+4\n49F2+4\n49F4, (S25)\nJ1=3\n49F2+20\n441F4, (S26)\nJ2=4\n49F2+5\n147F4, (S27)\nJ3=5\n63F4, (S28)\nJ4=1\n49F2+10\n147F4. (S29)\nThis representation of the local Coulomb interaction for d-\nelectrons is called the Slater Hamiltonian and is parameterized\nby the Slater integrals F0,F2andF4. The standard notation\nof the Slater Hamiltonian uses U≡F0,J≡(F2+F4)/14\nandF2/F4is fixed at 0.625.\nProjecting only on the t2gorbitals ( {dxy, dyz, dzx}), we\nfind\nUt2g=\nU0 U0−2J1U0−2J1\nU0−2J1 U0 U0−2J1\nU0−2J1U0−2J1 U0\n\nand\nJt2g=Kt2g=\nU0J1J1\nJ1U0J1\nJ1J1U0\n.\nIn this t2gsubspace, ˆU|t2gis called the Kanamori Hamiltonian\nand is parameterized solely by U0andJ1, referred to as UK\nandJKin the main text. One can show that the Slater and the\nKanamori parameters are related by\nU0≡UK=U+8\n7Jand (S30)\nJ1≡JK=6\n7F2\nF4+40\n63\n1 +F2\nF4J∼5\n7J. (S31)\nCorrelated band structure\nA band structure typically presents the single-particle en-\nergy states of infinite lifetime quasiparticles as a function of13\nmomentum, obtained using band theory. We call the corre-\nlated generalization the plot of the lattice spectral function\nA(k, ω), proportional to the density of states. In the non-\ninteracting case, it boils down exactly to a typical band struc-\nture, but in the presence of interactions, the bands can be\nbroadened by a finite quasi-particle lifetime acquired due to\ninteractions between electrons.\nTo obtain the lattice spectral function, we first have to con-\nstruct the lattice Green’s function because\nA(k, ω) =−1\nπImG(k, ω). (S32)\nThe lattice Green’s function is defined in the following way:\nG(k, ω) =1\nω+µ−ϵ(k)−∆Σ( k, ω)(S33)\nwhere µis the chemical potential, ϵ(k)is the non-interacting\nHamiltonian obtained within Wannier90 and ∆Σ( k, ω)is\nthe lattice self-energy for which double-counting was sub-\ntracted. This quantity is obtained by taking the impurity self-\nenergy that was analytically continued Σimp(ω), removing the\ndouble-counting ΣDC, and re-embedding to the lattice using\nthe Wannier90 projectors Pkνlthat allows to project the band\nµat the kmomentum to the lorbital. In the band basis, the\ncomponents of this self-energy are given by\n[∆Σ( k, ω)]νν′=X\nll′P∗\nkνl[Σimp(ω)−ΣDC]ll′Pkl′ν′.(S34)\nPerforming a summation over kof the spectral function\ngives us A(ω)which can be compared with the density of\nstates from DFT. Instead of the self-energy, one can also an-\nalytically continue the impurity Green’s function from the\nimaginary axis, Gimp(τ), to the real axis, Gimp(ω), using Max-\nEnt. Therefore, the spectral function A(ω)can also be ob-\ntained from Gimp(ω). The orbitally-resolved spectral func-\ntions of Fig. S2 are obtained from analytical continuation of\nthe impurity Green’s function.\nQuasi-particle Fermi surface\nThe lattice Green’s function in the band basis can written as\nGνν′(k, ω) =1\n(ω+µ−ϵν(k))δνν′−∆Σνν′(k, ω),(S35)\nwhere νν′are band indices.\nThe quasi-particle Fermi surface is the ω= 0 solution of the\npoles of the above Green’s function, i. e. when the quasi-\nparticle dispersion relation crosses the Fermi level\ndet[(ω+µ−ϵν(k))δνν′−∆Σ′\nνν′(k, ω)] = 0 (S36)\nwhere ∆Σ′\nνν′is the real part of the self-energy defined in\nEq. (S34). In the quasi-particle approximation, quasi-particles\nare presumed to have infinite lifetime and the imaginary part\n∆Σ′′is neglected.Mass enhancement\nFor an electron on the orbital l, the enhancement of the\neffective mass due to electronic correlations captured by the\nDMFT self-energy Σcompared to bare one given by DFT is\ngiven, on the imaginary-axis, by\nm∗\nmDFT\f\f\f\nl= 1−∂ImΣ l(iω)\n∂(iω)\f\f\f\niω→0+, (S37)\nwhere iωis the Matsubara frequency. This enhancement cap-\ntures the renormalization of the DFT bands due to electronic\ncorrelations. In a non-interacting system, there is no self-\nenergy ( Σ = 0 ) and the mass enhancement is 1, whereas in\nstrongly correlated systems,m∗\nmDFThas a value larger than one,\nwhich indicates that the quasi-particles have a heavier effec-\ntive mass due to the electron-electron interactions. Because\ninteractions generally affect each orbital differently,m∗\nmDFTis\norbital-specific.\nThe concept of quasi-particle becomes no longer relevant\nwhen electronic states are completely filled or empty. There-\nfore, we computed the mass enhancement only for the metal-\nlict2gorbitals of SFO under 40 GPa. These are obtained\nby fitting a fourth-order polynomial to the the imaginary part\nofΣl(iω)on the six lowest Matsubara frequencies. This\nfit allows us to extract the derivative∂ImΣ l(iω)\n∂(iω)\f\f\f\nω→0+, cor-\nresponding to the effective mass enhancement due to elec-\ntronic correlations. We can also extract the scattering rate\nΓl=−ZlImΣ l(iω)|ω→0+from this fit, as the intercept of\nthe polynomial with the y-axis.\nWe present the mass enhancement and scattering rates in\nTable I and Table II respectively, at fixed UK= 3 eV and as\na function of the inverse temperature βand Hund’s coupling\nJK. In Table I, we compare with the effective masses calcu-\nlated for SRO and reported in Ref. 32.\nWe keep UKfixed, because it corresponds to the standard\ncost of double occupancy in the second-quantized interacting\nHamiltonian of Eq. S2 and varying only JKhighlights better\nthe effect of Hund’s coupling and makes the comparison with\nRef. 32 straight forward.\nThe results reported in these tables highlight characteristics\nthat the clearly establish the metallic state of SFO under pres-\nsure as a Hund’s metal. Indeed, we observe that, similarly to\nwhat was observed in SRO [32], the Hund’s coupling leads to:\n(i) An increase of electronic correlations apparent in the\neffective masses and scattering rates,\n(ii) An orbital selective enhancement of the effective\nmasses of the Fe d-shell, and\n(iii) A push of the Fermi liquid crossover to lower tempera-\nture and a broader temperature range for the incoherent\nregime.\nThis last point is the reason why it is more difficult to calcu-\nlate the effective masses with increasing JK: we need to reach14\nTABLE I. Evolution of the orbital specific effective mass enhancement due to electronic correlations as a function of Hund’s coupling for both\n40GPa SFO in the three orbital metallic phase and SRO. We compute the enhancement at β= 1/kBT= 80 eV−1,100eV−1and150eV−1.\nWe keep UKfixed at 3eV . The uncertainties smaller than 0.1are not specified in the table.\nSFO ( 40GPa), UK= 3eV ,β= 80 eV−1β= 100 eV−1β= 150 eV−1SRO, UK= 2.3eV\nJK(eV)m∗\nmLDA\f\f\f\nxym∗\nmLDA\f\f\f\nyz/zxm∗\nmLDA\f\f\f\nxym∗\nmLDA\f\f\f\nyz/zxm∗\nmLDA\f\f\f\nxym∗\nmLDA\f\f\f\nyz/zxm∗\nmLDA\f\f\f\nxym∗\nmLDA\f\f\f\nyz/zx\n0.1 2.9 ±0.1 2.6 3.1 2.7 3.2±0.1 2.5 ±0.2 1.7 1.7\n0.2 3.6 ±0.1 3.4 4.2 3.7 5.2±0.2 3.9 ±0.1 2.3 2\n0.3 3.8 3.8 4.6±0.2 4.2 6.1±0.4 5.0 ±0.2 3.2 2.4\n0.4 3.7 ±0.1 3.6 4.4 4.2 6.3±0.3 5.4 ±0.1 4.5 3.3\nTABLE II. Evolution of the orbital specific scattering rate due to electronic correlations as a function of the Hund’s coupling for both 40GPa\nSFO in the three orbital metallic phase and SRO. We compute the enhancement at β= 1/kBT= 80 eV−1,100eV−1and150eV−1. We\nkeepUKfixed at 3eV . The uncertainties below 10 %are not explicitly specified.\nSFO ( 40GPa), UK= 3eV ,β= 80 eV−1β= 100 eV−1β= 150 eV−1\nJK(eV) Γxy(meV) Γyz/zx (meV) Γxy(meV) Γyz/zx (meV) Γxy(meV) Γyz/zx (meV)\n0.1 10.9 ±1.2 4.0 ±0.5 6.8±0.8 1.0 ±0.3 4.6±1.1 2.3 ±1.9\n0.2 29.3 12.1 18.7 5.6 8.4±1.3 2.2 ±0.7\n0.3 45.9 19.0 31.2 11.6 15.5±2.2 4.0 ±0.8\n0.4 62.1 28.0 44.4 17.8 22.1 6.8\nlower temperature to be in the coherent regime where the ef-\nfective masses saturate. This is also supported by the larger\nscattering rate. In our case, even at β= 150 eV , the effective\nmasses for JK= 0.4eV are far from this saturation.\namohaddeseh.kazemi.moridani@umontreal.ca\nbandre-marie.tremblay@usherbrooke.ca\ncMichel.Cote@umontreal.ca\ndogingras@flatironinstitute.org\n[1] P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas,\nPhysical Review 136, B864 (1964), publisher: American Phys-\nical Society.\n[2] W. Kohn and L. J. Sham, Self-Consistent Equations Including\nExchange and Correlation Effects, Physical Review 140, A1133\n(1965).\n[3] W. Kohn, A. D. Becke, and R. G. Parr, Density Functional The-\nory of Electronic Structure, The Journal of Physical Chemistry\n100, 12974 (1996).\n[4] G. Pizzi, V . Vitale, R. Arita, S. Bl ¨ugel, F. Freimuth,\nG. G ´eranton, M. Gibertini, D. Gresch, C. Johnson, T. Koret-\nsune, J. Iba ˜nez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand,\nA. Marrazzo, Y . Mokrousov, J. I. Mustafa, Y . Nohara, Y . No-\nmura, L. Paulatto, S. Ponc ´e, T. Ponweiser, J. Qiao, F. Th ¨ole,\nS. S. Tsirkin, M. Wierzbowska, N. Marzari, D. Vanderbilt,\nI. Souza, A. A. Mostofi, and J. R. Yates, Wannier90 as a com-\nmunity code: new features and applications, Journal of Physics:\nCondensed Matter 32, 165902 (2020).\n[5] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dy-\nnamical mean-field theory of strongly correlated fermion sys-tems and the limit of infinite dimensions, Rev. Mod. Phys. 68,\n13 (1996).\n[6] K. Held, Electronic structure calculations using dynamical\nmean field theory, Advances in Physics 56, 829 (2007).\n[7] G. Kotliar, S. Y . Savrasov, K. Haule, V . S. Oudovenko, O. Par-\ncollet, and C. A. Marianetti, Electronic structure calculations\nwith dynamical mean-field theory, Rev. Mod. Phys. 78, 865\n(2006).\n[8] X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet,\nJ.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet,\nN. Brouwer, F. Bruneval, G. Brunin, T. Cavignac, J.-B. Char-\nraud, W. Chen, M. C ˆot´e, S. Cottenier, J. Denier, G. Gen-\neste, P. Ghosez, M. Giantomassi, Y . Gillet, O. Gingras, D. R.\nHamann, G. Hautier, X. He, N. Helbig, N. Holzwarth, Y . Jia,\nF. Jollet, W. Lafargue-Dit-Hauret, K. Lejaeghere, M. A. L. Mar-\nques, A. Martin, C. Martins, H. P. C. Miranda, F. Naccarato,\nK. Persson, G. Petretto, V . Planes, Y . Pouillon, S. Prokhorenko,\nF. Ricci, G.-M. Rignanese, A. H. Romero, M. M. Schmitt,\nM. Torrent, M. J. van Setten, B. Van Troeye, M. J. Verstraete,\nG. Z ´erah, and J. W. Zwanziger, The Abinit project: Impact, en-\nvironment and recent developments, Computer Physics Com-\nmunications 248, 107042 (2020).\n[9] A. H. Romero, D. C. Allan, B. Amadon, G. Antonius, T. Ap-\nplencourt, L. Baguet, J. Bieder, F. Bottin, J. Bouchet, E. Bous-\nquet, F. Bruneval, G. Brunin, D. Caliste, M. C ˆot´e, J. Denier,\nC. Dreyer, P. Ghosez, M. Giantomassi, Y . Gillet, O. Gingras,\nD. R. Hamann, G. Hautier, F. Jollet, G. Jomard, A. Mar-\ntin, H. P. C. Miranda, F. Naccarato, G. Petretto, N. A. Pike,\nV . Planes, S. Prokhorenko, T. Rangel, F. Ricci, G.-M. Rig-\nnanese, M. Royo, M. Stengel, M. Torrent, M. J. van Setten,\nB. Van Troeye, M. J. Verstraete, J. Wiktor, J. W. Zwanziger,\nand X. Gonze, ABINIT: Overview and focus on selected capa-\nbilities, The Journal of Chemical Physics 152, 124102 (2020).15\n[10] P. E. Bl ¨ochl, Projector augmented-wave method, Physical Re-\nview B 50, 17953 (1994).\n[11] M. Torrent, F. Jollet, F. Bottin, G. Z ´erah, and X. Gonze, Im-\nplementation of the projector augmented-wave method in the\nABINIT code: Application to the study of iron under pressure,\nComputational Materials Science 42, 337 (2008).\n[12] F. Jollet, M. Torrent, and N. Holzwarth, Generation of Projector\nAugmented-Wave atomic data: A 71 element validated table\nin the XML format, Computer Physics Communications 185,\n1246 (2014).\n[13] M. van Setten, M. Giantomassi, E. Bousquet, M. Verstraete,\nD. Hamann, X. Gonze, and G.-M. Rignanese, The pseudodojo:\nTraining and grading a 85 element optimized norm-conserving\npseudopotential table, Computer Physics Communications 226,\n39 (2018).\n[14] A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards,\nS. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and\nK. A. Persson, Commentary: The materials project: A materi-\nals genome approach to accelerating materials innovation, APL\nMaterials 1, 011002 (2013).\n[15] O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko,\nL. Messio, and P. Seth, TRIQS: A toolbox for research on inter-\nacting quantum systems, Computer Physics Communications\n196, 398 (2015).\n[16] J. Kanamori, Electron Correlation and Ferromagnetism of Tran-\nsition Metals, Progress of Theoretical Physics 30, 275 (1963).\n[17] M. Aichhorn, L. Pourovskii, P. Seth, V . Vildosola, M. Zingl,\nO. E. Peil, X. Deng, J. Mravlje, G. J. Kraberger, C. Martins,\nM. Ferrero, and O. Parcollet, TRIQS/DFTTools: A TRIQS ap-\nplication for ab initio calculations of correlated materials, Com-\nputer Physics Communications 204, 200 (2016).\n[18] P. Werner, A. Comanac, L. de’ Medici, M. Troyer, and A. J.\nMillis, Continuous-time solver for quantum impurity models,\nPhys. Rev. Lett. 97, 076405 (2006).\n[19] E. Gull, P. Werner, S. Fuchs, B. Surer, T. Pruschke, and\nM. Troyer, Continuous-time quantum monte carlo impurity\nsolvers, Computer Physics Communications 182, 1078 (2011).\n[20] P. Seth, I. Krivenko, M. Ferrero, and O. Parcollet,\nTRIQS/CTHYB: A continuous-time quantum Monte Carlo hy-\nbridisation expansion solver for quantum impurity problems,\nComputer Physics Communications 200, 274 (2016).\n[21] L. Boehnke, H. Hafermann, M. Ferrero, F. Lechermann,and O. Parcollet, Orthogonal polynomial representation of\nimaginary-time Green’s functions, Phys. Rev. B 84, 075145\n(2011).\n[22] M. E. Merkel, A. Carta, S. Beck, and A. Hampel, solid dmft:\ngray-boxing DFT+DMFT materials simulations with TRIQS,\nJournal of Open Source Software 7, 4623 (2022).\n[23] G. J. Kraberger, R. Triebl, M. Zingl, and M. Aichhorn, Maxi-\nmum entropy formalism for the analytic continuation of matrix-\nvalued Green’s functions, Phys. Rev. B 96, 155128 (2017).\n[24] R. N. Silver, D. S. Sivia, and J. E. Gubernatis, Maximum-\nentropy method for analytic continuation of quantum Monte\nCarlo data, Phys. Rev. B 41, 2380 (1990).\n[25] J. E. Gubernatis, M. Jarrell, R. N. Silver, and D. S. Sivia, Quan-\ntum Monte Carlo simulations and maximum entropy: Dynam-\nics from imaginary-time data, Phys. Rev. B 44, 6011 (1991).\n[26] M. Jarrell and J. Gubernatis, Bayesian inference and the an-\nalytic continuation of imaginary-time quantum Monte Carlo\ndata, Physics Reports 269, 133 (1996).\n[27] F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Bier-\nmann, and A. I. Lichtenstein, Frequency-dependent local inter-\nactions and low-energy effective models from electronic struc-\nture calculations, Phys. Rev. B 70, 1 (2004).\n[28] K. Nakamura, Y . Yoshimoto, Y . Nomura, T. Tadano, M. Kawa-\nmura, T. Kosugi, K. Yoshimi, T. Misawa, and Y . Motoyama,\nRESPACK: An ab initio tool for derivation of effective low-\nenergy model of material, Computer Physics Communications\n261, 107781 (2021).\n[29] E. S ¸as ¸ıo ˘glu, C. Friedrich, and S. Bl ¨ugel, Effective coulomb in-\nteraction in transition metals from constrained random-phase\napproximation, Phys. Rev. B 83, 121101 (2011).\n[30] M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake,\nA. J. Millis, and S. Biermann, Low-energy models for corre-\nlated materials: Bandwidth renormalization from coulombic\nscreening, Phys. Rev. Lett. 109, 126408 (2012).\n[31] C. Honerkamp, H. Shinaoka, F. F. Assaad, and P. Werner, Lim-\nitations of constrained random phase approximation downfold-\ning, Phys. Rev. B 98, 235151 (2018).\n[32] J. Mravlje, M. Aichhorn, T. Miyake, K. Haule, G. Kotliar, and\nA. Georges, Coherence-Incoherence Crossover and the Mass-\nRenormalization Puzzles in Sr 2RuO 4, Physical Review Letters\n106, 096401 (2011)."    },    {        "title": "1402.3537v1.Scattering_Experiments_with_Microwave_Billiards_at_an_Exceptional_Point_under_Broken_Time_Reversal_Invariance.pdf",        "content": "arXiv:1402.3537v1  [nlin.CD]  14 Feb 2014Scattering Experiments with Microwave Billiards at an Exce ptional Point\nunder Broken Time Reversal Invariance\nS. Bittner,1,2B. Dietz,1,∗H. L. Harney,3,†M. Miski-Oglu,1A. Richter,1and F. Sch¨ afer4\n1Institut f¨ ur Kernphysik, Technische Universit¨ at Darmst adt, D-64289 Darmstadt, Germany\n2Laboratoire de Photonique Quantique et Mol´ eculaire,\nCNRS UMR 8537, Institut d’Alembert FR 3242,\nEcole Normale Sup´ erieure de Cachan, F-94235 Cachan, Franc e\n3Max-Planck-Institut f¨ ur Kernphysik, D-69029 Heidelberg , Germany\n4Division of Physics and Astronomy, Kyoto University,\nKitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Jap an\n(Dated: September 18, 2021)\nScattering experiments with microwave cavities were perfo rmed and the effects of broken time-\nreversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on\nan isolated doublet of nearly degenerate resonances were in vestigated. All elements of the effective\nHamiltonian of this two-level system were extracted. As a fu nction of two experimental parameters,\nthe doublet and also the associated eigenvectors could be tu ned to coalesce at a so-called exceptional\npoint (EP). The behavior of the eigenvalues and eigenvector s when encircling the EP in parameter\nspace was studied, including the geometric amplitude that b uilds up in the case of broken TRI. A\none-dimensional subspace of parameters was found where the differences of the eigenvalues are either\nreal or purely imaginary. There, the Hamiltonians were foun dPT-invariant under the combined\noperation of parity( P)andtime reversal ( T) inageneralized sense. TheEP is thepointof transition\nbetween both regions. There a spontaneous breaking of PToccurs.\nPACS numbers: 02.10.Yn, 03.65.Vf, 05.45.Mt, 11.30.Er\nI. INTRODUCTION\nThepresentarticleprovidesadetailedreviewofourex-\nperimental studies of two nearly degenerate eigenmodes\nin a dissipative microwave cavity with induced violation\nof time-reversal invariance (TRI). Since the underlying\nHamiltonian is not Hermitian [1–9] it may possess ex-\nceptional points (EPs), where two or more of its com-\nplex eigenvalues and also the associated eigenvectors co-\nalesce. An EP has to be distinguished from a diaboli-\ncal point (DP), i.e., a degeneracy of a Hermitian Hamil-\ntonian, where the eigenvectors are linearly independent\n[10, 11]. The occurrence of EPs [3–5, 12] in the spec-\ntrum of a dissipative system has been studied in classi-\ncal [13–19] and quantum systems [20–26]. The first ex-\nperimentalevidencefortheexistenceofEPswasachieved\nwith flat microwave cavities [27–32], that are analogues\nof quantum billiards [33, 34]. Later they were observed\nin coupled electronic circuits [35] and in chaotic micro-\ncavities and atom-cavity quantum composites [36, 37].\nThe present investigation focuses on TRI and its vio-\nlation in scattering systems, a subject which had been\nlargely investigated in nuclear and particle physics (see,\ne.g., Ref. [38, 39]).\nThe experiments were performed with flat cylindri-\ncal cavities, so-called microwave billiards [33, 34, 40–42].\n“Flat” means that for the considered range of excita-\n∗Electronic address: dietz@ikp.tu-darmstadt.de\n†Electronic address: hanns-ludwig.harney@mpi-hd.mpg.detion frequencies fthe height of the resonator is so small\nthat the electricfield strengthis perpendicular to the res-\nonator’s plane. Such resonators are very good test beds\nforthepropertiesoftheeigenvaluesandwavefunctionsof\nquantum billiards with corresponding shape and gener-\nallyforscatteringphenomena. Wespeakofscatteringex-\nperiments becauseresonantstateswere excited inside the\nresonator through an antenna reaching into its interior\nand the reponse was detected via another (or the same)\nantenna. The scattering matrix element [43] describes\nthe transfer of electromagnetic waves [44–48] from one\nantenna through the cavity to the other one. Violation\nof TRI was induced by inserting a ferrite into the cavity\nand magnetizing it with an external magnetic field [49–\n53]. Note that TRI violation caused by a magnetic field\nis commonly distinguished from dissipation [54]. In open\nsystems it is equivalent to violation of the principle of\nreciprocity of a scattering process, i.e., the symmetry of\nthe scattering matrix under the interchange of entrance\nand exit channels. Such systems are dissipative systems.\nThis property alone, however, does not imply violation\nof TRI because it is compatible with reciprocity [55–58].\nThe measurements of the resonance spectra allowed to\ncompletely specify the effective Hamiltonian of the scat-\ntering system together with the eigenvalues and eigen-\nvectors and to approach or encircle an EP in its eigen-\nvalue spectrum. In order to achieve the coalescence of\na doublet of eigenmodes two parameters were varied in\nthe experiments. Only doublets that were well separated\nfrom neighboring resonances were taken into consider-\nation. Therefore, the effective Hamiltonian was two-\ndimensional. Theexperimentswerecompletein thesense2\nthat they allowed to extract all four complex matrix el-\nements of the effective Hamiltonian as a function of the\nexcitation frequency and of the two parameters needed\nto tune the system to an EP.This allowedto quantify the\nsize of TRI violation and to measure to a high precision\nthe geometricphase [10, 11] and the geometricamplitude\n[1, 2, 59–61] that the eigenvectors gather when encircling\nan EP.\nFurthermore, we observed configurations with PT\nsymmetry, including a PTphase transition. It was\ndemonstrated in Ref. [62] that a non-Hermitian Hamil-\ntonianHhas real eigenvalues provided it respects PT\nsymmetry, i.e. [ PT,H] = 0 and has eigenvectors that\nare alsoPTsymmetric. The PTsymmetry of the eigen-\nvectors may be spontaneously broken by varying an ex-\nternal parameter. Then they are no longer eigenvectors\nofPT, although Hstill commutes with PT[62, 63]. As\na result, the eigenvalues of Hare no longer real, but\nratherbecome complexconjugatepairs. This phasetran-\nsition occurs at an EP. It was studied experimentally\nand theoretically in superconducting wires [64, 65], op-\ntical waveguides [66–73], NMR [74], lasers [75–78], elec-\ntronic circuits [79], photonic lattices [80–82] and atomic\nbeams [83, 84]. Further theoretical studies of PTsym-\nmetry based effects concern spectral singularities [85] as\nwell as Bloch oscillations in PT-symmetric lattice struc-\ntures [86]. The S-matrix formalism for PT-symmetric\nsystems was analyzed recently [87, 88].\nIn the present article we report on our experimental\nwork on EPs in the context of TRI that has been the\nbasis of three Letters [53, 89, 90]. We give more details\non the experimental setups as well as on the procedure\nused to extract the effective Hamiltonian from the ex-\nperimental resonance spectra. In order to straighten out\nthese and other shortcomings we provide a detailed de-\nscription of the unified analysis, that is, the scattering\nformalism and the derivation of the features of the as-\nsociated effective Hamiltonian at and in the vicinity of\nan EP. Furthermore we include still unpublished exper-\nimental results that corroborate these analytical ones.\nExperiments with two different setups were performed.\nThe first one, discussed in Sects. II to IV, deals with\ngeneral properties (experimental and formal) of scatter-\ning systems with broken TRI. The scattering formalism\nis then applied to the second setup that features an EP.\nIt is used in Secs. V through\nIX.\nSection II details the first experimental setup. The\nscattering formalism used throughout this article is in-\ntroduced in Sect. III. It is formally identical to the one\ndeveloped for nuclear reactions. The scattering matrix\nessentially is the resolvent of the effective Hamiltonian\nof the system of states within the cavity. This Hamil-\ntonian is non-Hermitian since it comprises not only the\ninteractionsbetweentheboundstatesbutalsothosewith\nthe exterior, i.e., the open decay channels. The scatter-\ning process is reciprocal if the Hamiltonian is symmet-\nric under transposition. This is the case for a vanishingexternal magnetic field. We extracted the full effective\nHamiltonian by exploring all elements of the scattering\nmatrix in a subspace of antenna channels. In the present\ncases the dimension of the effective Hamiltonian equaled\none or two, because we investigated an isolated state or\nan isolated doublet of nearly degenerate states. A theo-\nretical description of the measurements of Sec. II is given\nin Sec. IV. It provides a direct link between the extracted\neffective Hamiltonians and the ferromagnetic resonance\nakin to the ferrite.\nSection V describes the measurements with the second\nsetup. Two experimental parameters were introduced\nthat could be tuned to an EP.They wererestrictedin our\nexperiments to the neighborhood of an EP. The proper-\nties of EPs [11, 91–93] were well established by experi-\nment in systems with TRI [27–30, 35–37, 94]. We review\nour experimental results on their properties in systems\nwith TRI violation [89, 90].\nSection VI is concerned with the properties of the\neigenvalues and eigenvectors of the effective Hamiltonian\nat and around the EP [30, 89]. Section VII focuses on\nthe line shape of the resonance emerging from the coales-\ncence of the doublet of resonances at the EP. In Sec. VIII\nwe treat the transport of the Hamiltonian along a path\nencircling the EP [1, 2, 31, 89]. In both cases the re-\nsults differed from those obtained in the framework of\nreciprocal scattering.\nIf there is an EP then there is a one-dimensional sub-\nspaceof experimentalparameterswhere both eigenvalues\n— after a common shift — are either real or purely imag-\ninary. The transition takes place exactly at the EP. As\noutlined in Sec. VIII we identified a region in the param-\neter plane where the eigenvalues exhibit this property\nand found the corresponding set of Hamiltonians PT-\ninvariant in a generalized sense.\nII. EXPERIMENTAL SETUP I\nThe experiments were performed with flat cylindrical\nmicrowave resonators made of copper. They were con-\nstructed from three 5 mm thick copper plates that were\nsqueezed on top of each other with screws. The mid-\ndle plate had a hole with the shape of the resonator.\nViolation of TRI was induced by a magnetized ferrite\nplaced inside the resonators. In a first experiment —\ndiscussed in Sec. IV — the properties of the ferrite were\nstudied using a resonator with the shape of a circle of\n250 mm in diameter. It is depicted in Figs. 1 and 2.\nThe circular copper disk shown in both figures was in-\nserted into the resonator, thus transforming the circu-\nlar billiard into an annular one, to realize isolated reso-\nnances, i.e., singlets. A vector network anlyzer (VNA)\nof the type HP 8510C coupled microwave power into\nand out of the system via two antennas, 1 and 2, that\nwere attached to the top plate. These are metal pins\nof 0.5 mm in diameter reaching about 2 .5 mm into the\nresonator. The maximal excitation frequency of the mi-3\n1 2\nFIG. 1: Scheme of the experimental setup (not to scale) to\nstudy the properties of the ferrite. The antennas 1 and 2 are\nconnected to the vector network analyzer. The inner circle i s\na copper disk introduced into the resonator to realize singl et\nresonances.\ncrowaves was chosen such that the electric field strength\nwas perpendicular to the top and the bottom plate of\nthe resonator. Then the vectorial Helmholtz equation\nreduces to a scalar one which is mathematically equiva-\nlent to the two-dimensional Schr¨ odinger equation of the\ncorrespondingquantumbilliard[33,34]. TheVNAdeter-\nmined the relative phase and amplitude of the input and\noutput signals. This yields the complex elements Sba,\nwhereaandbtake the values 1 or 2, of the scattering\nmatrix describing the scattering process from antenna\nato antenna b. One of the antennas 1 ,2 was used as\nentrance, the other one as exit channel [44–48] in trans-\nmission measurements, and one of them as entrance and\nexit channel in reflection measurements. Effects intro-\nduced by the coaxial connectors were largely eliminated\nby calibrating the VNA via standards with well-known\ntransmission and reflection properties.\nFIG. 2: (Color online) Photograph of the microwave billiard .\nThe top plate has been removed. In the measurements it was\nscrewed tightly to the middle plate, which had a hole with\nthe shape of the resonator, and the bottom plate through the\ndisplayed holes. The ferrite is marked by an arrow. Rings of\nsolder are visible along the boundary of the resonator and th e\ninner disk. They ensured good electrical contact between th e\ntop and bottom plates of the resonator.\nAscatteringprocess a→bfora∝negationslash=biscalledreciprocalifSba=Sab. In the experiments presented in this paper\nreciprocity was broken by a magnetized ferrite inside the\ncavity [49–53]. The ferrite is a calcium vanadium gar-\nnet with the shape of a cylinder, 5 mm high and 4 mm\nin diameter [95]. The material had a resonance line of\nwidth ∆H= 17.5 Oe; the saturation magnetization was\n4πMS= 1859 Oe, where 1 Oe = 1000 /(4π) A/m. Two\nNdFeBmagnetswereplacedaboveandbelowthebilliard,\nperpendicular to its plane at the position of the ferrite,\nsee Fig. 3. They had cylindrical shapes with 20 mm in\nFIG. 3: Sectional drawing of the setup used to magnetize the\nferrite. The ferrite was placed inside the resonator and abo ve\nand below it were NdFeB magnets outside the cavity. Each\none was held in place by a screw thread mechanism allowing\nto vary the distance between the magnets and thus the field\nstrength at the ferrite.\ndiameter and 10 mm in height and produced a magnetic\nfieldBparallel to the ferrite’s axis. For the variation of\nBthe distance between the magnets was adjusted by a\nscrewthreadmechanism. Fieldstrengthsofupto120mT\n(with an uncertainty below 0 .5 mT) were used.\nDue to the external magnetic field the ferrite acquires\na macroscopic magnetization Mthat precesses with the\nLarmor frequency around B. Furthermore, the rf mag-\nnetic field inside the cavity (at the place of the fer-\nrite) is elliptically polarized and therefore can be decom-\nposed into two components of opposite circular polariza-\ntion. The component having the same rotational direc-\ntion as the electron spins is partly absorbed by the fer-\nrite, whereas the other one remains unaffected. Thus the\nmagnetizedferritebreaksreciprocitybecausetheelectron\nspins in the ferrite couple differently to the two polariza-\ntions. The absorption is strongest at the ferromagnetic\nresonance where the frequency of the Larmor precession\nmatches the rf frequency of the resonator. Reciprocity\nis experimentally tested by interchanging input and out-\nput at the antennas. This is equivalent to the change\nof the direction of time (and differs from the method of\nRef. [96]). Thus reciprocity is equivalent to TRI and\nlack of reciprocity to violation of TRI. The latter case\nhas been studied in numerous works [49–53, 97–100].4\nTo test the precision of the experiments we first looked\nat isolated resonances. They were obtained by inserting\na copper disk with a diameter of 187 .5 mm and a height\nof 5 mm into the circular resonator — as is illustrated\nin Figs. 1 and 2. The classical dynamics of the result-\ning annular billiard is fully chaotic [101, 102]. There-\nfore a close encounter of two states was improbable and\nthe measured spectrum consisted of well isolated reso-\nnances. Their widths were ≈14 MHz and their spacings\n≈300 MHz. We have studied eight singlets. For the one\natf= 2.84 GHz we show in Fig. 4 both, S12andS21.\nThey have been taken with the ferrite magnetized by a\n12\n121 2\nFIG. 4: The singlet at 2 .84 GHz in the annular billiard. The\ncomplex functions S12(f) (open circles) and S21(f) (solid cir-\ncles) have been measured at B= 119.3 mT. For clarity only\nevery 14thdata point is shown. The two complex functions\ncoincide up to a deviation due to errors of 5 ×10−3for the\nreal and imaginary parts. Thus reciprocity holds within thi s\nerror.\nstaticmagneticfieldof B= 119.3mT.Thecomplexfunc-\ntionsS12(f) andS21(f) agree to 0 .5% in amplitude and\nphase for a variety of field strengths Bbetween 28.5 mT\nand 119.3 mT. Thus an isolated resonanceexhibits recip-\nrocal scattering even for a non-vanishing magnetization\nof the ferrite, see Sec. IVA.\nDue to its rotational symmetry the circular billiard\nof Fig. 1 without the inner copper disk has numerous\ndegeneracies. The ferrite lifts the symmetry and thus\nthe resonances are split into doublets of close-lying ones.\nWe chose four doublets that are sufficiently isolated from\nneighboring ones at 2 .43,2.67,2.89and 3.2 GHz. For the\nsecond one, the violation of reciprocity is illustrated in\nFig.5. Similarresultswereobtainedatthefirstandthird\ndoublets, but not at the fourth one, where reciprocity\nholds as in the case of a singlet. In that case a simulation\nof the field patterns [103] in the resonator revealed that\nfor one of the two states the magnetic field vanished at\nthe position of the ferrite, see the upper mode in part A\nofFig.6. Movingtheferritetoaplacewhereitinteracted\nwith both states, see the lower and upper modes in part\nB of Fig. 6, resulted in a violation of reciprocity. The\nreasons for these observations are given in Sec. IVB.22\n11\n21\n121 2 2.696 GHz\nFIG. 5: The doublet at 2 .696 GHz in the circular billard with\nthe magnetic field B= 36.0 mT. The upper panel shows |S11|\n(solid line) and |S22|(dashed line), the lower panel |S12|(solid\nline) and |S21|(dashed line). Violation of reciprocity is clearly\nvisible.\nFIG. 6: (Color online) Field patterns of the fourth doublet.\nThe small triangles symbolize strength and direction of the\nmagnetic fields. The grey shades represent the electric field\nstrength. The darker the color the stronger is the electric\nfield. The upper modes are found at 3 .18 GHz, the lower\nones at 3 .20 GHz. The arrows point at the ferrite. In part A\nof the figure violation of reciprocity is not observed becaus e in\nthe upper mode the magnetic field vanishes at its position. In\npart B the ferrite has been shifted 20 mm towards the center\nof the circle, i.e., to a position where the field is non-zero i n\nboth modes.\nIII. ASPECTS OF SCATTERING THEORY\nIn this section, aspects of scattering theory and the\nconnection between reciprocity and TRI are discussed in\nmore detail. For the analysis of the experimental data\nwe used a formalism of scattering theory which had orig-\ninally been developed for nuclear reactions [43, 104] and\nlater had been successfully applied to the situation at\nhand [44–48, 87, 88]. As in Refs. [53, 89, 90, 99, 100,5\n105, 106], we used the ansatz\nSba(f) =δba−2πi2/summationdisplay\nµ,ν=1W∗\nµb/parenleftbig\n[f1−H]−1/parenrightbig\nµνWνa(1)\nfrom Sec. 4.2 of [43] together with [104] for the descrip-\ntion of the resonance spectra |Sba(f)|. The quantity fis\nthe excitation frequency of the ingoing wave, δbais the\nKroneckersymbol, 1 is the unit matrix, His the effective\nHamiltonian ofthe resonator,and the matrix Wwith the\nelementsWµa,Wµbcouples the resonator states µto the\nopen channels.\nThe dimension of the scattering matrix element Sbais\ngiven by the number of open channels. Explicitely, the\nresonators used in the experiments had two open chan-\nnels, the antennas1 and 2. Implicitly, they had a number\nof unspecified [100] open channels where only decay took\nplace due to Ohmic absorption in the walls of the ferrite\nand the cavity. Generally, any absorption, often called\ndissipation, is ascribed to open channels [99, 100, 107].\nWe measured Sbafor the two explicit channels, i.e. for\naas well asbequal to 1 or 2. Due to the presence of\nthe implicit channels, this two-dimensional S-matrix is\nsub-unitary.\nThe effective Hamiltonian\nH=H+F (2)\ntakes care of both, the Hermitian Hamiltonian Hof the\nclosed resonator(i.e. the microwavebilliard) and its cou-\nplingFto the open channels. Since we were interested in\nisolated and pairs of closely lying resonances that were\nwell apart from neighboring ones it was either one- or\ntwo-dimensional. The elements of Fare given by the\nintegral\nFµν(f) =/summationdisplay\nj=1,2,i/integraldisplay∞\n0df′Wµj(f′)W∗\nνj(f′)\nf+−f′,(3)\nwheref+=f+iǫis the frequency fshifted infinites-\nimally into the upper complex plane. The sum on the\nr.h.s. of this equation runs over the antenna channels\n1,2 as well as the implicit open channels i.\nEvery matrix with complex elements can uniquely be\nwritten as the sum of two Hermitian matrices Hintand\nHext— one of them being multiplied by the imaginary\nunitisuch that\nH=Hint+iHext. (4)\nHere\nHint\nµν=Hµν+/summationdisplay\nj=1,2,iP/integraldisplay∞\n0df′Wµj(f′)W∗\nνj(f′)\nf−f′,\nHext\nµν=−π/summationdisplay\nj=1,2,iWµj(f)W∗\nνj(f), (5)\nwhereP/integraltext\ndf′is a principle value integral which shifts\nand mixes the states of the closed resonator. The matrixHintrepresents the dynamics of the internal states µof\nthe resonator. The term iHextin Eq. (4) describes the\ndecay of the states µinto the open channels. Due to its\npresence the resonances acquire a line width and the ef-\nfective Hamiltonian His a non-Hermitian operator. This\nallows for the existence of an EP, as discussed below.\nIn the experiments on TRI violation the reciprocity,\ni.e., the symmetry\nSba=Sab (6)\nof theS-matrix was tested. This was possible since\nboth, amplitude and phase of the S-matrix elements,\nwere accessible. In nuclear physics [108–112] only the\nweaker principle of detailed balance, which is |Sba|2=\n|Sab|2, could be tested. Reciprocity occurs if and only if\nboth Hermitian matrices, HintandHext, are symmetric,\nwhence real. Thus it is equivalent to the invariance un-\nder time reversal [55–58, 113] of both, the interactions of\nthe statesµwith each other and their coupling Wto the\nopen channels. As outlined in Sec. II TRI breaking was\ninducedby a ferrite that was magnetized by an external\nmagnetic field B. This is to be distinguished from dis-\nsipation [54]. The reason is that for B= 0 dissipative\nsystems are described by a complex symmetric matrix\nH=HTso that reciprocity holds, i.e., S=ST.\nWithin the present experiments the coupling of the an-\ntennas to the resonator modes was time-reversal invari-\nant. Therefore the matrix elements Wµjwere real for\nj= 1,2. The implicit channels j= i, however, are essen-\ntially those of absorption within the ferrite. Thus when\nthe ferrite is magnetized the corresponding elements Wµi\ncannotbe chosenrealin a basiswhere the coupling to the\nantennas is real, and then the matrix Fis not symmetric\nunder transposition.\nWe focused on the properties of the eigenvalues and\neigenvectors of the effective Hamiltonian H. Its matrix\nelements as well as Wµjwere determined by fitting the\nscattering matrix elements of Eq. (1) to the measured\nones. We considered pairs of closely lying resonances\nthat are well isolated from neighboring ones. Then there\nare four real matrix elements Wµjcoupling the states µ\nto the antennas j= 1,2 and the 2 ×2 matrix Hhas\nfour complex elements. Because the scattering matrix of\nEq. (1) is invariant under orthogonal transformations of\nthe basis of Hthe latter has to be fixed. This reduces the\nnumber ofrealparametersof Hto seven. They aredeter-\nmined together with the four elements Wµjby measuring\nalargesetofthe four complexscatteringmatrixelements\nin small steps of faround the resonance frequencies and\nfitting the expression Eq. (1) to this set. Here we use the\nproperty that the parameters do not depend on fin the\nconsidered frequency range.\nOnceHhas been extracted it is most conveniently dis-\ncussed in terms of an expansion with respect to the Pauli\nmatrices\nσ1=/parenleftbigg\n0 1\n1 0/parenrightbigg\n;σ2=/parenleftbigg\n0−i\ni0/parenrightbigg\n;σ3=/parenleftbigg\n1 0\n0−1/parenrightbigg\n.\n(7)6\nWe write the effective Hamiltonian in the form\nH=/parenleftbigg\ne1HS\n12−iHA\n12\nHS\n12+iHA\n12e2/parenrightbigg\n.(8)\nHere, the notation of Refs. [89, 90] is used. The symbols\nHS\n12andHA\n12denote the symmetric and antisymmetric\nparts of H, respectively. They are complex, as are the\ndiagonalelements e1,e2. Anon-vanishingmatrixelement\nHA\n12∝negationslash= 0 is equivalent to TRI violation [114], whence in\nourcasetotheoccurrenceofcomplex Wµi. Onecanwrite\nH=e1+e2\n21+/vectorh·/vectorσ (9)\nwith the vector /vectorhdefined as\n/vectorh=\nHS\n12\nHA\n12\n(e1−e2)/2\n. (10)\nThe effective Hamiltonian His Hermitian if the entries\nof/vectorhas well ase1+e2are real.\nThe entries of /vectorhare given by\n2HS\n12= Tr(σ1H),\n2HA\n12= Tr(σ2H),\ne1−e2= Tr(σ3H). (11)\nThey allow to write down the invariants of H: The value\nofHA\n12is invariant under orthogonal transformations of\nH. This follows from the fact that σ2generates the or-\nthogonal transformations\nO(φ) =/parenleftbigg\ncosφ−sinφ\nsinφcosφ/parenrightbigg\n= exp(−iφσ2). (12)\nThereforeO(φ) commutes with σ2and thus Tr( σ2H) =\nTr(σ2OTHO). The quantity /vectorh2= (HS\n12)2+ (HA\n12)2+/parenleftbige1−e2\n2/parenrightbig2is invariant under all unitary transformations\nofHas are the eigenvalues\nE1,2=/parenleftbigge1+e2\n2±/radicalbig\n/vectorh2/parenrightbigg\n. (13)\nIV. EFFECT OF THE FERRITE\nTo investigate the effect of the magnetized ferrite we\nmeasured the four matrix elements Sab(f) at about 500\nvalues offfor 15 settings of the magnetic field B. From\nthese data the complex elements of the matrix Hand the\nmatrix elements Wµ1,Wµ2were determined as functions\nofBas described in the last section. We consider two\ncases, singlets and doublets of closely lying resonances.A. Test of TRI at singlets\nFor a singlet the effective Hamiltonian is one-\ndimensional. Let its only element be H11. With Eq. (1)\nwe obtain the off-diagonal element of the S-matrix\nS12=−2πiW∗\n11(f−H11)−1W12.(14)\nAs mentioned above the couplings of the antennas to\nthe singlet state, W11andW12, were real. Consequently\nS12=S21, i.e. reciprocity holds — independently of the\nvalueofH11andwhetherornotthe ferriteis magnetized.\nThis was confirmed experimentally using the microwave\nbilliard shown in Figs. 1 and 2. In Fig. 4 the matrix\nelementsS12andS21are compared to each other. Al-\nthoughB∝negationslash= 0 they agree up to the experimental error\nof 5·10−3. Thus singlets measured in the microwave ex-\nperiments presented in this paper may not be used for\ntests on TRI. Note, however, that in Refs. [112, 115] iso-\nlated nuclear resonancestates were shown to provide this\npossibility.\nB. TRI violation at doublets\nFigure 5 demonstrates that doublets of states show vi-\nolation of TRI when the ferrite is magnetized. Further-\nmore, we have seen that there are 11 real fit parameters\ninthe scatteringmatrixfordoublets. Thecouplingtothe\nantennas,Wµ1andWµ2, wasexpected to be independent\nofB. In practice we found a marginal dependence on B\ndue to a slight displacement of the electric field pattern\nwith its value. The other parameters depend on Bbut\nnot onf, and were obtained by fitting Eq. (1) simulta-\nneously to the four complex elements of S=S(f) at 500\nvalues off. Figure 7 demonstrates that the agreement\nbetween the data and the fits is very good. The elements\n2.696 GHz\n1221\nFIG. 7: Comparison of the fitted matrix elements |S12|(solid\nline) and |S21|(dashed line) to the experimental data points\n(circles) also shown in the lower panel of Fig. 5. Fitting of\nexpression (1) to the data reproduces the data points within\nerrors of ≈5×10−4for both, real and imaginary parts. For\nclarity only every 10thexperimental point is shown.7\nofHvary significantly with B. As an example, mod-\nulus and argument of HA\n12are plotted in Fig. 8 for the\ndoublet at 2 .914 GHz as functions of B. The maximum\n2.914 GHzrd\nf\nFIG. 8: The antisymmetric part HA\n12ofH. The data have\nbeen taken at the third doublet of Tab. I at a mean frequency\n¯f= 2.914 GHz in the circular billiard. The maximum in |HA\n12|\nand the decrease of Arg( HA\n12) by the amount of πdisplay the\nferromagnetic resonance. The error bars indicate the varia nce\nof the results obtained in five independent experiments [116 ].\nin|HA\n12(B)|and the monotonic decrease of Arg( HA\n12) by\nthe amount of πare the manifestation of the ferromag-\nnetic resonance within the ferrite. According to Sec. II\nthe rf magnetic field lines exhibit an elliptical polariza-\ntion which can be split into two components of opposite\ncircular polarization. Furthermore, the ferrite couples to\nonly one of them. This has been worked out formally in\nRef. [53] and led to the analytic expression [116–118]\nHA\n12(B) =1\n4λBTrelaxf2\nM\nf0(B)−f−i/Trelax(15)\nfortheT-breakingmatrixelement. Thefactor λBstands\nfor the coupling between the electron spins in the ferrite\nand the rf magnetic field which according to Fig. 6 de-\npends on the position of the ferrite within the field. We\nassumed that the matrix element HA\n12(B), and generally\nthe matrix H, are analytic functions of their parameters,\nwhence to leading order, it should be linear in Bbecause\nHA\n12(B) vanishes with B→0.\nEquation (15) depends on two parameters, fandλ,\nthat must be determined by a fit to the experimen-\ntal function HA\n12(B). The parameter fgives the cen-\nter position of the doublet. For the case displayed in\nFig. 8 the parameters are f= 2.914±0.003 GHz and\nλ= 37.3±1.6 Hz/mT.\nAt the ferromagnetic resonance, i.e., at the value of B\nwhere the real part of the denominator in Eq. (15) van-\nishes,HA\n12is purely imaginary, see Fig. 8. According to\nEqs. (4) and (8) it is given as the sum of the antisym-\nmetric parts of the Hermitian matrices HintandHext,\n2HA\n12=i(H12−H21) =i(Hint\n12−Hint\n21)−Hext\n12+Hext\n21.\nThey are purely imaginary at the ferromagnetic reso-\nnance. Thus, there HA\n12isgivenby2 HA\n12=−Hext\n12+Hext\n21,i.e.,Hintdoes not contribute. Far outside the ferromag-\nnetic resonance the reverse was found, HA\n12is real and\nthus TRI violation is determined by Hint. Our results\nshowthat the absorptiveproperties ofthe ferrite maybe-\ncome visible in both, the internal and the external parts\nofH, in agreement with Eq. (5). This proves that the\nprinciple value integral indeed is important for the de-\nscription of a scattering experiment.\nSummarizing this section the technique of inducing\nTRI violation via a magnetized ferrite has been reviewed\nandthe scatteringformalismdevelopedandconfirmedby\nthe experiments. We found that an isolated resonance\ndoes not reveal TRI violation, whereas a doublet of res-\nonances does.\nV. THE EXPERIMENTAL SETUP II\nIn the sequel we consider the occurrence of an excep-\ntional point (EP). At such a point the eigenvalues of H\nagreeand the eigenvectorsbecome linearlydependent [1–\n5, 12]. For these experiments a new resonator was con-\nstructed. It again was circular and 250 mm in diameter\n1 2\ns 15mmtop plate\nbottom plategate\n80 mm125 mm\nFIG. 9: The upper part sketches the resonator used in\nSecs. VI–IX. Two parameters can be set from outside, the\nopening sbetween the two approximate semicircles and the\nposition δof the Teflon piece with respect to the center of the\ncavity. As in Sec. II there are two antennas 1 and 2 reaching\ninto the cavity. The ferrite is denoted by F. The parameter\nsactually denotes the vertical position of the gate as shown\nin the lower part of the figure. The broken line indicates the\ngroove in the bottom plate.\nand the height of 5 mm as in Sec. II. A 10 mm thick\ncopper bar, shifted by 1 .8 mm to the left of the diame-\nter paralleling it, divided it into approximate semicircles\nconnected through a 80 mm long opening [90], see Fig. 9.\nThis avoidsdegeneraciesofthe doublets ofstates. An EP8\nwas approached or accessed by varying two experimental\nparameters, sandδ. One parameter was related to the\ncoupling between the electric field modes in each part. It\nwas controlled by a copper gate with tilted bottom which\nwasinsertedthroughaslit inthe top ofthe resonatorand\nmoved up and down. The bottom plate had a groove al-\nlowing to close the gate completely. The vertical position\nsof the gate was one of the experimental parameters.\nThe value of s= 0 corresponded to the closed gate. The\ngate was completely open, i.e., the coupling was maximal\nfors= 9 mm. The second parameter has been the posi-\ntionδof the center ofa semicircularpiece of Teflon in the\nleft part of the cavity with respect to the center of the\nresonator. Its radius was 30 mm and it was 5 mm high.\nThe positions of the gate and the Teflon semicircle were\ncontrolled by microstepper motors that allowed to scan\nthe parameter plane in steps of ∆ s= ∆δ= 0.01 mm.\nA VNA of the type Agilent PNA 5230A coupled mi-\ncrowaves into and out of the resonator. As mentioned in\nSec. II the VNA was calibrated by means of standards.\nThis procedure left us with small systematic errorsalbeit\nlarger than the VNA noise. These were eliminated with\ncorrection factors Kba(f) determined together with the\nparameters of the scattering matrix of Sec. III via fits to\nthe measured resonance spectra.\nLetSraw\nba(f)bethescatteringmatrixelementsobtained\nwith the calibrated VNA and Sba(f) the “true” ones de-\nscribed by the theory presented in Sec. III. Then the\nfactorsKba(f) are defined by the relation\nSraw\nba(f) =Kba(f)Sba(f). (16)\nIt is possible to obtain the parameters of both, S(f) and\nK(f), from a fit to SrawsinceS(f) depends on fin a\nway that is characteristicallydifferent from that of K(f).\nIndeed,K(f) accounts for the slow oscillations superim-\nposed with the comparatively rapidly varying resonance\nstructure described by S(f). For the correction factors\nthe ansatz\nKaa=|Kaa|exp(2πikaaf+iΘaa), a= 1,2;\nK12=K21=/radicalbig\n|K11||K22|exp(2πik12f+iΘ12)(17)\nwas used. The K-factors contain frequency dependent\nand frequency independent phases. There are eight\nreal parameters: |K11|,|K22|,k11,k22,k12,Θ11,Θ22,Θ12\nin addition to the eleven real parameters of Slisted in\nSec. III. Each of the four functions Sraw\nba(f) (whereaas\nwell asbmay be equal to 1 or 2) has been measured with\na resolution of ∆ f= 10kHz over a range of 10 MHz.\nHence, there were about 4000complex data to determine\nthe above 19 real parameters.\nAs discussed in Sec. III the scattering matrix is in-\nvariant under orthogonal transformations of the states\nµ. However, the eigenvectors of the effective Hamilto-\nnianH, to be discussed in the sequel, depend on the\nbasis. Thus we needed a convention for the choice of the\nbasis. If His not triangular then there is an orthogonaltransformation O(φ), see Eq. (12), such that the ratio of\nthe off-diagonal elements of\nH′=O(φ)HOT(φ) (18)\nequals the phase factor\nexp(2iτ) =H′S\n12+iH′A\n12\nH′S\n12−iH′A\n12, (19)\nwhereτisreal. Here, thenotationofEq.(8)isused[119].\nFor systems with TRI H′A\n12= 0 andτ= 0. Let us con-\nsider the case of TRI violation, i.e., H′A\n12∝negationslash= 0. For real\nτthe transformation must lead to H′S\n12/H′A\n12∈R. The\ntransformation Eq. (18) yields the symmetric part of H′\nas\nH′S\n12=e2−e1\n2sin(2φ)+HS\n12cos(2φ).(20)\nFor the antisymmetric part of H′we obtainH′A\n12=HA\n12\nas expected from Eq. (12). The imaginary part of the\nratioH′S\n12/HA\n12vanishes when\nIme2−e1\n2HA\n12sin(2φ)+ImHS\n12\nHA\n12cos(2φ) = 0.(21)\nHence, the orthogonal transformation Eq. (12) with the\nrotation angle\nφ=1\n2arctan/bracketleftbiggIm(HS\n12/HA\n12)\nIm((e1−e2)/(2HA\n12))/bracketrightbigg\n(22)\nleads to a real τ[90, 120]. Henceforth, we omit the\nprime in the Hamiltonian H′obtained with the trans-\nformation Eq. (18) from the experimentally determined\neffective Hamiltonian H.\nA triangular Hdid not occur in the present experi-\nments. Thus we express the lack of reciprocity via the\nphaseτin analogy to Hermitian Hamiltonians although\nHis not Hermitian. CharacterizationofTRI breakingby\na phase is a common practice in physics, e.g., in nuclear\nreactions, as in Sec. 4 of [112], and in weak as well as\nelectromagnetic decay [38].\nVI. THE EIGENVALUES AND\nEIGENVECTORS OF HAT AN EP\nAccording to Eq. (13) the effective Hamiltonian of\nEq. (8) has the eigenvalues\nE1,2=/parenleftbigge1+e2\n2±/radicalbig\n/vectorh2/parenrightbigg\n.\nwhere/vectorhis defined in Eq. (10). Using the fact that the\nquantitiesHS\n12±iHA\n12do not vanish in the relevant space\nof the parameters the associated left- and right-hand\neigenvectors can be written as\n/vectorl1,2=/parenleftBigg\n(e1−e2)/2±√\n/vectorh2\nHS\n12−iHA\n12\n1/parenrightBigg\n;/vector r1,2=/parenleftBigg\n(e1−e2)/2±√\n/vectorh2\nHS\n12+iHA\n12\n1/parenrightBigg\n.\n(23)9\nThe eigenvectors form a biorthogonal system, i.e.\n/vectorl1·/vector r2= 0 =/vectorl2·/vector r1, (24)\nhowever, they are not normalized. An EP occurs, when\n/vectorh2= (HS\n12)2+(HA\n12)2+/parenleftbigge1−e2\n2/parenrightbigg2\n= 0.(25)\nSince the quantity ( HS\n12)2+(HA\n12)2is different from zero\nwe have (e1−e2)∝negationslash= 0 at the EP.\nIn order to identify an EP the effective Hamiltonian\nHwas varied by changing the two parameters sandδ\nintroduced in Sec. V. In this way it was possible to reach\n/vectorh2= 0 at a point ( sEP,δEP) in the parameter space.\nGenerally, at this point (in the space of experimental\nparameters)twodifferentphysicalsituationsarepossible:\n(i) If all three components of /vectorhvanish one speaks of a\ndiabolical point (DP), following Berry [10]. This is not\nthe case here. (ii) If at least two of the components of /vectorh\ndiffer from zero at /vectorh2= 0, one speaks of an exceptional\npoint (EP), following Kato [12]. Accordingly, an EP can\narise only in dissipative systems [3–8, 20–31, 35–37, 91–\n94, 121] since at least one of the components of /vectorhmust\nbe complex.\nAt the EP the system of eigenvectors cannot be nor-\nmalized because the inner products\n/vectorl1·/vector r1∝/parenleftbigg\n/vectorh2+e1−e2\n2/radicalbig\n/vectorh2/parenrightbigg\n,\n/vectorl2·/vector r2∝/parenleftbigg\n/vectorh2−e1−e2\n2/radicalbig\n/vectorh2/parenrightbigg\n(26)\nvanish there and the two right as well as the two left\neigenvectors given in Eq. (23) coincide. One also says\nthat at an EP two or more eigenvalues and also the as-\nsociated eigenvectors “coalesce”,\n/vectorlEP∝/parenleftbigg1\n2e1−e2\nHS\n12−iHA\n12\n1/parenrightbigg\n;/vector rEP∝/parenleftbigg1\n2e1−e2\nHS\n12+iHA\n12\n1/parenrightbigg\n.(27)\nUsingEq.(25), thefirstcomponentof /vector rEPcanbebrought\nto the form\n1\n2e1−e2\nHS\n12+iHA\n12=i/radicalbig\n(HS\n12)2+(HA\n12)2\nHS\n12+iHA\n12\n=i/bracketleftbiggHS\n12−iHA\n12\nHS\n12+iHA\n12/bracketrightbigg1/2\n=ie−iτ, (28)\nand the first component of /vectorlEPequalsieiτ. So at the EP\nwe obtain the eigenvectors\n/vectorlEP∝/parenleftbigg\nieiτ\n1/parenrightbigg\n, /vector rEP∝/parenleftbigg\nie−iτ\n1/parenrightbigg\n.(29)\nThe ratio of the components of the left, respectively, the\nrighteigenvectoris aphasefactorat the EP.Forthe righteigenvector the phase equals Φ EP=π/2−τ, compare\nRefs. [6–8, 119], and for the left one it is φEP=π/2+τ.\nWhen reciprocity holds, i.e. HA\n12= 0, the phase Φ EPis\nπ/2, see Refs. [30, 121].\nThese analytical results were borne out by our exper-\niments. The EP was located by determining for each\nsetting of (s,δ) the effective Hamiltonian from the mea-\nsured scattering matrix. The real and imaginary parts of\nthe eigenvalues Ej=fj−iΓj/2 ofHare shown in Fig. 10\nas functions of δfors=sEP= 1.66 mm and B= 53 mT.\nThe crossing occurs at δEP= 41.25 mm. The eigenvalue\nat this EP is EEP= (2.728−i0.00104) GHz.\n1\n212\nFIG. 10: The eigenvalues fj−iΓj/2 ofHplotted as functions\nofδats=sEP= 1.66 mm and B= 53 mT. The eigenvalues\ncross at δEP= 41.25 mm. There fEP= 2.728 GHz and\nΓEP= 2.08 MHz.\nWe also determined the eigenvectors of Hin a neigh-\nborhood of ( sEP,δEP) and checked whether they coa-\nlesce there. In Fig. 11 modulus and argument of the\nratioνjof the components of the j-th left eigenvector\nare plotted for j= 1,2. At the point ( sEP,δEP) the\nmoduli equal |ν1|=|ν2|= 1 and the arguments equal\nΦ1= Φ2=π/2 +τas expected from Eq. (29) for /vectorlEP.\nNotethatbydrawingthelinesconnectingthedatapoints\nas shown in Figs. 10 and 11 we have anticipated the evi-\ndence provided below, that the eigenvalues and eigenvec-\ntors indeed cross, i.e., that there is no avoided crossingat\n(sEP,δEP). In Sect. VIII we show the differences of the\nreal and the imaginaryparts of the eigenvalues in the full\nparameterplanearoundthe crossingpoint andresultsfor\nthe geometric phases gathered by the eigenvectors on en-\ncircling it. These clearly demonstrate that there is an EP\nin the region ( sEP±0.01 mm,δEP±0.01 mm).\nOncetheEPhasbeenlocatedthe phaseΦ EP=τ+π/2\nin/vectorlEP, and thusτin Eq. (29), can be obtained. Figure12\nshows the experimental points with error bars as a func-\ntion ofB. The error bars result from the experimental\naccuracy in the determination of the position of the EP\nin the parameter plane. At B= 0 we found Φ EP=π/2\nas predicted by Eq. (28) for HA\n12= 0. With increasing\nBthe phase Φ, whence also τ, goes through an extreme\nvalue. We ascribethis to the ferromagneticresonance. In\nEq. (15) the TRI-violating matrix element HA\n12has been10\n/c116\nFIG. 11: Modulus and phase of the ratio νj=|νj|exp(iΦj)\nof the components of the left eigenvectors /vectorlj, wherej= 1,2,\nats=sEP= 1.66 mm and B= 53 mT. The eigenvectors\ncoalesce at δEP= 41.25 mm. There the TRI-breaking phase\nτcan be read off as the deviation of Φ 1,2fromπ/2. The\npresent figure relies on the same data as Fig. 10.\n 0.5 0.6 0.7\n 0  20  40  60  80ΦEP/π\nMagnetic field B (mT) 0.5 0.6 0.7\n 0  20  40  60  80ΦEP/π\nMagnetic field B (mT) 0.5 0.6 0.7\n 0  20  40  60  80ΦEP/π\nMagnetic field B (mT)\nFIG. 12: The relative phase (dots with error bars) of the com-\nponents of the left eigenvector at the EP given as a function\nof the magnetic field Bthat activates the ferrite. For B= 0\nthe phase equals π/2. Thus an earlier result [30] is recovered.\nThe model (15) for the TRI breaking coefficient HA\n12yields\nthe solid line, see text. The shaded vertical bar indicates t he\nrange of Bwhere the center of the ferromagnetic resonance is\nexpected.\nexpressed in terms of the ferromagnetic resonance. Pro-\nvided thatτis dominated by that resonance one expects\nto observe it in the phase factor Φ EP. This is confirmed\nby the solid line in Fig. 12 which shows the result ob-\ntained from Eq. (15). Due to the interference HS\n12+iHA\n12\nbetweenHS\n12andHA\n12implied by Eq. (28) the maximum\nof ΦEP= ΦEP(B) is shifted with respect to the center of\nthe ferromagnetic resonance given by Eq. (15).\nVII. THE LINE SHAPE AT AN EP\nIn this section we demonstrate that the scattering ma-\ntrix does not exhibit a simple pole at the EP although\nthere is only a single eigenstate at this point. UsingEq. (25) the eigenvalue of H, given in Eq. (8), equals\nEEP=e1+e2\n2. (30)\nWith the notation\nR=/radicalBig\n(HS\n12)2+(HA\n12)2 (31)\nwe obtain for the resolvent\n(f1−H)−1=1\n(f−EEP)2(32)\n×/parenleftbigg\nf−EEP+iRHS\n12−iHA\n12\nHS\n12+iHA\n12f−EEP−iR/parenrightbigg\n.\nAccording to Eq. (1) the non-diagonal element Sbaof the\nscattering matrix is given by\nSba=−2πi(W1b,W2b)(f1−H)−1/parenleftbigg\nW1a\nW2a/parenrightbigg\n.(33)\nHere we use the fact that the couplings Wja,Wjbof the\nantennas to the resonator modes do not break TRI and\ntherefore are real. Thus we obtain\nSba(f) =−2πi\n(f−EEP)2\n×/bracketleftBig\n(f−EEP)(W1bW1a+W2bW2a)\n+HS\n12(W1bW2a+W2bW1a)\n+iR(W1bW1a−W2bW2a)\n+iHA\n12(W2bW1a−W1bW2a)/bracketrightBig\n.(34)\nConsequently, Sba(f) corresponds to a combination of\nfirst and second order poles at the EP. The presence of\nthe second order pole is a result of the fact, that Hcan-\nnot be diagonalized at the EP, and can only be brought\nto Jordanian form. The effect of the double pole is illus-\ntrated in Fig. 13where the data ofRef. [32] arecompared\nto the modulus square of the Fourier transform F(t) of\nthe scattering matrix element Sba(f) given in Eq. (34).\nThe temporal decay |F(t)|2is proportional to t2mul-\ntiplied by an exponential function. Hence the function\nF(t) is dominated by the Fourier transform of the sec-\nond order pole in Sba(f). Note that the first three terms\non the r.h.s. of Eq. (34) are invariant under the inter-\nchange ofawithbwhereas the fourth term is not, i.e., it\nbreaks TRI.\nIn Refs. [29–31] the real and the imaginaryparts of the\neigenvalues of the effective Hamiltonian were determined\nby fitting a two-level Breit-Wigner function to the ex-\nperimental S(f). Equation (34) demonstrates that this\nprocedure fails at the EP, because there the shape of\nthe resonance is not given by a first order pole of the\nS-matrix [9, 10, 32].11\nData\nTheory of EP\n/c109\nFIG. 13: Modulus square of the Fourier transform of Sba(f).\nData taken from Ref. [32] (solid line) are compared to the\nFourier transform of Eq. (34) (dashed line). The sharp peak\natt= 30±5ns indicates the time needed for the signal to\ntravel through the coaxial cables connecting the VNA with\nthe antennas. At about t= 1.8µs the noise level is reached.\nIn between the temporal behavior is well described by the\nfunction t2exp(2Im EEPt) — in agreement with the second\norder pole enteringEq. (34). Compare with Fig. 3 of Ref. [32] ,\nwhere only a fraction of the available data points had been\nplotted.\nVIII. TRANSPORTING EIGENVECTORS\nAROUND THE EP\nThis section addresses the behavior of the eigenvectors\nunder a transport around the EP. In [122] and [29, 31]\nthe geometric phase gathered around a DP, respectively\nan EP, was obtained for just a few parameter settings,\nbecause the procedure – the measurement of the electric\nfield intensity distribution – is very time consuming. We\nnow have the possibility to determine the left and right\neigenvectors on a much narrower grid of the parameter\nplane. In the first part we describe how the eigenvectors\ntransform into each other upon transporting Halong a\npath in the parameter plane around the EP; in the sec-\nondwetreatthe geometricamplitude thatan eigenvector\npicks up while encircling the EP under TRI violation.\nA. A fourfold path around the EP\nBy a closed path or loop around the EP we understand\na path in the plane of the experimental parameters s,δ\nthat returns to its initial point and encloses the EP. Fig-\nure14displaysthe double looparoundthe EPconsidered\nin the following. Each dot corresponds to a pair of pa-\nrameters (s,δ) where the Smatrix was measured and\nthus the effective Hamiltonian Hamiltonian Hwas deter-\nmined. The path is parameterised by the ’time’ t. It\nstarts at the intersection of the inner and outer loops.\nThen the path is followed counterclockwise. At t=t1\nthe inner loop was completed; at t2the outer one. Thedifference of the complex eigenvalues\nE1,2=f1,2−iΓ1,2/2 (35)\nis plotted in a color code [89, 123]. The darker the color\nthe smaller is the respective difference. The difference\n|f1−f2|, shown in blue, is small only to the left of the\nEP. Similarly the difference |Γ1−Γ2|, shown in red, is\nsmall only to the right of the EP. In the white region\nboth differences are large beyond the range of the color\ncode. Along the darkest blue and red line, the differences\n|f1−f2|, respectively, |Γ1−Γ2|are vanishingly small.\nThus, Fig. 14 demonstrates that the frequency crossing\nis interchangedwith the width crossing[27, 28, 124] upon\npassingthe EP[29] fromthe left tothe right. This proves\nthat the point where the change takes place is indeed an\nEP. Ats= 1.59 mm a group of outliers is visible in\nFig. 14. These were due to experimental imperfections\nthat, e.g., occurred due to friction when the Teflon disk\nwas moved along the resonator surface.\n1.5 1.7 1.941.141.241.341.4\ns (mm)\n\u0001 (mm)\nEP|f  - f |1 2|Γ  - Γ | 1 2\nFIG. 14: (Color online) Differences of the real and the imag-\ninary parts of the complex eigenvalues in the notation of\nEq. (35). The data have been taken at B= 53 mT. The\ndarker the color the smaller is the respective difference. It is\nvanishingly small at the darkest colors. The differences of t he\nreal parts, shown in blue, are small to the left of the EP, thos e\nof the imaginary parts, shown in red, to the right. In the re-\ngions of white colors both differences are large and beyond\nthe scale of the color code. The dotted curve is the double\nloop around the EP discussed in the text.\nWe assumed and experimentally confirmed that the el-\nements of Hexhibit no singularity, neither on the path\nnorinthedomaindelimitedbythepath. Thenevery Hµν\nas well as/vectorh2defined in Eq. (10) returns to its original\nvalue when it is taken along the closed path. However,\nthe square-root function/radicalbig\n/vectorh2appearing in the eigenval-\nuesandeigenvectorsof H, seeEqs.(13)and(23), changes\nsign along the path around the EP because/radicalbig\n/vectorh2has a\nbranch point at the zero of its argument.12\nTo discuss the loops around an EP we shift, without\nloss of generality, the matrix Hsuch that its trace van-\nishes,\nH → H−1\n2(TrH) 1. (36)\nThen the eigenvalues are\nE1,2=±/radicalbig\n/vectorh2. (37)\nwhereas the eigenvectors do not change. In the sequel\nwe always refer to the shifted Hwhen talking about the\neffective Hamiltonian. The difference of the eigenvalues\nisE1−E2= 2E1= 2/radicalbig\n/vectorh2. Along the line of darkest\ncolor in Fig. 14 to the left of the EP, the eigenvalues are\npurelyimaginarywhereastotherighttheyarereal. Thus\nthe dark line is the locus of real squared eigenvalues.\n1. Encircling an EP under TRI\nIn the following two subsections the transformation of\nan eigenvector transported around an EP is worked out\nfirst for TRI systems and then for the case of TRI viola-\ntion. ForHA\n12= 0 equations (8) and (36) yield\nH=/parenleftbigge1−e2\n2HS\n12\nHS\n12−e1−e2\n2/parenrightbigg\n(38)\nand/vectorh2= (HS\n12)2+/parenleftbige1−e2\n2/parenrightbig2. Note that the squares of\nthe quantities\ne1−e2\n2/radicalbig\n/vectorh2andHS\n12/radicalbig\n/vectorh2\nadd up to unity. Therefore a complex ”angle” 2 θexists\nsuch that\nH=/parenleftbigg\ncos(2θ) sin(2θ)\nsin(2θ)−cos(2θ)/parenrightbigg/radicalbig\n/vectorh2.(39)\nThe right eigenvectors of Hare given by\n/vector r1=/parenleftbigg\ncosθ\nsinθ/parenrightbigg\n, /vector r2=/parenleftbigg\n−sinθ\ncosθ/parenrightbigg\n.(40)\nBecause of the symmetry of Hthey are equal to the left\neigenvectors /vectorl1,2. This system is biorthonormal. In anal-\nogy to Eq. (23) the eigenvectors can be written as\n/vector r1∝/parenleftbigg\ncotθ\n1/parenrightbigg\n, /vector r2∝/parenleftbigg\n−tanθ\n1/parenrightbigg\n.(41)\nThe comparison between the first component of /vector r2and\nthe corresponding one in Eq. (23) yields\ntanθ=−e1−e2\n2+/radicalBig/parenleftbige1−e2\n2/parenrightbig2+(HS\n12)2\nHS\n12.(42)As in Ref. [31] we define\nB=e1−e2\n2HS\n12(43)\nand obtain\ntanθ=−B+/radicalbig\nB2+1\n=−B+√\nB+i√\nB−i. (44)\nAn EP occurs for /vectorh2= 0 andHS\n12∝negationslash= 0, i.e. when\nB=BEP=±i. (45)\nOn a path around an isolated EP the quantity Bis taken\naroundBEP, i.e., one of the square root functions in the\nsecond line of Eq. (44) changes sign. Hence, the eigen-\nvalues in Eq. (37) are interchanged and\ntanθ→tanθ1≡ −B−/radicalbig\nB2+1 =−cotθ,(46)\nso that one loop around an EP implies\nθ→θ±π\n2. (47)\nThus the transport of the eigenvectors (40) around the\nEP in the direction of θ→θ+π/2 yields\n/vector r1→/vector r2,\n/vector r2→ −/vector r1. (48)\nThisimpliesthataneigenvectormustbetransportedfour\ntimes around the EP to recover the original situation.\nStarting with /vector r1the sequence is\n/vector r1→/vector r2→ −/vector r1→ −/vector r2→/vector r1. (49)\nWhen the eigenvectors are transported around the EP in\ntheoppositedirectionsothat θ→θ−π/2,theytransform\naccording to\n/vector r1→ −/vector r2\n/vector r2→/vector r1. (50)\nAgain the transport must be repeated four times to re-\nstore the original situation. The rules (48) and (50) have\nbeen experimentally confirmed in Ref. [29].\n2. Encircling an EP under violation of TRI\nLet us now discuss the case of violated TRI where\nHA\n12∝negationslash= 0. Using the definition of eiτand Eqs. (8) and\n(36) we obtain with the notation Eq. (31)\nH=/parenleftbigge1−e2\n2e−iτR\neiτR −e1−e2\n2/parenrightbigg/radicalbig\n/vectorh2. (51)\nIn analogy to the case discussed in the preceding subsec-\ntion the quantities\ne1−e2\n2/radicalbig\n/vectorh2andR/radicalbig\n/vectorh213\nare expressed as cos(2 θ) and sin(2θ), respectively. Thus\nEqs. (42, 43) are generalized to\ntanθ=−e1−e2\n2+/radicalbig\n/vectorh2\nR(52)\nand\nB=e1−e2\n2R. (53)\nThis yields\nH=/parenleftbigg\ncos(2θ)e−iτsin(2θ)\neiτsin(2θ)−cos(2θ)/parenrightbigg/radicalbig\n/vectorh2.(54)\nThe biorthogonal normalized system of eigenvectors be-\ncomes\n/vectorl1=/parenleftbigg\neiτ/2cosθ\ne−iτ/2sinθ/parenrightbigg\n;/vector r1=/parenleftbigg\ne−iτ/2cosθ\neiτ/2sinθ/parenrightbigg\n;\n/vectorl2=/parenleftbigg\n−eiτ/2sinθ\ne−iτ/2cosθ/parenrightbigg\n;/vector r2=/parenleftbigg\n−e−iτ/2sinθ\neiτ/2cosθ/parenrightbigg\n.(55)\nHere, the/vectorlkare the left eigenvectors and the /vector rkthe right\nones [89, 119]. When the EP is encircled the function\neiτ=/parenleftbiggHS\n12+iHA\n12\nHS\n12−iHA\n12/parenrightbigg1/2\n(56)\nreturns to its original value because the r.h.s. has no sin-\ngularity. By consequence τreturns to its original value\nwhen it is transported along the dotted path in Fig. 14.\nThis is illustrated in Fig. 15 where τis given as a func-\ntion of the “time” tthat parameterises the dotted path.\nThe value of τwas not constant along the path although\nthe magnetic field was fixed at B= 53 mT. Indeed, τde-\npended on sandδbecause both parameters shift the rf\nmagnetic field at the ferrite. Since ( HS\n12)2+(HA\n12)2does\nnot vanish, Eqs. (44), (45) and (47) remain valid. Fur-\nthermore, since τreturns to its original value the rules\n(48) and (50) apply whether or not TRI holds.\nB. The geometric amplitude along closed paths\nIn this section we focus on the dynamics of the motion\naround an EP. The paths ( s(t),δ(t)) around the EP are\nparameterised by a time variable t. In the last two sub-\nsections we have considered the local eigenvectors /vector rk(t)\nalong such a path. However, Berry [10] realized that this\nis a dynamical procedure to be described by a time de-\npendent Hamiltonian H(t) in the Schr¨ odinger equation.\nWe ask: What happens to a wave function /vectorψ(t) which\natt= 0 equals the eigenvector /vector r1(0) ofH(0)? Let the\nfirst turn around the EP be completed at t=t1and let\nthe turn be performed in the sense leading to the rule\n(48). Does /vectorψ(t1) equal the eigenvector /vector r2(0)? If TRI is\nviolated, the answer in general is “No”. If the motion0.60.8\n0 50 100 150τ(t)/π\ntt1t2\nFIG. 15: The TRI-violating phase τ(t) forB= 53 mT with t\nvaried along the dotted double loop shown in Fig. 14. At the\nend of either loop τreturned to its initial value. Counting\nthe points of measured Hamiltonians along the path yields\nthe “time” scale twitht1= 25,t2= 150.\nis sufficiently slow then for every tthe wave vector/vectorψ(t)\nsolving the time-dependent Schr¨ odinger equation will be\na local eigenstate multiplied with the “dynamical phase”\nfactore−iE1t1. In addition it will pick up a “geometric\namplitude” eiγ(t)along the path [1, 2]. Hence, it can be\nwritten as\n/vectorψ(t) = exp[−iE1t+iγ(t)]/vector r1(t).(57)\nWe show, that other than the dynamical phase, γmay\ndepend on the geometry of the path and it may be a\ncomplex function and thus modify the normalization of\n/vectorψalong the path. The ansatz (57) is called “parallel\ntransport” [1, 2, 10, 125] because /vectorψremains parallel to\nthe localeigenvectorduring the transportaroundthe EP.\nInserting Eq. (57) into the Schr¨ odinger equation\ni˙/vectorψ(t) =H(t)/vectorψ(t), (58)\nwe find\ni˙γ+/vectorl1·˙/vector r1= 0, (59)\nwhere the dot denotes the derivative with respect to t.\nThis yields with Eq. (55)\n/vectorl1·˙/vector r1=−i˙τ\n2cos(2θ), (60)\nand [89]\n˙γ=˙τ\n2cos(2θ). (61)\nThus, when TRI holds, i.e., τ≡0, ˙γvanishes and γ(t)≡\nγ(0) = 0. Examples of the geometric phase γ(t) for a\nnon-vanishing τare presented in Fig. 16. In panel a)\nγ(t) was determined along the dotted double loop shown\nin Fig. 14 where the EP was encircled counterclockwise.14\nFIG. 16: (Color online) Geometric phases γ(t) gathered when\nthe EP was experimentally encircled twice. Panel a) display s\nγ(t) along the dotted double loop marked in Fig. 14. The\ngreen triangle (upward) marks the initial point at t= 0. Mov-\ning counterclockwise along the dotted line, the red diamond\nwas reached at the end t1= 25 of the inner loop. The blue\ntriangle (downward) completes the outer loop at t2= 150.\nCompare Fig. 15. The points, where the direction of γ(t)\nswitches, occurred at the extreme values of τ(t). At the end\nof the path we found γ(t2)/negationslash=γ(0). Panel b) shows γ(t) when\nthe EP is encircled twice along the outer loop of Fig. 14. Then\nwe found γ(t2) =γ(0), i.e., the end point coincided with the\ninitial point.\nThe initial point is marked by a green triangle (upward).\nThe completion of the inner loop at t1= 25 is marked\nby a red diamond and the end point at t2= 150 by\na blue triangle (downward). The resulting curve of the\nimaginary versus the real part of γ(t) switches direction\nat the extreme values of τ. According to Fig. 15 these\noccur att= 12,33,80,135. We found the initial value\nγ(0) to differ from the final one γ(t2= 150). In panel\nb) the outer loop of Fig. 14 is followed twice. At the\nend of the second turn γreturned to its initial value,\ni.e., the green and blue (upward and downward)triangles\ncoincide. This can be understood from Eq. (61) together\nwith the ruleEq.(47) accordingto whichcos(2 θ) changes\nsign after each loop. Since the second loop covered the\nsame values of θas the first one, the integral over the\nr.h.s. of Eq. (61) along the second loop canceled the\nintegral along the first loop. This result and that shown\nin panel a), γ(0)∝negationslash=γ(t2), show that γgenerally depends\non the geometry of the path.\nEncircling the EP four times, i.e., twice along the dou-ble loop of Fig. 14 leads to Fig. 17. Accordingto Eq. (47)\nat the end of each double loop the angle θis shifted by\nπ. Thus integrating Eq. (61) over tyields\nγ(t4) = 2γ(t2), (62)\nwheret2denotes the time needed to traverse the first\ndouble loop, and t4= 2t2. Thus the difference γ(t2)−\nFIG. 17: (Color online) Geometric phase γ(t) gathered when\nthe EP is encircled four times by following twice the double\nloop shown in Fig. 14. The green triangle (upward) marks\nγ(0). With increasing tthe geometric phase follows the black\ndots counterclockwise. At the end of the first double loop\n(blue triangle downward) it continues along the red ones. It\nends at the blue diamond.\nγ(0) is doubled at the end of the second double loop.\nThis procedure can be repeated arbitrarily; it has been\ntermed “geometric instability” [126]. The drift γ(0)→\nγ(t2)→γ(t4)...can be reversed by simply retracing\nthe path.\nIX. THE OCCURRENCE OF PT-INVARIANCE\nThe experimental setup can also be used to study dis-\nsipativequantumsystemswhich haveaparity-time( PT)\nsymmetry, that is, are invariant under the simultaneous\naction of a parity ( P) and a time reversal ( T) after a\nsuitable width-offset. We demonstrate in the following\nthat the parameter space contains parts, where the effec-\ntive Hamiltonian Hexhibits a generalized form of PT-\nsymmetry.\nFigure 18 compares the differences of the complex\neigenvalues of Hfor three different magnetizations of the\nferrite in the neighborhood of an EP in the ( s,δ)-plane.\nThe EP is marked by a green dot. Blue colors represent\ndifferences |f1−f2|of the real part of the eigenvalues,\nred colors differences |Γ1−Γ2|of the imaginary part of\nthe eigenvalues. The darker the color the smaller is the\ndifference. — For B= 0 a jitter to the right of the EP is\nvisible which as explained in connection with Fig. 14, is\ndue to experimental imperfections. As in Fig. 14, small\nvalues of |f1−f2|occur only to the left of the EP, small15\nFIG. 18: (Color online) Differences of the complex eigenval-\nues of the effective Hamiltonians in a neighborhood of the\nEP, compare Fig. 14. The three panels show results for the\nmagnetization of the ferrite with B= 0,38,61 mT.\nvalues of |Γ1−Γ2|only to the right. In each one of the\nexamples shown in Figs. 14 and 18 we found a line in\nthe (s,δ)-plane— the line of darkest color — where the\neigenvalues of Hare either purely imaginary or purely\nreal. Since\nf1−f2= 2Re/radicalbig\n/vectorh2,\nΓ1−Γ2= 2Im/radicalbig\n/vectorh2, (63)\nthe line of darkest color is the locus of real /vectorh2. Although\nthe position of the EP weakly depends on the magnetic\nfieldBand some distortion of the dark line appears de-\npending on B, the locus of real /vectorh2is always present. It\nis defined by\nIm/vectorh2= 0 (64)\nwhich is equivalent to\nRe/vectorh·Im/vectorh= 0. (65)Note that the vector Re /vectorhis related to the matrix ˜Hint\nobtained from Eq. (4) by subtracting1\n2/parenleftbig\nTrHint/parenrightbig\nfrom\nHint. Actually, the entries of Re /vectorhare the expansion\ncoefficients of ˜Hintwith respect to the Paulimatrices, i.e.\n˜Hint= (Re/vectorh)·/vectorσ. Similarly, the vector Im /vectorhis related to\nthe matrix ˜Hextvia˜Hext= (Im/vectorh)·/vectorσ.\nThe Pauli matrices σk,k= 1,2,3,have the properties\nTrσ2\nk= 2 and Tr( σkσk′) = 0 fork∝negationslash=k′. From this\nfollows that the l.h.s. of Eq. (65) can be expressed as\nRe/vectorh·Im/vectorh= Tr(˜Hint˜Hext)/2. (66)\nThus the set of Hamiltonians on the locus of real /vectorh2can\nbe defined by the property\nTr(˜Hint˜Hext) = 0. (67)\nThisformulatesarelationbetweentheinternalandexter-\nnal parts of the effective Hamiltonian which is necessary\nand sufficient for the set under discussion. The trace is\ninvariant under unitary transformations. Therefore the\ncriterion (67) is independent of the choice of the basis for\nH.\nOnecanverifythatthecommutator[ ˜Hint,˜Hext]equals\n(Re/vectorh×Im/vectorh)·/vectorσ. Therefore [ ˜Hint,˜Hext]∝negationslash= 0 along the\nlocus of real /vectorh2. There, the eigenvalues of Hare either\npurely real or purely imaginary. The eigenvalues of PT-\ninvariant Hamiltonians have exactly this property [62,\n63]. Here,theparityoperatorisgivenbythePaulimatrix\nσ1in Eq. (7), i.e.\nP=/parenleftbigg\n0 1\n1 0/parenrightbigg\n, (68)\nandTis the operation of complex conjugation. Then\nthe question arises whether the effective Hamiltonian is\nPT-invariant along the locus of real /vectorh2. We have shown\nin Ref. [90] that every single Hamiltonian Hon the lo-\ncus can be transformed into a PT-invariant one by a\nunitary transformation Uof the basis, i.e., the matrix\nH′=U†HUisPT-invariant or the operator UPTU†\ncommutes with H. Thus we can speak of a generalized\nPT-invariance [90, 127]. As predicted, the change from\nreal eigenvalues for s > sEPto complex conjugate ones\nfors < sEPis accompanied by a sponteneous breaking\nofPTsymmetry of the eigenvectors of U†HUat the EP,\nthat is, they cease to be eigenvectors of PT[62, 127].\nX. SUMMARY AND CONCLUSIONS\nThe present article deals with a series of scattering\nexperiments performed with microwave resonators under\nviolation of TRI induced via a magnetized ferrite placed\ninside the resonators.16\nA. The first set of experiments\nThe first set of experiments described in Secs. II and\nIV explored the notion of TRI and the properties of the\nferrite. In scattering experiments, reciprocity is equiv-\nalent to TRI. To reveal violation of TRI the effective\nHamiltonian system must be at least two-dimensional.\nTo check this we looked at isolated resonances. They\nwere obtained in measurements with a resonator having\nthe shape of a classically chaotic annular billiard. In-\ndeed, isolated resonances showed reciprocal scattering,\ni.e.S12=S21, in Fig. 4 although the ferrite was mag-\nnetized. Doublets of resonances were obtained with a\ncircular resonator with slightly broken symmetry. They\nexhibitedlackofreciprocity,i.e., S12∝negationslash=S21inFig.5when\nTRI was violated. Varying the magnetization of the fer-\nrite revealed its ferromagnetic resonance. A model for\nthe TRI breaking matrix element of Hwas derived in\nSec. IVB.\nFrom the four S-matrix elements S11,S12,S21,S22\nmeasured as functions of the excitation frequency, the\nfour elements of the effective Hamiltonian Hof the two-\nstate system were obtained. This allowed in Sec. IV a\nsubtle test of scattering theory: The effect of the ferrite,\ni.e.,HA\n12∝negationslash= 0, was found in both, the internal and the\nexternal parts of Hin Eqs. (4,5). This is expected, be-\ncause the ferrite acts via its dissipative properties and\nscattering theory says that dissipation appears not only\ninHext, but — via the principle value integral in Eq. (5)\n— also inHint.\nB. The second series of experiments\nThe second series of experiments in Secs. V – IX dealt\nwith anexceptionalpoint (EP)thatwecouldlocate. Theresonatorusedin theseexperimentswascircularandpos-\nsessedanapproximatemirrorsymmetrywithrespecttoa\ndiameter, i.e. an approximateparity symmetry. Further-\nmore, a ferrite was placed in one of its parts. By help of\ntwo experimental parameters the EP could be accessed.\nThe experiments yielded overwhelming evidence that we\nindeed found an EP. (i) The eigenvectors coalesced to a\nsingle one. Its components differed by a phase factor, see\nFig. 11, which provides information on the strength of\nTRI violation. (ii) The line shape at the EP displayed\na pole of second order in the S-matrix, see Fig. 13. (iii)\nTransportingthe eigenvectorsonclosedpaths aroundthe\nEP yielded the expected transformation from one eigen-\nvectorto the otherone, seeSec. VIIIA. (iv) Garrisonand\nWright predicted [1, 2] that geometric amplitudes should\nbe picked up along the closed paths provided that TRI is\nviolated. The imaginary part of the complex phase γ(t)\nestablished the existence of the geometric amplitude, see\nFigs. 16. This was extended in Fig. 17 to verify the exis-\ntence of Bliokh’s geometric instability [126].\nIn the two-dimensional parameter space a one-\ndimensional subspace was found in Figs. 14, 18, in which\nthe eigenvalues of the effective Hamiltonian were either\nreal or purely imaginary. This was characteristic for —\nin our case a generalized — PT-invariance. The change\nfrom purely real to purely imaginary eigenvalues takes\nplace at the EP, i.e., there a spontaneous breaking of\nPT-invariance occurs.\nAcknowledgments\nIlluminating discussions with U. G¨ unther, O. Kirillov\nand H. A. Weidenm¨ uller are gratefully acknowledged.\nThis work was supported by the DFG within SFB 634.\n[1] J. C. Garrison and E. M. Wright, Phys. Lett. A, 128,\n177 (1988).\n[2] M. V. Berry, Proc. R. Soc. Lond. A 430, 405 (1990).\n[3] N. Moiseyev and S. Friedland, Phys. Rev. A 22, 618\n(1980).\n[4] W. D. Heiss and A. L. Sannino, J. Phys. A 23, 1167\n(1990).\n[5] E. Hernandez, A. Jauregui, A. Mondragon, J. Phys. A:\nMath. Gen. 33, 4507 (2000).\n[6] H.L. Harney and W.D. Heiss, Eur. Phys. J. D 29, 429\n(2004).\n[7] W.D. Heiss, J. Phys. A 39, 10077 (2006).\n[8] W.D. Heiss, J. Phys. A 45, 44016 (2012).\n[9] I. Rotter, J. Phys. A: Math. Theor. 42, 153001 (2009).\n[10] M. V. Berry, Proc. R. Soc. Lond. A 392, 45 (1984).\n[11] M. V. Berry and M. R. Dennis, Proc. R. Soc. Lond. A.\n459, 1261 (2003).\n[12] T. Kato, Perturbation Theory for Linear Operators\n(Springer, Berlin, 1966).\n[13] J. C. Schelling, J. Acoust. Soc. Am. 35, 326 (1962) G.Weinreich, J. Acoust. Soc. Am. 62, 1474 (1977).\n[14] J. Wiersig, S. W. Kim, and M. Hentschel, Phys. Rev. A\n78, 053809 (2008).\n[15] J.-W. Ryu, S.-Y. Lee, S. W. Kim, Phys. Rev. A 79,\n053858 (2009).\n[16] A. C. Or, Quart. J. Mech. Appl. Math. 44, 559 (1991).\n[17] M. Kammerer, F. Merz, F. Jenko, Phys. Plasmas 15,\n052102 (2008).\n[18] O. N. Kirillov, Proc. R. Soc. A 464, 2321 (2008).\n[19] S. Klaiman, U. G¨ unther, N. Moiseyev, Phys. Rev. Lett.\n101, 080402 (2008).\n[20] O. Latinne, N.J. Kylstra, M. D¨ orr, J. Purvis, M. Terao-\nDunseath, C. J. Joachain, P. G. Burke, and C. J. Noble,\nPhys. Rev. Lett. 74, 46 (1995).\n[21] E. Narevicius, N. Moiseyev, Phys. Rev. Lett. 84, 1681\n(2000).\n[22] H. A. Weidenm¨ uller, Phys. Rev. B, 68, 125326 (2003).\n[23] H. Cartarius, J. Main, G. Wunner, Phys. Rev. Lett. 99,\n173003 (2007).\n[24] P. Cejnar, S. Heinze, M. Macek, Phys. Rev. Lett. 99,17\n100601 (2007).\n[25] R. Lefebvre, O. Atabek, M. Sindelka, and N. Moiseyev,\nPhys. Rev. Lett. 103, 123003 (2009).\n[26] R. Lefebvre and O. Atabek, Eur. Phys. J. D. 56, 317\n(2010).\n[27] P. von Brentano and M. Philipp, Phys. Lett. B 454171\n(1999).\n[28] M. Philipp, P. von Brentano, G. Pascovici, and A.\nRichter, Phys. Rev. E 62, 1922 (2000).\n[29] C. Dembowski, H.-D. Gr¨ af, H.L. Harney, A. Heine,\nW.D. Heiss, H. Rehfeld, and A. Richter, Phys. Rev.\nLett.86, 787 (2001).\n[30] C. Dembowski, B. Dietz, H.-D. Gr¨ af, H.L. Harney, A.\nHeine, W.D. Heiss, and A. Richter, Phys. Rev. Lett. 90,\n034101 (2003).\n[31] C. Dembowski, B. Dietz, H.-D. Gr¨ af, H.L. Harney, A.\nHeine, W.D. Heiss, and A. Richter, Phys. Rev. E 69,\n056216 (2004).\n[32] B. Dietz, T. Friedrich, J. Metz, M. Miski-Oglu, A.\nRichter, F. Sch¨ afer, and C.A. Stafford, Phys. Rev. E\n75, 027201 (2007).\n[33] H.-J. St¨ ockmann andJ. Stein, Phys. Rev.Lett. 64, 2215\n(1990).\n[34] H.-D. Gr¨ af, H.L. Harney, H. Lengeler, C.H. Lewenkopf,\nC. Rangacharyulu, A. Richter, P. Schardt, and H.A.\nWeidenm¨ uller, Phys. Rev. Lett. 69, 1296 (1992).\n[35] T. Stehmann, W. D. Heiss, F. G. Scholtz, J. Phys. A\n37, 7813 (2004).\n[36] S.-B. Lee, J. Yang, S. Moon, S.-Y. Lee, J.-B. Shim,\nS.W. Kim, J.-H. Lee, and K. An, Phys. Rev. Lett. 103,\n134101 (2009).\n[37] Y. Choi, S. Kang, S. Lim, W. Kim, J.-R. Kim, J.-H.\nLee, and K. An, Phys. Rev. Lett. 104, 153601 (2010).\n[38] A. Richter, in Interaction Studies in Nuclei , ed. by H.\nJochim and B. Ziegler, (North Holland, Amsterdam\n1975) p. 191.\n[39] Parity and Time Reversal Violation in Compound Nu-\nclear States and Related Topics, ed. by N. Auerbach\nand J. D. Bowman (World Singapore Press, Singapore\n1996).\n[40] S. Sridhar, Phys. Rev. Lett. 67, 785 (1991).\n[41] A.Richter, in Emerging Applications of Number Theory ,\nedited by D. A. Hejhal, J. Friedmann, M. C. Gutzwiller,\nand A. M. Odlyzko, IMA Vol. 109 (Springer, NY, 1999),\np. 479.\n[42] H.-J. St¨ ockmann, Quantum Chaos: An Introduction\n(Cambridge University Press, Cambridge, 2000).\n[43] C. Mahaux and H. A. Weidenm¨ uller, Shell-model ap-\nproach to nuclear reactions , (North-Holland, Amster-\ndam, 1969).\n[44] S. Albeverio, F. Haake, P. Kurasov, M. Ku´ s, P. ˇSeba, J.\nMath. Phys. (NY) 37, 4888 (1996).\n[45] F. Haake, M. Ku´ s, P. ˇSeba, H.-J. St¨ ockmann, and U.\nStoffregen, J. Phys A 29, 5745 (1996).\n[46] H.-J. St¨ ockmann and P. ˇSeba, J. Phys. A 31, 3439\n(1998).\n[47] X.Zheng, T.M. Antonsen, andE.Ott, Electromagnetics\n26, 3 (2006).\n[48] B. Dietz, A. Heine, A. Richter, O. Bohigas, and P.\nLebœuf, Phys. Rev. E 73, 035201(R) (2006).\n[49] P. So, S.M. Anlage, E.Ott, and R.N. Oerter, Phys. Rev.\nLett.74, 2662 (1995).\n[50] U. Stoffregen, J. Stein, H.-J. St¨ ockmann, M. Ku´ s, and\nF. Haake, Phys. Rev. Lett. 74, 2666 (1995).[51] D.H. Wu, J.S.A. Bridgewater, A. Gokirmak, and S.M.\nAnlage, Phys. Rev. Lett. 81, 2890 (1998).\n[52] H. Schanze, H.-J. St¨ ockmann, M. Mart´ ınez-Mares, and\nC.H. Lewenkopf, Phys. Rev. E 71, 016223 (2005).\n[53] B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu, A.\nRichter, F. Sch¨ afer, and H.A. Weidenm¨ uller, Phys. Rev.\nLett.98, 074103 (2007).\n[54] F. Haake, Quantum Signatures of Chaos (Springer, New\nYork, 2001).\n[55] F. Coester, Phys. Rev. 84, 1259 (1951).\n[56] F. Coester, Phys. Rev. 89, 619 (1953).\n[57] E.M. Henley and B.A. Jacobsohn, Phys. Rev. 113, 225\n(1959).\n[58] H. Frauenfelder and E.M. Henley, Nuclear and Particle\nPhysics(W.A. Benjamin, Readin, MA, 1975).\n[59] A. A. Mailybaev, O. N. Kirillov, A. P. Seyranian, Phys.\nRev. A72, 014104 (2005).\n[60] H. Mehri-Dehnavi and A. Mostafazadeh, J. Math. Phys.\n49, 082105 (2008).\n[61] Soo-Young Lee, Phys. Rev A 82, 064101 (2010).\n[62] C.M. Bender and S. Boettcher, Phys. Rev. Lett. 80,\n5243 (1998).\n[63] C.M. Bender, Rep. Prog. Phys. 70, 947 (2007).\n[64] J. Rubinstein, P. Sternberg, Q. Ma, Phys. Rev. Lett.\n99, 167003 (2007).\n[65] N. M. Chtchelkatchev, A. A. Golubov, T. I. Baturina,\nand V. M. Vinokur, Phys. Rev. Lett. 109, 150405.\n[66] A. Guo, G.J. Salamo, D. Duchesne, R. Morandotti, M.\nVolatier-Ravat, V. Aimez, G.A. Siviloglou, and D.N.\nChristodoulides, Phys. Rev. Lett. 103, 093902 (2009).\n[67] C.E. R¨ uter, K.G. Makris, R. El-Ganainy, D.N.\nChristodoulides, M. Segev, and D. Kip, Nature Physics\n6,192 (2010).\n[68] M. V. Berry, J. Phys. A 41, 244007 (2008).\n[69] R. El-Ganainy, K. G. Makris, D. N. Christodoulides,\nand Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).\n[70] K. G. Makris, R. El-Ganainy, D. N. Christodoulides,\nand Ziad H. Musslimani, Phys. Rev. Lett. 100, 103904\n(2008).\n[71] Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and\nD. N. Christodoulides, Phys. Rev. Lett. 100, 030402\n(2008).\n[72] H. Ramezani, T. Kottos, V. Kovanis, and D. N.\nChristodoulides, Phys. Rev. A 85, 013818 (2012).\n[73] E.-M. Graefe and H. F. Jones, Phys. Rev. A 84, 013818\n(2011).\n[74] C. Zheng, L. Hao, and G. L. Long, Phil. Trans. R. Soc.\nA371, 20120053 (2013).\n[75] Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H.\nCao, and D. N. Christodoulides, Phys. Rev. Lett. 106,\n213901 (2011).\n[76] M. Liertzer, L.Ge, A.Cerjan, A. D.Stone, H.E. T¨ ureci,\nand S. Rotter, Phys. Rev. Lett. 108, 173901 (2012).\n[77] Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett.\n106, 093902 (2011).\n[78] A. Mostafazadeh, Phys. Rev. A 83, 045801 (2011).\n[79] J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T.\nKottos, Phys. Rev. A 84, 040101 (2011).\n[80] A. Regensburger, C. Bersch, M.-A. Miri, G. On-\nishchukov, D. N. Christodoulides, and U. Peschel, Na-\nture488, 167 (2012).\n[81] H. Ramezani, T. Kottos, R. El-Ganainy, and D. N.\nChristodoulides, Phys. Rev. A 82, 043803 (2013).\n[82] A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, and18\nM. Segev, Phys. Rev. A 84, 021806 (2011).\n[83] T. Bergmann, M. DeKieviet, T. Gasenzer, O. Nacht-\nmann, andM.-I.Trappe, Eur.Phys.J. D 54, 551(2009).\n[84] M. DeKieviet, T. Gasenzer, O. Nachtmann, and M.-I.\nTrappe, Hyperfine Interactions 200, 35 (2011).\n[85] A. Mostafazadeh, Phys. Rev. Lett. 102, 220402 (2009).\n[86] S. Longhi, Phys. Rev. Lett. 103, 123601 (2011).\n[87] H. Schomerus, Phys. Rev. Lett. 104, 233601 (2010).\n[88] Phys. Rev. A 83, 030101 (2011); P. Ambichl, K. G.\nMakris, L. Ge, Y. Chong, A. D. Stone, and S. Rotter,\nPhys. Rev. X 3, 041030 (2013).\n[89] B. Dietz, H.L. Harney, O.N. Kirillov, M. Miski-Oglu, A.\nRichter, and F. Sch¨ afer, Phys. Rev. Lett. 106, 150403\n(2011).\n[90] S. Bittner, B. Dietz, U. G¨ unther, H.L. Harney, M.\nMiski-Oglu, A. Richter, and F. Sch¨ afer, Phys. Rev.Lett.\n108, 024101 (2012).\n[91] W.D. Heiss, M. M¨ uller, and I. Rotter, Phys. Rev. E 58,\n2894 (1998).\n[92] W.D. Heiss, Eur. Phys. J. D 7, 1 (1999).\n[93] W.D. Heiss, Phys. Rev. E 61, 929 (2000).\n[94] F. Keck, H.J. Korsch, and S. Mossmann, J. Phys. A 36,\n2125 (2003).\n[95] AFTMATERIALSGmbH,Spinnerei44, D-71522Back-\nnang, Germany.\n[96] G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Mon-\ntaldo, and M. Fink, Phys. Rev. Lett. 92, 193904 (2004).\n[97] O. Hul, S. Bauch, P. Pakonski, N. Savytskyy, K. Zy-\nczkowski, and L. Sirko, Phys. Rev. E 69, 056205 (2004).\n[98] M. Vraniˇ car, M. Barth, G. Veble, M. Robnik, and H.-J.\nSt¨ ockmann, J. Phys. A 35, 4929 (2002).\n[99] B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu,\nA. Richter, F.Sch¨ afer, J. Verbaarschot, and H.A. Wei-\ndenm¨ uller, Phys. Rev. Lett. 103, 064101 (2009).\n[100] B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu, A.\nRichter, F. Sch¨ afer, and H.A. Weidenm¨ uller, Phys. Rev.\nE81, 036205 (2010).\n[101] O. Bohigas, D. Boos´ e, R. Egydio de Carvalho, and V.\nMarvulle, Nucl. Phys. A 560, 197 (1993).\n[102] C. Dembowski, H.-D. Gr¨ af, A. Heine, R. Hofferbert,\nH. Rehfeld, and A. Richter, Phys. Rev. Lett. 84, 867\n(2000).\n[103] CST Microwave Studio, CST GmbH, Bad Nauheimer\nStraße 19, D-64289 Darmstadt, Germany.\n[104] C. Mahaux and H.A. Weidenm¨ uller, Phys. Lett. 23, 100\n(1966).\n[105] T. Guhr, A. M¨ uller-Groeling, and H. A. Weidenm¨ uller ,\nPhys. Rep. 299, 189 (1998).\n[106] G. E. Mitchell, A. Richter, and H. A. Weidenm¨ uller,\nRev. Mod. Phys. 82, 2845 (2010).\n[107] B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu, A.\nRichter, F. Sch¨ afer, and H.A. Weidenm¨ uller, Phys. Rev.E78, 055204(R) (2008).\n[108] W. von Witsch, A. Richter, and P. von Brentano, Phys.\nLett.22, 631 (1966).\n[109] T.E.O. Ericson, Phys. Lett. 23, 97 (1966).\n[110] W. von Witsch, A. Richter, and P. von Brentano, Phys.\nRev. Lett. 19, 524 (1967).\n[111] E. Blanke, H. Driller, W. Gl¨ ockle, H. Genz, A. Richter ,\nand G. Schrieder, Phys. Rev. Lett. 51, 355 (1983).\n[112] H. Driller, E. Blanke, H. Genz, A. Richter, G. Schriede r,\nand J.M. Pearson, Nucl. Phys. A 317, 300 (1979).\n[113] P.A. Moldauer, Phys. Rev. 165, 1136 (1968).\n[114] Ref. [53] quantifies the asymmetry of HbyHa\n12=\n−iHA\n12.\n[115] J.M. Pearson and A. Richter, Phys. Lett. B 56, 112\n(1975).\n[116] In Fig. 4 of [53] the quantity Ha\n12= (H12− H21)/2 is\ngiven in units of ordinary frequency, not angular fre-\nquency, although Eq. (9) of the same reference gives\nHa\n12in units of angular frequency. In the present pub-\nlication the frequencies are ordinary ones throughout.\nThis required to replace the quantity Tof Ref. [53] by\nTrelax= 2πT.\n[117] B. Lax and K.J. Button, Microwave Ferrites and Ferri-\nmagnetics (McGraw-Hill, NY, 1962).\n[118] In Table I of [53] the numerical values of the quantity\nλare correct, its dimension, however, is Hz/mT not\nmT−1.\n[119] We are following the notation of Refs. [89, 90]. The defi -\nnition of τis given in the text below Eq. (1) of Ref. [89].\nIt differs from the corresponding quantity τin Refs. [6–\n8] which has the opposite sign. Thus the definition of\nτin [89] requires the factor e−iτin Eq. (2) of [89] (in-\nstead of the factor eiτ). In Eq. (3) of [89] the sign of τ\nis consistent with the present definition.\n[120] In Ref. [90] the expression for the rotation an-\ngle contains a misprint. It should read tan(2 φ0) =\nIm(h1/h2)/Im(h3/h2).\n[121] W.D. Heiss and H.L. Harney, Eur. Phys. J. D 17, 149\n(2001).\n[122] H.-M. Lauber, P. Weidenhammer and D. Dubbers,\nPhys. Rev. Lett. 72, 1004 (1994).\n[123] In the caption of Fig. 4 of Ref. [89] the imaginary part\nof the eigenvalues should read −Γ1,2/2.\n[124] W.D. Heiss, A. L. Sannino, Phys. Rev. A 43, 4159\n(2000).\n[125] A. Bohm (Editor), The Geometric Phase in Quantum\nMechanics , (Berlin: Springer) 2003.\n[126] K. Yu. Bliokh, J. Math. Phys. 32, 2551 (1999).\n[127] C. M. Bender, M. V. Berry, and A. Mandilara, J. Phys.\nA35, L467 (2002)."    },    {        "title": "1309.7956v1.Observation_of_plastoferrite_character_and_semiconductor_to_metal_transition_in_soft_ferromagnetic_Li0_5Mn0_5Fe2O4ferrite.pdf",        "content": "1 \n Observation of plastoferrite character and semiconductor to metal transition in soft \nferromagnetic Li 0.5Mn 0.5Fe2O4ferrite \nR. N. Bhowmik* \nDepartment of Physics, Pondicherry University, R.Venkataraman Nagar, Kalapet, \nPuducherry - 605 014, India \n*Corresponding author: Tel.: +91-9944064547; Fax: +91-413-2655734 \nE-mail: rnbhowmik.phy@pondiuni.edu.in \n \n               We prepared Li 0.5Mn 0.5Fe2O4 ferrite through chemical reaction in highly acidic \nsolution and subsequent sintering of ch emical routed powder at temperatures ≥ \n800 0C. Surface morphology showed plastoferrite character for sintering \ntemperature > 1000 0C. Mechanical softening of metal-oxygen bonds at higher \nmeasurement temperatures stimulated delocalization of charge carriers, w hich \nwere strongly localized in A and B sites of the spinel structure at l ower \ntemperatures. The charge delocalization process has activated semi conductor to \nmetallic transition in ac conductivity cu rves, obeyed by Jonscher power law and \nDrude equation, respectively. Metallic state is also confirmed by the frequenc y \ndependence of dielectric constant curves.  \nSpinel ferrites are attractive due to enriched magnetic and electrical  properties, which can be \ncontrolled by synthesis route and existence of different metal ions at tetrahedral (A) and \noctahedral (B) sites of sp inel structure [1, 2]. LiFe 2O4 ferrite is a soft ferromagnet, generally \nused as battery material [3]. MnFe 2O4 ferrite is another ferromagnet applied in power circuits \n[4]. The mixed compound of LiFe 2O4 and MnFe 2O4 has promised potential applications in \nmicroelectronics and information storage devices  due to soft ferromagnetic properties with \nexcellent square shaped loop, low electrical conductivity and low energy  loss [4-6]. Li-Mn \nferrite (Li 0.5Fe2.5-xMn xO4) has marked many interesting ferromagnetic and electrical 2 \n properties, which can be controlled by varying Fe and Mn ratio [3, 5, 7]. Here, we report on \nLi0.5Mn 0.5Fe2O4, a specific compound of Li 0.5Fe2.5-xMn xO4 series with Fe and Mn ratio 1:1.  \n The material was prepared by chemical reaction in highly acidic med ium. The \nstoichiometric amount of MnO, Li 2CO 3 and FeCl 3 were dissolved in concentrated HCl and a \nsolution of pH value ∼0.65 was prepared. The mixed solution was heated at 80-90 oC for 18 \nhrs in stirring condition, and finally, heated at 200 oC for 3 hrs and black color powder was \nobtained. The powder in pellet form was sintered at different temperat ures in air atmosphere \nto obtain single phased compound. Structural phas e of the sintered samples after cooling to \nroom temperature was studied using X-ray diffraction (XRD) pattern in the 2 ș range 20-80o \nwith step size 0.02o using CuK Į radiation. Profile fit of th e XRD pattern using Rietveld \nprogram, as in Fig. 1, confirmed single phased cubic spinel structure at sintering temperature \n≥ 800 oC for 6 hours. The samples sintered at 800 oC, 900 oC, 1000 oC, and 1100 oC were \ndenoted as S8, S9, S10, and S11, respectiv ely. Lattice parameter (8.322-8.36 Å) in the \nsamples increased with sintering temperature as an effect of ordering of cations in A and B \nsites of cubic spinel structure. Room temperature magnetic measure ment confirmed soft \nferromagnetic nature of the samples with coercivity 16-68 Oe and spontaneous ma gnetization \n34-58 emu/g. Lattice parameter and ferromagnetic parameters in the present Li-Mn ferrite are \nconsistent to reports [5, 7]. Apart from  coexistence of multivalent cations (Li+, Mn2+, Mn3+, \nFe2+, Fe3+), instability in the ordering of cations in A and B sites greatly modify conduction \nmechanism in ferrites. Especially, activation of  strong lattice vibration and electron-phonon \ninteractions play significant role on controlling the high temperature conduction me chanism. \nExcept our preliminary work [8], there is no report of frequency activated metalli c behavior \nat high temperature conductivity curves of ferrite. We demonstrate this iss ue and its possible \nmechanism using ac conductivity study of Li 0.5Mn 0.5Fe2O4 ferrite. 3 \n Fig.2 shows the surface morphology (SEM) of Li 0.5Mn 0.5Fe2O4 samples at different \nstages of sintering. SEM images showed spherical shaped (lower sintering temp erature: Fig. \n2(a-c)) and polygonal shaped (higher sintering te mperature: Fig. 2(d-e)) particles, whose size \nincreases with sintering temperature. Length and breadth of the particles varied in the range \n0.2-0.5 µm and 0.1-0.3 µm, respectively. However, grain (c rystallite) size of the samples \nobtained by analyzing XRD peaks using Debye Scherrer formula is in the range 3 0-50 nm. \nThis means particle size observed from SEM pict ures is poly-grained (crystalline) structure. \nSmall sized particles are melted across the interfaces to form micr on sized particles and the \nparticles form network structure (Fig. 2(b-d)). It appears that mechanical softness of the \nparticles increases for the samples sintered at higher temperature and l arge number of small \nparticles are accommodated inside a big sized particle (Fig. 2d). The  sample sintered at 1100 \noC showed ring shaped or wavy patterned surface. Such unique feature is expected in a \nspecial class of material, known as plastoferrite, which is a composite of ferrite particles and \norganic materials (synthetic rubber, plastic, et c). In fact, plastoferri te feature (thermal \nactivated surface strains) has been seen in many ceramics due to inhomogen eous grain \ngrowth process [9, 10]. Due to heterogeneities in system, some parts may be strong enough to \nresist local stress during cooling process and ot her parts become sufficiently soft so that \ndisplaced atoms can rearrange plas tically during cooling process. This develops elasto-plastic \nconstituents in the material. The elasto-plastic effect is prominent a t the interfaces (Fig. 2e) \nwhere broken bonds, local atomic displacements a nd effects of intra-grains porosity are easily \navailable. Recent interests for the plastoferrites are growing for understandi ng the effects of \nthermal induced visco-elasticity or plasticity on electro-magneti c properties or stress induced \ndeformation in complex network system [11]. Energy dispersive analysis of X-ray  (EDX) \nspectrum (e.g., Fig. 2(f)) indicated elementa l composition (Mn:Fe= 0.60:2) of the samples \nclose to expected value 0.5:2 in Li 0.5Mn 0.5Fe2O4. Li is not detected in the EDX spectrum due 4 \n to low atomic number (Z), but its presence was indicated in FTIR spectrum. E DX data \nindicated slight oxygen deficiency in the samples with oxygen content 4- δ (δ∼ 0.2). We \ncorrelate a small weight loss ( ≤ 2.5 %) in TGA curves above 800 oC to the oxygen loss and \nincreasing porosity that resulted in surface de formation in the samples sintered above 1000 \noC [12].  \nFrequency (1 Hz- 5 MHz) dependence of ac conductivity has been studied for two \nsamples with smaller grain size ( ∼ 30 nm and 35 nm for S8 and S9, respectively). The \nmeasurement was performed at field amplitude 1 Volt in the temperature ra nge 300-923 K \nusing broadband dielectric spectrometer (N ovo Control Technology, Germany). Disc-shaped \nsamples with ø ∼ 12 mm and thickness ∼ 2-3 mm were sandwiched between two platinum \nplates that were connected to the spectrometer. Fig. 3(a-b) shows frequency ( ν) dependent ac \nconductivity ( σn(ν)) (normalized by conductivity at 1Hz) at different temperatures. The \nimmediate observation is that σn(ν) is nearly frequency independent ( σdc limit) up to certain \nfrequency (say, νC). The ac conductivity is rapidly activated at higher frequencies ( ν>νC). \nThe remarkable feature is the observation of metallic character in ac conductivity curves \nabove semiconductor to metallic transition temperature (T SM) ≥ 740 K. In semiconductor \nregime (T <T SM), ac conductivity increases with the increase of frequency. In metallic  regime \n(T >T SM), ac conductivity decreases with the incr ease of frequency. The semiconductor and \nmetallic regimes are magnified in Fig. 3(c-d). This semiconductor to metallic transition is \ndifferent from the semiconductor to metallic tr ansition reported in other ferrites, e.g., NiFe 2O4 \nat ∼ 335 K [13], and CoFe 2O4 at ∼ 330-450 K [14-15]. First, metallic conductivity in these \nferrites was noted in the temperature dependence of grain boundary conductivity data, which \nwas derived from impedance spectra. Second, meta llic feature was not directly observed in ac \nconductivity curves, which may be related to not sufficiently high measurement temperatures \nor not intrinsic properties of the samples. In the present Li-Mn ferrite, metall ic response is 5 \n directly observed in ac conductivity curves within measurement temperat ures. We noted such \nsemiconductor to metallic transition and plastofe rrite character not only in chemical routed \nsamples, but also in solid state routed samples with micron-sized grains [8]. Hence, metallic \nconductivity in present  ferrite is not directly related to eith er grain size effect or structural \ndisorder (porosity, lattice defects), of course gr ain size and structural disorder influence up to \ncertain extent. Now, we demonstrate the mechanism in semiconductor and met allic regimes \nof the samples. \nThe frequency activated increase of conductivity [ ıac(ν,T < T SM)] in semiconductor \nregime obeys Jonscher’s power law [16]: ıac(ν,T) = α(T)νn with temperature dependent \nparameter α(T) and n, a dimension less parameter. The exponent n has been calculated from \nthe fit of conductivity curves (shown in magnified figures of Fig. 3(c-d)) for T < T SM. As \nshown in left hand side of Fig. 4(a), the obtained values of n are less than 1 and decrea ses \nwith increasing temperature up to 625 K. In the absence of free charge carriers, frequency  \nactivated conductivity in semiconductor regime of Li 0.5Mn 0.5Fe2O4 ferrite is explained by \nhopping of localized charge carriers between  B sites ions (electrons between Fe2+ and Fe3+ \nand holes between Mn3+ and Mn2+) [5]. Following earlier report [15], n value smaller than 1 \nsuggests long range hopping of charge carriers and decrease of n with increasing tempera ture \nindicates correlated barrier hopping of charge  carriers. Above 625 K, n fluctuates as the \ntemperature approaches towards T SM (metallic regime). In this mixed regime of conductivity, \nn values are affected due to increasing delocalization of charge carriers. In met allic regime of \nnanostructured materials having localized charge carriers [17], the ac  conductivity ( σ*(ω = \n2ʌν)) has been described by Drude-Smith model [18]: σ*(ω) = σబ\nଵି ωτሾͳ  σೕ\nሺଵି ωτሻೕ  ሿ. In our \nsamples, ac conductivity ( σ/(Ȧ)) curves in metallic regime (T > T SM) are well fitted according \nto Drude equation [19]: σ/(Ȧ) = σ0/(1+ Ȧ2IJs2). This is a special case of Drude-Smith model for \nisotropic scattering in free electrons system. Here, IJs is the relaxation time (collision time 6 \n between two scattering events, usua lly electron-phonon scattering) and σ0 is the dc limit of \nconductivity ( σdc) as we used for normalization of ac conductivity curves. The right hand side \nof Fig. 4(b) shows that relaxation time ( IJs) of the samples in metallic regime that obtained \nthrough fitting of σ/(ν) data (see Fig. 3(d)). The relaxati on time in metallic regime increases \nwith the increase of measurement temperature, which is understood as an effect of increasing \nelectron-phonon interactions. Remarkable feature is that magnitude of IJs (10-8 -10-9 s) in \nmetallic regime is few order less than the relaxation time (10-13 -10-15 s) for scattering of free \nelectrons usually occurs in optical frequency range. Hence, present ferrite represen ts a unique \nsystem where optical conduction resonance has shifted to lower frequencies [17]. One reason \nis that charge carriers are not completely free while moving insid e the crystal. The ions are \neither free to move within limited range or ex ecuting vibration about their mean positions so \nthat electrons clouds from neighbouring atoms can directly overlap and provide continuous \npath for charge motion. Goodenough [20] demonstrated that semiconductor feature is \nexpected in oxides when superexchange (cati on-anion-cation) interactions dominate over \ndirect (cation-cation) exchange interactions; otherwise metallic fe ature dominates in the case \nof strong cation-cation interactions. In this fe rrite, localization of charge carries at A and B \nsites at low temperatures exhibits semiconductor  feature. At higher temperatures, probability \nof transferring electrons between ions at adjacen t sites increases due to softening of elasticity \nor increasing plasticity in metal-oxygen bonds [11]. Fig. 4(b-c) shows a systematic change in \nconductivity regime with increasing temperatur e. As indicated in Fig. 4(c), conductivity \nincreases with the increase of frequencies in semiconducting regime and decreases in metallic \nregime and nearly frequency independent in mixed regime of conductivity. The frequency \ndependence of dielectric constant curves in metallic regime supports the correlation between \ndielectric constant ( ε*(ω) = ε/(ω) + i ε//(ω)) and ac conductivity ( σ*(ω) = σ/(ω) +iσ//(ω)), as \nestablished in electromagnetic theory using the relations ε*(ω) -1 = i σ*(ω)/ε0ω. This separates 7 \n out the real and imaginary parts as ε/(ω) -1 = - σ0IJs/ε0(1+Ȧ2IJs2) and ε//(ω) = σ0/ε0ω(1+Ȧ2IJs2). \nFig. 5(a-b) shows that ε/ is positive throughout the frequency range at lower temperatures \n(semiconductor regime). As metallic feature dominates at higher temp eratures, ε/ becomes \nincreasingly negative on lowering the frequency. On the other hand, İƎ(Ȟ) in Fig. 5 (c-d) \nremained positive throughout the frequencies fo r all measurement temperatures. The decrease \nof ε/(ν) with negative magnitude and increase of ε//(ν) with positive magnitude as ν→ 0 \nconfirms the metallic character in a material [17]. \nWe conclude that present system is not a typical metal, but metallic  feature appeared \nin the semiconductor ferrite due to increasing ch arge delocalization effect in bound ions at A \nand B sites of the cubic spinel structure. At higher temperatures, the developmen t of semi-\nelastic properties makes the metal oxygen (Li-O, Fe-O, Mn-O) bonds mechanic ally soft and \nflexible for overlapping electronic orbitals from adjacent ions and delocalization of electrons \nincreases. This process is accelerated by rapid vi bration of metals (Li, Mn, Fe) ions at higher \nfrequencies of ac field. This helps to break some of the Li-O bonds and produces Li+ ions that \nmove into interstitial sites. In the presence of oxygen vacancy (Fe3+--Fe2+, Mn3+--Mn2+, \nLi+--Fe3+), charge carriers in localized state (s emiconductor) of superexchange paths (Fe3+-\nO-Fe3+, Mn3+-O-Mn2+, Li+-O-Fe3+) transform to delocalized state (metallic). The plastoferrite \ncharacter may not be directly related to metal lic conductivity, but it indicates the materials \nwhere one expect greater probability of deloca lized charge carriers at higher temperatures. \nSuch ferrites can be used for correlating ther mal strain induced structural deformation and \nrelaxation in lattice dynamics. The important te chnological aspect is that same material can \nbe used as a semiconductor that allows electromagnetic wave to pass t hrough the material at \nlow temperature, but behave as a metallic reflector at high temperature .  \nAuthor thanks CIF, Pondicherry University, for providing experimental facilities. Author \nthanks to Miss. G. Vijayasri for assisting in experimental work.  8 \n [1] Y. Zhang, Z. Yang, D. Yin, Y. Liu, C. L. Fei, R. Xiong, J. Shi, and G. L.Yan, J. Magn. \nMagn. Mater. 322, 3470 (2010). \n[2] M. Srivastava, A.K. Ojha, S. Chaubey, P.K. Sharma, and A.C. P andey, Mater. Sci. Eng. B \n175, 14 (2010). \n[3] M. Gracia, J. F. Marco, J. R. Gancedo, J.L. Gautier, E.I. R ıғos, N. Menéndez, and J. \nTornero, J. Mater. Chem. 13, 844 (2003).  \n[4]. V.G. Harris et al., J. Magn. Magn. Mater. 321, 2035 (2009). \n[5] P.P. Hankare, R. P. Patil, U. B. Sankpal, S.  D. Jadhav, I. S. Mulla, K. M. Jadhav, and B. \nK. Chougule, J. Mag. Mag. Mater. 321, 3270 (2009). \n[6] M. P. Horvath, J. Magn. Magn. Mater. 215, 171 (2000). \n[7] Y. P. Fu, and C. S. Hsu, Solid State Comm. 134, 201 (2005). \n[8] G. Vijayasri, and R. N. Bhowmik, AIP Conf. Proc. 1512 , 1196 (2013). \n[9] M. Deepa, P.P. Rao, A.N. Radhakrishnan, K.S. Sibi, and P. Koshy, Mater. Res. Bull. 44, \n1481 (2009). \n[10] Li Lv, J.-P. Zhou, Q. Liu, G. Zhu, X. -Z. Chen, X. –B. Bian, and P. Liu, Physica E 43, \n1798 (2011). \n[11] C. Brosseau, and W. N. Dong, J. Appl. Phys .104, 064108 (2008). \n[12] C. Wende, and H. Langbein, Cryst. Res. Technol. 41, 18 (2006). \n[13] M. Younas, M. Nadeem, M. Atif, and R. Grossinger, J. Appl. Phys. 109, 093704 (2011). \n[14] A. U. Rahman, M. A. Rafiq, S. Karim, K. Maaz, M. Siddique, and M. M. Hasan, J. Phys. \nD: Appl. Phys. 44, 165404 (2011). \n[15] R. Kannan, S. Rajagopan, A. Arunkumar, D. Vanidha, and R. Murugaraj, J. Appl. Phys. \n112, 063926 (2012). \n[16] I.P. Muthuselvam, and R.N. Bhowmik, J. Phys. D: Appl. Phys. 43,465002 (2010). \n[17] M. Hövel, B. Gompf, and M. Dressel, Thin Solid Films 519, 2955(2011). 9 \n [18] N. V. Smith, Phys. Rev. B 64, 155106 (2001). \n[19] K. Lee, S. Cho, S. H. Park, A. J. Heeger, C. W. Lee and S. H. Lee, Nature  441, 04705 \n(2006). \n[20] J. B. Goodenough, Phys. Rev. 117, 1442 (1960). \n \nFigure captions: \nFig.1 (Colour online) Full Profile Fit of the XRD pattern of different annealed samples. \nFig. 2 SEM pictures for the samples S_8 (a), S_ 9 (b), S_10 (c), S_11 (d) and magnified form \nof surface strain (e). The EDX spectrum of sample S_11 is shown in (f). \nFig. 3 (Colour online) Frequency dependent ac conductivity ( σn(ν)) (normalized by the \nconductivity at 1 Hz ( σ1 Hz) for samples S8 (a) and S9 (b). The figures are magnified in (c) \nand (d) to clearly show the semiconductor to metallic transition.  \nThe lines in (c-d) are the fitted data according to Jonscher power law and Drude mo del for \nsemiconductor and metallic regimes, respectively. \nFig. 4 (Colour online) (a) temperature dependence of exponent obtained from fit of  \nconductivity data in semiconductor regime us ing Jonscher power law (left hand side)  \nand relaxation time obtained from fit of data in metallic regime using Drude model (right \nhand side). Temperature dependence of conductivity  at different frequencies for the samples \nS8 (b) and S9 (c). \nFig. 5 (Colour online) Frequency dependence of real part ( ε/) (a-b) and imaginary part  \n          ( ε//) (c-d) of dielectric constant at different measurement temperatures. 0.05.0x1091.0x1010\n-2x105-1x1050\n1001011021031041051061070.05.0x1091.0x1010\n100101102103104105106107-2x105-1x105012345678910111213 1415 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 6 6ABCDEFGHIJKLMN OPQRS TUVW XYZ AA AB AC AD AE AF AG AH AI AJ AK AL AM AN AO AP AQ AR AS AT AU AV AW AX AY AZ BA BB BC BD BE BF BG BH BI B Babcdefghijklmnopqrs t uvwxyz aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi b babcdefghijklmnopq rstu vw xyz aa abacad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh bi b b\nInterval 20K923K\n300K(c) S8Interval 20K\n923K923K(a) S8/g1/\nInterval 20K923K\n300K300K\n/g1// (d) S9\nFrequency (Hz) (log scale)Interval 20K300K\n(b) S9\nFrequency (Hz) (log scale)\nFig. 5 (Colour online) Frequency dependence of real part ( /g1/) (a-b) and imaginary part\n          (/g1//) (c-d) of dielectric constant at different measurement temperatures."    },    {        "title": "1804.07584v2.From_Charge_to_Orbital_Ordered_Metal_Insulator_Transition_in_Alkaline_Earth_Ferrites.pdf",        "content": "From Charge to Orbital Ordered Metal-Insulator Transition in Alkaline-Earth Ferrites\nYajun Zhang,1, 2Michael Marcus Schmitt,2Alain Mercy,2Jie Wang,1,\u0003and Philippe Ghosez2,y\n1Department of Engineering Mechanics, School of Aeronautics and Astronautics,\nZhejiang University, 38 Zheda Road, Hangzhou 310007, China\n2Theoretical Materials Physics, Q-MAT, CESAM, Universit\u0013 e de Li\u0012 ege, Belgium\n(Dated: May 4, 2018)\nWhile CaFeO 3exhibits upon cooling a metal-insulator transition linked to charge ordering, SrFeO 3\nand BaFeO 3keep metallic behaviors down to very low temperatures. Moreover, alkaline-earth\nferrites do not seem prone to orbital ordering in spite of the d4formal occupancy of Fe4+. Here, from\n\frst-principles simulations, we show that the metal-insulator transition of CaFeO 3is structurally\ntriggered by oxygen rotation motions as in rare-earth nickelates. This not only further clari\fes why\nSrFeO 3and BaFeO 3remain metallic but allows us to predict that an insulating charge-ordered phase\ncan be induced in SrFeO 3from appropriate engineering of oxygen rotation motions. Going further,\nwe unveil the possibility to switch from the usual charge-ordered to an orbital-ordered insulating\nground state under moderate tensile strain in CaFeO 3thin \flms. We rationalize the competition\nbetween charge and orbital orderings, highlighting alternative possible strategies to produce such a\nchange of ground state, also relevant to manganite and nickelate compounds.\nABO 3perovskite oxides, with a transition metal at the\nB-site, form a vast class of functional materials, fasci-\nnating by the diversity of their unusual properties [1{3].\nAmongst them, di\u000berent families of compounds with a\nformale1\ngoccupation of the dorbitals at the B-site, like\nrare-earth manganites ( d4=t1\n2ge1\ngin R3+Mn3+O3, with\nR a rare-earth element), rare-earth nickelates ( d7=t6\n2ge1\ng\nin R3+Ni3+O3), or alkaline earth ferrites ( d4=t1\n2ge1\ngin\nA2+Fe4+O3, with A = Ca, Sr or Ba) are similarly prone\nto show metal-insulator transitions (MIT). However, the\nmechanism behind such a transition can be intriguingly\ndi\u000berent from one family to the other.\nRNiO 3(except R=La) and RMnO 3compounds crys-\ntallize in the same metallic Pbnm GdFeO 3-type phase at\nsu\u000eciently high-temperature. This phase is compatible\nwith their small tolerance factor and labeled ( a\u0000a\u0000c+)\nin Glazers notation[4]. It di\u000bers from the aristotype cu-\nbic perovskite structure, only expected at very high tem-\nperature and not experimentally observed, by the coex-\nistence of two types of atomic distortions: (i) in-phase\nrotation of the oxygen octahedra along zdirection (M z)\nand (ii) anti-phase tilts of the same oxygen octahedra\nwith identical amplitude around xandydirections (R xy).\nOn the one hand, RNiO 3compounds show on cooling a\nMIT (TMIT = 0\u0000600K) concomitant with a structural\ntransition from Pbnm toP21=n[5]. This lowering of\nsymmetry arises from the appearance of a breathing dis-\ntortion of the oxygen octahedra (B oc), recently assigned\nto a structurally triggered mechanism [6] and produc-\ning a kind of charge ordering (CO)[7{10]. On the other\nhand, RMnO 3compounds also exhibit on cooling a MIT\n(TMIT\u0019750K) but associated to orbital ordering (OO)\nand linked to the appearance of Jahn-Teller distortions\n(MJT) compatible with the Pbnm symmetry [11, 12].\nIn comparison, AFeO 3compounds do not behave so\nsystemically and adopt seemingly di\u000berent behaviors.\nWhile SrFeO 3and BaFeO 3keep the ideal cubic per-ovskite structure and show metallic behavior at all tem-\nperatures [13, 14], CaFeO 3, which crystallizes above room\ntemperature in a Pbnm GdFeO 3-type phase, exhibits a\nbehavior similar to nickelates. At 290K, a MIT takes\nplace at the same time as its symmetry is lowered to\nP21=ndue to the appearance of a breathing distortion\n[15, 16]. A variety of explanations have been previ-\nously proposed to elucidate the MIT in CaFeO 3, includ-\ning orbital hybridization [17], electron-lattice interactions\n[18, 19], and ferromagnetic coupling [20]. However, no\nnet picture has emerged yet to rationalize its behavior\nand that of other ferrites.\nHere, we show from \frst-principles calculations that\nthe CO-type MIT in bulk CaFeO 3arises from the same\nmicroscopic mechanism as in the nickelates and must be\nassigned to a progressive triggering of B ocatomic distor-\ntions by M zand R xyatomic motions. We demonstrate\nthat this triggered mechanism is universal amongst the\nferrite family and that an insulating phase can be induced\nin metallic SrFeO 3from appropriate tuning of oxygen ro-\ntations and tilts. Going further, we reveal that CO and\nOO compete in AFeO 3compounds and we unveil the\npossibility to switch from CO-type to OO-type MIT in\nCaFeO 3thin \flms under appropriate strain conditions.\nThis o\u000bers a convincing explanation for the enormous re-\nsistivity at room-temperature recently found in CaFeO 3\n\flms grown on SrTiO 3[21].\nMethods - Our \frst-principles calculations relied on\ndensity functional theory (DFT) as implemented in\nVASP [22, 23]. We worked with the PBEsol [24]\nexchange-correlation functional including U and J cor-\nrections as proposed by Liechtenstein [25]. We used\n(UjJ) = (7:2j2:0)eV, a plane-wave energy cuto\u000b of 600 eV\nand Monkhorst-Pack[26] k-point samplings equivalent to\n12\u000212\u000212 for a 5-atoms cubic perovskite cell. The\nlattice parameters and internal atomic coordinates were\nrelaxed until atomic forces are less than 10\u00005eV=\u0017A. ThearXiv:1804.07584v2  [cond-mat.str-el]  2 May 20182\nFIG. 1: (a-c) Phonon dispersion curves of cubic CaFeO 3(a), SrFeO 3(b), and BaFeO3 (c) on which most relevant modes\nare pointed. (d-f) Evolution of the energy with respect to the breathing distortion amplitude ( QB) at \fxed rotation ( QM)\nand tilts (QR) amplitudes in CaFeO 3(d), SrFeO 3(e), and BaFeO 3(f). Opened (resp. \flled) symbols denote insulating\n(resp. metallic) states. (g) Electronic band structure of CaFeO 3along selected lines of the Pbnm orP21=nBrillouin zone\n(coordinates in pseudo-cubic notations) for di\u000berent amplitude of disortions. All results were calculated with FM spin order\nand using a \fxed cubic cell with the same volume as the ground state. Distortion amplitudes are normalized to those calculated\nbyISODISTORT [27] in the CaFeO 3AFM ground state.\nphonon dispersion curves were calculated with 2 \u00022\u00022\nsupercells using \fnite displacement method. A special\ncare was devoted to the determination of appropriate\nU and J parameters, which is discussed in detail in\nthe Supplementary Material (SM) [35]. We found that\n(UjJ) = (7:2j2:0) eV provides good simultaneous descrip-\ntion of the structural (lattice constant and distortion am-\nplitudes), electronic (insulating ground- state) and mag-\nnetic (AFM spiral-type ground state very close in energy\nto the FM con\fguration) properties of CaFeO 3.\nBulk CaFeO 3{In order to clarify the mechanism be-\nhind theP21=ninsulating ground state of CaFeO 3, we\n\frst focus on the phonon dispersion curves of its par-\nent cubic phase (Fig. 1a). Calculations are reported in\na ferromagnetic con\fguration, which is representative to\nunravel the essential physics. On the one hand, Fig. 1a)\nshows expected unstable phonon modes at M point ( M+\n2,\n!M= 181icm\u00001) and R point ( R\u0000\n5,!R= 197icm\u00001) of\nthe Brillouin zone, related respectively to the M zand R xy\ndistortions yielding the Pbnm phase. On the other hand,\nit attests that the R\u0000\n2mode related to the B ocdistortion\nis signi\fcantly stable ( !2\nB= 343cm\u00001), so questioning\nthe origin of its appearance in the P21=nphase.\nThe answer is provided in Fig. 1b), reporting the evo-\nlution of the energy with the amplitude of B oc(QB) at\n\fxed amplitudes of M z(QM) and R xy(QR). It demon-\nstrates that, although initially stable (single well { SW\n{ with a positive curvature at the origin \u000bB/!2\nB>0)\nin the cubic phase, B ocwill be progressively destabilized\n(double well { DW { with a renormalized negative curva-ture at the origin ~ \u000bB<0) as M zand R xydevelop in the\nPbnm phase. The curvature ~ \u000bBchanges linearly with\nQ2\nMandQ2\nR(~\u000bB=\u000bB+\u0015BMQ2\nM+\u0015BRQ2\nR) so that its\nevolution must be assigned to a cooperative biquadratic\ncoupling (\u0015BM;\u0015BR<0) ofBocwith M zand R xyas\nhighlighted by the following terms in the Landau-type\nenergy expansion around the cubic phase:\nE/\u000bBQ2\nB+\u0015BMQ2\nMQ2\nB+\u0015BRQ2\nRQ2\nB (1)\nFor large enough amplitudes of M zand R xy, Bocbecomes\nunstable and will spontaneously appear in the structure.\nIn Fig. 1b) we further notice that the amplitude of B oc\nrequired for making the system insulating decreases for\nincreasing M zand R xy, yielding therefore an insulating\nP21=nground state.\nThis behavior is point by point similar to that reported\nrecently in rare-earth nickelates by Mercy et al. [6] who\nsubsequently assigned the MIT to a structurally triggered\nphase transition, in the sense originally de\fned by Ho-\nlakovsk\u0013 y [28]. In Ref. [6], the unusual cooperative cou-\npling of B ocwith M zand R xyat the origin of this trig-\ngered mechanism was moreover traced back in the elec-\ntronic properties of nickelates and further related to a\ntype of structurally triggered Peierls instability.\nFig 1g) shows that this explanation still hands for fer-\nrites. In the cubic phase of CaFeO 3(Fe4+with formal\noccupation d4=t1\n2ge1\ng), the Fermi energy, E F, crosses\nanti-bonding Fe 3 d{ O 2pstates with a dominant egchar-\nacter. Activation of B occan open a gap in these partly\noccupiedegbands atqB= (1=4;1=4;1=4), but around an3\nenergy E Binitially above E F. The role of R xyandMz\nis to tune Fe 3 d{ O 2phybridizations in such a way that\nEBis progressively lowered towards E F. As they develop\ninto the structure, activating B oca\u000bects more and more\nsubstantially energy states around E Fand yields an in-\ncreasing gain of electronic energy explaining the progres-\nsive softening of !B. Theegbandwidth in CaFeO 3being\nsmaller than in the nickelates, E Bis initially closer to E F\nconsistently with a softer !Band the smaller amplitude\nof R xyand M zrequired to destabilize B oc.\nBulk SrFeO 3and BaFeO 3{The triggered mechanism\nhighlighted above further straightforwardly explains the\nabsence of MIT in other alkaline-earth ferrites. Because\nof their larger tolerance factors and as con\frmed from\nthe absence of unstable mode in their phonon dispersion\ncurves (Fig. 1b) and c)) SrFeO 3and BaFeO 3preserve\ntheir cubic structure down to zero Kelvin[13, 14] and so\ndo not spontaneously develop the oxygen rotation and\ntilts mandatory to trigger the MIT. The cooperative cou-\npling of B ocwith M zand R xyremains however a generic\nfeatures of all ferrite compounds.\nAs illustrated in Fig. 1e) and 1f), B ocis progres-\nsively destabilized when increasing arti\fcially the ampli-\ntudes of M zand R xydistortions in SrFeO 3and BaFeO 3.\nSince, in the cubic phase of these compounds, !Bis\noriginally at frequencies slightly larger than in CaFeO 3\n(!B= 362cm\u00001in SrFeO 3and!B= 415cm\u00001in\nBaFeO 3), larger distortions are required to induce the\nMIT. In SrFeO 3, amplitudes of M zand R xycorrespond-\ning to 75% of their ground-state values in CaFeO 3are\nnevertheless enough to force an insulating ground state.\nIn BaFeO 3, the cooperative coupling is less e\u000ecient and\nmuch larger amplitudes would be required.\nThis highlights the possibility of inducing a MIT in\nSrFeO 3thin \flms or heterostructures under appropriate\nengineering of R xyand M z. Moreover, it provides a vivid\nexplanation to the decrease of T MIT experimentally ob-\nserved in Ca 1\u0000xSrxFeO 3solid solutions as xincreases\n[29]. For increasing Sr concentrations, the average tol-\nerance factor increases and the mean amplitudes of M z\nand R xydecrease. This analysis is supported by DFT\ncalculation at 50/50 Ca/Sr composition using an ordered\nsupercell (see SM [35]).\nCharge versus orbital ordering { It remains intriguing\nwhy CaFeO 3(t3\n2ge1\ng) prefers to exhibit a breathing distor-\ntion (B oc) and CO as RNiO 3compounds ( t6\n2ge1\ng) rather\nthan a Jahn-Teller distortion (M JT) and OO as RMnO 3\ncompounds ( t3\n2ge1\ng). In Ref. [30] Whangbo et al. argue\nthat B ocis favored in CaFeO 3by the relatively strong co-\nvalent character of the Fe-O bond while the M JTdistor-\ntion is preferred in LaMnO 3by the weak covalent charac-\nter of the Mn-O bond. So, we anticipate that weakening\nthe covalence by increasing the Fe-O distance might fa-\nvor M JTand OO in CaFeO 3. To realize practically this\nidea, we investigated the role of tensile epitaxial strain\non the ground state of CaFeO 3thin \flms.\nFIG. 2: (a) Total energy as a function of tensile strain (or in-\nplane lattice constant) for CaFeO 3epitaxial \flms with c-axis\nout-of-plane, in CO and OO states with either FM or A-type\nAFM spin ordering; FM CO state with the long c-axis in-\nplane is plot in orange for comparison. A change of ground\nstate from FM-CO phase (yellow area) to A-type AFM-OO\nphase (blue area) is observed. Inset: c/a ratio of the ground\nstate structure as a function of strain. (b) Evolution of QB\n(green),QJT(red) and band gap (blue) as a function of strain\n(or in-plane lattice constant).\nCaFeO 3thin \flms { The phase diagram of CaFeO 3\n\flms epitaxially grown on a cubic perovskite (001)-\nsubstrate is reported Fig. 2a). The evolution of the en-\nergy with the lattice constant of the substrate is shown\nfor FM and A-type AFM orders with either charge or or-\nbital ordering. Although S- and T-type spiral magnetic\norders (not shown here) possess a slightly lower energy\nat the bulk level, the FM order becomes quickly the GS\nunder small tensile strain; C-type and G-type AFM order\nare much higher in energy and not shown. Both possi-\nble orientations of the orthorhombic ( a\u0000a\u0000c+) oxygen\nrotation pattern, with the long c-axis either in-plane or\nout-of-plane were also considered: while c-axis in-plane is\nfavored at zero strain, c-axis out-of-plane becomes more\nstable under tensile strains.\nFig. 2a) demonstrates the possibility of switching from\na CO to an OO ground state in CaFeO 3using strain engi-\nneering: under increasing tensile strain, the ground state\nof the \flm changes from an insulating FM-CO P21=n\ncon\fguration at small strain to an insulating A-type\nAFM-OO Pbnm con\fguration above 3% tensile strain\n(a=3.88 \u0017A). Fig. 2b) highlights the strain evolution of\nBocand M JTdistortions together with the change of\nband gap. Under increasing tensile strain, B ocslightly\ndecreases and is abruptly suppressed at the phase transi-\ntion; at the same time, the band gap { already reduced in\nthis FM phase { decreases, although much faster than B oc\nand the transition appears precisely when the bandgap\nconverges to zero. Conversely, M JTis nearly zero below\n3% tensile strain while it suddenly appears at the tran-\nsition and then continuously increases. Amazingly, the\namplitude of M JT(0.37 \u0017A) in a CaFeO 3\flm grown on a\nSrTiO 3substrate (a = 3.905 \u0017A) is comparable to that of\nbulk LaMnO 3(0.36 \u0017A). Such similar amplitude suggests\nthat theTMIT associated to the OO state in strained4\nFIG. 3: Evolution of the energy with Jahn-Teller distortion amplitude QJTin AFM-A magnetic order and at \fxed amplitudes\nof other distortion (see legend) for CaFeO 3epitaxial \flms under strain of (a) 0% ( a= 3:76\u0017A) and (b) 4% ( a= 3:91\u0017A). (c)\nEvolution of the total energy as a function of QBin FM-CO state (open symbol) and QJTin A-type AFM-OO state (\flled\nsymbol) for CaFeO 3thin \flm under 0% ( a= 3:76\u0017A, red) and 4% ( a= 3:91\u0017A, blue) strains. QM,QRandQXare \fxed to\ntheir amplitudes in the relevant phase (except for the FM-CO state at 4% which cannot be stabilized and for which we kept\npositions in the A-type AFM-OO phase).\nTABLE I: Top: Amplitudes of dominant distortions [27] in\nthe relaxed CO (FM) and OO (AFM-A) phases of CaFeO 3\nepitaxial \flms under 0% ( a= 3:76\u0017A) and 4% ( a= 3:91\u0017A)\ntensile strain. Bottom : Energy contributions associated to\nthe di\u000berent terms in Eq.(2), obtained from the amplitudes\nof distortion reported above.\nAmplitudes ( \u0017A)QJTQBQMQRQX\na = 3.76 \u0017A-CO 0.007 0.137 0.788 1.111 0.440\na = 3.76 \u0017A-OO 0.256 0.000 0.717 1.194 0.457\na = 3.91 \u0017A-OO 0.400 0.000 0.676 1.309 0.552\nEnergies (meV/fu) \u0001 E(1)\nJT\u0001E(2)\nJT\u0001E(3)\nJT\u0001EJT\u0001EAFM\u0000A\na = 3.76 \u0017A-OO 4.4 -43.6 -15.8 -55.0 74.5\na = 3.91 \u0017A-OO -104.3 -80.9 -31.0 -216.2 49.3\nCaFeO 3\flms might be much larger than the TMIT as-\nsociated to the CO state in bulk and comparable to the\none of LaMnO 3(TMIT = 750K).\nOur \fndings provide a convincing explanation for the\ninsulating character of CaFeO 3\flms on SrTiO 3at room\ntemperature and for the absence of CO MIT in the\n100-300K temperature range as recently pointed out in\nRef.[21]. They suggest to probe the presence of OO MIT\nat higher temperature. A key feature, highlighted in the\ninsert in Fig. 2a), is the jump of c/a ratio at the transi-\ntion boundary, which provides another concrete hint for\nexperimentalists to probe the CO-OO transition.\nCompetition between charge and orbital orders - To ra-\ntionalize the emergence of an OO ground state in CaFeO 3\n\flms, we quantify the lowest-order couplings of M JTwith\nother distortions in a Landau-type free energy expansion\nand investigate their sensitivity to magnetic order and\nepitaxial strain :\nE/\u000bJTQ2\nJT+\u0015MJQ2\nMQ2\nJT+\u0015RJQ2\nRQ2\nJT\n+\rQRQXQJT (2)The \frst term quanti\fes the proper harmonic energy con-\ntribution \u0001 E(1)\nJTassociated to the appearance of M JT.\nThe second and third terms in Eq. (2) account for a\nchange of energy \u0001 E(2)\nJTin presence of M zand R xy,\nlinked to their lowest bi-quadratic coupling with M JT.\nFinally, sizable anti-polar motions of the Ca cations\nand apical oxygens (X APmode of amplitude QX, see\nTable I), which are driven by M zand R xy[31], cou-\nple in a trilinear term with R xyand M JT(last term\nin Eq.(2)). This coupling produces an energy lowering\n\u0001E(3)\nJT<0, through a so-called hybrid improper mecha-\nnism yeilding an asymmetry in the M JTenergy well [36].\nCompendiously, appearance of a M JTdistortion requires\n\u0001EJT= \u0001E(1)\nJT+ \u0001E(2)\nJT+ \u0001E(3)\nJT<0.\nIn bulk CaFeO 3,\u000bJTis large (!JT(FM) = 390 cm\u00001)\nin the FM cubic phase, which prohibits \u0001 EJTto be-\ncome negative for sizable amplitudes of M JT. Switch-\ning to the A-type AFM spin order tremendously lowers\n\u000bJT(!JT(AFM\u0000A) = 144 cm\u00001) but simultaneously\nincreases the total energy by \u0001 EAFM\u0000A. The stabiliza-\ntion of an OO phase with M JTagainst the CO phase\nwith B ocso depends eventually on the counterbalance\nbetween \u0001EAFM\u0000Aand \u0001EJT.\nThis is quanti\fed for epitaxial thin \flms in Fig. 3 and\nTable I. Under negligible tensile strain (a= 3.76 \u0017A, Fig.\n3a), with A-type AFM order, !JTis even softer than in\nbulk CaFeO 3, yielding \u0001 E(1)\nJT\u00190. Then, similarly to\nwhat was discussed for Bocin bulk compounds, Rxyand\nMztriggerMJT(\u0015MJ;\u0015RJ<0), yielding \u0001 E(2)\nJT<0. Fi-\nnally, the hybrid improper coupling with XAPand R xy\nprovides a further \u0001 E(3)\nJT<0. However, although glob-\nally negative, \u0001 EJTcannot overcome \u0001 EAFM\u0000A(Fig.\n3c). Under large tensile strain (a= 3.91 \u0017A, Fig. 3b)\n\u000bJTis signi\fcantly reduced by coupling with the epi-\ntaxial tetragonal strain etz(\u000bJT/\rtJetz+\u0015tJe2\ntz[32]),\nyielding a huge negative \u0001 E(1)\nJT. Then, although \u0015MJ\nand\u0015RJare reduced and \rremains una\u000bected (see SM5\n[35]), \u0001E(2)\nJTand \u0001E(3)\nJTare increased roughly by a fac-\ntor of 2, mainly due to the increase of QJT. Globally,\nj\u0001EJTjin A-type AFM order is now much larger than\n\u0001EAFM\u0000A, which moreover has been slightly reduced,\nand the OO phase with M JTis stabilized against the CO\nphase with B oc(Fig. 3c). We notice that QMandQRare\nnot strongly a\u000bected by strain so that the stabilization\nof the OO phase must be primarily assigned to the strain\nremormalization of \u000bJT.E(2)\nJTand \u0001E(3)\nJTplay however\nan important complementary role and tuning QMand\nQRwould o\u000ber an alternative strategy to stabilize the\nOO phase.\nConclusions - We have rationalized the appearance of\na CO-type MIT in alkaline-earth ferrites, showing that,\nin CaFeO 3, such a MIT arises from the triggering of Boc\nby M zand R xyand that this mechanism can induce a\nCO insulating ground state in SrFeO 3under appropriate\ntuning of M zand R xy. Going further, we found that OO\nis also incipient to CaFeO 3and that an OO-type MIT\ncan be engineered in thin \flms under moderate tensile\nstrain. We have shown that the appearance of the OO-\ntype insulating ground state arises from a delicate bal-\nance between di\u000berent energy terms, suggesting di\u000berent\nstrategies to stabilize it. Interestingly, the emergence of\nthe OO phase in ferrites is the result of a purely structural\ninstability and we did not \fnd any gradient discontinuity\nin the energy (corner point), \fngerprint of the electronic\ninstability usually associated to OO phases[33]. Such a\nstructural stabilization of the OO phase might o\u000ber a\nreasonable explanation to the emergence of an OO phase\nin other materials like RNiO 3compounds [34][37].\nAcknowledgments - Work supported by the FRS-FNRS\nPDR project HiT4FiT and ARC AIMED. M.S. and Y.\nZ. acknowledge \fnancial support from FRIA (grants\n1.E.070.17. and 1.E.122.18.). Computational support\nfrom C\u0013 eci funded by F.R.S-FNRS (Grant No. 2.5020.1)\nand Tier-1 supercomputer of the F\u0013 ed\u0013 eration Wallonie-\nBruxelles funded by the Walloon Region (Grant No.\n1117545). M.S. and Y.Z. contributed equally to this\nwork.\n\u0003Electronic address: jw@zju.edu.cn\nyElectronic address: Philippe.Ghosez@ulg.ac.be\n[1] D. Khomskii, Transition metal compounds (Cambridge\nUniversity Press, 2014).\n[2] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.\n70, 1039 (1998).\n[3] P. Zubko, S. Gariglio, M. Gabay, P. Ghosez, and J.-M.\nTriscone, Annu. Rev. Conden. Ma. P. 2, 141 (2011),\nhttps://doi.org/10.1146/annurev-conmatphys-062910-\n140445 .\n[4] A. M. Glazer, Acta Crystallogr. B. 28, 3384 (1972).\n[5] M. L. Medarde, J. Phys.: Condens. Matter 9, 1679\n(1997).\n[6] A. Mercy, J. Bieder, J. I~ niguez, and P. Ghosez, Nat.Commun. 8, 1677 (2017).\n[7] I. I. Mazin et al. Phys. Rev. Lett. 98, 176406 (2007).\n[8] H. Park, A. J. Millis, and C. A. Marianetti, Phys. Rev.\nLett. 109, 156402 (2012).\n[9] S. Johnston, A. Mukherjee, I. El\fmov, M. Berciu, and\nG. A. Sawatzky, Phys. Rev. Lett. 112, 106404 (2014).\n[10] J. Varignon, M. N. Grisolia, J. I~ niguez, A. Barth\u0013 el\u0013 emy,\nand M. Bibes, npj Quantum Materials 2, 21 (2017).\n[11] T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T.\nTakahashi, K. Ishizaka, and Y. Tokura, Phys. Rev. B\n68, 060403 (2003).\n[12] M. C. S\u0013 anchez, G. Sub\u0013 \u0010as, J. Garc\u0013 \u0010a, and J. Blasco, Phys.\nRev. Lett. 90, 045503 (2003).\n[13] J. B. MacChesney, R. C. Sherwood, and J. F. Potter, J.\nChem. Phys. 43, 1907 (1965).\n[14] N. Hayashi et al. Angew. Chem. Int. Edit. 50, 12547\n(2011).\n[15] S. Kawasaki, M. Takano, R. Kanno, T. Takeda, and\nA. Fujimori, J. Phys. Soc. Jpn. 67, 1529 (1998).\n[16] P. M. Woodward, D. E. Cox, E. Moshopoulou, A. W.\nSleight, and S. Morimoto, Phys. Rev. B 62, 844 (2000).\n[17] T. Akao et al. Phys. Rev. Lett. 91, 156405 (2003).\n[18] J. Matsuno, T. Mizokawa, A. Fujimori, Y. Takeda,\nS. Kawasaki, and M. Takano, Phys. Rev. B 66, 193103\n(2002).\n[19] S. Ghosh et al. , Phys. Rev. B 71, 245110 (2005).\n[20] A. Cammarata and J. M. Rondinelli, Phys. Rev. B 86,\n195144 (2012).\n[21] P. C. Rogge et al. , Phys. Rev. Materials 2, 015002 (2018).\n[22] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).\n[23] P. E. Bl ochl, Phys. Rev. B 50, 17953 (1994).\n[24] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov,\nG. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke,\nPhys. Rev. Lett. 100, 136406 (2008).\n[25] V. I. Anisimov, F. Aryasetiawan, and A. I. et Lichten-\nstein, J. Phys.: Condens. Matter 9, 767 (1997).\n[26] H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188\n(1976).\n[27] B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M.\nHatch, J. Appl. Crystallogr. 39, 607 (2006).\n[28] J. Holakovsk\u0013 y, physica status solidi (b) 56, 615 (1973).\n[29] T. Takeda, R. Kanno, Y. Kawamoto, M. Takano,\nS. Kawasaki, T. Kamiyama, and F. Izumi, Solid State\nSci.2, 673 (2000).\n[30] M.-H. Whangbo, H.-J. Koo, A. Villesuzanne, and\nM. Pouchard, Inorg. Chem. 41, 1920 (2002), pMID:\n11925189, https://doi.org/10.1021/ic0110427 .\n[31] J. Varignon, N. C. Bristowe, E. Bousquet, and P. Ghosez,\nSci. Rep. 5, 15364 (2015).\n[32] M. A. Carpenter and C. J. Howard, Acta Crystallogr. B.\n65, 134 (2009).\n[33] W.-G. Yin, D. Volja, and W. Ku, Phys. Rev. Lett. 96,\n116405 (2006).\n[34] Z. He and A. J. Millis, Phys. Rev. B 91, 195138 (2015).\n[35] See supplementary material at URL for details about the\ndetermination of (U jJ) calculation parameters, support-\ning calculations on Sr/BeFeO 3solutions, and a deeper\nanalysis on the assymetry of the QJTenergy surface.\n[36] The coexistence of M zand R xyalready produces an\nasymmetry in the energy well through the term E/\n\u000eQ2\nRQMQJT. However, this asymmetry is in the negli-\ngible range of 1 meV (see Fig. 3a-b), and is not further\ndiscussed here.\n[37] Xu He et.al, in press."    },    {        "title": "1210.0997v1.Direct_calorimetric_measurements_of_isothermal_entropy_change_on_single_crystal_W_type_hexaferrites_at_the_spin_reorientation_transition.pdf",        "content": "arXiv:1210.0997v1  [cond-mat.mtrl-sci]  3 Oct 2012Direct calorimetric measurements of isothermal entropy ch ange on single crystal\nW-type hexaferrites at the spin reorientation transition\nM. LoBue,1,a)V. Loyau,1F. Mazaleyrat,1A. Pasko,1V. Basso,2M. Kupferling,2and C.\nP. Sasso2\n1)SATIE, ENS de Cachan, CNRS, UniverSud, 61 av du President Wil son,\nF-94230 Cachan, France\n2)Istituto Nazionale di Ricerca Metrologica, Strada delle Ca cce 91, 10135 Torino,\nItaly\n(Dated: 23 November 2018)\nWe report on the magnetic field induced isothermal entropy change ∆s(Ha,T) of\nW-type ferrite with CoZn substitution. Entropy measurement are performed by\ndirect calorimetry. Single crystals of composition BaCo 0.62Zn1.38Fe16O27, prepared\nby flux method, are measured at different fixed temperatures und er applied field\nperpendicular and parallel to the caxis. At 296K onededuces avalue of K 1= 8.7104\nJ m−3for the first anisotropy constant, in good agreement with literatu re. The spin\nreorientation transition temperature is estimated to take place be tween 200 and 220\nK.\nPACS numbers: 75.50.Gg, 73.30.Sg, 75.40.-s, 75.30.Gw\na)e-mail: martino.lo-bue@satie.ens-cachan.fr\n1I. INTRODUCTION\nHexagonal ferrites were intensely studied for permanent magnet s and microwave ab-\nsorber applications. The former related to their easy axis anisotro py configuration (e.g. in\nM-ferrites), the latter to an easy plane one (e.g. in Y-ferrites)1. Moreover, W-type fer-\nrites undergo spin reorientation transitions (SRT) between state s of different anisotropy on\nvarying temperature2and applied magnetic field3. In spite of the lesser magnitude of the\nanisotropy-driven magnetocaloric effect (MCE), with respect to o ther materials where en-\ntropy change is associated with a change in the spontaneous magne tisation, these transitions\nshow unique properties due to the vectorial nature of anisotropy related phenomena. The\nentropy change associated with SRT can be actually achieved by cha nging the direction\nof the applied magnetic field (i.e. by a rotating field) instead of changin g its amplitude.\nAnother relevant advantage of ferrites, with respect to other a lloys4, is that they contain no\ncritical rare-earth elements.\nThestructureofthe Wferritesisbuiltupbymixingtheunitcellsofthemagnetoplumbite\nM, with chemical composition BaFe 12O19, and that of the spinel S, Me2Fe4O8. A detailed\ndescription of this structure can be found in the literature1. The possibility to tune the SRT\ntemperature by changing the proportion between the Co and Zn su bstitutions2,5and its\nstructural origin have been extensively studied2,6. The system undergoes a SRT transition\nfromalowtemperatureeasyplane(EP)configurationtoanhightem peratureeasyaxis(EA)\nat a temperature Tsrthat increases with Co concentration x. For the x= 0.62 composition\nthat we investigate here, the transition takes place at about 215 K . As the magnetic field\ninduced SRT requires the presence of a well-defined orientation of t he magnetocrystalline\nanisotropy, the effect can be detected both in single crystal , and in aligned polycrystalline\nsamples. In this paper we shall limit our study to single crystal, where the entropy change is\nexpected to be greater. Comparison with polycrystalline textured samples will be presented\nelsewhere.\nII. EXPERIMENTAL\nSingle crystals of composition BaCo 0.62Zn1.38Fe16O27have been grown using a flux\nmethod3. The starting mixture was prepared from BaCO 3, CoO, ZnO, Fe 2O3and Na 2CO3\n2powders. The charge was packed into a platinum crucible and heated up to 1350◦C. The\nmelt was homogenized at this temperature for 24 h, slowly cooled dow n to 1000◦C at 3◦C/h\nand more rapidly to room temperature. Crystal structures were examined by PANalytical\nXPert Pro X-ray diffractometer (XRD) in Co-K αradiation with X’Celerator detector for\nrapid data acquisition.\nWeperformedmeasurements onasampleofmass m= 31.81mgandoflateral sizeofafew\nmillimetres. Due to the shape of the sample we estimated the demagne tising factors parallel\nandperpendiculartothe caxistoberespectively N/bardbl= 0.4andN⊥= 0.3. Isothermalentropy\nchange has been measured using a home-made calorimetric set-up w ith thin film Peltier cells\n(Micropelt MPG D751) as heat flux sensors, working in the temperat ure range77 −300 K by\nusing an Oxford Microstat He cryostat with liquid nitrogen (a similar se t-up working around\nroom temperature is described in7). The magnetic field is generated by an electromagnet\n(up to 2 T maximum). The measurements are performed by keeping t he temperature stable\nto the desired value, and meanwhile by measuring the heat flux qsduring application and\nremovalofthemagneticfield(upto1T)atarateof µ0dHa/dt= 0.033Ts−1. Aftercorrection\nof the measured heat flux for dynamic effects due to the heat tran sfer in the Peltier cell7and\nan eventual offset due to non ideal isothermal conditions, the mag netic field induced entropy\nchange is deduced by integrating qsover time. The result of the integration is represented\nversus the applied field Ha. In Fig.1andFig.2 theentropy change, measured by applying the\nmagnetic field respectively parallel and perpendicular to the caxis, are shown in a range of\ntemperatures spanning from 120 K to 300 K. In both cases we obse rve two different classes\nof ∆s(Ha) curves. The first is linear, ∆ s(Ha) =b(Ha−NdMs), with negative slope b. The\nsecond is composed by two regimes: a quadratic one with ∆ s(Ha) =cH2\na, fromHa= 0 up\nto a field value that we shall call H∗; a linear one with ∆ s(Ha) = ∆sk+b(Ha−NdMs), when\nHa≥H∗. The purely linear behaviour is observed in the temperature range w here the field\nis directed along the zero-field equilibrium configuration of the sample . The double regime\nis observed at temperatures where the field is applied perpendicular to the equilibrium state\nand therefore a field driven SRT, whose maximum entropy change is ∆ sk, takes place. From\nFig. 2and3weseethat∆ skispositiveunder applicationof Haparallelto cfortemperatures\nbelow about 200 K. This corresponds to a transition from a low entro py EP configuration\ntoward a high entropy EA one. On the contrary ∆ skis negative when Hais9perpendicular\ntocand the temperature is above 200 K. This corresponds to a transit ion from EA (high\n3/s48/s46/s48 /s48/s46/s50 /s48/s46/s52 /s48/s46/s54 /s48/s46/s56 /s49/s46/s48 /s49/s46/s50 /s49/s46/s52/s45/s48/s46/s49/s53/s45/s48/s46/s49/s48/s45/s48/s46/s48/s53/s48/s46/s48/s48/s48/s46/s48/s53/s48/s46/s49/s48/s48/s46/s49/s53\n/s32/s32/s115/s32/s40/s74/s107/s103/s45/s49\n/s75/s45/s49\n/s41\n/s48/s72\n/s97/s32/s40/s84/s41/s66/s97/s67/s111\n/s48/s46/s54/s50/s90/s110\n/s49/s46/s51/s56/s70/s101\n/s49/s54/s79\n/s50/s55\n/s72\n/s97/s32/s112/s97/s114/s97/s108/s108/s101/s108/s32/s116/s111/s32/s99/s45/s97/s120/s105/s115\n/s50/s56/s56/s75/s50/s52/s50/s75/s50/s50/s49/s75/s50/s49/s49/s75/s50/s48/s49/s75/s49/s56/s49/s75/s49/s54/s48/s75/s49/s52/s50/s75/s49/s50/s51/s75\nFIG. 1. Entropy change ∆ smeasured at different fixed temperatures by applying and remov ing a\nfield of 1 T parallel to the caxis.\nentropy) to EP (low entropy). In the main frame of Fig. 3 the entro py change ∆ sk(i.e.\nthe entropy change measured at a certain temperature under ap plication of a saturating\nmagnetic field after subtraction of the bHterm) is plotted against temperature when the\napplied field is parallel (triangles) and perpendicular (circles) to the caxis. The difference\nbetween the two curves, ∆ sdiff= ∆sk/bardbl−∆sk⊥(continuous line) is plotted too.The presence\nof an intermediate temperature range, between 200 K and 220 K, w here ∆skdepends on\ntemperature is apparent. The absence of detectable latent heat anomaly in DSC scans\nsuggests that this intermediate region should be rather associate d with the presence of\nan easy cone intermediate phase than with the phase coexistence r egion of a first order\ntransition. The maximum entropy change at the reorientation is ∆ s= 0.18 JKg−1K−1.\nThe inset of Fig. 3 shows an effective anisotropy field K(T), plotted against temperature,\nobtained from H∗after subtraction of the demagnetising field. We shall discuss the m eaning\nof this anisotropy in the following section.\nIII. ANALYSIS AND DISCUSSION\nThe system free energy with anisotropy term developed till the thir d order writes:\nGL(θ,H,T) =G0(T)+K1sin2θ+K2sin4θ+\n+K3sin6θ−µ0Ms(H/bardblcosθ+H⊥sinθ), (1)\nwhereθis the angle between the magnetisation Mand thecaxis,H/bardblandH⊥are the\n4/s48/s46/s48 /s48/s46/s50 /s48/s46/s52 /s48/s46/s54 /s48/s46/s56 /s49/s46/s48 /s49/s46/s50 /s49/s46/s52/s45/s48/s46/s51/s48/s45/s48/s46/s50/s53/s45/s48/s46/s50/s48/s45/s48/s46/s49/s53/s45/s48/s46/s49/s48/s45/s48/s46/s48/s53/s48/s46/s48/s48\n/s99/s40\n/s48/s72\n/s97/s41/s50\n/s97/s32/s43/s32/s98/s32\n/s48/s72\n/s97/s72/s42\n/s32/s32/s115/s32/s40/s74/s107/s103/s45/s49\n/s75/s45/s49\n/s41\n/s48/s72\n/s97/s32/s40/s84/s41/s66/s97/s67/s111\n/s48/s46/s54/s50/s90/s110\n/s49/s46/s51/s56/s70/s101\n/s49/s54/s79\n/s50/s55\n/s72\n/s97/s32/s112/s101/s114/s112/s101/s110/s100/s105/s99/s117/s108/s97/s114/s32/s116/s111/s32/s99/s45/s97/s120/s105/s115\n/s49/s52/s49/s75\n/s49/s54/s50/s75\n/s49/s57/s55/s75\n/s50/s48/s50/s75\n/s50/s49/s50/s75/s50/s50/s49/s75\n/s50/s52/s48/s75\n/s50/s54/s51/s75\n/s50/s57/s53/s75\nFIG. 2. Entropy change ∆ smeasured at different fixed temperatures by applying and remov ing a\nfield of 1 T perpendicular to the caxis.\n/s56/s48 /s49/s48/s48 /s49/s50/s48 /s49/s52/s48 /s49/s54/s48 /s49/s56/s48 /s50/s48/s48 /s50/s50/s48 /s50/s52/s48 /s50/s54/s48 /s50/s56/s48 /s51/s48/s48/s45/s48/s46/s51/s53/s45/s48/s46/s51/s48/s45/s48/s46/s50/s53/s45/s48/s46/s50/s48/s45/s48/s46/s49/s53/s45/s48/s46/s49/s48/s45/s48/s46/s48/s53/s48/s46/s48/s48/s48/s46/s48/s53/s48/s46/s49/s48/s48/s46/s49/s53/s48/s46/s50/s48\n/s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48/s45/s50/s48/s45/s49/s53/s45/s49/s48/s45/s53/s48/s53/s49/s48/s49/s53\n/s48/s46/s49/s55/s53/s42/s40/s84/s45/s50/s49/s53/s41/s115\n/s68/s105/s102/s102\n/s115\n/s75/s32/s61/s32/s97/s32/s43/s32/s98/s32/s78\n/s100 /s48/s32/s77\n/s115/s115\n/s75/s32/s40/s74/s107/s103/s45/s49\n/s75/s45/s49\n/s41/s32\n/s84/s32/s40/s75/s41/s112/s101/s114/s112/s101/s110/s100/s105/s99/s117/s108/s97/s114/s112/s97/s114/s97/s108/s108/s101/s108\n/s75/s32/s61/s32/s40/s49/s47/s50/s41/s77\n/s115/s32/s40/s72/s42/s45/s78\n/s100 /s48/s32/s77\n/s115/s41/s32/s75/s32/s40/s74/s107/s103/s45/s49\n/s41\n/s32/s32\n/s32/s84/s32/s40/s75/s41\nFIG. 3. Maximum isothermal entropy change ∆ skin saturating parallel (green triangles) and\nperpendicular (red circles) fields and difference between the two curves (continuous line). Inset:\nequivalent anisotropy as deduced from the measured H∗\n/bardbl(T) (green triangles) and H∗\n⊥(T) (red\nsquares) as a function of temperature\ncomponents of Hrespectively parallel and perpendicular to c,K1,K2,K3are the anisotropy\nconstants, and G0(T) is a term depending on temperature only. The entropy of the syst em\nunder a saturating field directed along the caxis (Ha/bardbl≥H∗\n/bardbl) is:\ns/bardbl=−dG0\ndT+µ0dMs\ndT/parenleftbig\nHa/bardbl−N/bardblMs/parenrightbig\n(2)\nWhen the field is perpendicular to c(Ha⊥≥H∗\n⊥) we have:\n5s⊥=−dG0\ndT−dK1\ndT−dK2\ndT−dK3\ndT+\n+µ0dMs\ndT(Ha⊥−N⊥Ms) (3)\nNow, whatever the initial state s(0) (i.e. the Ha= 0 entropy at a fixed temperature)\nfrom which the ∆ s(Ha) measurements are performed, s(0) will be nothing but a function\nofT. So under saturating applied field (i.e. when Ha≥H∗) from Eq. (2) and (3) we can\ndeduce that b=µ0dMs/dT. By fitting the linear part in the field region where Ha≥H∗we\nobtaindMs/dT= 802.5Am−1, ingoodagreementwithvaluesfromtheliterature6. Usingthe\ndMs/dTvalueandEq. (2)and(3)wecansubtractfrom∆ sthecontributionofparaprocesses\nand plot the SRT contribution to the entropy change ∆ skin parallel and perpendicular Ha.\nFrom Eq. (2) and (3) their difference is ∆ sdiff= ∆sk/bardbl−∆sk⊥=dK1/dT+dK2/dT+\ndK3/dT. From the data shown in Fig. 3 we find that ∆ sdiff= 0.2−0.610−3(T−205) with\na slight negative slope.\nNow, let us discuss the fields H∗\n/bardblandH∗\n⊥, representing the Havalue where ∆ s(Ha) pass\nfrom the quadratic regime to the linear one. During a uniform rotatio n of the magnetization\ndriven by Ha, the system reaches saturation when the applied field overcomes b oth the\ndemagnetisingandtheanisotropyfield. Therefore, forarotation fromtheeasyplanetowards\nthecaxis (i.e. the parallel field case) we have H∗\n/bardbl=Hk1+N/bardblMswhereHk1= 2|K1|/µ0Ms,\nwhereas when magnetisation rotates from the caxis to the plane, H∗\n⊥=Hk2+N⊥Mswhere\nHk2= 2|K1+2K2+3K3|/µ0Ms. It is worth recalling that, in the case where K2=K3= 0,\nthe quadratic expression ∆ s=cH2\naforHa< H∗can be deduced rigorously from expression\n(1)4. WhenK2andK3can not be neglected, stable zero-field easy-cone configuration m ay\nexist, and a simple expression for ∆ s(Ha) (when Ha< H∗) can be hardly worked out.\nNotwithstanding this limitation our measured ∆ s(Ha) curves actually show a quadratic\nand a linear regime as apparent from Fig. 1 and 2. So we must just kee p in mind that\nidentification of H∗is theoretically founded near room temperature, whereas it repre sents\njust a phenomenological fitting procedure for lower temperature s. FromH∗, by subtracting\nthe demagnetising field, we can calculate the value of Hk1andHk2and therefore we can\nrespectively workouttwoanisotropies: KEP=K1+2K2+3K3(redcirclesintheinset ofFig.\n3) andK1(green triangles in the inset of Fig. 3). As higher order anisotropy c onstants are\nexpected to vanish at room temperature, from the value of KEPat 296 K we can directly\n6estimate K1= 8.7104Jm−3, in good agreement with the literature3. By fitting KEP(T)\nandK1(T) together with a linear function we obtain: K(T) = 0.175(T−215) JKg−1. This\nresult is rather intriguing as, from magnetic measurements, it is gen erally argued that at low\ntemperature higher order anisotropy constants should not be ne gligible3,8. However, values\nand sign of the anisotropy constants deduced from magnetic and t orque measurements are\noften conflicting1,3,8. Indeed, the calorimetric measurement we present here, can be r ather\nwell described by using just one equivalent anisotropy constant th at changes its sign at\n215 K, inside the temperature interval where the SRT takes place. Discrepancies between\nthe values of Kdeduced from H∗\n⊥(red circles) and from H∗\n/bardbl(green triangles) are apparent\naround 200 K. Moreover, the slope of K(T) is constant, dK/dT= 0.175 JKg−1K−1, whereas\nfrom ∆sdiff(T) we found that K1+K2+K3presents a slight negative slope. This can\nbe ascribed as due to the contribution of higher order constant. F urther investigation on\nthis issue will be focused on temperature dependence of magnetisa tion curves and on more\ndetailed theoretical calculations.\nConcluding: we presented a detailed experimental investigation on S RT associated en-\ntropy change in W-type hexaferrite covering a wide temperature r ange. The data, the first\nin our knowledge obtained by direct calorimetry, allow to identify: the temperature interval\nwhere the transition takes place, the maximum entropy change ass ociated with SRT, and\ncan be described using a single anisotropy constant Kmodel where Kchanges sign at the\ntransitiontemperature. Furtherinvestigation will bedevoted tot heroleofhigher anisotropy\nconstants.\nACKNOWLEDGMENTS\nThe research leading to this results has received funding fromthe E uropean Community’s\n7thFramework Programme under Grant Agreement No. 214864 (proj ect SSEEC).\nREFERENCES\n1J. Smit and H.P. Wijn, Ferrites, Philips Technical Library, Eindhoven ( 1959)\n2G. Albanese, E. Calabrese, A. Deriu, and F. Licci, Hyper. Int. 28, 487 (1986)\n3G. Asti, F. Bolzoni, F. Licci, and M. Canali, IEEE Trans. Magn. 14, 883 (1978)\n74V.Basso, C.P.Sasso, M.Kuepferling, K.Skokov, O.Gutfleisch, J. Appl. P hys.109, 083910\n(2011)\n5E.P. Naiden, and S.M. Zhilyakov, Russ. Phys. J. 40, 86974 (1997)\n6A. Paoluzi, F. Licci, O. Moze, G. Turilli, A. Deriu, G. Albanese, and E. Ca labrese, J. Appl.\nPhys.63, 5074 (1988)\n7V. Basso, C. P. Sasso, and M. Kupferling, Rev. Sci. Instrum. 81, 113904 (2010)\n8E. P. Naiden, G. I. Ryabtsev, Sov. Phys. J. 33,318 (1990)\n8"    },    {        "title": "1508.07342v1.Wireless_Power_Transfer_for_High_precision_Position_Detection_of_Railroad_Vehicles.pdf",        "content": "  \n Wireless Power Transfer for High -precision \nPosition Detection of Railroad Vehicles  \n \nHyun -Gyu Ryu  \nGraduate School for Green Transportation   \nKAIST  \nDaejeon, Korea  \nhot6472@kaist.ac.kr  Dongsoo Har  \nGraduate School for Green Transportation   \nKAIST  \nDaejeon, Korea  \ndshar@kaist.ac.kr\n \n \nAbstract —Detection of vehicle position is critical for successful \noperation of intelligent transportation system. In case of \nrailroad transportation system s, position information of \nrailroad vehicles can be detected by GPS, track circuits, and \nso on. In this paper, position detection based on tags onto sleepers of the track is investigated. Position  information \nstored in the tags is  read by a reader placed at the bottom of \nrunning railroad vehicle. Due to limited capacity of battery or  \nits alternative in the tags, power requi red for transmission of \nposition  information to the reader is harvested by the tags \nfrom the power wirelessly t ransferred from  the reader. Basic \nmechanism in wireless power transfer is magnetic induction \nand power t ransfer efficiency according to the relati ve \nlocation of the reader to a  tag is discussed with simulation \nresults. Since power transfer efficiency is significantly affected \nby the ferromagnetic material  (steel)  at the bottom of the \nrailroad vehicle and the  track , magnetic beam shaping by \nferrite material  is carried out. With the ferrite material for \nmagnetic beam shaping, degradation of power transfer efficien cy due to the steel  is substantially reduced. Based on \nthe experimental results, successful wireles s power transfer to \nthe tag coil is po ssible when transmitted power from  the \nreader coil is close to a few watts.  \nKeywords -wireless power transfer; position detection; high \nspeed train; magnetic induction; power transfer efficiency \nI.  INTRODUCTION  \nPosition d etection of railroad vehicles is critical for \nintelligent control of train operation. Efficient scheduling of \nindividual trains is beneficial for avoidance of accident and \nenhancing the value of resource planning. Since sc heduling \nof individual trains  fundam entally depend s on position \ndetection of them, high precision in position detection is \nvery crucial. Considering cu rrent trend of increased driving  \nspeed of railroad vehicles, importance of high precision positio n detection will be escalated . To achieve high \nprecision in position detection, various approaches have been attempted so far.  \nUse of t rack circuits is  one of the most common  methods \nfor railroad  position detection. However, they  requir e \ninsulated rail joints for successful detection [ 1]. Eddy \ncurrent sensor  [2] supplies  non-contact speed and distance  \nmeasurement of rail road vehicles by detecting  the magnetic \nvariation  along the tra ck. The sensor work s well at high \nspeeds, but suffers  difficulties when the vehicles accelerate or decelerate. T rip sw itch mounted on the overhead lines \nrespond s when a train with pantograph passes  [3]. However, \nit cannot be used with  other type of railroad systems  \noperated by ground level or sub -ground level power lines. \nAxel counter [4] is also popularly adopted for pos ition \ndetection of railroad vehicles. It counts the number of wheel pairs passing the detection point. This causes a problem \nwhen its memory of the axle number is lost. GPS -based \nposition detection is discussed in [5]. However, GPS signal is not detectable  when railroad vehicles are in tunnels. In [6], \nposition detection of running train is performed by the combination of GPS data, track curvatu re, and tachometer \nfor secure position detection regardless of vehicle \nenvironment.  \nThis paper presents a position detection method for high \nspeed train by means of wireless power transfer to the tags \ninstalled on the sleeper s of track. Reader coil is placed at the \nbottom of running railroad vehicle s and tag coil s transpond \nto the request of the reader coil. Position information of the \ntag is stored in the memory of it and the power necessary for \nthe transmission of the position information to the reader \ncoil is harvested by the tag coil. This paper is organized as \nfollows. Section II gives the system model for wireles s \npower transfer and Section III provides experimental results as well as emulation results. Results in Section III are \nobtained with reader coil and tag coil, each designed by impedance matching. Section IV concludes this work.  \nII. S\nYSTEM MODEL FOR WIRE LESS P OWER TRANSFER   \n \n \n \n  \n \n \n \n \n  \n \n \n \n(a) \nThis research was supported by Ministry of Land, Infrastructure and \nTransport (MOLT) as Railr oad Specialized Graduate School  and a grant \nfrom Railroad Technology Research Program  \n   \n (b) \nFigure 1.  (a) Reader at railroad vehicle and (b) RFID tag on a sleeper of \ntrack  for position detection  (courtesy of Korea Railroad Research Institute) \nFig. 1 presents the reader placed at the bottom of \nrailroad vehicle and the tag on a sleeper of the track. The \nreader transfers power wirelessly to provide energy for the \ntag. The energy harvested by the tag is used for transmission \nof position information stored in the memory of it. This \nprocedure is carried out with the high train speed . Fig. 2 \ndepicts the situation  when the procedure for wireless power \ntransfer and position information transmission is conducted. \nBefore the reader is right above the tag, i.e., ∆ y takes \nnegative values, the reader starts power transferring and the \ntag is initiating data transmission a nd continues to transmit \nuntil it is complete.   \nCarrier  frequency for wireless power transfer is set to \n27MHz. Fig.  3 shows the reader coil and tag coil used for \nthis work. Reader coil for wireless power transfer is the inner loop of the two loops in Fig.  3(a). Position information \nobtained by the foregoing procedure is transmitted to the control center by a railroad communication system such as \nLTE-R OFDM system [7].  \n \nFigure 2.  Situation for wireless power transfer and position information \ntransmission.  \n   (a) \n(b) \nFigure 3.  Reader coil and tag coil for wireless power transfer.  \nIII. EXPERIMENTAL RESULTS   \nSimulation by HFSS tool and actual measurements to \nevaluate the impact of ferromagnetic material  (steel)  \nmodeling the track  are performed for this work. Results of \nexperiments a re also effective with the presence of the steel \nat the bottom of railroad vehicles. Fig.  4 illustrates the \nconfiguration of the reader coil and the tag coil. Coil separatio n d is set to  0.5m to be close to actual separation \nbetween the track and the botto m of train. Location of the \nreader coil in Fig.  4 corresponds to ∆y=0(see Fig.  2). When \n∆y is changed from 0  to 0.4m, received power at the tag coil \nvaries as shown in Fig.  5. Plot in Fig.  5 is obtained by HFSS \ntool. Fig.  5 suggests that beyond ∆y=0.4m received power \nwill be less than 15%. This level of power transfer \nefficiency might be admissible w ith transferred  power \ngreater than a few watts  and small power consumption by \nthe tag during position information transmission.  \nFigure 4.  Setup of reader coil and tag coi l for simulation  \n \n \n \n \n \nd \n   \n Figure 5.  Variation of power transfer efficiency according to ∆y.  \nActual measurements with a network analyzer as a \nsignal generator are executed as in Fig.  6. One port of the \nnetwork analyzer is used as the transmitter  (reader coil) and \nthe other port is use d as the receiver  (tag coil). Power \ntransfer efficiency is m easured with and without steel. Also, \npower transfer efficiency with and without ferrite material \n(sheet ) is measured. Ferrite material is known to be effective \nin magnetic beam shaping [8]  to increase power transfer \nefficiency . Ferrite sheet is attached t o the reader coil and the \ntag coil as shown in Fig.  7. The steel is placed behind the tag \ncoil with a gap 0.05m or 0.1m. In Table I and Table II, Steel (X) and Ferrite(X), for example, indicate that no steel is \nplaced behind the tag coil and no ferrite she et is attached to \nreader coil and tag coil. As seen in Table I and Table II, impact of steel is substantially adverse to power transfer \nefficiency. However, with ferrite sheet attached to reader \ncoil and tag coil, the power transfer efficiency becomes \n48.08% from 31.84%, when the gap is 0.05m. In case of the \ngap=0.1m, it is 52% with ferrite sheet attached, which is \nsignificantly increased from 45.28% without ferrite sheet. \nFrom the results in Table I and Table II, it is judged that \nferrite sheet is beneficial for sustaining power transfer \nefficiency with the presence of steel. It is noted that \nsimulation results obtained by HFSS tool and experimental \nresults are in good agreement.  \nFigure 6.  Experimental configuration of wireless power transfer.  \n TABLE I.   POWER TRANSFER EFFIC IENCY WHEN FERRITE S HEET AND \nSTEEL ARE TAKEN INTO ACCOUNT .  SEPARATION =0.5 M AND GAP BETWEEN \nTAG COIL AND STEEL IS 0.05 M. \n Ferrite (X) Ferrite (O) \nSteel (X) 53.57%  52.48%  \nSteel (O) 31.84%  48.08%  \nTABLE II.  POWER TRANSFER EFFICI ENCY WHEN FERRITE SH EET AND \nSTEEL ARE TAKEN INTO ACCOUNT .  SEPARATION =0.5 M AND GAP BETWEEN \nTAG COIL AND STEEL IS 0.1M. \n Ferrite (X) Ferrite (O) \nSteel (X) 53.57%  52.48%  \nSteel (O) 45.28%  52.00%  \n \n \n \n  \n \n \n \n \n \n(a) \n(b) \nFigure 7.  (a) Reader coil with ferrite sheet and (b) tag coil with ferrite \nsheet.  \nIV. CONCL USION  \nFor successful operation of high speed train, high \nprecision position  detection is critical for intelligent control \nof train operation. This paper presents wireless power \ntransfer to get the position information stored in the tags on \nthe sleepers of the track. Basic mechanism in wireless power \ntransfer is magnetic induction and power transfer effici ency \nis discussed with simulation results  and experimental results . \nSince power transfer efficiency is signific antly affected by \nthe steel, magnetic beam s haping by ferrite material is \ncarried out. It is shown here that with the ferrite material for \nmagnetic beam shaping, degradation of power transfer \nefficiency due to the steel is substantially reduced. Based on \n \n \n \n   \n the results, successful wireless power transf er to the tag coil \nis po ssible when transmitted power from  the reader coil is \nclose to a few watts  and power consumption of the tag for \nposition info rmation transformation is small.  \n \nREFERENCES  \n[1] A. P. Patra and U . Kumar, “Availability analysis of railway tr ack \ncircuit,” Institution of Mechanical  Engineers. Proceedings. Part F: \nJournal of Rail and Rapid Transit. 224. 2010. pp. 169 -177. \n[2] T. Engelberg  and F. Mesch, “Eddy current sensor system for non -\ncontact speed  and distance measurement of rail vehicles ,” Comp uters \nin Railways VII, eds.  J. Allen, R.J. Hill, C.A. Brebbia, G. Sciutto & \nS. Sone, WIT Press, Southampton,  pp. 1261 –1270,   2000.  [3] Transportation Research Board, National Research Council , “Traffic \nsignal operations near  highway -rail grade crossings,” 1999.  \n[4] W. Li , N. Jiang, J. Liu, and Y. Zhang , “Train axle counters by Bragg \nand chirped grating techniques, ” International Conference on Optical \nFibre Sensors, Proc. of SPIE vol. 7004, 2008.  \n[5] N. K. Das , C. K. Das, R. Mozumder, and J. Bhowmik , “Satellite \nBased Train Monitoring System, ” Journal of Electrical Engineering, \nThe Institution of Engineers, vol.36, no. 2, Dec. 2009.  \n[6] Y. Maki, “A new train position detection using GPS, ” Railway \nTechnology Avalanche,  no.9, Aug. 2005.  \n[7] E. Hong, H. Kim, and D . Har, “ SLM -based OFDM system without \nside information for data recovery, ” Electronics Letters, vol.46, no.3, \npp. 255 -256, 2010.  \n[8]  J. Shin et al., “Design and implementation of shaped magnetic -\nresonance -based wireless power transfer system for roadway -\npower ed moving electric vehicle, ” IEEE Transactions on Industrial \nelectronics, vol. 61, pp . 1179 -1192, 2013  \n "    },    {        "title": "1404.5593v1.Analytic_Modeling__Simulation_and_Interpretation_of_Broadband_Beam_Coupling_Impedance_Bench_Measurements.pdf",        "content": "arXiv:1404.5593v1  [physics.acc-ph]  22 Apr 2014Analytic Modeling, Simulation and Interpretation of Broad band Beam Coupling\nImpedance Bench Measurements\nUwe Niedermayer,1,a)Lewin Eidam,2and Oliver Boine-Frankenheim2\n1)Institut f¨ ur Theorie elektromagnetischer Felder, Techni cal University Darmstadt,\nSchlossgartenstr. 8 D-64289 Darmstadt, Germany\n2)GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Plancks tr. 1,\nD-64291 Darmstadt, Germany\n(Dated: 23 April 2014)\nIn the first part of the paper a generalized theoretical approach towards beam cou-\npling impedances and stretched-wire measurements is introduced. Applied to a cir-\ncular symmetric setup, this approach allows to estimate the system atic measurement\nerror due to the presence of the wire. Further, the interaction o f the beam or the\nTEM wave, respectively, with dispersive material such as ferrite is d iscussed. The de-\npendence of the obtained impedances on the relativistic velocity βis investigated and\nfound as material property dependent. The conversion formulas for the TEM scatter-\ning parameters from measurements to impedances are compared w ith each other and\nthe analytical impedance solution. In the second part of the paper the measurements\nare compared to numerical simulations of wakefields and scattering parameters. In\npractice, the measurements have been performed for the circula rly symmetric exam-\nple setup. The optimization of the measurement process is discusse d. The paper\nconcludes with a summary of systematic and statistic error source s for impedance\nbench measurements and their diminishment strategy.\na)niedermayer@temf.tu-darmstadt.de\n1I. INTRODUCTION\nThe field distribution of a single particle in free space approaches the one of a lossless\ncoaxial TEM transmission line in the ultrarelativistic limit. This motivates measuring the\nlongitudinal or transverse beam coupling impedance of accelerator components by replacing\nthe beam with one or two wires, respectively. The transmission line me asurement technique\nhas been introduced by Sands and Rees1for the determination of beam energy loss factors\nin Time Domain (TD) by pulse excitation. When using modern Vector Net work Analyzers\n(VNA) the beam coupling impedance can be determined in Frequency D omain (FD) by\nsweeping a narrow-band signal. Especially when looking at particular s idebands that are\nsusceptible to beam instabilities rather than on the total energy los s the FD method is to\nbe preferred.\nIn both TD and FD one has to make sure not to measure effects of th e setup. The de-\nembedding process to measure only the accelerator device under t est (DUT) is investigated\nespecially for lumped impedances by Hahn and Pedersen2. In order to enable de-embedding\nwithareference(REF)measurementofanemptyboxorbeampipe, theimpedancemismatch\nfromthecables tothemeasurement boxhastobeminimized. At highf requency onecanalso\nuse Time Domain Gating to disregard the mismatch reflections3, but this requires a very\nhigh bandwidth of the VNA to properly represent the spectrum of t he window-function.\nAnother option is to damp multiple reflections with RF attenuation foa m.\nWalling et al.4first introduced an approximative formula for measuring distribute d\nimpedances which was later replaced by the exact one by Vaccaro5and Jensen6.\nThis paper covers analytical and numerical models for longitudinal a nd transverse\nimpedance measurement of strongly lossy and broadband structu res. The models will\nbe applied to the example case of a dispersive Ferrite ring. Starting f rom a 2D analytical\nmodel, its limitations are illustrated by a 3D numerical model for finite le ngth.\nThe analytical models imply also that there cannot be a general form ula to scale the\nimpedance with the beam velocity. Also the bench measurements can not be scaled for\nβ <1, but the measurements can be used to validate numerical simulatio ns789, that allow\nvelocity scaling. Numerical simulations for β= 1 are also important to avoid wrong a\npriori assumptions in the measurements. The analytical model for the dispersive material\npresented heremotivatesalsoasimplifiedlowfrequency (LF)appro ach(”radialmodel”)that\n2plays an important role for the interpretation of LF impedance in gen eral and in particular\nof coil measurements for transverse impedance10.\nThe paper is structured as follows: Section II starts with the analy tical model for the\nbeam impedance and for the measurement, i.e. a model with excitatio n and an Eigenvalue\nproblem, respectively. Both are solved for circularly symmetric 2D g eometry. In Sect. III\nthe way to determine the impedance from scattering parameters is discussed (see also11).\nSection IV then draws an intermediate conclusion, comparing the an alytical results only.\nThese are the beam models for different velocity and the measureme nt model with different\nS-parameter conversion formulas and wire thicknesses.\nThe real Ferrite ring, as it was measured, was simulated with a partic le beam (TD) and\na wire (TD/FD), as described in Sect. V. This is followed by the discuss ion of measure-\nment results in Sect. VI. Section VII points out the commonalities an d differences for the\nlongitudinal and transverse measurements.\nThe paper concludes with summarizing measurement error sources and discussion of the\ninterplay between measurements and simulations, also for β <1 in Sect. VIII.\nII. ANALYTICAL MODEL\nIn a first analytical approach, the beam and the wire setup are con sidered as purely two\ndimensional. It will beseen insectionIII, thatthis isjustified forlarg elongitudinal electrical\nlength. From Maxwell’s equations we find the 2D Helmholtz equation\n(∆⊥+k2\n⊥)Ez=rhs, (1)\nand the dispersion relation\nk2\n⊥+k2\nz=ω2µǫ (2)\nwhich will be solved for three different assumptions:\n1. Beam model\nkz=ω\nβc(3)\nrhs=−iω\nβ2γ2µ0q\nπa2H(a−r) (4)\nwith beam radius aandHbeing the Heaviside step function\n32. Radial model obtained from beam model with β→ ∞, i.e.\nkz= 0, γ= 0, βγ=i,/vectorE⊥= 0 (5)\n3. Coaxial line model\nEz(r≤r0) = 0,Quasi−TEM−Eigenmode (rhs = 0) , (6)\nwhere the Eigenvalue kzis obtained from the equation\n(∆⊥+ω2µε)Ez=k2\nzEz. (7)\nThe range of validity of the radial model is also discussed in12and13.\nBefore solving Eq. 1 we take a closer look on the dispersion relation 2, rewritten for the\nbeam model as\nk2\n⊥=ω2\nc2\n0(µrεr−1\nβ2). (8)\nThe material properties are presented as\nµ=µ′−iµ′′andε=ε′−iε′′+κ\niω(9)\nwithκbeing the conductivity and µ′′andε′′being magnetization and polarization losses.\nNote that all these material properties are considered as functio ns of the frequency. Fur-\nthermore we define the lossless refraction index and the loss tange nts as\nn=/radicalbig\nµ′rε′r,tanδµ=µ′′\nr\nµ′\nrand tan δε=ε′′\nr+κ/ωε0\nε′\nr. (10)\nThis allows to rewrite Eq. 8 as\nk2\n⊥=ω2\nc2\n0/bracketleftbigg\nn2(1−tanδµtanδε)−1\nβ2−in2(tanδµ+tanδε)/bracketrightbigg\n(11)\nwhich shows that in the lossless case one has transversely propaga ting waves exactly when\nthe the Cerenkov-condition βn >1 is fulfilled. This still holds in the case of dielectric losses\nand nonconducting ferrites, but the product of the tangents ca nnot be dropped in the case\nof electrically conducting magnetic material such as Magnetic Alloys. For lossy material\nit makes sense to plot k2\n⊥in the complex plane parametrically, as a function of ωandβ.\nFigure 3 shows the properties of the different quadrants in the com plexk2\n⊥-plane. For\nfurther considerations we will focus on some material with propert ies shown in Fig. 2. The\n4loss\rgain\r\npropagating\r evanescent\rIm{k\r2\r}\r\nRe{k\r2\r}\r vacuum\rideal\r\ndielectric\r\nhighly\r\nconductive\r\nmetal (not to scale)\r\nFIG.1. Complex k2\n⊥plane(transversepropagationplot). Thevertical axisrep resentstheCerenkov-\ncondition.\n 0.1 1 10 100 1000\n 0.1  1  10  100  1000relativ permeability µr\nf [MHz]Re{µr}\n-Im{µr}\nFIG. 2. Material properties of the example ferrite material14. The permittivity is roughly constant,\nǫr= 10. Above 100MHz a power law extrapolation has been applied .\ntransverse wavenumber as calculated by Eq. 8 is plotted in Fig. 3 whe re one can see that\ntheβ-dependence is small if β >0.5 andf <100 MHz. This motivates again the radial\nmodel, i.e. neglecting the βdependence entirely. For simple analytical treatment due to\nk⊥=kr, we will focus on a concentrical cylinder setup, as shown in Fig. 4.\nFor all three models a solution is found from the ansatz\nEz=\n\n(A0+A1Jm(krr))e−ikzzr < a\n(B1·Jm(krr)+B2·Nm(krr))e−ikzza≤r < r1/parenleftbig\nC1·Jm(kF\nrr)+C2·Nm(kF\nrr)/parenrightbig\ne−ikzzr1≤r < r2\nD1/parenleftBig\nJm(krr)−Jm(krr3)\nNm(krr3)Nm(krr)/parenrightBig\ne−ikzzr2≤r≤r3(12)\nwhere the wavenumbers in radial direction are distinguished by krfor vacuum and kF\nrinside\nthe Ferrite. Note that this ansatz is invalid for the coaxial model in c ase of no losses, since\n5-3000-2500-2000-1500-1000-500 0\n-1200 -1000 -800 -600 -400 -200  0 200  400  600  800Im { kr2 } [m-2]\nRe {kr2 } [m-2]10MHz\n50MHz\n100MHzβ=0.05\nβ=0.1\nβ=0.5\nβ=0.99\nβ=1000\n 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000\n 0.01  0.1  1  10  100  1000  10000  100000  1e+006|Im { kr2 }| [m-2]\n|Re {kr2 }| [m-2]0.1MHz1MHz10MHz100MHz1GHz2GHz\nβ=0.05\nβ=0.1\nβ=0.5\nβ=0.99\nβ=1000\nFIG. 3. Transverse complex wavenumber in normal (see Fig. 3) and loglog display for the material\npresented in Fig. 2\nPEC\nvacuumferrite\nr1\nr2\nr3a\nFIG. 4. Ferrite ring for benchmarking the measurement setup . Dimensions: r1= 1.78cm; r 2=\n3.05cm; r 3= 3.3cm; L = 2 .54cm.\nEz= 0 for the pure TEM mode. For the coaxial model one applies A0=A1= 0 and B1\ndefines an arbitrary amplitude (Eigenvector scaling). The beam mod el requires additionally\na particular solution without boundary conditions, i.e.\nEz=A0·H(r−a), (13)\nsatisfying Eq. 1 with\nA0=iq\nωε0πa2. (14)\nNote that since A0is independent of β, theβdependence in the general ansatz Eq. 12 is\ngiven entirely through krandkF\nr. Therefore, since the impedance originates from the ferrite,\nthe relativistic βenters similar as a material property. Also one cannot expect to fin d a\ngeneral impedance scaling law with βsince the impact of βonkrandkF\nris different which\nmeans that the total impact depends on the geometry.\n6-20 0 20 40 60 80 100 120\n 0.1  1  10  100  1000Re{Z||} [Ω]\nf [MHz]Radial\nβ=0.01\nβ=0.1\nβ=0.5\nβ=0.99\n-150-100-50 0 50\n 0.1  1  10  100  1000Im{Z||} [Ω]\nf [MHz]Radial\nβ=0.1\nβ=0.5\nβ=0.99\nFIG. 5. Beam model: Longitudinal impedance for different beam velocity\nFor solving the equation system 12 one has to determine 5 constant s in the coaxial line\nmodel (B2,C1,C2,D1,kz) from 5 matching conditions and 6 constants in the beam model\n(A1,B1,B2,C1,C2,D1) from 6 matching conditions. The matching conditions are\nEz|ri+=Ez|ri− (15)\nHϕ|ri+=Hϕ|ri−, (16)\nwith\nHϕ=−iωǫ\nk2\nr·∂Ez\n∂r. (17)\nin all models, obtained from component-wise rearranging Maxwell’s eq uations.\nIn the Coaxial Line model one obtains a nonlinear transcendent Eige nvalue Equation,\nthat has the Eigenvalue kr= (ω2µε−k2\nz)1/2in the arguments of the Bessel functions. For\nthe simplified case of r2=r3the Eigenvalue equation reads\nε\nkrJ′\n0(krr1)N0(kra)−J0(kra)N′\n0(krr1)\nJ0(krr1)N0(kra)−J0(kra)N0(krr1)=εF\nkFrJ′\n0(kF\nrr1)N0(kF\nrr2)−J0(kF\nrr2)N′\n0(kF\nrr1)\nJ0(kFrr1)N0(kFrr2)−J0(kFrr2)N0(kFrr1).(18)\nThis can be solved only numerically and solution is a Quasi-TEM mode, hav ing a small\nEz-component but no cut-off frequency. The complex kzis shown in Fig 9 and determines\nthe transmission by S21=exp(−ikzl). The impedance is then found by a conversion formula\ndescribed in the next chapter. In the beam model one finds longitud inal impedance (m=0)\nfrom\nZ/bardbl(ω) =−1\nq2/integraldisplay\nbeam/vectorE·/vectorJ∗dV=−l\nq/parenleftbigg2J1(kra)\nkra/bracehtipupleft/bracehtipdownright/bracehtipdownleft/bracehtipupright\n≈1·A1+A0/parenrightbigg\n. (19)\n7The longitudinal impedance is shown in Fig. 5 for different β. As already expectable from\nFig. 3, the beam model agrees with the radial model for LF and not t oo small β.\nBeforewediscussing thewiretechnique weshortlysummarize somep arametersimportant\nfor the comparison of the models: The wave impedance is defined as Zwave=Sz/|/vectorH⊥|2and\nthe (measurable) characteristic impedance is\nZ0=/integraltextr3\n0/vectorE⊥·d/vector s/contintegraltext/vectorH·d/vector s. (20)\nThe longitudinal space charge impedance, as it will be dominating in Fig. 5 for very low β,\ncan also be deduced from the characteristic impedance (electric pa rt) and the image current\ninductance (magnetic part), i.e.\nEz=−∂z(Z0I)−∂t(µ0Igb\n2π). (21)\nSubsequently, one obtains for a perfectly conducting circular bea m pipe\nZspch\n/bardbl=−iωη\nclgb\n2π1\nβ2γ2. (22)\nIn the radial model one has only the magnetic part since the transv erse electric field is zero.\nTable I shows an overview of intrinsic parameters of the models. Not e that the geometry\nfactor for the beam and the coaxial line model are different due to t he presence of fields\nwithin the beam.\nBeam Model Radial Model Coaxial Line Model\nkzω\nβc0 Eigenvalue\nkr(vacuum)iω\nβγcω\nc/radicalbig\n(ω/c)2−k2z\nZREF\nwave η/β(!)0 η\nZDUT\nwavekz\nωε=1\nβcε0kz\nωε\nZ0(vacuum)gb\n2πZREF\nwave 0gc\n2πZREF\nwave\nZspch\n/bardbl(vacuum)−ikzlZ0/γ2iωµ0lgb\n2π0\ng-factor gb=1\n2+lnr3\nagb gc= lnr3\na\ncut-offωc≈βγc\na/radicalBig\n2\ngb– ≈2c\nπ(a+r3)\nTABLE I. Overview of properties in the different models ( η=/radicalbig\nµ0/ε0= 377Ω)\n8III. WIRE MEASUREMENT TECHNIQUE\nThe classical wire technique is based on a coaxial setup, where the d evice under test\n(DUT)canbeseenasanadditionalcompleximpedanceaddedintheco axiallinereplacement\ncircuit. Figure 6 shows the setup and the replacement circuit model of an infinitely short\npiece of it. Usually the measurement is performed with respect to a r eference line, which can\nbe either a piece of beam pipe or the vacuum vessel of the DUT. Ther e are also approaches\nto obtain the reference signals analytically, especially for plain beam p ipes. An important\nparameter in the analysis is the electrical length in units of radians, d efined by\nΘ = 2πl\nλ=kl (23)\nwhere the wavelength λ= 2π/kcan have different values in longitudinal and transverse\ndirectionandindifferent materials. Thereisalso animportant distinct ion between alumped\nimpedance, i.e.\n∂Z/bardbl(ω,z)\n∂z=Ztotal\n/bardbl(ω)δ(z−z0) (24)\nand a distributed impedance,\n∂Z/bardbl(ω,z)\n∂z=Ztotal\n/bardbl(ω)\nl. (25)\nIn practice, one has neither of the two but something in between. T he impedance jump\n(geometric impedance) at the beginning of the DUT is always lumped, w hile the body of\nthe DUT (resistive wall) is almost equally distributed. The modeling of lum ped impedances\nis just an impedance element in longitudinal direction, while distributed impedances are\nrepresented by a TEM-line with an impedance element Z/bardbl/lequally distributed to each\ninfinitely short transmission line element.\nA. Distributed Impedance\nFor equally distributed impedance sources the complex wave number s in the setup shown\nin Fig. 6 are given by15\nkDUT\nz=ω/radicalbig\nC′\n0L′\n0/radicalBigg\n1−iR′\n0+Z/bardbl/l\nωL′\n0kREF\nz=ω/radicalbig\nC′\n0L′\n0/radicalBigg\n1−iR′\n0\nωL′\n0(26)\nZ(REF)\n0=/radicalBigg\nR′\n0+iωL′\n0\niωC′\n0(27)\n9DUT\nFIG. 6. Transmission line replacement circuit for distribu ted impedance\nwhich can be solved as\nZ/bardbl=iZ0(k2\nz,DUT−k2\nz,REF)·l\nkz,REF=iZ0l·(kz,DUT−kREF\nz)·/parenleftbigg\n1+kDUT\nz\nkREFz/parenrightbigg\n(28)\nThese wavenumbers can be obtained from the scattering matrix me asured by the VNA. The\nscattering matrix of a piece of transmission line of length land characteristic impedance\nZ0,din an environment of characteristic impedance Z0is given by5\nS=\nS11S12\nS21S22\n=\n(Z2\n0,d−Z2\n0)sin(kzl)−2iZ0,dZ0\n−2iZ0,dZ0(Z2\n0,d−Z2\n0)sin(kzl)\n\n(Z2\n0,d+Z2\n0)sin(kzl)−2iZ0,dZ0cos(kzl)(29)\nIn case of no reflections at DUT, i.e. Z0,d≃Z0, Eq. 29 simplifies to\nS21=S12=e−ikzl. (30)\nOtherwise one has to introduce a corrected S21parameter SC\n21:= exp(−ikzl) that can be\nobtained by solving Eq. 29 for cos( kzl). The quadratic equation for SC\n21is called Wang-\nZhang16-formula,\n(SC\n21)2+S2\n11−S2\n21−1\nS21SC\n21+1 = 0 with |SC\n21|<1 (31)\nandrequires knowledge ofthe S11-parameter. The wavenumber kzisfoundfromthecomplex\nlogarithm of Eq. 30 with either original or corrected S21. It can be inserted into 28 to obtain\nZ/bardbl=Z0·ln/parenleftbiggSREF\n21\nSDUT\n21/parenrightbigg\n·/bracketleftbigg\n1+ln(SDUT\n21)\nln(SREF\n21)/bracketrightbigg\n. (32)\nIn the literature this is called (Vaccaro5-Jensen6-) improved-log formula. Although this\nformula is exact, it is in some cases disadvantageous since it is very se nsitive to statistical\nerrors of subsequent DUTand REF measurements. Its approxima tion under the assumption\n10of small |SDUT\n21−SREF\n21|, i.e. ln( SDUT\n21)≈ln(SREF\n21) is the more robust but less accurate\n(Walling4-) log-formula,\nZ/bardbl= 2·Z0·ln/parenleftbiggSREF\n21\nSDUT\n21/parenrightbigg\n. (33)\nB. Lumped Impedance\nFor purely lumped impedances, i.e. an impedance circuit Zdelement squeezed between\ntwo reference lines wit characteristic impedance Z0, one finds15\nS=\nS11S12\nS21S22\n=1\n2Z0+Zd\nZd2Z0\n2Z0Zd\n (34)\nresulting in the Hahn-Pedersen2formula,\nZ/bardbl= 2Z0SREF\n21−SDUT\n21\nSDUT\n21. (35)\nThis is an improvement of the original Sands and Rees1formula\nZ/bardbl= 2Z0SREF\n21−SDUT\n21\nSREF\n21. (36)\nBoth Eqs. 35 and 36 can be obtained from Taylor expansion of the po sitive/negative loga-\nrithm in Eq. 33. Note that the reflection S11does not play a role for the determination of\npurely lumped impedances.\nIV. DISCUSSION OF ANALYTICAL RESULTS\nThe impedance of the ferrite ring in Fig. 4 is determined from the Eigen valuekzand the\nformulas 32, 33, and 35. Figure 7 shows a comparison of the Eigenva lue impedances and\nthe impedances from the beam and current (radial model) excitatio n. One can see that the\nbeam and the radial model fit well for the real part, but at high fre quency the imaginary\npart deviates due to longitudinal phase shift. The improved-log impe dance deviates only\nslightly from the highly relativistic beam impedance whereas the lumped - and log-formula\ndeviate strongly. As visible in Fig. 8 the deviation for the improved-log -formula can be\naccounted to the finite wire thickness. When the wire becomes very thin (practically not\npossible), the Eigenvalue kzapproaches the the plane-wave wavenumber ω/c(see Fig. 9)\n11 0 20 40 60 80 100 120\n 0.1  1  10  100  1000Re{Z||} [Ω]\nf [MHz]radial model\nBeam model ∴β =0.99\nImp. log formula\nlog formula\nLumped formula\n-40-20 0 20 40 60\n 0.1  1  10  100  1000Im{Z||} [Ω]\nf [MHz]radial model\nBeam model ∴β =0.99\nImp. log formula\nlog formula\nLumped formula\nFIG. 7. Analytic coaxial wire method with different S21→Z/bardbl-conversion formulas vs. beam and\nradial model. The wire radius has been chose as r0= 0.225 mm as it was the smallest practically\nachievable.\n 0 20 40 60 80 100 120 140\n 1  10  100  1000Re{Z||} [Ω]\nf [MHz]radial model\nBeam model ∴β =0.99\na=2.25 10-3m\na=2.25 10-4m\na=2.25 10-5m\na=2.25 10-30m\n-60-40-20 0 20 40 60\n 1  10  100  1000Im{Z||} [Ω]\nf [MHz]radial model\nBeam model ∴β =0.99\na=2.25 10-3m\na=2.25 10-4m\na=2.25 10-5m\na=2.25 10-30m\nFIG. 8. Analytic coaxial wire method with (exact) improved- log-formula vs. radial model\nand therefore the transmission S21= exp(−ikzl) is equal to the one for the ultrarelativistic\nbeam.\nThis means that the improved-log-formula has to give the same imped ance as calcu-\nlated in the beam-excited model by Eq.19. Further one can see in Fig. 9 that the radial\nwavenumber in the ferrite depends only very little on the wire radius a. The losses enter the\nS21-parameter and the impedance via the imaginary part of kz, which depends on the wire\nradius. Nonetheless this error enters the distributed impedance o nly logarithmically. The\nconvergence of the measured impedance for a→0 is also discussed in17.\n12 1 10\n10-1100101102103Re[kz] ⋅ c0/ω\nf [MHz]a=2.25e-03\na=2.25e-04\na=2.25e-05\na=2.25e-30\n 0.001 0.01 0.1 1 10\n10-1100101102103-Im[kz] ⋅ c0/ω\nf [MHz]a=2.25e-03\na=2.25e-04\na=2.25e-05\na=2.25e-30\n 10 100\n10-1100101102103Re[kr] ⋅ c0/ω\nf [MHz]a=2.25e-03\na=2.25e-04\na=2.25e-05\na=2.25e-30 1 10\n10-1100101102103-Im[kr] ⋅ c0/ω\nf [MHz]a=2.25e-03\na=2.25e-04\na=2.25e-05\na=2.25e-30\nFIG. 9. Wavenumbers in Ferrite for the coaxial model\nV. NUMERICAL MODELLING\nBeam coupling impedances can be obtained from time domain simulations and FT of the\nwake potential. Also the S-parameters obtained in bench measurem ents can be numerically\nsimulatedinbothFDandTD.Theadvantageoftimedomainsimulations is thatonedirectly\nobtains broadband results. Frequency Domain methods use the (in terpolated) material data\nas given directly in FD, whereas in TD an impulse response, i.e. a rationa l transfer function,\napproximated to a certain order, is required. Detailscan beseen e.g . in18. The following will\nshow both wake simulations using CST Particle Studio (PS)7and S-parameter simulations\nin TD and FD using CST Microwave Studio (MWS)7. Figure 10 shows the setup, where\nopen boundaries or waveguide-ports are used for beam/waveguid e entry and exit planes.\nA. Impedance from wake field calculation\nThe beam in the wakefield-simulation is taken as infinitely (practically on e mesh cell)\nthin and with a Gaussian longitudinal profile with σ=10.5 cm. The integrated wakelength\n13open boundariesPEC boundaries\nferritevacuumexcitation and integration pathL\nFIG. 10. Longitudinal cut of the ferrite ring model and CST mo del\nis 50m. The mesh has 180,000 cells leading to a computation time of less t han 1 hour.\nThe practical limitations of the wakefield solver arise from the requir ed long wakelength\nfor low frequencies and the small time step required for stability. Th e wakefield solver\noperates (explicitly) in TD and is therefore subject to the Courant -critereon,\nδt≤min\ni,j,k/parenleftBigg\nc/radicalBigg\n1\nδx2\ni+1\nδy2\nj+1\nδz2\nk/parenrightBigg−1\n(37)\ni.e. the spacial mesh determines the maximum stable timestep. For low frequencies, the\naccuracy is also subject to the (K¨ upfm¨ uller-19) uncertainty principle,\n∆f≥1\n∆t=c\n∆l(38)\nwhere ∆ fis frequency-uncertainty of a given quantity (e.g. the impedance) and ∆lis\nthe wakelength. Via the discrete Fourier transform, ∆ fis proportional to the frequency\nresolution of the impedance. For low frequencies this way of comput ing impedances becomes\ninapplicable since ∆ lis proportional to the total computation time. A small relief to this\nlimitation is obtained for low- Qstructures by zero-padding before applying the FFT. A\nfrequency domain solver89, or an implicit time domain solver, would not be limited by this.\nFigure 11 shows the simulation results. Note that slight discrepancie s arise from the\nfitting of the material data on some rational transfer function an satz. The simulation has\nbeen rerunfordifferent lengths tocheck thescaling. Asvisible Fig. 1 1, thesimulation curves\nroughly approach the analytical ones for longer DUTs, i.e. fulfillment of the 2D assumption.\n14 0 20 40 60 80 100 120 140\n 1  10  100  1000Re{Z||} [Ω]\nf [MHz]Analytic Radial\nAnalytic Beam ∴β =0.99\nnumerical\nhalf Length ⋅ 2\ndouble Length ⋅ 1/2-40-20 0 20 40 60\n 1  10  100  1000Im{Z||} [Ω]\nf [MHz]Analytic Radial\nAnalytic Beam ∴β =0.99\nnumerical\nhalf Length ⋅ 2\ndouble Length ⋅ 1/2\nFIG. 11. CST PS simulation vs. analytical 2D beam and radial m odel\nB. Simulation of the Measurement Process\nThe measurement process has been simulated using CST MWS. In ord er to obtain higher\naccuracy by avoiding the material data fitting error, the FD solver has been employed.\nPorts with 20 waveguide modes serve as boundary condition. The lon gitudinal impedance\ncalculated from the S21-parameter is shown in Fig. 12. The curve for the improved-log\nformula shows a strong resonance, which is accounted to the refle ction at the edge of the\nDUT. This can be corrected using the Wang-Zhang-formula 31, pro viding new transmission\nparameters to insert into Eq. 33, 32 or 35. The corrected results are visible in Fig. 13.\n 0 50 100 150 200 250 300\n 1  10  100  1000Re{Z||} [Ω]\nf [MHz]PS\nMWS, log formula\nMWS, improved log formula\n-100-50 0 50 100\n 1  10  100  1000Im{Z||} [Ω]\nf [MHz]PS\nMWS, log formula\nMWS, improved log formula\nFIG. 12. MWS S-parameter simulation with different conversio n formulas vs. PS-solution\nThe match between the log-formula and the PS-curve is purely by ch ance. After reflection\ncorrection the improved-log-formula matches the PS simulation with in a deviation of about\n20%. This can be accounted to the finite wire radius (see also Fig. 8). Note that many\nmesh cells are required to resolve thin wires in S-parameter simulation s.\n15 0 20 40 60 80 100 120 140\n 1  10  100  1000Re{Z||} [Ω]\nf [MHz]PS\nMWS, log-formula\nMWS, improved-log-f.\n-40-20 0 20 40 60\n 1  10  100  1000Im{Z||} [Ω]\nf [MHz]PS\nMWS, log-f.\nMWS, improved-log-f.\nFIG. 13. MWS S-parameter simulation with reflection correct ion vs. PS-solution\nVI. MEASUREMENT DATA EVALUATION\nIn order to conclude on setup-independent properties of the DUT , the measurement has\nbeen performed for two different setups shown in Fig. 24. A copper wire of 0.225mm diam-\neter has been chosen because of its small thickness, good conduc tivity and low susceptibility\nto deformations. In the large setup the wires have been stretche d by tightening the screws\nof the end-plates about 3mm on the inner side of the box. In the sma ll setup, the fixation\nwas done using orthogonal PCBs, soldered together under tensio n of the wire.\nFIG. 14. Different measurement boxes\nThe two setups are supposed to have such different properties, t hat agreement of results\ncan be accounted to setup independent properties only. Both mea surements have been\nperformed for the Ferrite ring with changing DUT and REF multiple time s in order to\nobtain sufficiently well statistics. Due to the agreement for the simu lations as visible in\nFig. 12 the log-formula has been chosen for the evaluation since the improved-log-formula\nis supposed to show the strong resonance. The Wang-Zhang corr ection cannot be applied\n16sincethe S11-parametercannotbemeasuredduetomultiplereflectionsbetwee nthematching\nsection and the DUT. The results are show in Figs. 15 and 16. The das hed lines in the\nplots denote error bars. They are obtained from independent con sideration of systematic\n 1 10 100\n 0.1  1  10  100Re{Z||} [Ω]\nf [MHz]large setup\nsmall setup\nanalytical\n 1 10 100\n 0.1  1  10  100Im{Z||} [Ω]\nf [MHz]large setup\nsmall setup\nanalytical\nFIG. 15. Wire measurements vs. anayltical (radial and beam a gree for LF)\n 0 50 100 150 200 250\n 10  100  1000Re{Z||} [Ω]\nf [MHz]large setup\nsmall setup\nlarge setup w. foam\nCST PS\n-100-50 0 50 100\n 10  100  1000Im{Z||} [Ω]\nf [MHz]large setup\nsmall setup\nlarge setup w. foam\nCST PS\nFIG. 16. Measurements vs. wakefield simulation. At very high frequencies resonances of the setup\ncould be damped by the foam. The 2D assumption of the analytic al models is not valid here.\nFIG. 17. Dominating parasitic reflections for DUT and REF mea surements\nerrors, such as geometry and characteristic impedance uncerta inties, and statistical errors\n(standard deviation) such as noise, longitudinal shift and misalignme nt. The error due to\n17-18-17.5-17-16.5-16-15.5-15-14.5-14\n 0  200  400  600  800  1000|S21ref| [dB]\nf [MHz]measurement\napproximation\n-4-3.5-3-2.5-2-1.5-1-0.5 0\n 0 100 200 300 400 500 600 700 800 900 1000|S21dut/S21ref| [dB]\nf [MHz]distance: 10 cm\ndistance: 35 cm\nFIG. 18. Reference measurement and smooth approximation. T he DUT measurement depends on\nits longitudinal position.\nmultiple reflections at the DUT (see Fig. 17) has been treated statis tically for different\npositions of the DUT. In Fig. 18 one sees that the multiple reflections introduce a ripple on\nthe measured S21which is position dependent. This is canceled by averaging over differe nt\npositions. Also the REF measurement has been smoothed (note the scale in Fig. 17) to\nobtain similar smoothness as the averaged DUT signal.\nThe measurement results show that for low frequencies the agree ment with the analytical\ncalculation is well, while at larger frequencies discrepancies occur. At a first glance this\ncan be accounted to resonances in the large measurement box, wh ich can be partly damped\nby the RF attenuation foam. As always at high frequency, the smalle r setup shows the\nbetter results. Its discrepancies with the CST-PS simulation can be accounted mostly to\nthe material data fitting for TD simulation, the finite wire radius, and the uncertainty of\nthe manufacturer’s material data. For an estimation of the propa gation of material data\nuncertainties see also Appendix D.\nVII. TRANSVERSE IMPEDANCE\nThe dipolar transverse impedance can be measured by a two-wire se tup, run on the\ndifferential mode. The magnetic field of such a mode can be seen in Fig. 19. Note that the\nstandard port mode solver in CST gives two arbitrary orthogonal T EM modes when there\nare two pins in the port. In order to select the differential mode one can apply a ’multi-\npin-port’ with predefined polarity of the wires. Figure 20 shows the S21-parameter of the\nsimulation, as compared to the single-wire simulation. The magnitude a nd phase deviations\n18+-\nFIG. 19. Magnetic field of dipole TEM Eigenmode obtained by mu lti-pin-portmode-solver\n-1-0.8-0.6-0.4-0.2 0\n 1  10  100  1000|S21DUT|-|S21ref| [dB]\nf [MHz]longitudinal\ntransverse-5-4-3-2-1 0 1\n 1  10  100  1000Phasedif. ϕDUT-ϕref [°]\nf [MHz]longitudinal\ntransverse\nFIG. 20. S-parameters for the monopole and dipole TEM mode (s imulation)\n(to REF) are much smaller for the dipole mode. One finds that the maj or difficulty in the\ndipolar measurement is the bad signal-to-noise ratio (SNR). The adv antage of such a small\nS21is that the conversion formulas 33 and 32 can be linearized and agree with Eq. 35, i.e.\none does not have to distinguish between lumped and distributed impe dances. Also the\nreflection at the DUT is negligible. The characteristic impedance (REF ) for the differential\nTEM mode is (see also20)\nZ0=η\nπln/parenleftbiggd+√\nd2−a2\nab2−d√\nd2−a2\nb2+d√\nd2−a2/parenrightbigg\n(39)\nwhereais the wire radius, bis outer radius and 2 d= ∆ is the wire distance. The transverse\nimpedance is defined as\nZx(ω) =i\nq∆/integraldisplayl/2\n−l/2(/vectorE(ω)+/vector v×/vectorB(ω))xeiωz/vdz (40)\n=−v\nωq∆/integraldisplayl/2\n−l/2∂Ez(ω)\n∂xeiωz/vdz+/bracketleftbig\nExeiωz/v/bracketrightbigl/2\n−l/2(41)\n19with the second expression obtained from the Panofski-Wenzel21theorem. In good approx-\nimation one finds\nZx(ω)≈v\nω∆2δZ/bardbl, (42)\nwhereδZ/bardblis the impedance obtained from the S21conversion formula for the differential\nmode. Figure21showsthesameplotforthetransverseimpedance , alsowithgoodagreement\n 0 5 10 15 20\n 1  10  100  1000Z⊥ [kΩ/m]\nf [MHz]PS, Re\nMWS, Re\nPS, Im\nMWS, Im\nFIG. 21. Transverse impedance PS vs. MWS\nfor the real part. The disagreement for the imaginary part is acco unted to extremely small\nchange in the relative transmission, making it impossible to determine t he phase of S21\naccurate enough.\n 0 2 4 6 8 10 12 14\n 1  10  100  1000Re{Z⊥} [kΩ/m]\nf [MHz]small setup\nlarge setup\nCST PS\n 0 5 10 15 20 25\n 1  10  100  1000Im{Z⊥} [kΩ/m]\nf [MHz]small setup\nlarge setup\nCST PS\nFIG. 22. Transverse impedance: Measurement vs. wakefield si mulation\nIn a wakefield simulation the transverse impedance has been obtaine d by integrating the\nwake force on the beam axis and exciting the system by two particle b eams. Those beams\nare off-centered by ∆ /2 and carry equal oppositely signed charge. The linear behaviour\nwith ∆ has been confirmed. Figure 21 shows a comparison for wakefie ld and S-parameter\nsimulation. At low frequencies the S-parameter simulation becomes in accurate, since the\nsignal is smaller than the numerical errors.\n20The measurements together with the error estimates are shown in Fig. 22. Note that\nfor the two wire setup an autocal-kit can be recommended since oth erwise 18 different\nconnections have to be made which takes quite long and is quite susce ptible to errors. Both\nthe large and the small setup show good agreement with the wakefie ld simulation, but the\nerror-bars become intolerably large at low frequency. This can be im proved using the coil\nmeasurements, see10and Appendix C.\nVIII. CONCLUSION\nA generalized two-dimensional approach to the longitudinal impedan ce for a bench mea-\nsurement, using transmission line quasi-TEM eigenmodes, and for a p article beam has been\npresented. It was found that the beam velocity enters the impeda nce calculation in close\nrelation to the material properties. Therefore simple scaling laws wit hβonly exist in the\ncase of frequency independent material properties, see e.g.12.\nFrom the dispersion relation (Eq. 11) follows that for low frequency and velocities close\nto the speed of light, the radial model can be employed, i.e. the limit β→ ∞can be applied.\nThe radial model is used for simplified measurements, i.e. the coil met hod, or for impedance\nsimulations using the power dissipation method1012. Another important issue originating\nfrom the dispersion relation is that for very low βone requires a dense transverse mesh in\nnumerical simulations.\nThe interplay between simulations and bench measurements has bee n outlined: On the\none hand simulations are needed to crosscheck the ’a priori’ assump tions in the measure-\nments. In particular, the proper de-embedding of the measureme nt box has to be checked by\nsimulations. On the other hand measurements are needed to validat e simulations, which can\nthen be performed for arbitrary β. Note that the wire bench measurements are incapable of\nresembling β <1 since the wave impedance for the real beam is Zwave=η/βwhile a TEM\nwave in vacuum always has Zwave=η.\nForthedeterminationofthedistributedimpedancefrom S21measurementsthe’improved-\nlog-formula’ has been re-derived. It was found that for a perfec tly uniformly distributed\nimpedance, i.e. when the 2D assumptions are exactly fulfilled, the for mula recovers the\nimpedance from the scattering parameter exactly, provided the w ire radius tends to zero.\nNote that this convergence is very slow (logarithmic), such that in p ractice always an error\n21of about 10-20% remains. The ’log-formula’ and the ’lumped-formula ’ have been compared\nfor the example ferrite ring with the analytical S21and found too inaccurate. For the\nsimulation of the measurement setup the ’log-formula’ showed an ap proximate agreement\nto the wakefield simulation while the ’improved-log-formula’ showed a p arasitic resonance.\nThis could not be explained completely, but it is accounted to the ’log-f ormula’ being\nless sensitive. This was also observed in the practical measurement s, when errors due to\nsubsequent changing of DUT and REF measurements propagated t hrough the ’improved-\nlog-formula’ but not through the ’log-formula’. The parasitic reson ance in the simulation\nof the measurement evaluated by the ’improved-log-formula’ could be removed by applying\nthe Wang-Zhang reflection correction. This works very well in the s imulation but in the\nreal measurement S11cannot be determined properly due to multiple reflections between\nthe DUT and the matching resistors.\nFor the transverse impedance impedance it does not matter which S21→Zformula is\napplied since the measurement signal is extremely small. When linearizin g theS21→Z\nformulas for SDUT\n21≃SREF\n21, they all agree with each other. The limiting property of the\ntwo-wire measurement is the signal-to-noise-ratio (SNR) which bec omes poor, particularly\nat low frequencies. For those low frequencies the coil method is a we ll-working alternative.\nPriority Longitudinal Transverse\n1 S21→Z a priori Noise →Averaging\n2 Reflections →Average\nDUT positionRandom setup\nmodification→Averaging\n3 Wire thickness a priori Wire distance\n& thicknessa priori\n4 Noise →Averaging S21→Z a priori\n5 Random setup\nmodification→Averaging Reflections →average\nDUT position\n6 Misalignment →Averaging Misalignment →Averaging\nTABLE II. Prioritization of error sources in the measuremen ts and their diminishment\nAn overview of the measurement error sources is given in Tab. II. S tatistic errors can\nbe diminished by averaging over e.g. DUT position or many DUT/REF set up changes,\nprovided the SNR is reasonably high.\n22ACKNOWLEDGMENTS\nUN and LE wish to thank Elias Metral, Fritz Caspers, and Manfred Wen dt for the\nhospitality at CERN and inspiring discussions.\nAppendix A: Other Geometries and Material properties for th e Example Setup\nAnopenboundarycondition(radiationcondition)canbeappliedinEq. 12byexchanging\nthebracket afterthe D1constant bytheHankel function H(2)\nm(krr). This, andtheimpedance\n 0 20 40 60 80 100 120 140 160\n 1  10  100  1000Re{Z||} [Ω]\nf [MHz]material µr, pec boundary\nmaterial µr, open boundary\nZ||/20, µr=300-50i, pec boundary\nZ||/20, µr=300-50i, open boundary\n-80-60-40-20 0 20 40 60 80\n 1  10  100  1000Im{Z||} [Ω]\nf [MHz]material µr, pec boundary\nmaterial µr, open boundary\nZ||/20, µr=300-50i, pec boundary\nZ||/20, µr=300-50i, open boundary\nFIG. 23. Radial model: Comparison of real material paramete rs to dispersion-free (artificial)\nmaterial, open and closed boundaries. Only in the dispersio n-free case geometrical resonances are\nvisible.\nfor an artificial material with constant complex permeability is shown in Fig. 23. Without\nthe dispersion the geometric resonances become visible. Relevant f or the measurement is\nthat even in the large box the electrical lenght between the ferrite and the boundary is much\nsmaller than the electrical lenght of the ferrite itself. This motivate s neglecting the effect of\nthe boundary, especially at low frequency.\nAppendix B: Technical issues of the measurement setup\nThe cables connecting the box with the VNA have to be phase-stable , even in the case\nof manipulating them for subsequent DUT and REF measurements. S tandard SMA cables\nhave been tested and found insufficient. Of course, precision meas urement cables could do\nthe job, but they are very expensive. Acost effective alternative is foundby semi-rigid SMA-\n23FIG. 24. Different measurement boxes\ncables. Due to only small movements during setup changes, phase d eviations are tolerably\nsmall. Note that also the calibration of the VNA is made at the end of th e SMA cables.\nSMA-N adapters can be used for N-calkits since their electrical leng th can be neglected\nbelow 1GHz.\nFor frequencies below roughly 50 MHz resistive matching is the metho d of choice. It\nis based on building a resistive network that makes each side see its ow n characteristic\nimpedance. On the NWA side it makes sense to use a commercially availab le attenuator\npiece instead, since its Π or T-bridge network has very linear freque ncy and phase response\nand can therefore easily be accounted in the REF measurement. On the measurement box\nside a longitudinal resistor has to be used which is involved to optimize. The low-pass\ncut-off of real resistors determines the maximum frequency of th e resistively matched setup.\nDifferent end pieces for the wire(s) have been tried out:\n1. Orthogonal PCBs with SMD metal film resistors\n2. 90deg SMA flange with carbon or metal film resistors\nThe SMD resistors can be precisely mounted, nonetheless they sho w (dependent on type) a\nbad high frequency behaviour. Similarly bad behaviour is found for th e metal film resistors.\nComparably good rf-behaviour is found for particular carbon resis tors, so called ’grounding\nresistors’. They keep their purely real resistance up to about 30 M Hz. Nonetheless they\nare specified with a tolerance of 20%, which requires measuring each resistor with a precise\nMultimeter and choosing a proper combination. For frequencies abo ve 30 MHz reflections\non the resistive matching section occur. They can be damped using R F-attenuation foam.\nNonetheless, the changing of DUT/REF without changing the prope rties of the foam is\n24FIG. 25. Matching resistors with 10dB attenuator and absorb er foam\ntechnically involved.\nAppendix C: Transverse Impedance Coil Measurements\nIn order to enhance the extremely small signals in the two-wire meth od for low frequency,\na multiturn coil can be used10. Both the flux and the induced voltage are amplified by the\nnumber of turns N, and one finds instead of Eq. 42\nZ⊥=c·δZ\nω·∆2·N2. (C1)\nSince ferrite structures usually have only small transverse impeda nce contributions at such\nLCR-meter\nFIG. 26. Transverse impedance measurement for very low freq uency\nlow frequencies, the method is benchmarked using a metal pipe of 2 m m wall thickenss. Fig-\nure26showsthemeasurement setup, inwhichthecoilimpedancech angeδZ=ZDUT−ZREF\nis determined by a LCR-meter. The coil-method has an upper freque ncy limit, given by the\ncoil resonance. It can be increased by taking fewer turns and incr easing the turn distance\n25103104105\n102103104105106Re{Z⊥} [kΩ/m/m]\nf [Hz]N=53; constantan\nN=5; copper\nRewall\n103104105\n102103104105106-Im{Z⊥} [kΩ/m/m]\nf [Hz]N=53; constantan\nN=5; copper\nRewall\nFIG. 27. Transverse impedance at LF: Coil measurement vs. an alytical calculation by ReWall22.\nThe dashed lines indicate standard deviation.\n(decreasing theinter-turncapacitance). Atvery lowfrequency theaccuracylimitationcomes\nfrom the instrument noise ( δZ∝ω) and from temperature drift of the coil, i.e.\nR(T) =L\nπr2̺(T0)·(1+αT(T0)·(T−T0)) (C2)\nwithαT(T0) being the (linearized) material temperature coefficient at room te mperature\nT0= 300 K. Subsequently, it makes sense to use two coils, a temperatu re stable one made\nof constantan with many turns an one with few turns and low resistiv ity (copper). Fig-\nure 27 shows the measured impedance compared to analytical resu lts for beam impedance\n(Rewall22). The error-bars indicate systematic errors, dominated by ∆, an d statistical errors\nrepresented by the standard deviation of subsequent DUT and RE F measurements.\nThe coil measurements are not in accordance with an ultrarelativist ic beam, but rather\nwith the radial model. The equivalence of the analytical beam impedan ce results with\nthe radial model for low frequencies is shown in12. One does not have any longitudinal\npropagation, except the image current in the DUT, which is induced b y the magnetic field.\nNote that for DUTs which consist of two side parts (e.g. collimator ja ws) isolated from each\nother one gets two independently closed eddy current loops. Afte r connecting both sides at\ntheir ends one gets a current loop over the whole device, changing t he measured impedance\nsignificantly. This means that the measurement setup should be cho sen exactly as it is seen\nby the beam in the accelerator.\n26Appendix D: Material Data Uncertainties\nUsually the manufacturer of ferrite materials gives material curve s only for a particular\ntemperature and without remanence magnetization. Still the perm eability and magnetiza-\ntion loss ( µ=µ′−iµ′′) curves are mostly specified with an error bar of ±20%. There is some\nphysical motivation of the smoothness of such a material curve. T herefore it is sufficient for\na worst case estimate, to look at all frequency points for min and ma x perturbation at once.\nFigure 28 shows the error propagation in the MWS simulation of the wir e measurement.\n 0 20 40 60 80 100 120 140\n 1  10  100  1000Re{Z||} [Ω]\nf [MHz]original data\n± 20% Re {µr}\n± 20% Im{µr}\n± 20% Re {εr}\n-30-20-10 0 10 20 30 40 50 60\n 1  10  100  1000Im{Z||} [Ω]\nf [MHz]original data\n± 20% Re {µr}\n± 20% Im{µr}\n± 20% Re {εr}\n 0 2 4 6 8 10\n 1  10  100  1000Re{Z⊥} [kΩ/m]\nf [MHz]original data\n± 20% Re {µr}\n± 20% Im{µr}\n± 20% Re {εr}\n 0 5 10 15 20\n 10  100  1000Im{Z⊥} [kΩ/m]\nf [MHz]original data\n± 20% Re {µr}\n± 20% Im{µr}\n± 20% Re {εr}\nFIG. 28. Longitudinal impedance errors from material data d eviation\nAs expected, deviations in µ′′influence mostly the real part of the impedance. The uncer-\ntainties in the imaginary part of the impedance is dominated by µ′for below 100 MHz and\nabove the influences of the (strong) losses prevail. For Z⊥the error propagation is smaller\nand dominated by the image current losses due to µ′′.\n27REFERENCES\n1M. Sands and J. R. Rees, “A Bench Measurement of the Energy Los s of a Stored Beam\nto a Cavity,” (1974), 10.2172/878797.\n2H. Hahn and F. Pedersen, “On Coaxial Wire Measurements of the Lo ngitudinal Coupling\nImpedance,” (1978).\n3F. Caspers, “BENCH METHODS FOR BEAM-COUPLING IMPEDANCE MEA SURE-\nMENTS,” (1992).\n4L. S. Walling, D. E. Mcmurry, D. V. Neuffer, and H. A. Thiessen, “Tra nsmission-line\nimpedance measurements for an advanced Hadron facility,” Nucl. In strum. Meth. Section\nA Volume 281 281, 433–447 (1989).\n5V. G. Vaccaro, “Coupling Impedance Measurements: An improved w ire method,”\nINFN/TC-94/023 (1994).\n6E. Jensen, “AN IMPROVED LOG-FORMULA FOR HOMOGENEOUSLY DIS-\nTRIBUTED IMPEDANCE An improved log-formula for homogeneously,” CERN\nPS/RF/Note 2000-001 (2000).\n7“CST Studio Suite 2013,” (2013).\n8B. Doliwa, H. D. Gersem, T. Weiland, and T. Boonen, “Optimised electr omagnetic 3D\nfield solver for frequencies below the first resonance,” , 53–56 (20 07).\n9U. Niedermayer, “NUMERICAL CALCULATION OF BEAM COUPLING\nIMPEDANCES IN THE FREQUENCY DOMAIN USING FIT ,” (2012).\n10F. Roncarolo, F. Caspers, T. Kroyer, E. M´ etral, N. Mounet, B. S alvant,\nand B. Zotter, “Comparison between laboratory measurements, simulations, and\nanalytical predictions of the transverse wall impedance at low freq uencies,”\nPhysical Review Special Topics - Accelerators and Beams 12, 084401 (2009).\n11H. Hahn, “Interpretation of coupling impedance bench measureme nts,”\nPhysical Review Special Topics - Accelerators and Beams 7, 012001 (2004).\n12U. Niedermayer and O. Boine-Frankenheim, “Analytical and numeric al calcula-\ntions of resistive wall impedances for thin beam pipe structures at lo w frequencies,”\nNuclear Instruments and Methods in Physics Research Section A: A ccelerators, Spectrometers, Detectors\n13H.Hahn,“Matrixsolutionforthewallimpedanceofinfinitelylongmultila yercircularbeam\ntubes,” Physical Review Special Topics - Accelerators and Beams 13, 012002 (2010).\n2814“Amidon Material 43, http://www.amidon.de/contents/de/d542.ht ml,” .\n15D. Pozar, Microwave Engineering (John Wiley & Sons, Incorporated, 1998).\n16J. Wang and S. Zhang, “Measurement of coupling impedance of acce lerator devices with\nthe wire-method,” Nucl. Instrum. Meth. Section A Volume 459 , 381– 389 (2001).\n17A.Argan, I.Lnf,L.Palumbo, D.Energetica-roma, M.R.Masullo, I .Napoli,V.G.Vaccaro,\nI.-N. Dip, and S. Fisiche, “ON THE SANDS AND REES MEASUREMENT METH OD\nOF THE LONGITUDINAL COUPLING IMPEDANCE,” in Proc. of PAC , 8 (1999) pp.\n1599–1601.\n18S. Gutschling, H. Kr¨ uger, and T. Weiland, “Time-domain simulation of dispersive media\nwith the ” nite integration technique,” , 329–348 (2000).\n19K. K¨ upfm¨ uller, Einf¨ uhrung in die theoretische Elektrotechnik (Springer, 1932).\n20J. Wang and S. Zhang, “Coupling impedance measurements of a\nmodel fast extraction kicker magnet for the SNS accumulator ring ,”\nNuclear Instruments and Methods in Physics Research Section A: A ccelerators, Spectrometers, Detectors\n21W. K. H. Panofsky and W. A. Wenzel, “Some Considerations Concern ing the Transverse\nDeflection of Charged Particles in Radio-Frequency Fields,” Review of Scientific Instru-\nments Volume 27 , 967–968 (1956).\n22N. Mounet, “Electromagnetic field created by a macroparticle in an in finitel long and\naxisymmetric multilayer beam pipe,” CERN-BE-2009-039 (2009).\n29"    },    {        "title": "1307.5007v1.Numerical_response_of_the_magnetic_permeability_as_a_funcion_of_the_frecuency_of_NiZn_ferrites_using_Genetic_Algorithm.pdf",        "content": "arXiv:1307.5007v1  [cond-mat.mtrl-sci]  18 Jul 2013Numerical response of the magnetic permeability as\na funcion of the frecuency of NiZn ferrites using\nGenetic Algorithm\nSilvina Boggi, Adrian C. Razzitte,Gustavo Fano\n1 de septiembre de 2018\nResumen\nThe magnetic permeability of a ferrite is an important factor in\ndesigning devices such as inductors, transformers, and microwav e ab-\nsorbing materials among others. Due to this, it is advisable to study\nthe magnetic permeability of a ferrite as a function of frequency.\nWhen an excitation that corresponds to a harmonic magnetic field\nHis applied to the system, this system responds with a magnetic flux\ndensityB; the relation between these two vectors can be expressed as\nB=µ(ω)H. Where µis the magnetic permeability.\nIn this paper, ferriteswereconsideredlinear, homogeneous,and iso-\ntropic materials. A magnetic permeability model was applied to NiZn\nferrites doped with Yttrium.\nThe parameters of the model were adjusted using the Genetic Al-\ngorithm. In the computer science field of artificial intelligence, Gene -\ntic Algorithms and Machine Learning does rely upon nature’s bounty\nfor both inspiration nature’s and mechanisms. Genetic Algorithms ar e\nprobabilistic search procedures which generate solutions to optimiz a-\ntion problems using techniques inspired by natural evolution, such a s\ninheritance, mutation, selection, and crossover.\nFor the numerical fitting usually is used a nonlinear least square\nmethod, this algorithm is based on calculus by starting from an initial\nset of variable values. This approach is mathematically elegant com-\npared to the exhaustive or random searches but tends easily to ge t\nstuck in local minima. On the other hand, random methods use some\nprobabilistic calculations to find variable sets. They tend to be slower\nbut have greater success at finding the global minimum regardless o f\nthe initial values of the variables\n1. Magnetic permeability model\nThe ferrites materials have been widely used as various elec tronic devices\nsuch as inductors, transformers, and electromagnetic wave absorbers in the\nrelatively high-frequency region up to a few hundreds of MHz .\n1The electromagnetic theory can be used to describe the macro scopic pro-\nperties of matter. The electromagnetic fields may be charact erized by four\nvectors: electric field E, magnetic flux density B, electric flux density D,\nand magnetic field H, which at ordinary points satisfy Maxwell’s equations.\nThe ferrite media under study can be considerer as linear, ho mogeneous,\nand isotropic. The relation between the vectors BandHcan be expressed\nas :B=µ(ω)H. Where µis the magnetic permeability of the material.\nAnother important parameter for magnetic materials is magn etic susceptibi-\nlityχwhich relates the magnetization vector M to the magnetic fiel d vector\nHby the relationship: M=χ(ω)H.\nMagnetic permeability µand magnetic susceptibility χare related by the\nformula: µ= 1+χ.\nMagnetic materials in sinusoidal fields have, in fact, magne tic losses and this\ncan be expressed taking µas a complex parameter: µ=µ′+jµ” [2]\nIn the frequency range from RF to microwaves, the complex per meability\nspectra of the ferrites can be characterized by two different m agnetization\nmechanisms: domain wall motion and gyromagnetic spin rotat ion.\nDomain wall motion contribution to susceptibility can be st udied through\nan equation of motion in which pressureis proportional to th e magnetic field\n[7].\nAssuming that the magnetic field has harmonic excitation H=H0ejωt, the\ncontribution of domain wall to the susceptibility χdis:\nχd=ω2χd0\nω2d−ω2−jωβ(1.1)\nHere,χdis the magnetic susceptibility for domain wall, ωdis the resonance\nfrequency of domain wall contribution, χd0is the static magnetic susce-\nceptibility, βis the damping factor and ωis the frequency of the external\nmagnetic field.\nGyromagnetic spin contribution to magnetic susceptibilit y can be studied\nthrough a magnetodynamic equation [3][9].\nThe magnetic susceptibility χscan be expressed as:\nχs=(ωs−jωα)ωsχs0\n(ωs−jωα)2−ω2, (1.2)\nHere,χsis the magnetic susceptibility for gyromagnetic spin, ωsis the re-\nsonance frequency of spin contribution, χs0is the static magnetic suscepti-\nbility, and αis the damping factor and ωis the frequency of the external\nmagnetic field.\nThe total magnetic permeability results [6]:\n2µ= 1+χd+χs= 1+ω2χd0\nω2d−ω2−jωβ+(ωs+jωα)ωsχs0\n(ωs+jωα)2−ω2(1.3)\nSeparating the real and the imaginary parts of equation (1.3 ) we get:\nµ′(ω) = 1+ω2\ndχd0/parenleftbig\nω2\nd−ω2/parenrightbig\n/parenleftbig\nω2\nd−ω2/parenrightbig2+ω2β2+ω2\nsχs0/parenleftbig\nω2\ns−ω2/parenrightbig\n+ω2α2\n(ω2s−ω2(1+α2))2+4ω2ω2sα2(1.4)\nµ”(ω) = 1+ω2\ndχd0ω β\n/parenleftbig\nω2\nd−ω2/parenrightbig2+ω2β2+ωsχs0ω α/parenleftbig\nω2\ns+ω2/parenleftbig\n1+α2/parenrightbig/parenrightbig\n(ω2s−ω2(1+α2))2+4ω2ω2sα2,(1.5)\nMagnetic losses, represented by the imaginary part of the ma gnetic permea-\nbility, can be extremely small; however, they are always pre sent unless we\nconsider vacuum [5]. From a physics point of view, the existi ng relations-\nhip between µ′andµ” reflects that the mechanisms of energy storage and\ndissipation are two aspects of the same phenomenon [11].\n2. Genetic Algorithms\nGenetic Algorithms (GA) are probabilistic search procedur es which genera-\nte solutions to optimization problems using techniques ins pired by natural\nevolution, such as inheritance, mutation, selection, and c rossover.\nA GA allows a population composed of many individuals evolve according to\nselection rules designed to maximize ✭✭fitness✮✮or minimize a ✭✭cost function ✮✮.\nA path through the components of AG is shown as a flowchart in Fi gure\n(2.1)\n2.1. Selecting the Variables and the Cost Function\nA cost function generates an output from a set of input variab les (a chromo-\nsome). The Cost function’s object is to modify the output in s ome desirable\nfashion by finding the appropriate values for the input varia bles. The Cost\nfunction in this work is the difference between the experiment al value of the\npermeability and calculated using the parameters obtained by the genetic\nalgorithm.\nTo begin the AG is randomly generated an initial population o f chromo-\nsomes. This population is represented by a matrix in which ea ch row is a\nchromosome that contains the variables to optimize, in this work, the para-\nmeters of permeability model. [1]\n3Define cost function\nSelect GA parameters\nGenerate initial population\nFind cost for each chromosome\nSelect mates\nMaiting\nMutation\nConvergence check\nDONE\nFigura 2.1: Flowchart of a Genetic Algorithm.\n42.2. Natural Selection\nSurvival of the fittest translates into discarding the chrom osomes with the\nhighest cost . First, the costs and associated chromosomes a re ranked from\nlowest cost to highest cost. Then, only the best are selected to continue,\nwhile the rest are deleted. The selection rate, is the fracti on of chromosomes\nthat survives for the next step of mating.\n2.3. Select mates\nNow two chromosomes are selected from the set surviving to pr oduce two\nnew offspring which contain traits from each parent. Chromoso mes with\nlower cost are more likely to be selected from the chromosome s that survive\nnatural selection. Offsprings are born to replace the discard ed chromosomes\n2.4. Mating\nThesimplestmethods choose one or more points in the chromos ome to mark\nas the crossover points. Then the variables between these po ints are merely\nswapped between the two parents. Crossover points are rando mly selected.\n2.5. Mutaci´ on\nIf care is not taken, the GA can converge too quickly into one r egion of a\nlocal minimum of the cost function rather than a global minim um. To avoid\nthis problem of overly fast convergence, we force the routin e to explore other\nareas of the cost surface by randomly introducing changes, o r mutations, in\nsome of the variables.\n2.6. The Next Generation\nThe process described is iterated until an acceptable solut ion is found. The\nindividuals of the new generation (selected, crossed and mu tated) repeat\nthe whole process until it reaches a termination criterion. In this case, we\nconsideramaximumnumberofiterationsorapredefinedaccep table solution\n(whichever comes first)\n3. Results and discussion\nNi0,5Zn0,5Fe2−xYxO4samples were prepared via sol-gel method with\nx=0.01, 0.02, and 0.05. The complex permeability of the samp les was mea-\nsured in a material analyzer HP4251 in the range of 1MHz to 1 GH z.[10].\nThe experimental data of magnetic permeability have been us ed for fitting\nthe parameters of the model [6]. Firstly, we fitted the magnet ic losses based\nin equation (1.5) by the Genetic Algoritm method and we obtai ned the six\n510010110210310410002000300040005000600070008000\niterationsMinimum value of function cost in the population for each iteration\nFigura 3.1: Evolution of the error\nfitting parameters. We substituted, then, these six paramet ers into equation\n(1.4) to calculate the real part of permeability.\nThe variables of the problem to adjust were the six parameter s of the model:\n(χd,χs,ωd,ωs,βyα)\nMagnetic losses being a functional relationship:\nµ′′\najustado=f(ω,χd,χs,ωd,β,α) (3.1)\nwhereωis the frequency of the external magnetic field, y χd,χs,ωd,ωs,β\nαare unknown parameters, the problem is to estimate these fro m a set of\npairs of experimental: ( ωi,µ′′\ni);(i= 1,2,...,n) .\nThe cost function was the mistake made in calculating µ′′\najustadowith the\nexpression (1.5) using the parameters obtained from the gen etic algorithm\nand the experimental value of µ′′for each frequency.\nCost function =n/summationdisplay\ni=1(f(ωi,χd,χs,ωd,ωs,β,α)−µ′′\ni)2\n2000 iterations wereperformed,with a populationof 300 chr omosomes (each\nwith 6 variables). The fraction of the population that was re placed by chil-\ndren in each iteration was 0.5 and the fraction of mutations w as 0.25.\nThe figure 3 shows the evolution of the error in successive ite rations, we\ngraphed the minimum value of function cost in the population for each\niteration. It show that the error converges at minimum value quickly, and\nthen this value is stable.\n6Although in the equations (1.5) and (1.4), ωdandωsmust be in Hz, we\ncalculate in MHz and then multiplied in the equations by 1 ,106, the same\ntreatment we performed with the parameter beta, we calculat e its value in\nthe range between 1 and 2000, although in equations we multip lied by 1,107.\nThis treatment was necessary for that the AG values to variab les within a\nlimited range.\nTable 3.1 shows the parameters of the model calculated for th e three NiZn\nferrite samples doped with different amounts of Yttrium. Figu re 3.2 graphs\n(a), (b) and (c) shows the permeability spectra for the three ferrites. Solid\nlines represent the curves constructed from the adjusted pa rameters while\ndotted and dashed lines represent the curves from experimen tal data.\nThe frequency of the µ′′maximum for the spin component is calculated [12]:\nωs\nµ′′max=ωs√\n1+α2(3.2)\nAnd for the domain wall component:[12]:\nωd\nµ′′max=1\n6/radicalbigg\n12ω2\nd−6β2+6/radicalBig\n16ω4\nd−4ω2\ndβ2+β4 (3.3)\nIn these ferrites maximums are located in: ωs\nµ′′max∼=80MHzyωd\nµ′′max∼=\n1000MHz.\nχd0ωd(Hz)βχs0ωs(Hz)α\nNiZnY 0.01 22.051262·1061966·1074.481989·1061.8967\nNiZnY 0.02 24.791115·1061581·1075.501480·1061.40\nNiZnY 0.05 33.75 671·1061021·10710.751334·1063.477\nCuadro3.1: Adjustedparameters in thepermeability model f or NiZnferrites\ndoped with Yttrium.\n7h10610710810905101520253035\nf [Hz]µ  (a) µ r NiZnY 0,01.\n1061071081090510152025303540\nf [Hz]µ (b) µ r NiZnY 0,02.\n1061071081090102030405060\nf [Hz]µ r (c) µ r NiZn 0,05\n  µ' µ''\nµ''µ'\nµ'\nµ'\nFigura 3.2: (a)(b)y(c) Complex permeability spectra in NiZ n ferrites\nReferencias\n[1] Haupt R.L, Haupt S.E ✭✭Practical Genetic Algorithms. ✮✮Wiley-\nInterscience publication (1998)\n[2] A.Von Hippel. ✭✭Dielectrics and Waves ✮✮. J. Wiley Sons. (1954).\n[3] R. F. Sohoo. ✭✭Theory and Application of Ferrites ✮✮, Prentice Hall, NJ,\nUSA (1960)\n[4] Trainotti V. and Fano W. ✭✭Ingeniera Electromagnetica ✮✮. Nueva Libre-\nria, 2004.\n[5] Landau and Lifchitz. ✭✭Electrodinamica de los medios continuos ✮✮. Re-\nvert´ e, 1981.\n[6] W.G.Fano, S.Boggi, A.C.Razzitte, ✭✭Causality study and numerical res-\nponse of the magnetic permeability as a function of the frequ ency of\nferritesusingKramersKronigrelations ✮✮PhysicaB,403,526-530, (2008)\n[7] Greiner. ✭✭Clasical electrodynamics ✮✮. cap.16, Springer (1998)\n[8] Tsutaoka, T. ✭✭Frequency dispersi´ on of complex permeability in Mn-\nZn and Ni-Zn spinel ferrites and their composite materials ✮✮J ournal of\nApplied Physics,Volumen 93 (2003)\n8[9] Wohlfarth E. ✭✭Ferromagnetics Materials ✮✮, volumen 2. North Holland,\n1980.\n[10] S.E.Jacobo,SDuhalde,H.R.Bertorello, JournalofMag netismandMag-\nnetic Materials 272-276 (2004) 2253-2254.\n[11] Silvina Boggi, Adri´ an C. Razzitte and Water G.Fano, Non-equilibrium\nThermodynamics and entropy production spectra: a tool for th e cha-\nracterization of ferrimagnetic materials , Journal of Non-Equilibrium\nThermodynamics. Volume 38, issue 2 p.175-183 (2013).\n[12] T. Tsutaoka, T. Frequency dispersi´ on of complex permeability in Mn-\nZn and Ni-Zn spinel ferrites and their composite materials , Journal of\nApplied Physics,v 93 (2003)\n9"    },    {        "title": "0707.3823v2.Room_temperature_spin_filtering_in_epitaxial_cobalt_ferrite_tunnel_barriers.pdf",        "content": "arXiv:0707.3823v2  [cond-mat.mtrl-sci]  27 Jul 2007Room temperature spin filtering in epitaxial cobalt-ferrit e tunnel barriers\nA. V. Ramos, M.-J. Guittet, and J.-B. Moussy\nDSM/DRECAM/SPCSI, CEA-Saclay, 91191 Gif-Sur-Yvette Cede x, France\nR. Mattana, C. Deranlot, and F. Petroff\nUnit´ e Mixte de Physique CNRS/Thales, Route d´ epartementa le 128,\n91767 Palaiseau Cedex, and Universit´ e Paris-sud, 91405 Or say, France\nC. Gatel\nCEMES/CNRS, 31055 Toulouse, France\n(Dated: November 19, 2018)\nWereportdirectexperimentalevidenceofroomtemperature spinfilteringinmagnetictunneljunc-\ntions (MTJs) containing CoFe 2O4tunnel barriers via tunneling magnetoresistance (TMR) mea sure-\nments. Pt(111)/CoFe 2O4(111)/γ-Al2O3(111)/Co(0001) fully epitaxial MTJs were grown in order to\nobtain a high quality system, capable of functioning at room temperature. Spin polarized transport\nmeasurements reveal significant TMR values of -18% at 2 K and - 3% at 290 K. In addition, the\nTMR ratio follows a unique bias voltage dependence that has b een theoretically predicted to be the\nsignature of spin filtering in MTJs containing magnetic barr iers. CoFe 2O4tunnel barriers therefore\nprovide a model system to investigate spin filtering in a wide range of temperatures.2\nThe generation of highly spin-polarized electron currents is one of t he dominant focusses in the field of spintronics.\nFor this purpose, spin filtering is one very interesting phenomenon, both from a fundamental and from a technological\nstand point, that involves the spin-selective transport of electro ns across a magnetic tunnel barrier. Successful spin\nfiltering at room temperature could potentially impact future gener ations of spin-based device technologies [1, 2] not\nonly because spin filters may function with 100% efficiency [3], but they can be combined with any non-magnetic\nmetallic electrode, thus providing a versatile alternative to half-met als or MgO-based classic tunnel junctions.\nThe spin filter effect originatesfrom the exchangesplitting of the en ergy levels in the conduction band of a magnetic\ninsulator. As a consequence, the tunnel barrier heights for spin- up and spin-down electrons (Φ ↑(↓)) are not the same,\nleading to a higher probability of tunneling for one of the two spin orien tations : J↑(↓)∝exp(−Φ1/2\n↑(↓)t), where t\nis the barrier thickness. The spin filter effect was first demonstrat ed in EuS using a superconducting electrode as\na spin analyzer (i.e. Merservey-Tedrow technique) [4], and has sinc e been observed in EuSe [3] and EuO [5] by\nthis method. Because the Merservey-Tedrow technique is limited to low temperatures, tunneling magnetoresistance\n(TMR) measurements in magnetic tunnel junctions (MTJs) [6] have been used to show the spin filter capability of\nhigher temperature spin filters such as BiMnO 3[7] and NiFe 2O4[8]. However, no TMR effects are currently reported\nfrom any spin filter at room temperature.\nCoFe2O4is a very promising candidate for room temperature spin filter applica tions thanks to its high Curie\ntemperature ( TC= 793 K) and good insulating properties. Electronic band structure calculations from first prin-\nciples methods predict CoFe 2O4to have a band gap of 0.8 eV, and an exchange splitting of 1.28 eV betw een the\nminority (low energy) and majority (high energy) levels in the conduc tion band [9] (see Fig.3-b), thus confirming its\npotential to be a very efficient spin filter, even at room temperatur e. Recently, a tunneling spectroscopy study of\nCoFe2O4/MgAl 2O4/Fe3O4double barrier tunnel junctions revealed optimistic results for the spin-filter efficiency of\nCoFe2O4[10]. However, the polarization ( P) and TMR values obtained in this work were indirectly extracted from\na complex model developed to fit experimental current-voltage cu rves rather than from direct Merservey-Tedrow or\nTMR measurements.\nIn order to accurately demonstrate the spin filtering capabilities of CoFe2O4up to room temperature, we have\nprepared CoFe 2O4(111)/γ-Al2O3(111)/Co(0001)fully epitaxial tunnel junctions by oxygen plasma -assisted molecular\nbeam epitaxy (MBE) on Pt(111) underlayers. The details of the sam ple growth process are published elsewhere\n[11]. In this system, the spinel γ-Al2O3serves to decouple the CoFe 2O4and Co magnetic layers. Before any spin-\npolarized transport measurements were performed on the full MT J system, our CoFe 2O4(111)/γ-Al2O3(111) tunnel\nbarriers were carefully characterized by a wide range of technique s in order to optimize their structural and chemical\nproperties [11]. Fig. 1 shows a high resolution transmission electron m icroscopy (HRTEM) study demonstrating the\nhigh crystalline quality of our CoFe 2O4(5 nm)/γ-Al2O3(1.5 nm)/Co (10 nm) multilayers. In particular, we observe\nnear perfect epitaxy in the single crystalline CoFe 2O4(111)/γ-Al2O3(111) tunnel barrier, which is a consequence of\nthe optimized growth conditions and the spinel structure of both c onstituents.\nThe magnetic properties of a CoFe 2O4/γ-Al2O3tunnel barrier were measured at room temperature and at 4 K,3\nyielding coercivities ( Hc) of 220 Oe and 500 Oe respectively (not shown). We also observed a rather weak remanent\nmagnetization around 40% and lack of saturation and magnetic reve rsibility for fields as high as 5 T at 4 K. These\nproperties are common for spinel ferrite thin films and have been at tributed to the presence of antiphase boundaries\n[12]. We note the magnetic properties of the full Pt/CoFe 2O4/γ-Al2O3/Co MTJs were also characterized in order to\nverify the magnetic decoupling of the CoFe 2O4and Co layers, necessary for TMR measurements [11].\nSpin filter tunnel junctions werepatterned by advanced optical lit hography. Spin-polarized transportmeasurements\nwerecarriedoutin thetwoprobeconfiguration, asthe roomtempe raturejunction resistancewas3ordersofmagnitude\nhigherthan that ofthe Pt crossstrip and contacts. Fig.2-a,bclea rlydemonstratesthe TMR effect in aPt/CoFe 2O4/γ-\nAl2O3/Co tunnel junction both at 2 K and 290 K. This result is direct exper imental evidence of the spin filter effect in\nCoFe2O4at low temperature and at room temperature . At 2 K we calculate a TMR value of −18% using the relation\nTMR = ( RAP−RP)/RPwhereRAPandRPare the resistance values in the antiparallel and parallel magnetic\nconfigurations. At room temperature, TMR = -3%. The abrupt dro p in the TMR curve at ±200 Oe corresponds\nto the switching of the Co electrode, while the gradual increase bac k to±6 T agrees with the progressive switching\nand lack of saturation in CoFe 2O4seen in the magnetization measurements. The negative sign of the T MR indicates\nthat the CoFe 2O4spin filter and Co electrode are oppositely polarized which is most cons istent with the negative P\npredicted for CoFe 2O4in band structure calculations [9], and the positive Pmeasured for Co by the Meservey-Tedrow\ntechnique. Taking P Co=40% [13], we may approximate P CoFe 2O4from Julli` ere’s formula: TMR= 2P1P2/(1−P1P2)\nwhere P 1=PCoand P 2=PCoFe 2O4[14]. This gives P CoFe 2O4=-25% at 2K and P CoFe 2O4=-4% at room temperature.\nDue to the low remanence in our CoFe 2O4films, one could expect these values to increase significantly with the future\nimprovement of their magnetic properties, reaching 50% or higher. The considerable decrease of P CoFe 2O4at high\ntemperature could be explained by the thermal excitation of the sp in up electrons into their corresponding majority\nspin conduction band, if the conduction band splitting were small with respect to kBT.\nTheI−Vcharacteristics representative of the Pt/CoFe 2O4/γ-Al2O3/Co system are shown in Fig.2-c. Analyzing\nthe second derivative of these tunneling spectroscopy measurem ents, we obtain a good estimation of Φ from the bias\nvoltage at which these deviate from linearity. Fig.2-d clearly shows t hatd2I/dV2is linear for -60 mV < V <60 mV,\nindicating direct tunneling in this regime. We also obtain the same value o f Φ from the ( dI/dV)/(I/V) characteristics\nwhich show a peak at 60 mV corresponding to the onset of the condu ction band. We note that this Φ value does\nnot account for the voltage drop across the γ-Al2O3barrier, which should in fact lower it further. In either case, the\nrelatively small tunnel barrier height is quite consistent with the elec tronic band structure calculations schematized\nin Fig.3-b, which predict CoFe 2O4to have a small electronic band gap and an intrinsic Fermi level that is close to\nthe first level of the conduction band.\nIn addition, the I−Vcurves taken in the antiparallel ( ±0.08 T) and parallel ( ∓6 T) states may be used to extract\nthe TMR bias dependence by using the definition TMR = ( IP−IAP)/IAP. The result, shown in Fig.3-a, is a steady\nincrease in absolute value of the TMR with increasing Vup to a certain value, followed by a slight decrease for higher\nbiases. This exact behavior was theoretically predicted by A. Saffar zadeh to be the signature of spin filtering in MTJs4\ncontaining a magnetic barrier [15], and has only recently been observ ed experimentally with EuS at low temperature\n[16]. However, it has never been verified in higher TCmagnetic oxide tunnel barriers [7, 8]. The fact that the TMR\nincreases with increasing Vboth at low temperature and at room temperature proves that th e TMR we observe truly\nresults from spin filtering across the CoFe 2O4barrier. The onset of spin filtering, given by the region for which TMR\nincreases with V, may be identified from the low temperature curve in Fig.3-a around ±30 mV and persists until\n+130 mV (-100 mV) for positive (negative) bias.\nQuantitative comparison of the spin filter regime in our TMR( V) curves with the calculations of Szotek et al.\nyields an exchange splitting (in the tens of meV in our junctions) that is significantly lower than that predicted for\nthe inverse spinel structure (1.28 eV). This observation is consist ent with the temperature sensitivity of the TMR\nmeasurement discussed earlier. The electronic band structure of the CoFe 2O4barrier is likely influenced by the\npresence of structural and/or chemical defects, many of which are difficult to account for in model systems for such\ncalculations. The presence of Co3+, for example, is one defect that has been predicted by Szotek et al.[9] to reduce\nthe band gap as well as the conduction band splitting while favoring an energetically stable state. Furthermore, one\ncan not ignore the possible influence of oxygen vacancies or antipha se boundaries, as these are known to influence the\nmagnetic order in spinel ferrites [12], and thus likely the exchange sp litting as well. Further studies are underway to\nbetter quantify the effects of both structural and chemical def ects on the spin polarized tunneling across CoFe 2O4.\nIn summary, we have demonstrated room temperature spin filterin g in fully epitaxial Pt(111)/CoFe 2O4(111)/γ-\nAl2O3(111)/Co(0001) MTJs where CoFe 2O4was the magnetic tunnel barrier. TMR values of -18% and -3% were\nobserved at 2 K and 290 K respectively. Furthermore, the experim ental TMR ratio increased with increasing bias\nvoltage, reproducing the theoretically predicted behavior for a mo del spin filter system. The similarity between\nour experimental TMR( V) curves and those previously predicted in the literature not only pr oves the spin filtering\ncapability of CoFe 2O4, but also validates the theoretical and phenomenological models de scribing spin-polarized\ntunneling across a magnetic insulator.\nThe authors are very grateful to M. Gautier-Soyer for helpful d iscussions. This work is funded by CNANO ˆIle de\nFrance under the “FILASPIN” project.\n[1] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt , A. Waag, and L. W. Molenkamp, Nature 402, 787 (1999).\n[2] J. S. Moodera, T. S. Santos, and T. Nagahama, J. Phys. Cond . Mat.19, 165202 (2007).\n[3] J. S. Moodera, R. Meservey, and X. Hao, Phys. Rev. Lett. 70, 853 (1993).\n[4] R. Meservey and P. M. Tedrow, Phys. Repts. 238, 173 (1994).\n[5] T. S. Santos and J. S. Moodera, Phys. Rev. B 69, 241203 (2004).\n[6] P. LeClair, J. K. Ha, J. M. Swagten, J. T. Kohlhepp, C. H. va n de Vin, and W. J. M. de Jonge, Appl. Phys. Lett. 80, 625\n(2002).\n[7] M. Gajek, M. Bibes, A. Barth´ el´ emy, K. Bouzehouane, S. F usil, M. Varela, J. Fontcuberta, and A. Fert, Phys. Rev. B 72,\n020406 (2005).5\n[8] U. Luders, M. Bibes, K. Bouzehouane, E. Jacquet, J.-P. Co ntour, S. Fusil, J. Fontcuberta, A. Barth´ el´ emy, and A. Fer t,\nAppl. Phys. Lett. 88, 082505 (2006).\n[9] Z. Szotek, W. M. Temmerman, D. Kodderitzsch, A. Svane, L. Petit, and H. Winter, Phys. Rev. B 74, 174431 (2006).\n[10] M. G. Chapline and S. X. Wang, Phys. Rev. B 74, 014418 (2006).\n[11] A. V. Ramos, J.-B. Moussy, M.-J. Guittet, M. Gautier-So yer, C. Gatel, P. Bayle-Guillemaud, B. Warot-Fonrose, and\nE. Snoeck, Phys. Rev. B 75, 224421 (2007).\n[12] D. T. Margulies, F. T. Parker, M. L. Rudee, F. E. Spada, J. N. Chapman, P. R. Aitchison, and A. E. Berkowitz, Phys.\nRev. Lett. 79, 5162 (1997).\n[13] J. S. Moodera and G. Mathon, J. Magn. Magn. Mater. 200, 248 (1999).\n[14] M. Julli` ere, Phys. Lett. A 54, 225 (1975).\n[15] A. Saffarzadeh, J. Magn. Magn. Mater. 269, 327 (2004).\n[16] T. Nagahama, T. S. Santos, and J. S. Moodera, Phys. Rev. L ett.99, 016602 (2007).6\nFIGURE CAPTIONS\nFIG. 1: HRTEM image of a CoFe 2O4(5 nm)/γ-Al2O3(1.5 nm)/Co (10 nm) trilayer deposited directly on a sapphir e substrate,\nand showing the exceptional quality of the fully epitaxial s ystem.\nFIG. 2: TMR as a function of applied magnetic field for a Pt(20 n m)/CoFe 2O4(3 nm)/γ-Al2O3(1.5 nm)/Co(10 nm) tunnel\njunction at 2 K (a) and at room temperature (b) with an applied bias voltage of 200 mV. The junction area Awas 24µm2.\nA zoom of the Co switching at room temperature is shown in the i nsert of (b). The I−Vcharacteristics, and d2I/dV2fitted\nlinearly for −Φ≤V≤Φ are shown in (c) and (d).\nFIG. 3: (a) TMR as a function of bias voltage for a Pt(20 nm)/Co Fe2O4(3 nm)/γ-Al2O3(1.5 nm)/Co(10 nm) tunnel junction\nat 2 K and 300 K. The open data points correspond to TMR values o btained from R(H) measurements. (b) Schematic\nrepresentation of the CoFe 2O4band structure based on first principles studies [9].This figure \"ramos_TMR-CFO_fig1.jpg\" is available in \"jpg\"\n format from:\nhttp://arxiv.org/ps/0707.3823v2This figure \"ramos_TMR-CFO_fig2.jpg\" is available in \"jpg\"\n format from:\nhttp://arxiv.org/ps/0707.3823v2This figure \"ramos_TMR-CFO_fig3.jpg\" is available in \"jpg\"\n format from:\nhttp://arxiv.org/ps/0707.3823v2"    },    {        "title": "1508.05629v1.A_study_of_the_physical_properties_of_single_crystalline_Fe5B2P.pdf",        "content": "A study of the physical properties of single crystalline Fe 5B2P.\nTej N Lamichhanea,b, Valentin Taufourb, Srinivasa Thimmaiahb, David S. Parkerc, Sergey L. Bud’koa,b, Paul C. Canfielda,b\naDepartment of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, U.S.A.\nbAmes Laboratory, Iowa State University, Ames, Iowa 50011, U.S.A.\ncMaterials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831\nAbstract\nSingle crystals of Fe 5B2P were grown by self-flux growth technique. Structural and magnetic properties are studied. The Curie\ntemperature of Fe 5B2P is determined to be 655 \u00062 K. The saturation magnetization is determined to be 1 :72\u0016B/Fe at 2 K. The\ntemperature variation of the anisotropy constant K1is determined for the first time, reaching \u00180:50 MJ /m3at 2 K, and it is\ncomparable to that of hard ferrites. The saturation magnetization is found to be larger than the hard ferrites. The first principle\ncalculations of saturation magnetization and anisotropy constant are found to be consistent with the experimental results.\nKeywords: single crystal, magnetization, demagnetization factor, Arrott plot, transition temperature, anisotropy constant\n1. Introduction\nThe existence of the ternary Fe 5B2P phase was first reported\nin 1962[1, 2]. Both references reported the detailed structural\ninformation and the Curie temperature for the Fe 5B2P phase.\nIts structural prototype is tetragonal Cr 5B3with the space group\nDls\n4h\u0000I4=mcm . The Curie temperature was reported to fall be-\ntween 615 K to 639 K, depending upon the B content. In 1967,\nanother study reported a Curie temperature of 628 K and a satu-\nration magnetization of 1 :73\u0016B/Fe [3]. The Fe 5B2P phase was\nalso studied using M ¨ossbauer spectroscopy and X-ray di \u000brac-\ntion in 1975 [4]. In addition to confirming the Curie tempera-\nture range as well as the average saturation magnetic moment\nper Fe atom, the M ¨ossbauer study identified the average mo-\nment contributed by each of the Fe lattice sites in the Fe 5B2P\nunit cell. The Fe(2) (or 4c) sites contribute 2 :2\u0016B/Fe. The Fe(1)\n(or 16l) sites contribute 1 :6\u0016B/Fe. The average extrapolated\nmoment of the both sites at 0 K was reported to be 1 :73\u0016B/Fe.\nFe5B2P is specifically interesting as a possible high transi-\ntion temperature, rare earth free, hard ferromagnetic material.\nGiven that all prior work on Fe 5B2P was made on polycrys-\ntalline samples, we developed a single crystal growth proto-\ncol, measured thermodynamic and transport properties of single\ncrystalline samples, and determined the magnetic anisotropy of\nthis material. The anisotropy constant K1is positive, indicating\nthat the c axis is the easy axis of magnetization, and has a com-\nparable size and temperature dependence as hard ferrites such\nas SrFe 12O19and BaFe 12O19.\n2. Experimental Details\n2.1. Crystal growth\nAs part of our e \u000bort to search for new, or poorly charac-\nterized ferromagnetic compounds, we have developed single\ncrystal growth protocols for transition metal rich, chalcogenideand pnictide binary and ternary phases. In a manner similar to\nsome of our earlier transition metal - sulphur work, [5, 6] we\nstarted by confirming our ability to contain Fe-P binary melts\nin alumina crucibles sealed in amorphous silica ampules. As\noutlined by Canfield and Fisk [7] and Canfield, [8] sealed am-\npoules were decanted after slow cooling by use of a centrifuge.\nCrucibles with alumina filters [9] were used to allow assessment\nand even reuse of the decanted liquid. For this experiment, a\nmixture of freshly ball milled iron powder and red phosphorous\nlumps were placed in an alumina crucible in an atomic ratio\nof Fe : P =0.83 : 0.17. A homogenous liquid exists at 1060 °C\n(i.e. there was no crystal growth upon cooling from 1200 °C to\n1060 °C and all of the material decanted). For similar tempera-\nture profiles, an initial melt of Fe 0:86P0:14lead to the growth of\ndendritic Fe whereas for initial melts of Fe 0:81P0:19, Fe 0:79P0:21\nand Fe 0:77P0:23faceted Fe 3P was grown. These data are all con-\nsistent with the binary phase diagram [10] and indicate that the\nFe-P binary melt does not have a significant partial pressure of\nphosphorous and does not react with alumina.\nSilica ampouleG\nrowth crucibleAlumina filterCatch crucibleTop bufferq\nuartz woolB\nottom bufferq\nuartz woolBoron piecesRed P lumpsF\ne powder\nFigure 1: A schematic assembly of the crystal growth ampoule.\nAfter some optimization, an initial stoichiometry of\nPreprint submitted to Elsevier November 12, 2021arXiv:1508.05629v1  [cond-mat.mtrl-sci]  23 Aug 2015(c)(a)(\nb)[\n100][ 001]Figure 2: (a) The acid etched single crystals image of Fe 5B2P (b) Laue pattern\nalong the hard axis [100] and (c) Laue pattern along the easy axis [001] of\nmagnetization.\nFe72P18B10was used to grow single phase Fe 5B2P plates. Ball\nmilled Fe (Fe lumps obtained from Ames lab), red phospho-\nrous lumps (Alfa Aesar, 99.999% (metal basis)), and crystalline\nboron pieces (Alfa Aesar, 99.95%) were placed in an alumina\ncrucible /filter assembly, sealed in a partial pressure of Ar in an\namorphous silica tube (as shown schematically in figure 1). The\nampoule was heated over 3 hours to 250 °C, remained at 250 °C\nfor 3 hours, heated to 1200 °C over 12 hours, held at 1200 °C\nfor 10 hours, and then cooled to 1160 °C over 75 hours. After\ncooling to 1160 °C the ampoule was decanted using a centrifuge\nand plate like single crystals of Fe 5B2P could be found on the\ngrowth side of the alumina filter. In order to confirm that the\ngrowth of crystals took place from a complete liquid, we de-\ncanted one growth at 1200 °C, instead of cooling to 1160 °C,\nand indeed found all of the material decanted.\nAfter growth, single crystals were cleaned by etching in a\nroughly 6 molar HCl solution. Figure 2(a) shows a picture of\nthe etched single crystals.\n2.2. Physical properties measurement\nThe crystal structure and lattice parameters of Fe 5B2P were\ndetermined with both single crystal and powder x-ray di \u000brac-\ntion (XRD). The crystal structure of Fe 5B2P was determined\nfrom single-crystal XRD data collected with the use of graphite\nmonochromatized MoK \u000bradiation (\u0015=0:71073 Å) at room\ntemperature on a Bruker APEX2 di \u000bractometer. Reflections\nwere gathered by taking four sets of 360 frames with 0 :5\u000escans\nin!, with an exposure time of 25 s per frame and the crystal-\nto-detector distance was 5 cm. The measured intensities were\ncorrected for Lorentz and polarization e \u000bects. The intensities\nwere further corrected for absorption using the program SAD-\nABS, as implemented in Apex 2 package [11].\nFor powder XRD, etched single crystals of Fe 5B2P were\nselected and finely powdered. The powder was evenly spread\nover the zero background single crystal silicon wafer sample\nholder with help of a thin film of Dow Corning high vacuum\ngrease. The powder di \u000braction pattern was recorded with\nRigaku Miniflex di \u000bractrometer using copper K\u000bradiation\nsource over 8.5 hours (at a rate of 3 sec dwell time for per 0 :01\u000eto cover the 2 \u0012value up to 100\u000e).\nTo identify the crystallographic orientation of the single\ncrystal plates, Laue di \u000braction patterns were obtained using a\nMultiwire Laboratories, Limited spectrometer. The resistivity\ndata were measured in a four-probe configuration using a\nQuantum Design Magnetic Property Measurement System\n(MPMS) for temperature control and the external device\ncontrol option to interface with a Linear Research, Inc. ac\n(20mA, 16 Hz) resistance bridge (LR 700).\nThe sample preparation for magnetization measurements is a\nmajor step in a magnetic anisotropy study. The etched crystal\nwas cut into a rectangular prismatic shape and the dimensions\nwere determined with a digital Vernier caliper.\nTemperature and field dependent magnetization was mea-\nsured using the MPMS up to room temperature and a Quantum\nDesign Versalab Vibration Sample Magnetometer (VSM) with\nan oven option for higher temperature ( T<1000 K). In MPMS,\nplastic straw was used to align the sample in desired directions.\nThe sample was glued to the VSM sample heater stick with Zir-\ncar cement obtained from ZIRCAR Ceramics Inc.. While glu-\ning, the sample was pushed into the thin layer of Zircar paste\nspread on the heater stick to ensure a good thermal contact with\nthe heater stick. When the sample was firmly aligned with the\ndesired direction it was covered with Zircar cement uniformly.\nFinally, the VSM heater stick, with the sample glued on it, was\ncovered with a copper foil so as to (i) better control the heat\nradiation in the sample chamber, (ii) maintain a uniform tem-\nperature inside the wrapped foil (due to its good thermal con-\nductivity), and (iii) further secure the sample throughout the\nmeasurement.\nIn the VSM, both zero field cooled (ZFC) as well as field\ncooled (FC) magnetizations were measured and found to be al-\nmost overlapping. The di \u000berence between the measured data in\nthe VSM and the MPMS was found to be less than 3% at 300 K\n(i.e. at the point of data overlap). We normalized the magneti-\nzation data from the MPMS with FC VSM data to get a smooth\ncurve for the corresponding applied field.\n2.3. Determination of demagnetization factor for transition\ntemperature and anisotryopy constant measurement\nThe demagnetization factors along di \u000berent directions were\ndetermined by using a formula developed by Aharoni [12]. The\ncalculated demagnetization factors for the field along a, b, and\nc axes were determined to be 0.21, 0.29, and 0.50 respectively.\nTo verify that demagnetization factors were accurate, we pre-\npared a M2versusH\nMplot for the lower temperature M(H) data\nalong the easy axis of magnetization as shown in figure 3. The\nX-intercept gives the directly measured experimental value of\nthe demagnetization factor along the easy magnetization axis\n[13]. In figure 3, we can clearly see that all the M2curves are\noverlapping near the M2axis indicating that the demagnetiza-\ntion factor along the easy magnetization direction does not de-\npend on temperature. A value of demagnetization factor of 0.45\nwas determined along the c axis which is not that di \u000berent from\nthe value of 0 :50 inferred from the sample dimensions. Based\n20.00 .51 .01 .52 .02 .50.02.0x10114.0x10116.0x10118.0x10111.0x10121.2x1012 \n M2 (A/m)2H\n/MFe5B2PH\n || [001]D\nemagnetization factor = 0.45T = 2 KT\n = 300 KFigure 3: An analysis of M(H) isotherms taken at T=2, 50, 100, 150, 200, 250,\n300 K and plotted as M2versus H=Mto determine the demagnetization factor.\nTheH=Maxis intercept at 0 :45 is the experimental demagnetization factor for\neasy axis of magnetization.\non this result, we readjusted the two hard axes demagnetization\nfactors in proportion such that the total sum of all 3 of them\nis 1. The experimentally readjusted values for demagnetization\nfactors were 0 :231, 0:319 and 0:45 along a, b and c axes re-\nspectively. With the benefit of fourfold symmetry of Fe 5B2P\nunit cell perpendicular to its c axis, magnetization was mea-\nsured along a and c axes and corresponding demagnetization\nfactors were used to calculate the corrected internal magnetic\nfield ( Hint). Here Hint=Happlied \u0000NM, where Nis the demag-\nnetization factor and Mis the magnetization.\n3. Results and discussion\n IObserved \nICalculated \nI background4\n06 08 01 0002000400060003\n43 63 84 04 24 44 60250500750 \n Intensity (Counts)F\ne5B2P1\n2(a) \n Intensity (Counts)2\n/s61553 (degree)12(b)\nFigure 4: (a) Powder x-ray di \u000braction pattern of Fe 5B2P (b) Enlarged powder\nX-ray di \u000braction pattern in between 2 \u0012value of 34\u000eto 46\u000eto show the weak\nimpurity peaks 1 and 2.3.1. Lattice parameters determination\nThe structure solution and refinement for single crystal data\nwas carried out using SHELXTL program package [14]. The\nfinal stage of refinement was performed using anisotropic\ndisplacement parameters for all the atoms. The refined com-\nposition was Fe 5B2:12P0:88(1) with residual R1=2:3% (all\ndata). The o \u000b-stoichiometry was due to partial replacement\nof phosphorus by boron on 4a site in the structure. Accord-\ning to the previous report [4] Fe 5B2P shows a considerable\nphase width. All the details about the atomic positions, site\noccupancy factors, and displacement parameters for crystal of\nFe5B2:12P0:88(1)are given in tables 1, and 2.\nTable 1: Crystal data and structure refinement for Fe 5B2P.\nEmpirical formula Fe5B2:12P0:88\nFormula weight 329.42\nTemperature 293(2) K\nWavelength 0:71073 Å\nCrystal system, space group Tetragonal, I4/mcm\nUnit cell dimensions a=5.485(3) Å\nb=5.485(3) Å\nc=10.348(6) Å\nV olume 311.3(4) 103Å3\nZ, Calculated density 4, 7.029 g /cm3\nAbsorption coe \u000ecient 22.905 mm\u00001\nF(000) 615\nCrystal size 0.01 x 0.05 x 0.08 mm3\n\u0012range (\u000e) 3.938 to 31.246\nLimiting indices \u00007\u0014h\u00147\n\u00007\u0014k\u00147\n\u000014\u0014l\u001414\nReflections collected 2113\nIndependent reflections 152 [R(int) =0.0433]\nCompleteness to \u0012=25:242\u000e100:00%\nAbsorption correction multi-scan, empirical\nRefinement method Full-matrix least-squares\non F2\nData /restraints /parameters 152/0/17\nGoodness-of-fit on F21.101\nFinal R indices [I >2\u001b(I)] R1=0:0140, wR2=0:0289\nR indices (all data) R1=0:0180, wR2=0:0299\nExtinction coe \u000ecient 0.0243(3)\nLargest di \u000b. peak and hole 0.485 and -0.474 e.Å\u00003\nFe5B2P has a tetragonal unit cell with lattice constants\na=5.485 (3) Åand c=10:348(3) Å. While analysing the pow-\nder pattern, the CIF file obtained from single crystal data was\nused and the powder pattern was fitted with Rietveld analysis\nusing GSAS EXPGUI software package [15, 16]. During the\nRietveld analysis, Fe sites were supposed to be fully occupied\nand thermally rigid whereas P and B occupation number were\nreleased between each other with help of constraints. Finally, a\nwell fitted powder di \u000braction pattern with R p=0.0828 was ob-\n3Table 2: Atomic coordinates and equivalent isotropic displacement parameters\n(A2) for Fe 5B2P. U(eq) is defined as one third of the trace of the orthogonalized\nUi jtensor.\natom Occ x y z Ueq\nFe1 1 0.0000 0.0000 0.0000 0.005(1)\nFe2 1 0.1701(1) 0.6701(1) 0.1403(1) 0.005(1)\nP3 0.88(1) 0.0000 0.0000 0.2500 0.004(1)\nB3 0.12(1) 0.0000 0.0000 0.2500 0.004(1)\nB4 1 0.6175(2) 0.1175(2) 0.0000 0.005(1)\ntained as shown in figure 4(a). The lattice parameters from this\nmeasurement are in close agreement (less than 0.2 % deviation)\nwith our single crystal data as well as previously reported data\n[2, 4]. A final stoichiometry of the powder sample was deter-\nmined to be Fe 5B2:11P0:89. This stoichiometry is in agreement\nwith our single crystal XRD composition of Fe 5B2:12P0:88(1).\nTwo tiny unidentified peaks denoted by 1 and 2 in figure 4 were\nnoticed in all batches of Fe 5B2P measured. A possible origin\nfor these peaks is an excess amount of unreacted boron trapped\nin crystal. We suspected boron because it has many overlap-\nping di \u000braction peaks with Fe 5B2P as well as with these two\ntiny humps denoted by 1 and 2 and enlarged in figure 4(b).\n3.2. Identification of crystallographic orientation\nThe Laue di \u000braction pattern shown in figure 2(b) was ob-\ntained with the X-ray beam parallel to the plane of the plate\n[100]. The Laue pattern shown in figure 2(c) was obtained with\nthe X-ray beam perpendicular to the plane of the plate [001].\nThe obtained Laue di \u000braction patterns were analysed with the\nOrientExpress analysis software [17]. The Laue pattern anal-\nysis revealed that the crystals facets were grown along [100],\n[010], and [001] directions.\n3.3. Resistivity measurement\n05 01 00150200250300010203040506070 \n /s61554/s61472(µΩcm) \nT (K)Fe5B2Pi\n || [100]\nFigure 5: Resistivity of Fe 5B2P below the room temperature with an excitation\ncurrent being parallel to [100] direction.\nThe resistivity data of a single crystalline sample helps to\ntest its quality. The resistivity of Fe 5B2P with current parallelto [100] is measured from room temperature down to 2 K; the\nresistivity is found to be metallic in nature as shown in figure 5.\nThe residual resistivity ratio ( RRR =\u001a(300 K)=\u001a(2 K)) of the\nFe5B2P sample is estimated to be nearly 3 :6. The residual resis-\ntivity\u001a(2 K) is roughly 20 \u0016\ncm. These values are consistent\nwith some residual disorder in the sample (e.g. the P an B site\ndisorder on the P 3site).\n02 004 006 008 001 0000.00.20.40.60.81.01.21.41.61.8F\ne5B2P \n Ms \nH || [001] 1 T \nH || [100] 1 T \nH || [001] 0.1 T \nH || [100] 0.1 T \n M (µΒ/Fe)T\n (K)\nFigure 6: Temperature dependent magnetization of Fe 5B2P at various magne-\ntizing field along [100] and [001] directions and saturation magnetization, Ms,\ninferred from M(H) isotherms.\n3.4. Measurement of magnetization and saturation magnetiza-\ntion\nThe temperature dependent magnetization of Fe 5B2P along\nthe easy [001] and hard [100] axes in various magnetizing field\nstrengths in terms of \u0016B/Fe are reported in figure 6. As the field\nstrength increases, the moment increases and saturates. The\nsaturating field for the easy axis was found to be nearly 0 :8 T\nandM(T) data in an applied field of 1 T is the same as satu-\nration magnetization obtained from M(H) isotherms data (not\nshown here). The magnetization along the hard axis has not\nreached saturation in an external field of 1 T as shown in the\ngreen curve of figure 6. Below the Curie temperature, the M(T)\ncurves at low field are almost constant because the applied field\nis less than the demagnetizing field. The saturation magnetiza-\ntion ( Ms) data were determined from the Y-intercept of linear fit\nofM(H) isotherms plateau (as shown in figure 8) at 2 K, 50 K\nand in an interval of 50 K up to 650 K. The saturation magneti-\nzation at 2 K was found to be 1 :72\u0016B/Fe which is very close to\nthe previously reported value of 1 :73\u0016B/Fe [3, 4].\n3.5. Determination of transition temperature\nA M2versus Hint=MArrott plot was used to determine the\nCurie temperature. The Curie temperature corresponds to Ar-\nrott plot curve that passes through the origin. For our sample,\nthe Arrott curve corresponding to 655 K is passing through the\norigin. Hence the Curie temperature of Fe 5B2P is determined\nto be 655 \u00062 K, where the error includes an instrumental un-\ncertainty of \u00061 K inherent to such a high temperature measure-\nment in a VSM and a reproducibility error due to sample gluing\n402 4 6 8 0.05.0x10101.0x10111.5x10112.0x1011T\nc = 655 K Fe5B2PH\n || [001] \n M2 (A/m)2H\nint/MT = 648 KT\n = 668 KFigure 7: The Arrott plot of Fe 5B2P. Here M(H) isotherms were measured for\nthe prismatic sample from 648 K to 668 K with a spacing of 1 K. Internal\nmagnetic field ( Hint) was determined with an experimentally measured demag-\nnetization factor (0 :45) for the easy axis of magnetization. The temperature\ncorresponding to M2versus Hint=Misotherm passing through origin gives the\nCurie temperature. The Curie temperature is determined to be 655 \u00062 K.\nprocess on the heater stick resulting in a variation in thermal\ncoupling. This Curie temperature is a little bit higher than the\npreviously reported window of 615 K to 639 K [3, 4].\nTo make sure our measurement was correct, magnetization of\na piece of a nickel wire obtained from the Alfa Aesar company\n(99:98 % metal basis) was measured with the same VSM heater\nstick. Using the criterion from reference [18], the Curie temper-\nature of nickel sample was determined to be 625 \u00062 K which is\nin agreement with VSM Tech Note [19]. The Curie temperature\nof nickel is reported to fall between 626 to 633 K [20]. These\nresults confirm the accuracy of measured Curie temperature.\n01 2 3 02004006008001000 \nH || [001] \nH || [100] \n M (kA/m)/s61549\n/s61488Hint (T)Fe5B2PT\n = 300 KA\nrea = K1 = 0.38 MJ/m3\nFigure 8: An example of determination of K 1at 300 K with an appropriate axes\nunits so as to obtain the area in terms of MJ /m3unit.\n3.6. Determination of anisotropy constant K 1\nThe anisotropy constant K 1is the measure of anisotropy en-\nergy density and strongly depends on the unit cell symmetry\nand temperature. One of the conceptually simplest methodsof measuring the anisotropy constant of an uniaxial system is\nto determine the area between the easy and hard axes M(H)\nisotherms [21]. Here we measured both the easy and hard axes\nisothermal M(H) curves starting from 2 K. Then we measured\nM(H) curves from 50 K to 800 K in 50 K intervals. A typical\nexample of determination of the anisotropy constant by mea-\nsuring the anisotropy area between two magnetization curves is\nshown in figure 8.\n01002003004005006007000.00.10.20.30.40.50.6 \nFe5B2P \n SrFe12O19 \nBaFe12O19 \n K1 (MJ/m3)T\n (K)\nFigure 9: Temperature variation of the anisotropy constant K 1of Fe 5B2P and\ncomparison with SrFe 12O19and BaFe 12O19from ref. [22].\nThe temperature dependence of K1is shown in Fig. 9. K1is\npositive, indicating that the c axis is the easy axis of magneti-\nzation, in agreement with a previous calculation using a simple\npoint charge model [4].\n010020030040050060070080002004006008001000 Fe5B2P \nSrFe12O19 \n BaFe12O19 \n Ms (kA/m)T\n (K)\nFigure 10: Temperature variation of the saturation magnetization M sof Fe 5B2P\nand comparison with SrFe 12O19and BaFe 12O19from ref. [22].\nWe have compared the anisotropy constant K1and satura-\ntion magnetization Msof Fe 5B2P with the single crystal data\nof hard ferrites SrFe 12O19and BaFe 12O19[22]. The anisotropy\nconstant of Fe 5B2P is greater at low temperature than either of\nthese ferrites. The Fe 5B2P sample becomes comparable to that\nof SrFe 12O19at room temperature but decreases slightly faster\nthan both BaFe 12O19and SrFe 12O19above room temperature as\n5shown in figure 9. However, the nature of variation of the satu-\nration magnetization of Fe 5B2P is di \u000berent than the hard ferrites\nas shown in figure 10. Both of the ferrites show a roughly linear\ndecrease of saturation magnetization with increasing tempera-\nture whereas the saturation magnetization of Fe 5B2P is found\nto be significantly non-linear in T and also significantly larger\nforT<600 K. The saturation magnetization of Fe 5B2P is\n1:53\u0016B/Fe at 300 K, which is already larger than the value\nof 1:16\u0016B/Fe in SrFe 12O19. Since Fe 5B2P contains less non-\nmagnetic elements, the volume magnetization of 915 kA /m for\nFe5B2P is more than twice that of SrFe 12O19(377 kA /m [22]).\n4. First principles calculations\nIn an e \u000bort to understand the observed magnetic properties\n- in particular, the saturation magnetization and magnetocrys-\ntalline anisotropy - of Fe 5B2P, we have performed first prin-\nciples calculations using the augmented plane-wave density\nfunctional theory code WIEN2K [23] within the generalized\ngradient approximation (GGA) of Perdew, Burke and Ernzer-\nhof [24]. Sphere radii of 1 :77, 2:15 and 2:06 Bohr were used for\nB, Fe and P, respectively, and an RK maxof 7:0 was employed,\nwhere RK maxis the product of the smallest sphere radius and\nthe largest plane-wave expansion wave vector. The experimen-\ntal lattice parameters from Ref. [2] were used and all internal\ncoordinates were relaxed. All calculations, the internal coor-\ndinate relaxation excepted, employed spin-orbit coupling and a\ntotal of approximately 10 ;000k-points in the full Brillouin zone\nwere used for the calculation of magnetic anisotropy. For these\ncalculations we computed total energies for the magnetic mo-\nments parallel to (100) and (001) and computed the anisotropy\nas the di \u000berence in these energies.\nAs in the experimental work we find a strong ferromag-\nnetic behavior in Fe 5B2P, with a saturation magnetic moment\nof 1:79\u0016Bper Fe, which includes an average orbital moment\nof approximately 0 :03\u0016Bfor each of the Fe sites. We present\nthe calculated density-of-states in Fig. 11. The theoretical sat-\nuration value is in good agreement with the experimental 2 K\nmoment of 1 :72\u0016Bper Fe. Small negative moments of \u00000:1\u0016B\nand\u00000:06\u0016Bper atom are found for the B and P atoms re-\nspectively, while the spin moments for the three distinct in-\nequivalent Fe atoms are 1 :79, 1:79 and 2:08\u0016B. These are\nsignificantly smaller than the values for bcc Fe (approximately\n2:2\u0016B) and for the Fe atoms in hexagonal Fe 3Sn (approxi-\nmately 2:4\u0016B/Fe [25]), limiting the potential performance as a\nhard magnetic material. Figure 11 displays the reason for this,\nwith the spin-minority DOS substantially larger than the spin-\nmajority DOS around the Fermi energy, reducing the moment.\nAs in the experiment, the calculated easy axis of the magne-\ntization is the c-axis, with a T=0 value for the first anisotropy\nconstant K 1of 0:46 MJ /m3, which is in excellent agreement\nwith the experimental value of 0 :48 MJ /m3. On a per-Fe ba-\nsis this is 44 \u0016eV . This is much larger than the \u00181\u0016eV value\nfor bcc Fe [26], as might be expected given the non-cubic sym-\nmetry of Fe 5B2P, but is roughly consistent with the 60 \u0016eV/Co\nvalue for hcp Co. This is again indicative of the usual require-\nment of an anisotropic crystal structure for significant mag-\n-5 -2.502.5 5E-EF (eV)-20-15-10-505101520N(E) (states/eV/unit cell)totalBFe1Fe2PFigure 11: The calculated density-of-states of Fe5PB 2\nnetic anisotropy. Regarding the structure itself, in the per-\nfectly ordered Fe 5B2P structure, eight of the ten Fe atoms have\nthree boron nearest neighbors and two next-nearest phospho-\nrus neighbors, with the other two Fe atoms having four boron\nnearest neighbors. There are no nearest-neighbor Fe-Fe bonds,\nwhich is perhaps surprising in a structure which is over 60\natomic percent Fe. One may suppose that a variegated bond-\ning configuration, with a range of atoms bonding with the Fe\natoms, might be favorable for the magnitude, though not neces-\nsarily the sign (i.e. axial or planar) of the anisotropy, but this is\napparently not realized in this material. In any case, the theoret-\nical calculations are generally quite consistent with the results\nof the experimental work performed.\n5. Conclusions\nSingle crystals of Fe 5B2P were grown using a self flux\ngrowth method within a 40 °C window of cooling. The Curie\ntemperature of Fe 5B2P was determined to be 655 \u00062 K. The sat-\nuration magnetization was determined to be 1 :72\u0016B/Fe at 2 K.\nThe temperature variation of the anisotropy constant K1was de-\ntermined for the first time, reaching \u00180:50 MJ /m3at 2 K, and\nfound to be comparable to that of hard ferrites. The saturation\nmagnetization, in unit of kA /m is found to be larger than the\nhard ferrites. The first principle calculation values of saturation\nmagnetization and anisotropy constant using augmented plane-\nwave density functional theory code were found to be consistent\nwith experimental work.\n6. Acknowledgement\nWe thank T. Kong, U. Kaluarachchi, K. Dennis, and A. Sap-\nkota for useful discussion. The research was supported by the\nCritical Material Institute, an Energy Innovation Hub funded by\nU.S. Department of Energy, O \u000ece of Energy E \u000eciency and Re-\nnewal Energy, Advanced Manufacturing O \u000ece. This work was\nalso supported by the O \u000ece of Basic Energy Sciences, Materi-\nals Sciences Division, U.S. DOE. The first principle calculation\nof this work was performed in Oak Ridge National Laboratory.\n6References\n[1] E. Fruchart, A.-M. Triquet, R. Fruchart, A. Michale, Two New Ferro-\nmagnetic Compounds in the Ternary System Iron-Phosphorous-Boron (in\nFrench), Compt. Rend. Acad. Sci. Paris 255 (1962) 931–933.\n[2] S. Rundqvist, X-Ray Investigation of the Ternary System Fe-P-B. Some\nFeatures of the System Cr-P-B, Mn-P-B and Ni-P-B, Acta Chem. Scand.\n16 (1962) 1.\n[3] A.-M. Blanc, E. Fruchart, R. Fruchart, Magnetic and Crystallographic\nStudies of the (Fe 1\u0000xCrx)3P Solution Solids and the Ferromagnetic Phase\nFe5B2P (in French), Ann. Chim., t.2.\n[4] L. H ¨aggstr ¨om, R. W ¨appling, E. Ericsson, Y . Andersson, S. Rundqvist,\nMssbauer and X-ray studies of Fe 5PB2, J. Solid State Chem. doi:10.\n1016/0022-4596(75)90084-5 .\n[5] X. Lin, S. L. Bud’ko, P. C. Canfield, Development of viable solutions for\nthe synthesis of sulfur bearing single crystals, Philos. Mag. 92 (19-21)\n(2012) 2436–2447. doi:10.1080/14786435.2012.671552 .\n[6] Q. Lin, V . Taufour, Y . Zhang, M. Wood, T. Drtina, S. L. Budko, P. C.\nCanfield, G. J. Miller, Oxygen trapped by rare earth tetrahedral clus-\nters in Nd 4FeOS 6: Crystal structure, electronic structure, and magnetic\nproperties, J. Solid State Chem. 229 (0) (2015) 41 – 48. doi:http:\n//dx.doi.org/10.1016/j.jssc.2015.05.020 .\n[7] P. C. Canfield, Z. Fisk, Growth of single crystals from metallic fluxes, Phi-\nlos. Mag. 65 (6) (1992) 1117–1123. arXiv:http://dx.doi.org/10.\n1080/13642819208215073 ,doi:10.1080/13642819208215073 .\n[8] P. C. Canfield, Solution Growth of Intermetallic Single Crystals: A Be-\nginners Guide, Properties and Appl ications of Complex Intermetallics,\n(World Scientific, Singapore, 2010) (2010) 93–111.\n[9] C. Petrovic, P. C. Canfield, J. Y . Mellen, Growing intermetallic single\ncrystals using in situ decanting, Philos. Mag. 92 (19-21) (2012) 2448–\n2457. doi:10.1080/14786435.2012.685190 .\n[10] H. Ohtani, N. Hanaya, M. Hasebe, S. Teraoka, M. Abe, Fe-P Phase Dia-\ngram, ASM Alloy Phase Diagrams Database, P. Villars, editor-in-chief;\nH. Okamoto and K. Cenzual, section editors.\nURL http://www1.asminternational.org/AsmEnterprise/\nAPD,ASMInternational,MaterialsPark,OH,2006.\n[11] Bruker, APEX-2, Bruker AXS Inc., Madison, Wisconsin, USA, 10th ed.\n(2013).\n[12] A. Aharoni, Demagnetizing factors for rectangular ferromagnetic prisms,\nJ. Appl. Phys. 83 (6) (1998) 3432–3434. doi:10.1063/1.367113 .\n[13] A. Arrott, Criterion for ferromagnetism from observations of magnetic\nisotherms, Phys. Rev. 108 (1957) 1394–1396. doi:10.1103/PhysRev.\n108.1394 .\nURL http://link.aps.org/doi/10.1103/PhysRev.108.1394\n[14] SHELXTL-v2008 /4, Bruker AXS Inc., Madison, Wisconsin, USA, 2013.\n[15] A. Larson, R. V . Dreele, ”General Structure Analysis System (GSAS)”,\nLos Alamos National Laboratory Report LAUR (1994) 86–748.\n[16] B. H. Toby, EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst.\n34 (2001) 210–213.\n[17] J. laugier, B. Bochu, LMGP-Suite Suite of Programs for the interpreta-\ntion of X-ray Experiments, ENSP /Laboratoire des Matriaux et du Gnie\nPhysique, BP 46. 38042 Saint Martin d’Hres, France.\nURL WWW:http://www.inpg.fr/LMGPandhttp://www.ccp14.ac.\nuk/tutorial/lmgp/\n[18] A. Arrott, J. E. Noakes, Approximate equation of state for nickel near its\ncritical temperature, Phys. Rev. Lett. 19 (1967) 786–789. doi:10.1103/\nPhysRevLett.19.786 .\nURL http://link.aps.org/doi/10.1103/PhysRevLett.19.786\n[19] Quantum Design, Tech Note 1097-202, Measured Curie Temperature of\nthe VSM Oven Nickel Standard Sample .\n[20] B. Legendre, M. Sghaier, Curie temperature of nickel, Journal of Ther-\nmal Analysis and Calorimetry 105 (1) (2011) 141–143. doi:10.1007/\ns10973-011-1448-2 .\nURL http://dx.doi.org/10.1007/s10973-011-1448-2\n[21] R. M. Bozorth, Determination of ferromagnetic anisotropy in single crys-\ntals and in polycrystalline sheets, Phys. Rev. 50 (1936) 1076–1081. doi:\n10.1103/PhysRev.50.1076 .\nURL http://link.aps.org/doi/10.1103/PhysRev.50.1076\n[22] B. T. Shirk, W. Bussem, Temperature dependence of M sand K 1of\nBaFe 12O19and SrFe 12O19single crystals., J. Appl. Phys.\n[23] P. Blaha and K. Schwarz and G. Madsen and D. Kvasnicka and J. Luitz,WIEN2k, An Augmented Plane Wave +Local Orbitals Program for Cal-\nculating Crystal Properties(K. Schwarz, Tech. Univ. Wien, Austria, 2001).\n[24] Perdew, John P. and Burke, Kieron and Ernzerhof, Matthias, Generalized\nGradient Approximation Made Simple, Phys. Rev. Lett. 77 (1996)\n3865–3868. doi:10.1103/PhysRevLett.77.3865 .\nURL http://link.aps.org/doi/10.1103/PhysRevLett.77.\n3865\n[25] B. C. Sales and B. Saparov and M. A. McGuire and D. J. Singh and D. S.\nParker, Ferromagnetism of Fe 3Sn and alloy., Sci Rep 4 (2014) 7024.\n[26] G. H. O. Daalderop, P. J. Kelly, M. F. H. Schuurmans, First-principles\ncalculation of the magnetocrystalline anisotropy energy of iron, cobalt,\nand nickel, Phys. Rev. B 41 (1990) 11919–11937. doi:10.1103/\nPhysRevB.41.11919 .\nURL http://link.aps.org/doi/10.1103/PhysRevB.41.11919\n7"    },    {        "title": "1008.2861v1.Imaging_ferroelectric_domains_in_multiferroics_using_a_low_energy_electron_microscope_in_the_mirror_operation_mode.pdf",        "content": "  Imaging ferroelectric domains in multiferroics using a low-\nenergy electron microscope in the mirror operation mode\nSalia Cherifi*,1,2, Riccardo Hertel3, Stéphane Fusil4,5, Hélène Béa6, Karim Bouzehouane4, Julie Allibe4, \nManuel Bibes4 and Agnès Barthélémy4 \n1 IPCMS, CNRS and UDS, 23 rue du Lo ess, BP43, F-67034 Strasbourg, France \n2 Institut Néel, CNRS and UJF, 25 rue des Martyrs, BP166, F-38042 Grenoble, France \n3 Forschungszentrum Jülich GmbH, IFF-9, Le o-Brandt-Str., D-52425 Jülich, Germany \n4 Unité Mixte de Physique CNRS/Thales, 1 Av. A. Fresnel, F-91767 Palaiseau and Un iversité Paris-Sud, F-91405 Orsay, France \n5 Université d’Evry-Val d'Essonne, Bd. F. Mitterrand, F-91025 Evry, France \n6 DPMC, University of Geneva, 24 quai Er nest-Ansermet CH-1211 Geneva, Switzerland \n \nSubmitted to Phys. Status Solidi Rapid Research Letters – Accepted 16 November 2009  \n \nPACS 77.80.Dj, 77.90.+k, 75.50.-y.\n                                                           \n* Corresponding author: e-mail cherifi@ipcms.u-strasbg.fr , Phone +33 3 8810 7218, Fax +33 3 8810 7248 \n \n \nWe report on low-energy electron microscopy imaging of ferroelectric domains with s ubmicron resolution. Periodic \nstrips of ‘up’ and ‘down’-polar ized ferroelectric domains in \nbismuth ferrite –a room temperature multiferroic– serve as a model system to compare low-energy electron microscopy \nwith the established piezoresponse force microscopy. The \nresults confirm the possibility of full-field imaging of ferroelectric domains with short acquisition times by exploiting the sensitivity of ultraslow electrons to small variations of the electric potential near surfaces in the \n“mirror” operation mode.  \n \n  \nThe manipulation of magneti c structures by electric \nfields and currents, rather than by magnetic fields, has \nrecently evolved into one of the most intensively studied \ntopics in magnetism. Since el ectric currents and fields are \neasier to generate on the nanoscale than focussed magnetic \nfields of well-defined strength, the fundamentally \ninteresting electric control of magnetism is also appealing \nfor applications like non-volatile memory devices. For \nsuch purposes, magnetoelectric multiferroics with coupled \nferroelectric and ferro- or antiferromagnetic order are \nparticularly promising materials [1]. Investigations on \nstatic and dynamic processes in these complex systems \nrequire sophisticated multi-method instruments capable of \nproviding detailed information on the coupled magnetic \nand electric domain structures with short acquisition times.  \n Ferroelectric domain stru ctures are routinely \ninvestigated with piezorespon se force microscopy (PFM) \n[2], a scanning probe technique which utilizes the converse piezoelectric effect in ferroe lectric materials. PFM is \nusually sufficient to obtain complete information on the static ferroelectric properties of the system. The analysis of multiferroic materials, however, additionally requires the visualization of (anti)-ferromagnetic domains. Therefore complementary analysis tools are required to obtain also \nthe magnetic properties of the magnetoelectric system. X-\nray magnetic linear and circular dichroism using a photoemission electron microscope (XM(L,C)D-PEEM) was recently employed for this  purpose to image magnetic \ndomains in bismuth ferrite (BFO)-based heterostructures as a complementary method to the ex-situ PFM-study [3,4]. \n \nHere we show the possibility of imaging ferroelectric \ndomains in BFO films with sub-micron lateral resolution by using the mirror electron microscopy mode (MEM) [5] of a non-scanning Low-Energy Electron Microscope (LEEM) [6,7]. Although MEM is an old and ripened \ntechnique -since basic mirror electron micrographs have    Ferroelectric domains \nrevealed by slow electrons\nBiFeO 3 \nU=Const.\ne \n70nm \nCalculated equipotential surfaces close \nto the ferroelectric su rface S. Cherifi et al,  Imaging ferroelectric domains using a low-energy electron microscope     R 2  \nbeen constructed long before LEEM- only little has been \nreported on the applicatio n of slow electrons for \nferroelectric surface potential detection in this imaging mode since the seventies [8-11]. The use of MEM mode in nowadays advanced LEEM microscopes allows both high-lateral resolution and permits the combination of MEM \nwith other complementary imaging modes of the LEEM \nsystem. Changing the operation mode of the microscope from the electron reflection mode to the established photoemission PEEM mode makes it possible to image also the magnetic domain structure with the same experimental setup [12], i.e., without any modification of \nthe measurement configurati on. Owing to these unique \nfeatures, we anticipate that the combination of LEEM and \nPEEM will become the method of choice for future experimental investigations on multiferroics, in particular for studies on dynamic processes in multiferroics, such as domain wall propagation or magnetoelectric switching \nprocesses. \n A 70 nm-thick antiferromagn etic-ferroelectric BiFeO\n3 \n(BFO) film was grown with pulsed laser deposition on a (001)-oriented SrTiO\n3 substrate coated with a conductive \nbuffer layer of La 2/3Sr1/3MnO 3 (LSMO). A detailed \ndescription of the growth conditions and the film \ncharacteristics can be found in Ref. [13]. ‘Up’ and ‘down’-polarized ferroelectric strip domains were written into the \nBFO layer by alternate applications of negative and positive voltage (± 8 V) between the conductive PFM tip and the LSMO base electrode. Such well-defined \ngeometric domain patterns can be easily identified in the \nLEEM system. \n The PFM-written ferroelectric domains are imaged in \nthe electron microscope by placing the specimen surface at a potential slightly more negative than the electron source. \nIn this case, the incident u ltraslow electrons (energy below \n3 eV) do not penetrate the specimen surface as they are reflected shortly before reac hing it. An electric field E \napplied perpendicular to the specimen surface reaccelerates the reflected electrons towards the microscope imaging column. Atomic force microscopy (AFM) was performed \nto ensure that the PFM-writing did not alter the surface \ntopography of the BFO films [F ig. 1(a)]. Perfect agreement \nbetween the PFM ferroelectric domain patterns [Fig. 1(b)] and the observed MEM contrast [Fig. 1(c)] is found down to the sub-micron scale. Th e corresponding AFM images \ndemonstrate that the contrast  does not originate from \ntopography. This agreement between PFM and MEM \ncontrast is not specific to BFO. We have confirmed this result also in other systems su ch as Pb(Zr,Ti) layers and \nBaTiO\n3 (1-2 nm) ultra-thin films (not shown). The \nferroelectric contrast is easily observed at electron energies \nbelow 1 eV but the best contrast is obtained at 1-2 eV, \ndepending on the considered surface. \n  Figure 1  Comparison between (a) AFM topography images, (b) \nferroelectric domains imaged with PFM, and (c) the \ncorresponding MEM images of ‘up’ and ‘down’-polarized stripe \ndomains in BFO ranging from 20 µm to 400 nm. \nThe MEM image formation mechanism has been \ndescribed, e.g., Nepijko et al. [14] with calculations on the \nshift of the reflected electron trajectories induced by local \nmicrofields. These authors have also described the specimen surface potential distribution by using the current density distribution on the microscope screen [15]. \nAnother convenient way to el ucidate the ferroelectric \ncontrast mechanism in MEM consists in representing three-dimensional equipotential surfaces (isosurfaces) U = \nconst. In the case of an elect rostatically neutral and ideally \nflat sample exposed to an electric field oriented \nperpendicular to the surface, the isosurfaces are parallel to \nthe specimen surface; each one representing an energy level. Electrons accelerated towards the sample with a \ngiven energy reach the isos urface of the corresponding \nenergy value and are subseque ntly re-accelerated by the \nelectric field, which is by definition perpendicular to the \npotential isosurface. Ferroelectric domains with negative \nand positive surface charge distributions modify the \nelectrostatic isosurfaces near the surface leading to eggbox-like convex and concav e curvatures. The resulting \ncurved equipotential surfaces locally act as focussing or defocussing mirrors of the reflected electrons, thereby \nleading to dark or bright contrasts in the MEM image. The \ncurvature of the isosurfaces is most pronounced close to the specimen surface, and flattens gradually with \n(b)  (c) \n10 µm \n 5 µm \n 2 µm \n 0.4 µm (a) S. Cherifi et al,  Imaging ferroelectric domains using a low-energy electron microscope     R 3  \nincreasing distance. Therefore the contrast sensitivity of \nthe mirror mode depends strongl y on the distance at which \nthe electrons are reflected. Op timum contrast is obtained \nwith electron energies at whic h the reflection occurs in a \nregion where the isosufaces di splay pronounced  curvatures. \nIdeally, the point of reflection should only be about few \ntens of nanometres above the sample surface. An example \nof electrostatic potential is osurfaces calculated with the \nfinite element method is displayed in the abstract figure. A weaker contrast can also be  obtained at higher electron \nenergies in the standard LEEM mode (> 3 eV), where the electrons impinge the sample an d interact directly with the \nmaterial. In this case the cont rast arises from the electric \npotential variations experienced by the electrons inside the ferroelectric material and from field distortions close to the \ndomain boundaries which modify the trajectories of the backscattered electrons. In addition, when the energy of the incident electron beam is tuned to the low-energy \ncrossover of the secondary electron yield of the material, \nthe emitted secondary electrons  can be used to image the \nsurface. Low-resolution ferroel ectric contrast can also be \nobtained in this secondary el ectron emission mode due to \nthe polarization dependence of the emission threshold, as previously demonstrated using UV-PEEM [16]. Such \ncontrast can also be obtained in XMLD-PEEM mode, since \nx-ray linear dichroism is not only sensitive to the antiferromagnetic order but also  to the electric polarization \n[4]. In contrast to this, the mirror electron mode is \nexclusively sensitive to the ferroelectric contribution [Fig.2 (a)]. In the secondary electron emission mode, the lateral \nresolution is however about tw o to three times lower than \nin the MEM reflection mode [Fig.2 (a,b)] because of the large solid angle of electro n emission and the energy \nspread of the emitted electro ns, leading to spherical and \nchromatic aberrations. From line scans across opposite ferroelectric domains we could deduce that the lateral \nresolution in the MEM mode is better than 15 nm. While \nultimate resolution in MEM has not yet been quantitatively demonstrated, a lateral resolution of few nanometres has been predicted by Remfer and Griffith [17]. \nFigure 2  (a) Low-energy electron microscopy (MEM-mode) \nimage of PFM-written perpendicular ferroelectric domains and \n(b) the corresponding XMLD-PEEM image displaying the local electron emission yield obtained with X-rays tuned at the FeL\n3 \nmultiplet in BFO. The linear polarization vector E is oriented \nparallel to the film plane. Spectroscopic LEEM can be used to \nimage (a) reflected electrons or  (b) x-ray induced photo-emitted \nelectrons as illustrated in the sketches. Imaging ferroelectric doma ins with slow electrons \noffers several advantages: (a) MEM is a ‘zero-impact’ technique where charging eff ects are minimized since the \nelectron-probe does not penetrate or even reach the specimen surface; (b) No partic ular sample preparation is \nneeded for imaging (such as thinning procedures in \ntransmission microscopy) and the base electrode \n(necessary for PFM) is not required for MEM, thereby allowing also the analysis of bulk materials; (c) Short acquisition times in the quasi-static mode (e.g., during in \nsitu growth) and fast time-resolved measurements in the \npump-probe scheme are both possible [18]; (d) In addition \nto ferroelectric domains, spectroscopic-LEEM instruments \n[12] make it also possible to image magnetic domains with the same setup in static (Fig.2b) or time-resolved X-PEEM mode. High-resolution imaging of ferromagnetic domains is also accessible in the LEEM system when using a spin-polarized electron source in the SP-LEEM mode. \nIn conclusion, we have demonstrated the imaging of \nferroelectric domains with low-energy electron microscopy in the mirror mode down to the sub-micron scale. This \nsetup is particularly versatile for the study of magnetic multiferroics and should allow for fast imaging of both ferroelectric and magnetic domains. The possibility of \napplying in situ magnetic and electric fields further \nenhances the potential of this instrumentation for future investigations on the magnetoelectric coupling and to dynamic processes in multiferroics.  \nAcknowledgements   The authors thank the team of \nNanospectroscopy beamline for the assistance during the \nexperiment at Elettra. SC ta nks A. Fraile-Rodriguez and F. \nNolting for the support during the first exploratory experiment at the SLS. \nReferences \n[1] N. A. Spaldin and M. Fiebig, Science 309, 391 (2005). \n[2] S. V. Kalinin and D. A. Bonnell, Phys. Rev. B 65, 125408 \n(2002) \n[3] Y. -H. Chu et al., Nature Mater. 7, 478 (2008). \n[4] T. Zhao et al., Nature Mater. 5, 823 (2006). \n[5] L. Mayer, J. Appl. Phys. 26, 1228 (1955). \n[6] E. Bauer, Rep. Prog. Phys. 57, 895 (1994). \n[7] E. Bauer, Surf. Rev. Lett. 5, 1275 (1998). \n[8] G. V. Spivak et al., Sov. Phys. -Crystallogr. 4, 115 (1959). \n[9] K. N. Maffitt, J. Appl. Phys. 39, 3878 (1968). \n[10] F. L. English, J. Appl. Phys. 39, 128 (1968). \n[11] Le Bihan et al., Ferroelectrics 13, 475 (1976). \n[12] Th. Schmidt et al., Su rf. Rev. Lett. 5, 1287 (1998). \n[13] H. Béa et al., Appl. Phys. Lett. 87, 072508 (2005). \n[14] S. A. Nepijko et al., J. Microsc. 203, 269 (2001). \n[15] S. A. Nepijko and G. Schönhense, J. Microsc., doi: \n10.1111/j.1365-2818.2009.03340.x \n[16] W. -C. Yang et al., Appl. Phys. Lett. 85, 2316 (2004). \n[17] G. F. Rempfer and O. H. Griffith, Ultramicroscopy 4, 35 \n(1992). \n[18] H. Kleinschmidt and O. Bost anjoglo, Rev. Sci. Instrum. 72, \n3898 (2001). \n(b) \n (a) \n2µm "    },    {        "title": "2010.11739v1.Structural_and_Magnetic_Characterization_of_CuxMn1_xFe2O4__x__0_0__0_25__Ferrites_Using_Neutron_Diffraction_and_Other_Techniques.pdf",        "content": " \n Structural and Magnetic Characterization  of Cu xMn 1-xFe2O4 (x= 0.0, 0.25) Ferrites Using Neutron \nDiffraction and Other Techniques  \nI.B.Elius1†, A.K.M. Zakaria1,5, J.Maudood1, S. Hossain1, M.M. Islam2, A. Nahar3, Md Sazzad Hossain4, \n I. Kamal5 \n1Institute of Nuclear Science and Technology, Bangladesh Atomic Energy Commission, GPO Box \nNo.3787, Dhaka -1000 Bangladesh  \n2Department of Applied Chemistry and Chemical Engineering, University of Dhaka, Dhaka -1000  \n3Materials Science Division, Atomic Energy Centre, Dhaka -1000  \n4 Department of Physics , University of Dhaka, Dhaka -1000 \n5Bangladesh Atomic Energy Commission, Agargaon, Dhaka -1207  \n \n†Corresponding author: iftakhar.elius@gmail.com  \nABATRACT  \nManganese ferrite (MnFe 2O4) and copper doped manganese ferrite (Mn 0.75Cu 0.25Fe2O4) soft \nmaterials were synthesized through solid -state sintering method. The phase purity and quality were \nconfirmed from x -ray diffraction patterns. Then the samples were subjected to neutron diffraction \nexperiment and the diffraction data were analyzed using FullProf software package. The surface \nmorphology of the soft material samples was studied using a scanning electron microscope (SEM). \nCrystal parameters, crystallite parameters, occupancy at A and B sites of the spinel structure, \nmagnetic moments of the atoms at various lo cations, symmetries, oxygen position parameters, bond \nlengths  etc. were measured and compared with the reference data. In MnFe 2O4, both octahedral \n(A) and tetrahedral (B) positions are shared by Mn2+ and Fe2+/3+ cations, here A site is \npredominantly occupi ed by Fe2+ and B site is occupied by Mn at 0.825 occupancy. The Cu2+ ions in \nCu 0.25Mn 0.75Fe2O4 mostly occup y the B site. Copper mostly occupy the Octahedral (16d) sites. The \nlength of the cubic lattice decreases with the increasing Copper content. The magnetic properties , \ni.e. A or B site magnetic moments,  net magnetic moment etc.  were measured using neutron \ndiffraction analysis and  compared with the bulk magnetic properties measured with VSM studies.  \nKeywords:  Spinel Ferrites, Neutron Diffraction, structural parameters, magnetic materials , Electron \nmicroscopy .  \n1. Introduction  \nManganese ferrites  (MnFe 2O4) are soft ferrite \nmaterials that have properties like high \nsaturation magnetization,  high permeability, low \ncoercivity (H c), low magnetostriction, low \nanisotropy, high curie temperature (T c), high \nelectrical resistivity etc. Thus soft magnetic \nmaterials have wide use in computer memory \ndevices, microwave devices, RF -coil fabrication, \nantennas, transformer cores, magnetic recording \nmedia etc. [1] Since the last few decades , ferrites \nhave also bee n used in wastewater treatment \nprocesses, carbon dioxide decomposition for the \nutilization of carbon as solar hydrogen  carriers, \nhybridization process for mixing solar and fossil fuel sources , and conversion  of solar energy  into \nhydrogen energy [2].Ferrites are also used in \nbiomedical sector for drug delivery, to mark \nparticular cells explicitly , peptide synthesis, for \nenhancement of X -ray imaging, MRI, sono -\nimaging, in tumor treatment etc. [3] \nSince Bragg and Nishikawa determined the \nspinel structure  in 1915 [4], undoubtedly , spinel \nferrites are one of the most studied clas ses of \nmaterials because of its novel magnetic and \nelectric properties. Spinel ferrites are in general \nrepresented by the formula AB 2O4. In the \nformula AB 2O4, ‘A2+’ are divalent cations  (i.e. \nMn2+, Zn2+, Ni2+, Fe2+ etc.) which occupy the \ntetrahedral interstitial positions . On the other \nhand,  ‘B3+’ are trivalent cations (i.e. Fe3+, Mn3+,  \n etc.) that occupy the octahedral sites.  However,  \nthis general formula  is not always necessarily \nfollowed ; trivalent cations can take over \ntetragonal sites , and as a result , the divalent ions \nare made to occupy the octahedral sites i mproper  \nfraction making the spinel structure fractionally \nor even fully inverted [5]. T he cation \nconcentrations of spinel ferrites depend upon \nfactors like  cations, their fractions, method of \nsynthesis , which may eventually show different \nstructural, magnetic , and electrical properties.    \nOne of the essential factors that control different \nproperties of ferrites is the structural \narrangements of the cations. Hence, in this \nstudy, various structural parameters by Rietveld \nrefinement of the XRD pattern and neutron \ndiffraction analysis were determined and \ncompared with the theoretical calculations. The \nparameters include the cell parameter, oxygen \nposition parameter, space group, the bond \nlengths, and interaction ang les. Moreover, the \nM-H curves were determined to study the impact \nof the Cu -doping in the samples.    \n \n2. Experimental  \nThe polycrystalline samples of MnFe 2O4 and \nMn 0.75Cu0.25Fe2O4 spinel oxides were prepared \nby conventional solid -state sintering method at \nthe sample preparation laboratory of Institute of \nNuclear Science and Technology, Atomic \nEnergy Research Establishment (AERE), \nBangladesh Atomic Energy Commission  \n(BAEC) . High purity oxides of Fe 2O3 (99.00%), \nCu(II)O ( 99.00% ), MnO 2 (99.00% ) Sigma -\nAldrich, UK, were mixed thoroughly by \nmaintaining the stoichiometric proportions using \nan agate mortar and pestle for 2h. Then the \nmixtures were ground for 6 h in a stainless -steel \nball mill. To ensure fine mixing, a small amount \nof distilled water  was used as a milling fluid. \nThen the mixture was dried using a magnetic \nheater in the air until it turned into powder. The \nmixture was then calcined at 1000°C for 12 \nhours in the air. The temperature was raised at a \nrate of 2°C per minute and after heati ng the \ncooling rate was 4°C per minute. Then the \nmixtures were mixed again in an agate mortar \nand pressed into pellets using a hydraulic press. Then the pellets were heated in a muffle furnace  \nwhere  the final firing temperature was 1050°C \nfor MnFe 2O4 and M n0.75Cu0.25Fe2O4 were heated \nat a final temperature of 1100°C for 24 h. The \ntemperature was raised at a rate of 2°C per \nminute and after heating , the cooling rate was \n4°C per minute.  \nTo determine  the phase purity and quality , the \nsamples were subjected to X -ray diffraction \nexperiment at CARS, University of Dhaka with \nCu(Kα)  radiation of wavelength 1.54178 Å in \nthe span of  10°≤2θ≤70° with a step size of \n0.02°. Both the diffraction patterns exhibit ed \nsharp peaks corresponding t o the characteristic \npeaks of cubic spinel structure.  \nNeutron diffraction analysis is a unique \ntechnique which can provide insights into the \nmagnetic structure of the ferromagnetic , anti-\nferro magnetic  or paramagnetic materials. To \ninvestigate the magnetic structure along with the \nmolecular structure , the samples were subjected \nto neutron diffraction experiment at Savar \nNeutron Diffractometer (SAND) which utilizes \nthermal neutron beam emerging from TRIG A \nMark-II research reactor at Atomic Energy \nResearch Establishment (AERE), Savar. The \nmachine is a set of 15 3He2 gas-filled neutron \ndetectors, which can maneuver around the \nsample table from 2θ range of 5 ˚ to 115˚. The \npowder sample was kept in a Vanadium  can (as \nVanadium  is transparent to thermal neutrons), on \na rotating table . The neutron beam is \nmonochromated using a set of silicon single \ncrystal to a single wavelength beam of λ = \n1.5656  Å. The readings of the fifteen parallel \ndetectors are then averaged and noise from stray \nradiations are suppressed at a data accusation \nunit[6].  \nAfter the neutron diffraction experiment,  the \ndiffraction data w ere refined using Reitveld  \nbased refinement code FullProf. The s tructural \nsymmetry, cell parameters, atomic position \nparameters, magnetic moments of different ions \nat different positions were measured using this \ncode. \n \n440  \n Fig.1: X-ray diffraction patterns of (i) MnFe 2O4 and (ii) Mn 0.75Cu0.25Fe2O4, fitted with FullProf refinement \nsoftware. The red points are observed data points, the dark solid line indicates the refined model, the \ngreen markers are the peak locations and the blue points below are the difference curve between the Y obs \nand the Y calc. \n \n \n111 220 311 \n222 400 \n220 333 \n511 440 (i) \n \n111 220 311 \n222 400 \n220 333 \n511  (ii) \n  \n  \n \n \nFig. 2:  Structure of MnFe 2O4 crystal generated \nfrom the refinement of XRD data using VESTA \nsoftware.  \nAfter that , Scanning Electron Micro scopy  \n(SEM)  experiment  were done  using an FEI \nInspect S50 to study the grain size distribution as well as the surface properties of the materials. \nThe images were taken at 5000 times \nmagnification applying 12.50 kV potential \ndiffere nce for MnFe 2O4 and 20.00 kV for \nCu0.25Mn 0.75Fe2O4.    \n3. Results and Discussion  \n3.1 XRD Analysis  \nThe X -ray diffraction patterns of the samples \nwere yielded from a Rigaku X -ray \ndiffractometer  within  a 2θ range of 10° to 70°. \nThe XRD patterns show prominent peaks at the \nlocations identical to that of spinel ferrites \nhaving Fd-3m crystal symmetry. The a bsence of \nnon-identical peaks indicates the phase purity of \nthe synthesized samples. The indexing of the \nXRD peaks was done with the software \n‘Chekcell ’, a small but elegant software that \naffirmed the assumed symmetry and provided a \npreliminary idea about the cel l parameters [7]. \nThe refined parameters are presented in table 1.  \n \nTable 1 : The Rietveld refined parameters from XRD pattern s. \n \n3.2Cation distribution  \nThe cation distribution of the spinel ferrites is \nsensitive to the observed and calculated intensity \nratios of peaks at (220), (400) and (440) planes. \nThis method selects ratios of pairs of  intensities,  \n𝑰𝒉𝒌𝒍𝑶𝒃𝒔\n𝑰𝒉′𝒌′𝒍′𝑶𝒃𝒔= 𝑰𝒉𝒌𝒍𝑪𝒂𝒍\n𝑰𝒉′𝒌′𝒍′𝑪𝒂𝒍 (1) \n where the relative integrated intensity of the \nXRD peaks can be calculated from the following \nformula  \n𝐼ℎ𝑘𝑙=|𝐹|2𝑃𝐿𝑝 \n (2) \nwhere F is the structure factor, P is the \nmultiplicity factor  and Lp is the Lorentz \npolarization factor which in fact depends solely \non Bragg’s angle 2θ, as stated below [8] \nSample  Symmetry  Cell \nparameter,  \na (Å)  Oxygen position \nparameter,  \nu (𝟒𝟑𝒎) X-ray density,  \ndxray  \n(gm/cc)  \nMnFe 2O4 \nFd3̅m 8.377974  0.397837253  3.63826  \nMn 0.75Cu0.25Fe2O4 8.402696  0.391561301  3.63985   \n 𝐿𝑝= 1+ 𝑐𝑜𝑠22𝜃\n𝑠𝑖𝑛22𝜃𝑐𝑜𝑠  2𝜃  \n (3) \nConsidering all possible cation distributions of \nMn2+, Fe2+, Fe3+, Cu2+ at tetrahedral and \noctahedral positions both the composition \nminimizing the agreement factor  (R), yield the \ncorrect cation distribution.  𝑅=|𝐼ℎ𝑘𝑙𝑂𝑏𝑠\n𝐼ℎ′𝑘′𝑙′𝑂𝑏𝑠 −𝐼ℎ𝑘𝑙𝐶𝑎𝑙\n𝐼ℎ′𝑘′𝑙′𝐶𝑎𝑙 |  \n (4) \nThe cation distribution is presented below in \ntable 2.  \n \nTable 2: The crystallographic parameters, peak positions, half-width parameters , along with the observed \nand calculated intensities of the major peaks.  \nSample  obs h k l Multiplicity  dhkl Half -width \nparam eter \n(W) Observed \nintensity \n(Iobs) Calculated \nIntensity \n(Iclac) MnFe 2O4 1 1 1 1 8 4.861413  0.102705  8.1 7.3 \n2 2 2 0 12 2.976995  0.138635  22.6 21.7 \n3 3 1 1 24 2.53879  0.148486  38.8 36.5 \n4 2 2 2 8 2.430707  0.150685  6.6 7 \n5 4 0 0 6 2.105053  0.156895  19 13.5 \n6 3 3 3 8 1.620471  0.156264  2.5 2.3 \n7 4 4 0 12 1.488498  0.148942  35.8 32.2 Cu0.25Mn 0.75Fe2O4 1 1 1 1 8 4.84621  0.114235  9.9 7.9 \n2 2 2 0 12 2.967685  0.145975  26.9 26.7 \n3 3 1 1 24 2.530851  0.154694  90.5 83.9 \n4 2 2 2 8 2.423105  0.156778  8.3 6.1 \n5 4 0 0 6 2.098471  0.162237  21.3 16.7 \n6 3 3 3 8 1.615403  0.16059  2.8 2.4 \n7 4 4 0 12 1.483843  0.153124  36.7 33.4 \nThe peak heights of the XRD patterns were \nmeasured using the WinPlotr  software and then \nthe ratios (observed) were calculated using equation 4 for the selected planes, which are \npresented below in the table 3. The calculated \nvalues are from the refined model.  \nTable 3: The calculated cationic distributions of the samples and th e ratios of intensities of (220), (440), \n(400) peaks.  \nSample  A site  B site  I220/I440 I220/I400 \nObs Calc  Obs Calc  \nMFO  Mn 0.179Fe0.817 Mn 0.825Fe1.178 0.6312  0.6739  1.8 1.607  \nCMFO  Mn 0.245Fe0.76225 Cu0.005 Mn 0.505Fe1.2341Cu0.245 0.7329  0.7994  1.46 1.59 \n \nThe I220/I440, I220/I400 ratios indicate the accuracy \nof the theorized cation distribution among the A \nand B sites.   \n  \n 3.3 Calculation of Lattice Parameter using N -R \nfunction  \nThe angular positions of the peaks can be used \nto determine the cell parameter by Nelson -Riley  \n(N-R) method [9]. The cell parameter (a) is \ndetermined from every set of corresponding dhkl \nspacing and h,k,l values for each peak , then \nplotted against the N -R function as defined \nbelow,  𝐹𝑁𝑅=(cos2𝜃\n𝑠𝑖𝑛𝜃)+(cos2𝜃\n𝜃) \n (5) \nThe y -intercept of the linear regression of the \ncell parameter vs . FNR plot gives the exact value \nof the cell parameter. Figure 3 shows the \ndetermination of the cell parameter  via the \naforementioned method and the values of a  \ndetermined via this method  are listed in table 4.  \n \nFig. 3:  Lattice parameter vs. Nelson -Riley \nfunction of (i) MnFe 2O4 and (ii) \nCu0.25Mn 0.75Fe2O4 3.4 Calculation of cell parameter and other \nstructural parameters  \nThe cell parameter can also be calculated \ntheoretically from the cation -anion distances \nusing the formula below , which can be  \ncalculated from the cationic compositions \nmeasured experimentally by any other means. If \ndA-O and dB-O are the average cation -anion bond \nlengths of A and B sites respectively, the \nrelation between lattice parameter,  a and the \nbond lengths can be expressed through the \nfollowing formula,  \n𝑎𝑐𝑎𝑙𝑐 = 8\n9(√3𝑑𝐴−𝑂+ 3𝑑𝐵−𝑂) \n (6) \nThere is more than one type of atoms occupying \nthe same position . So weighted mean values of \nthe crystal/ionic radii calculated by R. D. \nShanon  [10] were used to calculate effective \nvalues of dA-O and d B-O. The composition \ncalculated by Rietveld refinement method was \nused to determine the ionic distances.\n  \nTable 4: The cell parameters determined by N -R method, theoretically calculated form ionic distances \ncompared with the cell parameter, oxygen position par ameter values calculated with the Rietveld method.  \nSample  aNR \n(Å) Ionic distances  acalc \n(Å)  arietveld  \n(Å) rA \n(Å) rB \n(Å) dAO \n(Å) dBO \n(Å) \ny= 8.38047 -(0.00685)x  \nR2 (COD) = 0.46379  \ny= 8.40921 -(0.00021)x  \nR2 (COD) = 0. 22941  \n \n (i) \n(ii)  \n MnFe 2O4 8.38047  2.03726  1.96188  8.344086958  8.377974  0.77726  0.69282  \nMn 0.75Cu0.25Fe2O4 8.40921  2.05056  1.96207  8.36307995  8.402696  0.790555  0.6922665  \nThe effective radii of the tetrahedral and \noctahedral sites were again calculated using the \nfollowing formulae , \n𝑟𝐴=𝐶(𝑀𝑛𝐴+2)∙𝑟(𝑀𝑛𝐴+2)+ 𝐶(𝐶𝑢𝐴+2)∙𝑟(𝐶𝑢𝐴+2)\n+𝐶(𝐹𝑒𝐴+3)∙𝑟(𝐹𝑒𝐴+3) (7) \n 𝒓𝑩=𝟏\n𝟐[𝑪(𝑴𝒏𝑩+𝟐)∙𝒓(𝑴𝒏𝑩+𝟐)+ 𝑪(𝑪𝒖𝑩+𝟐)∙𝒓(𝑪𝒖𝑩+𝟐)+\n𝑪(𝑭𝒆𝑩+𝟑)∙𝒓(𝑭𝒆𝑩+𝟑)] (8) \n The crystal radii of Mn2+, Cu2+, Fe3+cations at A \nsite have coordination number 4 compared to \nthese ions at site B having coordination number \n6.  \nThe position of the O2- anion in the face -\ncentered cubic (fcc) lattice is referred to as a \nquantity called Oxygen position parameter or \nanion param eter, u. For ideal spinel structures , \nuideal is 0.375  [11,12] . To accommodate \nsubstituted cations, the oxygen ions reposition \nthemselves , which gives rise to change in the \noxygen position parameter. The relation between \neffective radii r A, rB and r O-2 are as follows, \nwhich can be further exploited to calculate the \nvalue of u.  \n𝑟𝐴(𝑇𝑒𝑡)=(𝑢−1\n4)𝑎√3−𝑟𝑂−2 \n (9) \n𝑟𝐵(𝑂𝑐𝑡 )=(5\n8−𝑢)𝑎−𝑟𝑂−2 \n (10) \nEvidently, the value of u is larger than that of \nideal spinel structure , because of  the \nreplacement of Fe3+ with larger Mn2+ ions and \nlarger Cu+2 ions.  \nThe values of the tetrahedral and octahedral \nbond lengths ( dAL and dBL), tetrahedral edge ( dAE) \nand shared and unshared bond lengths ( dBE and \ndUBE) can be calculated using the following \nformulae,  𝑑𝐴𝐿=𝑎√3(𝑢−1\n4) (11) \n𝑑𝐵𝐿=𝑎[(3𝑢2−(11\n4)𝑢+ 43\n64]1/2\n \n (12) \n𝑑𝐴𝐸= 𝑎√2(2𝑢−1\n2) \n (13) \n𝑑𝐵𝐸=𝑎√2 (1−2𝑢) \n (14) \n𝑑𝐵𝐸𝑈 =𝑎[4𝑢2−3𝑢+11\n16]1\n2\n \n (15) \nThe hopping lengths, L A and L B between the \nmagnetic ions located at A site and B site \nrespectively can be calculated from the \nequations below , \n𝐿𝐴=𝑎√3\n4 \n (16) \n𝐿𝐵=𝑎√2\n4 \n  (17) \n \nThe bond lengths, angles  and hopping lengths \nare listed in table 5.  \nReduction of  θ1, θ 2 and θ5 are indicative of \nstrengthening A -A, A -B interaction, while on \nthe other hand increase in θ 3, θ 4 indicates \nstrengthening of B -B interaction. These effects \nof super -exchange interactions between A -sites \nand B -sites ultimately decrease magnetization.  \nIn this case, it can be seen as the Cu2+ was \nincorporated θ1, θ2 and θ 5 increase and the other \ntwo angles got reduced. The change s in the \nlengths are presented in ta ble 5.  \n  \n Table 5: The calculated values of the ionic distances and the bond angles  along with the ideal values of \nthe bond angles  [13]. \nx dAL \n(Å)  dBL \n(Å)  dAE \n(Å)  dBE \n(Å)  dBUE  \n(Å)  θ1 \n(°) θ2 \n(°) θ3 \n(°) θ4 \n(°) θ5 \n(°) \nIdeal  - - - - - 125.150  154.560  90.000  125.033  79.633  \n0.0 1.9223  2.0338  3.1391  2.7850  2.9647  122.8732  142.9196  93.5867  126.0800  73.2277  \n0.25 1.8636  2.0858  3.0432  2.9182  2.9810  124.4189  150.0871  91.2207  125.5486  77.4939  \nThe cation -oxygen distances p,q,r,s, cation –\ncation distances b, c, d, e, f and the interaction angles were calculated using the relations listed \nin table 6. \n \nTable 6 :The f ormula for the cation -anion distances, cation - cation distances and the bond angles [14]. \n \nTable 7:  Various possible distances between the ions in spinel structure.  \nx p(Å)  q(Å)  r(Å) s(Å) b(Å)  c(Å) d(Å)  e(Å) f(Å) \nMnFe 2O4 2.0319  1.9223  3.6809  3.6639  2.96206  3.47332  3.62776  5.44165  5.13044  \nMn 0.75Cu0.25Fe2O4 2.0496  1.9077  3.6529  3.6679  2.97080  3.48357  3.63847  5.45771  5.14557  \n \n Cation -anion distances  \nM-O (Å)  Cation - cation distances  \nM-M(Å)  Bond Angles  \nθ (°) \n𝑝=𝑎( 5\n8−𝑢) 𝑏=√2\n4𝑎 𝜃1= (𝑝2+ 𝑞2−𝑐2\n2𝑝𝑞) \n𝑞=𝑎√3(𝑢−1\n4) 𝑐=√11\n8 𝜃2= (𝑝2+ 𝑟2−𝑒2\n2𝑝𝑟) \n𝑟=𝑎√11(𝑢−1\n4) 𝑑=√3\n4𝑎 𝜃3= (2𝑝2−𝑏2\n2𝑝2) \n𝑠=𝑎√3(𝑢\n3+1\n8) 𝑒=3√3\n8𝑎 𝜃4= (𝑝2+ 𝑠2−𝑓2\n2𝑝𝑠) \n 𝑓=√6\n4𝑎 𝜃5= (𝑟2+ 𝑞2−𝑑2\n2𝑟𝑞)  \n `  \nFig. 4:  The bond lengths and the interaction angles of an ideal spinel structure . A and B are cations (Cu2+, \nMn2+ or Fe2+/3+) represented by blue and brown balls respectively  and the oxygen anion  (O-) is represented \nby O.  \n3.5 Neutron Diffraction  (ND)a nalysis, structure refinement  and magnetic properties  \n \n(i) \np \nq p \nr p \np p \ns r q A \nB \nO A-B \n \n \n \n \nAB B-B \n \n \n \n \nAB A-A \n \n \n \n \nAB c \ne \nb r \nd  \n  \n(ii) \nFig. 5: The fitted neutron diffraction patterns of (i) Manganese Ferrite (MnFe 2O4) and (ii) Cu doped \nManganese Ferrite (Mn 0.75Cu0.25Fe2O4). The red dots represent the observed data and the solid  black  line \nrepresents the calculated pattern by FullProf  Rietveld refinement software. The first row of blue markers  \nindicates the structural peaks and the red markers in the  row below represents the peaks from the \nmagnetic structure.  \nThe magnetic structure of a material may \nconform with or differ f rom the molecular \nstructure of the parent material. In this case, \nfrom refinement , it was seen that the magnetic \npeaks (indicated by the red ticks in the fig. 5) \ncoincide with the structural peaks (indicated \nwith the blue ticks). So the structure of both the \nmaterials is commensurate and the magnetic \npropagati on vector, K is (0,0,0)  [15]. The \nmagnetic moments of site A (1/ 8, 1/8, 1/8) and \nsite B  (1/2, 1/2, 1/2)  calculated from FullProf code are presented in table 8 . The negative sign \nof the moment of site A indicated  that it is \nantiparallel to the orientation of the B site \nmoment. As all the ca tions here had a non-zero \nmagnetic moment (Cu, Mn and Fe) , Neel’s co -\nlinear model was considered appropriate to \nexplain the magnetism of the materials.  The \nresults are compared with the magnetic \nmeasurements with the VSM [16–18].  \n \n \nTable 8:  The magnetic moments of A and B sites and net magnetic fields of manganese ferrite and copper \ndoped manganese ferrite samples, calculated from neutron diffraction experiments.  \nCation distribution  Moment of  \nsite A, m A \n(µB) Moment of  \nsite B, m B \n(µB) Net magnetic \nmoment,  \nmnet =| m A - mB | \n(µB) \n \n (Mn 0.179Fe0.817)A[Mn 0.825Fe1.178]BO4 -5.8305  8.6839  2.8534  \n(Mn 0.245Fe0.76225 Cu0.005)A[Mn 0.505Fe1.2341Cu0.245]BO4 -5.9242  7.60073  1.6765  \n3.6 The refinement parameters  \nThe measure ment  of the accura cy of  a Rietveld \nbased fitting is represented by the ‘Goodness of \nfit’ parameters . The Rp, Rw, R e, Rf, RBragg and  χ2 \nare profile factor, weighted profile factor, \nexpected weighted profile factor, \ncrystallographic Rf factor , Bragg’s R  factor and \nthe reduced Chi -square value  respectively  \n[19,20] . The refinement parameters of XRD and neutron diffraction pattern of the samples are \nlisted in table 9 along with the formulae used by \nthe refinement software . The X -ray data has \nsingle -phase hence the overall χ2 values are \nconsiderably below 2 , which is indicative of \ngood agreement between the model and the \nXRD pattern. Unlike XRD , the neutron \ndiffraction data has not only structural phase but \nalso the magnetic phase ; hence χ2 value  is \nslightly over 3, in which the structural \nparameters investigated accords with the X -ray \ndiffraction studies.  \nTable 9: The goodness of fit parameters of the XRD and Neutron diffraction pattern refinements of the \nsamples.  \nR-factors  MnFe 2O4 Mn 0.75Cu 0.25Fe2O4 \nXRD  Neutron  \nDiffraction  XRD  Neutron  \nDiffraction  \nRp [∑|𝑌𝑖𝑜𝑏𝑠−𝑌𝑖𝑐𝑎𝑙𝑐| 𝑖\n∑𝑌𝑖𝑜𝑏𝑠\n𝑖] \n 59.5 13.8 54.3 15.9 \nRw \n[∑𝑤𝑖|𝑌𝑖𝑜𝑏𝑠−𝑌𝑖𝑐𝑎𝑙𝑐|2\n𝑖\n∑𝑤𝑖𝑖𝑌𝑖𝑜𝑏𝑠2]1\n2\n 45.9 13.4 48.4 15.6 \nRe \n[𝑁−𝑃+𝐶\n∑𝑤𝑖𝑖𝑌𝑖𝑜𝑏𝑠2]1\n2\n 43.3 7.4 44.6 7.89 \nRf ∑ ||𝐹ℎ𝑘𝑙𝑖𝑛|2−|𝐹ℎ𝑘𝑙𝑜𝑢𝑡|2| ℎ𝑘𝑙\n∑ |𝐹ℎ𝑘𝑙𝑖𝑛|2\nℎ𝑘𝑙 13.7 3.72 11.6 3.34 \nRBragg  [∑|𝐼𝑘𝑜𝑏𝑠−𝐼𝑘𝑐𝑎𝑙𝑐| 𝑘\n∑𝐼𝑘𝑜𝑏𝑠\n𝑘] 15.3 5.79 12.6 5.08 \nχ2 (𝑅𝑤𝑃\n𝑅𝐸)2\n 1.122  3.28 1.18 3.893  \n \n3.7 Magnetic measurements  using VSM  \nThe magnetic properties of spinel ferrites largely \ndepend  on the cation distribution (the \ndistributions of the substitutes in A or B position), which can be varied by synthesis \nmethod, annealing temperature, reactants etc. \nThe magnetic hysteresis loops (M -H) are given \nin figure  6. \n  \n  \nFig. 6:  Magnetic hysteresis, M(H)  curves of ( a) Manganese  Ferrite (MnFe 2O4) and (b) Cu doped \nManganese Ferrite (Mn 0.75Cu0.25Fe2O4) represented with blue circles and red squares respectively at \nTa=300K.  \nThe magnetic moment per unit formula can be \ncalculated using the following formula,  \n𝜂=𝑀𝑤𝑀𝑠\n5585 \n (18) Here , Mw is the molecular weight of the sample  \nand Ms is the saturation magnetization.   \n \nTable 10: The Magnetic properties of the samples.  \nSample  Saturation \nMagnetization,  \nMs (emu/gm ) Remnant \nMagnetization , \nMr (emu/gm ) Mr/Ms Coercive field, \nHc (Oersted ) Magnetic \nMoment per \nunit formula, 𝜂 \nMn 0.75Cu0.25Fe2O4 54.24861  3.873  0.07139  31.825  2.26103 2 \nMnFe 2O4 31.77113  2.574  0.08101  17.7528  1.311956  \nThe values of the magnetic properties like \nSaturation magnetization (M s), Remnant \nmagnetization (M r), their ratio, Coercive field (Hc), Magnetic moment per unit formula ( 𝜂) etc. \nwere in accordance with the values investigated \nby L. A. Kafshgari  et. al.  and M. Khaleghi et. al.  \n \n [21,22] , the difference in the v alues can be \nexplained from the different methods of \nsynthesis and annealing temperature. In the  afore \nmentioned works, the samples were synthesized via sol -gel, co -precipitation or hydrothermal \nmethod, though solid -state method is exclusively \nfor bulk syn thesis and widely used for its \nfeasibility and quality of yielded sample.  \n3.8 Scanning Electron Microscopy (SEM) studies  \n \n(i)  SEM image of MnFe 2O4 \n \n \n(ii)  SEM image of  Mn 0.75Cu0.25Fe2O4 \n \n  \n(iii-a)                                                                              (iii-b) \nFig.7: The scanning electron microscope images of the samples. (i) SEM image  of MnFe 2O4, (ii) SEM \nimage of  Mn 0.75Cu0.25Fe2O4, (iii) size distributions of the samples.  \nThe SEM images revealed the morphology of \nthe soft manganese ferrite samples. It showed \nthat the sample surface had large grain size with \nbroken edges. It also revealed nonporous and \nrough surface , which remained the same for both \ndoped and n on-doped material. But the \nmorphology of the materials changed with the \nincrement of  Cu concentration [23]. The major \nchange could be observed regarding grain size. \nIt could be seen from figure (iii) that the doped \nsample had more grains in the range of 0 -2 \nmicrometer and 2 -4 micrometer, while the \nundoped material had lower number of grains in \n0-2 micrometer region but higher number of \ngrains in 2 -4 micrometer region.  \n4. Conclusion  \nIn this study, MnFe 2O4 and Cu-doped MnFe 2O4 \nwere synthesized in the conventional solid -state \nsintering method. The XRD analysis confirms \nthe single -phase formation of the samples, and \nthe surface morphology study showed proper \ndensification of the particles. Furthermore, \nvarious parameters were studied  and compared  \nby the Rietveld refinement of the XRD pattern \nand ne utron diffraction analysis  to observe the \neffect of doping in the samples.  The observed  \nnet magnetic moment declined in both as Mn2+ \nion has larger magnetic moment compared to Cu2+. Though, saturation magnetization (M s) and \nremnant magnetization (M r) both were reduced , \ntheir ratio (M s/Mr) increased . The SEM \nmicrographs indicate s the abundance of particles \nhaving size 0 -2 µm and 4 -6 µm in  Cu doped \nMnFe 2O4 compared to MnFe 2O4.  \nAcknowledgements  \nThe research group is thankful to Centre for \nResearch Reactor (CR R) of Bangladesh Atomic \nEnergy Commission (BAEC) for the operation \nof research reactor during the experiments, Dr. \nSheikh Manjura Hoque, Head & CSO  of \nMaterials Science Division, AECD, BAEC for \nSEM and VSM facilities.  \n \nReferences  \n[1]  Goodarz, M., and E. B., 2012, \n“Crystalization in Spinel Ferrite \nNanoparticles”, In Advances in \nCrystallization Processes. InTech, pp \n341–380. \n[2]  Valenzuela, R., 2012, “Novel \napplications of ferrites”, Phy sics \nResearch International, 2012(Special \nIssue), pp 591839.  \n \n [3]  Hyeon, T., H.B. Na, and I.C. Song, 2009, \n“Inorganic Nanoparticles for MRI \nContrast Agents”, Advanced Materials, \n21(21), pp 2133 –2148.  \n[4]  Authier, A., 2013, “Early Days of X -ray \nCrystallogr aphy”, Oxford University \nPress.  \n[5]  Grimes, N.., 1975, “The spinels: versatile \nmaterials”, Physics in Technology, 6(1), \npp 22 –27. \n[6]  Kamal, I., S.M. Yunus, T.K. Datta, \nA.K.M. Zakaria, A.K. Das, S. Aktar, S. \nHossain, R. Berliner, and W.B. Yelon, \n2016, “A  high performance neutron \npowder diffractometer at 3 MW Triga \nMark -II research reactor in Bangladesh”, \nAIP Conference Proceedings,.  \n[7]  Azad, A.K., S.G. Eriksson, S.A. Ivanov, \nR. Mathieu, P. Svedlindh, J. Eriksen, and \nH. Rundlöf, 2004, “Synthesis, structu ral \nand magnetic characterisation of the \ndouble perovskite A 2MnMoO 6(A = Ba, \nSr)”, Journal of Alloys and Compounds, \n364(1 –2), pp 77 –82. \n[8]  Han, Q.J., D.H. Ji, G.D. Tang, Z.Z. Li, X. \nHou, W.H. Qi, S.R. Liu, and R.R. Bian, \n2012, “Estimating the cation distr ibutions \nin the spinel ferrites Cu 0.5-xNi 0.5ZnxFe2O4 \n(0.0≤x≤0.5)”, Journal of Magnetism and \nMagnetic Materials, 324(12), pp 1975 –\n1981.  \n[9]  Razik, N.A., 1985, “Precise lattice \nconstants determination of cubic crystals \nfrom x -ray powder diffractometric \nmeasurements”, Applied Physics A \nSolids and Surfaces, 37(3), pp 187 –189. \n[10]  Shannon, R.D., and C.T. Prewitt, 1970, \n“Revised values of effective ionic radii”, \nActa Crystallographica Section B \nStructural Crystallography and Crystal \nChemistry,.  \n[11]  Jahan, N ., A.K.M. Zakaria, F.U.Z. \nChowdhury, M.S. Aktar, and T.K. Datta, \n2017, “Study of the cation distribution \nand crystallographic properties of the \nspinel system NiCr xFe2-xO4 (0.0≤x≤1.0) by neutron diffraction”, Materials \nChemistry and Physics, 202, pp 225 –233. \n[12]  Khanam, S., A.K.M. Zakaria, M.H. \nAhsan, T.K. Datta, S. Aktar, S.I. Liba, S. \nHossain, A.K. Das, I. Kamal, S.M. \nYunus, D.K. Saha, and S. -G. Eriksson, \n2015, “Study of the Crystallographic and \nMagnetic Structure in the Nickel \nSubstituted Cobalt Ferrite s by Neutron \nDiffraction”, Materials Sciences and \nApplications, 06(04), pp 332 –342. \n[13]  Zipare, K. V., S.S. Bandgar, and G.S. \nShahane, 2018, “Effect of Dy -\nsubstitution on structural and magnetic \nproperties of Mn –Zn ferrite \nnanoparticles”, Journal of Rare  Earths, \n36(1), pp 86 –94. \n[14]  Pawar, R.A., S.M. Patange, A.R. Shitre, \nS.K. Gore, S.S. Jadhav, and S.E. \nShirsath, 2018, “Crystal chemistry and \nsingle -phase synthesis of Gd3+ \nsubstituted Co -Zn ferrite nanoparticles \nfor enhanced magnetic properties”, RSC \nAdvances, 8(44), pp 25258 –25267.  \n[15]  Zimmermann, A., 2014, “Representation \nTheory”,  19, pp 1 –48. \n[16]  Hanson, R.M., K. Momma, I. Aroyo, and \nG. Madariaga, 2016, “MAGNDATA: \ntowards a database of magnetic structures \n. I . The commensurate case research \npapers”, pp 1750 –1776.  \n[17]  Rana, M.U., M. Ul -Islam, I. Ahmad, and \nT. Abbas, 1998, “Determination of \nmagnetic properties and Y -K angles in \nCu-Zn-Fe-O system”, Journal of \nMagnet ism and Magnetic Materials, \n187(2), pp 242 –246. \n[18]  Smart, J.S., 1955, “The Néel Theory of \nFerrimagnetism”, American Journal of \nPhysics, 23(6), pp 356 –370. \n[19]  Rodríguez -Carvajal, 2014, “Tutorial on \nMagnetic Structure Determination and \nRefinement using Neutron Powder \nDiffraction and FullProf”,  \n[20]  Rodríguez -Carvajal, J., 1993, “Recent  \n advances in magnetic structure \ndetermination by neutron powder \ndiffraction”,  Physica B: Physics of \nCondensed Matter, 192(1 –2), pp 55 –69. \n[21]  Kafshgari, L.A., M. Ghorbani, and A. \nAzizi, 2019, “Synthesis and \ncharacterization of manganese ferrite \nnanostructure by co -precipitation, sol -\ngel, and hydrothermal methods”, \nParticulate Sci ence and Technology, \n37(7), pp 904 –910. \n[22]  Khaleghi, M., H. Moradmard, and S.F. Shayesteh, 2018, “Cation Distributions \nand Magnetic Properties of Cu -Doped \nNanosized MnFe 2O4 Synthesized by the \nCoprecipitation Method”, IEEE \nTransactions  on Magnetics , 54(1 ). \n[23]  Judith Vijaya, J., G. Sekaran, and M. \nBououdina, 2014, “Effect of Cu2+ doping \non structural, morphological, optical and \nmagnetic properties of MnFe 2O4 \nparticles/sheets/flakes -like \nnanostructures”, Ceramics International, \n41(1), pp 15 –26. \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n "    },    {        "title": "1706.08473v1.Magnetic_Proximity_Effect_in_Pt_CoFe2O4_Bilayers.pdf",        "content": "\t1\tMagnetic Proximity Effect in Pt/CoFe2O4 Bilayers Walid Amamou,1* Igor V. Pinchuk,2* Amanda Hanks,3,4 Robert Williams,3 Nikolas Antolin,4 Adam Goad,2,5 Dante J. O’Hara,1 Adam S. Ahmed,2 Wolfgang Windl,4 David W. McComb,3,4 and Roland K. Kawakami1,2** 1Materials Science and Engineering, University of California, Riverside, CA 92521 2Department of Physics, The Ohio State University, Columbus, OH 43210 3Center for Electron Microscopy and Analysis, The Ohio State University, Columbus, OH 43210 4Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210 5Department of Physics, University of Maryland, Baltimore County, MD 21250 \t Abstract We observe the magnetic proximity effect (MPE) in Pt/CoFe2O4 bilayers grown by molecular beam epitaxy (MBE). This is revealed through angle-dependent magnetoresistance measurements at 5 K, which isolate the contributions of induced ferromagnetism (i.e. anisotropic magnetoresistance) and spin Hall effect (i.e. spin Hall magnetoresistance) in the Pt layer. The observation of induced ferromagnetism in Pt via AMR is further supported by density functional theory calculations and various control measurements including insertion of a Cu spacer layer to suppress the induced ferromagnetism. In addition, anomalous Hall effect measurements show an out-of-plane magnetic hysteresis loop of the induced ferromagnetic phase with larger coercivity and larger remanence than the bulk CoFe2O4. By demonstrating MPE in Pt/CoFe2O4, these results establish the spinel ferrite family as a promising material for MPE and spin manipulation via proximity exchange fields.          * equal contributions **email: kawakami.15@osu.edu \t2\tSpin manipulation inside a nonmagnetic (NM) material using internal effective fields (spin orbit or exchange) is a very promising avenue toward the realization of next generation spintronic devices (spin transistors, magnetic gates, etc.) [1,2]. In particular, magnetic proximity effect (MPE) at the interface of a NM spin channel and a ferromagnetic insulator (FMI) is of great importance for generating exchange fields and induced ferromagnetism in the NM layer. Recently, spin manipulation by MPE has been realized in experiments that modulate spin currents in graphene on YIG (yttrium iron garnet) [3,4]. In addition, proximity exchange fields induced by FMI have been observed for graphene and monolayer transition transition metal dichalcogenides [5,6]. Among FMIs, members of the spinel ferrite family (MFe2O4, with M=Co, Ni, etc.) are attractive because their magnetic properties can be tuned by alloy composition [7,8] as well as epitaxial strain [9-11]. In particular, CoFe2O4 (CFO) is a hard ferrimagnetic insulator which exhibits high Curie temperature (728 K), spin-filtering properties [12-14], magneto-electric switching [15], and is readily integrated with practical spintronic materials (MgO, Fe, Cr). Unfortunately, all previous experiments have failed to observe MPE using CFO. To test for MPE in NM/FMI systems, Pt is widely used as the NM material due its closeness to fulfilling the Stoner criteria and thus allowing it to become ferromagnetically ordered at the interface with the FMI. Initial studies of Pt/CFO grown by pulsed laser deposition (PLD) utilized magnetotransport measurements and observed no MPE in the Pt layer [16]. Subsequent transport and element-specific magnetization measurements by x-ray magnetic circular dichroism (XMCD) also found no evidence for induced ferromagnetism in the Pt layer [17-20] contributing to a growing consensus that CFO cannot be used to obtain MPE. However, because the length scale of exchange interactions is on the order of angstroms, it should depend on the atomic structure and alternative growth methods may be needed for its realization. In this Letter, we utilize molecular beam epitaxy (MBE) to synthesize Pt/CFO bilayers and observe induced ferromagnetism (i.e. MPE) in the Pt layer at 5 K. This is revealed through angle-dependent magnetoresistance measurements, which isolate the contributions of induced ferromagnetism (i.e. anisotropic magnetoresistance, AMR) and spin Hall effect (i.e. spin Hall magnetoresistance, SMR) in the Pt layer. The observation of induced ferromagnetism in Pt via AMR is further supported by density functional theory (DFT) calculations and various control measurements including insertion of a Cu spacer layer to suppress the induced ferromagnetism. In addition, anomalous Hall effect (AHE) measurements show an out-of-plane magnetic hysteresis loop of the induced ferromagnetic phase with larger coercivity and larger remanence than the bulk CFO. By demonstrating MPE in Pt/CFO, these results establish the spinel ferrite family as a promising material for MPE and spin manipulation via proximity exchange fields. \t3\tThe CFO thin films are grown on MgO(001) substrates by reactive MBE (details in Supplementary Materials) and are characterized by reflection high-energy electron diffraction (RHEED), atomic force microscopy (AFM), x-ray diffraction (XRD), and high angle annular dark field scanning transmission electron microscopy (HAADF STEM). Figure 1a shows a RHEED pattern of CFO(40 nm)/MgO(001) taken along the [110] in-plane direction. The image displays streaky and sharp diffraction maxima, indicating a flat and single crystal surface.  This is confirmed by AFM, which exhibits very smooth morphology over large areas (Figure 1b) with an rms roughness of 0.06 nm over a 10 µm x 10 µm area of a 40 nm CFO film. The crystallinity is confirmed by θ-2θ XRD scans on Pt(1.7 nm)/CFO(40 nm)/MgO(001), which exhibit clear MgO(002) and CFO(004) peaks and no other phases within the scan range (Figure 1c). A clearly separable CFO (004) (inset, Figure 1c) peak gives a perpendicular lattice constant of 8.365 Å, indicating a CFO film under slight tensile strain compared to bulk CFO lattice constant of 8.392 Å[10]. Finally, a cross-sectional HAADF STEM image shows an atomically sharp interface between the MgO substrate and CFO thin film with an epitaxial relationship of [100]MgO∥[100]CFO and [010]MgO∥[010]CFO, as indicated in Figure 1d. The appearance of the lattice varies across the CFO thin film, switching between a cubic appearance and that which resembles a spinel structure. We believe this contrast variation is due to changes in the degree of inversion, ƛ.  In AB2O4 spinels, ƛ adopts values between 0 (normal) and 1 (inverse), and is equal to the fractional occupancy of the trivalent B3+ cation on the tetrahedral A-site sub-lattice. Bulk magnetic properties of a Pt(1.7 nm)/CFO(40 nm) sample are measured at 5 K by vibrating sample magnetometry (VSM) (Figure 1e). An in-plane hysteresis loop taken along the [100] axis (red curve) has a coercivity µ0HC of 0.34 T, saturation field of µ0Hs of 3.3 T and a remanence ratio MR/MS of 0.1. An out-of-plane hysteresis loop (black curve) has similar characteristics, coercivity µ0HC of 0.18 T, saturation field of µ0HS of ~4.25 T and a remanence ratio MR/MS of 0.06. To detect MPE in Pt/CFO, we perform magnetotransport measurements that are sensitive to the presence of magnetization within the Pt layer. In ferromagnets, two well-known phenomena are the anomalous Hall effect (AHE) which is sensitive to the out-of-plane magnetization, and the anisotropic magnetoresistance (AMR) which is sensitive to the orientation of magnetization relative to the current direction. With induced magnetization in the Pt layer along unit vector mPt, these appear in the longitudinal and transverse resistivities as:  ρxx = ρ0 + ∆ρAMRm2 Pt, j       ρxy = ∆ρAMRmPt, tmPt, j + ρAHEmPt, n     (1)  \t4\twhere mPt, n ,mPt,jt  mPt, t are the out-of-plane (n), in-plane along current (j), and in-plane transverse to current (t) components of the Pt magnetization unit vector (see Figure 3(a)), ρ0 is the background resistivity of Pt, and ∆ρAMR  and  ρAHE  are the MPE-induced AMR and AHE, respectively. In addition to AHE and AMR, a recently discovered pure spin current effect based on the spin Hall effect in Pt and interfacial spin scattering at the FMI interface generates additional contributions to ρxx and ρxy given by:   ρxx = ρ0 + Δρ1m2 CFO,t ρxy = −Δρ1mCFO,tmCFO,j + Δρ2mCFO,n    (2)  where mCFO,j ,mCFO,t,  mCFO,n  are components of the magnetization unit vector in the FMI, Δρ1 is known as the spin Hall magnetoresistance (SMR), and Δρ2 is the spin Hall anomalous Hall-like signal (SH-AHE). The SMR stems from the reflection of spin current (generated by spin Hall effect) from the FMI interface which is subsequently converted to a charge current through the inverse spin Hall effect (ISHE) [21]. The SH-AHE stems from reflection of the spin current at the FMI interface, where an out-of-plane component of FMI magnetization rotate the spin orientation of the spin current and generate a transverse voltage via ISHE. Finally, in addition to the AMR and SMR effects, one must also consider the ordinary magnetoresistance (OMR) and ordinary Hall effect (OHE) that occur due to the presence of Lorentz forces acting on charge carriers in a magnetic field. With the possibility of many different effects (OMR, AMR, SMR, OHE, AHE, SH-AHE) contributing to ρxx and ρxy, a systematic approach is essential for identifying the presence of MPE. We begin with angle-dependent (AD) magnetoresistance measurements to separate the contributions from AMR, SMR, and OMR (see Supplementary Materials for measurement details). Considering that AMR depends on the j-component of magnetization (equation 1) and SMR depends on the t-component of magnetization (equation 2), the two effects can separated by rotating the magnetization within different planes. For ADAMR, the relevant angular scan is in the n-j plane, where γ is defined as the angle measured from the normal axis (n) (see Figure 2a) while ADSMR does not depend on γ. For ADSMR, the relevant angular scan is in the n-t plane, where β is defined as the angle measured from the normal axis (n) (see Figure 2b) while ADAMR does not depend on β. Finally, the contribution from OMR has the same functional form as AMR (i.e. depends on γ), but the OMR can be determined independently. OMR in most materials has a larger resistance when the magnetic field is perpendicular to the current (γ = 0°) as compared to parallel to the current (γ = 90°), and we have verified this for our Pt films on MgO(001) substrates as well (inset Figure 2c). To determine if the Pt/CFO system exhibits MPE, we therefore perform a γ-scan to look for the presence of AMR. Figure 2c shows clearly the presence of angle-dependent MR with lower resistivity for γ = 0° and higher resistivity for γ = 90°. Because this cannot be \t5\texplained by OMR (opposite polarity) and the γ-scan is insensitive to SMR, it is clear evidence for AMR and induced ferromagnetism in the Pt layer. By comparison, Figure 2c inset shows γ scans of Pt/MgO and Cu/CFO with both displaying OMR oscillations. This is the strongest evidence for MPE in Pt/CFO in our study. Such an AMR signature has never been observed in previous studies of Pt/CFO, but it has been previously reported for other Pt/FMI systems and is accepted as the most reliable test among transport measurements for MPE [22-24]. We also perform the β-scan and observe SMR with similar magnitude as reported in previous studies [16-18,20] of Pt/CoFe2O4 (Figure 2d). We also perform Hall measurements to further support the presence of induced ferromagnetism in the Pt layer. Measurement of Rxy at 5 K for the Pt (1.7 nm)/CFO(40 nm) sample (Figure 2e red curve) exhibits a nonlinear hysteretic signal commonly associated with AHE (and thus ferromagnetism) and a linear OHE background. The absence of such nonlinear features in Cu (8 nm)/CFO(40 nm) and Pt (5 nm)/MgO control samples rule out magnetic fringe fields or magnetic impurities in Pt, respectively, as the origin of the hysteresis loop in the Pt/CFO sample. It is interesting to note that after the linear OHE contribution is subtracted (Figure 3a, red curve), the remaining hysteretic signal of Pt/CFO shows higher coercivity and substantially larger remanence ratio than the out-of-plane hysteresis loop of bulk CFO (Figure 1e). These different interfacial magnetic properties might be due to the exchange interaction between the CFO and Pt moments or a surface magnetic anisotropy at the CFO/Pt interface. The Hall resistivity ρxy in Figure 3a can come from two sources as shown in Equations (1) and (2): MPE- AHE and SH-AHE. To further distinguish between these mechanisms, we insert a 2 nm Cu spacer between Pt and CFO layers. We utilize Cu because it has (1) filled d-shells which prevents induced ferromagnetism, and (2) a long spin diffusion length (hundreds of nm), which makes it transparent to spin currents. Therefore, a Cu spacer should suppress induced magnetism in Pt while leaving SH-AHE and SMR unaffected (except for shunting effects). The Hall measurement of the Pt/Cu/CFO sample (Figure 4a, blue curve) indeed shows a reduction in magnitude compared to Pt/CFO, which can come from a loss of induced ferromagnetism and/or a reduction of the overall signal by shunting. Further insight is gained through ADMR measurements comparing Pt/Cu/CFO and Pt/CFO. Figure 3b shows a plot of the resistivity ratio Δρ1/ρ0 as a function of angle 𝛽 for Pt/CFO and Pt/Cu/CFO at 5 K. Notably, the ADSMR signal yields nearly the same modulation as the direct contact, with the Δρ1/ρ0 magnitude practically unchanged. This suggests that the shunting through the 2 nm Cu layer is minimal. Furthermore, Figure 3c compares the ADAMR signal in the Pt/Cu/CFO bilayer (blue curve) and the Pt/CFO bilayer (red curve). Indeed, the Pt/Cu/CFO sample does not show any modulation arising from the AMR. Although this does not prove an absence of AMR (because it might be getting cancelled by OMR), it nevertheless shows a significant reduction compared to the Pt/CFO sample. This reduction in \t6\tAMR provides additional evidence for induced ferromagnetism in Pt/CFO and suggests that the reduction in AHE in Pt/Cu/CFO is primarily due to the reduction of induced ferromagnetism. Finally, we investigate the MPE in Pt/CFO using density functional theory calculations. Using the Vienna Ab-initio Simulation Package (VASP), we relax cubic CFO cells consisting of 5 F.U. with the Co atoms placed only on the tetrahedral sites, ordered octahedral sites, random octahedral sites, and a combination of random tetrahedral and octahedral sites\t[25]. These calculations indicate CFO favors Co occupancy of the octahedral sites to minimize structural energy with random distribution and no preference for ordering. Using the lowest energy CFO structure, we construct calculation cells consisting of either one or two cubic CFO cells topped with either 4 (~1 nm) or 8 (~2 nm) layers of Pt with an (001)/(001) interface and at least 10 Å of vacuum. After comparing several Pt positions over the CFO cells, the positions directly over the cation sites are found to be energetically favorable, as shown in Fig. 5b. Finally, we relax the interface calculation cells in the plane of the interface to determine the electronic and magnetic structure of the CFO/Pt interface. All calculations are performed using generalized gradient approximation pseudopotentials in the formulation of Perdew et al.; on-site corrections for Coulomb interactions (DFT+U) are applied based on previous DFT work\t[26,27]. Calculations utilize spin polarization and Monkhorst-Pack k-point meshes consisting of 7 points in periodic directions and a single point in vacuum directions. Figure 4a displays the layer-averaged magnetic moments on Pt atoms in layers adjacent to the CFO/Pt interface. The large error bars in the interface layer comes from site-specific variations between the Pt atoms that we will discuss in the Supplementary Materials (section 3). We observe decreasing moment on Pt atoms as a function of distance from the CFO/Pt interface, indicating that the presence of the Pt moments should be due to induced magnetism from the CFO substrate. The magnetic effect does not persist after the first two Pt planes, giving a length scale for the proximity effect. Figure 4b displays the magnetic moments on Pt atoms in the 8-layer calculation cell with isosurfaces at 0.0025 µB, showing that the induced negative moments (red) are only present in the first few atomic planes.  To investigate the nature of the induced moments at the interface, we examine the orbital density of states of interfacial Pt atoms on top of various CFO sites (e.g. octahedral Fe, tetrahedral Fe, oxygen, octahedral Co).  In particular, as shown in Figure 4c, we observe a strong spin asymmetry (bold line) and induced moment in the density of states of the dz2 orbitals of Pt on top of octahedral Fe, while the other orbitals show much less spin asymmetry. Furthermore, a comparison with the d-DOS of Pt on top of other CFO sites and an examination of the d-DOS of Fe suggests that magnetism is primarily induced in the dz2 orbital of the Pt atoms by moments in the dxy, dyz, and dxz orbitals of Fe atoms located no more than one layer below the CFO/Pt interface (see section 3 of the Supplementary Material for details). \t7\tIn conclusion, we obtain strong evidence for the presence of induced ferromagnetism (i.e. MPE) in Pt/CFO at 5 K including the first measurement of ADAMR in this system. Studies of Hall resistivity, ADSMR, insertion of Cu spacers, and DFT calculations provide additional evidence for MPE. Additional measurements at 300 K indicate the possibility of induced ferromagnetism, but the results are less conclusive due to the absence of a definitive ADAMR signal (see Supplementary Materials). Nevertheless, the observation of MPE in Pt/CFO opens the door to utilizing the family of spinel ferrites for MPE and spin manipulation via proximity exchange fields for novel spintronic devices.  Acknowledgments We would like to thank Felix Casanova for insightful discussions. Primary funding for this research was provided by the Center for Emergent Materials: an NSF MRSEC under award number DMR-1420451. NA and WW acknowledge computational support by the Ohio Supercomputer Center under Grant No. PAS0072, and partial funding from AFOSR, award no. FA9550-14-1-0322.   \t8\t \n  FIG. 1. (a) RHEED image of 40 nm CFO film grown on MgO (001) substrate, taken along the [110] in-plane direction. (b) Representative atomic force microscopy image taken over a 10 μm x 10 μm scan size with rms roughness of 0.14 nm. (c) θ-2θ x-ray diffraction scan of Pt(1.7 nm)/CFO(40 nm)/MgO heterostructure. Inset: A fine scan showing a clear CFO (004) peak. (d) HAADF STEM micrograph of a CFO film on an MgO substrate. (e) Magnetic hysteresis loop of of Pt(1.7 nm)/CFO(40 nm)/MgO for both in plane (red) and out-of-plane (black) applied magnetic field. \n1\tµm\n1\tnm0nm\nCFO\t(001)[110]\n2\tnmMgOCFO[100]ntj(a)(b)(c)\n(d)\n(e)\t9\t FIG. 2. (a) Measurement geometry for ADAMR (γ scan in n-j plane). (b) Measurement geometry for ADSMR (β scan in n-t plane). (c) γ dependence of Δρxx/ρ0 of Pt/CFO taken with µ0H = 10 T, showing the presence of AMR. (d) β dependence of Δρxx/ρ0 of Pt/CFO taken with µ0H = 10 T, showing the presence of SMR. (e) Hall resistance for Pt(1.7 nm)/CFO (red curve), Pt(5 nm)/MgO (green curve), and Cu(8 nm)/CFO (black curve). All measurements are taken at T = 5 K. \nnjtg\nbjtn(c)(a)(b)\n(d)(e)\n\t10\t \n FIG. 3. (a) Hall resistivity of Pt(1.7 nm)/CFO (red curve) and Pt(1.7 nm)/Cu(2 nm)/CFO (blue curve) with linear OHE background subtracted. Addition of the Cu spacer heavily suppresses the magnitude and coercivity. (b) ADSMR scans of Pt/CFO (red curve) and Pt/Cu/CFO (blue curve), (c) ADAMR scans of Pt/CFO (red curve) and Pt/Cu/CFO (blue curve). All measurements are taken at T = 5 K. \n(a)\n(b)(c)\t11\t FIG. 4. (a) Average magnetic moment per Pt atom in µB for Pt layers adjacent to the CFO/Pt (001)/(001) interface, calculated with DFT. Layer averages decrease sharply to zero in 1-2 layers from interface. (b) Magnetic moment isosurfaces at 0.0025 µB for Pt atoms in the 8-layer calculations cell. Strong negative moments (red) are observed only in the layers closest to the interface, diminishing to zero by the fourth layer of Pt atoms.  (c) Orbital-resolved d-DOS of a Pt atom located directly over a magnetic Fe atom at CFO/Pt interface. The thin lines are spin up (positive values) and spin-down (negative values) DOS, and the bold line is their sum. \n\t12\tReferences \t[1] H. Haugen, D. Huertas-Hernando, and A. Brataas, Physical Review B 77, 115406 (2008). [2] H. X. Yang, A. Hallal, D. Terrade et al., Physical Review Letters 110, 046603 (2013). [3] S. Singh, J. Katoch, T. Zhu et al., Phys. Rev. Lett. 118, 187201 (2017). [4] J. C. Leutenantsmeyer, A. A. Kaverzin, M. Wojtaszek et al., 2D Materials 4, 014001 (2017). [5] P. Wei, S. Lee, F. Lemaitre et al., Nat. Mater. 15, 711 (2016). [6] C. Zhao, T. Norden, P. Zhang et al., Nat Nano advance online publication (2017). [7] T. N. Koichiro Suzuki, Yohtaro Yamazaki, Japanese Journal of Applied Physics 27, 361 (1988). [8] J. A. Moyer, C. A. F. Vaz, E. Negusse et al., Physical Review B 83, 035121 (2011). [9] Y. Suzuki, G. Hu, R. B. van Dover et al., Journal of Magnetism and Magnetic Materials 191, 1 (1999). [10] G. Hu, J. H. Choi, C. B. Eom et al., Physical Review B 62, R779 (2000). [11] K. U. H. Yanagihara, M. Minagawa, E. Kita, N. Hirota, Journal of Applied Physics 109, 07C122 (2011). [12] A. V. Ramos, Universite Pierre et Marie Curie (Thesis), 2008. [13] A. V. Ramos, M.-J. Guittet, and J.-B. Moussy, Applied Physics Letters 91, 122107 (2007). [14] M. Jean-Baptiste, Journal of Physics D: Applied Physics 46, 143001 (2013). [15] X. Chen, X. Zhu, W. Xiao et al., ACS Nano 9, 4210 (2015). [16] M. Isasa, A. Bedoya-Pinto, S. Vélez et al., Applied Physics Letters 105, 142402 (2014). [17] M. Valvidares, N. Dix, M. Isasa et al., Physical Review B 93, 214415 (2016). [18] M. Isasa, S. Vélez, E. Sagasta et al., Physical Review Applied 6, 034007 (2016). [19] H. Wu, Q. Zhang, C. Wan et al., IEEE Transactions in Magnetics 51, 4100104 (2015). [20] T. N. Takeshi Tainosho, Jun-ichiro Inoue, Sonia Sharmin, Eiji Kita, AIP Advances 7, 055936 (2017). [21] Y.-T. Chen, S. Takahashi, H. Nakayama et al., Physical Review B 87, 144411 (2013). [22] S. Y. Huang, X. Fan, D. Qu et al., Physical Review Letters 109, 107204 (2012). [23] C. Tang, P. Sellappan, Y. Liu et al., Physical Review B 94, 140403 (2016). [24] X. Zhou, L. Ma, Z. Shi et al., Physical Review B 92, 060402 (2015). [25] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 169 (1996). [26] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). [27] A. Walsh, S.-H. Wei, Y. Yan et al., Phys. Rev. B 76, 165119 (2007). \t\t1 Supplementary Materials for: Magnetic Proximity Effect in Pt/CoFe2O4 Bilayers Walid Amamou,1* Igor V. Pinchuk,2* Amanda Hanks,3,4 Robert Williams,3 Nikolas Antolin,4 Adam Goad,2,5 Dante J. O’Hara,1 Adam S. Ahmed,2 Wolfgang Windl,4 David W. McComb,3,4 and Roland K. Kawakami1,2** 1Materials Science and Engineering, University of California, Riverside, CA 92521 2Department of Physics, The Ohio State University, Columbus, OH 43210 3Center for Electron Microscopy and Analysis, The Ohio State University, Columbus, OH 43210 4Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210 5Department of Physics, University of Maryland, Baltimore County, MD 21250 \t\t1. Methods Samples are grown in a molecular beam epitaxy (MBE) chamber with base pressure of ~1x10-10 torr. MgO(001) substrates (10 mm × 10 mm × 0.5 mm, double-sided polished from MTI) are rinsed in de-ionized water, loaded into the MBE chamber, annealed at 600 ˚C for 30 minutes, and smoothed by subsequent deposition of a ~5 nm electron-beam evaporated MgO buffer layer grown at 350˚C at a rate of ~1 Å/min. Growth temperatures are measured by a thermocouple placed near the substrate and deposition rates are measured by a quartz crystal monitor. CFO films are deposited at ~4 Å/min in an oxygen partial pressure of 5×10-7 torr by co-depositing elemental Co (99.99%, Alfa Aesar) and Fe (99.99%, Alfa Aesar) from thermal effusion cells. The substrate temperature is maintained at 200 ˚C during CFO growth and in situ reflection high energy electron diffraction (RHEED) is used to monitor the sample surface throughout the growth and annealing process. CFO films are then cooled to room temperature and capped with either Pt, Pt/Cu or Cu. Pt films are deposited at ~0.06 Å/min using an electron beam source while Cu films are grown at 1 Å/min using a thermal effusion cell. The described heterostructures are deposited without breaking UHV conditions in order to preserve the quality of the Pt/CFO and Cu/CFO interfaces. Magnetization measurements are performed using a Quantum Design 14 Tesla Physical Properties Measurement System (PPMS) with a vibrating sample magnetometer (VSM) module. The samples are patterned into Hall bars (width W=100 µm, length L = 800 µm) for subsequent DC magnetoresistance and Hall measurements. DC transport measurements are obtained in the same PPMS using resistivity mode. For all Hall measurements, we apply a DC current (I = 20 µA) and measure the transverse voltage Vxy as an out-of-plane magnetic field is swept. The Hall resistivity is given by rxy = (Vxy/I)t, where t is the thickness \t2 of the Pt channel. Angle-dependent magnetoresistance measurements are performed by placing Hall bars into a constant magnetic field of 10 Tesla and rotating the sample stage. 2. Room temperature measurements In order to test for the presence of MPE at room temperature, we repeat the Hall measurement and angle-dependent magnetoresistance measurements at 300 K with the results shown in Figures S1. In Figure S1a, we show the Hall resistivity after subtraction of the OHE linear background. Interestingly, the Hall signal still shows a nonlinear, hysteretic signal with a smaller coercivity and remanence than observed at 5 K. Figure S1b shows the angle-dependent b-scan of longitudinal resistance, which is sensitive to SMR. The SMR ratio Drxx/r0 has nearly the same magnitude at 300 K as at 5 K (Fig. 3b of the main text), demonstrating negligible temperature dependence similar to previous reports in Pt/CFO bilayers [1]. Figure S1c shows the angle-dependent g-scan of the longitudinal resistance, which is sensitive to AMR and OMR. The most notable feature is the opposite polarity of the angle-dependence in the γ-scan at 300 K compared to 5 K (Fig. 3c of the main text). Because the 5 K scan has the same polarity as OMR, there are two possible scenarios: (1) only OMR is present and there is no induced ferromagnetism in Pt (i.e. no AMR signal), or (2) AMR is present due to induced ferromagnetism in Pt, but the OMR signal dominates over the AMR signal. Therefore, the negative polarity of the g-scan at 300 K means that it cannot provide conclusive evidence for MPE at room temperature. This contrasts with the case at 5 K where the positive polarity of the g-scan which requires the presence of AMR and induced ferromagnetism to explain the observed signal.  \n\tFIG. S1. Room temperature measurements. (a) Anomalous Hall effect for Pt/CFO. The linear OHE background has been subtracted. (b) Angle-dependent b-scan of Pt/CFO, showing SMR. (c) Angle-dependent g-scan of Pt/CFO, exhibiting negative polarity of the MR signal. \t\t\t\n(a)(b)(c)\t3  3. Orbital density of states DFT calculation \n \n  \ndxy\t\ndyz\t\ndz2\t\ndxz\t\ndx2-y2\t\n(a)\t\n(b)\t\n(c)\t\n(d)\t\n(e)\t\nFIG. S2. (a) Orbital-resolved d-DOS of a Pt atom located directly over an octahedral Fe atom at the CFO/Pt interface. (b) Orbital-resolved d-DOS of a Pt atom located over an Fe atom in a tetrahedral site that is one layer away from the interface. (c) Orbital-resolved d-DOS of a Pt atom located over an oxygen atom at the interface. (d) Orbital-resolved d-DOS of a Pt atom located over an octahedral Co atom at the interface. (e) Orbital-resolved d-DOS of an Fe atom located at the CFO/Pt interface. For (a-d), the thin lines are spin up (positive values) and spin-down (negative values) DOS, and the bold line is their sum. Panel (e) only shows the sum.  \t4 In Figure 4a of the main text, the large error bar for the average magnetic moment per Pt atom in Pt layer #1 (interfacial layer) reflects the site-specific variation of the induced magnetic moment. To investigate the nature of the induced moments, we examine the orbital density of states of various Pt atoms in layer #1. Figure S2a shows the d-DOS of a Pt atom located directly over an octahedral Fe atom. Here, we observe substantial spin asymmetry of the density of states (bold line) for the 𝑑#$ orbitals, but much weaker spin asymmetry for the other orbitals. This indicates a strong magnetic proximity effect for Pt atoms on top of octahedral Fe atoms, due to induced spin polarization in the 𝑑#$ orbitals. Figure S2b shows the d-DOS of a Pt atom located over a Fe atom in an tetrahedral site, which lies one layer away from the interface. As is clear from the calculation, none of the Pt d-orbitals show any substantial spin asymmetry. Similarly, the Pt atoms on top of an O atom (Figure S2c) and on top of a Co atom (Figure S2d) show very little spin asymmetry of the DOS for all Pt d orbitals. Thus, the induced magnetism in Pt is due to spin polarization of the 𝑑#$ orbitals for Pt atoms on top of an octahedral Fe atom. To investigate which d-orbitals of the Fe atom contribute to the magnetic exchange coupling, we consider the d-DOS of the octahedral Fe atoms located at the CFO/Pt interface, as shown in Figure S2d. Notably, only the Fe dxy, dyz, and dxz orbitals show the strong spin asymmetry and magnetic moments, which suggests that magnetism is primarily induced in the 𝑑#$ orbital of the Pt atoms by moments in the dxy, dyz, and dxz orbitals of Fe atoms no more than one layer removed from the CFO/Pt interface.  \t"    },    {        "title": "1808.07208v1.Microwave_Conductivity_of_Ferroelectric_Domains_and_Domain_Walls_in_Hexagonal_Rare_earth_Ferrite.pdf",        "content": "1 \n Microwave Conductivity of Ferroelectric Domains and  Domain Wall s in \nHexagonal Rare -earth Ferrite  \n \nXiaoyu Wu1, Kai Du2, Lu Zheng1, Di Wu1, Sang -Wook Cheong2, Keji Lai1 \n1Department of Physics, University of Texas at Austin , Austin TX 78712, USA  \n2Rutgers Center for Emergent Materials and D epartment of Physics and Astronomy, Rutgers \nUniversity , Piscataway NJ 08854, USA  \n \n \nAbstract  \nWe report the nanoscale electrical imaging results in hexagonal Lu 0.6Sc0.4FeO 3 single crystals \nusing conductive atomic force microscopy (C -AFM) and scanning microwave impedance \nmicroscopy (MIM) . While the dc and ac response of the ferroelectric domains can be explained  by \nthe surface band bending, the drastic enhancement of domain wall (DW) ac conductivity is clearly \ndominated b y the dielectric loss due to  DW vibration  rather than mobile -carrier  conduction . Our \nwork provides a unified physical picture to describe the local  conductivity  of ferroelectric domains \nand domain walls,  which will be important for future incorporation of  electrical conduction, \nstructural dynamics, and multiferroicity into high -frequency nano -devices.   2 \n Domain walls (DWs) i n ferroelectric  material s are natural  interfaces that can be readily \nwritten, erased, and manipulate d by external electric fields. Since  the discovery of DW conduction \nin BiFeO 3 thin films1 by conductive atomic -force microscopy (C -AFM) , similar phenomena  have \nbeen reported in a wide range of ferroelectrics including PbZr 0.2Ti0.8O3 (PZT)  2, LiNbO 3 3, BaTiO 3 \n4, hexagonal manganite h-RMnO 3 (R = Sc, Y, Ho to Lu) 5-7, and (Ca,Sr) 3Ti2O7 8. It is now generally \naccepted that the prominent conductivity difference between domains and DWs is a norm rather \nthan an exception9. Consequently, much effort has been made to demonstrate DW-based nano -\ndevices10, such as nonvolatile memory11,12, field effect transistors ( FETs )13, reconfigurable \nchannels14,15, and DW -motion logics16. While many functionalities are achieved  at zero ( dc) or \nlow frequencies, practical devices  usually demand  much higher operation frequencies . In the giga -\nHertz (GHz) range, the dielectric loss due to dipolar relaxation may become significant. In other \nwords, the effective ac conductivity would contain contributions from both mobile carrier \nconduction and bound charge oscillation.   The understanding of DW response  in the microwave \nregime is therefore desirable for the continued research in DW nanoelectronics.  \nThe GHz DW conductivity has been recently studied by scanning microwave impedance \nmicroscopy (MIM) in several ferroelectrics17-19. In particular, charge -neutral DWs on the (001) \nsurface of h -RMnO 3, which show vanishingly small electrical conduction at dc5, exhibit very large \nac conductivity at radio frequencies due to the collective DW vibration around its equilibrium \nposition19. In this Rapid Communication , we report  a combined C -AFM and MIM study on \nhexagonal ferrite Lu0.6Sc0.4FeO 3, which is isomorphic to h-RMnO 3 in the crystalline structure20-23. \nWhile mobile carriers are responsible for the DW dc conduction , the large  ac conductivity at 1 \nGHz is clearly dominated by the dielectric loss due to  DW oscillations. By applying a tip bias \nduring the MIM imaging, we observe d that the signals on the two types of ferroelectric  domains  \ncould  be described by the surface band bending, whereas the GHz conductivity at the DWs remains \nlargely unchanged.  Our work provides a platform to explore the interplay between electrical \nconduction and structural dynamics in multiferroic DWs and generates new impetus to incorporate \nnanometer -sized DWs into multifu nctional nanoelectronic devices.  \nHexagonal rare-earth ferrites h -RFeO 3 (R = Sc, Y, Ho to Lu) have attracted  much interest in \nthe past decade due to the possible coexistence of ferroelectric ity and antiferromagneti sm at room  \ntemperature20-23. While only the orthorhombic  phase is thermodynamically stable  for bulk LuFeO 3, 3 \n it is found that h exagonal LuFeO 3 crystals can be stabilized by Sc substitution  without the loss of \nmultiferroicity23. In this work, bulk Lu 0.6Sc0.4FeO 3 (LSFO) crystals (lattice structure shown in Fig. \n1a) were grown using the optical floating zone method under 0.8 MPa O 2 atmosphere. The  crystals \nwere  annealed at 1400° C in air for 24 hours and then cooled down to 1200° C with 1° C/h cooling \nrates , followed by the final annea ling at 1000° C  under 20 MPa O 2 pressure  in a high -pressure \noxygen furnace to remove  oxygen vacancies.  Analogous  to h-RMnO 3, LSFO crystals after such \ntreatments show weak p -type conduction , presumably  due to the interstitial oxygen doping24. As \nshown in Fig. 1b, the two -terminal resistance along the hexagonal c -axis of a LSFO sample  (~ 0.5 \nmm in height and ~ 1 mm2 in area) is around 1 ~ 2   M at high dc  bias. Assuming that the contact \nresistance is insignificant in this regime, one can estimat e that the bulk dc conductivity σbulkdc is \naround  10-4 ~ 10-3 S/m, which is similar to that of h-RMnO 3 in earlier works25.  \n \nFIG. 1. (a) Crystal structure of hexagonal Lu 0.6Sc0.4FeO 3 (LSFO). (b) Two-terminal I-V characteristics \non a bulk LSFO single crystal . The dashed line  is a linear fit to deduce the resistance. The inset shows \na picture of typical LSFO crystals. (c-e) AFM, out-of-plane  PFM , and C-AFM images acquired on the \nsame area from the cleaved surface of (001) LSFO . The enhanced C -AFM signals at  the step terraces \nare presumably due to th e sudden change of tip -sample contact area during the scanning.  The s cale bars  \nare 500 nm. (f) Fixed -point I -V curves on up domain  (orange), down domain  (green), and domain wall \n(purple) indicated in (e). (g) Semi -log plot of the data in (f). The black lines are exponential fit s for |Vtip| \n< 1.5 V.  \n4 \n The as -grown LS FO crystals were cleaved to expose the (001) surface for imaging studies.  \nThe AFM image in Fig. 1c shows micrometer -scale flat terraces. Cloverleaf -like f erroelectric \ndomain patterns , reminiscent of that observed in h -RMnO 3, could  be seen in the out -of-plane piezo -\nresponse force microscopy (OOP -PFM) image ( Fig. 1d ). Different from h -RMnO 3 where DWs on \nthe (001) surface are more resistive than the adjacent domains5, however, the C -AFM image in the \nsame area (Fig. 1e) indicates that the LSFO (001) DWs  exhibit enhanced conduction  under a tip \nbias Vtip of -2 V. To estimate the local dc conductivity , we measured the fixed -point (labeled in \nFig. 1e) I-V characteristics  on DW and up -polarized /down -polarized domains  (hereafter \nabbreviated as up  and down  domains , respectively ) in Fig. 1f . Similar results can be observed in \nother locations of the sample . Consistent with an earlier report on HoMnO 3 25, the signals on the \ntwo domains can be explained by the polarization -modulated rectification at the metal -\nsemiconductor junction. For small bias values | Vtip| < 1.5 V, the curves can be fitted by the \nShockley diode equation I = IS[exp( eV/nkBT) - 1], where e is the electron charge, kB is the \nBoltzmann constant, T is the temperature, IS is the saturation current, and n is the ideality factor26. \nThe asymmetric bias -dependent current is presumably due to the tip-sample Schottky barrier.  In \nthe high forward bias ( Vtip < 0) regime, the current measured at the DW is ~ 5 times larger than \nthat at the domains. Considering that the typic al tip -sample contact diameter of  10 nm is another  \n~ 5 times larger than the ferroelectric DW width (1~3 nm), we estimat e the DW dc conductivity \nσDWdc to be 10-2 ~ 10-1 S/m, i.e., 1 ~ 2 orders of magnitude higher than σbulkdc. We note that several \ntheories have been proposed to explain the e nhanced dc conductivity in nominally uncharged  DWs , \nincluding  the band -gap narrowing effect1,27, accumulation of charged defects28, and flexoelectric \neffect29. While the exact nature of the DW dc conduction in LSFO is not clear at this point, the \nlevel of conductivity enhancement is consistent with other investigations27-29. \nAt GHz frequencies, it has been reported that DWs on (001) h -RMnO 3 exhibit strong \ndielectric loss due to the periodic vibration around the equilibrium position19. Since hexagonal \nmanganites and ferrites share the same lattice structure  and origin of ferroelec tricity, similar DW \ndynamics is also expected in the LSFO sample. Fig. 2a shows the MIM images at f = 1 GHz when \na dc voltage is applied  to the tip through a bias-tee. At zero tip bias, the MIM images are dominated \nby the pronounced DW signals.  As Vtip increases from 0 V, contrast between opposite domains \nemerge s, with up  domains showing higher MIM signals.  The domain contrast reverses sign for a 5 \n negative tip bias. The evolution of domain signals can be qualitatively described by the band \nbending at the  tip-sample interface25, as illustrated in Fig. 2b.  Here  the overall Schottky barrier  \nincreases with increasing forward bias ( Vtip > 0) and decreases with increasing absolute reverse \nbias ( Vtip < 0).  Different from non -ferroelectric semiconductors, the polarization -induced surface \ncharge  leads to an additional modification to the Schottky barrier  height . As a result, in the \naccumulation regime, the valence band maximum EV of down  domains will reach the Fermi level \nEF before the up d omains.  Conversely, th e surface inversion of carrier type when the conduction \nband minimum EC meets EF will occur first at  the up  domains. At intermediate Vtip, the \nsemiconductor is in the depletion regime, where EF is distant from both conduction and val ence \nbands. T he polarization -mediated band bending25 is thus consistent with the domain contrast in the \nMIM images.  \n \nFIG. 2. (a) MIM -Im/Re images on (001) LSFO  at different bias voltages. The s cale bars  are 1 µ m. The \nimages were acquired with  monotonically increasing Vtip from -3 V to +2 V. The up and down domains \nare marked by orange and green dots, respectively. (b) Schematic diagrams of interfacial band diagrams \nbetween the MIM  tip and FE domains. EC, EV and EF are energy level s of the conduction band, valence \nband a nd Fermi energy of semiconductor, respectively.  B is the difference in Schottky barrier height \nbetween the two domains.  \n6 \n To quanti fy the MIM data, we first analyze the DW signals when both domains are highly \nresistive , i.e., in the depletion regime . The MIM line profiles across a single DW (indicated in Fig. \n2a) are plotted in Fig. 3a. The full width at half maximum (FWHM) of ~ 100 nm is limited by the \nspatial resolution , which is  determined by the diameter  of the tip apex that is in close proximity \nwith the sample . The MIM -Im/Re signals are proportional to the real and imaginary parts of the \ntip-sample admittance , which can be computed  by finite -element analysis (FEA)30. Here the DW \nis modeled as a vertical 2 -nm-wide slab  sandwiched between adjacent insulating domains. The \nsimulated MIM signals as a function of the DW ac conductivity σDWac are shown in Fig. 3b, from \nwhich σDWac ~ 600 S/m at 1 GHz can be estimated by comparing the measured signals and the FEA \nresults. The fa ct that σDW ac is about 4  orders  of magnitude higher than σDWdc strongly suggests that \nthe DW vibration19, rather than mobile carrier conduction, is responsible for the energy dissipation \nat microwave  frequencies.  \n \nFIG. 3. (a) MIM -Im/Re line profiles across a single DW , labeled as dashed lines in Fig. 2a. The full \nwidth at half maximum is ~ 100 nm. (b) Simulat ed MIM signals  as a function of the DW ac conductivity. \nThe signal levels in (a) are consistent with σDWac ~ 600 S/m, as denoted  by the dashed li ne. σbulkdc and \nσDWdc are also indicated in the plot. The inset shows the tip -sample configuration  for the FEA  simulation .  \nWe now turn to the quantitative analysis of bias -dependent MIM images. As discussed before, \nthe surface conductivity is modified by the tip bias due to  the band bending at the tip -sample \ninterface . In principle, the spatial  distribution of conductivity underneath the biased tip can be \nnumerically computed by self -consistent Schrodinger -Poisson equations31. Such an approach, \nhowever, requires extensive knowledge on the band parameters,  carrier mobility, and the exact  tip-\n7 \n sample contact condition s, which are difficult to evaluate from our  data. Since the dimension of \nthe tip -sample contact area is much smaller  than that of the space charge region , we approximate \nthe tip-induced surface effect by a semi -spherical region (radius rsurf = 100 nm ) with a uniform \nconductivity surf. The MIM response as a function of surf is included in Appendix A. Moreover, \nusing a simple dielectric gap model32,33, one can estimate the difference in the Schottky barrier \n(B) between the two domains  to be  0.1 ~ 0.2 eV. As a result, for the same Vtip, the surface \nconductivity differs by a factor of 100 ~ 1000 when the tip scans across  the DW. Since  the MIM \nsignals saturate for surf < 10-2 S/m (Appendix A), we further assume that the less conductive \ndomain for a given  Vtip is at the insulating limit, as schematically illustrated in Fig. 4a. The bias-\ndependent MIM data across the DW (in dicated in Fig. 2a) are plotted in Fig. 4b  and 4c . The \naveraged MIM signals on the DW and up/down domains over the entire image are shown in Figs. \n4d and 4 e, using  the less conductive domain  as a reference . Using the tip -sample configuration  in \nFig. 4a, we  can simulate the line profiles (overlaid in Fig. 4b  and 4c) and the results are in good \nagreement with the measured data. Fig. 4 f summarizes the calculated surf and σDWac from the \nsimulation. Again, while the domain signals can be described by the Schottky  band bending, the \nlarge  σDWac with virtually no bias dependence s ignifies the strong dynamic response of ferroelectric \nDWs at GHz frequencies . \n \n8 \n FIG. 4. (a) Schematic of the tip -sample  configuration when a positively biased tip scans across the DW. \nThe yellow hemisphere represents  the region with enhanced surface conductivity σsurf. (b) MIM -Im and \n(c) MIM -Re line profiles across a single DW at different tip bias es. The dashed lines show  simulated \nMIM signals to  fit the experiment al data.  (d) Averaged MIM -Im and (e) MIM -Re signals in Fig. 2a, \nusing the less conductive domain as the reference. (f) Surface conductivity  of domains and ac \nconductivity of DWs as a function of Vtip. The dash-dotted line indicates the MIM sensitivity  floor when \nmeasuring σsurf. \nFinally, the implications of our results are briefly discussed. In conventional  C-AFM  \nmeasurement s, a high Vtip is usually required to inject a current across  the Schottky barrier. The \ncurrent then enters the surface  accumulation or inversion region  and finds its way to the counter  \nelectrode through an intricate matrix of domains and DWs. The measured conductance is largely \nlimited by the bulk semiconductor, making it formidable to q uantify the local  dc. The MIM, on \nthe other hand, probes the local ac impedance  by an oscillating GHz voltage ( 𝑉tipac < 0.1 V)  through \nthe near -field interaction, which decays rapidly away from the tip19,30. As a result, it is \nstraightforward to interpret the MIM data as an averaged response over a spatial extent determined \nby the tip diameter. For the ferroelectric domains, t he extracted surface conductivity (Fig. 4 f) can \nbe satisfactorily explained by the band -bending picture25 (Fig. 2b), which is not surprising since \nelectrical  conduction due to mobile carriers does not differ much between dc and f = 1 GHz. In \ncontrast, the measured σDWac at 1 GHz  is nearly bias -independent and the value is  ~ 104 times greater \nthan σDWdc, indicative of the predominance of dielectric loss due to DW vibration at microwave \nfrequencies19. Our results thus provide a unified physical picture to analyze nanoscale dc and ac \nresponse of ferroelectric domains and domain wall s, which will be invaluable for future DW \nnanoelectronics operating in the microwave regime.  \nIn summary, we perform ed electrical mapping on  (001)  hexagonal Lu 0.6Sc0.4FeO 3 single \ncrystals at dc and GHz frequencies by a combination of C -AFM and MIM techniques. The dc \nconductivity  of the DWs is moderately enhanced over that o f the domains owing to the excess \nmobile carriers. MIM studies demonstrate that the microwave response of DWs is dominated by \ntheir vibrational dyn amics, resulting in a  bias-independent effective ac conductivity higher than \nthe dc value by a factor of ~ 104. As h -Lu0.6Sc0.4FeO 3 is a room -temperature multiferroic 9 \n material23,34, our results shed new lights on the interplay among  electrical conduction, stru ctural \ndynamics, ferroelectricity , and magnetism in small band -gap multiferroics.  \n \nACKNOWLEDGMENTS   \nThe MIM work (X.W., L.Z., D.W., K.L.)  was supported by NSF Award  DMR -1707372 . The work \nat Rutgers (K.D., S. -W. C.) was supported by  the Gordon and Betty Moore Foundation’s EPiQS \nInitiative through Grant GBMF4413 to the Rutgers Center for Emergent Materials.  The authors \nthank W. Wu for helpful discussion s. \n \nAPPENDIX A:  Finite -element analysis of the MIM results   \n \nFIG. A1. Simulat ed MIM signals  as a function of the surface  conductivity  of the domains . The bulk dc \nconductivity  is also indicated in the plot. The inset shows a side view of the tip -sample geometry for \nthe FEA  simulation . \nFinite -element analysis (FEA)  of the MIM data30 was performed by the commercial software \nCOMSOL 4.4. The tip diameter of 100 nm is the same as the full width at half maximum of the \nMIM line profile across the DW, which is modeled as a 2 -nm slab sandwiched between up and \ndown domains19. To analyze t he bias -dependent images, we assume that Vtip induces a semi -\nspherical region ( rsurf = 100 nm) underneath the tip with a uniform conductivity surf. Fig. A1 shows \nthe FEA results as a function of surf using the 2D axisymmetric model. The MIM signals saturate \n10 \n for surf below 10-2 S/m so that the bulk domains ( bulk ~ 10-3 S/m) can be regarded as in the \ninsulating limit. Note that the tip -sample configurations involving the DW (Fig. 3b inset and Fig. \n4a) are no longer axisymmetric around  the tip. The full 3D FEA is thus needed to generate the \nsimulation results in Fig. 3b and Fig. 4b.  The simulated curves in Fig. 3b are also different from \nthat in Fig. A1.  \n  11 \n References:  \n1. J. Seidel, L. W. Martin, Q. He, Q. Zhan, Y. H. Chu, A. Rother, M. E. Hawkridge, P. \nMaksymovych, P. Yu, M. Gajek, N. Balke, S. V. Kalinin, S. Gemming, F. Wang, G. \nCatalan, J. F. Scott, N. A. Spaldin, J. Orenstein , and R. Ramesh, “Conduction at domain \nwalls in oxide multiferroics ”, Nature Mater . 8, 229 (2009).  \n2. J. Guyonnet, I. Gaponenko, S. Gariglio , and P. Paruch, “Conduction at Domain Walls in \nInsulating Pb(Zr 0.2Ti0.8)O3 Thin Films”, Adv. Mater . 23, 5377 (2011).  \n3. M. Schrö der, A. Hauß mann, A. Thiessen, E. Soergel, T. Woike, and L. M. Eng, \n“Conducting Domain Walls in Lithium Niobate Single  Crystals”, Adv. Func t. Mater . 22, \n3936 (2012).  \n4. T. Sluka, A. K. Tagantsev, P. Bednyakov, and N. Setter, “Free -electron gas at charged \ndomain walls in  insulating BaTiO 3”, Nature Commun . 4, 1808  (2013). \n5. T. Choi, Y. Horibe, H. T. Yi, Y. J. Choi,  W. Wu, and S. -W. Cheong , “Insulating interlocked \nferroelectric and structural  antiphase domain walls in multiferroic YMnO 3”, Nature Mater . \n9, 253 (2010). \n6. D. Meier, J. Seidel, A. Cano, K. Delaney, Y. Kumagai, M. Mostovoy, N. A. Spaldin, R. \nRamesh, and M. Fiebig, “Anisotropic conduc tance at improper ferroelectric  domain walls”, \nNature Mater . 11, 284 (2012).  \n7. W. Wu, Y. Horibe, N. Lee, S. W. Cheong and J. R. Guest, “Conduction of Topologically \nProtected Charged Ferroelectric Domain  Walls ”, Phys. Rev. Lett . 108, 077203 (2012).  \n8. Y. S. Oh, X. Luo, F. -T. Huang, Y. Wang, and S. -W. Cheong, “Experimental demonstration \nof hybrid improper ferroelectricity and the presence of abundant  charged walls in \n(Ca,Sr) 3Ti2O7 crystals”, Nature Mater . 14, 407 (2015).  \n9. R. K. Vasudevan, W. Wu, J. R. Guest, A. P. Baddorf, A. N. Morozovska, E. A. Eliseev, N. \nBalke, V. Nagarajan, P. Maksymovych, and S. V. Kalinin, “Domain Wall Conduction and \nPolarization -Mediated  Transport in Ferroelectrics ”, Adv. Func t. Mater . 23, 2592  (2013). \n10. G. Catalan, J. Seidel, R. Ramesh , and J. F. Scott, “Domain wall nanoelectronics ”, Rev. Mod. \nPhys . 84, 119 (2012).  \n11. P. Sharma, Q. Zhang, D. Sando, C. H. Lei, Y. Liu, J. Li, V. Nagarajan , and J. Seidel, \n“Nonvolatile ferroelectric domain wall memory ”, Sci. Adv . 3, e1700512 (2017) . \n12. J. Jiang, Z . L. Bai, Z. H. Chen, L. He, D. W. Zhang, Q. H. Zhang, J. A. Shi, M. H. Park, J. \nF. Scott, C. S. Hwang , and A. Q. Jiang, “Temporary formation of highly conducting \ndomain  walls for non -destructive read -out of ferroelectric domain -wall resistance \nswitching m emories”, Nature Mater . 17, 49 (2017).  \n13. J. A. Mundy, J. Schaab, Y. Kumagai, A. Cano, M. Stengel, I. P. Krug, D. M. Gottlob, H. \nDoğanay, M. E. Holtz, R. Held, Z. Yan, E. Bourret, C. M. Schneider, D. G. Schlom, D. A. \nMuller, R. Ramesh, N. A. Spaldin, and D. M eier, “Functional electronic inversion layers \nat ferroelectric domain walls”, Nature Mater . 16, 622 (2017).  12 \n 14. I. Stolichnov, L. Feigl, L. J. McGilly, T. Sluka, X. -K. Wei, E. Colla, A. Crassous, K. \nShapovalov, P. Yudin, A. K. Tagantsev, and N. Setter, “Bent Ferroelectric Domain Walls \nas Reconfigurable Metallic -Like Channels”, Nano Lett . 15, 8049 (2015).  \n15. J. R. Whyte, R. G. P. McQuaid, P. Sharma, C. Canalias, J. F. Scott, A. Gruverman , and J. \nM. Gregg, “Ferroelectric Domain Wall Injection ”, Adv. Mater . 26, 293 (2014).  \n16. L. J. McGilly, P. Yudin, L. Feigl, A. K. Tagantsev , and N. Setter, “Controlling domain \nwall motion in ferroelectric  thin films”, Nature Nanotech . 10, 145 (2015).  \n17. A. Tselev, P. Yu, Y. Cao, L. R. Dedon, L. W. Martin, S. V. Kalinin, and P. Maksymovych , \n“Microwave a.c. conductivity of domain walls  in ferroelectric thin films ”, Nature Commun . \n7, 11630 (2016).  \n18. T. T. A. Lummen, J. Leung, A. Kumar, X. Wu, Y. Ren, B. K. Van Leeuwen, R. C. \nHaislmaier, M. Holt, K. Lai, S. V. Kalinin, and V. Gopalan, “Emergent Low-Symmetry \nPhases and Large Property  Enhancements in Ferroelectric KNbO 3 Bulk Crystals ”, Adv. \nMater . 29, 1700530  (2017).  \n19. X. Wu, U. Petralanda, L. Zheng, Y. Ren, R. Hu, S. -W. Cheong, S. Artyukhin, and K. Lai, \n“Low -energy structural dynamics of ferroelectric domain  walls in hexagonal rare -earth \nmanganites”, Sci. Adv . 3, e1602371 (2017).  \n20. W. Wang, J. Zhao, W. Wang, Z. Gai, N. Balke, M. Chi, H. N. Lee, W. Tian, L. Zhu, X. \nCheng, D. J. Keavney, J. Yi, T. Z. Ward, P. C. Snijders, H. M. Christen, W. Wu , J. Shen \nand X. Xu, “Room -Temperature Multiferroic Hexagonal LuFeO 3 Films ”, Phys. Rev. Lett . \n110, 237601 (2013).  \n21. S. M. Disseler, X. Luo, B. Gao, Y. S. Oh, R. Hu, Y. Wang, D. Quintana, A. Zhang, Q. \nHuang, J. Lau, R. Paul, J. W. Lynn, S. -W. Cheong , and W. R atcliff, “Multiferroicity in \ndoped hexagonal LuFeO 3”, Phys. Rev. B  92, 054435 (2015).  \n22. S. M. Disseler, J . A. Borchers, C . M. Brooks, J . A. Mundy, J . A. Moyer, D . A. Hillsberry, \nE. L. Thies, D . A. Tenne, J . Heron, M . E. Holtz, J . D. Clarkson, G . M. Stiehl, P . Schiffer, \nD. A. Muller, D . G. Schlom, and W . D. Ratcliff , “Magnetic Structure and Ordering of \nMultiferroic Hexagonal LuFeO 3”, Phys. Rev. Lett . 114, 217602  (2015). \n23. L. Lin, H. M. Zhang, M. F. Liu, S. Shen, S. Zhou, D. Li, X. Wang, Z. B. Yan, Z. D. Zhang, \nJ. Zhao, S. Dong , and J. M. Liu, “Hexagonal phase stabilization and magnetic orders of \nmultiferroic Lu 1−xScxFeO 3”, Phys. Rev. B  93, 075146 (2016).  \n24. S. H. Skjærvø , E. T. Wefring, S. K. Nesdal, N. H. Gaukå s, G. H. Olsen, J. Glaum, T. Tybell, \nand S. M. Selbach , “Interstitial oxygen as a source of p -type conductivity in hexagonal \nmanganites ”, Nature Commun . 7, 13745 (2016).  \n25. W. Wu, J. R. Guest, Y. Horibe, S. Park, T. Choi, S. W. Cheong, and M. Bode, \n“Polarization -Modulated Rectification at Ferroelectric Surfaces ”, Phys. Rev. Lett . 104, \n217601 (2010).  \n26. S. M. Sze, Physics of Semiconductor Devices  (John Wiley  and Sons, Inc., New York, 1981).  \n27. A. Lubk,  S. Gemming,  and N. A. Spaldin, “ First-principles study of ferroelectric domain \nwalls in multiferroic bismuth ferrite ”, Phys. Rev. B  80, 104110 (2009).  13 \n 28. T. Rojac, A. Bencan, G. Drazic, N. Sakamoto, H. Ursic, B. Jancar, G. Tavcar, M. \nMakarovic, J. Walker, B. Malic, and D. Damjanovic, “Domain -wall conduction in \nferroelectric BiFeO 3 controlled by accumulation of charged defects”, Nature Mater . 16, \n322 (2016).  \n29. E. A. Eliseev, A . N. Morozovska, G . S. Svechnikov, P . Maksymovych,  and S . V. Kalinin, \n“Domain wall conduction in multiaxial ferroelectrics ”, Phys. Rev. B  85, 045312 (2012).  \n30. K. Lai, W. Kundhikanjana, M. Kelly, and Z. X. Shen, “Modeling and characterization of a \ncantilever -based near -field scanning  microwave impedance microscope ”, Rev. Sci. Instrum . \n79, 063703 (2008).  \n31. I‐H. Tan, G. L. Snider, L. D. Chang, and E. L. Hu , “A self -consistent solution of \nSchrö dinger -Poisson equations using a nonuniform mesh ”, J. Appl. Phys . 68, 4071 (1990) . \n32. L. Pintilie and M. Alexe , “Metal -ferroelectric -metal heterostructures with Schottky \ncontacts. I. Influence of the ferroelectric properties ”, J. Appl. Phys . 98, 124103 (2005) . \n33. L. Pintilie, I. Boerasu, M. J. M. Gomes, T. Zhao, R. Ramesh, and M. Alexe, “Metal -\nferroelectric -metal structures with Schottky contacts. II. Analysis of the experimental \ncurrent -voltage and capacitance -voltage characteristics of Pb(Zr,Ti)O 3 thin films” , J. Appl. \nPhys . 98, 12410 4 (2005) . \n34. K. Du, B . Gao, Y . Wang, X . Xu, J . Kim, R . Hu, F .-T. Huang & S .-W. Cheon g, “Vortex \nferroelectric domains, large -loop weak ferromagnetic domains, and their decoupling in \nhexagonal (Lu, Sc)FeO 3”, npj Quantum Mate r. 3, 33 (2018).  "    },    {        "title": "1006.1161v1.A_Robust_Approach_for_the_Growth_of_Epitaxial_Spinel_Ferrite_Films.pdf",        "content": " 1  A Robust Approach for the Growth of Epitaxial Spinel Ferrite Films \nJ. X. Ma, D. Mazumdar, G. Kim, H.  Sato, N . Z. Bao , and A. Gupta*  \nCenter for Materials for Information Tec hnology, 205 Bevill Building, Box 870209, \nUniversity of Alabama, Tuscaloosa, AL 35487  \nAbstract:  \n         Heteroepitaxial spinel ferrites NiFe 2O4 and CoFe 2O4 films have been prepared by pulsed \nlaser deposition (PLD) at various temperature s (175 - 690 °C ) under ozone /oxygen pressure of \n10 mTorr.  Due to enhanced kinetic energy of ablated species at low pressure and enhanced \noxidation power of  ozone, epitaxy has been achieved at significantly lower temperatures than \npreviously reported. F ilms grown  at temperature below 550 °C show  a novel growth mode , \nwhich we term “vertical step -flow” growth mode . Epitaxial spinel  ferrite  films with atomically \nflat surface  over large areas  and enhanced magnetic moment  can be routinely obtained. \nInterestingly,  the growth mode is independent of the nature of substrates ( spinel MgAl2O4, \nperovskite  SrTiO3, and rock salt MgO) and film thicknesses . The underlying growth mechanism \nis discussed.  \n       \nTo whom correspondence should be addressed:  \nagupta@mint.ua.edu   2 I. Introduction \nThere is considerable interest  in the g rowth of high- quality , single crystal spinel ferrites  \n(general formula AB 2O4) films because to their  numerous technological applications in areas \nsuch as microwave integrated devices ,1 magnetoelectric (ME) coupling heterostructures,2,3,4 and \npotentially as an active barrier material in an emerging class of spintronic devices called spin \nfilters .5,6,7 This is in large part due to the unique property of a large class of spinel ferrites, \nincluding CoFe 2O4 (CFO) and NiFe 2O4 (NFO), of being magnetic insulators with a high \nmagnetic ordering temperature. The net magnetization in these materials is due to the existence \nof two magnetic sublattices, and they are thus strictly ferrimagnetic. S pinel  oxides have a \ncomplex crystal structure with a large  unit cell consisting of  man y interstitial sites. Moreover, the \ntransition metals can adopt various oxidation states.  Thus, i t is a challenging task to  grow \nepitaxial spinel films ( especially thick film s) with low defect  density  and excellent magnetic \nproperties. Up to date, various thin film techniques , including pulsed laser deposition (PLD) , \nsputtering, evaporation and chemical techniques have been used  to grow  epitaxial ferrite \nfilms.8,9,10,11,12 But the magnetic properties of epitaxially grown spinel ferrite films are \ngenerally far from ideal in comparison to those in the  bulk, particularly for as -deposited films \nwithout post -anneal . The saturation magnetic moment ( MS) of CFO films is generally between  \n120-350 emu/cm3, well below the bulk value of 450 emu/cm3. Suzuki et al. reported a MS value \nof 400 emu/cm3 for CFO films grown on CoCr 2O4-buffered MgAl 2O4 substrate s.13 For NFO \nfilms, Venzke et al.  obtained a MS value of 190 emu/cm3, also quite a bit lower than the bulk \nvalue of 300 emu/cm3.14 Recently, Luders et al.  reported significantly enhanced MS of 1050  3 emu/cm3 in ultrathin films  of 3 nm in thickness , which they attributed to stabilization of the \nnormal spinel near the interface.5 \nOne of the major obstacles  in obtaining high -quality  epitaxial  ferrite films with bulk \nmagnetic properties is the lack of availability of isostructural substrates with good lattice match.  \nSo far, ferrite films have primarily been grown on oxides substrates such as perovskite SrTiO 3 \n(STO),14 rock-salt MgO ,15 13 isostructural spinel MgAl 2O4 (MAO),  and various buffered \nsubstrates . None of these are ideal for the growth of ferrite films. MAO, with a lattice constant of \n8.08 Å, has a large mismatch with NFO and CFO of over 3% ( a = 8.34Å f or NFO and 8.38Å for \nCFO). On the other hand, rock- salt MgO is better lattice matched with the ferrites, with a lattice \nparameter almost twice that of MgO ( a = 4.212Å). But spinel ferrite films grown on MgO are \nprone to anti -phase boundaries (APBs) from ca tion stacking defects originating from equivalent \nnucleation sites. Such films do not saturate even at magnetic fields as high as 5  Tesla and ultra-\nthin films have been reported to be even superparamagnetic .16 An additional  problem is the \ninter-diffusion associated with high growth temperature of ferrite films. Inter -diffusion is an \nespecially seriously issue for the growth of ferrite/ferroelectric heterostructures , since  a number \nof ferroelectric materials of interest consi st of volatile elements. Also, high temperature growth \non large mismatched substrates results in  3D island growth mode  leading to a rough surface \nmorphology  which is linked with misfit dislocation introduction .17\nIt is well known that for high- misfit heteroepitaxial growth of semiconductor such as Ge \non Si, an  effect ive approach  to suppre ss island formation and achieve laye r-by-layer growth is by  \nreduction of the growth temperature . In order to circumvent th ese \nissues, a low t emperature epitaxial growth method that results in films with excellent structural \nand magnetic properties is highly desirable .  \n18 The degree to which one can control island formation by  4 low-temperature growth depends  on the minimum temperature at which deposition leads to \nepitax ial growth.  In the case of  complex oxides  including spinel ferrites, epitaxial growth is very  \nsensitive to phase equilibrium and the oxidation kinetics , both of which are generally not favored  \nat low temperatures.  Nevertheless, Kiyomura et al . 19 have reported growth of  NiZn and MnZn-\nferrites films at relatively low temperature ( 200 ºC ). This is  likely because Zn ions readily form \noxygen tetrahedrons at a lower temperature. Similarly, in the case of Fe 3O4, simultaneous \nstabilization of Fe2+ and Fe3+ oxidation states requires that the films be grown under fairly \nreducing conditions (~10-6 Torr) and at low substrate temperatures (~350 ºC).20\n To realize epitaxial growth of NFO and CFO films  at lower temperatures , one needs to \nenhance the oxidation ability and also the  kinetic energy of the ablated species. For conventional \nPLD in oxygen ambient , the background pressure used is generally in the range of  several \nhundred mTorr. In this case, the mean free path of molecules is much shorter than the target -\nsubstrate distance and the kinetic energy of ablated species is  dramatically reduced  because of  \ngas phase scatt ering  and reaction . For NFO and \nCFO , which are not easily oxidized, films are generally grown and /or ex-situ annealed at \nrelatively high temperatures  (≥ 600 °C) . \n21 The oxidation capability at lower temperatures can be \nsignificantly enhanced by using ozone, thereby also enabling reduction of the background \npressure required for stoichiometric film growth. If the pressure can be reduced to a few mTorr while maintaining the oxygen activity,  the mean free path of molecules will be  comparable to the \ntarget -substrate distance  and the high kinetic energy of the ablate species reaching the substrate \ncan be preserved  to enable film growth at lower temper atures . In this study, we report  a robust \nepitaxial growth mode for spinel ferrite films which can overcome the obstacles incurred in conventional film growth mode. Specifically, we  demonstrate that epitaxial Ni/Co spinel ferrites  5 films , with large- scale atomic ally flat surface and enhanced magnetic moment , can to be grown \nat significantly lower temperature s than previously reported.  \n \nII. Experimental  \n   We prepared a series of NFO and CFO on (100) -oriented MAO substrates at various \ntemperatures (175, 250, 325, 400, 550, 690 ºC), all under identical laser conditions of near 1.5 \nJ/cm2 and high repetition rate of 10 Hz, and with background oxygen pressure of 10 mTorr \nmixed with 10 -15% of ozone. The film growth was monitored in situ  using reflection high \nenergy electron diffraction (RHEED). After growth, the samples were cooled down to room temperature under an ozone/oxygen pressure of 100 mTorr. Prior to deposition, the substrates were annealed between 1300 -1400 ºC in air for 6 hrs to obtain an atomically -flat step and terrace \nprofile. NFO films were also grown at temperatures as low as 100 ºC but they showed poor magnetic properties, although the surface morphology and RHEED pattern were similar to higher temperature grown films. Films grown at room temperature were  amorphous. For \ncomparison purpose, some films were also deposited on (100) -oriented STO and MgO substrates \nat 250 ºC.    A standard θ -2θ x-ray diffraction setup (Phillips X’ pert Pro) was used to determine the \nphase and epitaxy of the films. XRD measureme nts were performed using a CuK α source \noperating at 45kV and 40 mA. Films surface morphology was characterized using atomic force microscopy (Veeco NanoScope) scanned in the tapping mode. The growth rate was calibrated using X -ray reflectivity, and film th icknesses were measured by Dektak surface profilometer and \nAFM. Energy -Dispersive X -ray Spectroscopy (EDS) was used to determine the film cation  6 stoichiometry. Magnetic properties of the NFO and CFO films were measured using a \nsuperconducting quantum inter ference device (SQUID) magnetometer.  \nIII. Results and Discussion  \nAtomic force microscopy (AFM) measurements reveal  that all films grown at and below \n550 ºC on MAO substrate are  atomic ally flat with clear steps, virtually identical to the substrate -  \neven for films thicker than 200 nm, as shown in Fig. 1(a) and (b)  for NFO films.  Typical step \nheights are nearly 4 Å (half unit -cell) or 8  Å (one unit -cell), as shown in Fig. 1(d). On increasing \nthe temperature to 690 ºC, quasi -3D growth is observed for the NFO film as shown in Fig. 1(c), \nbut the step pattern of the substrate can still be faintly distinguished. A 1×1 µm2 image of the \nfilm is provided in the inset to Fig. 1(c) exhibiting islands  of less than 3 nm  in height (Fig. 1(e). \nAlmost identical surface morphology has also been observed as a function of growth temperature \nfor CFO films (not shown). The AFM measurements are consistent with the RHEED patterns recorded after films growth, as shown i n the upper -left insets of Figures 1(a) and 1(c). All the \nfilms  (except the film grown at 690 ºC) show very clear streaky RHEED patterns, indicating \ntwo-dimensional (2D) type epitaxial growth . No RHEED oscillations are observed, but  the \nRHE ED pattern and s treak intensities remain  essentially unchanged throughout the growth  \nprocess , similar to that observed for step flow growth mode. Moreover, w e have determined  that \nthe surface morpholog y, as determined using AFM, remains essentially the same for films with \ndifferent th icknesses. Films grown at 690 ºC exhibit a spotty RHEED pattern, indicating island \ngrowth (3D). We have also grown NFO and CFO films on STO and MgO substrates at 250 ºC, all of which show atomically flat surfaces, essentially id entical to the substrate morphology as \nshown in Fig. 2, suggesting that the growth mechanism is independent of the substrate. We have \nused Energy -Dispersive X -ray Spectroscopy (EDS) to determine the film stoichiometry. For all  7 the NFO and CFO films, the Fe  to Ni/Co ratio is found to be close to the expected value of 2.0 \nbased on the target composition.  \nWe have carried out detailed texture and epitaxy analysis of our films, including \nsymmetric 2θ-θ scans, rocking curves, phi scans and reciprocal space maps. Large -angle 2θ-θ \nscans show only diffraction peaks corresponding to NFO or CFO film and the MAO substrate. \nNo evidence of any secondary phases is found. In Fig. 3(a) and (b) we plot θ  - 2θ spectr a near the \n(400) reflection of the MAO substrate  of NFO and C FO films , respectively,  grown at different \ntemperatures. All  the films  exhibit clear x-ray diffracti on peaks corresponding to the (400) film \nreflections, with the peak position gradually shifting to higher angles with increasing substrate \ntemperature, indicating a decrease in the out -of-plane lattice parameter ( az). This can either be \ndue to increasing strain relaxation or reduced oxygen deficiency with increasing growth temperatures.  Either way, since all films are nominally of the same thickness (with in 5% of each \nother), this effect is completely temperature driven .  \nIn Fig. 3(c) we plot  the growth temperature dependence of the calculated a\nz values . As is \nclear from the plots, NFO and CFO films behave quite differently. For NFO films , az decreases \nalmost monotonically from 175 ºC to 690 ºC but still above the bulk value (8.340Å, blue line) \neven at the highest growth temperature ( az = 8.361Å at 690 ºC) . For CFO films , az increases \nmuch more rapidly  for films grown below 325 ºC. At higher temperatures, the lattice consta nt \nappears to saturate to a value of nearly 8.405 Å, somewhat above the bulk value of 8.390 Å for CFO (red line) .  \nEpitaxial analysis has been further carried out by performing phi -scans around the (311) \nreflection of the film and substrate. In Fig. 3( d) we show the phi -scans for the NFO films (CFO \nfilms show qualitatively similar behavior). Four sharp peaks, 90 degree s apart, confirm cubic  8 symmetry of the films down to the lowest temperature (175 ºC). Higher temperature improves \nboth the FWHM and peak intensities of the phi scans, consistent with  the texture analysis from \nrocking curves measurements  as shown in Fig. 4. We observe  more than a factor of five \nimprovement in full -width at half -maxima (FWHM) and intensity for NFO films grown at 550 \nºC (FWHM ~ 0.3º) and 690 ºC (FWHM ~ 0.2º) as compared to the low temperature films (FWHM ~ 1.0º). For the CFO films, the improve ment in texture is more gradual as compared to \nNFO.  \nOverall, x -ray measurements reveal varying degree of epitaxy for all films, with \nincreasing temperature improving both the film texture and epitaxy. This conclusion, even though understandable is still s urprising for the following reason: One straight -forward \nconsequence of low temperature growth is the lack of surface diffusion for the incident species, and at a low enough temperature this is expected to prevent single phase formation and, therefore, cry stalline growth . This clearly is not the case for our films. Since we do not find any \nevidence of temperature -related phase instability, we conclude that the temperature requirement \nfor the NFO and CFO phase formation is lower than 175 ºC, particularly in the phase space of our deposition conditions. Once phase formation is guaranteed, epitaxy and texture improves steadily with temperature, as expected. Also, the epitaxy and texture improvement can be roughly correlated with smoothening of the step -terrace features of the AFM images at higher \ntemperatures. We next present our magnetic analysis.  \nIn Fig. 5(a) we plot magnetization loops measured at 5K for NFO (blue) and CFO (red) \nfilms grown at 325 ºC . Films grown at other temperatures exhibit a  similar loop s hape and \ncoercivity, differing only in the saturation magnetization. The magnetization saturate s fairly well \nat around 3 Tesla, suggestive of  a low density of anti -phase boundaries (APB s), consistent with  9 the report of Rigato et al .22\n5 The coercive fields are about 0.3 T and 1.1 T for NFO and CFO \nfilms , respectively. Th ese value s are higher than the literature reports, but it is well known that \ncoercivity depends on extrinsic factors such as  growth conditions, post -deposition annealing, etc.  \nFig. 5(b) shows the growth temperature dependence of the saturation magnetization  (MS) values \nof NFO and CFO films . For both films, a similar qualitative trend is observed. The MS values are \nclose to the bulk values of 300 emu/cc and 450 emu/cc for NFO and CFO , respectively , for the \nfilms grown at higher temperatures (550  ºC and 690 ºC). Among the films grown at lower \ntemperatures, we observe an enhanced  magnetization for films grown at 400  ºC and 325  ºC, \nwhile the values are somewhat  below that for the bulk for films deposited at or lower than 250  \nºC. The increase in the saturation magnetization value of CFO films grown at intermediate \ntemperatures is especially striking, over 500 emu/cm3 - about 15- 20% higher than the bulk value. \nAs mention ed earlier, s uch anomalous values have previously been reported in ultra -thin NFO \nfilms . In our films, the high magnetization values are also likely  due to te mperature -induced \ncation -disorder.  It is encouraging that even for films grown at 175 ºC the MS values are still \nclose to the bulk values implying even these films are not far from the expected inverse -spinel \nconfiguration. The NFO and CFO films grown on STO substrates show reduced saturation \nmagnetization of nearly 200 emu/cc for NFO, and less than 300 emu/cc for CFO. This is \nconsistent with earlier literature reports.14 \n Here we discuss the possible growth mechanism. As illustrated in Fig. 6(a), the (100) \nspinel surface has a relatively open structure with both the octahedral and tetrahedral surface \nsites not being blocked during the growth process. The tetrahedral sites form a ( 2/2)as×(2\n/2)as-45º ( as = lattice constant) unit cell at the surface (marked as black square in Fig. 6(a))  and \nthe octahedral sites (marked as red rectangle) forms a ( 2/2)as×(2/4)as-45º unit cell. For the  10 inverse spinel ferrites NFO and CFO, the Fe ions will occupy both the octahedral and tetrahedral \nsites, while Ni/Co ions will occupy only the octahedral sites. The relatively lo w ozone/oxygen \npressure used during growth ensures that the incident species have sufficient kinetic energy required for such an activity. Furthermore, ozone helps in enhancing  the oxidation kinetics  at low \ntemperatures . We speculate that the ablated catio n species  that reach the s ubstrate surface locally \ncrystallize at the nearest available site without requiring long -range surface diffusion. This, we \nbelieve, is unique to spinels and maybe related to the fact that many equivalent configurations are possib le that maintain the spinel crystallographic symmetry. We term this growth as “vertical \nstep-flow mode” since it is reminiscent  of the “lateral” step -flow growth where the adatoms \nnucleate at the step terrace and propagate to the step edge (see Fig. 6 (b)). This helps explain why the streaky RHEED pattern remains essentially unchanged during growth and atomically flat surfaces are preserved even for thick films.  \nIV. Summary  \nIn summary, we have demonstrated a novel growth mode, which we term “vertical step-\nflow”, for spinel ferrite films that results in high quality films with large -scale atomically flat \nsurface and enhanced magnetic moment. The growth mode is independent of the nature of substrates (MAO, STO, MgO) and film thicknesses, and results in epitax y at significantly lower \ntemperatures than previously reported. While the underlying mechanism is not completely understood, we speculate that our study will inspire further investigation for this novel growth \nprocess and promote device applications of spi nel films.  \nAcknowledgements  \nThis work was supported by ONR (Grant No. N00014- 09-0119). We thank G. Srinivasan of \nOakland University for helpful discussions and suggestions.   11 Figure Captions  \nFig. 1. 10 µm ×10 µm AFM images of NFO films grown at (a) 250 ºC, (b) 550 ºC, and (c) 690 ºC \non MAO (100) substrate s. Upper -left insets in (a) and (c) are the RHEED patterns recorded at the \ncompletion of film growth. The lower -left inset in (a) is the typical morphology (10  µm×10 µm) \nof a high temperature annealed MAO  (100) substrate. The lower -left inset in (c) is a zoom- in of \nthe film surface (1 µm × 1 µm). Fig. 1(d) and (e) are line profiles as marked in (a) and (c).  \nFig. 2. 2×2 μm2 AFM image of a 120 nm NFO thin film grown at 250 ° C on (001) STO substrate. Clear \nstep and terrace features of height 4Å are observed, similar to the MAO substrate.  Lower -left inset shows \nthe substrate morphology.  \nFig. 3. X-ray diffraction θ -2θ scans of (a) NFO and (b) CFO films grown at different \ntemperatures. (c) Growth temperature dependences of the determined lattice constants in the film \nnormal direction . Solid lines are the bulk NFO/CFO lattice constants.  (d) Phi scans of NFO films \ngrown at different temperature.  \nFig. 4.  Full width at half maxima (FWHM) values from the rocking curve measurements and phi scans of \nNFO films  grown at various temperatures. All the samples are between 200 -220 nm thick. The films  \ngrown at temperatures of 550 °C and 690 °C exhibit better e pitaxy and texture as compared to the low \ntemperature films .  CFO films  also show a similar (but slower) trend with increasing temperature.  \nFig. 5.  (a) Typical m agnetic hysteresis loops of NFO and  CFO films  grown at 325 ºC,  measured \nat 5K with magnetic field applied along the [001] in- plane direction. ( b) Plot of the saturation \nmagnetization of NFO and CFO films v ersus  growth temperature . \nFig. 6. (a) Surface structure of AB 2O4 spinel (001) with three layers illustrated. The black square \nrepresents the tetrahedral lattice sites and the red rectangle represents the octahedral sites. (b) and  12 (c) illustrate the propose “vertical” and its comparison with  the well established “lateral” step -\nflow growth mode, respectively.  \n \nReferences  \n                                                           \n1  J. D. Adams, S. V. Krishnaswamy, S. H. Talisa and K. C. Yoo, J. Magn. Magn. Mater . 83, 419  \n(1990) . \n2 Chaoyong Deng, Yi Zhang, Jing Ma, Yuanhua Lin, and Ce -Wen Nan, J. Appl. Phys . 102, \n074114 ( 2007) . \n3 Yi Zhang, Chaoyong Deng, Jing Ma, Yuanhua Lin, and Ce -Wen Nan, Appl. Phys. Lett. 92, \n062911( 2008) . \n4 J. J. Yang, Y. G. Zhao, H. F. Tian, L. B. Luo, H. Y. Zhang, Y. J. He, and H. S. Luo, Appl. Phys. \nLett. 94, 212504 ( 2009) . \n5 U. Luders, A. Barthé lemy, M . Bibes, K. Bouzehouane, S. Fusil, E. Jacquet, J.- P. Contour, J.- F. \nBobo, J. Fontcuberta, and A. Fert, Adv. Mater. 18 , 1733 ( 2006) . \n6 Michael G. Chapline and Shan X. Wang, Phys. Rev. B , 74, 014418 ( 2006) . \n7 A. V. Ramos, M.- J. Guittet, J.- B. Moussy, R. Mattana, C. Deranlot, F. P etroff, C. Gatel, Appl. \nPhys. Lett.  91, 122107 ( 2007) . \n8 C. M. Williams, D. B. Chrisey, P. Lubitz, K. S. Grabowski, and C. M. Cotell, J. Appl. Phys . 75, \n1676 ( 1994) . \n9 R. B. van Dover, S. Venske, E. M. Gyorgy, T. Siegrist, J. M. Phillips, J. H. Marshall, and R. J. \nFelder, Mater. Res. Soc. Symp. Proc . 341, 41( 1994) . \n10 Z.-J. Zhou, and J. J. Yan, J. Magn. Magn. Mater. 115, 87 ( 1992) .  13                                                                                                                                                                                            \n11 D. T. Margulies, F. T. Parker, F. E. Spada, and A. E. Berkowitz, Mater. Res. Soc. Symp. Proc.  \n341, 53 ( 1994) . \n12 S. A. Chambers, F. F. C. Farrow, S. Maat, M. F. Toney, L. Folks, J. G. Catalano, T. P. Trainor, \nG. E. Brown Jr., J. Magn. Magn. Mater. 246, 124 (2002) . \n13 Y. Suzuki, G. Hu, R. B. van Dover, R. J. C ava, J. Magn. Magn. Mater. 191, 1 ( 1999) . \n14 S. Venzke, R. B. van Dover, J. M. Phillips, E. M. Gyorgy, T. Siegrist, C. H. Chen, D. W erder, \nR. M. Fleming, R. J. Felder, E. Coleman, and R. Opila, J. Mater. Res.  11, 1187 ( 1996) . \n15 P. C. Dorsey, P. Lubitz, D. B. Chrisey, and J. S. Horwitz, J. Appl. Phys. 79, 6338 (1996) . \n16 a) D. T. Margulies , F. T. Parker, M. L. Rudee, F. E. Spada, J. N. Chapman, P. R. Aitchison, \nand A. E. Berkowitz , Phys. Rev. Lett. 79, 5162 (1997) ; b) W. Eerenstein, T. T. M. Palstra, T. \nHibma, S. Celotto , Phys . Rev. B 68, 014428 (2003) ; c) F. C. Voogt, T. T. M. Palstra, L. Niesen, \nO. C. Rogojanu, M. A. James, and T. Hibma Phys. Rev.  B 57, R8107 ( 1998) . \n17 F. K. LeGoues, M. Copel, and R. Tromp, Phys. Rev. Lett.  63, 1826 ( 1989) . \n18 D. J. Eaglesham and M. Cerullo, Appl. Phys. Lett. 58, 2276( 1991) ; D. J. Eaglesham, J. Appl. \nPhys.  77, 3597 ( 1995) . \n19 Takakazu Kiyomura and Manabu Gomi, Jpn. J. Appl. Phys. 40, 118 ( 2001) .  \n20 X. W. Li, A. Gupta, G. Xiao, W. Qian, and V. P. Dravid, Appl. Phys. Lett.  73, 3282 ( 1998).  \n21  A. Gupta, J. Appl. Phys. 73, 7877 ( 1993) . \n22  A. F. Rigato, S. Estrade, J. Arbiol, F. Peiro, U. Luders, X. Marti, F. Sanchez, J. Fontcuberta, \nMater. Sci . Eng. B  144, 43 ( 2007) . \n Substrate(a)\n1μm x 1μm (c)\nMa et al, Fig. 1 \n(b)\n00.81.62.43.2\n0 1 2 3 4(d)\n(µm)\n-0.80.82.445.6\n0 0.25 0.5 0.75 1(e)(nm)\n(µm)(nm)Ma et al, Fig. 2 (c) (d)\nMa et al, Fig. 3(a)\n175 °C250 °C325 °C400 °C690 °C\n550 °C(b)\n175 °C250 °C325 °C400 °C690 °C\n550 °C\n175 °C250 °C325 °C400 °C690 °C\n550 °C42 43 44 45\n  Log Intensity (arb. unit)\n2 T het a (Degr ee)(400) CFO MAO\n42 43 44 45\n  Log Intensity (arb. unit)\n2 Theta  (Degree)  (400) NFO MAO\n0 50 100 150 200 250 300 350 \n Intensity ( arb. unit)\nϕ (Degree )0 100 200 300 400 500 600 7008.208.258.308.358.408.458.508.558.60\n  Lattice Constant az (Å)\nGrowth Temperature ( °C)NFO\nCFOMa et al, Fig. 4 Ma et al, Fig. 50100 200 300 400 500 600 700 8000100200300400500600\nNFOCFO \n Growth Temperature (°C)Ms (emu/cm3)\n  \n(b)-4 -2 0 2 4-600-400-2000200400600 \n Magnetic Moment (emu/cm3)\nMagnetic Field (T)TS= 325 °C (a)Ma et al, Fig. 6AB2O4Spinel (100)  Surface Structure \n5.6 Ǻ\nA\nB\nO\n[100] [010](a)\nSubstrateSubstrate(b)\n(c)"    },    {        "title": "1905.13081v1.Determination_of_the_magnetic_permeability__electrical_conductivity__and_thickness_of_ferrite_metallic_plates_using_a_multi_frequency_electromagnetic_sensing_system.pdf",        "content": "1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial Informatics\nTII-18-2870                                                                                                                     1 \n \n  Abstract—In this paper, an inverse method was developed \nwhich can, in principle, reconstruct arbitrary permeability, \nconductivity, thickness, and lift-off with a multi-frequency \nelectromagnetic sensor from inductance spectroscopic \nmeasurements. \nBoth the finite element method and the Dodd & Deeds \nformulation are used to solve the forward problem during the \ninversion process. For the inverse solution, a modified Newton –\nRaphson method was used to adjust each set of parameters \n(permeability, conductivity, thickness, and lift-off) to fit \ninductances (measured or simulated) in a least-squared sense \nbecause of its known convergence properties. The approximate \nJacobian matrix (sensitivity matrix) for each set of the parameter \nis obtained by the perturbation method. Results from an \nindustrial-scale multi-frequency sensor are presented including \nthe effects of noise. The results are verified with measurements \nand simulations of selected cases. \nThe findings are significant because they show for the first time \nthat the inductance spectra can be inverted in practice to \ndetermine the key values (permeability, conductivity, thickness, \nand lift-off) with a relative error of less than 5% during th e \nthermal processing of metallic plates. \n \nIndex Terms —Electrical conductivity, electromagnetic sensor, \ninversion, lift-off, magnetic permeability, measurements, \nmulti-frequency, non-destructive testing (NDT), thickness \nI. INTRODUCTION  \nULTI-frequency electromagnetic sensors, such as EM- \nspec [1], are now being used to non-destructively test the \nproperties of strip steel on-line during industrial \nprocessing. These sensors measure the relative permeability of \nthe strip during process operations such as controlled cooling \nand the permeability values are analyzed in real time to \ndetermine important microstructural parameters such as the \ntransformed fraction of the required steel phases.  These \nparameters are critical to achieving the desired mechanical \nproperties in the strip product. The inductance spectra produced \n \nThis work was supported by [UK Engineering and Physical Sciences \nResearch Council (EPSRC)] [grant number: EP/M020835/1] [title: \nElectromagnetic tensor imaging for in-process welding inspection]]. Paper no. \nTII-18-2870. (Corresponding author: Yuedong Xie .)  \nThe authors are with the School of Electrical and Electronic Engineering, \nUniversity of Manchester, Manchester, M13 9PL UK (e-mail: \nmingyang.lu@manchester.ac.uk; yuedong.xie@warwick.ac.uk; wenqian.zhu \n@manchester.ac.uk; a.peyton@manchester.ac.uk; wuliang.yin@manchester \n.ac.uk). \n by the sensor are not only dependent on the magnetic \npermeability of the strip but is also an unwanted function of the \nelectrical conductivity and thickness of the strip and the \ndistance between the strip steel and the sensor (lift-off). The \nconfounding cross-sensitivities to these parameters need to be \nrejected by the processing algorithms applied to inductance \nspectra. \nIn recent years, the eddy current technique (ECT) [2-5] and \nthe alternating current potential drop (ACPD) technique [6-8] \nwere the two primary electromagnetic non-destructive testing \ntechniques (NDT) [9- 21] on metals’ permeability \nmeasurements. However, the measurement of permeability is \nstill a challenge due to the influence of conductivity, lift-off, \nand thickness of the detected signal. Therefore, decoupling the \nimpact of the other parameters on permeability is quite vital in \npermeability measurement [22-24]. Some studies have been \nproposed for the ferrous metallic permeability prediction based \non both the eddy current technique and alternative current \npotential drop method. However, these methods all use a low \nexcitation frequency (typically 1 Hz-50 Hz), which may reduce \nthe precision of the measurement. Yu has proposed a \npermeability measurement device based on the conductivity \ninvariance phenomenon (CIP) [25], and the measured results \ntested by the device were proved to be accurate. The only \nimperfection of this device is requiring substrate metal on the \ntop and bottom sides of the sample, which is impractical in \nsome applications, for example, in cases where only one side of \nthe sample is accessible. Adewale and Tian have proposed a \ndesign of novel PEC probe which would potentially decouple \nthe influence of permeability and condu ctivity in Pulsed \nEddy-Current Measurements (PEC) [26]. They reveal that \nconductivity effects are prominent on the rising edge of the \ntransient response, while permeability effects dominate in the \nstable phase of the transient response; this is as we encountered \nin multi-frequency testing, as the rising edge of the transient \nresponse contains high-frequency components while the stable \nphase contains lower frequency components and low frequency \nis more related to permeability contribution due to \nmagnetization. They use normalization to separate these \neffects. \nThis paper considers the cross-sensitivity of the complex \nspectra from a multi-frequency inductance spectrum to the four \nvariables namely, permeability, conductivity, thickness, and \nlift-off with tested sensors.  The paper then goes further to \nconsider the solution of the inverse problem of determining \nunique values for the four variables from the spectra. There are \ntwo major computational problems in the reconstruction Determination of the magnetic permeability, \nelectrical conductivity, and thickness of ferrite \nmetallic plates using a multi -frequency \nelectromagnetic sensing system  \nMingyang Lu , Yuedong Xie, Wenqian Zhu, Anthony Peyton, and  Wuliang Yin , Senior Member, IEEE   \nM 1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial Informatics\nTII-18-2870                                                                                                                     2 \n \n  process: the forward problem and the inverse problem. The \nforward problem is to calculate the frequency-dependent \ninductance for metallic plates with arbitrary values of \npermeability, conductivity, thickness, and lift-off (i.e. the \ndistance between the sensor and test sample). The inverse \nproblem is to determine each profile’s sensitivity, i.e. the \nchanges in each profile (permeability, conductivity, thickness, \nand lift-off with tested sensors) from the changes in \nfrequency-dependent inductance measurements. A dynamic \nrank method was proposed to eliminate the ill-conditioning of \nthe problem in the process of reconstruction. Profiles of \npermeability, conductivity, thickness, and lift-off have been \nreconstructed from simulated and measured data using an EM \nsensor, which has verified this method .  \nII. SAMPLES & FORWARD PROBLEM  \nBoth the finite-element method and the Dodd and Deeds \nformulation [27] are used to solve the forward problem during \nthe inversion process.  The sensor is composed of three \ncoaxially arranged coils, configured as an axial gradiometer; \nwith the three coils having the same diameter.  The central coil \nis a transmitter and the two outer coils are receivers and \nconnected in series opposition.  A photograph of the sensor is \nshown in figure 1, with its dimensions in Table I. The design of \nthis sensor is such that both the measurements and the \nanalytical solution of Dodd and Deeds are accessible, however, \nthe geometry of the sensor has also been designed so that a \nhigh-temperature version can be fabricated for use at high \ntemperatures in a production furnace and consequently \nmagnetic components such as a magnetic yoke cannot be used. \nThe detailed design of the industrial high-temperature version \nof the sensor is beyond the scope of this paper. \nThe samples were chosen to be a series of dual-phase steel \n(DP steel) samples - DP600 steel (with an electrical \nconductivity of 4.13 MS/m, relative permeability of 222, and \nthickness of 1.40 mm), DP800 steel (with an electrical \nconductivity of 3.81 MS/m, relative permeability of 144, and \nthickness of 1.70 mm), and DP1000 steel (with an electrical \nconductivity of 3.80 MS/m, relative permeability of 122, and \nthickness of 1.23 mm)  and same planar  dimensions of 500 × \n400 mm size. The same probe was used for measurements at \nseveral lift-offs of 5 mm, 30 mm, 50 mm, and 100 mm. All \nthese samples parameters are obtained from our previous work \nin [33]. The steels contained 0.1-0.2 wt% C and 1.5 – 2.2 wt% \nMn, the amount of these elements generally increasing with \nincreasing strength. Additions of Nb and Ti are also used to \nachieve strength levels of DP800 and DP1000. The exact \nchemical composition is confidential. The microstructure is \nproduced by controlling the transformation of austenite after \nhot rolling. Metallographic samples were taken in the \ntransverse direction, prepared to a 1/4-micron polish finish, and \netched in 2% nital. The samples were imaged using a \nJEOL7000 SEM (SEM micrograph in figure 1 (c)). The ferrite, \nbainite/tempered martensite, and martensite phases were \nmanually distinguished based on the contrast within the grains, \nand the percentage of each phase present was quantified using \n“Image J” image analysis software. Results are included in \nTable II. For the experimental setup, a symmetric electromagnetic \nsensor was designed for steel mic ro-structure monitoring in the \nContinuous Annealing & Processing Line (CAPL). There are \nthree coils winded for the CAPL sensor. The excitation coil sits \nin the middle and two receive coils at bottom and top \nrespectively. One receive coil is used as the test coils; the other \nis used as a reference. The difference between the two receive \ncoils is recorded.  In order to better understand the CAPL \nsensor performance, a dummy sensor has been built for the lab \nuse, shown in figure 1(a). The diameter of the sensor is 150 \nmm. Each of the coils has 15 turns, and the coil separation is 35 \nmm. Details of sensor dimensions are shown in Table I. \nSolartron Impedance Analyzer SI1260 is used to record the \nexperimental sensor output data. \nSteel users are placing increasing competitive pressure on \nproducers to supply ever more sophisticated steel grades to \ntougher specifications, especially in the automobile and \npipeline sectors. This drives the need to monitor microstructure \nonline and in real time to help control material properties and \nguarantee product uniformity. To achieve this task, robust and \nprocess-compliant instrumentation is required. There are a \nsmall number of commercial systems that can assess steel \nquality by exploiting changes in magnetic properties. These \nsystems typically operate at positions in the processing route \nwhere the steel is at ambient or relatively low temperatures. \nHowever, it is important to log and control microstructure \nduring hot processing, where the hot steel is undergoing a \ndynamic transformation. Figure 1(b) shows the development \nand implementation of a new electromagnetic (EM) inspection \nsystem - EMspec for assessing microstructure during controlled \ncooling on a hot strip mill. The EM inspection system exploits \nmagnetic induction spectroscopy, i.e., the frequency dependent \nresponse of the strip, to determine a transformation index which \ncan characterize the evolution of the microstructure during \ncooling. This system is able to link microstructure of steel, via \nits EM properties, to the response of the EM inspection system \noverall. \n \n(a) \n \n(b) \n \nReceive coil1  \nReceive coil2  \nExcitation coil  \n1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial Informatics\nTII-18-2870                                                                                                                     3 \n \n   \nFig. 1.  (a)Sensor configuration (b) EMspec system (c) Images by JEOL7000 \nSEM micrograph \n \nTABLE I \nCOILS PARAMETERS \nParameters  Value  Unit \nInner diameter  150 mm \nOuter diameter  175 mm \nlift-offs 5, 30, 50, 10 0 mm \nCoils height  10 mm \nCoils gap  35 mm \nNumber of turns    \n N1(Excitation coil) = N2(Receive \ncoil1) = N3(Receive coil2)  15 / \n \nTABLE II \nFERRITE FRACTIONS OF DP SAMPLES \nDP samples  Percentage of \nferrite (%)  \nDP600  83.6 \nDP800  78.4 \nDP1000  40.0 \nHere, the Dodd Deeds analytical solution is chosen to be \nthe forward problem solver.  \nThe Dodd Deeds analytical solution describes the \ninductance change of an air-core coil caused by a layer of the \nmetallic plate for both non-magnetic and magnetic cases [28, \n29]. Another similar formula exists [30]. The difference in the \ncomplex inductance is  ΔL(ω)= L(ω)− L A(ω), where the coil \ninductance above a plate is  L(ω), and LA(ω) is the inductance \nin free space.   \nThe formulas of Dodd and Deeds are: \n      \n2\n60P ( )L( ) K A( ) ( )d                       (1) \nWhere, \n          \n1\n12c\n1 1 1 1\n2c\n1 1 1 1( )( ) ( )( )e()( )( ) ( )( )e\n                   \n     (2) \n   \n2\n1 r 0 j                                    (3) \n                          \n2\n0\n22\n12NKh (r r )                                  (4) \n          \n2\n1r\n1rP( ) xJ (x)dx\n                              (5) \n                    \n0(2l h g) 2h) 1 ( A e (e )                               (6) \nWhere, 0 denotes the permeability of free space. r \ndenotes the relative permeability of plate. N denotes the \nnumber of turns in the coil; r 1 and r 2 denote the inner and outer \nradii of the coil; while 𝑙0 and h denote the lift-off and the height \nof the coil, g denotes the gap between the exciting coil and \nreceiver coil. Here, both the finite-element method (FEM) and Dodd & \nDeeds simulations were computed on a ThinkStation P510 \nplatform with Dual Intel Xeon E5-2600 v4 Processor, with 16G \nRAM. FEM was scripted and computed by Ansys Maxwell; \nDodd & Deeds method was simulated on MATLAB. \n \nFig. 2 Finite element modeling of the CAPL dummy sensor \n \nFEM can also be used in this process. Ansys Maxwell is \nemployed for the finite element modeling of the CAPL dummy \nsensor. The FEM 3D model is shown in figure 2 above. Bot h \nthe sensor and steel sheet have the same dimension as the one \nused for the lab experiment.  \nFor the experimental data, the real part of the inductance is \ndefined from the mutual impedance of the transmitter and the \nreceiver coils:  \n( ) ( )Im( ) Im( )2air Z f Z fLjf\n  ( ) ( )Re( )2air Z f Z f\nf\n       (7) \n( ) ( )Re( ) Re( )2air Z f Z fLjf\n( ) ( )Im( )2air Z f Z f\nf\n     (8) \nWhere 𝑍(𝑓)  denotes the impedance of the coil with the \npresence of samples while 𝑍𝑎𝑖𝑟(𝑓)  is that of the coil in the air. \nIII. INVERSE PROBLEM  \nThe inverse problem, in this case, is to determine the \npermeability, conductivity, thickness, and lift-off with tested \nsensors profiles from the frequency-dependent inductance \nmeasurements. A modified Newton –Raphson method is used to \nadjust each profile to fit inductances (measured or simulated) in \na least-squared sense because of its known convergence \nproperties [35]. \n  Definition of the problem is shown in follows. \n  1)\n0LRm  : observed inductances arranged in a vector \nform (In this paper, a corresponded expansion matrix \n0L with a \nreal part and imaginary part of observed inductance listed on \nthe top and bottom \nm rows of the matrix - i.e. \n00 [Re(L );Im(L )]0L\nis presented). And \nm is the number of \nfrequencies at which the inductance measurements are taken \n(here we select 10 frequency samples, i.e. \nm  = 10). \n  2)\nR  : electrical conductivity of the tested sample. \n  3)\nR  : permeability of the tested sample. \n  4)\ntR  : thickness of the tested sample. \n  5)\nlR  : lift-off of the sensors with respect to the sample \nplate. \n  6)\nf : R Rnm  is a function mapping an input signal \n[σ μ t l]\n with \nn  degrees of freedom (here \nn  = 4) into a set of \nm\napproximate inductance observations(In this paper, a \n1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial Informatics\nTII-18-2870                                                                                                                     4 \n \n  corresponded expansion matrix \nf with real part and imaginary \npart of observed inductance listed on the top and bottom \nm\nrows of the matrix - i.e. \nf  = [Re(f); Im(f)] is included). Here \nf\ncan be calculated by the forward problem method such as Dodd \nand Deeds method. \n  7)\n(1/ 2)[ ] [ ]   T\n00 f L f L is the squared error of the \nmeasured and estimated inductance. \nNote that \nf is a function of sample’s properties\n( , , , )σ μ t l  \nunder fixed measurement arrangements. The problem is to find \na point\n( , , , )   σ μ t l that is at least a local minimum of\n . To \nfind a candidate value of\n( , , , )   σ μ t l  that minimize\n ,\n is \ndifferentiated with respect to\n( , , , )σ μ t l  and the result is set \nequal to the zero vector 0. \n' [ '] [ ]   T\n0 f f L 0\n                             (9) \nThe term\n'f  is known as the Jacobian matrix, an m×n \nmatrix defined by (13). \nSince\ni, j[ ']f is still a nonlinear function of\n( , , , )σ μ t l , the \nTaylor series expansion of \ni, j[ ']f is taken from the reference \npoint\n( , , , )r r r rσ μ t l  and keeping the linear terms \n' ' ''   T\nr r r r r r r r ([σ ,μ ,t ,l ]) ([σ ,μ ,t ,l ])[Δσ Δμ Δt Δl]\n \n(10) \nWhere, \nT T T\nr r r r [Δσ Δμ Δt Δl] [σ μ t l] [σ  μ  t  l ] .The \nterm \n''r r r r(σ ,μ ,t ,l ) is called the Hessian matrix, which is \ndifficult to calculate explicitly, but can be approximated within \nthe small region about \nT\nr r r r[σ  μ  t  l ] by \nT'' [ ] [ ] r r r r r r r r r r r r (σ ,μ ,t ,l ) f'(σ ,μ ,t ,l ) f'(σ ,μ ,t ,l )\n  (11) \nSubstituting (9) and ( 11) into ( 10) and solving for\n[]TΔσ Δμ Δt Δl\n , we obtain \n 1T\nT[ ] [ ]\n                        [ ]\nT\nr r r r r r r r\nr r r r r r r r 0Δσ Δμ Δt Δl f'(σ ,μ ,t ,l ) f'(σ ,μ ,t ,l )\nf'(σ ,μ ,t ,l ) f(σ ,μ ,t ,l ) L\n(12) \nWhere,\n( , , , )r r r r fσ μ t l is the calculated inductance for \nconductivity profile \n()σ,μ,t,l using the forward solution, and\n0L\n is the measured inductance for the sample. From (12), in \norder to calculate\n[]TΔσ Δμ Δt Δl , we need to have the \nsensitivity matrix\n'( , , , )r r r rfσ μ t l , which can be written in a \nmatrix form\n( ) [Re(f ');Im(f ')] r r r rf'σ ,μ ,t ,l with, \n1111\n2222\nmmmmffff,,,tl\nffff,,,f' tl\nffff,,,tl\n      \n\n   \n                     (13) \nOne method of obtaining \n'( , , , )r r r rfσ μ t l is to derive it \nfrom the Dodd and Deeds forward formulation (1). However, \nthe resulting expression would be extremely complex even for \nmore parameters needed to be estimated. Alternatively, the \nperturbation method can be used. The principle of the \nperturbation method is that the sensitivity of the inductance \nversus the \n( , , , )σ μ t l (essentially\n'( , , , )r r r r fσ μ t l ) can be approximated by the inductance change, in response to a small \nperturbation from one of the\n( , , , )σ μ t l , divided by the \npermeability change. Therefore,\n'( , , , )r r r rfσ μ t l can be calculated \nin a column-wise fashion. The sensitivity matrix (14) can be \nobtained by dividing the inductance changes caused by a small \nparameter’s change.  \n \n1111\n2222\nmmmmffff1111\nffff 2222\nmmmm ffffIIII ffff,,, ,,,tl tl\nIIII ffff,,, ,,,tl tl\nffff IIII,,, ,,,tl tl                                  \n      (14) \nTo use (14) for the calculation of the sensitivity is \nessentially a first-order finite difference approach to \napproximate the derivatives. To evaluate the effect of using \nfinite changes of \n( , , , )σ μ t l in (14), different values of \n Δσ Δμ Δt Δl\nwere used to calculate the sensitivity matrix. It is \nfound that as we decrease the changes of\n Δσ Δμ Δt Δl , the \nsensitivity map approach a set of slightly increased absolute \nvalues. However, as can be seen from figures 3-6 , further \ndecreasing \n Δσ Δμ Δt Δl  would not make a significant \ndifference to sensitivity.  \nThe physical phenomena show that the eddy currents \ndecay exponentially or diffuse from the surface into the metal. \nIn its discrete form, the ill-conditioning in the Hessian matrix \ncan result in the magnification of measurement error and \nnumerical error in the reconstructed permeability profile. The \nsingularity of the Hessian matrix is caused by the insensitivity \nor the mutual inductance with respect to one of the parameters \nunder a specific frequency. For instance, the mutual inductance \nwill be immune to the thickness on a specific high frequency \ndue to the skin effect. Previously, the Tikhonov regularization \nmethod has been widely used in many inverse problems to deal \nwith the ill-conditioning. However, the estimated error \nresulting from the regularization cannot be neglected due to the \namendment of the sensitivity matrix. Here, a dynamic rank \nmethod is adopted to maintain that the results are estimated \nfrom the original unmodified sensitivity matrix, which has \nmuch improved the estimation accuracy. To simplify the \nnotation, using J to represent\n'( , , , )r r r r fσ μ t l , (12) becomes \n 1TT\n0 () T\nr r r r [Δσ Δμ Δt Δl] J J J f σ ,μ ,t ,l L\n    (15) \n \n[] T T T\nr r r r [σ μ t l] [σ  μ  t  l ] Δσ Δμ Δt Δl         (16) \nThe principle of the dynamic rank method is indexing the \ncolumns whose elements are all zeros or nearly zeros (This \nbecause some parameters may not influence or sensitive to the \ninductance under a certain frequency, as shown in Fig.3, i.e. the \nconductivity sensitivity map). Then reduce the rank of the \nsensitivity matrix J by omitting the indexed columns. For each \nstep in the iterative procedure, the corresponded rows of the \nestimated \nT[Δσ Δμ Δt Δl] should be valued zeros. 1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial Informatics\nTII-18-2870                                                                                                                     5 \n \n  Equations (15) and (16) can be used in an iterative fashion \nto find\n()σ*,μ*,t*,l* . This formulation is known as the \nGauss-Newton method. For each step in the iterative procedure, \nthe Jacobian matrix J needs to be updated, which involves a \nconsiderable amount of computation.  \nIV. PARAMETERS SENSITIVITY OF MULTI-FREQUENCY \nSPECTRA  \nThe following figures illustrate the effects of different \ndelta profiles (Δσ Δµ Δt Δl) on both the real part (a) and imaginary part (b) of the sensor and samples mutual inductance \nchange rate on the referred point ( σr µr tr lr) relative to \nsamples’ electrical conductivity (Re(∆L)\n∆σ  &  Im(∆L)\n∆σ), relative \npermeability (Re(∆L)\n∆μ & Im(∆L)\n∆μ), thickness (Re(∆L)\n∆t &  Im(∆L)\n∆t) and \nlift-off (Re(∆L)\n∆l & Im(∆L)\n∆l). Here the referred point \nr r r r(σ  μ  t  l )  is \nselected to be the properties of DP 600 steel sample with \nproperty profiles of (4.13 MS/m 222 1.4 mm 5 mm). \n \n(a)                                                                                               (b) \nFig. 3 Effects of different  (Δσ Δµ Δt Δl) on both real part (a) and imaginary part (b) of conductivity sensitivity of the referred point (Re(ΔL)/Δσ & Im(ΔL)/Δσ)  \n \n(a)                                                                                               (b) \nFig. 4 Effects of different  (Δσ Δµ Δt Δl) on both real part (a) and imaginary part (b) of relative permeability sensitivity of the referred point (Re(ΔL)/Δμ & \nIm(ΔL)/Δμ)  \n \n(a)                                                                                              (b) \nFig. 5 Effects of different  (Δσ Δµ Δt Δl) on both real part (a) and imaginary part (b) of sample thickness sensitivity of the referred point (Re(ΔL)/Δt & Im(ΔL)/Δt)  \n1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial Informatics\nTII-18-2870                                                                                                                     6 \n \n   \n(a)                                                                                             (b) \nFig. 6 Effects of different  (Δσ Δµ Δt Δl) on both real part (a) and imaginary pa rt (b) of sensors lift- offs sensitivity of the referred point (Re(ΔL)/Δl & Im(ΔL)/Δl)  \n \nFigures 3 to 6 show the frequency-dependent sensitivity of \nthe sample electrical conductivity, relative permeability, \nsample thickness, and sensor lift-off when different delta \nprofiles \nT[Δσ Δμ Δt Δl]  within in the sensitivity matrix are \nselected to be 1%, 5%, 10% and 50% of referred properties \nT\nr r r r[σ  μ  t  l ]\n ([4.13 MS/m 222 1.4 mm 5 mm]) respectively. It \nis found that as we decrease the changes of\n Δσ Δμ Δt Δl , the \nsensitivity curves approach a set of saturation curves. Further \ndecreasing \n Δσ Δμ Δt Δl  would not make a significant effect \non sensitivity spectra. Moreover, as can be seen from figure 3 to \n6, the thickness sensitivity generally leads the parameters effect \non inductance change rate. Since small changes in thickness \nwill result in significant changes in the inductance when \ncompared with other paramete rs, the reconstructed sample’s \nthickness, in general, should be the most accurate values among \nthe reconstructions of the samples’ properties (electrical \nconductivity relative permeability μ, sample thickness t, and \nsensors lift-offs  𝑙). \nV. RECONSTRUCTION  \nAs can be seen from Table III, the samples profiles are \nreconstructed more accurately from the Dodd and Deeds \nanalytical solution with a relative error of less than 5%, which \nis achieved by utilizing the proposed dynamic rank method to eliminate the ill-conditioning problem in the process of \nreconstruction. Currently, there is still no commercial system \nthat can simultaneously predict the four parameters (i.e. \nelectrical conductivity, magnetic permeability, thickness, and \nlift-off) from the measured inductance/impedance signals. \nCommonly, most of the commercial system can accurately \npredict single parameter from the measurements. Here, the \ninitial values \nT\nr r r r[σ  μ  t  l ] for the iterative search of the solution \nare 5M S/m, 100, 2 mm, and 4 mm; The FEM method used is a \ncustom-built solver software package which is more efficient \nthan the canonical FEM method especially on the \nfrequencies-sweeping mode. The solution of the field quantities \nunder each frequency, which involves solving a system of \nlinear equations using the conjugate gradients squared (CGS) \nmethod, is accelerated by using an optimized initial guess-the \nfinal solution from the previous frequency. More details of the \ncustom-built FEM software package are included in [34]. The \nsteel samples are finely meshed into a total number of 369 k \nelements prior to the FEM calculation. Besides, the inversion \nsolver using Dodd and Deeds analytical method shows a more \nefficient performance than FEM due to a significantly reduced \niteration number and operation time. Therefore, the following \nresults are all deduced from the inversion method using Dodd \nand Deeds method. \n \nTABLE III \n RECONSTRUCTION OF THE SELECTED SAMPLES ’ PROPERTIES (ELECTRICAL CONDUCTIVITY RELATIVE PERMEABILITY , SAMPLE THICKNESS , SENSORS LIFT-O FFS)  \nWHEN CALCULATED BY THE PROPOSED INVERSE SOLVER  \n Actual value  \n Estimated value by the proposed inverse \nsolver using Dodd and Deeds  Estimated value by the proposed inverse \nsolver using FEM  \nCase No.  1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 \nConductivity - σ (M S/m)  4.13 3.81 3.80 3.80 3.80 4.06 3.70 3.68 3.65 3.63 4.03 3.67 3.65 3.63 3.59 \nPredicted σ error (%)  / / / / / 1.69 2.89 3.16 3.95 4.47 2.42 3.67 3.95 4.47 5.53 \nRelative permeability - μ 222 144 122 122 122 229 138 120 119 116 231 134 117 116 113 \nPredicted μ error (%)  / / / / / 3.15 4.17 1.64 2.46 4.92 4.05 6.94 4.10 4.92 7.38 \nThickness - t (mm)  1.40 1.70 1.23 1.23 1.23 1.41 1.69 1.23 1.23 1.24 1.42 1.65 1.22 1.21 1.25 \nPredicted t error (%)  / / / / / 0.71 0.59 0 0 0.81 1.43 2.94 0.81 1.63 1.63 \nLift-off - l (mm)  5 5 5 30 50 5.02 5.03 5.06 30.41  50.63  5.04 5.05 5.08 30.83  50.92  \nPredicted l error (%)  / / / / / 0.40 0.60 1.20 1.37 1.26 0.80 1.00 1.60 2.77 1.84 \nIteration No.  / / / / / 7 5 4 15 22 89 67 103 77 92 \nComputation time \n(seconds)  / / / / / 21 19 23 17 26 556 523 583 537 563 \n1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial InformaticsTII-18-2870                                                                                                                     7 \n \n   \nFig. 7 Proposed inverse solver results and measurements of DP600 steel \ninductance multi-frequency spectra \n \nFig. 8 Proposed inverse solver results and measurements of DP800 steel \ninductance multi-frequency spectra \n  \nFig. 9 Proposed inverse solver results and measurements of DP1000 steel \ninductance multi-frequency spectra \n \nFigures 7 - 9 shows the inductance multi-frequency spectra \nof DP600, DP800, and DP1000 steel for both simulations from \nthe estimated samples’ properties calculated by the proposed inverse solver and measured results under a lift-off of 5 mm. It \ncan be seen that the real part and imaginary part of the \nmeasured inductance multi-frequency spectra curves are close \nto that of the proposed inverse solver results for all the DP steel \nsamples. \nIn practice, the observed inductance L0contains noise. \nTherefore, in this part, series of inductance L0 are produced by \nadding noise to the observed inductance  L0 . The noise has an \namplitude value of 1%, 5% and 10% of L0and fluctuate \nrandomly with frequency (i.e. L0± 1% × L0×R(f), L0± 5% \n×L0× R(f), L0± 10% × L0× R(f) with R(f) randomly fluctuat e \nin the range from 0 to 1 with frequencies). And the noise effect \non the estimation of DP600 steel sample is illustrated in Table \nIV. \nTABLE IV \nNOISE EFFECT ON THE ESTIMATION OF DP600  STEEL SAMPLE PROPERTIES \nWHEN CALCULATED BY THE PROPOSED INVERSE  \nParameters  Actual \nvalue  Estimated value by the \nproposed inverse solver  Unit \nFluctuate noise  threshold \n(error magnitude)  / 0 1% 5% 10% / \nConductivity  - σ 4.13 4.06 4.03 4.27 4.43 M S/m \nPredicted σ error  / 1.69 2.42 3.39 7.26 % \nRelative permeability  - μ 222 229 213 209 203 / \nPredicted μ error  / 3.15 4.05 5.86 8.56 % \nThickness  - t 1.40 1.41 1.41 1.42 1.45 mm \nPredicted t error  / 0.71 0.71 1.43 3.57 % \nLift-off - l 5 5.02 4.96 4.93 4.84 mm \nPredicted l error  / 0.40 0.80 1.40 3.20 % \nIteration No.  / 7 9 18 25 / \n \nAs can be seen from Table IV, with the introduction of \nmeasurements noise, the reconstructed parameters move \nfurther away from its actual value. But the reconstruction is still \naccurate with a relative error of less than 8.6 %. Same trends \nhave been observed for DP800 and DP1000 steel samples. \nVI. CONCLUSION  \nIn this paper, a method is presented which has the potential \nto reconstruct an arbitrary permeability, conductivity, \nthickness, and lift-off from inductance spectroscopic \nmeasurements with an EM sensor. The forward problem was \nsolved numerically using both the finite-element method \n(FEM) and the Dodd and Deeds formulation [13].  \nNormally, the Dodd and Deeds analytical method is the \nprimary choice, as it is much faster than FEM. For this reason, \nthe proposed solver has its limitations – it requires lots of \ncomputation time for the reconstruction of the parameters for \nthe samples excluded from the plate and cylinder geometry, \nsuch as a bent or defected plate. This is because the Dodd and \nDeeds methods can only valid for the simulation of plate and \ncylinder geometry. \nIn the inverse solution, a modified Newton –Raphson \nmethod was used to adjust the permeability profile to fit \ninductances (measured or simulated) in a least-squared sense. \nIn addition, a dynamic rank method was proposed to eliminate \nthe ill-conditioning of the problem in the process of \nreconstruction. Permeability, conductivity, thickness, and \nlift-off have been reconstructed from simulated and measured \ndata with a small error of 5% only within an operation time \n30seconds. However, the actual permeability used in our paper \nis only under room temperature. In fact, the steel’s permeability \n1551-3203 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE\nTransactions on Industrial InformaticsTII-18-2870                                                                                                                     8 \n \n  will change with temperature; and the changes rate varies for \ndifferent types of steel material, which will require lots of \nfurther measurements. Therefore, the inversion method \nperformance of steels under different temperature should be \nanalyzed for the next step. \nREFERENCES  \n \n[1] A. J. Peyton, C. L. Davis, F. D. Van Den Berg and B. M. Smith, “EM \ninspection of microstructure during hot processing: the journey from \nfirst principles to plant”,  Iron & Steel Technology , vol. 24, no. 11, pp. \n3317-3325, 2014. \n[2] M. Nabavi and S. Nihtianov, \"Eddy-Current Sensor Interface for \nAdvanced Industrial Applications\", IEEE Transactions on Industrial \nElectronics , vol. 58, no. 9, pp. 4414-4423, 2011. \n[3] A. Lumsdaine and J. Lang, \"State observers for variable-reluctance \nmotors\", IEEE Transactions on Industrial Electronics , vol. 37, no. 2, \npp. 133-142, 1990. \n[4] Y. He, M. Pan, F. Luo and G. Tian, \"Pulsed eddy current imaging and \nfrequency spectrum analysis for hidden defect nondestructive testing \nand evaluation\", NDT & E International , vol. 44, no. 4, pp. 344-352, \n2011. \n[5] Y. He and R. Yang, \"Eddy Current Volume Heating Thermography \nand Phase Analysis for Imaging Characterization of Interface \nDelamination in CFRP\", IEEE Transactions on Industrial Informatics , \nvol. 11, no. 6, pp. 1287-1297, 2015.  \n[6] X. Yuan, W. Li, G. Chen, X. Yin, W. Yang and J. Ge, \"Two-Step \nInterpolation Algorithm for Measurement of Longitudinal Cracks on \nPipe Strings Using Circumferential Current Field Testing System\", \nIEEE Transactions on Industrial Informatics , vol. 14, no. 2, pp. \n394-402, 2018. \n[7] N. Bowler and Y. Huang, \"Electrical conductivity measurement of \nmetal plates using broadband eddy-current and four-point methods\", \nMeasurement Science and Technology , vol. 16, no. 11, pp. 2193-2200, \n2005. \n[8] S. Sadeghi and D. Mirshekar-Syahkal, \"Scattering of an induced \nsurface electromagnetic field by fatigue cracks in ferromagnetic \nmetals\", IEEE Transactions on Magnetics , vol. 28, no. 2, pp. \n1008-1016, 1992. \n[9]  D. L. Wu D. Chatzigeorgiou K. Youcef-Toumi and R. Ben-Mansour \n“Node localization in robotic sensor networks for pipeline inspection ” , \nIEEE Transactions on Industrial Informatics , vol. 12 no. 2 pp. 809 –\n819 Apr. 2016.  \n[10] D. Naso, B. Turchiano and P. Pantaleo, \"A Fuzzy-Logic Based Optical \nSensor for Online Weld Defect-Detection\", IEEE Transactions on \nIndustrial Informatics , vol. 1, no. 4, pp. 259-273, 2005. \n[11] D. Tsai, I. Chiang and Y. Tsai, \"A Shift-Tolerant Dissimilarity \nMeasure for Surface Defect Detection\", IEEE Transactions on \nIndustrial Informatics , vol. 8, no. 1, pp. 128-137, 2012. \n[12] B. Gao, W. Woo, Y. He and G. Tian, \"Unsupervised Sparse Pattern \nDiagnostic of Defects With Inductive Thermography Imaging System\", \nIEEE Transactions on Industrial Informatics , vol. 12, no. 1, pp. \n371-383, 2016. \n[13] G. Wang and S. Yin “Quality -related fault detection approach based on \northogonal s ignal correction and modified PLS ”, IEEE Transactions \non Industrial Informatics , vol. 11 no. 2 pp. 398 –405 Apr. 2015. \n[14] G. Wang S. Yin and O. Kaynak “An LWPR -based data-driven fault \ndetection approach for nonlinear process monitoring ”, IEEE \nTransactions on Industrial Informatics , vol. 10 no. 4 pp. 2016 –2023 \nNov. 2015. \n[15] X. W. Dai and Z. W. Gao “From model signal to knowledge: A \ndata- driven perspective of fault detection and diagnosis ”, IEEE \nTransactions on Industrial Informatics , vol. 9 no. 4 pp. 2226 –2238 \nNov. 2013. \n[16] M. Staroswiecki “Intelligent sensors: A functional view ”, IEEE \nTransactions on Industrial Informatics , vol. 1 no. 4 pp. 238 –249 Nov. \n2005. \n[17] B. Gao, Y. He, W. Lok Woo, G. Yun Tian, J. Liu and Y. Hu, \n\"Multidimensional Tensor- Based Inductive Thermography With \nMultiple Physical Fields for Offshore Wind Turbine Gear Inspection\", \nIEEE Transactions on Industrial Electronics , vol. 63, no. 10, pp. \n6305-6315, 2016. [18] B. Gao, W. Woo, G. Tian and H. Zhang, \"Unsupervised Diagnostic \nand Monitoring of Defects Using Waveguide Imaging With Adaptive \nSparse Representation\", IEEE Transactions on Industrial Informatics , \nvol. 12, no. 1, pp. 405-416, 2016. \n[19] F. Adly, O. Alhussein, P. Yoo, Y. Al-Hammadi, K. Taha, S. Muhaidat, \nY. Jeong, U. Lee and M. Ismail, \"Simplified Subspaced Regression \nNetwork for Identification of Defect Patterns in Semiconductor Wafer \nMaps\", IEEE Transactions on Industrial Informatics , vol. 11, no. 6, pp. \n1267-1276, 2015. \n[20] F. Adly, O. Alhussein, P. Yoo, Y. Al-Hammadi, K. Taha, S. Muhaidat, \nY. Jeong, U. Lee and M. Ismail, \"Simplified Subspaced Regression \nNetwork for Identification of Defect Patterns in Semiconductor Wafer \nMaps\", IEEE Transactions on Industrial Informatics , vol. 11, no. 6, pp. \n1267-1276, 2015. \n[21] G. Wang and S. Yin, \"Enhanced quality-related fault detection \napproach based on OSC and M-PLS\", IEEE Transactions on Industrial \nInformatics , pp. 1-1, 2015. \n[22] W. Yin, X. Hao, A. Peyton, M. Strangwood and C. Davis, \n\"Measurement of permeability and ferrite/austenite phase fraction \nusing a multi-frequency electromagnetic sensor\", NDT & E \nInternational , vol. 42, no. 1, pp. 64-68, 2009. \n[23] A. Goldberg, J. Kassakian and M. Schlecht, \"Issues related to \n1-10-MHz transformer design\", IEEE Transactions on Power \nElectronics , vol. 4, no. 1, pp. 113-123, 1989. \n[24]  Y. Tian, \"Electrical conductivity and magnetic permeability \nmeasurement of case hardened steels.\" AIP Conference Proceedings,  \nvol. 1650. no. 1. AIP, 2015. \n[25] Y. Yu, Y. Zou, M. Hosani and G. Tian, \"Conductivity Invariance \nPhenomenon of Eddy Current NDT: Investigation, Verification, and \nApplication\", IEEE Transactions on Magnetics , vol. 53, no. 1, pp. 1-7, \n2017. \n[26] I. Adewale and G. Tian, \"Decoupling the Influence of Permeability and \nConductivity in Pulsed Eddy-Current Measurements\", IEEE \nTransactions on Magnetics , vol. 49, no. 3, pp. 1119-1127, 2013. \n[27] C. Dodd and W. Deeds, \"Analytical Solutions to Eddy ‐Current \nProbe ‐Coil Problems\", Journal of Applied Physics , vol. 39, no. 6, pp. \n2829-2838, 1968. \n[28] W. Yin, R. Binns, S. Dickinson, C. Davis and A. Peyton, \"Analysis of \nthe Liftoff Effect of Phase Spectra for Eddy Current Sensors\", IEEE \nTransactions on Instrumentation and Measurement , vol. 56, no. 6, pp. \n2775-2781, 2007. \n[29] W. Yin, A. Peyton and S. Dickinson, \"Simultaneous Measurement of \nDistance and Thickness of a Thin Metal Plate With an Electromagnetic \nSensor Using a Simplified Model\", IEEE Transactions on \nInstrumentation and Measurement , vol. 53, no. 4, pp. 1335-1338, \n2004. \n[30] A. Bernieri, G. Betta, L. Ferrigno and M. Laracca, \"Crack Depth \nEstimation by Using a Multi-Frequency ECT Method\", IEEE \nTransactions on Instrumentation and Measurement , vol. 62, no. 3, pp. \n544-552, 2013. \n[31] W. Yin, S. Dickinson and A. Peyton, \"Evaluating the Permeability \nDistribution of a Layered Conductor by Inductance Spectroscopy\", \nIEEE Transactions on Magnetics , vol. 42, no. 11, pp. 3645-3651, \n2006. \n[32] X. Luo, M. Zhou, Y. Xia and Q. Zhu, \"An Efficient Non-Negative \nMatrix-Factorization-Based Approach to Collaborative Filtering for \nRecommender Systems\", IEEE Transactions on Industrial Informatics , \nvol. 10, no. 2, pp. 1273-1284, 2014. \n[33] M. Lu, H. Xu, W. Zhu, L. Yin, Q. Zhao, A. J. Peyton and W. Yin, \n\"Conductivity Lift-off Invariance and measurement of permeability for \nferrite metallic plates\", NDT & E International , vol. 95, pp. 36-44, \n2018 \n[34] M. Lu, A. J. Peyton and W. Yin, \"Acceleration of Frequency Sweeping \nin Eddy-Current Computation.\" IEEE Transactions on Magnetics , vol. \n53, no. 7, pp. 1-8, 2017. \n[35] M.J. Lindstrom, and D.M. Bates,  \"Newton —Raphson and EM \nalgorithms for linear mixed-effects models for repeated-measures \ndata.\" Journal of the American Statistical Association , vol. 44, no. 404, \npp. 1014-1022, 1988. "    },    {        "title": "1710.08604v1.Peculiar_metastable_structural_state_in_carbon_steel.pdf",        "content": "PECUL IAR METASTABLE  STRUCTURAL STATE IN  CARBON STEEL  \nS.A. Murikov1, A.V. Shmakov1, V.N. Urtsev1, I.L. Yakovleva2, Yu.N. Gornostyrev2,3,4, \nM.I. Katsnelson4,5, M.L. Krasnov5 \n1Research and Technological Center Ausferr, Magnitogorsk 455000, Russia  \n2Institute of Metal Physics, Ural Division of RAS, Ekaterinburg 620041, Russia  \n3Institute of Quantum Materials Science, Ekaterinburg 620075, Russia  \n4Ural Federal University, Ekaterinburg 620002, Russia  \n5Radboud University Nijmegen, Nijmegen 6525AJ, The Netherlands  \n6Magnitogorsk Iron and Steel Works, Magnitogorsk 455000, Russia  \n \nThe k inetics of phase transformations at cooling of carbon steel  in dependence on the \ntemperature of  preliminary annealing  Tan is studied . It is shown  that the cooling  from  Tan > A3 \n(i.e. above the temperature  of ferrite  start) with the rate  90 – 100 K/s results in  structural state \nwhich  essentially dependent on  Tan; at 7500С < Tan < 8300C the transformation is of perlite type \nwhereas at Tan > 8300C the martensitic structure arises. Our  results  evidence  the formation of a \nspecial structural state  in a certain range of temperatures near  and above  the boundary of two \npase region  which is characterize d by  a substantially nanoscale heterogene ity in carbon \ndistribution , lattice distortions , and magnetic short -range  order.  \n \n \n1. Introduction   \nBy now steel remains the main construction material of our technology due to high \navailability of its main components (Fe and C) and diversity of properties reached by realization \nof various structural states. The latter is possible due to a rich phase diagram of iron with several \nstructural transformations  at coo ling from high temperatures  (paramagnetic bcc Fe) → \nparamagnetic fcc Fe ) → ferromagnetic bcc Fe . The presence of carbon adds carbide \nphases , cementite Fe 3C being the most important one  [1,2].   \nDevelopment of the phase transformations in steel includes two main types of processes: the \ncrystal lattice reconstruction and redistribution of carbon between the phases.  Competition  of \nthese processes  results in diversity of structural states of steel which can be realized depending  \non composition and c ondition s of thermal treatment. As it commonly accepted (see  discuss ion in \nRefs [3,4,5]), the variation of magnetic order plays a decisive role in  regular  evolution  of \ntrans formation mechanism  with temperature from martens ite (development of lattice instability  \nat rather  deep overcooling ) to ferrite (nucleation  and growth just below the temperature  of  –  \nequilibrium ). Whereas,  the bainite and pearlite transformation s take place at intermediate \ntemperature range due to an  interplay  of diffusion and shear processes  [5,6] and results in \nmicrostructure with alternati ng -Fe and cementite phases .   \nIt is commonly  accepted , that the realization of a certain microstructure  during thermal \ntreatment depend s on the cooling regime, chemical composition [ 1,2] and the prior austenite \ngrain size [ 7]. At the same time , the achieved structural state  is not sensitive to the start  \ntemperature  of cooling in austenite region (if other conditions  remain the same ). Such an \nassumption is based on the idea that the austenite is a homogeneous solid solution of carbon in \nfcc iron in whole  its phase stability region . This concept is supported by  the results of X -ray and \nneutron diffraction [ 8] as well a s the Mössbauer spectroscopy [ 9,10] which did not reveal \ndeviations from a random distribution of carbon impurity atoms in fcc iron.  As a result, the \nstructural state of  the overcooled austenite does  not depend on the initial  annealing  conditions .  \nIn this paper, we demonstrate that this concept is not complete . We show that holding  of \naustenite just above the two-phase   +  region  followed by a rapid cooling  results in  pearlite transformation while annealing  of austenite at higher temperature lead s to martensite \ntransformation. The r esults obtained demonstrate the  existence of  a peculiar  state of austenite in \nthe temperature region close to the boundary of two-phase  region  what provides a new \nperspective  at the phase transformation in steel.  \n \n2. Experimental  methods   \nThe transformation kinetics was studied by using the specially designed research facility that \nallows us to measure with high accuracy t he temperature changes  during cooling /heating  and the \nheat of phase trans formation. The samples were made of carbon steel with  the base composition \n0.65C–0.26Si–0.99Mn (wt%) ; they were rectangular plates with a thickness of 0.6 mm. To \nachieve an equilibrium state , the sample was heated in an electric furnace followed by holding \nfor 5 – 10 minutes  at temperature  Tan above the eutectoid point  in the range  7200 – 9500C. The \nsample was then quickly removed from the furnace by a special mechanical device while  air \ncooling system was be ing activated. The rate of the cooling was ranged  by change of pressure \nbefore greed of nozzles. The temperature of the sample  was measured by three pyrometers  \noperating at  different temperature ranges; the following results w ere obtained by combining  \nindications of all of them . Two pyrometers Raytek  Marathon FR1A were operating in the \ninterval of the infrared spectrum corresponding 550-1100° С and the third one was high -speed \npyrometer OPTRIS CTfast  working in middle infrared interval 50 -775° С. One infrared \npyrometer was used for calibration, that ens ured high accuracy of measurements. The \nmicrostructure of samples subjected to thermal treatment and cooling w ere studied by using \nSEM QUANTA -200. Investigations  of fine features of microstructure were carried out using \nTEM JEM -200CX.   \n \n3. Experimental results  \nAs a first step, we investigated the kinetics of transformation in dependence on the cooling \nrate Vc after exposure  of samples  at fixed  temperature  Tan = 9000C. In this case the obtained \ntemperature change with time  follows  the standard  concepts  [1,2]: for the composition under \nconsideration the diffusi ve pearlite  transformation  occurs when the cooling is rather slow and \nshear martensite colonies gradually  replac e the pearlite  microstructure  when the cooling rate \nincreases. The characteristic value of the cooling rate  which correspond s to the  switching of the  \ntransformation mechanism was  found  at about 10 0 grad/sec.  \nThe temperature variation during  the cooling of samples with initial  rate Vc = 100 - 110 \ngrad/sec [11] starting from different annealing temperatures Tan is shown in Fig. 1.  One can see \nthat the temperature profile of the cooling is change d essentially when the temperature Tan \nincrease s from 7200 to 9500C. A preliminary exposure of sample  just above the two -phase region  \n(7500C < Tan < 8300C) leads to a peak in the cooling curve s at about  6000C.  This peak \ndisappears when Tan > 8300C and an inflection point is observe d on the curve s near 2400C. The \nlatter feature is typical for the martensitic transformation  develop ing very quickly  as a result of a \nlattice  shear  instability;  the microstructure observed  in this case  is shown in Fig. 2 b.  In contrast , \nthe cooling after the exposure  at lower  temperature, 7500C < Tan < 8300C, results in the \nformation of a fine pearlite structure (Fig. 2a)  which represents  regular alternated plates of -Fe \nand cementite Fe 3C. It should  be noted that the pearlite form s very rapidly in this case , in about  5 \nsec.    \nThus, the observations  lead to a surprising conclusion that the mechanism of transformation \ndepends (at least for the steel composition  under consideration ) on the temperature of pre-\nannealing  in austenite region. For the given cooling rate, the pearlite transformation  develops  \nafter exposure  near the boundary of the austenite region  and an increase of the annealing \ntemperature switch es the transformation mechanism  from pearlitic to martensitic . It should be \nnoted that an increase in the cooling rate above 130 grad/sec ( keeping  annealing temperature ) \nchanges the  transformation scenario by replacing pearlite transformation to the martensite  one.   Since the used cooling rate was the same for smaller and higher  annealing  temperature Tan, it \nmust be assumed that the phase/structural state of the austenite just before the cooling is rather \ndifferent in these two cases. To qualify the features of the structural state of austenite in the \ntemperature region near the two-phase boundary, an exp eriment  that included the variation of the \ntemperature in the cycle fast heating – cooling (Fig.1 b) starting from the same initial state \ncorrespond ing to the fine perlite (Fig.2 a)  was carried out in Ref. [ 12]. A characteristic feature of \nheating curve in this case is well -pronounced plateau near temperature  7500C which correspond \nto the boundary of two -phase region (for the given composition). This plateau is a manifestation \nof the heat absorption (endothermic reaction) due to dissolution of pearlite colon ies. The fast \ncooling after the  fast heating to temperatures above  7500C results in pearlite transformation  (as is \nevidenced by the kink on the curves 2-4 in Fig. 1b) or ma rtensite transformation (curve 5  in Fig. \n1b).  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig. 1. Temperature of  steel samples in dependence on time during fast cooling after annealing \nabove A 3 (a) and in cycle fast heating – cooling (b) . Curves 1 -9 in Fig.1 (a) match  annealing \ntemperature s Ta = 7200, 7500, 7700, 7900, 8100, 8300, 8500, 9000, 9500C, respectively .  The \ncooling curves  are shifted from each other for convenience of the eye. Note, the temperature start \nof measurement  in Fig.1(a)  is slightly lower than  corresponding  value  Ta due to  delay caused by  \nmovement of the sample from the furnace into the measuring system. Temperature s start of \ncooling  in Fig.1b are  equal 7650, 8400, 8750, 9200C, 9300C (curves 1 -5, respectively) . \n \n \nOne can assume that the fast heating up to temperature at 7500C < Tan < 9000C leads to the \nformation of a microstructure with partially undissolved cementite that initiates perlite \ntransformation during the following fast cooling. However, as one can see from Fig.1a, a \npreliminary relatively long exposure (5 -10 min) in this tempera ture interval does not change the \nmechanism of the transformation at the subsequent cooling. These observations clearly point out \nthat a special metastable structural phase/state of austenite that is realized after exposure at \ntemperature region just above  two-phase boundary  should be differ ent from normal mixture \naustenite  and undissolved pearlite (as assumed in Ref s. [12,13]).    \n \n \n \n \n  \n \n \n \n \n \n \n \n \n \n \n \n \n \nFig. 2. Microstructure of samples after fast cooling  with rate  of 110 grad/sec. ( a) Tan = 7700C, \nfine plate pearlite;  (b)  Tan = 8500C, martensite.  \n \n \n4. Discussion and  conclusions   \nThe p resented results  clearly demonstrate  that the scenario of austenite decomposition may \nbe quite  compl icated and essentially dependent  on pre-history of the system in austenite region. \nThis conclusion disagree s with the commonly accepted image of  austenite as a homogeneous \nsolid solution of carbon in fcc Fe . Our fi nding suggests that annealing  in a certain range of \ntemperatures near  and above  the boundary of the austenite region  (7500C < Tan < 8300C for the \ncomposition  under consideration ) leads to the formation of a special structural state (SSS ). The \ndecomposition  of this SSS  results in the fine pearlite formation (if the cooling rate is not too \nhigh) while cooling from a higher temperature (with the same cooling rate) leads to the \nconven tional martensitic transformation.  On the other hand, quenching of SSS results in the \nmartensite  formation  with unusually low tetragonality [13,14]. Based on these observations , the \nsuggestion was made [ 13,14] that SS S is differ ent from usually assuming homogeneous solid \nsolution of carbon in fcc -Fe and should be considered as  a substantially nanoscale heterogene ity \nin carbon distribution , lattice distortions , and magnetic short -range  order (MSR O) [15].   \nGenerally, a short rang e order corresponding to the low -temperature  phase  is usually \nobserved in a narrow interval just above  the transition temperature. However, the SS S discussed \nhere exist s within a rather broad  temperature interval. It is known that well-pronounced short -\nrange  order or heterogeneity in few or ten nanometers (so called “heterophase  fluctuations”) are \noften observed in a certain interval of temperature in magnetic alloys with strong coupling \nbetween magnetic and lattice degrees of freedom (or chemical composition), such as Cu – Mn or \nFe – Ni invar alloys  [16,17]. Usually,  the appearanc e of such internal heterogeneity  in varied \nsystems is associated with frustrations which can be of  crystallographic origin  [18] or result  from  \ncompetition of different interatomic interaction mechanisms [19,20]. The possibility of the \nformation of some  special  heterogeneous structural  state of Fe -C in austenite region was already  \nbriefly discussed in Ref. [ 13] where it was assigned  to a strong coupling between  lattice and \nmagnetic degrees of freedom in fcc Fe [ 21,22].  \nAs follows from the results  of ab initio  calculations the ferromagnetic state of γ-Fe can \nreduce  essentially  its energ y if its formation is accompanied by tetragonal distortions  of crystal \nlattice  [22]; the gain in the magnetic exchange energy  is about  0,1 eV (about 1000 K) in this \ncase. It means  that, besides the global minimum matching paramagnetic fcc lattice , there is an \nadditional minimum in energy  of Fe which correspond s to a  metastable magnetically -ordered \nand tetragonal distorted (fct) state. Wherein, the presence of carbon atoms can increase exchange \nenergy and stabilize fct state [ 21]. Based on these arguments one should expect the appearance \nof a heterogeneous SSS of Fe -C with fcc and fct regions alternate each other in  some \ntemperature region where MSR is rather strong to  provide fct state.  \nThe heterogeneous  state discussed here is closely connected to the  so called Metastable \nIntermediate State (MIS)  which was recently discussed in detail in Refs. [ 23,24] based on  the \nresults of first principle calculations. According to Ref. [23] MIS  can be considered as a \ntetragonal distorted ferromagnetic austenite with carbon  distributed over the interstitial position s. \nThis structure is linked to austenite,  ferrite  and cementite  by natural  ways; the use of the concept \nof MIS allow s us to  describe  correctly  austenite decomposition with the pearlite formation  [6]. \nAn important condition of  the MIS stabilization is the existence of magnetic order (MSRO at \nleast) in the temperature range of interest (7500C - 8300C). Based on  the results of ab -initio \ncalculations [ 5,21] we should  expect a pronounced  increase of the  exchange energy in distorted \naustenite with the moderate carbon  concentration  and, as follow, stabilization of MIS.   \nThus, the concept of a SS S formation in a certain temperature  near and above the boundary \nof the austenite region are supported by current views based  on results of ab initio calculations of \nFe-Cu system.  Further development of such ideas is to be essential for progress in metallurg y \ntechnology.   \n \n \n \nReferences  \n1. W. C. Leslie and E. Hornbogen, in Physical Metallurgy of Steels, edited by R. W. Cahn and P. \nHaasen, Physical Metallurgy Vol. 2 (Elsevier, New York, 1996), pp. 1555 –1620.  \n2. R. W. K. Honeycombe and H. K. D. H. Bhadeshia , Steels: Microstructure and Properties, 2nd \ned. (Butterworth -Heinemann, Oxford, 1995 ). \n3. L. Kaufman, E . V. Clougherty , R.J. Weiss , Lattice stability of metals -III-iron, Acta Metall. , 11 \n(1963) 323-328 \n4. H. Hasegawa , D.G. Pettifor , Microscopic Theory of the Temperature -Pressure Phase Diagram \nof Iron , Phys. Rev. Lett. 50  (1983 ) 130-133 \n5. I. K. Razumov, D. V. Boukhvalov, M. V. Petrik, V. N. Urtsev, A. V. Shmakov, M. I. \nKatsnelson , and Yu. N. Gornostyrev, Role of magnetic degrees of freedom in a scenario of \nphase transformations in steel, Phys. Rev. B, 90, (2014)  094101 . \n6. I. K. Razumov, Yu. N. Gornostyrev, M. I. Katsnelson, Autocatalytic Mechanism of Pearlite \nTransformation in Steel , Phys. Rev. App., 7, (2017) , 014002  \n7. M. M. Aranda, B.  Kim, R.  Rementeria, C.  Capdevila, C.  García  de Andrés, Effect of Prior \nAustenite Grain Size on Pearlite Transformation in a Hypoeuctectoid Fe -C-Mn Steel, \nMetallurgical and  Materials Transactions A, 45, (2014)  1778–1786 . \n8. B. I. Mogutnov, I. A. Tomilin, and L. A. Shvartsman, Thermodynamics of Iron -Carbon \nAlloys , (Metallurgiya, Moscow, 1972 , 328p ) [in Russian].  \n9. W. K. Choo and R. Kaplow, Acta Metall. , Mossbauer Measurements on the Aging of Iron -\nCarbon Martensite , 21, (1973)  725-732.  \n10. H. K. D. H. Bhadeshia, Carbon-Carbon Interactions in Iron, J. Mater. Sci. 39, (2004)  3949 -\n3955 . \n11. The rate Vc was defined by the slope of the initial part of the cooling curve  \n12. D. A. Mirzaev , I.L. Yakovleva , N.A. Tereschenko , V.N. Urtsev , V.N. Degtyarev , A.V. \nShmakov,  Origin of abnormal formation of pearlite in medium -carbon steel under \nnonequilibrium conditions of heating , Phys . Met. Metallography, 116, (2016 ) 572–578 \n13. V. N. Urtsev, Yu. N. Gornostyrev, M. I. Katsnelson, A. V. Shmakov, A. V. Korolev, V. N. \nDegtyarev, E. D. Mokshin, and V. I. Voronin, Steel in Translation , 40, (2010)  671-675.  \n14. Publication No US -2013 -0153090 -A1. \n15. Early this special  structural state of austenite was called as “marinite” [ 13,14]. \n16. Y. Tsunoda , N. Orishi, N. Kunitomi, Elastic Moduli of γ -MnCu Alloys , J. Phys. Soc. Japan , \n53, (1984) 359-364. \n17. E. F. Wasserman, in Ferromagnetic Materials, edited by K. H. J.  Buschow and E. P. \nWohlfarth (North -Holland, Amsterdam, 1990),  Vol. 5, p. 237 . \n18. M. Kleman , Curved Crystals,  defects and disorder,  Adv. Phys ., 38, (1989)  605-667. \n19. G. Tarjus, S.A. Kivelson, Z. Nussinov, P. Viot, The frustration based approach of \nsupercooled liquids and the glass transition: a review and critical assessment,  J. Phys. : \nCondens. Matter. 17, (2005 ) R1143 . \n20. I.K. Razumov, Yu. N. Gornostyrev, M.I. Katsnelson , Intrinsic nanoscale inhomogeneity in \nordering systems due to  elastic -mediated interactions , Europhysics Letters, 80, (2007 ) 66001 -\n66005 . \n21. D. W. Boukhvalov , Yu. N. Gornostyrev, M. I. Katsnelson, and A. I. Lichtenstein, Magnetism \nand Local Distortions near Carbon Impurity in γ -Iron, Phys. Rev. Lett. 99, (2007)  247205 . \n22. S. V. Okatov , A.R. Kuznetsov , Yu. N. Gornostyrev , V.N. Urtsev , M.I. Katsnelson , Effect  of \nmagnetic  state on the - transition  in iron: First-principles  calculations  of the Bain  \ntransformation  path, Phys . Rev. B 79, (2009)  094111 . \n23. X. Zhang, T. Hickel, J. Rogal, S. Fähler, R. Drautz, and J. Neugebauer, Structural \ntransformations among austenite,  ferrite and cementite in Fe -C alloys: A unified theory based  \non ab initio simulations, Acta Mater. 99, (2015)  281-289. \n24. X. Zhang, T.  Hickel, J. Rogal, and J. Neugebauer, Interplay between interstitial displacement \nand displacive lattice transformations, Phys. Rev. B 94, (2016)  104109 . "    },    {        "title": "2206.15070v1.Modified_Z_Phase_Formation_in_a_12__Cr_Tempered_Martensite_Ferritic_Steel_during_Long_Term_Creep.pdf",        "content": "Graphical Abstract\nModified Z-Phase Formation in a 12% Cr Tempered Martensite Ferritic Steel during Long-Term Creep\nJohan Ewald Westraadt, William Edward Goosen, Aleksander Kostka, Hongcai Wang, Gunther Eggeler\narXiv:2206.15070v1  [cond-mat.mtrl-sci]  30 Jun 2022Highlights\nModified Z-Phase Formation in a 12% Cr Tempered Martensite Ferritic Steel during Long-Term Creep\nJohan Ewald Westraadt, William Edward Goosen, Aleksander Kostka, Hongcai Wang, Gunther Eggeler\nFormation of modified Z-phase in a 12Cr1MoV\nsteel during long-term interrupted creep-testing up\nto 139 kh was quantitatively evaluated.\nImproved methods to estimate the quantitative vol-\numetric precipitate measurements from extraction\nreplicas were applied.\nModified Z-phase was first identified in gauge sec-\ntion of the sample tested to 51 kh using electron\ndi\u000braction.\nApplied stress and localised creep-strain (deforma-\ntion) promoted the formation of modified Z-phase.Modified Z-Phase Formation in a 12% Cr Tempered Martensite Ferritic Steel\nduring Long-Term Creep\nJohan Ewald Westraadt\u0003, William Edward Goosen\nCentre for HRTEM, Nelson Mandela University, Box 77000, Gqeberha, 6031, South Africa\nAleksander Kostka\nCentre for Interface-Dominated High Performance Materials (ZGH), Ruhr-University, Bochum, D-44801, Germany\nHongcai Wang\nInstitute for Materials, Ruhr-University, Bochum, D-44801, Germany\nGunther Eggeler\nCentre for Interface-Dominated High Performance Materials (ZGH), Ruhr-University, Bochum, D-44801, Germany\nAbstract\nThe formation of modified Z-phase in a 12Cr1MoV (German grade: X20) tempered martensite ferritic (TMF) steel\nsubjected to interrupted long-term creep-testing at 550 °C and 120 MPa was investigated. Quantitative volumetric\nmeasurements collected from thin-foil and extraction replica samples showed that modified Z-phase precipitated in\nboth the uniformly-elongated gauge ( fv: 0.23 \u00060.02 %) and thread regions ( fv: 0.06 \u00060.01 %) of the sample that\nruptured after 139 kh. The formation of modified Z-phase was accompanied by a progressive dissolution of MX\nprecipitates, which decreased from ( fv: 0.16 \u00060.02%) for the initial state to ( fv: 0.03 \u00060.01%) in the uniformly-\nelongated gauge section of the sample tested to failure. The interparticle spacing of the creep-strengthening MX\nparticles increased from ( \u00153D: 0.55 \u00060.05\u0016m) in the initial state to ( \u00153D: 1.01 \u00060.10\u0016m) for the uniformly-elongated\ngauge section of the ruptured sample, while the thread region had an interparticle spacing of ( \u00153D: 0.60 \u00060.05\n\u0016m). The locally deformed fracture region had an increased phase fraction of modified Z-phase ( fv: 0.40 \u00060.20%),\nwhich implies that localised creep-strain strongly promotes the formation of modified Z-phase. The modified Z-phase\nprecipitates did not form only on prior-austenite grain boundaries and formed throughout the tempered martensite\nferritic grain structure.\nKeywords: Tempered martensite ferritic steels, modified Z-phase, long term creep, energy filtered TEM\n1. Introduction\nTempered martensite ferritic (TMF) steels with 9-\n12%Cr are used extensively for steam pipes, turbines\nand boilers in fossil fired steam power plants. These\nsteels have high creep strength, good oxidation resis-\ntance, good thermal fatigue properties and a moderate\ncost. The most common commercial material grades are\n9Cr1Mo grade 91 (T /P91) or 9Cr2W grade 92 (T /P92),\n\u0003Corresponding author\nEmail address: johan.westraadt@mandela.ac.za (Johan\nEwald Westraadt)but older 12Cr1MoV (German grade: X20) is currently\nstill in operation at several power utilities [1].\nThe TMF steel structure consists of a hierarchical\narrangement of prior-austenite grains (PAG), packets,\nblocks and micro-grains with a high density of free dis-\nlocations [2, 3, 4, 5, 6, 7]. TMF steels are stable dur-\ning creep-exposure due to the pinning forces exerted by\nparticles of di \u000berent origin. M 23C6carbides, located\nat grain boundaries, and MX carbonitrides, distributed\nhomogeneously throughout the ferrite matrix, acts as\npinning agents, by impeding free-dislocation movement\nand suppresses the movement of grain boundaries dur-\nPreprint submitted to Materials Science and Engineering: A July 1, 2022ing creep [3, 8]. During creep conditions, coarsening\nof M 23C6and Laves phase and dissolution of MX car-\nbonitrides occurs, which decreases the pinning forces\nexerted by the particles. This promotes the evolution\nof low angle grain boundaries, which is considered to\nbe the most important strengthening mechanisms of 9-\n12%Cr TMF steels, leading to a decrease in the long-\nrange internal stress field [8, 9, 10].\nNew generation TMF steels are typically designed\nwith an 11-12 wt.% chrome content to have su \u000ecient\noxidation resistance at the higher operation tempera-\ntures (650 °C) needed for improved power plant e \u000e-\nciency. Although, short-term testing on these new gen-\neration steels (up to 10 kh) has shown an enhance-\nment in creep-strength and oxidation resistance, long-\nterm testing (longer than 50 kh) revealed microstruc-\ntural instabilities resulting in a creep-strength break-\ndown [11]. Extensive microstructural investigations\nperformed by Strang and V odarek [12], Danielsen [13,\n14] and Sawada [15, 16] on service exposed and lab-\ntested TMF steels have shown that this creep-strength\nbreakdown, in 11-12%Cr TMF steels, is associated with\nthe transformation of fine MX carbonitrides into larger\nmodified Z-phase particles, which results in an increase\nin the inter-particle spacing. In addition, the interface\nbetween coarse modified Z-phase and the iron matrix\ncould serve as a nucleation site for creep voids. In\ncontrast, the creep-strength breakdown in 9% Cr TMF\nsteels is not considered to be related to the MX to Z-\nphase transformation [17, 18, 19, 20].\n1.1. Modified Z-Phase formation in 9-12%Cr TMF\nsteels\nThe formation of Cr(Nb,V)N modified Z-phase in 9-\n12% Cr TMF steels has been the subject of numerous\nstudies [21, 13, 15, 22, 17]. Danielsen [13] gives an\nexcellent historical review of modified Z-phase precip-\nitation in steels and investigated ten 9-12%Cr service\nexposed TMF steels for the presence of modified Z-\nphase. A more recent review of the modified Z-phase\nbehaviour in 9-12%Cr steels by Danielsen [11] was\nmade in reference to the design of next-generation steels\nto overcome this microstructural instability.\nThe modified Z-phase has a chemical composition\nclose to 1 /3Cr, 1 /3(V+Nb) and 1 /3N, where the V /Nb\nratio can vary significantly for precipitates in a partic-\nular steel. Two types of modified Z-phase are found in\n9-12% Cr TMF steels: (1) a metastable fcc phase with\na lattice parameter of 0.405 nm, and (2) a stable tetrag-\nonal phase which is a distortion of the NaCl-type lat-\ntice. Electron di \u000braction measurements of Cr(V ,Nb)Nand CrVN particles showed that both cubic and tetrago-\nnal di \u000braction patterns could be obtained from the same\nparticles [23, 24]. This dual cubic /tetragonal crystal\nstructure is believed to be connected to the transfor-\nmation process, with the cubic crystal structure being\na metastable step towards the more stable tetragonal\ncrystal structure. Two types of nucleation mechanisms\nare reported for modified Z-phase particles in 9-12%\nCr TMF steels. The most commonly observed mech-\nanism, involves direct transformation of MX carboni-\ntrides into modified Z-phase by di \u000busion of chromium,\nwhich leads to the formation of coarse particles. Nu-\ncleation of modified Z-phase on the surface of MX car-\nbonitrides is rarely observed and leads to the formation\nof nanoscale modified Z-phase particles.\nThermodynamical calculations have shown that ma-\ntrix concentration of chromium is the most influential\nelement driving the formation of modified Z-phase [25].\nThe nitrogen content also increases the formation of\nmodified Z-phase since it is a relatively pure nitride\ncompared to the stable MX carbo-nitrides that can form\nin relatively low nitrogen environments. MX particles\nconsisting of Nb-rich (Nb,V)N were found to prefer-\nentially transform into modified Z-phase during high-\ntemperature exposure [26]. This result is consistent\nwith the analysis performed on an 12%Cr Nb-free X20\nsteel grade, which show relatively slow precipitation of\nCrVN modified Z-phase compared to the Nb-containing\nsteel grades [13]. It was then suggested that new gener-\nation steels with increased chromium content (11% Cr)\nfor oxidation resistance should be developed with a low-\nered niobium content to slow down modified Z-phase\nformation. A new generation steel (THOR115) was de-\nveloped based on this principle and has shown good mi-\ncrostructural stability for creep-testing up to 60 kh [27],\nbut longer-term testing is still in progress.\nPrevious experimental observations based on extrac-\ntion replicas found that the modified Z-phase precip-\nitated preferentially along prior-austenite and packet\ngrain boundaries [15, 28, 16]. Investigations performed\non ruptured creep-tested samples have shown that the\ngauge portions of the ruptured samples contained 2-\n4 times the number density of modified Z-phase par-\nticles compared to the thread portions of the samples\nafter creep-rupture [15, 16]. These investigations were\nperformed on the locally deformed (necking) sections\nof the gauge area, which were subjected to long-term\nstress /temperature as well as creep-strain deformation.\nRecent thermodynamical kinetic precipitate modelling\nthat includes the e \u000bects of the volumetric misfit across\nthe precipitate /matrix interface, has shown that this mis-\nfit may influence the transformation and growth kinetics\n2of modified Z-phase significantly [29].\n1.2. Microstructural evolution of 12Cr1MoV (German\ngrade: X20) during long-term creep\nX20 is an older German steel grade based on 12%Cr\nwith a relatively high carbon content of 0.2 wt%. The\nchemical composition of the steel used in this study can\nbe seen in Table 1, which includes measurements for\nthe N and Nb content, which are not typically controlled\nduring manufacturing, but are considered to be impor-\ntant in the formation of modified Z-phase.\nThe presence of modified Z-phase in X20 grade steels\nwas first observed by Danielsen [23] in the analysis of\na service exposed sample (150 kh at 600 °C). A few\nparticles of modified Z-phase (CrVN), exhibiting a cu-\nbic crystal structure (a 0=0:405 nm) were identified with\nSTEM-EDS and SAED analysis, while several MX par-\nticles were still observed in the sample. In comparison,\nthey found that the Nb-containing steel grades consis-\ntently contained more Cr(Nb,V)N modified Z-phases.\nThe microstructural evolution of the 12Cr1MoV\nTMF steel samples exposed to long-term interrupted\ncreep-testing at near operating temperatures (550 °C)\nand 120 MPa stress has been the subject of several ex-\ntensive investigations. The gauge and thread portions\nof the interrupted creep-tested samples have been char-\nacterised to quantify precipitates [30, 2, 31], disloca-\ntions [5, 6], and sub-grains [7] previously. The previ-\nous precipitate analyses were performed on thin-foils\nusing HAADF-STEM combined with EDS and SAED\nanalysis to determine the compositional and crystallo-\ngraphic information. Modified Z-phase precipitation\nwas not observed in any of the samples and the MX\nprecipitate population was found to be stable up to 139\nkh [2]. However, recent experimental work [32] based\non EFTEM analysis performed on extraction replicas\nprepared from the samples of the previous investiga-\ntion showed clear evidence of modified Z-phase for-\nmation in the uniformly-elongated gauge section after\n51 kh of creep-testing. Recent studies [33] conducted\non ex-service 12Cr1MoV material grades exposed to\nlong-term operation, show clear evidence of modified\nZ-phase formation, but this microstructural instability\nhas not yet been the subject of a systematic investiga-\ntion for this steel grade.\n1.3. Quantitative characterisation of modified Z-phase\nInvestigations of modified Z-phase precipitation in 9-\n12%Cr TMF steels have been mainly performed on ex-\ntraction replicas using TEM-based techniques (SAED,\nEFTEM and STEM-EDS /EELS). Extraction replicasare relatively easy to prepare and provide large elec-\ntron transparent areas available for analysis of the pre-\ncipitate phases, without the influence of the magnetic\nmatrix. However, the sampled volume is unknown and\nquantitative results are often reported as the projected\narea measurements to quantify the phase fraction ( fA)\nand number density ( NA) of precipitates [34, 4]. Bulk\nSEM based methods can also be used to quantify the\nprecipitate species in 9-12%Cr TMF steels [35], but the\nquantification of the fine MX carbonitrides are not pos-\nsible due to insu \u000ecient spatial resolution. Thin-foils\nhave been used extensively to study precipitates in 9-\n12%Cr CSEF steels [16, 30, 31]. The main advantage of\nthin-foils is that the location specific information of the\nprecipitates are preserved, the analysed volume can be\ndetermined by measuring the thickness of the foil, and\nthe spatial resolutions in the TEM is su \u000ecient to resolve\nthe very fine MX precipitates. However, the available\nsample volumes are limited to the electron transparent\nareas of the foil.\nThe present experimental study applies volumetric\nquantification methods to systematically study the for-\nmation of CrVN modified Z-phase and the associated\ndissolution of the MX precipitates during long-term\ncreep in a 12Cr1MoV steel. In addition, results on\nthe reaction kinetics (time), e \u000bects of stress, localised\ncreep-deformation, and the preferential nucleation sites\nof the modified Z-phase are presented.\n2. Materials and Methods\nThe TMF steel investigated in this study was sup-\nplied by Salzgitter Mannesmann Research Centre, Duis-\nburg. The chemical composition given in Table 1 was\nmeasured using optical emission spectroscopy from the\nthread section of the sample tested to rupture. The steel\nwas austenitized at 1050 °C for 30 minutes followed by\nair-cooling to room temperature. The steel was then\ntempered at 770 °C for 2 hours and allowed to air-cool\nto room temperature.\nFour identical samples were tested simultaneously at\n550 °C with an applied stress of 120 MPa. Three in-\nterrupted experiments were tested to creep-strain val-\nues of 0.5% (12 kh), 1.0% (51 kh), and 1.6% (81 kh)\nrespectively, and one sample was taken to rupture at\na creep-strain value of 11.5% after 139 kh. Figure 1\nshows the interrupted material states that were inves-\ntigated. For each creep-tested sample the gauge and\nthread regions were investigated to study the e \u000bects of\nstress (120 MPa) on the microstructure. The fractured\nregion, which experienced localised creep-deformation,\n3Table 1: Chemical composition (in mass%) of the steel grade.\nGrade C Si Mn S Ni Cr Mo V Nb N Al Fe\nX20 0.21 0.15 0.63 0.010 0.76 12.1 1.00 0.24 \u00140.004 0.044 0.006 bal.\nFigure 1: Material states investigated in this study. The insert shows\nthe sample tested to failure, which fractured after 139 kh, indicating\nthe di \u000berent areas that were investigated. This includes the thread\nregion, uniformly-elongated gauge region, and fracture region which\nexperienced localised creep-deformation.\nwas also investigated to study the e \u000bects of the tertiary\ncreep-deformation on the microstructure.\nThin-foils were prepared from the uniformly-\nelongated gauge and thread sections of the creep-tested\nsamples for each of the material states. In addition, thin-\nfoils were prepared from a reference X20 steel in the as-\ntempered state. Thin slices were cut from the sample,\nmechanically thinned down to 300 \u0016m, punched into 3\nmm disks, and mechanically thinned down to 80 \u0016m in\nthickness. The disks were then electropolished to elec-\ntron transparency using a 5% perchloric acid /methanol\nsolution at \u000020 °C and 21 V with a Struers Tenupol 5\ntwin-jet electro-polisher. Extraction replicas were pre-\npared from the same set of material states, by first etch-\ning the surface for 30 seconds with Viella’s solution,\ndepositing a 30 nm thick layer of carbon, scoring the\nsurface into 1 mm blocks and then placing it back in the\nsolution. The liberated carbon films contain the precipi-\ntates in the steel, which are then collected, washed with\na methanol /ethanol solution, then placed onto a copper\nTEM grid, and allowed to air dry. FIB lamellae were\nprepared from ten sites in the fracture region in the rup-\ntured sample (139 kh) using a Ga-ion FIB-SEM. Ex-\ntraction replicas were also prepared from this fracture\nregion.\nThe chemical composition of the precipitates was\ninvestigated using scanning transmission electron mi-croscopy (STEM) combined with energy dispersive X-\nray spectroscopy (EDX) and electron energy loss spec-\ntroscopy (EELS) on a JEOL2100 (LaB 6) TEM fitted\nwith an Oxford X-Max (80 mm2) X-ray spectrometer\nand a Gatan Quantum GIF electron energy loss spec-\ntrometer. The crystallographic information of the pre-\ncipitates was determined using selected area electron\ndi\u000braction (SAED) patterns taken from several di \u000ber-\nent zone-axes and matching it to theoretically simulated\npatterns. The precipitates (M 23C6, MX and modified Z-\nphase) were mapped on ten sites of interest using en-\nergy filtered TEM (EFTEM) (512x512 pixels; 5x5 \u0016m2)\nfor each material state and sample preparation method\n(thin-foil and extraction replica). The signals for Cr\n(green) and V (red) were overlayed to produce a RGB\ncomposite image. M 23C6precipitates rich in chromium\nappeared as green particles, while the vanadium rich\nMX precipitates appeared as red particles. Modified Z-\nphase contains both chromium and vanadium and ap-\npeared as orange particles. A thickness map using the\nlog-ratio method was collected on the thin-foil samples\nsites of interest, which was used to determine the sam-\npled volume.\nThe composite RGB images were segmented into\nM23C6, MX and modified Z-phase precipitates with the\nMIPAR [36] image analysis software based on colour.\nThe projected areas, centroid position and equivalent\ncircle diameters for each precipitate were measured and\nexported to a text file. These centroid positions were\nthen used to read the thickness of the foil from the\nthickness map. Stereological corrections described in\n[37] were applied to the exported precipitate measure-\nments to calculate the corrected values for the volumet-\nric phase fraction ( fv), mean precipitate size ( dm), and\nmean precipitate spacing ( \u00153D) of a particular precipi-\ntate species.\nThe corrections and calculations were performed sep-\narately for each site of interest, which resulted in ten\nmeasured values for each material state. This distribu-\ntion of measurements was then plotted as a box plot to\nshow the distribution of values obtained from each site\nof interest, which was then used to calculate the mean\nvalue and the standard error in the mean for a particu-\nlar material state. Any data points falling outside 1.5\nx interquartile range (IQR) were considered outliers for\nthe box plots, but these outliers were still used to de-\n4termine the quantitative measurements. A total area of\n10x25\u0016m2was investigated for each material state. The\ntotal material volume investigated depends on the sam-\nple preparation method (thin-foil or extraction replica).\nThe sampled volume can be calculated by multiplying\nwith the foil thickness (80 nm) or the extraction depth\n(1\u0016m) in the case of the extraction replica with the pro-\njected area in the field of view. The extraction depth is\nunknown for the extraction replica preparation method,\nhowever, it can be estimated with the assumption that\nthe M 23C6precipitate phase fraction remains constant\nduring long-term creep [2]. The M 23C6projected area\nphase fraction measurements from the extraction repli-\ncas were combined for the ten sites of interest for a\nparticular material state and normalised to have a volu-\nmetric phase fraction of 4.5 %, which was based on the\nchemical composition and equilibrium thermodynamic\nmodelling. This was then used to calculate the total pre-\ncipitate extraction volume which was then divided by\nthe total area (250 \u0016m2) to estimate the average extrac-\ntion depth for a particular material state.\nSAED experiments are very time-consuming and dif-\nficult to perform in the case of magnetic samples. Trans-\nmission Kikuchi di \u000braction [38] provides an easy and\naccessible alternative method that can be routinely per-\nformed on most modern SEMs fitted with an EBSD de-\ntector. This method allows for crystallographic phase\nand orientation information to be collected with step\nsizes as small as 10 nm for electron transparent samples,\nwhich is a significant improvement over bulk EBSD\nmethods. In addition, the di \u000braction data is automati-\ncally processed during the data acquisition and does not\nrequire additional indexing, as is the case with SAED.\nThe samples were investigated using TKD combined\nwith EDS in a JEOL7001F FEG-SEM fitted with a\nNordlys HKL EBSD detector. Step sizes of 10-50 nm\nwere used depending on the objective of the experiment\nat an accelerating voltage of 30 kV and a sample tilt of\n\u000020°.\n3. Results\nFigure 2 shows typical EFTEM RGB composite el-\nemental maps taken from the replica samples prepared\nfrom the initial state and the uniformly-elongated gauge\nsection of the ruptured sample. The initial state shows\nthe Cr-rich M 23C6particles in green and several smaller\nV-rich MX particles in red. The MX particles in the\nruptured sample decreased in number density and sev-\neral additional Cr-V orange particles, with a chemical\ncomposition consistent with the modified Z-phase can\nbe seen.\nFigure 2: EFTEM elemental maps shown as a colour overlay\n(Cr:green; V:red) for the starting material (New) and the uniformly-\nelongated gauge section of the sample creep-tested to failure\n(G139kh) collected from extraction replicas.\n3.1. Identification of the modified Z-phase precipitates\nThe identification of modified Z-phase /MX/M2X pre-\ncipitates based only on EFTEM maps must be done with\ncare, since all of these particles contain chromium and\nnitrogen. The identification of the modified Z-phase\nbased on the EFTEM RGB composite elemental map\noverlay was confirmed using di \u000braction (SAED and\nTKD) and compositional (STEM-EDS /EELS) measure-\nments. Figure 3 shows a TKD crystallographic phase\nmap and the corresponding EFTEM RGB composite el-\nemental map taken from an extraction replica prepared\nfrom the uniformly-elongated gauge section of the frac-\ntured sample. Both the cubic and tetragonal modified\nZ-phase as well as M 23C6, Laves phase, and MX can-\ndidate crystal structures were provided to the indexing\nsoftware. The energy loss spectrum (bottom left insert)\nshows that the precipitate consisted of Cr-V-N, with\nEDS analysis (not shown) confirming that the Cr:V ele-\nmental ratio is close to unity. The SAED zone-axis pat-\ntern taken from this precipitate, exhibits both the cubic\nB=[101] reflections (red) and the additional tetragonal\nB=[100] (blue) reflections (insert bottom right), which\nwas first observed by Danielsen [23]. Several additional\nzone-axis SAED patterns taken from the same precipi-\ntate (not shown), confirmed this observation.\n3.2. Quantification of the MX /modified Z-phase precip-\nitates\nFigure 4 shows the corrected volumetric phase frac-\ntion ( fv) of the modified Z-phase and MX precipitates\nfor the uniformly-elongated gauge sections of the creep-\ntested samples and the initial state, as measured on the\nthin-foils (left) and extraction replicas (right). The box\nplots show the distribution of the mean values calcu-\nlated for each of the ten sites of interest. Quantitative\nmeasurements based on TEM analyses should be done\n5Figure 3: (a) TKD crystallographic phase map showing the distribu-\ntion of modified Z-phase particles with a tetragonal crystal structure,\n(b) EFTEM elemental map overlay showing the modified Z-phase par-\nticles in orange. A modified Z-phase particle (white arrow) was anal-\nysed using (c) STEM-EELS indicating that the particle consists of\nCr-V-N and (d) SAED on a B=[100] tetragonal zone axis, showing\nthe reflections of the tetragonal phase (Z-blue) and reflections of the\ncubic variant B=[101] (FCC-red), the 200-type reflections are indi-\ncated with red circles.\nwith care, due to the small volumes of material that are\ninvestigated. If the number density of features are high\nenough such that the field of view is representative of\nthe bulk, then the standard deviation of the mean values\nof measurements taken from each site of interest should\nbe small. The standard deviation for the measured phase\nfraction ( fv) for the MX precipitates are much less for\nthe measurements taken from the extraction replicas,\ndue to the larger sampling volume of this method. The\nphase fraction of MX precipitates is relatively stable ( fv\n=0.16\u00060.02) to a test duration of 51 kh, but decreases\nsharply afterwards. This is accompanied by an increase\nin the phase fraction of modified Z-phase. This result\nis consistent with the precipitation of modified Z-phase\nand dissolution of the MX precipitates as observed by\nprevious investigations by Sawada [15] and Danielsen\n[13].\nFigure 5 shows the distribution of the corrected mean\nequivalent circle diameters (left) ( dm) and volumetric\nnumber density ( Nv) (right) of the MX and modified\nZ-phase precipitates based on measurements performed\non the thin-foils prepared from the uniformly-elongated\ngauge sections and the initial state material. The size of\nthe MX precipitates remained relatively constant during\nlong-term creep-testing and with sizes ranging between\nFigure 4: Phase fraction (f v) of MX and modified Z-phase precipi-\ntates in the gauge sections as a function of creep-testing time for data\ncollected from the thin-foils and extraction replicas.\nFigure 5: Mean corrected size (d m: left) and corrected number den-\nsity (N V: right) of MX and modified Z-phase precipitates for di \u000berent\ncreep-testing times in the uniformly-elongated gauge regions for data\ncollected from the thin-foil samples.\ndm=50-60 nm. This result is in agreement with previ-\nous studies [2]. The size of the modified Z-phase pre-\ncipitates increases from starting values similar to MX\nprecipitates in the early stages (51kh) to dm=0.113\n\u00060.001\u0016mfor the modified Z-phase precipitates ob-\nserved in the uniformly-elongated gauge section tested\nto rupture. The number density of the MX particles de-\ncreases sharply from Nv=16\u00062\u0016m\u00003in the initial state\ntoNv=2\u00061\u0016m\u00003for the ruptured sample. The num-\nber density of the modified Z-phase remains relatively\nconstant at Nv=3\u00061\u0016m\u00003.\nFigure 6 shows the calculated [39] average 3D\ncentroid-centroid spacing ( \u00153D) between the MX parti-\ncles as a function of creep-testing time in the uniformly-\nelongated gauge and the thread portions of the creep-\ntested samples, based on measurements performed on\nthe thin-foils. The results from the thread sections show\nthe e\u000bect of thermal ageing of the material at a temper-\nature of 550 °C, while the results from the (uniformly-\nelongated) gauge sections include the e \u000bects of the 120\nMPa stress that was applied. The average MX spacing\nfor the initial material state is \u00153D=0.55\u00060.05\u0016m\nand only increases slightly for creep-testing to 81 kh\nfor both the gauge and thread sections, which were very\nsimilar in value. There is, however, a large di \u000berence\nbetween the MX precipitate spacing in the uniformly-\nelongated gauge section ( \u00153D=1:01\u00060:10\u0016m) as com-\n6Figure 6: Mean 3D centroid-centroid distance between the MX pre-\ncipitates for the di \u000berent material states for data collected from the\nthin-foil samples. Outliers are data points falling outside 1.5*IQR of\nthe 25th and 75th percentiles.\npared to the thread section ( \u00153D=0:60\u00060:10\u0016m) for\nthe sample tested to failure, which implies that creep-\nstrain and /or stress promotes the formation of modified\nZ-phase.\n3.3. E \u000bect of creep-strain on the formation of modified\nZ-phase\nIn order to investigate the e \u000bects of creep-strain, ap-\nplied stress and ageing temperature on the formation\nof modified Z-phase and the associated dissolution of\nthe MX precipitates, the di \u000berent sections ( Fracture ;\nGauge ;Thread ) of the ruptured creep-tested sample\n(139 kh) were compared to the initial state. Figure 7\nshows the RGB EFTEM maps taken from extraction\nreplicas prepared from the di \u000berent locations of the rup-\ntured sample. At the location of fracture the test spec-\nimen underwent a significant reduction in cross-section\narea (approximately 50% for a diameter decrease from\n6.0 mm to 4.2 mm) and most of the creep-strain (11.9%)\nwould have been localised in this region. FIB-lamellae\n(5x5\u0016m2) were prepared from ten random sites very\nclose to the fracture surface and an extraction replica\nsample was also prepared from this region. Quantitative\nanalysis of the modified Z-phase and MX precipitates\nwas performed on the extraction replicas as previously\ndescribed. The phase fractions of MX and modified Z-\nphase are shown as an insert to Figure7.\nThe thread region still had numerous MX precipitates\ncompared to the low number of MX carbonitride parti-\ncles observed in the (uniformly-elongated) gauge region\nand the fracture region. Additionally, the projected area\nFigure 7: EFTEM elemental maps shown as a colour overlay\n(Cr:green; V:red) for the di \u000berent regions of the ruptured sample, con-\nsisting of the Thread ,Gauge andFracture area, where the localised\ncreep-strain resulted in rupture of the creep specimen.\nnumber density of precipitates is much lower for the ex-\ntraction replica prepared from the fracture region. This\nis probably due to the significant microstructural coars-\nening that occurred during the final stages of tertiary\ncreep, prior to fracture. Consequently, the calculated\nsampled depth for the extraction replica prepared from\nthe fracture region was only 0 :5\u0016mcompared to 1 \u0016m\nfor the extraction replicas prepared from the other ma-\nterial states. The phase fraction of modified Z-phase in\nthe fracture region ( fv=0.40\u00060.20 %) is significantly\nhigher than in the uniformly-elongated gauge section.\nThis implies that the localised creep-strain is correlated\nwith modified Z-phase formation.\n3.4. Preferential nucleation sites for modified Z-phase\nformation\nThe analysis was then performed at prior austenite\ngrain interiors and at prior-austenite boundaries on the\nextraction replica prepared from the gauge region of\nthe ruptured sample. Figure 8 shows two representative\nEFTEM elemental maps for the two di \u000berent locations\nof a prior-austenite grain. When viewed in projection,\nit appears that the PAGB locations contain more modi-\nfiedZ-phase particles, however, the PAGBs had a signif-\nicantly larger number density of M 23C6precipitates in a\ngiven field of view, which resulted in a larger extraction\ndepth estimation. The values of the modified Z-phase\n7Figure 8: Typical EFTEM elemental maps shown as a colour overlay\n(Cr:green; V:red) for the extraction replica prepared from the gauge\nregion of the ruptured sample, showing the PAGB interior (left) and\nthe PAGB (indicated by a white broken line on the right).\nvolumetric phase fraction ( fv) are not significantly dif-\nferent for the two locations when the correction is made\nfor the extraction depth. This remains a limitation for\nquantitative analysis performed on 5x5 \u0016m2areas of an\nextraction replica and it could not be confirmed whether\nor not the prior-austenite grain boundaries promote the\nformation of the modified Z-phase.\nTKD-EDS analyses were performed on the thin-foil\nsample prepared from the uniformly-elongated gauge\nregion of the sample tested to rupture. The thin-foil\nwas scanned with a step size of 20 nmacross two prior-\naustenite grains, which was confirmed by employing a\nreconstruction algorithm (results not shown). Figure 9\nshows the results of the scan. Several vanadium-rich\nprecipitates can be seen in the EDS map. Two of the\nlarger precipitate phases (white arrows) indexed suc-\ncessfully as the modified Z-phase precipitates with a\ntetragonal crystal structure. However, they were not\nlocated exactly on the PAGB or a packet boundary.\nThe distribution of vanadium-rich precipitates, which\ndid not index successfully, were also not preferentially\naligned along the PAGB. EFTEM elemental mapping of\nthis area is shown for comparison.\n4. Discussion\nThis study investigated the formation of modi-\nfied Z-phase and the associated dissolution of creep-\nstrengthening MX precipitates in a 12%Cr (German-\ngrade) X20 TMF steel using quantitative electron mi-\ncroscopy. The previous investigations by Aghajani et.\nal[2] used HAADF-STEM imaging and EDS mapping\non thin-foils to identify the MX precipitates, and found\nthe phase fraction of MX precipitates to be constant un-\ntil rupture and they did not find the modified Z-phase.\nThe current study used EDS detectors with an improved\nFigure 9: Combined TKD-EDS maps of over a PAGB in a thin-foil\nsample prepared from the gauge area of the ruptured sample. The\nlower right image is an EFTEM composite elemental map taken from\nthe exact same area.\ncollection e \u000eciency, employed more sensitive EFTEM\nelemental analysis and performed measurements on ex-\ntraction replicas for a more representative sampling vol-\nume. Clear evidence (crystallographic and chemical) of\nmodified Z-phase was observed after a creep-test dura-\ntion of 51 kh in the uniformly-elongated gauge section.\nThe phase fraction ( fv) and size ( dm) of the modified\nZ-phase increased with increasing testing time, with an\nassociated decrease in the phase fraction ( fv) and num-\nber density ( Nv) of the MX particles for the samples in\nthe uniformly-elongated gauge sections. This resulted\nin an increase in the inter-particle distance for the MX\ncarbonitrides ( \u00153D) as compared to the initial state ma-\nterial.\n4.1. Quantitative characterisation methods\nSeveral quantitative microscopy techniques were\nused in this study. Extraction replication is a rela-\ntively simple sample preparation technique, which al-\nlows for investigations on large areas without the influ-\nence of the magnetic iron matrix. However, the extrac-\ntion volume for this preparation method is unknown.\nWe provided a way to estimate this volume and used\nit quantify the volumetric phase fractions of MX parti-\ncles based on EFTEM analysis. Previous investigations\n[13, 15, 40, 16] used projected area number density ( NA)\nas a quantitative measure. However, variations in sam-\nple preparation procedures and the microstructural state\ncan strongly influence the sampling depth from which\nthe precipitates are extracted. The method proposed in\nthis study attempts to correct for this variation in the ex-\ntraction depth for the replica samples. The measured\n8values of the volumetric phase fraction for MX carboni-\ntrides are systematically lower for the extraction replica\nsamples. This could be due to lower extraction e \u000e-\nciency of smaller particles or systematic over-estimation\nof the extraction volume, due to approximations in the\nmethod that was employed to determine the sampled\nvolume from the extraction replica samples.\nThin-foils preserve the precipitate locations and the\ninvestigated volume can be accurately determined by\nmeasuring the thickness of the foil with EELS. How-\never, the precipitate feature measurements have to be\nstereologically corrected to calculate the volumetric\nmeasurements, due to the fact that the precipitates are\nsectioned and then viewed as a projected area. The sam-\npled volume for thin-foils is approximately 10% of that\nof the extraction replica method for a given site of in-\nterest. It is important to perform measurements from\nseveral sites of interest per material state and then to\ncalculate the mean value for each area. The standard\ndeviation in the mean values will be an indication of the\nrepresentative nature of the measurements for a particu-\nlar microstructural feature. Combined TKD-EDS SEM\nanalyses performed on the thin-foils were able to map\nout the precipitate species with a spatial resolution in\nthe order of 20 nm to obtain crystallographic phase, ori-\nentation and compositional information.\nThe modified Z-phase particles were quantified from\nRGB EFTEM elemental maps. Image segmentation was\nperformed to identify the modified Z-phase based on the\nintensity of the chromium and vanadium signals. It is\nvery di \u000ecult to distinguish between a modified Z-phase\nparticle and an MX /M23C6overlap for the early stages\n(12 kh). Segmentation errors are an important consid-\neration that could influence the quantitative results in\nthis study and it must be performed with care. Modified\nZ-phase particles identified in the uniformly-elongated\ngauge section of the sample creep-tested to 12 kh should\nbe interpreted with care, since these particles almost ex-\nclusively occurred adjacent to M 23C6precipitates and\ncould be due to MX /M23C6overlapping Cr /V signals.\nThese phases could not be identified as the modified Z-\nphase using electron di \u000braction due to their small size\nand close proximity to the M 23C6particles.\n4.2. E \u000bects of creep-strain on modified Z-phase forma-\ntion\nCharacterisation of extraction replicas by Sawada et.\nal[15, 16] found that the gauge sections contained 2-4\ntimes the phase fraction of modified Z-phases as com-\npared to the thread regions of the creep-ruptured sam-\nples. The phase fraction of modified Z-phase of the de-\nformed fracture region, in this study, was significantlyhigher ( fv: 0.40 \u00060.02 %) compared to uniformly-\nelongated zone ( fv: 0.23 \u00060.20 %) of the sample tested\nto rupture. This suggests that localised creep-strain and\nincreased stress due to necking promoted the forma-\ntion of modified Z-phase. Recent thermo-kinetical mod-\neling by Svoboda [29] suggests that deformation pro-\ncesses may relax the volumetric back-pressure created\nduring the formation of modified Z-phase, but this is\ndi\u000ecult to model accurately. If localised creep-strain\nenhances the formation of the modified Z-phase, then it\ncould possibly explain the low number density of modi-\nfiedZ-phase particles observed by Danielsen [23] in the\nservice-exposed X20 sample that was probably not sub-\njected to significant levels of localised creep-strain.\n4.3. Influence of modified Z-phase on creep-strength\nIt is quite challenging to quantify the contribution of\nthe MX precipitate dissolution towards the progressive\nloss of creep-resistance, since it is also influenced by\na combination of several microstructural mechanisms\nas discussed by Aghajani et. al [2]. Recent develop-\nments in microstructurally based semi-physical mod-\nels [41] use quantitative microstructural data directly\nto calculate the time-to-rupture diagrams and can esti-\nmate the e \u000bects of individual microstructural features\non the creep-resistance. The e \u000bects of MX dissolution\non the creep-resistance using this approach will be the\nsubject of a follow-up study, since it can’t be quantita-\ntively described without taking the evolution of all the\nmicrostructural features (including sub-grains, M 23C6,\nLaves, and dislocations) during creep-testing into ac-\ncount [42].\n4.4. Nucleation sites for modified Z-phase\nPrevious investigations found that the modified Z-\nphase formed preferentially on prior-austenite and\npacket boundaries [15, 16, 13]. Extraction replicas were\nused and it was assumed that the lines of enlarged M 23C6\nprecipitates delineate the prior-austenite grain bound-\naries, since the iron grain information is lost during the\nextraction process. The projected area number density\n(NA) of the precipitates from the extraction replica sam-\nple was presented as a quantitative measure in those\ninvestigations, but the extraction depth is very depen-\ndent on the sample preparation and the underlying mi-\ncrostructural grain-size as previously discussed.\nThe quantitative investigations performed in this\nstudy to determine the preferential nucleation sites for\nthe modified Z-phase, could not conclusively show\nwhether modified Z-phase forms preferentially on the\nPAGB in this X20 steel grade, since several particles\n9were distributed throughout the grain structure away\nfrom the PAGB. Qualitative evaluation found that most\nof the modified Z-phase particles were located adja-\ncent to the M 23C6precipitates and the modified Z-phase\nformed through the transformation of MX particles by\nchromium di \u000busion. The modified Z-phase number\ndensity remains constant ( Nv=3\u00061\u0016m\u00003) once formed\nand only increases in size by further dissolution of MX\nparticles through the matrix di \u000busion of vanadium and\nchromium. A detailed study of the preferential nucle-\nation sites of the modified Z-phase will be the subject of\na follow-up study using TKD-EDS, HR(S)TEM-EELS,\nand atom-probe tomography.\n5. Conclusions\n1. Modified Z-phase was observed in German-grade\n(X20) material after creep-testing for 51 kh (120 MPa at\n550 °C) in the uniformly-elongated gauge portion of the\nsample. This phase increased in size with an accompa-\nnied dissolution of MX particles until rupture after 139\nkh.\n2. The e \u000bects of stress and localised creep-strain sig-\nnificantly increased the formation of the modified Z-\nphase for the sample tested to failure.\n3. The modified Z-phase (CrVN) formed pref-\nerentially near M 23C6precipitates and no conclusive\nevidence for preferential formation at PAGBs could\nbe found based on investigations performed on the\nuniformly-elongated gauge section of the ruptured X20\ngrade sample.\n4. The modified Z-phase formation and dissolution\nof MX is considered to be an important microstruc-\ntural degradation mechanism that results in a non-linear\ndecrease in creep-strength for 11-12% Cr TMF steels.\nThe microstructural characterisation techniques demon-\nstrated in this study can be applied to quantitatively\ncharacterise the finest microstructural features (MX)\nwhich are considered critical to the creep-strength of 9-\n12% TMF steel grades.\nData availability\nThe raw data required to reproduce these finding are\navailable to download after a request to the correspond-\ning author.\nDeclaration of Competing Interest\nThe authors declare that they have no known com-\npeting financial interests or personal relationships thatcould have appeared to influence the work reported in\nthis paper.\nAcknowledgement\nJEW and WEG gratefully acknowledge financial sup-\nport of the National Research Foundation of South\nAfrica (Grant number 70724) and the Materials and Me-\nchanics Specialisation Group at the University of Cape\nTown through the Eskom Power Plant Engineering In-\nstitute (EPPEI). HW, AK and GE acknowledge support\nfrom the Centre for Interface Dominated High Perfor-\nmance Materials (German abbreviation: ZGH)\nReferences\n[1] M. van Rooyen, T. Becker, J. Westraadt, G. Marx, Creep Dam-\nage Assessment of Ex-Service 12% Cr Power Plant Steel Us-\ning Digital Image Correlation and Quantitative Microstructural\nEvaluation, Materials 12 (19) (2019) 3106. doi:10.3390/\nma12193106 .\n[2] A. Aghajani, C. Somsen, G. Eggeler, On the e \u000bect of long-\nterm creep on the microstructure of a 12% chromium tempered\nmartensite ferritic steel, Acta Materialia 57 (17) (2009) 5093–\n5106. doi:10.1016/j.actamat.2009.07.010 .\n[3] A. Kostka, K. Tak, R. Hellmig, Y . Estrin, G. Eggeler, On the\ncontribution of carbides and micrograin boundaries to the creep\nstrength of tempered martensite ferritic steels, Acta Materialia\n55 (2) (2007) 539–550. doi:10.1016/j.actamat.2006.08.\n046.\n[4] K. Sawada, H. Kushima, M. Tabuchi, K. Kimura, Microstruc-\ntural degradation of Gr.91 steel during creep under low stress,\nMaterials Science and Engineering: A 528 (16) (2011) 5511–\n5518. doi:10.1016/j.msea.2011.03.073 .\n[5] J. Pe ˇsiˇcka, R. Ku ˇzel, A. Dronhofer, G. Eggeler, The evolution of\ndislocation density during heat treatment and creep of tempered\nmartensite ferritic steels, Acta Materialia 51 (16) (2003) 4847–\n4862. doi:10.1016/S1359-6454(03)00324-0 .\n[6] J. Pe ˇsiˇcka, A. Aghajani, C. Somsen, A. Hartmaier, G. Eggeler,\nHow dislocation substructures evolve during long-term creep of\na 12% Cr tempered martensitic ferritic steel, Scripta Materialia\n62 (6) (2010) 353–356. doi:10.1016/j.scriptamat.2009.\n10.037 .\n[7] E. Payton, A. Aghajani, F. Otto, G. Eggeler, V . Yardley, On\nthe nature of internal interfaces in a tempered martensite fer-\nritic steel and their evolution during long-term creep, Scripta\nMaterialia 66 (12) (2012) 1045–1048. doi:10.1016/j.\nscriptamat.2012.02.042 .\n[8] F. Abe, Analysis of creep rates of tempered martensitic 9%Cr\nsteel based on microstructure evolution, Materials Science and\nEngineering: A 510–511 (2009) 64–69. doi:10.1016/j.\nmsea.2008.04.118 .\n[9] M. Meier, W. Blum, Modelling high temperature creep of aca-\ndemic and industrial materials using the composite model, Ma-\nterials Science and Engineering: A 164 (1) (1993) 290–294.\ndoi:10.1016/0921-5093(93)90680-D .\n[10] W. Blum, P. Eisenlohr, Dislocation mechanics of creep, Mate-\nrials Science and Engineering: A 510–511 (2009) 7–13. doi:\n10.1016/j.msea.2008.04.110 .\n10[11] H. K. Danielsen, Review of Z phase precipitation in 9–12 wt-\n%Cr steels, Materials Science and Technology 32 (2) (2016)\n126–137. doi:10.1179/1743284715Y.0000000066 .\n[12] V . V odarek, A. Strang, Z phase precipitation in martensitic 12Cr-\nMoVNb steels, http: //dx.doi.org /10.1051 /jp4:2003921 112 (Oct.\n2003). doi:10.1051/jp4:2003921 .\n[13] H. K. Danielsen, J. Hald, Behaviour of Z phase in 9–12%Cr\nsteels, Energy Materials 1 (1) (2006) 49–57. doi:10.1179/\n174892306X99732 .\n[14] H. K. Danielsen, Z-phase in 9-12% Cr Steels, Ph.D. the-\nsis, Technical University of Denmark, Lyngby, Denmark (Feb.\n2007).\n[15] K. Sawada, H. Kushima, K. Kimura, Z-phase Formation dur-\ning Creep and Aging in 9–12% Cr Heat Resistant Steels,\nISIJ International 46 (5) (2006) 769–775. doi:10.2355/\nisijinternational.46.769 .\n[16] K. Sawada, H. Kushima, M. Tabuchi, K. Kimura, E \u000bect of\ncreep deformation on Z phase formation in Gr.91 steel, Ma-\nterials Science and Technology 30 (1) (2014) 12–16. doi:\n10.1179/1743284713Y.0000000309 .\n[17] A. Fedoseeva, N. Dudova, R. Kaibyshev, Creep strength break-\ndown and microstructure evolution in a 3%Co modified P92\nsteel, Materials Science and Engineering: A 654 (2016) 1–12.\ndoi:10.1016/j.msea.2015.12.027 .\n[18] A. Fedoseeva, N. Dudova, R. Kaibyshev, E \u000bect of Tungsten on\na Dispersion of M(C,N) Carbonitrides in 9 % Cr Steels Under\nCreep Conditions, Transactions of the Indian Institute of Metals\n69 (2) (2016) 211–215. doi:10.1007/s12666-015-0767-6 .\n[19] M. Yoshizawa, M. Igarashi, K. Moriguchi, A. Iseda, H. G. Ar-\nmaki, K. Maruyama, E \u000bect of precipitates on long-term creep\ndeformation properties of P92 and P122 type advanced ferritic\nsteels for USC power plants, Materials Science and Engineer-\ning: A 510–511 (2009) 162–168. doi:10.1016/j.msea.\n2008.05.055 .\n[20] K. Sawada, K. Suzuki, H. Kushima, M. Tabuchi, K. Kimura, Ef-\nfect of tempering temperature on Z-phase formation and creep\nstrength in 9Cr–1Mo–V–Nb–N steel, Materials Science and En-\ngineering: A 480 (1) (2008) 558–563. doi:10.1016/j.msea.\n2007.09.031 .\n[21] A. Strang, V . V odarek, Z phase formation in martensitic 12Cr-\nMoVNb steel, Materials Science and Technology 12 (7) (1996)\n552–556. doi:10.1179/mst.1996.12.7.552 .\n[22] X. Zhou, C. Liu, L. Yu, Y . Liu, H. Li, Phase Transforma-\ntion Behavior and Microstructural Control of High-Cr Marten-\nsitic/Ferritic Heat-resistant Steels for Power and Nuclear Plants:\nA Review, Journal of Materials Science & Technology 31 (3)\n(2015) 235–242. doi:10.1016/j.jmst.2014.12.001 .\n[23] H. K. Danielsen, J. Hald, F. B. Grumsen, M. A. J. Somers, On\nthe crystal structure of Z-phase Cr(V,Nb)N, Metallurgical and\nMaterials Transactions A 37 (9) (2006) 2633–2640. doi:10.\n1007/BF02586098 .\n[24] H. K. Danielsen, J. Hald, Tantalum-containing Z-phase in\n12%Cr martensitic steels, Scripta Materialia 60 (9) (2009) 811–\n813. doi:10.1016/j.scriptamat.2009.01.025 .\n[25] H. K. Danielsen, J. Hald, A thermodynamic model of the Z-\nphase Cr(V, Nb)N, Calphad 31 (4) (2007) 505–514. doi:10.\n1016/j.calphad.2007.04.001 .\n[26] L. Cipolla, H. K. Danielsen, P. E. Di Nunzio, D. Venditti,\nJ. Hald, M. A. J. Somers, On the role of Nb in Z-phase forma-\ntion in a 12% Cr steel, Scripta Materialia 63 (3) (2010) 324–327.\ndoi:10.1016/j.scriptamat.2010.04.025 .\n[27] M. Ortolani, M. D’Incau, R. Ciancio, P. Scardi, Microstruc-\ntural Evolution of Thor 115 Creep-Strength Enhanced Fer-\nritic Steel, Metallurgical and Materials Transactions A 48 (12)\n(2017) 6111–6117. doi:10.1007/s11661-017-4353-x .[28] L. Cipolla, H. K. Danielsen, D. Venditti, P. E. Di Nunzio,\nJ. Hald, M. A. J. Somers, Conversion of MX nitrides to Z-phase\nin a martensitic 12% Cr steel, Acta Materialia 58 (2) (2010)\n669–679. doi:10.1016/j.actamat.2009.09.045 .\n[29] J. Svoboda, H. Riedel, Modeling of spontaneous transformation\nof nitrides to Z phase accounting for stress relaxation by di \u000bu-\nsion and interface activity, Computational Materials Science 161\n(2019) 24–34. doi:10.1016/j.commatsci.2019.01.030 .\n[30] G. Eggeler, J. Earthman, N. Nilsvang, B. Ilschner, Microstruc-\ntural study of creep rupture in a 12% chromium ferritic steel,\nActa Metallurgica 37 (1) (1989) 49–60. doi:10.1016/\n0001-6160(89)90265-4 .\n[31] A. Aghajani, F. Richter, C. Somsen, S. Fries, I. Steinbach,\nG. Eggeler, On the formation and growth of Mo-rich Laves\nphase particles during long-term creep of a 12% chromium tem-\npered martensite ferritic steel, Scripta Materialia 61 (11) (2009)\n1068–1071. doi:10.1016/j.scriptamat.2009.08.031 .\n[32] H. Wang, A. Kostka, W. E. Goosen, G. Eggeler, J. E. Westraadt,\nTEM replica analysis of particle phases in a tempered marten-\nsite ferritic Cr steel after long term creep, Materials Characteri-\nzation 181 (2021) 111396. doi:10.1016/j.matchar.2021.\n111396 .\n[33] G. Marx, Microstructural Evolution of Welded Creep Aged 12%\nCr Martensitic Stainless Steel, Ph.D. thesis, Nelson Mandela\nUniversity, Port Elizabeth (Apr. 2019).\n[34] K. Sawada, H. Kushima, K. Kimura, M. Tabuchi, Z-phase\nformation and its e \u000bect on long-term creep strength in\n9–12%Cr creep resistant steels, Transactions of the Indian In-\nstitute of Metals 63 (2-3) (2010) 117–122. doi:10.1007/\ns12666-010-0016-y .\n[35] R. G. Byrne, R. J. McGladdery, Z. Zhou, R. C. Thomson, S. S.\nDoak, M. A. E. Jepson, Detection and quantification of precip-\nitates in 11–12 wt% Cr steels using in-column secondary elec-\ntron detectors, Materials Characterization 165 (2020) 110356.\ndoi:10.1016/j.matchar.2020.110356 .\n[36] J. M. Sosa, D. E. Huber, B. Welk, H. L. Fraser, Development and\napplication of MIPAR : A novel software package for two- and\nthree-dimensional microstructural characterization, Integrating\nMaterials and Manufacturing Innovation 3 (1) (2014) 123–140.\ndoi:10.1186/2193-9772-3-10 .\n[37] B. Sonderegger, Modifications of stereological correction meth-\nods for precipitate parameters using transmission microscopy,\nUltramicroscopy 106 (10) (2006) 941–950. doi:10.1016/j.\nultramic.2006.04.004 .\n[38] G. C. Sneddon, P. W. Trimby, J. M. Cairney, Transmission\nKikuchi di \u000braction in a scanning electron microscope: A re-\nview, Materials Science and Engineering: R: Reports 110 (2016)\n1–12. doi:10.1016/j.mser.2016.10.001 .\n[39] I. Holzer, Modelling and Simulation of Strengthening in Com-\nplex Martensitic 9-12% Cr Steel and a Binary Fe-Cu Alloy,\nPh.D. thesis, Graz University of Technology, Graz, Austria\n(2010).\n[40] L. Cipolla, Conversion of MX Nitrides to Modified Z-Phase in\n9-12%Cr Ferritic Steels PhD Thesis, Ph.D. thesis (Jun. 2010).\ndoi:10.13140/RG.2.1.4368.8729 .\n[41] F. Riedlsperger, B. Krenmayr, G. Zuderstorfer, B. Fercher,\nB. Niederl, J. Schmid, B. Sonderegger, Application of an ad-\nvanced mean-field dislocation creep model to P91 for calcula-\ntion of creep curves and time-to-rupture diagrams, Materialia\n12 (2020) 100760. doi:10.1016/j.mtla.2020.100760 .\n[42] I. Holzer, E. Kozeschnik, H. Cerjak, New approach to pre-\ndict the long-term creep behaviour and evolution of precip-\nitate back-stress of 9–12% chromium steels, Transactions of\nthe Indian Institute of Metals 63 (2) (2010) 137–143. doi:\n10.1007/s12666-010-0019-8 .\n11"    },    {        "title": "1803.09656v1.Uniaxial_anisotropy_and_enhanced_magnetostriction_of_CoFe__2_O__4__induced_by_reaction_under_uniaxial_pressure_with_SPS.pdf",        "content": "Uniaxial anisotropy and enhanced magnetostriction of CoFe 2O4\ninduced by reaction under uniaxial pressure with SPS\nA. Aubert*, V. Loyau, F. Mazaleyrat and M. LoBue\nSATIE UMR 8029 CNRS, ENS Cachan, Universit\u0013 e Paris-Saclay,\n61, avenue du pr\u0013 esident Wilson, 94235 Cachan Cedex, France\nAbstract\nIn this study, we have compared magnetic and magnetostrictive properties of polycrystalline\nCoFe 2O4pellets, produced by three di\u000berent methods, focusing on the use of Spark Plasma\nSintering (SPS). This technique allows a very short heat treatment stage while a uniaxial\npressure is applied. SPS was utilized to sinter cobalt ferrite but also to make the reac-\ntion and the sintering (reactive sintering) of the same ceramic composition. Magnetic and\nmagnetostrictive measurements show that the reactive sintering with SPS induces a uniaxial\nanisotropy, while it is not the case with a simple sintering process. The induced anisotropy is\nthen expected to be a consequence of the reaction under uniaxial pressure. This anisotropy\nenhanced the magnetostrictive properties of the sample, where a maximum longitudinal\nmagnetostriction of \u0000229 ppm is obtained. This process can be a promising alternative to\nthe magnetic-annealing because of the short processing time required (22 minutes).\nKeywords: Magnetostriction, Reactive sintering, Magnetic anisotropy, Spark plasma\nsintering, Cobalt ferrite\n1. Introduction\nIn the recent years, there has been an increasing interest in improving magnetostriction of\noxide-based materials, which are suitable alternative for rare earth alloys (such as Terfenol-\nD) due to their low cost, ease of fabrication and high electrical resistivity. Polycrystalline\ncobalt ferrite is an excellent candidate because various techniques of preparation permits an\nenhancement of the maximum longitudinal magnetostriction and piezomagnetic coe\u000ecient\n(d\u0015/dH). Both properties are essential to obtain actuators and sensors exhibiting great\nperformances, which are the main applications for these materials. To achieve high mag-\nnetostrictive properties, the most common technique is to induce a magnetic anisotropy by\n\u0003Corresponding author\nA. Aubert et al. / Journal of the European Ceramic Society 37 (2017) 3101-3105\nDOI : http://dx.doi.org/10.1016/j.jeurceramsoc.2017.03.036\nEmail address: alex.aubert@satie.ens-cachan.fr (A. Aubert*)\nPreprint submitted to Elsevier June 28, 2021arXiv:1803.09656v1  [cond-mat.mtrl-sci]  26 Mar 2018applying a strong magnetic \feld during an annealing between 300 and 400\u000eC [1, 2, 3, 4, 5].\nThis permits a rearrangements of Co and Fe ions [6, 7] and leads to a uniaxial anisotropy\nparallel to the direction of the magnetic annealing \feld, hence tuning the magnetostrictive\nproperties. Wang et al. [8] proposed another technique in which particles were oriented\nthrough a magnetic \feld before the sintering, thus introducing a texture in the polycrys-\ntalline sample, which also contributes to better magnetostrictive properties. In this work, a\nnew technique that induces uniaxial anisotropy is reported, based on a reaction under uniax-\nial pressure using Spark Plasma Sintering (SPS) method of production. SPS process allows\nthe fabrication of high-density bodies at much lower temperature with short processing time.\nDuring the procedure, a high uniaxial pressure is applied while a pulsed electric current heats\nup the die and the sample [9]. SPS can be used either to activate the reaction [10] or to\nsinter [11, 12] oxide-based materials. This paper will focus on the e\u000bect of reaction and/or\nsintering of the cobalt ferrite by SPS. Magnetic and magnetostrictive behavior of the distinct\nsamples are then compared regarding the process of fabrication employed.\n2. Experimental Details\n2.1. Samples Fabrication\nPolycrystalline CoFe 2O4samples were prepared by three di\u000berent methods. In all the\ncases, nanosize ( <50 nm) oxides Fe 2O3and Co 3O4(Sigma-Aldrich) were used as precursors\nin molar ratio of 3:1. Powders were mixed in a planetary ball mill during 30 min at 400 rpm,\nand then grinded during 1 hour at 600 rpm. Initially, the classic ceramic method was used to\nproduce our sample. Mixture was \frst calcined at 900\u000eC during 12 hours to form the spinel\nphase, and then grinded at 550 rpm during 1 hour. After uniaxial compaction at 50 MPa in\na cylindrical die of 10 mm diameter, sample was sintered at 1250\u000eC during 10 hours. This\nsample will be referred as CF-CM. In the second method, the synthesis of the spinel phase\nwas achieved under the same condition as for the ceramic method. However, the sintering\nprocess was done by SPS. In all SPS experiments, a graphite die of 10 mm diameter was\nused and the heating was carried out under neutral atmosphere (argon). The sintering was\nperformed under a pressure of 100 MPa, with a 5 minutes temperature ramp from 20\u000eC\nto 980\u000eC followed by a stage of 2 min at 980\u000eC before cooling down. This sample will\nbe referred as CF-S-SPS. Finally, in the last method, the SPS was utilized to make both\nthe synthesis and the sintering (reactive sintering). The reaction stage was performed at\n500\u000eC for 5 min and the sintering stage at 750\u000eC for 3 min, both under a pressure of\n100 MPa. The thermal cycle was chosen based on the observation of the displacement\nrate of the pistons versus the temperature, as shown in Fig. 1. We assume that when the\ndisplacement rate brings back down, this signify that the reaction or sintering stage is well\nadvanced, meaning that the temperature is properly chosen. This sample will be referred\nas CF-RS-SPS. Regardless of the method used, cylindrical pellets of 10 mm diameter and\n2 mm thick were obtained.\n2.2. Measurement Procedures\nThe crystal structures of the ceramics were characterized by X-Ray Di\u000braction (XRD).\nXRD patterns of the samples were purchased from the pellets' surfaces and the experimental\n2Figure 1: Temperature (black), Pressure (green) and Displacement rate (red) pro\fles for the SPS process\nof the CF-RS-SPS sample. Stage at 500\u000eC correspond to the reaction and stage at 750\u000eC to the sintering.\ninstrument employed is a Bruker D2 phaser 2nd Gen di\u000bractometer using CoK \u000bradiation.\nDi\u000braction patterns were recorded in the angular range from 15\u000eto 100\u000ewith a scan step size\nof 0.02\u000e. The re\fnement is done by applying the Rietvield Method using MAUD software.\nThe surface morphology are analysed using scanning electron microscope (SEM) Hitachi\nS-3400N model. A hydrostatic balance was utilized to determine the density of our ceramics.\nThe magnetic measurements were carried out on samples, cut into cube shape of 8 mm3,\nusing a vibrating sample magnetometer (VSM, Lakeshore 7400) up to a maximum \feld of\n1 T. Magnetostriction measurements were performed at room temperature by the strain\ngauge method with an electromagnet supplying a maximum \feld of 700 kA/m. The gauges\nwere bonded on the pellets' surface along the direction (1) and the magnetic \feld was applied\nin the three directions (1), (2) and (3) of the Cartesian coordinate system, (1) and (2) being\nin the plane of the disc and (3) out of plane.\n3. Results and discussion\n3.1. Microstructure\nAll samples were initially characterized by X-Ray Di\u000braction analysis, and in all cases\nthe desired cobalt ferrite spinel structure has been obtained, as shown in Fig. 2.\nTo make sure that no secondary phase was present after the calcination and before the\nsintering process of CF-CM and CF-S-SPS, the XRD analysis was also performed on the\ncobalt ferrite powder (Fig. 2) and pure spinel phase was obtained. However, on the ceramics,\nthe only sample free from secondary phase is CF-CM. Purity of the spinel phase for each\nsample are reported Table 1. CF-S-SPS sample sintered at 980\u000eC presents a small amount\n3of CoO phase (7 wt%). This secondary phase, already reported in previous papers [11, 12],\nmight be a result of partial reduction of the ferrite to CoO in the graphite die during the\nSPS sintering. CF-RS-SPS sample, obtained by reactive sintering, shows 9 wt% of hematite\n(Fe 2O3). This can be a consequence of the precursor oxides Fe 2O3that did not completely\nreact with the Co 3O4during the short reaction stage (5 min).\nFrom MAUD re\fnement, it was possible to retrieve the average crystallite size (precisely\nthe size of coherent di\u000braction domain < L XRD>) for each sample (see in Table 1). As\nexpected, the size decreases with the reaction time and sintering time of the sample. To\ninvestigate the microstructure of the produced materials in more details, SEM observations\nwere performed. The recorded SEM micrographs for the three di\u000berent samples CF-CM,\nCF-S-SPS and CF-RS-SPS are shown in Fig. 3. It is apparent that CF-CM's grain size\nare much larger than for the sample CF-S-SPS, which was sintered with SPS. On the other\nhand, the grain size of CF-RS-SPS is not easily visible since SPS permits a short reaction\ntime (5 min) thus little grain growth [10], the grain size might be of the order of 50 nm, as\nthe precursor oxides, which is too small to be seen with our SEM model. This goes along\nwith the crystallite size estimated previously for CF-RS-SPS of 100 nm. Hence, only the\ngrain size of CF-CM and CF-S-SPS are reported Table 1. Density of the ceramics were also\nmeasured and it appears that sintering with SPS techniques permits higher density (97 %)\nthan with the ceramic method (90 %). It is worth noticing that XRD patterns show no\nsigni\fcant di\u000berence in the relative intensities of the peaks for the samples. This similarity\nindicates that, apparently, no texture was induced during reactive sintering (CF-RS-SPS). In\nfact, texturing would improve the peak intensity of speci\fc crystallographic families, which\nis not the case here.\nTable 1: Results of structural and magnetic measurements of CF-CM, CF-S-SPS and CF-RS-SPS. Properties\nreported are : purity of the phase CoFe 2O4, crystallite size ( <LXRD>), grain size ( <D SEM>), relative\ndensity (RD) of the sample, coercive \feld ( Hc), remanent magnetization along the hard axis ( MHA\nr) and\nthe easy axis ( MEA\nr), and saturation magnetization ( Ms).\nPurity<L XRD><D SEM>RDHcMHA\nrMEA\nrMs\n(wt%) (nm) (\u0016m) (%) (kA/m) (mT) (mT) (mT)\nCF-CM 100 250\u000625 4.2\u00060.4 90 21 102 102 510\nCF-S-SPS 93 120\u000612 0.3\u00060.1 97 19 229 229 505\nCF-RS-SPS 91 100\u000610 97 53 205 301 452\n3.2. Magnetism\nThe magnetic hysteresis loops of the three samples are shown in Fig. 4. Measurements\nwere performed on cubes because this shape exhibits the same demagnetizing factor in\nthe three directions [13]. Thus, the magnetometric demagnetizing coe\u000ecient of a cube\n(Nm= 0:2759) was taken into account to plot the curves as a function of the internal \feld.\nThe magnetic measurements were done in the three directions (1), (2) and (3) of the cube\nas sketched in Fig. 4 (a). CF-CM and CF-S-SPS are represented in Fig. 4 (a) and Fig. 4 (b),\nrespectively. As they exhibit considerably similar loops in the three directions with the\n4Figure 2: XRD patterns of CoFe 2O4samples CF-RS-SPS, CF-S-SPS and CF-CM. The XRD results of the\ncobalt ferrite powder after calcination is also plotted.\nsame remanent magnetization ( Mr) and coercive \feld ( Hc), we have represented only one\ncurve out of three. This shows the isotropic behavior of such ceramics. On the other hand,\nit is apparent that the M-H loops of CF-RS-SPS in Fig. 4 (c) present uniaxial magnetic\nanisotropy in the direction (3), because the remanent magnetization is higher than that for\nthe directions (1) and (2).\nThe values of coercive \feld ( Hc), remanent magnetization ( Mr) for the easy/hard axis,\nand saturation magnetization ( Ms) are reported in Table 1. The di\u000berence in coercive\n\feld (Hc) and saturation magnetization ( Ms) for CF-RS-SPS compared to the other two\nceramics is most likely due to the the secondary phase Fe 2O3. Indeed, it has been reported\nthat the impurity Fe 2O3has a direct impact on the magnetic properties of the cobalt ferrite\nby increasing its coercive \feld and decreasing the saturation magnetization [14]. Here, the\nchange in coercive \feld could also be a consequence of the discrepancy of the grain size. On\nthe other hand, CF-S-SPS has similar values of coercive \feld and saturation magnetization\ncompared with CF-CM despite the presence of CoO. This is because a small amount of CoO\n(7 wt%) has a very low impact on these two magnetic properties [15]. One can notice that\nthe susceptibility at low \feld is higher for CF-S-SPS ( \u001f= 20) than for CF-CM ( \u001f= 4:8).\nThis could be a consequence of the higher density of the sample sintered with SPS and\n5Figure 3: SEM images of samples (a) CF-CM, (b) CF-S-SPS and (c) CF-RS-SPS.\nit lower grain size [16]. Also, CF-RS-SPS exhibit very high susceptibility in the easy axis\ndirection (\u001f= 26:3), but lower suceptibility in the hard direction ( \u001f= 6:2). These results\nfrom the uniaxial anisotropy found for this sample. It is interesting to note that the magnetic\nanisotropy appears when the synthesis of the spinel phase is performed with SPS, and does\nnot occur when there is only a sintering stage with SPS. Thus, the key step that induces\nthe magnetic anisotropy is the reaction during the SPS process.\nIt is known that anisotropy and magnetostriction of cobalt ferrite stem from the spin-orbit\ncoupling of Co2+ions, usually distributed randomly among the octahedral sites (B sites).\nSome authors [2, 6, 7, 17] reported that when a magnetic annealing is done on CoFe 2O4, the\nsuperimposed induced uniaxial anisotropy is a consequence of Co cations di\u000busion to partic-\nular B sites, thus leading to a preferential magnetic axis close to the magnetic \feld applied\nduring the annealing. In our case, the magnetoelastic coupling is involved by the uniaxial\npressure applied on the magnetostrictive material, thus promoting a preferred orientation\nof the magnetic moments [18]. Moreover, the temperature of the synthesis stage with SPS\nis 500\u000eC (see in Fig. 1), keeping the material below the theoretical Curie temperature of\nthe cobalt ferrite (520\u000eC). In this way, when the reaction stage is performed under uniaxial\npressure, the material is ferrimagnetic and the applied stress in\ruences the position of Co2+\nions leading to a uniaxial anisotropy in the direction of the pressure. This could explain\nwhy the direction (3) is the easy axis in the M-H loop of the CF-RS-SPS. It also justi\fes\nwhy there is no induced anisotropy when SPS sintering is performed on the already formed\nphase. In fact, during the classical reaction of the sample CF-S-SPS, Co2+ions migrate\nrandomly to the di\u000berent B sites in an equilibrium position and they remain pinned there\nduring the sintering because the stage is too short (2 min) to permit the di\u000busion.\n3.3. Magnetostriction\nThe results of magnetostriction measurements at room temperature are shown in Fig. 5.\nMagnetostriction is always measured along the direction (1) but the magnetic \feld is ap-\nplied in the three directions (1), (2) and (3), thus leading to \u001511,\u001521and\u001531respectively.\nWe observe negative \u001511and positive \u001521and\u001531in the case of CF-CM and CF-S-SPS.\nThe maximum longitudinal magnetostriction for CF-CM is \u0000204 ppm and for CF-S-SPS is\n\u0000161 ppm.\nThe reduction of the saturation magnetostriction for CF-S-SPS is possibly a consequence\nof the secondary phase CoO. In fact, this phase was found to a\u000bect strongly the saturation\n6Internal Field (kA/m)Magnetization (T)(1) (2) HA\n(3) EA\n(1)(a) CF-CM (b) CF-S-SPS (C) CF-RS-SPS\n(1) (2) (3)0.6\n0.4\n0.2\n 0\n- 0.2\n- 0.4\n- 0.6(2)(3)(1) (2) (3)0.6\n0.4\n0.2\n0\n- 0.2\n- 0.4\n- 0.60 400 800 -400 -800 0 400 800 -400 -800 0 400 800 -400 -800Figure 4: Hysteresis loop M-H of samples (a) CF-CM, (b) CF-S-SPS and (c) CF-RS-SPS cut into cube.\nMeasurements are done in the three directions of the cube (1), (2) and (3) as represented on the drawing.\nmagnetostriction [15]. Moreover, density does not seem to be the determining factor for\nthe amplitude of the magnetostriction in our study, as it was also reported in other stud-\nies [16, 19, 20]. However, the ratio between longitudinal and transverse magnetostriction\nis of approximatively 3:1 for both samples. The change in slopes present at high \felds are\ndue to the contribution of the positive magnetostriction constant \u0015111of the cobalt fer-\nrite [4]. These data con\frm the isotropic behavior of such ceramics and corroborate the\nmagnetic hysteresis loops presented in the previous paragraph. The magnetostriction curves\nof CF-RS-SPS are quite di\u000berent compared to the other two samples, especially \u001521and\n\u001531. The maximum longitudinal magnetostriction is enhanced to \u0000229 ppm while \u001521and\n\u001531become negative once a certain magnetic \feld is reached. The ratio between longitu-\ndinal and transverse magnetostriction is of 19:1, which is much more than the theoretical\nisotropic value of 2:1. This type of curves is characteristic of cobalt ferrite with an induced\nuniaxial anisotropy along the direction (3) and it has been reported in several papers in\nthe case of CoFe 2O4after magnetic annealing [3, 4]. The change in sign of both \u001521and\n\u001531might be a consequence of the modi\fcation in contribution of the two parameters that\nde\fne polycristalline magnetostriction, mainly \u0015100at low \feld and \u0015111at high \feld. The\nmagnetostrictive curves of CF-RS-SPS also agree with the magnetic measurements of such\nsample, where an induced uniaxial anisotropy along the direction (3) was observed.\nAnother \fgure of merit for magnetostrictive materials is the piezomagnetic coe\u000ecient (or\nstrain derivative) de\fned as the slope of the magnetostrictive coe\u000ecient qm=d\u0015=dH . In\nmagnetoelectric layered devices, the transverse ME e\u000bect depends directly on the sum of the\nlongitudinal and transversal piezomagnetic coe\u000ecient qm\n11+qm\n21[21]. In Fig. 6, the maximum\npiezomagnetic coe\u000ecient qmax\n11,qmax\n21and the sum of both qmax\n11+qmax\n21are represented for the\nthree samples CF-CM, CF-S-SPS and CF-RS-SPS. It is interesting to note that CF-S-SPS\nhas the highest qmax\n11(-1.7 nm/A) compared to CF-CM (-0.73 nm/A) and CF-RS-SPS (-\n1.3 nm/A). This high longitudinal strain derivative for CF-S-SPS might be a consequence of\nits high permeability at low applied \feld. The magnetostriction being a quadratic function of\nthe magnetization, [18, 22, 23] the slope is hence directly in\ruenced by the permeability. But\nas CF-S-SPS is isotropic, it also exhibits the highest qmax\n21(0.55 nm/A). On the other hand,\nCF-RS-SPS is anisotropic, resulting in a very low qmax\n21(0.1 nm/A). Hence, by summing up\n7-240-200-160-120-80-4004080\n0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700-240-200-160-120-80-4004080\n0 100 200 300 400 500 600 700\nApplied Field (kA/m)Magnetostriction (ppm)(a) CF-CM (b) CF-S-SPS (c) CF-RS-SPS\nλ11λ21\nλ31λ11λ21\nλ31λ11λ21\nλ31Figure 5: Magnetostriction curves of (a) CF-CM, (b) CF-S-SPS and (c) CF-RS-SPS. The green line with\ncircles (\u001511) correspond to the measurement when the applied \feld is along the direction (1), the red solid\nline (\u001521) when the applied \feld is along the direction (2) and the blue dotted line ( \u001531) when the applied\n\feld is along the direction (3). The strain gauge is bonded along the direction (1) for all measurements.\nCF-S-SPS CF-RS-SPS CF-CM1.5\n1\n0.5\n0\n-1\n-2q11max\nq21max\nq11maxq21max+d\n/dH (nm/A)1.5\n1\n0.5\n0\n-0.5\n-1\n-1.5\n-2-0.5\n-1.5\nFigure 6: Maximum piezomagnetic coe\u000ecient obtained in the longitudinal ( qmax\n11) and transverse ( qmax\n21)\ndirection for CF-CM, CF-S-SPS and CF-RS-SPS. The sum of both coe\u000ecients qmax\n11+qmax\n21is also plotted.\nqmax\n11andqmax\n21, it results in a qmax\n11+qmax\n21lower for CF-S-SPS (-1.15 nm/A) than for CF-\nRS-SPS (-1.2 nm/A). For magnetoelectric purpose, CF-RS-SPS is then expected to exhibit\na better e\u000bect than CF-CM or CF-S-SPS.\n4. Conclusion\nIn summary, we compared the magnetic and magnetostrictive properties of cobalt ferrite\ndiscs obtained with three di\u000berent methods. It has been demonstrated that samples made by\nthe classic ceramic method and the classic reaction plus sintering with SPS behave as near-\nisotropic materials, while the reactive sintering with SPS induced a uniaxial anisotropy. An\neasy direction is found in the M-H loops, parallel to the applied pressure during the synthesis\nwith SPS. This has a direct e\u000bect on the magnetostrictive behavior, where measurements\nin the three directions gave magnetostriction of the same sign once a high magnetic \feld is\napplied. It also enhances the maximum longitudinal magnetostriction of the sample.\n8This enhancement could be even improved by optimizing the SPS processing parameters\nand hence trying to reduce the secondary phase Fe 2O3or increasing the uniaxial anisotropy.\nAnyway, ceramic with such properties could be of great interest for magnetoelectric com-\nposites to improve their performances. The reactive sintering at SPS can be a promising\nalternative to the magnetic annealing process because the time required to produce a sample\nis much shorter than any other technique (22 min for the reaction and the sintering).\n9References\nReferences\n[1] C. C. H. Lo, A. P. Ring, J. E. Snyder, D. C. Jiles, Improvement of magnetomechanical properties of\ncobalt ferrite by magnetic annealing, IEEE Trans. Magn. 41 (10) (2005) 3676{3678.\n[2] Y. X. Zheng, Q. Q. Cao, C. L. Zhang, H. C. Xuan, L. Y. Wang, D. H. Wang, Y. W. Du, Study of\nuniaxial magnetism and enhanced magnetostriction in magnetic-annealed polycrystalline cofe2o4, J.\nAppl. Phys. 110 (4) (2011) 043908.\n[3] K. Khaja Mohaideen, P. A. Joy, High magnetostriction and coupling coe\u000ecient for sintered cobalt\nferrite derived from superparamagnetic nanoparticles, Appl. Phys. Lett. 101 (7) (2012) 072405.\n[4] A. Muhammad, R. Sato-Turtelli, M. Kriegisch, R. Grossinger, F. Kubel, T. Konegger, Large enhance-\nment of magnetostriction due to compaction hydrostatic pressure and magnetic annealing in cofe2o4,\nJ. Appl. Phys. 111 (1) (2012) 013918.\n[5] K. Khaja Mohaideen, P. Joy, Studies on the e\u000bect of sintering conditions on the magnetostriction\ncharacteristics of cobalt ferrite derived from nanocrystalline powders, J. Eur. Ceram. Soc. 34 (2014)\n677{686.\n[6] J.-G. Na, T.-D. Lee, S.-J. Park, Migration path and charge conversion of cations in co-substituted\nspinel ferrite thin \flms during magnetic annealing, Jpn. J. Appl. Phys. 33 (1994) 6160.\n[7] J. C. Slonczewski, Origin of magnetic anisotropy in cobalt-substituted magnetite, Phys. Rev. 110 (1958)\n1341{1348.\n[8] J. Wang, X. Gao, C. Yuan, J. Li, X. Bao, Magnetostriction properties of oriented polycrystalline\ncofe2o4, J. Magn. Magn. Mater. 401 (2016) 662{666.\n[9] Z. A. Munir, U. Anselmi-Tamburini, M. Ohyanagi, The e\u000bect of electric \feld and pressure on the\nsynthesis and consolidation of materials: A review of the spark plasma sintering method, J. Mater. Sci.\n41 (3) (2006) 763{777.\n[10] R. Orr\u0013 u, R. Licheri, A. M. Locci, A. Cincotti, G. Cao, Consolidation/synthesis of materials by electric\ncurrent activated/assisted sintering, Mater. Sci. Eng. R-Reports 63 (46) (2009) 127{287.\n[11] N. Millot, S. L. Gallet, D. Aymes, F. Bernard, Y. Grin, Spark plasma sintering of cobalt ferrite\nnanopowders prepared by coprecipitation and hydrothermal synthesis, J. Eur. Ceram. Soc. 27 (23)\n(2007) 921{926.\n[12] T. Gaudisson, M. Artus, U. Acevedo, F. Herbst, S. Nowak, R. Valenzuela, S. Ammar, On the mi-\ncrostructural and magnetic properties of \fne-grained cofe2o4 ceramics produced by combining polyol\nprocess and spark plasma sintering, J. Magn. Magn. Mater. 370 (2014) 87{95.\n[13] D.-X. Chen, E. Pardo, A. Sanchez, Demagnetizing factors for rectangular prisms, IEEE Trans. Magn.\n41 (6) (2005) 2077{2088.\n[14] I. C. Nlebedim, J. E. Snyder, A. J. Moses, D. C. Jiles, E\u000bect of deviation from stoichiometric compo-\nsition on structural and magnetic properties of cobalt ferrite, coxfe3xo4 (x=0.2 to 1.0), J. Appl. Phys.\n111 (7) (2012) 07D704.\n[15] I. Nlebedim, A. Moses, D. Jiles, Non-stoichiometric cobalt ferrite, coxfe3xo4 (x=1.0 to 2.0): Structural,\nmagnetic and magnetoelastic properties, J. Magn. Magn. Mater. 343 (2013) 49{54.\n[16] I. C. Nlebedim, D. C. Jiles, Dependence of the magnetostrictive properties of cobalt ferrite on the initial\npowder particle size distribution, J. Appl. Phys. 115 (17) (2014) 17A928.\n[17] J. Ding, P. McCormick, R. Street, Magnetic properties of mechanically alloyed cofe2o4, Solid State\nCommun. 95 (1) (1995) 31{33.\n[18] E. Du Tr\u0013 emolet de Lacheisserie, Magnetostriction, Theory and Applications of Magnetoelasticity, Boca\nRaton, FL, USA:CRC Press, 1993.\n[19] I. Nlebedim, J. Snyder, A. Moses, D. Jiles, Dependence of the magnetic and magnetoelastic properties\nof cobalt ferrite on processing parameters, J. Magn. Magn. Mater. 322 (24) (2010) 3938{3942.\n[20] K. Khaja Mohaideen, P. A. Joy, In\ruence of initial particle size on the magnetostriction of sintered\ncobalt ferrite derived from nanocrystalline powders, J. Magn. Magn. Mater. 346 (2013) 96{102.\n10[21] V. Loyau, V. Morin, G. Chaplier, M. LoBue, F. Mazaleyrat, Magnetoelectric e\u000bect in layered ferrite/pzt\ncomposites. study of the demagnetizing e\u000bect on the magnetoelectric behavior, J. Appl. Phys. 117 (18)\n(2015) 184102.\n[22] D. C. Jiles, Theory of the magnetomechanical e\u000bect, Journal of Physics D: Applied Physics 28 (8)\n(1995) 1537.\n[23] Y. K. Fetisov, D. D. Chashin, N. A. Ekonomov, D. A. Burdin, L. Y. Fetisov, Correlation between\nmagnetoelectric and magnetic properties of ferromagnetic-piezoelectric structures, IEEE Trans. Magn.\n51 (11) (2015) 1{3.\n11"    },    {        "title": "1609.08333v1.A_Noninvasive_Magnetic_Stimulator_Utilizing_Secondary_Ferrite_Cores_and_Resonant_Structures_for_Field_Enhancement.pdf",        "content": "1  \n A Noninvasive Magnetic Stimulator  \nUtilizing Secon dary Ferrite Cores and  \nResonant  Structures for Field  \nEnhancement  \n \nRaunaq Pradhan1 and Yuanjin Zheng  1  \n \n 1School of Electrical and Electronic Engineering, Na nyang Technological University , \nSingapore  \n \nAbstract: In this paper, secondary ferrite cores and resonant structures have been used for \nfield enhancement. The tissue wa s placed between the double square source coil and the \nsecondary ferrite core. Resonant coils were added which aided in modulating the electric \nfield in the tissue. The field distribution in the tissue was measured using electromagnetic \nsimulations and ex -vivo measurements with tissue.  Calculations involve the use of finite \nelement analysis (Ansoft HFSS) to represent the electrical properties of the physical \nstructure. The setup was compared to a conventional design in which the secondary ferrite \ncores wer e absent. It was found that the induced electric field could be increased by 122%, \nwhen ferrite cores were placed below the tissue at 450 kHz source frequency. The induced \nelectric field was found to be localized in the tissue, verified using ex -vivo exper iments . This \nprelimin ary study maybe further extended  to establish the verified proposed concept with  \ndifferent complicated body parts modelled using the software and in-vivo experiments as \nrequired to obtain the desired induced field.  \n \nCorrespon ding author: Raunaq Pradhan ; email: raunaq.pradhan @gmail.co m; phone: \n+65-83132872   \n \nI. INTRODUCTION  \n The development of ferrite cores which could be used for power applications at kHz \nfrequencies have helped in the manufacture of magnetic stimulators working at these \nfrequencies. Ferrite cores have been utilized to increase the electric field in the nerve. \nMagnetic stimulators provide a spatial rate of change of electric field in the tissue by \nproducing a magnetic field created by a varying current flowing thr ough the primary coil. \nThe major advantages of this type of stimulation include minimal discomfort to patients and \nits noncontact, noninvasive nature. Clinical applications predominantly use the Figure of \nEight (FOE) coils. Other topologies like the double  square coils, Cadwell coils, and the quad \nsquare coils also exist. Literature estimates that larger activation per unit current is produced 2  \n when quad and square coils are used [1]. For low frequency magnetic stimulation, air cores \nhave been used.  \n \nPower consumption for these magnetic stimulators, which consists of Transcranial Magnetic \nStimulation (TMS) and repetitive Transcranial Magnetic Stimulation (rTMS) modalities are \nvery high. The study of pulsed electromagnetic fields in human tissues required the  scaling \ndown of the stimulation systems. One such work involves the use of ferrite cores in quad \ncoils at frequencies between 200 kHz - 1 MHz to achieve stimulation [2]. The stimulation \ndepends on three parameters, 1) the orientation of the coil with resp ect to the head or body as \nthe case may be, 2) the current waveform through the coil and 3) the type of coil.  \n \nSince Baker introduced the use of magnetic fields to stimulate the human motor cortex and \nthe peripheral nerves, which can produce effects like muscle twitches; there has been \ntremendous interest in the medical field. Design of full scale magnetic stimulation systems \nconsists of many challenges. During the discharge phase, a magnetic stimulator typically \nproduces an output power of 5 MW. In the ca se of TMS/rTMS, this would imply that a \ncapacitor needs to convert the charge stored into a magnetic energy in 100µs [3]. When \nhigher frequencies are chosen, this results in stringent requirements for capacitor selection \nand eventually becomes a bottle -neck. Extensive work on the use of rTMS and TMS for \ncuring various diseases like visceral pain, chronic neuropathic pain and fibromyalgia has \nbeen presented in literature. These modalities involve passing high intensity current pulses \nthrough a coil of wire, thereby inducing a magnetic field as high as 2 -4 T [4]. Fast changing \ncurrents can be produced by two approaches, namely, using the SCR (silicon controlled \nrectifier) based charging and discharging circuit, controlled by a PWM input, using similar \ncircuits  as IGBTs [5 -6]. \n \nIncreasing the field localization for stimulation has been yet another field of research.  3D \nfinite element simulation has been used to determine the field localization and the electric \nfield at the point of stimulation. Stimulation is c arried out by using a FOE coil, with a \nconductive plate having a window placed under it. The field localization was improved due \nto the addition of the conductive plate, but the electric field in the tissue decreased 2 fold for \nthe same FOE coil dimensions  [7]. \n \nThis paper proposes a setup which utilizes the use of ferrite cores and resonant structures to \nenhance the induced electric field, and compares it to a conventional design. A tissue model \nis used to simulate the stimulation, followed by ex -vivo expe riments using pork tissue, where \nthe findings have been validated.  \n \nII. BACKGROUND THEORY  \nA) Frequency selection for stimulation  \nRecently there have been studies which estimate the effects of magnetic fields and time \nvarying currents from kHz to MHz f requencies. It has also been found that the membrane \nvoltage increased with increase in frequency of the applied magnetic field [8]. The increase 3  \n in membrane voltage is considered enough evidence to perform frequency selection for \nmagnetic stimulation. It should be noted that at lower frequencies, the induced electric field \nin the tissue is smaller. The membrane voltage alone does not help in determining the suitable \nvalue for stimulation. It is shown in literature that the nerve acts as a low pass filter a nd \ninternally amplifies low frequency signals compared to high frequency signals. This is \nbecause the nerve consists of capacitors and resistors which help in functioning as a low pass \nfilter with a large DC gain. At higher frequencies capacitors tend to a ct as short circuits \nlowering the DC gain. The initial estimate of the electric field’s amplification factor is given \nby the following equation:  \n \n                              \n  ( )   ( )\n      \n   \n                            ( ) \nWhere \n \n                    \n     \n       \n                                            ( ) \n \n \nWhere,    is the cell radius,   is the membrane thickness which is equal to 3x10-9,    is the \ncondu ctivity of the cytoplasm,    is the conductivity of the membrane,    is the \nconductivity of the extracellular.    is the electric field inside the membrane. However, this \nmodel does not consider the second order effects.          are th e permittivity of the \ncytoplasm, the membrane and the extracellular medium respectively.    was taken as 77.8 \nand    was taken as 3.95. A more precise version of the amplification factor is given below.  \n \n \n  ( )     [        (          )(       )]\n   (    ) (       )(       )         ( ) \nWhere,  \n \n      (        )(     \n    \n)                       ( ) \n \n \nwhere,         . Here, second order effects are also considered. The nerve \namplification function generates a zero at 100 MHz, the effects felt by the zero were not \nconsidered in the first order solution. The above calculation is not exact because it  considers \nthe nerve as a cylinder [9 -11]. \n 4  \n Exact formulation is tedious because the exact geometry of the nerve is to be incorporated \nand solved by numerical methods and hence is not considered in this work. By substituting \nthe extracellular medium, the  amplification factor was plotted to get an approximate estimate \nof the frequency range to be chosen. Four extracellular mediums, namely blood, fat, bone and \nmuscle where chosen for the estimation for which the conductivities are obtained from \nliterature [ 11-12]. The logarithmic magnitude of the amplification factor and the log \nmagnitude of the frequ ency were plotted to obtain Fig  1. It was seen that the decrease in the \namplification factor was predominant for frequencies greater than 1 MHz In the case o f fat \ntissue, the amplification factor had significant reduction even before 1 MHz; hence \nfrequencies in the order of hundreds of kHz were chosen for analysis.  \n \n \nFig. 1. Amplification factor as a function of frequency  \n \nB) Primary Electric field due t o the coils  \nNeural stimulation can be achieved by a spatial change of electric field along the nerve. It can \nbe expressed as  \n \n      ⃗⃗⃗⃗ (   )\n       (   )\n          (   )\n      (   )    ( )  \n \nwhere the length and time co nstants are defined as  \n \n   √  \n                                             ( ) \n \nWhere, x is the distance along the axis of the nerve fibre when the nerve fibre is aligned along \nthe   axis.    is the electric field along   axis.    is the trans -membrane voltage which is \nthe voltage difference between the intracellular and extracellular fluid.    and    is the \nmembrane resistance times unit length and the intracellular resistance respectively. c m is the \nmembrane capacitance  per unit length.        is the activation function.  \n \n   The primary electric field generated due to the magnetic field created by a rate of change \nof current through the coil is given by the following equation:  \n5  \n    ⃗⃗⃗⃗⃗⃗⃗      (  \n  )  ⃗⃗⃗ \n                                 ( ) \n \n \nwhere,     is the primary electric filed,    is the permeability of free space,   \n   is the rate \nof change of electric current,    is an element of the coil,   is the number of turns and   is \nthe distanc e between the coil element and the point where the electric field is calculated.  \n \n    For generating the required electric field in the nerve, various types of coils have been \nused for magnetic stimulation in literature. This is because magnetic stimulatio n provides the \nfollowing advantages: 1) no contact to skin and non -invasive, 2) Ability to move and control \nthe point of stimulation with ease. Though other coil structures have also been used, larger \nactivating function per unit area has been achieved whe n square and quad coils are used. \nElectric field induced in the tissue can be calculated from the equation  \n \n ⃗       (  )     \n    \n  ∫   ⃗⃗       \n|     ⃗⃗⃗ |    \n              ( ) \n \n where,  ⃗        is the electric field produced in the tissue due to a current carrying source \ncoil,    is an infinitesimal coil section and    is the vector from each section to the point  . \n   is the electric potential due to surface charge accumulation. F or our calculations here, a \ndouble square coil is used. Adopting the methods proposed [1], we obtain the following \nrelations for activation function.  \n \n            \n       \n  { (   \n  )(            )}                      ( )        \n \nwhere  \n \n   \n√      (   )  \n   \n√(   )     (   )  \n   \n√(   )     (   )  \n   \n√(   )  (   )  (   )  6  \n    \n√(   )  (   )  (   )  \n   \n√   (   )  (   )                 (  ) \n \n where,   and   are the co -ordinates in the plane of the coil.   is the length of a side of the \nsquare coil.   is the total distance between the source and the receiver coil.   is the point at \nwhich the elect ric field is measured.   denotes the number of turns in the primary coil.  \n \nC) Use of Resonant Structures for field enhancement  \nNow, it is to be estimated if a secondary structure is able to help the increase of the electric \nfield at the nerve. We kn ow from Maxwell’s equations that  \n \n∮       \n  ∫     \n                        (  ) \n \n Where,   is the electric field and   is the magnetic field. Ferrites can be used as flux \nconcentrators, thereby increasing the flux in the path between t he primary and the secondary \nferrite. This leads to the increase in electric field induced at the tissue.  \n \nSoft ferrites are hard, brittle and chemically inert. These materials are black or dark -grey.  \nCompounds of either Manganese/Zinc or of Nickel/Z inc are primarily used. Magnetic \nproperties are exhibited if below the Curie temperature. They possess high resistivity and \nhigh permeability. Composition of the oxides can be adjusted to tune the permeability during \nmanufacturing process. Addition of reso nating structures help in modifying the electric field. \nRate of change of current in the primary coil can cause currents to flow in the secondary coil. \nThis provides a change in the field distribution, thereby modifying the electric field to a small \nextent . \n \nWireless power transfer experiments were first carried out by Nikola Tesla. Recent interest in \nwireless power transfer is due to the work reported which used the method of resonant \ncoupling for mid -range wireless power transfer. This was based on the  understanding that a \nphysical system can be reduced to a set of differential equations by using coupled mode \ntheory  [13].  \n \n ̇    (      )                           (  ) \n \n ̇    (      )                            (  ) \n 7  \n where,    and    are the resonant frequencies of the isolated objects and    and    are \nthe intrinsic decay rates due to absorption and radiated losses. k is the coupling co -efficient. F \nis the driving te rm and a is a variable defined so that the energy contained in the object is \n|aS,D(t)|2. When such a resonating structure is placed, it will generate an electric field which is \ngiven by:  \n \n ⃗         (  )     \n    \n  ∫   ⃗⃗         \n       ⃗⃗⃗⃗              (  )\n  \n \n   Assuming that a current flows in the secondary structure due to resonance, the electric \nfield created by it on the nerve is given by:  \n \n                    \n       \n  [ (   \n  )( \n√(    )  (    )    )]            (  ) \n \nThis field has a vectorial additive effect to the electric field produced due to the primary coil, \nthereby modulating the electric field in the nerve. Here,    and    refer to points on the \nreceiver coil.   is used to refers to the number of turns in the receiver coil.     is the \neffective permittivity [2].  \n \nIII. Materials and Methods  \nA) Simulation Set -up \nThe Ansoft Simulation setup, shown below in Fig . 2 consist ed of a primary coil (double \nsquare coil) for focusing the electric field to the tissue. The primary coil had ferrite cores for \nconcentrating the flux. The secondary structure was varied as ferrite cores, ferrite cores and \nresonating/non -resonating coil, d ouble square coils and vacuum. A pork fat tissue was \nmodelled using the software (where conductivity values were taken from literature \nmentioned below [12]) was placed in between the primary coil and the secondary structure. \nThe structure was enclosed in a n air box. Finite Element -Boundary Integral (FE -BI) method \nwas used to solve the structure. The simulation setup used in A nsoft HFSS [14] is shown in \nFig. 2. \n 8  \n  \nFig. 2.  a) Top view of the simulation setup, b) Bottom view of the simulation \nsetup, c) Si de view of the simulation setup. Ferrites, fat tissue, copper are shown in \nlight blue, brown and grey respectively.  \n \nFE-BI method available in HFSS was used because of the wavelength of the fields being in \nthe order of hundreds of kilometers and hence using the ABC boundary condition which \nrequires setting the air box length as λ/4 would be futile, due to large time for processing. Air \nbox size was chosen as 11.1x11.1x11.1 m3. The values of ε r, µr and σ of the fat tissue were \n31.565, 1 and 0.024906 S/m respectively. The values of ε r, µr and σ for the ferrite were 12, \n1000 and 0.01 Siemens/m respectively and the values of ε r, µr and σ of copper were taken as \n1, 0.999991 and 5.8x107 Siemens/m. The fat tissue, the air box, the secondary coil, the ferrite \ncores, the input capacitor, the secondary ferrite core, secondary capacitor and the primary \ncoil had 1912, 45996, 3577, 935, 6708, 912, 117 and 4066 tetrahedron mesh elements \nrespectively at 550 kHz. An input power of 500 W was provided to the source coil. T he fat \ntissue had a thickness of 0.25 cm. Fields 0.2 cm below the tissue were analyzed.  \n \nB) Parameter estimation based on circuit calculations  \nThe parameters were chosen based on theoretical circuit model calculations and used as \nparameters for software base d electromagnetic computation. The calculations of the \nparameter values are shown below.  \n \n1) Receiver coil resistance  (R) r: Because of skin effect, the current density on the surface of \nthe wire is higher than that at the center of the wire. This is taken  into consideration while \ncalculating the resistance of the wire. The resistance is given as follows:  \n \n       \n                                                 (  ) \n \n \n9  \n Where, a is the radius of the coil, M is the number of turns, r is the cross sectional area of the \nwire (0.071 cm), σ is the conductivity of the wire. The material chosen for the wire is copper \nand so σ=5.8∙107. δ is the skin depth [15].  \n \n           \n√                                              (  ) \n \n \nwhere, µ 0 is the permeability of free space (µ 0 =4π∙10-7). Solving for δ and substituting in \n(16), we obtain the resis tance values at 450 kHz, 500 kHz and 550 kHz for the wires of radius \n2 cm and 3 cm.  \n \n2) Coil resistance  RL: The measurement. is done by taking R L as 50 Ω. R r is negligible \ncompared to R L. \n \n3) Source coil resistance  Rs: The source coil is a double -square co il with each side, s=5 cm. \nNumber of turns, N=1. Number of coils is 2, because the coil is a double -square coil. D is the \nwidth of the wire.  \n \n                      \n                   (  ) \n \n \nwhich gives R s=1.75 mΩ at 450 kHz, 1.84 5 mΩ at 500 kHz and 1.935 mΩ at 550 kHz. It \nshould be noted that the calculations in this section do not take into consideration the effects \ncaused due to the ferrites. Calculations of resistances for the copper coils are carried out.  \n \nC) Ex-vivo experimental  set-up  \nBesides, validation of the simulations, experiments for determining the electric field induced \ndue to the stimulation set -up has also been carried out using a pork tissue with the dimensions \nof 2 cm x 2.5 cm x 2 cm. Here, the voltage across th e tissue was measured using electrodes, \nboth with and without the presence of ferrite cores. The primary coil is used as double square \ncoils, whereas for the secondary structures, resonant structures have been used. The \nsecondary ferrite was chosen as a cy linder.  The motivation behind using this simple \nexperimental set -up is to test the designed coils for their efficacy in achieving the required \nelectric field enhancement via the use of proposed resonant coil structures and ferrite core \nstructures at the de sired site of stimulation. The voltage induced across the pork tissue \nconnected with metal electrodes is observed using an oscilloscope. The set -up is described in \nFig. 3.  \n 10  \n  \n \nFig. 3.  Ex-vivo experimental set -up to measure voltage across electrodes f or the \nsimulated set -up \n \nIV. Results and Discussion  \nFig. 4. shows the maximum electric field observed in the tissue when the radius of the  ferrite \ncore is varied. In Fig . 4, for calculation it should be noted that the secondary structure is only \na ferrite core. It was observed that when the radius of the ferrite core was chosen as 3 cm, the \nmaximum magnitude of induced electric field in the tissue was obtained.  \n \n \nFig. 4.  Variation of maximum electric field with respect to  \nfrequency for different ferrite radius  \n \n11  \n  \n \nFig. 5. Comparison studies with different dimension of coils and resonant structures \n(a) Left handed coils of radius 2 cm with ferrite, double square coils and vacuum \nplaced under the tissue. (b) Right handed coils of radius 2 cm with ferrite, double \nsquare coils and vacuum placed under the tissue. (c) Left handed coils of radius 3 cm \nwith ferrite and vacuum placed under tissue (d) Right handed coils of radius 3 cm \nwith ferrite and vacuum placed under the tissue.  \n                                                                                           \nPower transfer between  coils placed was found to be the maximum, when the radius of the \ncoil was chosen to be 2 cm and hence calculations were adopted for coils and ferrite \nstructures ha ving radius of 2 cm. It is to be noted that the coils were wound around the ferrite \ncore. Two terminologies are adopted in the calculation of these values. The coils which are \nwound in the anticlockwise direction when viewed from the source coil are called  right \nhanded coils and the coils which are wound in the clockwise direction when viewed from the \nsource coil are called left handed coils.  \n \nThe primary coil was kept constant as a double square coil. The secondary coils and cores \nwere varied and the results fo r the same are indicated in Fig . 4 and Fig.  5. It is to be no ted that \nin Fig . 5a and Fig . 5b, double square coils are used as secondary coils. For obtain ing each \npoint in Fig . 4 and Fig . 5, calculations were carried out separately in HFSS. Resonant coils \nwere those coils which satisfied the values for the equation     \n  √  ., where    is the \nresonant frequency and   and   are the inductance and capacitance of the secondary coils \nwith or without the ferrites. The non -resonant  coils were simulated by replacing the capacitor \nwith a short when simulation was performed.  \n12  \n  \nFrom simulation results in Fig . 5c and Fig . 5d where ferrite cores were used, it was shown \nthat the electric field increased by 121.71% at 450 kHz, 112.8% at 500 kHz and 109.8% at \n550 kHz. Placing ferrite cores under the tissue hence, led to considerable difference in the \nelectric field distribution. Modulation of electric field thus produced was also possible by \nadding resonating/ non -resonating coils in th e presence or absence of these ferrite cores. \nInferences obtained are stated as follows 1) power consumption can be reduced for \ngenerating the same electric field by using secondary ferrite cores, 2) Scaling of devices is \npossible since the power can be re duced, 3) Modulation of electric field is performed by the \nuse of coils, 4) The theory explained earlier is validated.  \n \nAC\nRLCSL\nL\nrr\nr C\nRS\nS RHuman Body\n \nFig. 6. Equivalent circuit diagram of the entire system  \n \n     \n \nFig. 7. Induced electric field at a fre quency of 450 Khz when (Left) vacuum is \nplaced below the tissue (b) a ferrite core of radius 2 cm is placed under the tissue  \n \nFig/ 6. shows the equivalent circuit diagram of the system. Calculations of these individual \nvalues can be obtained by follo wing the procedure described earlier in equations 17 -19. \nSimulation results obtained from the electromagnet ic analysis is presented in Fig . 7. for \nvisualization of the electric fields, when vacuum and ferrite core of radius 2 cm is placed \nunder the tissu e at a frequency of 450 K Hz. Fig . 8-9 depicts the measurement results using \nthese coils which have been performed according to the set -up shown in Fig . 3. The \nmeasurements for the proposed set -up have been performed in both scenarios; by using only  \nelectrodes (with air between the electrodes) and pork tissue connected to the electrodes for \n13  \n measurement  The use of ferrite core structures for both the above mentioned set -ups, has \nbeen found to increase the induced electric field across the electrodes by 12 2% as opposed to \nno use of ferrite cores measurement results.   The results therefore, were both verified in \nexperiment and theory  for the simulation models and experimental set -ups described earlier . \nThese are preliminary results establishing the proposed  concepts. Different human body \nmodels modelled using the software and their corresponding body parts maybe used in place \nof the pork tissue used here, for obtaining the desired electric field to be induced. This may be \npotentially explored in further stud ies.   \n \n   \nFig. 8. Measured voltage at 450 kHz across normal electrodes (Left) without ferrite \ncores (Right) with ferrite cores  \n \n   \nFig. 9. Measured voltage at 450 kHz across pork tissue (Left) without ferrite cores \n(Right) with ferrite cores  \n \nV. Conclusion  \nIn summary, mathematical modeling and analysis are carried out in the first section which \naids in estimation of frequency and selection of primary coil and secondary structures. This \nwork estimated that the electric field improved by 122% at 4 50 kHz when ferrite cores where \nplaced below the tissue. It was found out that modification of the electric field is possible \nthrough the addition of secondary resonant and non -resonant coils in the absence and \n14  \n presence of ferrite cores. This device set -up can aid in stimulation and also can be used for \ncarrying out experiments on the analysis of high frequency magnetic fields in the human \nbody at reduced power consumption. The simulation has been carried out in an environment \nwhich can mimic the real scena rio. Measurements are performed by using coils connected to \ninstrumentation amplifiers are performed with normal electrodes and tissue placed in \nbetween, for both ferrite cores and no ferrite cores. The measurement results are found to be \nsimilar to that o f simulation results.   \n  \nFerrite cores operating at these frequencies which are used for high power applications are \navailable in the market. Materials like material 79 from the ferrite corporation can be used as \nthe core. Power amplifier topologies are a vailable in market which can provide the input \npower required for stimulation (AP400B by Advanced Test Equipment Corporation). The \nstimulator can be used for various neural stimulation applications which require modulation \nof electric fields in the brain, such as pain, depression, insomnia, epilepsy etc, presently being \naddressed using implant solutions placed within the brain . Studying of small structures like \nretina and the effects of magnetic fields on them can also be accomplished because of the \nscalab ility of the stimulator.  \n \nAcknowledgments:  This research is supported by the Singapore National Research \nFoundation under Exploratory/ Developmental Grant (NMRC/EDG/1061/2012) and \nadministered by the Singapore Ministry of Health’s National Medical Research  Council.   \n \nConflicts of Interest:  The authors declare no conflict of interest .  \n \nReferences : \n1. Esselle KP, Stuchly MA. Neural stimulation with magnetic fields: analysis of induced \nelectric fields. IEEE Transactions on Biomedical Engineering 1992 ; 39: 693 -700.  \n2. Basham E, Zhi Y, Wentai L. Circuit and Coil Design for In -Vitro Magnetic Neural \nStimulation Systems. IEEE Transactions on Biomedical Circuits and Systems  2009 ; \n3:321 -31.  \n3. Rossini PM, Rosinni L, Ferreri F. Brain -Behavior Relations: Transcranial Magnetic \nStimulation: A Review. IEEE Engineering in Medicine and Biology Magazine  2010 ; \n29:84 -96.   \n4. Lefaucheur JP. Methods of therapeutic cortical stimulation. Neurophysiologie \nClinique/Clinical Neurophysiology  2009 ; 39:1 -14.  \n5. Burunkaya M. Design and Construction of  a Low Cost dsPIC Controller Based \nRepetitive Transcranial Magnetic Stimulator (rTMS). J. Med. Syst.  2010 ; 34:15 -24.  \n6. Peterchev AV, Jalinous R, Lisanby SH. A Transcranial Magnetic Stimulator Inducing \nNear -Rectangular Pulses With Controllable Pulse Width (c TMS).  IEEE Transactions \non Biomedical Engineering  2008 ; 55: 257 -66.  \n7. Dong -Hun K, Georghiou GE, Won C. Improved field localization in transcranial \nmagnetic stimulation of the brain with the utilization of a conductive shield plate in the \nstimulator.  IEEE Transactions on Biomedical Engineering  2006 ; 53: 720 -25.   15  \n  \n \n \n \n8. Alkhateeb A.  Gaumond RP. Excitation of frog sciatic nerve using pulsed magnetic \nfields effect of waveform variations.  IEEE 17th Annual Conference Proceedings in \nEngineering in Medicine and Biolog y Society 1995 ; 2: 1119 -20.   \n9. Kotnik T, Miklavcic D.  Second -order model of membrane electric field induced by \nalternating external electric fields.  IEEE Transactions on Biomedical Engineering  2000 ; \n47: 1074 -81.   \n10. Chen A,  Moy VT.  Cross -linking of cell sur face receptors enhances cooperativity o f \nmolecular adhesion. J Biophys  2000 ; 78: 2814 -20.   \n11. Simeonova M,  Gimsa J. The Influence of the Molecular Structure of Lipid Membranes \non the Electric Field Distribution and Energy Absorption. J Bioelectromagnetics  2006; \n27: 652 -66.  \n12. Dielectric Properties for Body Tissues. Institute for Applied  Physics (IFAC)  \nhttp://niremf.ifac.cnr.it /tissprop/  2016 [accessed 26.04 .16].  \n13. Karalis A, Joannopoulos JD, Soljačić M. Efficient wireless non -radiative mid -range \nenergy transfer.  Annals of Physics  2008 ; 323: 34 -48.  \n14. Ansoft HFSS Software, http://www.ansys.com/Products/Electronics/ANSYS -HFSS.  \n15. Cannon BL, Hoburg JF, Stancil DD, Goldste in SC. Magnetic Resonant Coupling As a \nPotential Means for Wireless Power Transfer to Multiple Small Receivers. IEEE \nTransactions on Power Electronics  2009 ; 24: 819-25. \n \nBibliographies   \n \n \n \n \n \n \nRaunaq Pradhan received his bachelors degree in  Biomedical Engineeri ng \nfrom National Institute of Technology, Rourkela in 2012. He has submitted his PhD \nthesis at Nanyang Technological University, Singapore in the year 2016 and is currently \nworking as a research engin eer at Nanyang Techn ological University, Singapore. His \nareas of interest  are medical device development, magnetic/ acoustic stimulation, drug \nand gene delivery using magnetic fields.   \n \n \n \n \n \n \nDr. Zheng Yuanjin  received his B.Eng. from Xi'an Jiaotong University, \nP. R. China in 1993, M. Eng. from Xi'an Jiaotong University, P. R. China in 1996, and \nPh.D. from Nanyang Technological University, Singapore in 2001 . Since July, 2009, \nhe joined Nanyang Technological University as an assistant professor.  He has been \nworking on el ectromagnetic and acoustics physics and devices, biomedical imaging \nespecially photoacoustics / thermoacoustics imaging and 3D imaging, energy \nharve sting circuits and systems etc.       \n  \n "    },    {        "title": "1502.00220v1.Magnetoelectric_field_helicities_and_reactive_power_flows.pdf",        "content": "Magnetoelectric-field helicities and reactive power flows \n \n \nE. O. Kamenetskii, M. Berezin, and R. Shavit  \n \nMicrowave Magnetic Laboratory  \nDepartment of Electrical and Computer Engineering \nBen Gurion University of the Negev, Beer Sheva, Israel \n \nJanuary 25, 2015 \n \nAbstract \nThe dual symmetry between the electric and magne tic fields underlies Ma xwell's electrodynamics. \nDue to this symmetry one can desc ribe topological properties of an  electromagnetic field in free \nspace and obtain the conservation law of optical (e lectromagnetic) helicity. What kind of the field \nhelicity one can expect to see when the electroma gnetic-field symmetry is broken? The near fields \noriginated from small ferrite particles with magnetic -dipolar-mode (MDM) oscill ations are the fields \nwith the electric and magnetic components, but with broken dual (electric-magnetic) symmetry. \nThese fields – called magnetoelectric (ME) fields – have topological properti es different from such \nproperties of electromagnetic fields. The helicity st ates of ME fields are topologically protected \nquantum-like states. In this pape r, we study the helic ity properties of ME fields. We analyze \nconservation laws of the ME-field helicity and show  that the helicity density is related to an \nimaginary part of the complex power-flow density. We show also that the heli city of ME fields can \nbe a complex value.   PACS number(s): 41.20.Jb; 42.50.Tx; 76.50.+g  \nI. Introduction \n \nSymmetry principles play an important role with  respect to the laws of nature. To put into a \nsymmetrical shape the equations, co upling together the electric and magnetic fields, Maxwell added \nan electric displacement current. Such an additive, introduced for reasons of symmetry, resulted in \nappearing a unified-field structure:  the electromagnetic field. The electric displacement current in \nMaxwell equations allows correct prediction of ma gnetic fields in regions where no free current \nflows and prediction of wave propagation of el ectromagnetic fields. The dual symmetry between \nelectric and magnetic fields underlies the conser vation of energy and momentum for electromagnetic \nfields [1]. It can be connected also with conserva tion of polarization of the electromagnetic field. In \nparticular, this symmetry underlies the conservation of optical (elect romagnetic) helicity [2 – 4]. As \nit is stated in Ref [4], the dual electromagnetic theory inherently contai ns straightforward and \nphysically meaningful descriptio ns of the helicity, spin and or bital characteristics of light. \n    What kind of the source-free time-varying fiel d structure one can expect to see when an electric \ndisplacement current is neglected and so the el ectromagnetic-field symmetry (dual symmetry) of \nMaxwell equations is broken? As one of examples of such a symme try breaking, we can refer to the \nfield structures studied in non-c onductive artificial electromagnetic  materials that exhibit zero (or \nnear-zero) permittivity [5, 6]. For these materials, no Maxwell correction (no electric displacement  2current) exists and the fields are described by th ree differential equations (instead of the four-\nMaxwell-equation description of  electromagnetic fields): \n \n                                                                   0B∇⋅ =r\n,                                                                        (1)                        \n \n                                                                   BEt∂∇× =−∂rrr\n,                                                                (2)                        \n \n                                                                   0H∇× =rr\n.                                                                     (3)                        \n  \nIn an assumption that a zero-permittivity medium is  magnetically isotropic, from Eqs. (2), (3) it \nfollows that 20E∇=rr. One has the static-like fields. Li ght passing through such a material \nexperiences no phase shift. Evid ently, no unified-field retarda tion effects can be observed in \nstructures created by the materi als described in Refs [5, 6]. \n    It appears, however, that even without th e Maxwell's displacement current, certain retardation-\neffect fields, described by Eqs. (1) – (3), can ex ist. Such fields, lacking a dual electric-magnetic \nsymmetry, are exhibited in a small sample of a diel ectric medium with strong temporal dispersion of \nmagnetic susceptibility – a ferrom agnetic-resonant medium. For harmon ic fields in this medium, an \naveraged density of the electromagnetic energy is expressed as \n() 1\n2UE E H Hαβ\nαα α βωμ\nεω∗∗⎡⎤\n⎢⎥⎢⎥⎣⎦∂\n=+∂, where ε is the medium scalar permittivity and αβμ are the \ncomponents of the permeability tensor μt. In a small ferrite sample (with sizes much less than the \nfree-space electromagnetic wavelength), one has neglig ibly small variation of electric energy, so that \na dynamical process in a sample is described by three differential equations (1) – (3) [7]. Contrary to \nnon-magnetic structures with zero permittivity [5, 6], in this case one  can observe the unified-field \n(with coupled electric and magnetic  field components) retardation effects. These oscillations in \nsmall ferrite particles are called magnetostatic -wave (MS-wave) or magnetic-dipolar-mode (MDM) \noscillations [7 – 10].      MDM oscillations in small ferrite sphe res excited by external microwave fields were \nexperimentally observed, for the first time, by Wh ite and Solt in 1956 [11]. Afterwards, experiments \nwith disk-form ferrite specimens revealed unique spect ra of oscillations. While in a case of a ferrite \nsphere one observed only a few wide absorption p eaks of MDM oscillations [11], for a ferrite disk \nthere was a multiresonance (atomic-like) spectrum with very sharp resonance peaks [12 – 14]. Analytically, it was shown [ 15, 16] that, contrary to spherical geom etry of a ferrite particle analyzed \nin Ref. [17], the quasi-2D geometry of a ferrite disk gives the Hilbert-space energy-state selection \nrules for MDM spectra. MDM oscillations in a quasi -2D ferrite disk are macroscopically coherent \nquantum states, which experience broken mirror symme try and also broken time-reversal symmetry \n[18, 19]. There are helical-wavefr ont oscillations [20 – 24]. Free-sp ace microwave fields, emerging \nfrom magnetization dynamics in quasi-2D ferrite disk, carry orbital angular momentums and are \ncharacterized by power-flow vortices and non-zero he licity. Symmetry propert ies of these fields – \ncalled magnetoelectric (ME) fields – are diffe rent from symmetry pr operties of free-space \nelectromagnetic (EM) fields. For an  incident electromagnetic field, the MDM ferrite disk looks as a \ntrap with focusing to a ri ng, rather than a point.   3    ME-coupling properties, observed in the near-f ield structure, are originated from magnetization \ndynamics of MDMs in a quasi-2D ferrite disk. In ge neral, ME-coupling effects manifest in numerous \nmacroscopic phenomena in solids. Physics underl ying these phenomena becomes evident through a \nsymmetry analysis. In isolating cr ystal materials, in which both spatial inversion and time-reversal \nsymmetries are broken, a magnetic field can induce el ectric polarization and, conversely, an electric \nfield can induce magnetization [7, 25 ]. Without requirements of a speci al kind of a crystal lattice, a \nME-coupling term appears in magne tic systems with topol ogical structures of  magnetization. In \nparticular, there can be chiral, toroidal, and vortex structures of ma gnetization [26, 27]. Other \nexamples on a role of magnetiz ation topology in th e ME-coupling effect s concern orbital \nmagnetization. As it was discussed in Refs. [28, 29], an adequate descri ption of magnetism in \nmagnetic materials should not only include the spin  contribution, but also s hould account for effects \noriginating in the orbital magnetism. It was shown that in the two-dimensional case, orbital magnetization is exhibited due to exceeding of chiral -edge circulations in one direction over chiral-\nedge circulations in opposite dire ction [29]. Recently, it was shown that ME coupling can occur also \nin isotropic dielectrics due to an effect of orb ital ME polarizability – topological ME-coupling effect \n[30 – 32]. In such a case, one has the contribution of orbital currents to th e ME coupling. The orbital \nME polarizability is due to the pseudoscalar part of the ME coupling and is equivalent to the \naddition of a term to the electromagnetic Lagrangi an – the axion electrodynami cs term [33]. That is \nwhy the orbital ME response in isotropic dielectrics is referred as the axion orbital ME polarizability \n[30, 31].  \n    In this paper, we will show how both the pr oblems of optical (electromagnetic) helicity [2 – 4] \nand the problems of ME-coupling effects due to magnetization topology [25 – 32] can underlie the \nhelicity properties of microwave ME fields or iginated from quasi-2D ferrite disks with MDM \noscillations. We analyze conserva tion laws of the ME-field helici ty. The paper is organized as \nfollows. Study of helicity of ME fields is preced ed by an analysis of helicity in Maxwell's \nelectromagnetism. This analysis is given in Secti on II of the paper. In Section III, we study general \nproperties of helicity of ME fields . In Section IV, we analyze how the helicity density is related to \nreactive power flows originated from MDM ferrite  disks. In Sections V and VI, we show the \nnumerical studies of complex pow er flows and complex helicity parameters. Quantized topological \ncharacteristics of the ME fields arise from th e MS-wave spectral-problem solutions for MDMs in a \nquasi-2D ferrite disk. In Section VII, we make a brief analytical examination of the ME-field \nhelicities and power flows based on such MS-wave spectral-problem solutions. In Section VIII, we \ndiscuss general aspects of the ME -field topology and give a conclusi on of our studies shown in the \npaper. \n \nII. FIELD HELICITY IN M AXWELL'S ELECTROMAGNETISM  \n \nAt the beginning of this section, we should, probably, raise the issue:  Which term is more relevant \nfor description of the light twistness in free sp ace: \"chirality\" or \"helic ity\"? There is evident \nambiguity in using these terms in literature. Chirality  is usually considered as the property related to \nhandedness. In condensed matter phys ics, chirality is to be associ ated with enantiomorphic pairs \nwhich induce optical activity. At the same time, th e wave helicity, related to a Faraday effect, does \nnot require a lack of structural symmetry. In elem entary particle physics, helicity represents the \nprojection of the particle spin at the direction of motion. In this case , chirality is considered as the \nsame as the helicity only when the particle mass is  zero or it can be negl ected. On the other hand, \none can be faced with misuse of the term chiral ity as a synonym of handedness. Simplest examples  4are a Cartesian coordinate system and a Lorentz fo rce. Both structures are handed. However, based \non the known definition “An object is chiral if no mi rror image of the object can be superimposed on \nitself”, one can see that a Cartesian coordinate syst em (three unit polar vectors) is chiral, while a \nLorentz force (one axial v ector and two polar vectors) is achiral . This discussion shows that there is \nno definite answer to the above question. We will use both terms relating, mainly, to  the literature \nsources.     Helicity admits topological interpretation in re lation to the linkage of vortex lines of the flow. In \nplasma physics, the helicity of a static magnetic fiel d is considered as a meas ure of the screwness of \nthe magnetic line and is defined as  \n                                                             \nAA d V=⋅ ∇ ×∫rr\nM ,                                                             (4) \n \nwhere Ar\n is a vector potential related to the magnetic induction field: B A =∇×rr\n. For the static \nmagnetic field, the helicity character izes to what extent magnetic lin es are coupled with each other. \nFor a single magnetic line, the helicity parameter estimates the screwness of this line. It shows the \nextent to which a magnetic field \"wraps around itself\" [34 – 36].   \n    Helicity of electromagnetic fields is describe d by different aspects. All these aspects are related, \nanyway, to symmetry properties of Maxwell equations. The relativis tic generalization of helicity for \nan arbitrary free-space electromagnetic  field is defined as [37, 38]  \n \n                                                     ()1\n2AA CC d V =⋅ ∇ × − ⋅ ∇ ×∫rrr r\nH ,                                               (5) \n \nwhere Cr\n is a vector potential related to the electric field: EC=∇×rr\n. In such a relativistic \ngeneralization, the electromagnetic (optical) he licity is a measure of the screwness of the \nelectromagnetic field. In the quantum electr odynamics representation, it coincides with the \ndifference between the number of the right and left circularly polarized photons composing the \nelectromagnetic field. The electromagnetic helicity H is a time-even Lorentz pseudoscalar with the \ndimensions of an angular momentum. It is a conserved quantity in that:  0d\ndt=H [2 – 4, 37].         \n    Maxwell’s equations are invariant when the electric and the magnetic fields Er\n and Br\n mix via a \nrotation by an arbitrary angle ξ, as \n \n                                                     cos sin\nsin cosEE\nBBξξ\nξξ⎛⎞ ⎛⎞′⎛⎞=⎜⎟ ⎜⎟⎜⎟⎜⎟ ⎜⎟ − ′⎝⎠⎝⎠ ⎝⎠rr\nrr .                                                    (6) \n \nFor a real angle ξ, this transformation leaves invariant such  quadratic forms as the Poynting vector \nand energy density [1]. The duality rotation (6) generates the same ro tation of the vector potentials: \n                                                                                                                  \n                                                      cos sin\nsin cosA A\nCCξξ\nξξ⎛⎞ ⎛⎞′⎛⎞=⎜⎟ ⎜⎟⎜⎟⎜⎟ ⎜⎟ − ′⎝⎠⎝⎠ ⎝⎠rr\nrr .                                                   (7) \n  5It means that the electromagnetic helicity density ()1\n2hA A C C=⋅ ∇ × − ⋅ ∇ ×rrr r\n retains its form under a \nduality rotation (7) [3, 4]. The electromagnetic helicity is not the only quantity in electromagnetic \ntheory that describes the angular  momentum associated with polar ization. Also, one can obtain the \nspin angular momentum of light. The spin density of the field, ()1\n2sE A B C=× + ×rrrrr, has the \ndimension of an angular momentum per unite volu me and retains its form under a duality rotation \n(7). The helicity density h and the spin density sr are related by a continuity equation. Similar to \nelectromagnetic helicity, electromagnetic-field sp in is a conserved quantity. The symmetries \nunderlying these conservation laws are dual symmetri es for the electric and magnetic fields in \nMaxwell equations [3, 4].     While reference to the vector potentials  raises the question on ga uge dependence, explicit \nreference to the fields is gauge invariant. Recen tly, considerable interest has been aroused by a \nrediscovered measure of helicity in optical radiation – commonl y termed optical chirality density – \nbased on the Lipkin's \"zilch\" for the fields [39]. The optical chirality density is defined as [39 – 42]:  \n                                                     \n0\n01\n22EE BBεχμ=⋅ ∇ × + ⋅ ∇ ×rrr r\n.                                                   (8) \n \nThe optical chirality dens ity is related to the corresponding chirality fl ow via the differential \nconservation law:  \n                                                                  \n0ftχ∂+∇⋅ =∂rr\n,                                                                 (9) \n \nwhere  \n                                                    \n()()2\n0\n2cf EB BEε⎡ ⎤ = × ∇× − × ∇×⎣ ⎦r rrr r\n.                                          (10) \n \nFor time-harmonic fields (with the field time dependence iteω), the time-averaged optical chirality \ndensity is calculated as [39 – 42] \n \n                                                                  ()* 0Im2EBωεχ=⋅rr\n,                                                      (11) \n \nwhere vectors Er\n and Br\n are complex amplitudes of the electric and magnetic fields. This is a time-\neven, parity-odd pseudoscalar parame ter. Lipkin showed [39], that th e chirality density is zero for a \nlinearly polarized plane wave. However, for a circularly polarized wa ve, Eq. (11) gives a \nnonvanishing quantity. Moreover, for right- and le ft-circularly polarized waves one has opposite \nsigns of parameter χ.  \n    The effect of optical chirality was applied r ecently for experimental detection and characterization \nof biomolecules [43]. The chiral fields were gene rated by the optical excitation of plasmonic planar \nchiral structures. Excitation of molecules is considered as a product of the parameter of optical  6chirality with the inherent enantiometric properties of the material. In experiments [43], the \nevanescent near-field modes of plasmonic oscillations  are involved. In conti nuation of thes e studies, \na detailed and systematic numerical analysis of the near-field chirality in different plasmonic \nnanostractures was made in Ref [44]. However, in connection with the results obtained in Refs. [43, 44], an important question arises: Wh ether, in general, the expressions  (8), (11) are applicable for \ndescription of the chiroptical n ear-field response? The near-field chiroptical  properties shown in \nRefs. [43, 44], are beyond the scope of the Lipk in's analysis, which was made based only on the \nplane wave consideration.     In a case of Eq. (11), the electric field is pa rallel to the magnetic field with a time-phase delay of \n90o. In Ref. [45], it was shown that in an electr omagnetic standing-wave structure, designed by \ninterference of two counter-propa gating circular polari zed plane waves with the same amplitudes, \nthere are certain planes where the electric and magne tic fields are collinear with each other and are \nnot time-phase shifted. Such a fiel d structure results in appearance  of the energy density expressed \nas  \n                                                                 \n()() * 1Re2meWE B ∝⋅rr\n.                                                     (12) \n \nThe authors in Ref. [45] call this energy as the magnetoelectric energy. Intuitively, it was assumed \n[45] that this ME energy density of plane monoch romatic waves can be related to the reactive power \nflow density (or imaginary Poynting vector) [1]:  \n                                                                  \n()() * 1Im2meSE B ∝×r rr\n.                                                     (13) \n \n   In Refs. [21 – 24, 46], it was shown that the ME properties can be obser ved in the vacuum-region \nfields originated from ferrite-disk particles with MDM oscillations. Contrary to Refs. [45], there are \nnot the states of propagating-wave fields. There are quantized states of the ME near fields.  \n  \nIII. HELICITY OF THE ME NEAR FIELDS \n \nDifferential Eqs. (1) – (3), together with the constitutive relation \n \n                                                                     B Hμ=⋅rrt ,                                                                  (14)                        \n \ndescribe the fields in small ferrite particles at the ferromagnetic-resonan ce frequencies [7 – 10]. \nHowever, formal use of these three differential equa tions, Eqs. (1) – (3), does not allow formulation \nof the spectral problem for MDM os cillations. Without Eq. (2), usi ng only Eqs. (1) and (3) [and the \nconstitutive relation (14)], one obtains the Wa lker equation for magnetostatic-potential (MS-\npotential) wave function ψ (introduced based on a relation H ψ =− ∇rr\n) [17]. For a quasi-2D ferrite \ndisk, the Walker-equation differential operator (together with the homogeneous boundary conditions \nfor function ψ and its derivatives) gives the energy eigenstate spectru m of MDM oscillations [15, \n16, 18]. There are so called G-mode spectral solutions. When we aim to obtain the MDM spectral \nsolutions taking into account also the electric fields in a ferrite disk, we have to consider the \nboundary conditions for a magnetic flux density, B μψ=− ⋅ ∇rrt. In this case (because of specific  7boundary conditions on a lateral surface of a ferrite disk), one has the helical-mode resonances and \nthe spectral solutions are described by double-valu ed functions [18, 19,]. There are so called L-mode \nspectral solutions. For L modes, the electric field in a vacuum region near a ferrite disk has two \nparts: the curl-f ield component cEr\n and the potential-field component pEr\n [21]. While the curl \nelectric field cEr\n in vacuum we define from the Maxwell equation 0 cHEtμ∂∇× =−∂rrr\n, the potential \nelectric field pEr\n in vacuum is calculated by integrati on over the ferrite-disk region, where the \nsources (magnetic currents ()m mjt∂=∂rr) are given. Here mr is dynamical magnetization in a ferrite \ndisk. It was shown that in vacuum near a ferrite  disk, the regions with non-zero scalar product \n()pcEE⋅∇ ×rr r\n can exist [21].  \n    In a general form, we introduce a notion of th e ME-field helicity density  expressed as [21 – 23, \n46]:   \n                                                                \n() ( ) pc EE E EF∝ ⋅ ∇× = ⋅ ∇×rrr r rr\n.                                      (15) \n \nFormally, this parameter can be considered as a parameter χ described by Eq. (8), but with an \nadditional condition of the magnetostatic ( 0H∇× =rr\n) description. With such a meaning, we \nrepresent the ME-field helicity density as \n \n                                                                 0\n2FE Eε=⋅ ∇ ×rr\n.                                                             (16) \n \nThe product ()EE⋅∇ ×rrr\n is a measure of the screwness of the electric field. It is equal to the electric \nfield Er\n on the points lying in the screw axis times the vorticity E∇×rr\n. As the curl of a vector \nmeasures its rotation ar ound a point, the product ()EE⋅∇ ×rrr\n gives how much Er\n rotates around \nitself times its own modulus. This pr oduct evaluates to what degree vector Er\n resembles a helix.  \n    For time-harmonic fields (iteω∝ ), the time-averaged helicity density parameter was calculated in \na vacuum near-field region as [21 – 23, 46]: \n \n                                                                ()0*\nIm4F EEε⎧ ⎫⎨ ⎬⎩⎭=⋅ ∇ ×rrr\n.                                              (17) \n \nThe ME-field helicity density is nonzero only at the resonance frequencies of MDMs. It arises from \ndouble-helix resonances of MDM oscillations in a quasi-2D fe rrite disk [19]. At the MDM \nfrequency MDM ωω= , we have for magnetic induction  ()\nMDMiB Eω=∇ ×r rr\n. So, Eq. (17) can be \nrewritten as \n  8                              { } { } { }00\n2** *Im Re Re44 4MDM MDM MDMF iE B E B E Hcεε ωω ω=⋅ = ⋅ = ⋅rr rr rr\n,             (18) \n \nwhere 00 1c εμ = . From this equation, one can see that the helicity density F transforms as a \npseudo-scalar under space reflection P and it is odd under time reversal T. This is a time-odd, parity-\nodd pseudoscalar parameter. At the MDM resona nces, one observes macroscopically coherent \nvacuum states near a ferrite disk. These vacu um states of the field experience broken mirror \nsymmetry and also broken time-reversal symmetry. Whenever a pseudo-scalar  axion-like field is \nintroduced in the theory, the dual symmetry is spont aneously and explicitly broken [33]. Our studies \nshown in Refs. [21 – 24, 46] clearly verify the pr operties of helicity for ME fields originated from \nMDM resonances in a ferrite disk. Eviden tly, for regular electromagnetic fields { }*0 ReEB ≡ ⋅rr\n,   \n    We represent now the potential electric field as pE φ =− ∇rr\n, where φ is an arbitrary electrostatic-\npotential function. With this representation, we can write: \n \n              { } { } () { }* 00 0 **Re Re Re44 4MDM MDM MDMB FE B Bεε εφωω ωφ −= − =⋅ = ∇ ⋅ ∇ ⋅r rr r r r\n.              (19) \n \nHere we took into account that 0B∇⋅ =r\n. Based on this equation, one can introduce a quantity of the \ntime-averaged ME-energy density: \n \n                                                                            ()*Re Bφ η≡− ∇⋅rr\n.                                               (20) \n \nThe quantity *Bφr\n can be considered as the time-averaged ME-energy flow.  For the helicit y density \nwe can write:  \n \n                                                                           0\n4MDMFεηω= .                                                      (21) \n \nThe regions of the positive and nega tive helicity density [ 21 – 24, 46] can be desc ribed, respectively,  \nas the regions with positive and negative ME-energy density η. Since the helicity factor F shows \nwhat is degree of a twist between the Er\n and Hr\n vectors compared to a regular EM-field \nconfiguration (with mutually perpendicular Er\n and Hr\n vectors), the ME energy can be considered as \nenergy of a torsion degree of freedom [21 – 23]. B ecause of time-reversal symmetry breaking, all \nthe regions with positive helicity  become the regions with negativ e helicity (and vice versa), when \none changes a direction of a bias magnetic field:  \n \n                                                                      00HHFF↑↓=−r r\n.                                                           (22) \n \nThis equation can be written also as  \n                                                                 \n00() ( )HHηη−= −r r\n.                                                          (23)  9     \n    Let us define the helicity as an integral of the ME-field helicity density over the entire near-field \nvacuum region of volume V (which excludes a regi on of a ferrite disk): \n \n                                { }00 *Re44MDM MDM\np\nVV VFdV dV dV EBεεηωω== =⋅∫∫ ∫rr\nH .                             (24) \n \nThe question arises: Whether do we have the “helicity neutrality”, i. e. 004MDM\nVdVεηω==∫H ? To \nanswer this question we can rely on the following simple analysis.  With use of the transformation \n \n                            (){ } { }* 00 *Re Re44MDM MDM\nVSB dV dS Bnεεφωωφ =− =− ∇⋅ ⋅∫∫rr rr H ,                     (25)  \n \nwe can conclude that when the normal component of Br\n vanishes at some boundary inside which the \nfields Br\n and pEr are confined (i.e. when 0 Bn⋅=rr at the boundary), the quantity H is equal to zero. \nThe quantity H is also equal to zero when the fields  are with finite energy and the quantity *Bφr\n \ndecreases sufficiently fast at infinity.  \n    On the other hand, in side the vacuum-region volume V there are a region  ()V+ where the helicity \nis a non-zero positive quantity:  \n \n                                                         \n()() () 004MDM\nVdVεηω\n+++=>∫H                                                 (26) \n \nand a region  ()V− where the helicity is a non-zero negative quantity:  \n \n                                                         \n()() () 004MDM\nVdVεηω\n−−−=<∫H .                                               (27) \n \nFor the entire volume () ()VV V+−=+ , we have  \n \n                                                                 () ()0+−=+=HH H .                                                     (28) \n \nAlso, we should have  \n                                                                        \n() ()+−=HH .                                                         (29)  \n \nSuch “helicity neutrality” can be considered  as a specific conservation law of helicity.  \n    The helicity appears only at the MDM resonan ces. This quantized quantit y of the helicity is \nrepresented as   10                          \n() ()() () () () 00\n44MDM MDM\nVVdV dV nεεηηωω\n+−+− + −== = = ∫∫HH k,                        (30) \n \nwhere n = 1, 2, 3 … is the MDM-resonance number and kis a dimensional coefficient \nproportionality. Eq. (30) shows also quantizati on of the positive and negative ME-energy. \n \nIV. THE HELICITY FACTOR AND REACTIVE POWER FLOW \n \n    For time-variation harmonic electromagnetic fields (iteω∝ ), in the absence of losses and electric-\ncurrent sources, the imaginary part of the energy  balance equation shows that the density of the \nreactive or stored energy is related to an imaginary part of the complex power-flow density: \n()*2( ) I m\n8emcww E Hω\nπ−= ∇ ⋅ ×rr r\n, where the energy densities ()*\n16ecwE Dπ=⋅rr\n and \n()*\n16mcwB Hπ=⋅rr\n are real quantities [1]. By analogy with  electromagnetic fields, we will call the \nvector *ImEH×rr\n reactive power flow density. In our case of the MDM ME fields, we have reactive \npower flows in the near-field vacuum regions, wh ich are different from such flows of regular \nelectromagnetic fields.      In the near-field vacuum area of a quasi-2D ferrite disk with MDM resonances, one has in-plane \nrotating electric- and magnetic-field vectors localized at  a center of a disk [21]. This field structure, \nshown schematically in Fig. 1, is characterized by the helicity factor. As we will show, for the \nspinning electric- and magneti c-field vectors, a time averaged real part of a scalar product is related \nto a time averaged imaginary part of a vector pr oduct of the electric and magnetic fields. This will \nallow making a definite conclusion th at for ME fields, the helicity density is related to the reactive \npower flow density \n*ImEH×rr\n. Let us consider the electric- and magnetic-field vectors circularly \nrotating in the xy plane in a near-field vacuum region at the disk center. Assuming the \ncounterclockwise rotation, we have  \n                                                 ˆˆ() Ea x i y=+rrr   and    ˆˆ() Hb x i y=+rrr,                                               (31) \n \nwhere aa= and ibb eϑ= are complex amplitudes, ˆxr and ˆyr are unit vectors of the corresponding \nvectors along x and y axis, and ϑ is an arbitrary angle within 09 0ϑ≤<o. A scalar product of the \nelectric-field vector and the complex conjugate magnetic-fi eld vector gives: \n \n                          []*1ˆˆˆˆ() () c o s s i n2iEH a b e x i y x i y a b iϑϑϑ−⋅= + ⋅ −= −rr rrrr.                                   (32) \n \nWe have ()* 11Re cos22EH a b ϑ ⋅=rr\n. Now consider the magnetic-field vector H′r\n, which is 90o \ntime-shifted with respect to vector Hr\n, that is ˆˆ() Hi H b y i x′== − +rrrr. For a vector product of the \nvectors Er\n and ()*H′r\n, we have: \n  11                       () []*1ˆˆ ˆˆ ˆ () ( ) c o s s i n2iEH a b e x i y y i x a b z iϑϑϑ−′ ×= + × − − = − −rr rr rr r,                       (33) \n \nwhere ˆzris the unit vector along z axis. At the same time, a vector product of the electric-field vector \nand the complex conjugate magnetic-field vector Hr\n gives: \n \n             [] []*)1ˆˆ ˆˆ ˆˆ () () c o s s i n s i n c o s2iE H ab e x i y x i y i abz i abz iϑϑϑ ϑ ϑ−×= + × − = − − = − +rr rr rr rr.     (34) \n \nEvidently, ()**Im ReEH E H ′ ×= ×rr r r. When one changes a direction of  a bias magnetic field to an \nopposite direction, cosϑ changes its sign and so the helicity density parameter F changes its sign as \nwell [21 – 23, 46]. Since, in this case, the elect ric- and magnetic-field vectors also change a \ndirection of their rotation, the imaginary part of a vector *EH×rr\n is invariant with respect to a \ndirection of a bias magnetic field. From the above  analysis it follows that the vacuum regions above \nand below a quasi-2D ferrite disk, wh ere the helicity density parameter F is nonzero, are also the \nregions where the imaginary part of a vector *EH×rr\n exist as well. For the near-field vacuum areas, \nlocalized at an axis of a quasi-2D ferrite disk, we can represent this connection by the following \nrelation:   \n                                                      \n()** 11Re Im22 zEH E H⎡ ⎤⋅= ×⎢ ⎥ ⎣ ⎦rrr r\n.                                             (35) \n \nSo, in a region near a ferrite disk , reactive power flow is accompanie d by the helicity factor or, in \nother words, by the ME-energy density. Our numerical re sults in the next section clearly show that    \nin a vacuum region where the reacti ve power flow is observed, the he licity density factor exist as \nwell.      In vacuum regions near a ferrite disk, the helicity density \nF appears due to the potential electric \nand potential magnetic fields ( 0E∇× =rr\n, 0H∇× =rr\n). For such a field structure, \n** *() 0EH H EE H∇⋅ × = ⋅∇× − ⋅∇× ≡rrr rrrr rr\n. At the same time, in a fe rrite-material region, where \n0E∇× ≠rr\n [21], we have **() 0EH H E∇⋅ × = ⋅∇× ≠rrr rrr\n. Inside a ferrite disk, one has a localized twist \nof the field vectors due to the MDM-resonance magnetization motion [19, 21]. It means that a \nferrite-material region can be considered  as a source region  for the vector *ImEH×rr\nobserved in a \nvacuum area. Integration over the disk surfaces and ove r the ferrite-material-region volume gives       \n \n                                       () ( )**Im Im\ndisk diskdisk disk disk\nSVEHd S EHd V Q×= ∇ ⋅ ×≡∫∫rrr r rr ,                            (36) \n \nwhere diskQ can be considered as a certai n “charge” – a local source of the *ImEH×rr\n vector field in \nvacuum. We can also conclude that the helicity H should be related to diskQby the following \nintegral-form expression: \n  12                                                               () ()\ndiskQ+−+∝HH .                                                        (37)  \n \nV. NUMERICAL RESULTS: ME-FIELD ACTI VE AND REACTIVE POWER FLOWS AND \nHELICITY DENSITY \n \nOur numerical studies are based on a commercial finite-element  electromagnetic solver (HFSS, \nAnsoft). In the previous publications [20 – 23, 46, 47], we analyzed numerically the active power \nflows *ReEH×rr\n and the helicity density F for ME fields originated from a ferrite disk with MDM \noscillations. A numerical analysis in the present paper is ai med to study the reactive power flows \n*ImEH×rr\n in relation with the active power flows and the helicity density. In the analysis, we use \nthe same disk parameters as in Refs. [20, 21]: the yttrium iron ga rnet (YIG) disk has a diameter \nof 3=D mm and the disk thickness is 05.0=t mm; the disk is normally magnetized by a bias \nmagnetic field  49000=H Oe; the saturation magnetization of the ferrite is  1880  4 =sMπ G. A \nferrite disk is placed inside a 10TE -mode rectangular X-band waveguide  symmetrically to its walls \nso that the disk axis is perpendicular to a wide  wall of a waveguide. The waveguide walls are made \nof a perfect electric conductor (P EC). For better understanding the fi eld structures, we assume in our \nstudies that a ferrite disk has very sma ll losses: the linewidth of a ferrite is 0.1 OeHΔ= . Fig. 2 \nshows the module of the reflection (the 11S scattering-matrix parameter) coefficient. The resonance \nmodes are designated in succession by numbers n = 1, 2, 3… An insert in  Fig. 2 shows geometry of \nthe structure. One can see that, starting from th e second mode, we have Fano resonances. For every \nmode number, these coalescent resonances  are denoted by single and double primes. \n    Figs. 3 and 4 show the active and reactive power flows of the ME field near  a ferrite disk for the \n1st MDM, at the resonance frequency 8.523 GHzresf= . We can see that while the active power flow \nis characterized by the vortex t opology, the reactive power flow ha s a source which is originated \nfrom a ferrite disk. The regions of localization of the active and reactive power flows are different. \nWhile the active power flow is localized at the disk periphery,  the reactive power fl ow is localized at \na central part of the disk. This is well illustrated in Figs. 5 and 6 where inte nsities of the power flows \nnear a ferrite disk are show n. The helicity density near a ferrite disk for the 1st MDM is shown in \nFig. 7. When one compares Fig. 7 ( a) with Fig. 6 ( b) and Fig. 7 (b) with Fig. 5 (b), one finds good \ncoincidence between the regions of the reactive -power-flow localization and the helicity-density \nlocalization. We have pred icted theoretically such a coincidence in the above  analysis. It is worth \nalso noting here the regions of localization of the re active-power-flow and the helicity-density \ncorrespond to the region of lo calization of the potential el ectric field [21 – 23, 47]. \n      When one changes a direction of a bias fiel d, the active power flow cha nges its direction as well. \nAlso, the helicity-density factor F changes its sign in this case. At the same time, the reactive power \nflow does not change its direction when the direct ion of a bias field is changed. The active and \nreactive power flows are mutually perpendicular.  These flows constitute surfaces, which can be \nconsidered as deformed versions of the complex planes, i. e. as Riemann surfaces. These behaviors \nare illustrated in Fig. 8. The helicity-densi ty distribution is related to the angle ϑ between the \nspinning electric and magnetic fiel ds. When one moves from the fe rrite surfaces, above or below a \nferrite disk, one observes reduction of the fiel d amplitudes and also variation of the angle ϑ \nbetween spinning electric and magnetic fields. This angle varies from 0o or 180o (near the disk \nsurfaces) to 90 ±o (sufficiently far from a ferrite disk). Fi g. 9 shows variation of the angle between \nspinning electric and magneti c fields along the disk axis at different direc tions of a bias magnetic  13field. The angle ϑ gives evidence for a torsion structure of  the ME field above and below a ferrite \ndisk. The ME-energy density η appears due to such a torsion de gree of freedom of the field.  \n    Topological characteristics of  the ME fields are qua ntized quantities . The ME-field topologies \nappear only at the MDM-resonance frequenc ies. The ME-field pictures for the 2nd MDM (the peak \n2′′ in Fig. 2) are shown in Figs . 10 – 14. The main conclusions regarding the power-flow-density \nand helicity-density distri butions expressed for the 1st MDM are also applicable for the 2nd MDM.  \n    In the shown pictures of the power flows and helicity densities , we can observe some small non \nsymmetry, especially for the 2nd MDM. This non symmetry is due to influence of the external \nmicrowave radiation which propagates in  a waveguide from port 1 to port 2 (see an insert in Fig. 2).   \n \nVI. THE REAL AND IMAGI NARY HELICITY DENSITIES OF THE ME FIELDS \n \nAs we discussed above, near a ferrite disk with  MDM resonances there ex ist the vacuum regions \nwhere the electric and magnetic fields are collinear with each other and are not time-phase shifted. These regions are described by the helicity factor  defined by Eq. (18). No w the question arises: \nWhether there exist also the vacuum near-field regions with collinear the electric and magnetic \nfields which are time-phase shifted at \n90o? In a case of a positive an swer, we should classify the \nhelicity-density factor de fined by Eq. (18) (and anal yzed in the above study) as a real helicity-\ndensity factor:  \n                         \n{ } { } { }00\n2** *Im Re Re44 4MDM MDM MDM\nrealF iE B E B E Hcεε ωω ω=⋅ = ⋅ = ⋅rr rr rr\n                (38) \n  \nand introduce also the notion of an imaginary helicity-density factor: \n \n                      { } { } { }00\n2** *Re Im Im44 4MDM MDM MDM\nimagF iE B E B E Hcεε ωω ω=⋅ = ⋅ = ⋅rr rr rr\n.                (39) \n \nWhile the regions of realF  are characterized by the potential electric field pEr\n, the regions of imagF  \nhave the curl-field component cEr\n. Based on our numerical analysis, we can show that at the MDM \nresonances, the near-field regions with imaginary helicity factor exist. The results are represented in \nFigs. 15 and 16 for the 1st and 2nd MDMs. There is strong differe nce between the regions of \nlocalization of the real and imaginary helicity-den sity factors. Formally, the imaginary helicity-\ndensity factor, espressed by Eq. (39), resembles the optical chirality density [see Eq. (11)]. In our case, however, we do not consider regular electromagne tic fields. Nevertheless, a role of the external \nelectromagnetic fields is evident in Figs. 15 an d 16. The pictures are azi muthally nonhomogeneous. \nDue to the waves propagating in  a waveguide, one can see devia tion of the topol ogical pictures. \nImportantly, when one changes a direction of pr opagation of microwave ra diation in a waveguide, \nthe pictures azimutha lly turn at angle 180\no.  \n    Could the imaginary helicity-density factor imagF  be also related to an imaginary part of the \npower flow density, as it takes plac e for a real helicity-density factor realF ?  And, if it is so, what \nkind of an imaginary part of the power flow density we will have in a case of the imaginary helicity  14factor imagF ? To a certain extent, as a prel iminary analytical study, we wi ll clarify these questions in \nthe next section. \n \nVII. THE ME-FIELD HELICITIES AND POWER FLOWS: A VIEW FROM THE MS-\nWAVE SPECTRAL PROBLEMS  \n \nQuantized topological characterist ics of the ME fields arise fr om the MS-wave spectral-problem \nsolutions for MDMs in a quasi-2D ferrite disk [15,  16, 18 – 21]. Detailed analytical studies of the \nME-field helicities and power flows based on such MS-wave sp ectral-problem solutions (being \nimportant for our future investig ations) are beyond the frames of this work. Nevertheless, a brief \nexamination of this problem is  relevant and useful here.  \n    It is worth noting, once again, that the main difference between th e active and reactive power \nflows, as well as between the real and imaginary helic ities, appear due to diffe rence of a character of \nelectric fields in the ME-field structure. There are or potential or curl electric fields. In a case of a \npotential electric field pEr\n (and a potential magnetic field H ψ =− ∇rr\n), we have to solve an integro-\ndifferential MS-wave problem. The MS-potential eigenfunction ψ of a certain MDM gives us a \npotential magnetic field a nd a dynamical magnetization () m χψ=− ⋅ ∇rtr, where χt is a magnetic \nsusceptibility tensor [10]. The potential electric field pEr\n in vacuum is calcula ted by integration over \nthe ferrite-disk region, where the sources – magnetic currents (()mj imω=rr) – are given [21]. For a \npotential electric field pEr\n and a potential magnetic field, one has a reactive power flow and a real \nhelicity density. In the present paper, we obtai ned these quantities only  numerically. Finding of \nthese parameters analytically, based on the integr o-differential-problem solu tions, is a goal of our \nfuture studies.   \n    For a curl electric field cEr\n (and a potential magnetic field H ψ =− ∇rr\n), one has an active power \nflow and an imaginary helicity dens ity. In this case, the differential-problem analytical solutions for \nMS waves in a ferrite disk can be easily co rrelated with our numerical results. A simple \nmanipulation (taking into account that 0B∇⋅ =rr\n and H ψ =− ∇rr\n) shows that in this case inside a \nferrite region there is: \n  \n                                         ()** * *()EH H E i Bi B ωψ ω ψ ∇⋅ × = ⋅∇× = ∇ ⋅ = ∇⋅rrr rrr r r r r\n.                              (40) \n \nWith use of the homogeneous boundary conditions, one has the same relation also in a vacuum \nregion near a ferrite disk. Follo wing Ref. [48], one can conclude  that this equation gives  \n \n                                                              **EHi B ωψ ×=rrr\n.                                                               (41) \n \nA simple analysis of the energy balance equati on for monochromatic MS waves in a magnetic \nmedium with small losses [18] shows that, definitely, ()*ReiBωψr\n is a real power flow density. So, \nfor MS waves the quantity ()*ReEH×rr\n appears as real power flow density as well. Importantly,  15despite the fact that expression ()*ReEH×rr\n looks like the Poynting vect or, the MS-wave real power \nflow density cannot be interpreted as the EM-wave real power flow density. The Poynting vector is \nobtained for EM radiation which is described by the two curl operator Maxwell equations for the \nelectric and magnetic fields. This is not th e case of the MS waves, where we have potential \nmagnetic  and curl electric  fields. Since Eqs. (40) a nd (41) are relevant only fo r a curl electric field in \na vacuum region near a ferrite di sk, there is no connection of th ese equations to the quantity \n()*ImEH×rr\n which is related to a potentia l electric field in vacuum.  \n    We consider now the spectral problem of MDM oscillations in a quasi-2D ferrite disk. For a \ncoordinate system shown in Fig. 1, the MS-potential wave function ψ for a certain mode  n can be \nrepresented as [16, 18, 19, 47] \n \n                                                                ( ) ( , )nn n nCzr ψξ ϕ θ = % ,                                                      (42)  \n \nwhere ( )nzξ  is an amplitude factor, nC is a dimensional coefficient, and ( , )nrϕ θ%  is a dimensionless \nmembrane function. The function ( )nzξ  describes a standing wave along z axis. For membrane \nfunction, we have ( ) ( )nn n r ϕϕ ϕ θ =%%% , where ( )nrϕ% is a Bessel function and ( ) ~ni\nn eνθϕθ−% . Here nν is \nan integer ( n is a number of radial variati ons for a given azimuth number ν). For magnetic flux \ndensity (  nnB μψ=− ⋅ ∇rrt), we have  \n \n                                                               ()nn z n zB BeB e⊥ =+r rr% ,                                                       (43) \n \nwhere    \n                                                             \n()()(, )n\nnn nzzB Crzξϕ θ∂=−∂%                                                 (44) \n \nand   \n                                                           ( ) ( , )\nnn n nB Cz r eξμϕ θ⊥⊥ ⊥⎡ ⎤ =− ⋅ ∇ ⋅⎣ ⎦rt r% % .                                     (45)  \n \nHere subscript ⊥ corresponds to the transv ersal (with respect to z axis) vector and tensor \ncomponents.      The real power flow density for a MDM \nn is expressed as \n \n                                                       () ()** *Re2nn n n n n nip iB B Bωωψ ψ ψ == −r rr r.                                    (46) \n \nIt is easily to show [47] that () () 0nnrzpp == . The only non-zero component of the real power flow \ndensity is the azimuth component , which is expressed as [47]: \n  16                 () ()\n()**\n2 2* *\n2\n2 2 21(, ) ()2\n(, ) 1                  ( ) ( , ) ,2nn nn\nnn n n a n n\nn\nnn n n aipr z C z irr r\nrCz rrrθϕϕ ϕϕ ωξμ ϕ ϕ μ ϕ ϕθθ\nϕθ μωξ ν ϕ θ μ⎡⎤⎛⎞ ⎛⎞∂∂ ∂∂=− − + + ⎢⎥⎜⎟ ⎜⎟∂∂ ∂∂⎝⎠ ⎝⎠⎣⎦\n⎡⎤ ∂=− + ⎢⎥∂ ⎢⎥⎣⎦%% %%%% %%\n%%          (47)                      \n \nwhere μ and aμ are, respectively, the diagonal and off-diagonal components of the tensor μt.  \n    The quantities ()(, )nprzθ, circulating around a circle 2rπ, are the MDM power-flow-density \nvortices with cores at the disk center.  At a vortex center the amplitude of ()npθ is equal to zero. It \nfollows from Eq. (47) that  for a given mode number n, characterizing by a certain function ( )nrϕ% , \nthere are oppositely directed power-flow vortices  for different signs of the azimuth number nν.  In a \nvacuum region, outside a ferrite disk we have from Eq. (47) \n \n                                             () ()2 2 21(, )  () (, )nn n n npr z C z rrθων ξϕ θ =− % .                                      (48) \n \n    It is clear that 0np∇⋅ =rr, both inside and outside a ferrite di sk. The analytical results for MDM \npower-flow-density vorti ces, obtained based on Eqs. (47), (48) are in good correlation with the \nnumerical results. It is worth noti ng, once again, that following Eqs. (40), (41), analytical solutions \nfor ()npθ in vacuum are obtained for the curl electric fields.  \n    Let us extend our analysis by introduction also an imaginary MS-wave power flow . It means that \nwe will consider now the complex quantity  \n                                                                       \nsp i q=+rrr,                                                                 (49) \n \nwhere () ()** *Re2ip iB B Bωωψ ψ ψ == −rr r r and () ()** *Im2qi B B Bωωψ ψ ψ == +r rr r. The physical \nmeaning of the quantity ()*ReiBωψr\n is clear from the above analysis. Now the question arises: \nWhat does it mean the quantity ()*ImiBωψr\n?  \n    For the imaginary power flow density of a MDM n, one has  \n \n                                                           ()**\n2nn n n nqB Bωψψ =+rr r.                                                       (50) \n \nIn this case, we have () 0nqθ=, while () 0nrq ≠ and () 0nzq ≠. For ()nrq, we obtain: \n  17        () ()\n()**\n2 2* *\n2\n2 2 21() ()2\n() 1            ( ) ( ) .2nn nn\nnn n n a n n r\nn n\nna nqz C z irrr\nrCz rrrϕϕ ϕϕ ωξμ ϕ ϕ μ ϕ ϕθθ\nϕ νωξ μ μ ϕ⎡⎤⎛⎞ ⎛⎞∂∂ ∂∂=− + + − ⎢⎥⎜⎟ ⎜⎟∂∂ ∂∂⎝⎠ ⎝⎠⎣⎦\n⎡⎤ ∂=− − ⎢⎥∂⎢⎥⎣⎦%% %%%% %%\n%%                     (51) \n \nOutside a ferrite disk we have   \n                                             \n() ()2\n2 2 ()(,) ()2n\nnn rrqz C zrϕ ωθξ∂=−∂%.                                           (52) \n \nFor ()nzq, we obtain: \n                                                  ()2 2 ()() (, )n\nnn n nzzqC z rzξωξϕ θ∂=−∂% .                                            (53) \n \n    Since the quantity nq is related to a curl electric field in a vacuum region, it does not describe \nanalytically the obtained above quantity ()*ImEH×rr\n, which is related to a potential electric field in \nvacuum. We can suppos e, however, that the analytical quantity nq is related to the imaginary \nhelicity-density factor imagF , which corresponds to a curl electric  field in vacuum. Study of this \nrelationship is a goal for our future  analysis. In solving this probl em we should take into account \nalso a role of the external microwave radiation. The azimuth nonhomogeneity of imagF , shown in \nFigs. 15 and 16, is due to these external RF fields.  \n \nVIII. DISCUSSION AND CONCLUSION \n The dual symmetry between electric and magnetic fi elds underlies the cons ervation of energy and \nmomentum for electromagnetic fields and also the conservation of optical (electromagnetic) helicity. \nSymmetry properties of the ME fields are different from symmetry prope rties of free-space \nelectromagnetic fields. The near fi elds originated from small ferrite  particles with MDM oscillations \nare the fields with the electric and magnetic com ponents, but with broken dual (electric-magnetic) \nsymmetry. These fields – the ME fields – have topological propertie s different from such properties \nof electromagnetic fields. In this paper, we show ed that topological propert ies of ME fields are \npresented by a very complicated picture. There are real and imaginary ME power flows and real and \nimaginary helicity densities. These quantities are re lated to the analytically  derived MS-potential \nquadratic relations.       In classical electrodynamics, the imaginary pa rt of the Poynting vector gives information about \nevanescent (i.e. non-propagating) fi elds. For a plane wave, the imagin ary part of the Poynting vector \nis zero. When, however, the Poynti ng vector is calculated from the fields in some below-cut-off \nwaveguiding structures, a non-zero imaginary part  of the Poynting vector  can be found. This \nindicates that there are resona nt, non-propagating fields  at that location. In regular lossless \nstructures, or real or imaginary P oynting vector exists. In a case of the ME-field structure, situation \nwith the power flows is completely different. In this  paper we showed that in the vacuum area near a  18ferrite disk with MDM resonanc es, one can observe both active (*ReEH×rr\n) and reactive \n(*ImEH×rr\n) power flows. While activ e power flows are characterized by the vortex topology, \nreactive power flows are source originated from a ferrite disk. These flows constitute surfaces, which can be considered as deformed versions of the complex planes, i. e.  as Riemann surfaces. The \nregions of localization of the ac tive and reactive power flows are different. When the active power \nflow is localized at the disk peri phery, the reactive power flow is lo calized at a central part of the \ndisk. There is also an evident coincidence between the regions of the reactive-power-flow \nlocalization and the real-helicity-density localization. We showed that in an area of these localizations, there is variation of the angle between spinning el ectric and magnetic fields along the \ndisk axis. This angle gives evidence for a torsion structure of the ME field above and below a ferrite \ndisk. The ME-energy density \nη appears due to the torsion degree of freedom of the field. The near-\nfield vacuum regions where the electric and magnetic  fields are collinear with each other and are not \ntime-phase shifted are the regions with the real helic ity-density factor. We show ed that together with \nsuch regions there are also the va cuum near-field regions where the electric and magnetic fields are \ncollinear with each other but are time-phase shifted at 90o. In the last case, we are talking about the \nimaginary helicity-density factor. The observed qua ntized topological charac teristics of the ME \nfields arise from the MS-wave spectral-problem solutions for MDMs in a quasi-2D ferrite disk. A \npreliminary analytical examination of the ME-fiel d helicities and power flows based on such MS-\nwave spectral-problem solutions, made in the pa per, shows important re lationship between the \nnumerical and analytical results.       The shown topological proper ties of the ME fields can be us eful for novel near- and far-field \nmicrowave applications. Strongly lo calized ME fields, having both th e real and imaginary helicity \nparameters, open unique perspective for sensitive microwave probing of structural characteristics of chemical and biological objects. Th e presence of a biological sample  with chiral properties will \nnecessarily alter the near-field distribution which in turn will change the spectral characteristics of a \nMDM ferrite disk. Regarding the fa r-field applications, some intere sting questions can be expressed \nhere. The active (\n*ReEH×rr\n) and reactive (*ImEH×rr\n) power flows exist together and are mutually \nperpendicular one to another. We can also see that  the sources of the reactiv e power flows are at the \ncenters of active-power-flow vortices. With thes e topological properties,  the following question \narises: Can we observe free space transportation of reactive energy by an active power flow? In Ref. \n[22], we showed the effect of long-distance interacti on between two MDM ferrite disks. We have \nfound that the split-resonance response for c oupled MDM particles is weakly dependent on \ndistances between disks. Such coupling was clear ly observed even at extremely long distances \nbetween the disks. One of the prope r explanations of the effect in Ref. [22] can, probably, appear \nbased on our studies in the present paper. Becaus e of a joint structure of the reactive and active \npower flows and transportation of  reactive energy by an active pow er flow, we may have a long-\ndistance (reactive) coupling betwee n two MDM ferrite disks. This is a quasistatic phase coupling \nbetween two MDM disks, which very weakly depe nds on a distance between the disks. It can be \nsupposed that in Ref. [22], we observed such  an effect of a quasi static MDM coupling. \n \nReferences \n [1] J. D. Jackson, \nClassical Electrodynamics , 2nd ed. (Wiley, New York, 1975). \n[2] M. M. Coles and D. L. Andrews, Phys. Rev. A 85, 063810 (2012). \n[3] R. P. Cameron, S. M. Barne tt, and A. M. Yao, New J. Phys. 14, 053050 (2012).  19[4] K. Y. Bliokh, A. Y. Beksh aev, and F. Nori, New J. Phys. 15, 033026 (2013). \n[5] A. Alù, M. G. Silveirinha, A. Sa landrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007). \n[6] J. Schilling, Nature photon. 5, 449 (2011). \n[7] L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media , 2nd  ed (Pergamon, \nOxford, 1984). \n[8] D. C. Mattis, The Theory of Magnetism  (Harper & Row Publishers, New York, 1965). \n[9] A. I. Akhiezer, V. G. Bar'ya khtar, and S. V. Peletminskii, Spin Waves  (North-Holland, \nAmsterdam, 1968).  \n[10] A. G. Gurevich and G. A. Melkov, Magnetic Oscillations and Waves  (CRC Press, New York, \n1996). \n[11] R. L. White and I. H. Solt, Jr., Phys. Rev. 104, 56 (1956). \n[12] J. F. Dillon, Jr., J. Appl. Phys. 31, 1605, (1960). \n[13] T. Yukawa and K. Abe, J. Appl. Phys. 45, 3146 (1974). \n[14] E. O. Kamenetskii, A. K. Saha, and I. Awai, Phys. Lett. A 332, 303 (2004). \n[15] E.O. Kamenetskii, Phys. Rev. E 63, 066612 (2001). \n[16] E. O. Kamenetskii, M. Sigalov, and R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005). \n[17] L. R. Walker, Phys. Rev. 105, 390 (1957). \n[18] E. O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007). \n[19] E. O. Kamenetskii, J. Phys.: Condens. Matter 22, 486005 (2010). \n[20] E. O. Kamenetskii, R. Joffe, and R. Shavit, Phys. Rev. A 84, 023836 (2011). \n[21] E.O. Kamenetskii, R. Jo ffe, R. Shavit, Phys. Rev. E 87, 023201 (2013).  \n[22] M. Berezin, E. O. Kamenetskii, and R. Shavit, J. Opt. 14, 125602 (2012). \n[23] M. Berezin, E. O. Kamenetskii, and R. Shavit, Phys. Rev. E 89, 023207 (2014). \n[24] E. O. Kamenetskii, E. Hollander, R. Joffe, R. Shavit, J. Opt. 17, 025601 (2015). \n[25] M. Fiebig, J. Phys D: Appl. Phys. 38, R123 (2005).  \n[26] M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006). \n[27] N. A. Spaldin, M. Fiebig, and M. Mostovoy, J. Phys.: Condens. Matter 20, 434203 (2008).  \n[28] T. Thonhauser, D. Cere soli, D. Vanderbilt, and R.  Resta, Phys. Rev. Lett. 95, 137205 (2005). \n[29] D. Ceresoli, T. Thonhauser, D. Va nderbilt, and R. Resta, Phys Rev. B 74, 024408 (2006). \n[30] A. M. Essin, J. E. Moore, and D. Vanderbilt, Phys. Rev. Lett. 102, 146805 (2009). \n[31] A. Malashevich, I. Souza, S. Coh, and D. Vanderbilt, New J. Phys. 12, 053032 (2010).  \n[32] S. Coh, D. Vanderbilt, A. Malashevich, and I. Souza, Phys. Rev. B 83, 085108 (2011). \n[33] F. Wilczek, Phys. Rev. Lett. 58, 1799 (1987). \n[34] H. Pfister and W. Gekelman, Am. J. Phys. 59, 497 (1991).  \n[35] H. K. Moffatt and A. Tsi nober, Annu. Rev. Fluid Mech. 24, 281 (1992).  \n[36] M. A. Berger, Plasma  Phys. Control. Fusion 41, B167 (1999). \n[37] G. Afanasiev and Y. Stepanovsky, IL Nuovo Cimento 109 A , 271 (1996). \n[38] J. L Trueba and A. F. Rañada, Eur. J. Phys. 17, 141 (1996). \n[39] D. M. Lipkin, J. Math. Phys. 5, 696 (1964).  \n[40] Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010). \n[41] K. Bliokh and F. Nori, Phys. Rev. A 83, 021803(R) (2011). \n[42] J. S. Choi and M. Cho, Phys. Rev. A 86, 063834 (2012). \n[43]  E. Hendry et al, Nat. Nanotechnol. 5, 783 (2010). \n[44] M. Schäferling, D. Dr egely, M. Hentschel, and H. Giessen, Phys. Rev. X 2, 031010 (2012). \n[45] K. Y. Bliokh, Y. S. Kivsha r and F. Nori, Phys. Rev. Lett. 113, 033601 (2014). \n[46] R. Joffe, E.O. Kamenetski i and R. Shavit, J. Appl. Phys. 113, 063912 (2013).   20[47] M. Sigalov, E. O. Kamenetskii, and R. Shavit, J. Phys.: Condens. Matter 21, 016003 (2009). \n[48] D. D. Stancil, Theory of Magnetostatic Waves  (Springer-Verlag, New York, 1992). \n                        \n \n                    21\n \nFig. 1. Spinning electric- and magnetic-field vectors in vacuum regions above and below a MDM-\nresonance ferrite disk.  \n \n \n \nFig. 2. Frequency characteristics of a module of the reflection coeffi cient for a rectangular \nwaveguide with an enclosed thin-film ferrite  disk. The resonance modes are designated in \nsuccession by numbers n = 1, 2, 3… The coalescen t (Fano-type) resonances are denoted by single \nand double primes. An insert show s geometry of a structure. \n   \n                \n         \n  \n                                              ( a)                                                                       ( b) \n \nFig. 3. Active power flow density  near a ferrite disk for the 1st MDM ( 8.523 GHzresf= ). A bias \nmagnetic field is upward directed along z axis. ( a) A view on a vacuum plane parallel to the ferrite-\ndisk plane and at distance 50 microns above a disk, ( b) a view on a cross-section plane perpendicular \nto the ferrite-disk plane.  22        \n        \n  \n                                         ( a)                                                                       ( b) \n   \nFig. 4. Reactive power flow density  near a ferrite disk for the 1st MDM ( 8.523 GHzresf= ). (a) A \nview on a vacuum plane parallel to the ferrite-disk plane and at distance 50 microns above a disk, \n(b) a view on a cross-section plane perpe ndicular to the ferrite-disk plane. \n       \n     \n    \n  \n                                         ( a)                                                                    ( b) \n Fig. 5. Intensity of the power flows near a ferrite disk for the 1\nst MDM on a cross-section plane \nperpendicular to the ferrite-disk plane. ( a) Active power flow; ( b) reactive power flow.  \n \n          \n     \n    \n                                         ( a)                                                                       ( b) \n Fig. 6. Intensity of the power fl ows near a ferrite disk for the 1\nst MDM ) on a vacuum plane parallel \nto the ferrite-disk plane and at distance 50 microns above a disk. ( a) Active power flow; ( b) reactive \npower flow.              23          \n                     \n                       \n                                          ( a)                                                                     ( b) \n Fig. 7. The helicity density near a ferrite disk for the 1\nst MDM. A bias magnetic field is upward \ndirected along z axis. ( a) A view on a vacuum plane parallel to the ferrite-disk plane and at distance \n50 microns above a disk, ( b) a view on a cross-section plane perp endicular to the ferrite-disk plane. \n        \n  \n \n(a) \n \n \n(b) \n Fig. 8. The helicity density and ac tive and reactive power flows for the 1\nst MDM \n( 8.523 GHzresf= ). (a) An upward directed bias magnetic field; ( b) a downward directed bias \nmagnetic field. The active and reactive power fl ows are mutually perpendicular. These flows \nconstitute surfaces, which can be considered as defo rmed versions of the complex planes, i. e. as \nRiemann surfaces. When one changes a direction of a bias field, the active power flow changes its \ndirection as well. Also, the helicity-density factor F changes its sign in this case. At the same time, \nthe reactive power flow does not cha nge its direction when the directi on of a bias field is changed.  24              \n                \n  \n                                     ( a)                                                                        ( b) \n   Fig. 9. Variation of the angle be tween spinning electric and magnetic  fields along the disk axis for \nthe 1\nst MDM. This angle gives evidence for a torsion structure of the ME field above and below a \nferrite disk. The ME-energy density η appears due to the torsion degr ee of freedom of the field. ( a) \nAngle ϑ for an upward directed bias magnetic field; ( b) angle ϑ for a downward directed bias \nmagnetic field.  \n \n  \n          \n  \n                                   ( a)                                                                            ( b) \n \nFig. 10. Active power flow density  near a ferrite disk for the 2nd MDM ( 8.653 GHzresf= ).  A bias \nmagnetic field is upward directed along z axis. ( a) A view on a vacuum plane parallel to the ferrite-\ndisk plane and at distance 50 microns above a disk, ( b) a view on a cross-section plane perpendicular \nto the ferrite-disk plane.  \n  \n  \n                                         ( a)                                                                       ( b) \nFig. 11. Reactive power flow density  near a ferrite disk for the 2nd MDM ( 8.653 GHzresf= ). (a) A \nview on a vacuum plane parallel to the ferrite-disk plane and at distance 50 microns above a disk, \n(b) a view on a cross-section plane perpe ndicular to the ferrite-disk plane.  25 \n          \n  \n        \n  \n                                             ( a)                                                                    ( b) \n Fig. 12. Intensity of the power fl ows near a ferrite disk for the 2\nnd MDM on a cross-section plane \nperpendicular to the ferrite-disk plane. ( a) Active power flow; ( b) reactive power flow.  \n \n     \n  \n                                ( a)                                                                               ( b) \n Fig. 13. Intensity of the power flows near a ferrite disk for the 2\nnd MDM on a vacuum plane parallel \nto the ferrite-disk plane and at distance 50 microns above a disk. ( a) Active power flow; ( b) reactive \npower flow.   \n             \n              \n                                    ( a)                                                                              ( b) \n \nFig. 14. The helicity density near a ferrite disk for the 2nd MDM. A bias magnetic field is upward \ndirected along z axis. ( a) A view on a plane parallel to the fe rrite-disk plane and at distance 50 \nmicrons above a disk; ( b) a view on a cross-section plane perp endicular to the ferrite-disk plane. \n  26        \n     \n  \n                                        ( a)                                                                  ( b) \n \n          \n      \n  \n                                           ( c)                                                                   ( d) \n \nFig. 15. The imaginary helicity dens ity near a ferrite disk for the 1st [(a) and ( b)] and the 2nd [(c) and \n(d)] MDMs. A bias magnetic fi eld is upward directed along z axis. Microwave ra diation propagates \nin a waveguide from port 1 to por t 2 (see an insert in Fig. 2). ( a), (c) A view on a vacuum plane \nparallel to the ferrite-disk plane and at distance 50 microns above a disk; ( b), (d) a view on a cross-\nsection A-A perpendicular to the ferrite-disk pl ane.                     \n                   \n   \n      \n  \n                                         ( a)                                                                 ( b) \n  27   \n     \n  \n                                        ( c)                                                                ( d) \n  Fig. 16. The imaginary helicity dens ity near a ferrite disk for the 1\nst [(a) and ( b)] and the 2nd [(c) and \n(d)] MDMs. A bias magnetic fi eld is upward directed along z axis. Microwave ra diation propagates \nin a waveguide from port 2 to por t 1 (see an insert in Fig. 2). ( a), (c) A view on a vacuum plane \nparallel to the ferrite-disk plane and at distance 50 microns above a disk; ( b), (d) a view on a cross-\nsection A-A perpendicular to  the ferrite-disk plane.  "    },    {        "title": "1103.5840v1.Giant_coercivity_of_dense_nanostructured_spark_plasma_sintered_barium_hexaferrite.pdf",        "content": "arXiv:1103.5840v1  [cond-mat.mtrl-sci]  30 Mar 2011Giant coercivity of dense nanostructured spark plasma sint ered barium\nhexaferrite\nF. Mazaleyrat,1,a)A. Pasko,1A. Bartok,1,b)and M. LoBue1\nSATIE, ENS Cachan, CNRS, Universud, 61 av President Wilson, F-94235, Cachan,\nFrance\n(Dated: 20 July 2021)\nEnhencement of the coercivity of ferrite magnets in order to make them true hard magnets – i.e. to get\na coercive field higher than the residual magnetization– is s till a very important issue due to the limited\nressource in rare-earth. Thus, an alternative can be found i n making very fine grain ferrite magnets but it\nis usually impossible to get small grains and dense material together. In this paper, it is shown that the\nspark plasma sintering method (SPS) is able to produce close to 80% dense material with crystallites smaller\nthan 100 nm. The as prepared bulk sintered anisotropic magne ts exibits coercive field of 0.5 T which is close\nto 60% of the theoretical limit and only few % below that of loo se nano-powders. As a result, the magnets\nbehave nearly ideally (-1.18 slope in the BH plane second qua ndrant) and the energy product reaches 8.8\nkJm−3, the highest value achieved in isotropic ferrite magnet to o ur knowledge.\nPACS numbers: 75.50.Tt, 75.50.Ww, 75.50.Gg, 75.75.Cd,\nI. INTRODUCTION\nIn the last years, much efforts have been devoted to the\nenhancement of the coercivity of hexagonal M-ferrites.\nThe most fructuous results have been obtained by sub-\nstitution of La and Co in strontium ferrite according to\nthe formula Sr 1−xLaxFe12−yCoyO191. A very good com-\npromize have been found for equi-molar La and Co com-\npound with x=y= 0.2. Under optimal processing and\nsintering conditions, anisotropic magnets have been ob-\ntained with a very good rectangularity and an intrinsic\ncoercivity as high as 334 kAm−1(viz.µ0HCJ= 0.42T)\nwhich represents a 20% improvement compared to reg-\nular anisotropic Sr magnets. This very good result,\nhowever, has to be compared with the anisotropy field\nµ0HK= 2.27T of this compound, showing that, all-\ntogether, the coercivity is only a fifth of the anisotropy\nfield. This effect, known as Brown’s paradox, is related\nto magnetic domain structure. On the other hand, a\nstrong enhencement of the coercivity can be obtained by\nreducing the grain size below the single domain limit as\nit was proposed by Néel in 1942 (published ony after\nWorld War 22,3). According to this theory –usually re-\nferred under the name of Stoner & Wohlfarth4– the upper\nlimit of the coercivity is HKfor perfectly oriented and\n0.48×HKfor an assembly of non-interacting uniaxial\nparticles with isotropic distribution of easy axes. Severa l\nauthors have succeed to produce BaFe 12O19nanoparti-\ncles by soft chemical route and they have found coer-\ncivities as high as 0.58 T for a mean grain size about\n100 nm5,6. As the anisotropy field is 1.7 T, the theoret-\nical value for an isotropic magnet is 0.82 T, so that they\nreached 70% of the upper limit, showing how promising\na)Electronic mail: mazaleyrat@satie.ens-cachan.fr;\nhttp://www.satie.ens-cachan.fr\nb)Presently at LGEP, Universite Paris Sud, Orsay.should be this route. There is however a big drawback\nwith this approach: these results have been obtained with\nloose powders only, whereas in practice, it is necessary\nto supply solid magnets. On the one hand, embeding in\nresin can keep this high coercivity but reduce dramat-\nically the residual induction (due to dilution effect) in\nsuch a way that the energy product is not improved. On\nthe other hand, sintering produce grain growth and the\ncoercivity drops down to about 0.2 T. In this paper, we\nare showing that, starting from hexaferrite nanopowder,\nSpark Plasma Sintering (SPS) allows to produce nonos-\ntructured Ba-ferrite with a density close to 90% with al-\nmost no reduction in coercivity by opposition to SPS\nsynthesis of nanosize Ba-ferrite in a single step7,8.\nII. EXPERIMENTAL DETAILS\nBarium hexaferrite powders have been prepared by\na sol-gel citrate precursor method9–11. High purity\niron(III) nitrate, barium hydroxide and citric acid were\nused as starting materials with the molar ratio of citrate\nto metal ions 2:1. Iron(III) nitrate was dissolved in deion-\nized water and quantitatively precipitated with excess of\nammonia solution as iron(III) hydroxide. The precipi-\ntate was filtered and washed with water until neutrality.\nThen the obtained iron(III) hydroxide was dissolved in a\nvigorously stirred citric acid solution at 60-70°C. Barium\nhydroxide was added according to the desired composi-\ntion. Polycondensation reaction with ethylene glycol to\nprevent segregation9was not used. Instead, pH value\nof the solution was adjusted to 6 for better chelation of\nmetal ions11. Water was slowly evaporated at 80-90°C\nwith continuing stirring until a highly viscous residue is\nformed. The gel was dried at 150-170°C and heat treated\nat 450°C for 2 hours for total elimination of organic mat-\nter. Finally, the inorganic precursor with homogeneous\ncationic distribution was calcined at 900°C for 2 hours2\nSample Sintering Lattice constants Cr. size Density Hyster esis parameters\nRef. time (min) a(nm)c(nm)v(nm3)D(nm) (%) mS(Am2kg−1)mR/mSµ0HC(T)\nLit* single cryst. 0.58920 2.31830 0.69699 – 100\nCom† coarse grain 0.58928 2.32010 0.69772 >1000 >95 62 0.51 0 .26\nCP as calcinated 0.58946 2.32185 0.69867 60 – 55 0.51 0.56\nSPS1 0 0.58878 2.32378 0.69764 70 76 66 0.57 0.51\nSPS3 13 0.58858 2.32224 0.69670 84 88 66 0.57 0.49\nSPS4 20 0.58892 2.32259 0.69761 77 86 62 0.58 0.49\nTABLE I. Structural and magnetic parameters of calcinated p owder and SPS samples. Accuracy is ±5 nm for grain size (from\nXRD) and ±1% for density. *Litterature values are given for reference ; †refers to commercial magnet.\nFIG. 1. Typical hexaferrite particle as received after clac ina-\ntion\nwith heating/cooling rate 200 K/hour to synthesize the\nbarium hexaferrite phase. The calcination temperature\nhave been chosen high enough to allow complete forma-\ntion of the M phase and low enough to prevent grain\ngrowth. A representative TEM image of grain size and\nmorphology is given in Fig.1. Details of this optimization\nprocedure will be given in a forthcoming paper.\nThe samples have been sintered in a Sumitomo Dr Sin-\nter spark plasma sintering (SPS) machine under a pres-\nsure of 50 MPa and neutral atmosphere in a graphite\ndie. The heating rate was 160 Kmin−1, up to 800°C.\nThis temperature was kept for a duration between 0 and\n20 min and then cooled at a rate of 200 K.min−1.\nXRD diffractograms have been recorded using a PAN-\nalytical X’Pert Pro equiped with a linear detector and\nthe analysis of spectra was conducted with the Rietveld\nbased software MAUD12. The morphology of sinterd\nsample was obsvered with a Hitachi SEM. Density was\nmesured using standart Archimedes method and the hys-\nteresis loops where recorded at room temperature using a\nLakeShore vibrating sample magnetometer with a maxi-\nmum field of 2 T.III. RESULTS AND DISCUSSION\nX-ray diffractogram of the powder after calcination\nshows all characteristic peaks of M-type hexaferrite\n(magnetoplumbite) with relatively broad shape. The lat-\ntice parameters are very close to those of literature ref-\nerence samples and the average grain size was found to\nbe about 60 nm (see Table I). This value obtained by\nfitting diffractograms with MAUD is confirmed by TEM\n(see Fig.1). Although some particles are bigger than 100\nnm, most of then remains close to 50 nm. A slight de-\ncrease in the aaxis paramer has been observed together\nwith a increase of the caxis parameter upon sintering but\nit doesn’t seem to be significant as the unit cell volume is\nalmost constant. If this variation could be considered as\nsignificant, one would attribute it to internal stresses pro -\nduced by the sintering process under uniaxial pressure.\nAs expected with the SPS process, the average crystallite\nsize is not much enhanced even after 20 min compared to\nthe calcinated powder. This effect is related to the high\nspeed of the process which allows atomic short range dif-\nfusion (involved in sintering process) but not long range\ndiffusion (involved in grain growth process). In contrast,\nthe density changes appreciably with time as it has been\nobserved with most of materials sintered by SPS. A non\nnegligible porosity remains after sintering as it is also\nseen in the SEM picture in Fig. 2. Only the sample\nSPS4 is shown but others exhibits very similar features.\nFrom these pictures, it is concluded that the material is\ncomposed of approximatively 1 µm grains composed of\n70-80 nm crystallites with ∼500 nm node pores.\nThe hysteresis loops of the different samples are shown\nin Fig. 3. Comparison with conventional coarse-grain\nsample (commercial) immediatly shows the interest of\nreducing the grain size down to nm range: the sample\nmeasured after calcination in the form of loose powder\nexhibits a coercive field of 0.56 T, which is twice that\nof the coarse grain counterpart. In comparison with the\ntheoretical field for an anisotropic magnet, this value is\n70%, very close to results obtained by others5,6. The rect-\nangularity of the loop is very close to 50% as expected\nfrom Néel calculations for a uniform distribution of easy\naxes. After SPS sintering, the density is already high,\neven for a very short heating-cooling cycle. A marked3\nFIG. 2. SEM picture of sample SPS4\nincrease in saturation magnetization is observed, proba-\nbly due to uncomplete transformation of the precursors\nduring calcination. However, samples sintered for 0 to\n13 min, still have sensitively higher value than the coarse\ngrain sample, and drop to the same value for longer treat-\nment time. This effect is probably due to an excess in\noxygen gradually released due to the slightly reducing\nconditions.\nThe most stricking effect of SPS processing is the high\nvalue of the coercivity. Indeed, sintering reduces the co-\nercive field, by only several tens of mT, so that coerciv-\nity values remain very close to 0.5 T for all SPS samples.\nThis feature is due to the fact the crystallite size remains\nunchanged clearly under 100 nm, much below the single\ndomain limit, DSD= 36µ0√AK1/J2\nS= 235nm given af-\nter Kittel formula, where K1= 338kJm−3,A= 5pJm−1\nandJS= 0.5T. As a consequence, nucleation of domain\nwalls is impossible and the magnetization reversal should\nbe processed by rotation. Although it is still far from the\ntheoretical limit for isotropic magnets 0.48HK≈0.85T\nthe coercivity is doubled compared to regular isotropic\nferrite magnets. This feature is very important in ap-\nplications, since it considerably improves the resistance\nupon demagnetization. From pratical point of view the\ncharacteristic in the BH plane is more relevant. Com-\nputation of the BH loop B=µ0(σρδ+H), withσthe\nspecific magnetization, ρthe bulk specific mass and δ\nthe relative density, yields for the extrinsic coercivity\nµ0HCB= 0.2T, the remnant induction BR= 0.23T\nand the energy product (BH)max= 8.9kJm3compared\nwith 0.15 T, 0.22 T and 7 kJm3respectively for regualar\nsample.\nIV. CONCLUSION\nIt has been demonstrated that SPS technique is an\nefficient and powerful tool for the sintering of nanostruc-\ntured isotropic ferrite magnets as the coercivity of the\npowder can be obtained in dense samples. The energyproduct have been improved by 30% and the hardness\nσ (Am²/kg)\n-80-60-40-20020406080\nμ0H (T)-2 -1,5 -1 -0,5 0 0,5 1 1,5 2\nFIG. 3. Hysteresis (specic magnetization as a function of\napplied induction field) loops of commercial, as-calcinate d and\nSPS sintered samples.\nagainst demagnetization by a factor 2. In addition low\ntemperature sintering meets the requirement of LTCC\ntechnology with no need of glass addition13.\n1P. Tenaud, A. Morel, F. Kools, J. Le Breton, and L. Lechevalli er,\nJ. Alloys & Compounds 370, 331 (2004).\n2L. Néel, Comptes Rendus. Acad. Sci. 224, 94 (1947).\n3L. Néel, Comptes Rendus.Acad.Sci. Paris 224, 1550 (1947).\n4E. Stoner and E. Wohlfarth, Trans. Roy. Soc. A 240 , 599 (1948).\n5Q. Pankhurst, G. Thompson, D. Dickson, and V. Sankara-\nnarayanan, J. Magn. Magn. Mat. 155, 104 (1996).\n6W. Zhong, W. Ding, N. Zhang, Y. Du, Q. Yan, and J. Hong, J.\nMagn. Magn. Mat. 168, 196 (1997).\n7W. Zhao, Q. Zhang, X. Tang, H. Cheng, and P. Zhai, J. Appl.\nPhys.99, 08E909 (2006).\n8W. Zhao, P. Wei, X. Wu, W. Wang, and Q. Zhang, Scripta\nmaterialia 59, 282 (2008).\n9F. Licci and T. Besagni, IEEE Trans. Magn. 20, 1639 (1984).\n10A. Srivastava, P. Singh, and M. Gupta, J.Mat. Science 22, 1489\n(1987).\n11H. Yu and P. Liu, Journal of Alloys and Compounds 416, 222\n(2006).\n12L. Luterotti, “Materails analysis using diffraction,” Tech . Rep.\n(Universita di Trento, Italia, http://www.ing.unitn.it/ lut-\ntero/maud/index.html, 2003).\n13Y. Liu, Y. Li, H. Zhang, D. Chen, and Q. Wen,\nJ. Appl. Phys. 107, 09A507 (2010).\nACKNOWLEDGMENTS\nThis work was partly supported by the EC FP7 project\nSSEEC under grant number NMP-SL-2008-214864. A.B.\ngreatly aknowledge ENS Cachan for a 6 month scolar-\nship in the frame of international scolarship program\n2008/2009.\nP. Audebert, Pr at ENS Cachan Chemical department\nPPSM-CNRS is greatly acknowledged for his advices in\nsol-gel production."    },    {        "title": "1010.1877v1.Superparamagnetism_in_Nanocrystalline_Copper_Ferrite_Thin_Films.pdf",        "content": " 1SUPERPARAMAGNETISM IN NANOCRYSTALLINE \nCOPPER FERRITE THIN FILMS \n \nPrasanna D. Kulkarni1, R.P.R.C. Aiyar2, Shiva Prasad1, N. Venkataramani2, R. Krishnan3, \nWenjie Pang4, Ayon Guha4, R.C. Woodward4, R.L. Stamps4.  \n(1) Physics Department, IIT Bombay, Po wai, Mumbai 400076, (India) (2) ACRE, IIT \nBombay, Powai, Mumbai 400076 (India), (3) Labor atoire de Magnetisme et d’optique de \nVersailles, CNRS, 78935 Versailles (France), (4) School of Physics, M013, The University of Western Australia, 35 Stirling Hwy, Crawley WA 6009 (Australia).  Keywords: Ferrimagnetic thin films, Nanocrystalline, Ferrimagnetism, Superparamagnetism  \nABSTRACT \n \n   The rf sputtered copper ferrite films contain nanocrystalline grains. In these films, the \nmagnetization does not saturate even in high magnetic fields. This phenomenon of high field \nsusceptibility is attributed to the defects and/ or superparamagnetic grains in the films. A \nsimple model is developed to describe the observed high field magnetization behavior of \nthese films. The model is found to fit well to th e high field part for all the studied films. An \nattempt is also made to explain the temperat ure variation of the ferrimagnetic contribution on \nthe basis of reported exchange constants.   \nINTRODUCTION \n \n   One of the observations made in a number of ferrite thin film studies is the departure of \nthe magnetization from the established bulk value and non saturation even under high magnetic fields. The deviation from the known bul k value of magnetization is attributed to \nthe presence of nanocrystallinity and change in cation distribution. The non saturation aspect is postulated to arise from local defects, anisotropy and superparamagnetic grains. This is discussed earlier [1-3] on the basis of approach to saturation of magnetization using the Chikazumi expression [4], where the high field susceptibility (HFS) is related to the defects present in the films. However, it is not po ssible to completely understand the temperature \ndependence of the high field susceptibility, using th is model in the case of copper ferrite thin \nfilms. Because for room temperature as depos ited films, the high field susceptibility is found \nto increase when the temperature increases from  5K to 300K. If the H FS is purely related to \nthe anisotropic effects, it is expected to decrease with increasing temperature. The rf \nsputtered copper ferrite thin films have nanocry stalline grains, therefore there is a likelihood \nof a large fraction of particles falling in the superparamagnetic regime. In such a case, the magnetic moments of the nanocrystalline particle s are unable to align in the field direction \nbecause of the dominant thermal fluctuations . Bean and Livingston [5] have discussed a \ncritical volume for particles to become superparamagnetic in zero field. Above this critical volume, the particles are stable at a given temperature.   2   In this paper, we report the superparama gnetism in rf sputtered copper ferrite films using \na theoretical model. A similar type of work  on amorphous ribbons is reported by Wang et. al. \n[6].     Copper ferrite can be stabilized in two differe nt phases in thin film form, viz., a cubic and \na tetragonal phase [7]. Quenching the copper fe rrite films after carrying out a post deposition \nannealing stabilizes the cubic phase. The slow c ooling of the films afte r the annealing, on the \nother hand, results in the tetragonal phase. High field magnetization studies are carried out for as deposited and annealed films of copper ferrite.   \nEXPERIMENTAL \n \n   Copper ferrite films are deposited us ing a Leybold Z400 rf sputtering system on \namorphous quartz substrates. No heating or cooling is carried out during the sputter \ndeposition of the films. The rf  power employed during the deposition of the films reported in \nthe present study is 200W. The thickness of the f ilms is ~2400 Å. The films are subsequently \nannealed in air at 800 °C for 2 hours, followed by either sl ow cooling or quenching in liquid \nnitrogen. The temperature dependence of magne tic properties is studied using a SQUID \nmagnetometer for as deposited (Asd), slow cool ed (SC) and quenched (Q) copper ferrite thin \nfilms. M vs T data is recorded in temperature range 5K to 300K at a field of 3T for Asd and \nSC film and at 1T for the Q film. The M vs H curves are traced at various temperatures from \n5K to 300K at a field upto 7T.   \nRESULTS \n  \n   The normalized M vs. T curves for the Asd, SC and Q films are shown in Fig.1. The \nsubstrate contribution is subtracted from the total magnetization. The data is normalized with \nrespect to the corresponding magnetization at 5K . The M vs T curve shows a faster decrease \nfor Asd and Q films than for the SC film. This shows that temperature dependence of \nmagnetization is different for the two phases of copper ferrite. The M vs. T data is fitted to a \ntheoretical M vs. T curve of copper ferrite, based on the calculations of Srivastava et. al. [8]. \nThese calculations are an extension of Neel’s model for cubic inverse spinel ferrite. It is observed that the M vs. T curves of the films are not described adequately by the fittings. The \ncalculated M values are lower than the M values  observed for the copper ferrite thin films. \nThe reason could be the field at  which M vs. T curves are recorded does not saturate the \nmagnetization in copper ferrite thin films. Ther efore, there is a contribution to the total \nmagnetization from the non saturating part of th e M vs H curve in the case of nanocrystalline \nsystems.     The rf sputtered copper ferrite thin f ilms are nanocrystalline with a wide grain size \ndistribution (Asd - 5nm–25nm, SC and Q - 10nm- 100nm) [7]. A fraction of these grains may \nfall in the superparamagnetic regime. The superparamagnetic grains may contribute significantly to the net magnetization of the films.      We have developed a simple model to take  into account the contribution of the high field \npart of M vs. H curve to the total magnetization of the film. In this model, as a first approximation, the superparamagnetic grains  at each temperature are replaced by non  3interacting clusters. These clusters, which represent the superparamagnetic grains, show \nsubstantially large moment in the applied fi eld. The average moment with each cluster is \nassumed to be the same. The magnetization of th ese clusters is then expected to follow a \nLangevin function [5]. However, the total magne tization which is experimentally observed, is \nthe sum of the contributions from both superp aramagnetic and ferrimagnetic particles. This \nmay be represented as,                        M\nT = MFE + M SP                                      ( 1 )  \n    where M\nSP represents the total magnetic moment due to superparamagnetic contribution \nand MFE represents the ferrimagnetic contribution to the total magnetization.  \n    The high field part of the M Vs H curve can be fitted to the expression,                       M = M\nFE [ 1 + a L(µH/kT )  ]                              ( 2 )  \n    H e r e ,  M\nFE is the saturation magnetization of the ferri magnetic part of th e M vs H curve, µ \nis the average magnetic moment per superparam agnetic cluster in terms of Bohr magneton, k \nis the Boltzmann constant, T is the temperature. The parameter ‘ a’ is the ratio of \nsuperparamagnetic contribution to the ferrimagnetic contribution of the magnetization. The Eqn (2) is found to fit to the high field part of magnetization for Asd, SC and Q films at all \ntemperatures. The results of these fittings for Asd, SC and Q films are shown in Fig. 2, only for the 5K and 300K data. From th ese fittings the parameters µ, ‘ a’ and M\nFE are determined. \nFig.3 shows the temperature dependence of µ for Asd, SC and Q films. The temperature \ndependence of normalized magnetization for the fe rrimagnetic part for the Q film is shown in \nFig 4, along with the normalized theoretical M vs. T curve.  \nDISCUSSION \n \n   The average magnetic moment per superparamagnetic cluster reduces with temperature as shown in Fig. 3. This is due to the freezing in of  the larger superparamagnetic clusters when \nthe temperature is reduced. These ‘blocked’ clusters then contribute to the ferrimagnetic part of the magnetization. The smaller sized cl usters continue to contribute to the \nsuperparamagnetic part of the magnetization at lower temperature. The numerical value of µ \nfor Asd film is lower than the corresponding µ value for annealed films. This shows a \npresence of smaller grain sizes in the Asd film . The grain size increases when the films are \nex-situ annealed and this is reflected in the higher value of µ for the annealed films.     The temperature dependence of ferrimagnetic part shows that M\nFE increases with \ndecrease in temperature for the cubic phase Q f ilm, as seen in Fig. 4. For the cubic phase Q \nfilm having the largest magnetization, the MFE vs T follows the theoretical M vs. T curve \nobtained from Srivastava et. al. [8]. However, for Asd and SC films, the temperature \ndependence of magnetization is not properly de scribed by the ferrimagnetic component of the \nmagnetization obtained by Eq. (2). The parameter ‘ a’ is also obtained from the fittings of Eq. \n(2) to the high field magnetization data. Th is parameter represents the ratio of  4superparamagnetic contribution and the ferroma gnetic contribution to the total magnetization. \nBecause of blocking of the superparamagnetic pa rticles at lower temperatures, the value of \n‘a’ is expected to decrease as the temperature is reduced for all the three films of copper \nferrite. However, the variation of ‘ a’ is also observed to be inconsistent as the temperature is \nlowered. The simple model, presented in this  paper, work well for obtaining the cluster \nmoments. But, it needs modification to determin e the ferrimagnetic contributions to the total \nmagnetization in the case of Asd and SC film by considering the particles to be interacting \nand modifying the Langevin func tion accordingly [6]. A refinement of the simple model is \nunder progress.       \nCONCLUSION \n \n     A model involving the Langevin func tion describes the high field magnetization \nbehavior of nanocrystalline copper ferrite thin films at all temperatures. The magnetic moment of the superparamagnetic clusters re duces with temperature due to freezing of the \nmoment at lower temperatures. For the cubic phase Q film, the model works well in separating the ferrimagnetic and superparamagne tic contributions to the total magnetization \nof the film.   \nREFERENCE \n  \n[1] D.T. Margulies, F.T. Parker, F.E. Spada, R. S. Goldman, J. Li, R. Sinclair, A.E. Borkowitz, \nPhysical Review B , 53 (1996-II) 9175. \n[2] J. Dash, S. Prasad, N. Venkataramani, R. Krishnan, P. Kishan, N. Kumar, S.D. Kulkarni, \nS.K. Date, Journal of Applied Physics, 86 (1999) 3303. [3] P. D. Kulkarni, S. Prasad, N. Venkatara mani, R. Krishnan, Wenjie Pang, Ayon Guha, R.C. \nWoodward, R.L. Stamps, 9\nth International Conference on Fe rrites, Aug. 22-27, San Francisco, \nCalifornia, American Ceramic Society Proceeding (2005) 201.  [4] S.\n Chikazumi, S.Charap, Physics of Magnetism, John Wiley & Sons, New York (1964). \n[5] C. P. Bean, J.D. Livingston, Journal of Applied Physics 30, (1959) 120S. [6] L. Wang, J. Ding, Y. Li, Y.P.  Feng, N.X. Phuc, N. H. Dan, Journal of Applied Physics 89 \n(2001) 8046. [7] M.Desai, S. Prasad, N. Venkataramani, I. Samajdar, A.K. Nigam, R. Krishnan, Journal of \nApplied Physics, 91 (2002) 2220. [8] C. M. Srivastava, G. Srinivasan, and N. G. Nanadikar, Physical Review B, 19 (1979) 499. \n          5LIST OF FIGURES: \n \nFig.1.  Temperature dependence of normalized magne tization of SC, Q and Asd copper ferrite \nfilms.  \nFig.2.  High field part of the magnetization fitted with Eqn (2) for (a) SC, (b) Q, (c) Asd \ncopper ferrite films.  \nFig.3.  Temperature dependence of superparama gnetic cluster moment for SC, Q and Asd \ncopper ferrite films.  \nFig.4.  Temperature dependence of the ferrimagnetic  component of the magnetization for the \nQ film.                                  6 \n                         Fig.1. \n \n \nPrasanna D. Kulkarni et. al. “SUP ERPARAMAGNETISM IN NANOCRYSTALLINE \nCOPPER FERRITE THIN FILMS” \n \n \n \n    \n         0 50 100 150 200 250 3000.800.840.880.920.961.00\n SC\n Q\n Asd\n  Normalized Magnetization\nTemperature (K) 7 \n                            \n \n \n Fig.2.   Prasanna D. Kulkarni et. al. “SUP ERPARAMAGNETISM IN NANOCRYSTALLINE \nCOPPER FERRITE THIN FILMS”         \n20000 40000 600001400160018002000220024002600\n(a)\n200W Slow cooled film\n 5K\n 300K\n Fit of eqn (2)\n  M (Gauss)\nH (Oe)\n20000 40000 60000100020003000\n(c)\n  \n200W As deposited film\n 5K\n 300K\n Fit of Eqn (2)M (Gauss)\nH (Oe)20000 40000 60000300035004000450050005500\n  \n200W Quenched film\n 5K\n 300K\n Fit of Eqn (2)M (Gauss)\nH (Oe)(b) 8 \n                    \n \n  Fig.3. \n \nPrasanna D. Kulkarni et. al. “SUP ERPARAMAGNETISM IN NANOCRYSTALLINE \nCOPPER FERRITE THIN FILMS”                  0 50 100 150 200 250 3000100200300400500600700800 SC\n Q\n Asd\n  Cluster moment (µΒ)\nTemperature (K) 9 \n                      \nFig.4. \n Prasanna D. Kulkarni et. al. “SUP ERPARAMAGNETISM IN NANOCRYSTALLINE \nCOPPER FERRITE THIN FILMS”   0 50 100 150 200 250 3000.80.91.0\n  \n Brillouin function\n MFE vs T 200W Q film Normalized magnetization\nT (K)"    },    {        "title": "1109.6491v1.Ratchet_effects_for_paramagnetic_beads_above_striped_ferrite_garnet_films.pdf",        "content": "Ratchet e\u000bects for paramagnetic beads above striped ferrite-garnet \flms\nJ. I. Vestg\u0017 arden1and T. H. Johansen1\n1Department of Physics, University of Oslo, P. O. Box 1048 Blindern, 0316 Oslo, Norway\nWe calculate the motion of a small paramagnetic bead which is manipulated by the stripe domain\npattern of a ferrite-garnet \flm. A model for the bead's motion in a liquid above the \flm is developed\nand used to look for ratchet solutions, where the bead acquires net coherent motion in one direction\nwhen the external \feld is modulated periodically. We consider three cases. First, the ratchet,\nwhere the beads all go in the same direction. Second, the height dependent ratchet, where beads\nat di\u000berent heights go in opposite direction. This case can be used to separate beads of di\u000berent\nsizes, as considered in J. Phys. Chem. B 112, 3833 (2008). Third, we describe how the separation\nthreshold can be tuned by changing the amplitude of the applied \feld. Finally, we describe a\npseudo ratchet, where the external modulation is not periodic and the ratchet changes direction\nperiodically.\nI. INTRODUCTION\nFunctionalized micrometer-sized beads have for a long\ntime been used for medical and biological applications\nwhere a typical application is to attach biologically ac-\ntive molecules to the beads and use the beads as carriers.\nHowever, the setup for such applications is usually lim-\nited to bulk manipulation where the beads are contained\nin an aqueous solution, and such setups do not o\u000ber pre-\ncise positioning of individual beads. Recently this sit-\nuation has improved and several devices demonstrating\ncontrolled manipulation of a small number of beads have\nbeen realized, for example by using a thin zig-zag elec-\ntric wire1or by a hybrid device magnetic bead separator\ndevice using current wires and magnetic \felds combined\nwith micro\ruidic channels.2\nOne promising way to realize devices that manipulate\nindividual beads is to use domain patterns in ferrite gar-\nnet \flms. (For a review, see. Ref. 3) Because the para-\nmagnetic beads get strongly pinned to the domain walls\nthe in\ruence of thermal noise and other perturbations\nis small. Also, the beads can easily be moved from the\ndomain walls by an external \feld interacting both with\nthe beads and the domain pattern. An additional level of\ncontrol can be archived by monitoring the domain pat-\nterns by exploiting the larger Faraday rotation of ferrite\ngarnet \flms. All these features where demonstrated in\nRef. 4 in which the stripe pattern of a ferrite garnet \flm\nin an harmonic applied \feld created a magnetic ratchet\ne\u000bect, where beads jumped from domain wall to domain\nwall in just one direction. In the same system, with a\nmore complex applied \feld, Ref. 5 demonstrated an even\nmore surprising e\u000bect: beads of di\u000berent sizes go in op-\nposite directions. The motion in this double ratchet, as\nas in the original rathet, was synchronized so beads jump\nonly one wavelength of the stripe pattern per period of\nthe external \feld.\nIn this work we model the the system of Refs. 4 and\n5 and discuss the cause of the e\u000bects and tuning of the\ndevices.\n/0/0/0/0\n/1/1/1/1 λ\nd FGFxzBeadFIG. 1. A side-view of the stripe domain pattern of a ferrite\ngarnet \flm. The \flm has thickness dand pattern wavelength\nis\u0015. A paramagnetic bead with radius ais pinned to the\ndomain wall.\nII. MODEL\nConsider a paramagnetic bead dispensed in a liquid\nabove the surface of the \flm. The bead motion is mainly\ndetermined by the hydrodynamic force Fh\nxand magnetic\nforceFm\nx. Then the equation of motion is\nFh\nx+Fm\nx= 0: (1)\nThis overdamped motion is a reasonable approximation\nfor slow dynamics and it is also reasonable to neglect\nother forces, provided the beads avoid direct contact with\nthe surface. The hydrodynamic drag of slowly moving\nbeads dispensed in a liquid is quanti\fed by Stoke's law\nFh\nx= 6\u0019fa\u0011 _x; (2)\nwhereais bead radius, \u0011is the dynamic viscosity of\nwater and fis a correction factor due to the presence\nof the \flm, f=f(z)\u00151. In experiments the \flm is\ntypically electrostatically charged to prevent sticking, so\nthat the beads leviate a distance a few nanometer above\nthe \flm, yielding f <3.6\nThe magnetic force on the paramagnetic bead with\nvolumeVand magnetic susceptibility \u001fis\nFm\nx=\u0000@U\n@x: (3)\nwith potential\nU=\u00001\n2\u0016V\u001fH2(4)arXiv:1109.6491v1  [cond-mat.soft]  29 Sep 20112\nxTime\n−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.400.20.40.60.811.21.41.61.8\nFIG. 2. The ratchet e\u000bect. The horizontal axis is the position\nxand the vertical axis is time t. The particle path is plotted\nas a solid line above the landscape formed by the sign of Fm\nx.\nBlue means Fm\nx<0 and white is Fm\nx<0\nwhere\u0016\u0019\u00160= 1:26\u000210\u00006Tm/A is the permeability\nof water,\nConsider a magnetic \flm with stripe domains. Above\nthe surface of the \flm, the total magnetic \feld is\nH(r;t) =Ha(t) +Hf(r;t) (5)\nwhere Hais applied \feld and Hfis the inhomogeneous\n\feld from the stripe pattern of the \flm. The applied \feld\nis periodic, with\nHa\nz=H0sin(2\u0019\u0017t)\nHa\nx=sH0sin(g2\u0019\u0017t)(6)\nwheregis an integer and sis an arbitrary number.\nFor a \flm with stripe domains and magnetization Ms,\nthe magnetic \feld above the \flm can be expressed as\nHf\nx=Ms\n\u0019Re \nHf\nz=Ms\n\u0019Im (7)\nwhere the complex auxiliary function  is\n = log\u00121\u0000e\u00002\u0019(z+i(x+\u0001))=\u0015\n1 +e\u00002\u0019(z\u0000i(x\u0000\u0001))=\u0015\u0013\n+ log\u00121 +e\u00002\u0019(z+d+i(x+\u0001))=\u0015\n1\u0000e\u00002\u0019(z+d+i(x\u0000\u0001))=\u0015\u0013\n:(8)\nwheredis \flm thickness, \u0015is the wavelength of the stripe\npattern and \u0001 is the domain wall displacement. The sec-\nond term in Eq. (8) comes from the bottom surface of\nthe \flm and it can be neglected when beads are close to\nthe \flm, i.e., when z\u001cd. The domain wall displace-\nments depends on the applied \feld, and for for small and\nxTime\n−0.5 0 0.5 100.511.5\nxTime\n−1.5 −1 −0.5 000.511.5FIG. 3. Separation e\u000bect, in which beads at di\u000berent heights\nmove in opposite directions. The bead's trajectory is plot-\nted above the sign of the interaction force. Top: z= 0:1\u0015,\nbottom:z= 0:05\u0015. All other parameters are equal: H0=\n0:18Msand \u0001 0= 0:05.\nmedium amplitudes we assume it to be proportional to\nHa\nz, i.e.\n\u0001(t) = \u0001 0Ha\nz(t)\nH0: (9)\nIII. RESULTS\nWhen the external \feld is modulated there will be re-\nsponse in the width of the strip domains and the para-\nmagnetic bead will move according to Eq. (1). We will\nnow consider several solutions: the ratchet, the pseudo\nratchet and the size dependent ratchet.\nRatchet - An example of coherent dynamics is the\nratchet. In the ratchet the paramagnetic beads gain a\nnet coherent motion in one direction, despite a periodic3\nMoves right\nMoves left\nAt rest\nH0z\n0.15 0.2 0.250.020.040.060.080.1\nFIG. 4. Tuning of the separation height by changing the\nstrength of the applied \feld H0from Eq. (6). The part with\ninverted ratchet direction is seen as a white line.\nmodulation of the external \feld. The bead's motion is\nplotted in Fig. 2. The external \feld is in this setup con-\nstantly at angle 45\u000ecorresponding to s= 1 andg= 1\nin Eq. (6). The motion of the will nonetheless acquire a\ncoherent motion to the right, as seen in Fig. 2.\nSeparation - Complex modulation of Haopens the pos-\nsibility even more strange ratchet solutions of Eq. (1), for\nexample ratchets that go in opposite directions at di\u000ber-\nent heights. This e\u000bect was exploited in Ref. 5 to yield\nseparation of beads of di\u000berent sizes. The height depen-\ndent ratchet appears for g= 3 in Eq. (6) and the results\ntrajectories for beads at heights z= 0:1\u0015andz= 0:05\u0015\nare plotted in Fig. 3. There is a clear di\u000berence: the\nlarge bead jumps three times during a half-period and\nacquires a net motion to the right while the small bead\njumps only once and acquires a net motion to the left, all\nin perfect agreement with Ref. 5. The two trajectories\nare entirely as expected from the sign of Fxwhich are\nplotted in the background. However, we notice that the\nbeads do not follow the edge of the signs exactly, because\nof the \fnite viscosity. Only in the limit \u0011!0, the beads\nwould follow the edges exactly.\nTuning of separation threshold - The height dependent\nratchet will only be useful as a separation device if the\nseparation threshold zthis possible to tune. The only\nrealistic parameter to change is Ha, but since the \flm\nreacts toHa\nzthe most robust approach is to keep Ha\nz\n\fxed and just change Ha\nx. The e\u000bect of changing sis seen\nin Fig. 5 which is plotted in the style of phase diagram,\ndistinguishing tree outcomes: motion to the left, to the\nright and at rest.\nPseudo ratchet - The ratchet e\u000bect is a consequence of\nphase coherence between the Ha\nxandHa\nzand the ratchet\nfails when there is a drift in Ha\nx, i.e., when gfrom Eq. (6)\nis not an integer. We will no consider the pseudo ratchet\nMoves right\nMoves left\nAt rest\nsz\n0.5 1 1.50.020.040.060.080.1FIG. 5. Tuning of the separation height by the amplitude\nasymmetry of the applied \feld sfrom Eq. (6). H0= 0:18Ms.\nThe part with inverted ratchet direction is seen as a white\nline.\nsolutions which appear when\ng= 1 + 1=N (10)\nwhereNis an integer. Since sin( !(1 + 1=N)t) =\nsin(!t) cos(!=N t ) + cos(!t) sin(!=N t ) we can expect\nto see some e\u000bect of some convolution with the longer\nperiodN=!, but what is surprising is that the coherent\ndynamics is intact. We then get the pseudo ratchet solu-\ntions of Fig. 6 for N= 2;3;4 and 5 in which the ratchet\nchanges direction after Nperiods.\n0 5 10 15−2.5−2−1.5−1−0.500.5\nTimex\nFIG. 6. Pseudo ratchet, in which the ratchet direction\nchanges after a N= 2;3;4 and 5 periods.4\nIV. SUMMARY\nWe have done theoretical modeling of the dynamics of\nsmall paramagnetic beads manipulated by the stripe do-\nmain pattern of a ferrite garnet \flm. The simple model,\nonly taking into account the paramagnetic interaction\nand linear hydrodynamics, is su\u000ecient to explain sev-\neral non-trivial dynamical phenomenon occurring in thesystem. In particular the model is capable of explain-\ning the recti\fed motion occurring in a harmonic external\n\feld and also the more complicated separation e\u000bect, in\nwhich a driving with di\u000berent frequencies in xandzdi-\nrection cause beads of di\u000berent heights to go in di\u000berent\ndirections. We \fnd that this e\u000bect can be explained as a\nconsequence of an asymmetry in the magnetic interaction\npotential.\n1G. Vieira, T. Henighan, A. Chen, A. J. Hauser, F. Y. Yang,\nJ. J. Chalmers, and R. Sooryakumar, Phys. Rev. Lett. 103,\n128101 (2009).\n2K. Smistrup, H. Bruus, and M. F. Hansen, J. Mag. Magn.\nMat311, 409 (2007).3P. Tierno, F. S. T. H. Johansen, and T. M. Fischer, Phys.\nChem. Chem. Phys. 11, 9615 (2009).\n4P. Tierno, S. V. Reddy, T. H. Johansen, and T. M. Fisher,\nPhys. Rev. E 75, 041404 (2007).\n5P. Tierno, S. V. Reddy, M. G. Roper, T. H. Johansen, and\nT. M. Fisher, J. Phys. Chem. B 112, 3833 (2008).\n6L. E. Helseth, H. Z. Wen, and T. M. Fischer, J. Appl. Phys.\n99, 024909 (2006)."    },    {        "title": "0904.3069v1.Quasi_Optical_Characterization_of_Dielectric_and_Ferrite_Materials.pdf",        "content": "arXiv:0904.3069v1  [physics.optics]  20 Apr 2009Quasi-Optical Characterization of Dielectric and Ferrite Materials\nM. Goy, F. Caroopen, M. Gross\nAB Millimetre, 52 rue Lhomond 75005 Paris: France\ntel: +33 1 47 07 71 00, fax: +33 1 47 07 70 71, abmillimetre@wana doo.fr\nR.I. Hunter and G.M. Smith\nMillimetre Wave and High Field ESR Group, University of St An drews\nNorth Haugh, St Andrews, Fife KY 16 9SS, Scotland, United Kin gdom\ntel: +44 1334 463156, 2669, fax: 463104, rihl, gms@st-and.a c.uk\nc/circlecopyrt2018 Optical Society of America\nOCIS codes:\n17th International Symposium on Space THz Technol-\nogy, Paris 2006 May 10-12\n1. Introduction\nIn the millimeter-submillimeter range, Quasi-Optical\n(QO) benches can be relatively compact, typically of or-\nder 10cm wide and 1m long. The focussing elements used\nin these benches are dielectric lenses, or off-axis ellipti-\ncal mirrors. Simultaneous Transmission T(correspond-\ning to the complex S21 parameter), and Reflection R\n(corresponding to the complex S ii parameter) are vec-\ntorially detected versus frequency in the frequency range\n40-700 GHz. A parallel-faced slab, thickness e, of dielec-\ntric material is placed at a Gaussian beam waist within\nthe system. It is straightforwardto determine the refrac-\ntive index n(withε′=n2) of this sample from the phase\nrotation ∆Φ:\n(n−1)e/λ= ∆Φ/360 (1)\nThe loss factor tan δis known from the damping of the\ntransmitted signal, Fig. 1:\ntanδ= 1.1α(dB/cm) /nF(GHz) (2)\nThe samples in this measurement system act as Fabry-\nPerot resonators with maximum transmission corre-\nsponding to minimum reflection, and vice-versa (see\nFig.2), with a period ∆ F=c/(2ne). For very low loss\nmaterials, there is however some difficulty in measuring\nthe loss term by a single crossing, since the maximum\ntransmission is very close to 0 dB. One uses the cav-\nity perturbation technique, which makes visible the low\nlosses after many crossings through the dielectric slab\n(see Fig.3).\n2. Experimental Setup for free-space propaga-\ntion\nIn V-W-D bands (extended down to ca 41 GHz, close to\nthe V-band cutoff), we use the following waveguide com-\nponents. Onthe sourceside, the harmonicGeneratorHG\nsends its millimeter power through a full-band Faraday\nFig. 1. Transmission through 10.95 mm nylon. (a) thick\nline is the observed amplitude in V-W bands. (b) is the\ncorresponding phase (represented in opposite sense for\nclarity). Around 305 GHz, the measured (d) phase value,\nin good alignment with extrapolated (b), shows that the\npermittivity ε′= 3.037 is constant with frequency. On\nthe contrary, the position ofthe amplitude (c) showsthat\nthe loss, which was tan δ= 0.013 at low frequencies, has\nincreased to tan δ= 0.019, since (c) is far from the ex-\ntrapolated (a).\nisolator FI1, cascaded with a fixed attenuator AT1, a di-\nrectional coupler DC (from port 2 to port 1) and a Scalar\nHorn SH1. The reflection (Channel 1) is detected by a\nHarmonie Mixer HM1 attached to output 3 of the DC\nthrough the isolator F12. On the transmission detection\nside, the Scalar Horn SH2 sends the collected wave to\nthe Harmonic Mixer HM2 (Channel 2) through cascaded\nAT2 and FI3.\n3. Isolators FIs and Attenuators ATs, what for?\nThe first use of isolators is to assume a one-way prop-\nagation. The non-linear devices HG and HMs contain\nSchottly diodes. In case the wave can travel go-and-\nback from one device to the other, the combination of\nnon-linear and standing waves effect can send microwave2\nFig. 2. Transmission (a) and reflection (b) through 9.53\nmm AIN. The dielectric parameters, observed in V-W-D\nbands, are constant with ε′= 8.47S, tanδ= 0.0007, also\nmeasured the same in cavity at 140.4 GHz.\nFig. 3. Resonances observed in an open Fabry-Perot\ncavity loaded by a 10.03 mm thick slab of slightly bire-\nfringent Teflon. In (a) the RF field is along the large\nindex axis ε′= 2.0664, in (b) along the small index axis\nε′= 2.0636. In (c), is the empty cavity resonance. The\nε′anisotropyis exactly the same as observedat 135GHz.\nThe loss has increased from tan δ= 0.0003 at 135 GHz\nto 0.0008 at 660 GHz.\npowerfromagivenharmonictoanotherharmonic1. This\nis why multiplierscascadedwithout isolation(like ×2×3\n) can create unexpected harmonics (like ×5×7). We\nhave also observed, for instance with cascaded tripiers\n(×3×3), measurableamounts ofunexpected ×10,×11,\nor×122. The devices HG and HMs can be viewed as\nSchottky diodes across waveguides, meaning unmatched\nstructures. The second use of the FIs is to reduced the\nVSWR. Their typical return is -20 dB (VSWR ca1.22).\nWe improve this value down to - 30 dB (VSWR ca1.07)\nwhen introducing the fixed attenuators ATs.\nFig. 4. Transmission (a) and reflection (b) through a\n3 mm thick MgAl 2O3slab. These raw data show para-\nsitic standing waves appearing as noise\nFig. 5. Polar plot of Fig.5\n4. Experimental difficulties\nEven with our best benches using the complete chains\nassuming a low VSWR ( <1.1 see sec 3), the parasitic\nstanding waves effects are clearly visible on raw data,\nFig.4-5. They are due to multiple reflections between\nthe sample, placed perpendicular to the beam, and the\ncomponents of the bench. However, they can be com-\npletely filtered by FT calculations (see Figs.6-7). There\nis a lack of FIs waveguide isolators above 220 GHz and,\nas far as we know, of DCs above 400 GHz. As a conse-\nquence, characterization at submillimeter wavelengths is\noperated by transmission only, and is much more diffi-\ncult, Fig.8, than in V-W-D-bands, due to large parasitic\nstanding waves.\n5. Non-magnetized ferrites characterization\nIn the case of ferrite materials, the properties are very\nstrongly frequency dependent. Non-magnetized ferrites\nshow a strong resonance in the range 50-60 GHz (see3\nFig. 6. Same as Fig.4 after FT filtering.. The measured\ndielectric parameters are ε′= 8.080, and tan δ= 0.0005.\nFig. 7. Polar plot of Fig.6\nFig. 8. Transmission across 9.97 mm sapphire, from\n469 GHz, point (a), to 479 GHz, point (b), with ab-\nsorbers, total 30 dB, between source and detection, in\norder to reduce the parasitic standing waves. Despite\nthis strong attenuation, the measurement quality is far\nfrom being as good as at lower frequencies, like in Fig.7.\nIn (c) is the 473.3to 474.5GHz sweep without absorbers,\nshowing big standing waves effects.\nFig. 9. Transmission (a), and reflection (b) through a\n2.55 mm thick non-magnetized TDK ferrite sample.\nFig. 10. Transmission through 2 mm magnetized sample\nFB6H1, (a) is −45◦, (b) is +45◦. Experimental traces\nand superimposed fittings.\nFig.9), and the asymptotic behavior, far from resonance,\nstarts to be visible beyond 200 GHz. Measurements per-\nformed at 475 GHz on six samples give ε′in the range\n18.8 to 21.4, and tan δin the range 0.012 to 0.018.\n6. Magnetized ferrites\nWhen a ferrite is submitted to an external, or internal,\nmagnetic field, there is a strong anisotropy of propaga-\ntion according to the circular polarization of the crossing\nelectromagneticwave3. The two refractive indices n±are\ngiven by:\n(n±)2=ε′[1+Fm/(F0±F)]\n, where Fis the frequency, F0the Larmor frequency,\nFmis proportional to the remanent magnetization of the\nferrite, and ε′is the dielectric constant. Any linearly po-\nlarized wave, like ours at the SH outputs, can be viewed\nas the superposition of two opposite senses circularly po-4\nFig. 11. Same as Fig.10, where (a) is 90◦and (b) is 0◦.\nFig. 12. Reflection at 0◦from the magnetized sample\nFB6H1, experiment and fit.\nlarized components. After crossing the ferrite, one of the\ncomponentshasexperiencedalargerretardationthanthe\nother, so that, when recombining the two, the plane of\nlinear polarization has been rotated. In order to charac-\nterize magnetized ferrite samples, it is necessary to mea-\nsure not only the transmitted signals with a polarization\nparallel to the source, but also those with polarization at\n±45 degrees, and 90 degrees, see Figs.10-11-12.\nWhen adding an anti-reflection coating on each side\nof the magnetized ferrite, the thickness of the ferrite be-\ning chosen so that the rotation through it is 45◦at the\nrequired frequency, one can obtain a good QO Faraday\nRotator, Fig.13. The performances observed around the\ncentral frequency, Figs.14-15, are at least similar (for iso-\nlation or matching) or better (for insertion loss) than the\nequivalent waveguide isolators.\n7. QOFRs expected to become submillimeter\nisolators and directional Couplers\nOur QO benches studying samples perpendicular to the\nwave beam, are, up to now, less performing in submil-\nFig. 13. Reflection at 0◦from the magnetized sample\nFB6H1, experiment and fit.\nFig. 14. Reflection at 0◦from the magnetized sample\nFB6H1, experiment and fit.\nFig. 15. Reflection at 0◦from the magnetized sample\nFB6H1, experiment and fit.5\nFig. 16. Schematic diagram of a QOFR used as an iso-\nlator (there is a inatched load at (g) ) Port 3, or as\na Directional Coupler DC for detecting reflected waves\nat (g). The vertical polarisation at (a), fully transmit-\nted through the horizontal grid (b), rotates by +45◦\nthrough the magnetized ferrite (c), then is fully trans-\nmitted through the −45◦grid (d). Any reflected signal\nwithout polarisation change will cross back (d) without\nloss, then will rotate by +45◦again across (c), becoming\nhorizontal, then will be totally reflected by the horizontal\ngrid (b), towards Port 3.\nlimeter (Fig.8) than in the millimeter domain (Fig.7),\ndue to parasitic standing waves. Introducing the appro-priate QO Faraday Rotators will reduce this effect. On\nfigure 16 one can see how a QOFR can be simply config-\nurated for that purpose.\n8. Conclusion\nPrecise and quick QO measurements in the 40-170 GHz\ninterval, in particular for ferrites characterization, opens\nthe possibility of similar precise and easy measurements\nat high frequencies, including the submillimeter domain,\nby using these ferrites in QOFRs in progress4. At the\nsame time, widely sweepable solid-state submillimeter\nsources must be developed.\nReferences\n1. P. Goy, M. Gross, and S. Caroopen. Millimeter\nand Submillimeter Wave Vector Measurements with\na network analyzer up to 1000 GHz. Basic Principles\nand Applications. In 4th International Conference\non Millimeter and Submillimeter Waves and Appli-\ncations, San Diego, California USA, 1998 Jul 20-23 .\n2. P. Goy. Private communicatuions. 2005-2006.\n3. R.I. Hunter, D.A. Robertson, and G.M. Smith. Fer-\nrite Materials for Quasi-Optical Devices and Appli-\ncations. In Int Confon IR and mmWaves, Karlsruhe,\n2004 Sep 27 - Oct 1 .\n4. P.GoyR.I.Hunter, D.A. RobertsonandG.M.Smith.\nCharacterizationofFerriteMaterialsforuseinQuasi-\nOptical Faraday Rotators. In to be published ."    },    {        "title": "0804.1666v1.Eigen_power_flow_density_vortices_of_magnetostatic_modes_in_thin_ferrite_disks.pdf",        "content": "Eigen power-flow-density vortices of magn etostatic modes in thin ferrite disks \n \n \nM. Sigalov, E. O. Kamenetskii, and R. Shavit \n \nBen-Gurion University of the Negev, Beer Sheva 84105, Israel \n \nApril 9, 2008 \n \n In confined magnetically orde red structures one can observe  vortices of magnetization and \nelectromagnetic power flow vortic es. There are topologically distin ct and robust st ates. In this \npaper we show that in a normally magnetized quas i-2D ferrite disk there exist eigen power-flow-\ndensity vortices of magnetic-dipol ar-mode oscillations. Because of such circular power flows, the \noscillating modes are characterize d by stable magnetostatic energy  states and discrete angular \nmoments of the wave fields. We show that th e power-flow-density vortices of magnetostatic \nmodes can be excited by electromagnetic fields  of a microwave cavity. There is a clear \ncorrespondence between the power-flow- density vortex structures in a ferrite disk derived from an \nanalytical solution of the magnetostatic-wave spectral problem and obt ained by the numerical-\nsimulation electromagnetic program.   PACS numbers:  76.50.+g, 68.65.-k, 03.75.Lm \n------------- ---------- \n In spite of the fact that vorti ces are observed in different kind s of physical phenomena, yet such \n\"swirling\" entities seem to elude an all-inclusive definition. In quite  a number of problems one can \ndefine a vortex as a circular flow which is attri buted with a certain phase  factor and a circular \nintegral of a gradient of the phase gives a non- zero quantity. This quantity is multiple to a number \nof full rotations.      In ferromagnetic systems, one can clearly dis tinguish three characterist ic scales. There are the \nscales of the spin (exchange interaction) fields, the magnetostatic (dipole-dipole interaction) fields, \nand the electromagnetic fields. These characterist ic scales may define different vortex states. \nTogether with magnetization vortices in micromet er- or submicrometer-size ferromagnetic samples \n[1, 2] and the magnetostatic (MS)  vortex behaviors in thin ferr ite films [3], one can observe \nelectromagnetic vortices originated from ferrite sa mples in microwave cavities [4 – 7]. In the last \ncase, vortices appear because of the time-revers al-symmetry-breaking (TRSB) effects resulting in \na rich variety of the electromagnetic wave topological phenomena [4 – 7]. \n    In their studies, Boardman et al [3] showed that for MS waves excited by three planar antennas \nin a normally magnetized ferrite film one can fo rm a stationary linear phase defect structure \nresulting in appearance of the pow er-flow-density vortices. There are induced  MS-wave vortices. \nIn this paper we show that th ere is a possibility to obtain eigen  power-flow-density vortices of MS \noscillations which appear due to special topological effects in a normally magnetized quasi-2D \nferrite disk. Based on numerical simulations, we show that the eigen power-flow-density vortices \nof MS modes in a ferrite disk can be excited by  electromagnetic fields of a microwave cavity. \nWhile for thick ferrite disks studied in [5 – 7]  no multiresonance absorption spectra were observed \nin a frequency range of the cavity  resonance, in a case of a quasi -2D ferrite disk with MS modes \none obtains eigenstates of  the vortex structures. \n    The magnetic dipole interaction provides us  with a long-range mechan ism of interaction, where \na magnetic medium is considered as a continuum. It is well know n that MS ferromagnetism has a \ncharacter essentially different from exchange fe rromagnetism [8, 9]. This statement finds a strong  2confirmation in confinement phenomena of magne tic-dipolar-mode (MDM) (or MS) oscillations. \nA recently published spectral theory of MDMs in quasi-2D ferrite disks [10 – 12] gives a deep \ninsight into an explanation of the experimental  multiresonance line absorption spectra shown both \nin well known previous [13, 14] and new [15, 16] studies. This th eory suggests an existence of \nothogonality relations for the MS-potential eigen wave functi ons [10, 11] and dynamical symmetry \nbreaking effects for MDM oscillat ions [12]. One of th e most attractive aspects of the symmetry \nbreaking effects in MDM oscillations is the pres ence of the vortex states which appears due to \nspecial boundary conditions on a la teral surface of a normally ma gnetized quasi-2D ferrite disk \n[12]. Based on the MS spectral problem solutions, in this paper we show that  the border states of \nMDM oscillations lead to eigen MS power-flow-density vortices in a ferrite disk. Due to these \ncircular eigen power flows, the MDMs are ch aracterized by stable MS energy states.  \n    For MDMs in a normally magne tized ferrite disk, circular flows of power densities are attributed \nwith the phase factors of MS-potential wave functions. For monochromatic fields with time \nvariation ~tie ω the power flow density for a certain magnetic dipolar mode n is expressed in \nGaussian units as [12]:  \n \n                                                           ( )* *\n16nn nn n B Biprr rψψπω− = ,                                                      (1) \n                        \nwhere nψ is the MS-potential wave function, n nB ψµ∇⋅−=rtr\n , and µt is the permeability tensor. In \na normally magnetized (with  a normal directed along z axis) quasi-2D ferrite disk, the mode fields \ncan be represented as [10 – 12]: ) ,(~)( yx z Cn nn n ϕξψ= , ()( )⊥⊥+= e B eB Bn zzn nr r r\n, where \n() ),(~\n )(yxzzC Bnn\nn zn ϕξ\n∂∂−=  and () [ ]⊥ ⊥⊥ ⊥⋅ ∇⋅ −= eyx z C Bn nn nr rt),(~)( ϕµξ , ) (znξ  is an amplitude \nfactor, nC is a dimensional coefficient, and ) ,(~yxnϕ  is a dimensionless membrane function for \nmode n. Subscript ⊥ corresponds to transversal (with respect to z axis) components. In a \ncylindrical coordinate system, it is easy to show that for oscillating MDMs in a quasi-2D ferrite disk, the z and r components of the power flow density ar e equal to zero. There is the only real \nazimuth component:  \n                        \n() () \n\n\n\n\n\n\n\n∂∂+∂∂+\n\n\n\n∂∂−∂∂− =r rirz Cipn\nnn\nn an\nnn\nn n n*\n**\n* 2 2~~~~~~~~1)(16ϕϕϕϕµθϕϕθϕϕµξπω\nθ.        (2) \n \nThe total MS-potential membrane function ϕ~ is represented as a produc t of two functions [12]: \n \n                                                                 ± =δθηϕ  ),(~~r .                                                                (3)                    \n \nFunction ),(~θηr is a single-valued memb rane function written as \n \n                                                               ()()()θφθη rR r=,~,                                                            (4) \n \nwhere ) (rR  is described by the Bessel functions and θνθφ ~)(ie−, .... 3,2,1±±±=ν                  \nFunction ±δ is a double-valued (spin-c oordinate-like) function, which is represented as \nθδ±−\n±±≡iqef , where 21±=±q . For amplitudes f we have − +−=f f  with normalization ±f = 1.    3    Circular flows of the power density in a MDM ferrite disk are attributed with phase factors of a \nMS-potential wave function. Th e MDM topological effects are ma nifested through the generation \nof relative phases which accumulate on the boundary wave functions ±δ. Due to this function one \nhas a phase factor which define s a power-flow-density vortex of a MDM. With use of Eq. (4) one \nrewrites Eq. (2) as \n  \n                                  () ()\n\n∂∂− − =rrR\nrrR z CrRrpn\na n n n nn\nn)()()( )(  8)()(2 2µνµξωπθ.                      (5) \n \nThere is non-zero circulation quantities ()θ)(rpn  around a circle rπ2. An amplitude of a MS-\npotential function is equal to zero at 0=r . For a scalar wave function, this presumes the Nye and \nBerry phase singularity [17] . Circulating quantities ()θ)(rpn  are the MDM power-flow-density \nvortices with cores at the disk center. At a vortex center amplitude of ()θnp is equal to zero. It \nfollows from Eq. (5) that for a given mode number n characterizing by a certain Bessel function \n)(rRn there will be different functions of the power flow density  ()θ)(rpn  for different signs of \nthe azimuth number nν. \n    To find functions ) (zξ and ) (rR we have to solve a system of the following two equations [11]: \n                                                            ()()µµβ+−−=12tan hF                                                          (6) \nand \n                                                            0 )(21\n=′+′−\nνν\nννµKK\nJJ,                                                             (7) \n \ncorresponding to the so-called essential boundary conditions well known in variational methods \n[18]. This gives the energy orthogonality  relations for magnetic-dipolar modes ),(~θηr [11, 12]. \nHere h and ℜ are, respectively, a thickness and a radius of a ferrite disk, ()Fβ is the wave number \nof a MS wave propagating in a ferri te along a bias magnetic field, ν ννν K KJJ ′ ′  and , , ,  are the \nvalues of the Bessel functions of order ν and their derivatives (with respect to the argument) on a \nlateral cylindrical surface ( hz r ≤≤ℜ= 0  ,) .   \n    In further analysis we consider MDMs having fundamental thickness and firs t-order-azimuth \ndistributions. Numbers n in Eq. (5) correspond to different radial variations. Fig. 1 gives the \ncalculated distributions of ()θnp for first two modes ( n = 1, 2) at 1 +=nν  when a bias magnetic \nfield is directed along z axis. These distributions clearly s how the power-flow-de nsity vortices. For \nour calculations we used a lossless norma lly magnetized ferrite disk with diameter 3 2=ℜ mm and \nthickness 05.0=d mm. The ferrite saturation magnetization is G  1880  40=Mπ  and a bias \nmagnetic field is Oe  49000=H . One can see that there are eige n power-flow-density vortices with \nvery different topolog ical structures.  \n    It follows, however, that an analysis of excitation of these power-flow-density vortices by \nexternal electromagnetic fields is beyond the fram es of any analytical solutions. Because of the \nTRSB effects, a system of a cavity with an embedded inside fe rrite disk (even having sizes much \nsmall compared with the cavity sizes) is not a weakly pertur bed integrable system, but a non-\nintegrable system [5 – 7].  Based on the H FSS-program numerical studi es [19], we analyze \nexcitation of the power-flow-density vortices in a ferrite disk placed in  a microwave cavity. For \nour numerical studies we used a short-wall rectangular waveguide  section. The disk axis was  4oriented along the E-field of a waveguide 10TE  mode. The disk parameters were the same as for \nthe above analytical calculations. Additionally, we took into account the material losses as the \nlinewidth Oe 8.0=∆H . This corresponds to the parameters us ed in experiments [16]. Fig. 2 shows \nnumerically obtained frequency characteristic of an absorption coefficient for a ferrite disk in a \nwaveguide cavity. One clearly sees the multiresona nce absorption spectra. The peak amplitudes \nreflect the fact of different wavegui de field structures at different frequencies of  the disk modes. In \nFig. 2 we also show the resonance peak positions  obtained from an analytic al solution of Eqs. (6) \nand (7). There is a very good correlation between the analytical and numerical peak positions. For \nnumerically obtained modes, one can observe topol ogical resonant states. Ev ery resonant state is \ncharacterized by a strong pronounced  eigenfunction pattern with a topologically di stinct vortex \nstructure. As an example, Fig. 3 shows a typical gallery of the magnetic fi eld distributions on the \nupper plane of a ferrite disk for the second mode at different time phases. A very peculiar property \nof these pictures is the fact of the azimuthal rotation of the mode magnetic field. When the transverse mode is transformed following a closed path in the space of modes, the phase of the \nfinal mode state differs from that of the initial state by \ng dφφφ+= , where dφ and gφ are the \ndynamical and geometrical phases, respectively [ 20]. In a supposition of possible analytical \ndescription, the modes with π4 azimuthal rotation should be represented by double-valued \nfunctions.  \n    Based on numerical studies, we can represent the Poynting-vector  distributions inside a ferrite \ndisk corresponding to the observed resonant states. Fig. 4 gives su ch distributions  for first two \nmodes ( n = 1, 2). There are the power-flow vortices . The black arrows clarify the power-flow \ndirections inside a disk for every given mode . One can find a very good  correspondence between \nthe numerical-simulation Poynting- vector vortices in Fig. 4 and analytically calculated eigen \nMDM power-flow-density vortices shown in Fig. 1. When comparing the vortices in Figs. 1 and 4, \none should take into account the fact that in the numerical-simulation analys is, the ferrite material \nlosses were taken into consideration. This presumes  certain diffusion of the vortex pictures in Fig. \n4.          We showed that in a normally magnetized qu asi-2D ferrite disk there exist eigen power-flow-\ndensity vortices of MDM oscillations.  Based on the HFSS-program numerical studies, we showed \npossibility of excitation of the MDM power-flow- density vortices in a ferrite disk placed in a \nmicrowave cavity. The pictures of  the vortex structures obtained from the numerical-simulation \nelectromagnetic program are in a good corresponden ce with the analytica lly derived eigen MS \npower-flow-density vortices in a ferrite disk. \n \n----------- \n[1] T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, Science \n289, 930 (2000). \n[2] K. Yu. Guslienko, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, Phys. Rev. B 65, \n024414 (2002). \n[3] A. D. Boardman, Yu. G. Rapo port, V. V. Grimalsky, B. A. Ivanov, S. V. Koshevaya, L. \nVelasco, and C. E. Zaspel, Phys Rev. 71, 026614 (2005). \n[4] M. Vrani čar, M. Barth, G. Veble, M.  Robnik, and H.-J. Stöckmann,  J. Phys. A: Math. Gen. 35, \n4929 (2002). \n[5] E. O. Kamenetskii, M. Sigal ov, and R. Shavit, Phys. Rev. E 74, 036620 (2006). \n[6] M. Sigalov, E. O. Kamenetskii, and R. Shavit, Phys. Lett. A 372, 91 (2008). \n[7] M. Sigalov, E. O. Kamenetskii, and R. Shavit, J. Appl. Phys. 103, 013904 (2008). \n[8] J. M. Luttinger and L. Tisza, Phys. Rev. 70, 954 (1946). \n[9] H. Puszkarski, M. Krawczyk, an d  J.-C. S. Levy, Phys. Rev. B 71, 014421 (2005). \n[10] E. O. Kamenetskii, Phys. Rev. E  63, 066612 (2001). \n[11] E. O. Kamenetskii, M. Sigalov, and R. Shavit, J. Phys.: Condens. Matter 17, 2211 (2005).   5[12] E. O. Kamenetskii, J. Phys. A: Math. Theor. 40, 6539 (2007).  \n[13] J. F. Dillon Jr., J. Appl. Phys. 31, 1605 (1960).  \n[14] T. Yukawa and K. Abe, J. Appl. Phys. 45, 3146 (1974). \n[15] E. O. Kamenetskii, A.K. Saha, and I. Awai, Phys. Lett. A 332, 303 (2004). \n[16] M. Sigalov, E. O. Kamenets kii, and R. Shavit, arXiv:0712.2305. \n[17] J. F. Nye and M. V. Berry , Proc. R. Soc. London Ser. A 336, 165 (1974).  \n[18]  S. G. Mikhlin, Variational Methods in Mathematical Physics  (New York, McMillan, 1964). \n[19] High Frequency Structure Simulator, www. hfss.com, Ansoft Corporation, Pittsburgh, PA \n15219. \n[20] E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, Phys \nRev. Lett. 90, 203901 (2003). \n  \nFigure captions \n Fig. 1. Power-flow-density vortices for magnetic-di polar modes in a ferrite disk for first two   \n            modes. Disk diameter \n3 2=ℜ mm. \nFig. 2. Spectrum of MDMs in a ferrite disk. (a) A numerically obtained frequenc y characteristic of   \n           an absopption coefficient for a ferrite disk in a waveguide cavity; an  insertion shows a disk   \n           position in a cavity. (b) Anal ytically calculated MDM resonance peak positions. \nFig. 3. A gallery of the magnetic field distributions  on the upper plane of a ferrite disk for the    \n            second mode at different time phases. There is the mode with π4 azimuthal rotation. \nFig. 4. The Poynting-vector distri butions inside a ferrite  disk corresponding to  the topological   \n           resonant states. The black arrows clar ify the power-flow directions in side a disk for every    \n           given mode.                    6\n   \n  \n \n                             ( a)                                                                       ( b) \n \n  \n  \n  \nFig. 1. Power-flow-density vortices for magnetic dipolar  modes in a ferrite disk for first two      \n           modes. Disk diameter \n3 2=ℜ mm. \n \n    \n  x y \nz  0HrMode 1 Mode  2 7\n  \n  \n    \nFig. 2. Spectrum of MDMs in a ferrite disk. (a) A numerically obtained fre quency characteristic of \nan absorption coefficient for a ferrite disk in  a waveguide cavity; an insertion shows a disk \nposition in a cavity. (b) Analytically cal culated MDM resonance peak positions. \n \n                                      (a) \n(b)  8\n  \n  \n  \nFig. 3. A gallery of the magnetic field distributions  on the upper plane of a ferrite disk for the    \n            second mode at different time phases. There is the mode with π4 azimuthal rotation. \n  \n \n                         Mode 2 \n°=0tω °=90tω\n°=180tω °=270tωx y \nz 0Hr 9                                                    Mode 1  \n  \n                       \n  \n                                                        ( a) \n    \n    Mode 2                                                   \n  \n                      \n \n                                                       ( b) \n      \nFig. 4. The Poynting-vector distri butions inside a ferrite  disk corresponding to  the topological   \n           resonant states. The black arrows clar ify the power-flow directions inside a disk for every   \n           given mode. \n  x y \nz 0Hr\nx y \nz 0Hr"    }]